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Thread: Contradiction in special relativity

  1. #1 Contradiction in special relativity 
    Forum Freshman HAL ON EARTH's Avatar
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    “It is always due to human error”.
    Theorists have relied on the Michelson-Morley experiment or the “light-clock” to investigate how a photon can take a longer double-diagonal path for a mirror- system in motion. I want to highlight how the conventional explanation of time dilation’s co-existence with length contraction seems self-contradictory.

    Conventionally, the mirror problem is framed in terms of time and distance within the same question, which I call “the first question”.

    The first question is “if the time and distance a photon travels is constant, then how can a photon travel a longer distance in the same time?” The answer is distance contracts and time expands. The magnitude of time’s expansion is equal to the gamma factor.

    A second question is analogous to the first question, but the terms are, it seems, legitimately invertible. We ask “if the time and distance a photon travels is constant then how can a photon travel a longer time in the same distance?” Surely the answer must be distance expands and time contracts.Again, the magnitude of the distance expansion is equal to the gamma factor.

    These two questions cancel each other out because the answers are contradictory, leaving nothing to interpret. Hence, it is a falsehood to ask either of these questions without reference to the other.

    So I propose two alternative questions:

    Alternative question 1
    If the distance between two mirrors is constant how can it take a longer distance for a photon to travel the double diagonal path?
    Answer: The distance is longer from an external view. Therefore as viewed from the external view distance expands for the mirror system.

    Alternative question 2
    If the time between two mirrors is constant how can it take a longer time for a photon to travel the double diagonal path?
    Answer: The time is longer from an external view. Therefore as viewed from the external view time expands for the mirror system.

    Thus, when each question is framed independently – i.e. without trying to prise time and distance apart- we conclude time expansion is accompanied by distance expansion. The degree of this “spacetime expansion” is exactly equal to the gamma factor.

    This conclusion leads me to question whether the first principles of conventional SR are correct.

    So let us consider the evidence from experiments. The relativity of motion determines the importance of the electromagnetic field. When fields interact the evidence shows the results are consistent with the possibility of length contraction. However, if the paradigm of length contraction is replaced by the paradigm of isotropic spacetime expansion (which is of course consistent with the gamma factor) then the results may be equally explainable. This is because we cannot (I think) decide between a field that is contracted and a field that is expanded, if the stationary frame is always the opposite. I think the mathematics will be the same, just as “up” is to “down”, as “down” is to “up “depending on the chosen view.

    I am not questioning the empirical evidence for time dilation. But I do question the idea the principles of SR ineluctably lead to length contraction. In its place, I suggest a spacetime sphere paradigm. I understand this opens a can of worms in terms of fitting in with other principles of SR. However, the logic of spacetime isotropy seems internally self-consistent, whereas spacetime anisotropy seems anti-logical.

    If I made any human errors in this argument, could someone please point them out.
    thanks in advance
    -HOT


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  3. #2  
    Moderator Moderator Markus Hanke's Avatar
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    *sigh*
    Yet another anti-relativity thread. When will it ever end.

    Quote Originally Posted by HAL ON EARTH View Post

    Theorists have relied on the Michelson-Morley experiment or the “light-clock” to investigate how a photon can take a longer double-diagonal path for a mirror- system in motion.
    No they haven't. The MM was just simply one of the earliest such experiments, but countless others have been performed in the past century or so to test the isotropy of the speed of light. Some of them also used mirrors, others used other principles. The result, however, was always the same. No violation of Lorentz invariance has ever been observed in any experiment. That is not surprising, because fundamentally the speed of light is a direct result of vacuum permittivity and permeability :



    Special relativity is then simply born out of the requirement that all observers must measure the same speed of light, which is achieved through simple Lorentz transformations between reference frames.

    Thus, when each question is framed independently – i.e. without trying to prise time and distance apart- we conclude time expansion is accompanied by distance expansion. The degree of this “spacetime expansion” is exactly equal to the gamma factor.
    No, you are quite wrong. Time dilation is the same effect as length contraction, only seen in a different frame of reference. It is a direct result of the Lorentz transformation which is used to go from one inertial frame to another :



    This is a simple matrix multiplication, so if you look at the matrix elements for the ct and x coordinates you will immediately see that the elements are just the inverses of one another.

    This conclusion leads me to question whether the first principles of conventional SR are correct.
    And it leads me to questions whether you really understand Lorentz transformations. I think not. We have been using SR for a century now, and a large part of our everyday technology is based on it - we know it gives the correct predictions through empirical evidence.

    However, if the paradigm of length contraction is replaced by the paradigm of isotropic spacetime expansion (which is of course consistent with the gamma factor) then the results may be equally explainable.
    Space-time expansion only happens on global scales, specifically on scales governed by the Friedman-Lemaitre metric of general relativity, which is basically galaxy clusters and above. It is not a local phenomenon. Furthermore, it's magnitude is most certainly not related to the Lorentz gamma factor.
    Length contraction is not a paradigm - it is a direct result of the maths underlying SR, see above.

    This is because we cannot (I think) decide between a field that is contracted and a field that is expanded, if the stationary frame is always the opposite. I think the mathematics will be the same, just as “up” is to “down”, as “down” is to “up “depending on the chosen view.
    The maths are not the same - see the transformation matrix above. If you change around the elements you obtain a completely different transformation, and thus different laws of physics - in contradiction to experiment and observation.

    I am not questioning the empirical evidence for time dilation. But I do question the idea the principles of SR ineluctably lead to length contraction.
    The two are the same effect seen from different reference frames, see above.
    So yes, one immediately and automatically follows from the other.

    However, the logic of spacetime isotropy seems internally self-consistent, whereas spacetime anisotropy seems anti-logical. If I made any human errors in this argument, could someone please point them out.
    The error is : you think it seems anti-logical, thus it must be wrong. That's a basic fallacy.
    The mathematics of time dilation and length contraction are clear, consistent, and experimentally very well verified. It is a simple linear transformation of vectors, you can't get it any easier - that is the beauty of SR.


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  4. #3  
    Forum Freshman HAL ON EARTH's Avatar
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    Quote Originally Posted by HAL ON EARTH View Post


    The first question is “if the time and distance a photon travels is constant, then how can a photon travel a longer distance in the same time?” The answer is distance contracts and time expands. The magnitude of time’s expansion is equal to the gamma factor.

    A second question is analogous to the first question, but the terms are, it seems, legitimately invertible. We ask “if the time and distance a photon travels is constant then how can a photon travel a longer time in the same distance?” Surely the answer must be distance expands and time contracts.Again, the magnitude of the distance expansion is equal to the gamma factor.

    You sound knowledgable.

    I do not understand how the matrix explains away the existence of the above contradiction. Are the terms in your matrix totally invertible, or does the matrix operate on the basis time has one dimension and space has three? When I swapped the terms in the Lorentz Transformation (i.e. space for distance and vice-versa) and applied it to the Michelson-Morley experiment I found the result was in accord with question #2. In other words, the light waves remaining in phase are explainable by an inverted set of assumptions.

    Is this illegal? How would the universe know the difference between space and time?
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  5. #4  
    Moderator Moderator Markus Hanke's Avatar
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    Quote Originally Posted by HAL ON EARTH View Post
    I do not understand how the matrix explains away the existence of the above contradiction.
    What contradiction ? I don't see any contradiction at all.

    Are the terms in your matrix totally invertible,
    They do not invert as such ( an unfortunate choice of words on my part ) - look closely at the matrix, the factors are crossed over. Time dilation in one frame is length contraction in the other, and vice versa.

    or does the matrix operate on the basis time has one dimension and space has three?
    Obviously yes, this is a linear transformation in Minkowski space. The entire physics of SR is based on that fact - it is not an assumption.

    When I swapped the terms in the Lorentz Transformation
    I don't understand what you mean by this. Please write down the maths of what you propose. You cannot in the general case just swap factors and expect the results to still be the same.

    Is this illegal?
    The question is rather - are the results in accordance with experimental evidence ?

    How would the universe know the difference between space and time?
    The universe has three spatial and only one temporal dimension. Also, temporal dimensions are different from spatial ones, in that they have a different metric signature.
    So no, you cannot just swap them without effecting the maths, and if you do that the results won't square up to experimental evidence any more.
    Last edited by Markus Hanke; August 5th, 2012 at 08:19 AM.
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  6. #5  
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    Why bother with all this ? SR works perfectly fine, as shown by a huge amount of experimental and observational evidence. Trying to disprove it would mean denying a vast body of facts and evidence, not to mention a substantial amount of common place technology like GPS, computers etc, all of which are based on relativistic principles in one form or another. It's a foolish proposition.
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  7. #6  
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    Quote Originally Posted by HAL ON EARTH View Post
    We ask “if the time and distance a photon travels is constant then how can a photon travel a longer time in the same distance?”
    I think here is where your problem lies - this does not make any sense. If anything the photon would have to travel a longer time in a shorter distance so that its speed is measured to be the same for all observers. This is then just the normal time dilation and length contraction, just as predicted. Where's your contradiction ?

    we conclude time expansion is accompanied by distance expansion
    This is completely wrong, it should read distance contraction.
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  8. #7  
    Brassica oleracea Strange's Avatar
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    Quote Originally Posted by HAL ON EARTH View Post
    If the distance between two mirrors is constant how can it take a longer distance for a photon to travel the double diagonal path? [/COLOR]
    Answer: The distance is longer from an external view. Therefore as viewed from the external view distance expands for the mirror system.
    Your understanding, and hence the questions, are so confused it is hard to follow.

    In the case you are describing here, the distance between the mirrors is constant (in both frames of reference) because that is orthogonal to the direction of travel. The diagonal path is used to explain why the two observers measure different times.
    Without wishing to overstate my case, everything in the observable universe definitely has its origins in Northamptonshire -- Alan Moore
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  9. #8  
    Forum Freshman HAL ON EARTH's Avatar
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    By the way, how do I post equations? I have them in word format. Maybe I'll figure out myself...

    The following question seems valid:

    If the distance travelled and time elapsed for a photon is constant in every frame of reference (i.e. speed of light is constant) then how can a photon, in the frame of reference of a "stationary observer", travel a longer double diagonal distance in the same time?

    But the following question , even though it is identical save for a swapping of terms, is wrong?:

    If the distance travelled and time elapsed for a photon is constant in every frame of reference (i.e. speed of light is constant) then how can a photon, in the frame of reference of a "stationary observer", travel a longer double diagonal TIME in the same DISTANCE?

    As I asked, how does the universe know which values we mean when we make these substitutions? Tellingly, a "light year" is both the distance a photon travels in a time AND the time it travels over a distance. Right? We could also say a "light 1/100000 second" (or whatever it is) is a metre, for examle. So if time and space are measured in terms of the other, why should the second question be wrong?

    If you don't know the deep reason for this, and just rely on textbook assumptions, then you cannot really answer my question. I appreciate your knowledge of textbook assumptions is nevertheless very good.
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    Brassica oleracea Strange's Avatar
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    Quote Originally Posted by HAL ON EARTH View Post
    By the way, how do I post equations?
    Latex (between [tex] tags). If you are not familiar with Latex (it is worth learning) there are lots of references/tutorials online. And a nice interactive editor: Online LaTeX Equation Editor - create, integrate and download

    A save the Word equations as images and upload that.

    If the distance travelled and time elapsed for a photon is constant in every frame of reference (i.e. speed of light is constant) then how can a photon, in the frame of reference of a "stationary observer", travel a longer double diagonal distance in the same time?
    The starting point is that the speed of light is constant in every frame of reference. This means that if, in one frame of reference, the path is longer (diagonal) then the time taken will be longer as well. Therefore this observer will see things requiring more time (clocks running slower) in the moving frame.

    This does not mean "the distance travelled and time elapsed for a photon is constant in every frame of reference". Almost the exact opposite, in fact (unless you just phrased that poorly).

    I think you need to go back to whatever source you used to learn this from and go through it a bit more carefully, working through any examples.

    If you don't know the deep reason for this, and just rely on textbook assumptions
    The "deep reason" (if that means anything) is the geometry of space-time.

    And these are not "assumptions"; this is a solid theory based on mathematics and experiment (there is a straight line from Faraday's experiments, Maxwell's equations and the development of relativity by Lorentz, Einstein, Poincare and others). It has been tested to a high degree of accuracy by hundreds (maybe thousands) of different experiments. It also has many practical applications.
    Without wishing to overstate my case, everything in the observable universe definitely has its origins in Northamptonshire -- Alan Moore
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  11. #10  
    Moderator Moderator Markus Hanke's Avatar
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    Quote Originally Posted by HAL ON EARTH View Post
    If the distance travelled and time elapsed for a photon is constant in every frame of reference
    They are not constant in every frame of reference. The only thing that is constant is the relation between the two, i.e. the speed of light.

    then how can a photon, in the frame of reference of a "stationary observer", travel a longer double diagonal distance in the same time?
    It doesn't. The time is either dilated, or the length is contracted, or both. It depends exactly what frame you are in, and which way you look at the event. Once again, the important part here is that the relation between distance and time is always constant. The reason for that is that you go from one frame to another by performing a Lorentz transformation, and that transformation ensures that the light speed is always constant by introducing adjustments to time and length measurements.

    If the distance travelled and time elapsed for a photon is constant in every frame of reference
    It is not, see above. Only the relation between the two is constant.

    Tellingly, a "light year" is both the distance a photon travels in a time AND the time it travels over a distance.
    No, it is only a relation between distance and time, and only from a particular reference frame's point of view. If you travel at relativistic velocities towards a distant star, the distance you need to cross appears shorter to you, while for the stationary observer staying behind the on-board clock in your spaceship appears to go slower. If you relate the two, the gamma factors cancel out and you arrive at the same speed of light in both reference frames. There is no absolute 'light year' against which we can measure anything.

    So if time and space are measured in terms of the other, why should the second question be wrong?
    The question does not appear to make any sense. What do you mean by "how does the universe know which values we mean" ? All physical laws within SR are formulated as relations between reference frames, there is no absolute point of view. Therefore the universe does not need to 'know' anything. All points of view by all inertial observers are equal.

    If you don't know the deep reason for this, and just rely on textbook assumptions, then you cannot really answer my question.


    There is no such thing as textbook assumptions; SR was born out of the simple experimental observation that the speed of light is always constant.
    The problem is rather that your question is meaningless, because it appears your understanding of the basic premises of SR is not correct. There is no absolute frame of reference, only relations between equally valid inertial frames. Measurements of time and distance change, but the relations between them do not.
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  12. #11  
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    P.S. The important thing with SR is to look exactly who measures what and from which frame, and apply the appropriate laws accordingly. The confusions always start when people begin to mix up reference frames, and are not careful in determining what it actually is that is being measured, and by who. SR can be a bit tricky in that regard sometimes, especially in non-trivial scenarios, but so long as its laws are applied correctly there are never any paradoxes.
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  13. #12  
    Forum Freshman HAL ON EARTH's Avatar
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    Quote Originally Posted by Markus Hanke View Post
    *sigh*
    Yet another anti-relativity thread. When will it ever end.
    I like relativity!
    SR results in disagreements between observers, and jokingly, between opinions! Maybe that’s why this topic never ends.

    I understand your arguments, Strange and Marcus. They rest on a particular mathematical formalism that are outside the internal logic of my argument. I am offering a twist so it seems confusing. My equations are in a rather long document.

    I will improve my two “alternative” questions, and then I will improve my earlier “first question” and “second question”.

    Alternative Question 1 If the apparent time it takes light to travel between two mirrors is measurably constant in the moving frame, how can it take a longer apparent time (from the stationary frame) to travel the double diagonal path?
    Answer: the time is judged to be longer from the stationary frame. Therefore time expands for the moving frame, from the viewpoint of the stationary frame.

    ...now the offending

    Alternative Question 2 If the apparent DISTANCE light travels between two mirrors is measurably constant in the moving frame, how can it take a longer apparent distance (from the stationary frame) to travel the double diagonal path?

    Answer: the distance is judged to be longer from the stationary frame. Therefore distance expands for the moving frame, from the viewpoint of the stationary frame.

    Conclusion: time and space expand together. This does not dispute the empirical evidence for time dilation, but it does bring into doubt the necessity for length contraction. So length contraction may be a mathematical formalism to justify the constancy of light in one view, which I termed “the first question” in my first post. The “second question” gave an opposite answer. I will repeat them below with improvements.

    The first (improved ) question is : if the apparent speed of light is constant in the moving frame then how can a photon travel a longer distance in the same time, from the view of a stationary frame?

    Answer: distance contracts and time expands

    The second (improved ) question is : if the apparent speed of light is constant in the moving frame then how can a photon travel a longer TIME in the same distance, from the view of a stationary frame?

    Answer: time contracts and distance expands

    Conclusion: the answers to both questions contradict each other. Can you see how this result is additionally obtained by swapping the terms for time and distance in the Lorentz transformations?

    There is no absolute preferred term for space and time. That’s what I mean by asking “how does the universe know the difference between space and time?” May we regard them as the same mathematical quantity? The distinction is useful in non-relativistic situations only.

    Before bringing in the big guns of Maxwell, Lorentz and Einstein to blast me out of the water, can you see that I’m on a totally different ocean?

    There is a body of work that springs from this viewpoint, which is why I’m interested in hearing objections and opinions.
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    Before bringing in the big guns of Maxwell, Lorentz and Einstein to blast me out of the water, can you see that I’m on a totally different ocean?
    You're in a totally different universe.
    Its the way nature is!
    If you dont like it, go somewhere else....
    To another universe, where the rules are simpler
    Philosophically more pleasing, more psychologically easy
    Prof Richard Feynman (1979) .....

    Das ist nicht nur nicht richtig, es ist nicht einmal falsch!"
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    Forum Freshman HAL ON EARTH's Avatar
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    Regarding to the Michelson-Morley experiment, Richard Feynman, on page 58 of "Six Not So Easy Pieces", points out :

    "Although the contraction hypothesis successfully accounted for the negative result of the experiment, it was open to the objection that it was invented for the express purpose of explaining away the difficulty, and was too artificial".

    I admire Feynman not for this comment, but for his general willingness to question authority.

    The relationship between time and space is always the same. It would be interesting to investigate if time and space hypothetically expand together (isotropy) whether this relationship is preserved just as it is preserved when time expands and space contracts (anisotropy). I think the answer is obvious. Shouldn’t both views lead to the same result i.e. slowing of clocks, light shifts and field differences? Regarding field differences, a localised spacetime expansion (a possibility too easily dismissed) will cause a difference in potential between inertial and non-inertial bodies. How can one be certain this difference will not be identical in effect? Has anyone investigated it empirically?
    By the way, a localised spacetime expansion can be visualised as a sphere, whose radius is the lengthening double diagonal path in the light-clock example. The changing ratio of the sphere’s surface area to the volume is exactly equal to – guess what?- the gamma factor. Just an interesting coincidence that nobody seems to pay attention to.
    The Lorentz transformation is based on the theorem of Pythagoras, the right triangle. Try swapping the meanings of the terms for two of the triangle’s sides to find the mathematics is still the same. From there, the rest is easy.
    Wow. These simple views seem to genuinely confuse. Maybe there’s something to them.
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  16. #15  
    Brassica oleracea Strange's Avatar
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    Quote Originally Posted by HAL ON EARTH View Post
    The first (improved ) question is : if the apparent speed of light is constant in the moving frame then how can a photon travel a longer distance in the same time, from the view of a stationary frame?
    Answer: You are mixing frames of reference. From the view of the stationary frame, the photon travels a longer distance in a longer time. It must do because the speed of light is constant.

    The second (improved ) question is : if the apparent speed of light is constant in the moving frame then how can a photon travel a longer TIME in the same distance, from the view of a stationary frame?
    Answer (ignoring your rather garbled wording): You are mixing frames of reference. From the view of the stationary frame, the photon takes the same time to travel the same distance. It must do because the speed of light is constant.

    You really need to think through things more carefully and be very (very) careful about which time and which distance you are talking about.
    Without wishing to overstate my case, everything in the observable universe definitely has its origins in Northamptonshire -- Alan Moore
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  17. #16  
    Forum Freshman HAL ON EARTH's Avatar
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    Quote Originally Posted by Strange View Post

    Answer: You are mixing frames of reference. From the view of the stationary frame, the photon travels a longer distance in a longer time. It must do because the speed of light is constant.

    Answer (ignoring your rather garbled wording): You are mixing frames of reference. From the view of the stationary frame, the photon takes the same time to travel the same distance. It must do because the speed of light is constant.
    I think you are mixing the frames of reference, not me.

    In your first statement you say the photon travels a longer distance in a longer time. Not according to SR! From the stationary frame the photon is deemed to travel a contracted distance in a longer time.

    In your second statement you say the photon takes the same time to travel the same distance. Well, that's only from the moving frame, not the stationary frame. But according to SR the photon still travels a contracted distance in a longer time. However, my argument is this is logically inconsistent. The photon should take a contracted time in an expanded distance.

    If we could forget about calling the terms time and distance, and used meaningless symbols like x and y, there would be no way the conclusions would be identical. That is my argument in a nutshell.
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    Quote Originally Posted by HAL ON EARTH View Post
    In your first statement you say the photon travels a longer distance in a longer time. Not according to SR! From the stationary frame the photon is deemed to travel a contracted distance in a longer time.
    And there you go again. Whose distance? Whose time? While you make generic statements about "distance" and "time" your statements are not just wrong but meaningless.

    This is why you need to present a formal (mathematical) description of this claimed contradiction. Or at least, provide a diagram and make it explicit which distance & time you are talking about at any point.

    If the photon traveled "a contracted distance in a longer time" then you would be denying one of the postulates of relativity. In which case you are no longer talking about the theory of relativity but some alternative (and, presumably, wrong) theory.

    If we could forget about calling the terms time and distance, and used meaningless symbols like x and y, there would be no way the conclusions would be identical.
    So, don't use "meaningless" x & y, use d & d' for the distance in each frame and t & t' for the time in each frame. Although why the choice of symbols will make any difference is beyond me.

    What? You mean that by using the formalism of math instead of imprecise and inconsistent words, you will get the right answer?
    Without wishing to overstate my case, everything in the observable universe definitely has its origins in Northamptonshire -- Alan Moore
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    Forum Freshman HAL ON EARTH's Avatar
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    Forums are a kind of brainstorming, and you’ve been patient and cooperative . Re-reading one of Marcus Hanke’s comments, I should have couched my ideas in terms of a hypothesis.

    HYPOTHESIS: Both distance and time with regard to the phenomenon of light are equally constant in every proprietary frame of reference. I use the term proprietary in a specific way i.e. “belonging to one’s frame of reference”. I proceed on this basis, using the moving light-clock.

    Case A: IF the time elapsed between ticks of the light-clock is constant in all proprietary frames, how can this time be regarded as longer by the stationary frame?

    Answer: From the stationary frame, time expands for the moving mirror system. Both frames of time are proprietary, but relative to each other.

    Case B: IF the distance travelled by a photon between two mirrors is constant in all proprietary frames, how can this distance be regarded as longer in the stationary frame?

    Answer: From the stationary frame, the distance expands for the moving mirror system. Both frames of distance are proprietary, but relative to each other.

    By this logic, cases A and B are symmetrical. Time expands in A, and distance expands in B.

    Now, this hypothesis of the constancy of distance and time is a big IF. So if I proceed to apply the Lorentz transformation on this basis (which I think I must post separately as an attachment) I will need to show how the mathematics supports it.

    Phew. I’ve knocked myself out.
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    Brassica oleracea Strange's Avatar
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    Quote Originally Posted by HAL ON EARTH View Post
    I use the term proprietary in a specific way i.e. “belonging to one’s frame of reference”.
    The normal term for this is "proper" (distance, time, etc). This is one's length as measured in one's own frame of reference, for example.

    Case A: IF the time elapsed between ticks of the light-clock is constant in all proprietary frames, how can this time be regarded as longer by the stationary frame?
    The time between ticks is not constant (I'm assuming you mean "the same" rather than constant(*)) between all frames. (I'm not sure what "proprietary frames" means, given your earlier definition.)

    The proper (proprietary) time between ticks in a given frame of reference is related to the time between those ticks as seen from another frame of reference by the Lorentz transform.

    If the time is the same for all frames of reference, then those frames are not in relative motion and hence they are all the same frame of reference.

    Ditto for case B.


    (*) If, by "constant", you don't mean "the same" for all frames, could you clarify what you do mean.
    Last edited by Strange; August 6th, 2012 at 10:45 AM.
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    Moderator Moderator Markus Hanke's Avatar
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    Ok, there seems to be major confusion going on here - let's have look at this carefully. Your contention is basically that the speed of light is not the same for all observers, because you cannot figure out the correct relations for times and distance.

    Firstly, you need to understand that time dilation and length contraction are relational laws. What that means is that you can only tell that a clock is dilated as compared to another clock, and that a ruler is contracted as compared to another ruler. Dilation and contraction in just one frame without relation to another is meaningless.
    What this also means is that, if both clock and ruler are in the same frame of reference as the observer, then nothing special will be detected, because their relative velocity is zero.

    So let's look at the possible scenarios :

    1. Both clock and ruler are in the same frame of reference as observer ( either at rest or moving, does not matter ). Nothing special will be detected because the relative velocity is zero, and the speed of light is always measured as



    2. Observer at rest, clock & ruler moving at speed v



    because for the resting observer the moving clock appears to go slower, and the moving ruler appears shorter.

    3. Observer moving, clock & ruler at rest



    because for the moving observer the resting clock appears to go faster, and the ruler at rest appears to be longer.

    As you can see the speed of light is always the same, regardless of whether the observer is at rest or moving. It remains to be noted that time and distance measurements need to be performed in the same frame, or else the notion of speed becomes meaningless.

    So where is that contradiction you keep referring to ?
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    IF the time elapsed between ticks of the light-clock is constant in all proprietary frames
    It is not constant in all frames.

    IF the distance travelled by a photon between two mirrors is constant in all proprietary frames
    It is not constant in all frames.

    I will need to show how the mathematics supports it.
    I have just done that. Refer to the previous post.
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    I’ll change tack, if you guys still have the patience.

    Thanks for refreshing my memory of why c is always constant in every frame of reference. I’m having trouble uploading equations onto this site, which is a pity. I have a really entertaining take on the Michelson-Morley experiment, with many equations. Does this site let me upload a word document?

    **********************************
    Betty is from a parallel but inverted universe, like the mould in a die. Or like the inside-out part of a 3D movie we never see. Her universe is called “X”.


    Betty from “X” finds herself in our familiar universe “Y”. She can’t imagine why the “Y” inhabitants claim time has one dimension, and space has three dimensions. Bill from “Y” can only shrug and explain “that’s our reality, it’s the way things are”. Moreover, he complains that her inverted universe is outside his knowledge too. “Oh”, she says, “then you only understand what you call objective reality, which to me seems more like subjective reality”. She’s a smart one, this Betty.

    Betty’s universe has three time dimensions and one space dimension. Yet everything is symmetrical and parallel to “Y”, although famous names are different. For example, back in 1887 the null result of the Richardson- Worley experiment led to the conclusion that light’s speed is constant in every frame of reference. Florenz then suggested that the times for material bodies contract when they are elapsing, and that this foreshortening in time is only in the direction of the elapse. A guy called Ironstein took up the idea and got famous.

    Back in the “Y” universe, after the Michelson-Morley experiment, of course Lorentz had suggested that the distances for material bodies contract when they are moving, and that this foreshortening in distance is only in the direction of the motion.

    Lorentz had made some substitutions in Maxwell’s equations, which were mostly exactly the opposite of Paxwell’s equations in the “X” universe. The only equation that remained the same were the terms for the gamma factor.

    Now, when Florentz transformed Paxwell’s equations they remained in the same form. (For the eggheads, the equations became known as a Florentz transformation).

    Betty explains to Bill why the light waves in the Richardson-Worley experiment remained in phase. It was rather a long explanation involving a schematic of the apparatus used, full of equations. In fact, she lifted it straight out of Richie Feynman’s “Six Really Hard Pieces”. Her explanation was exactly the same as how Bill would have explained it, except she swapped the terms for time and distance around. For example, “length” in Bill’s universe becomes “period” in Betty’s universe. It got a very confusing for Bill, hearing terms used inversely. He got stuck on how someone could measure the period of time between two points in space. Anyway...

    Betty concludes that in her universe, time contracts in the direction of the elapse while distance expands. Bill objects and claims time expands while distance contracts in the direction of motion.

    Now, as the reader of this story how would you want Betty and Bill to reconcile their opposing, but symmetrical, conclusions? Do you just say “Betty’s world is a fantasy”? Or, for the sake of the story, do we consider the common factors? We can decide that since time expands in Bill’s world and distance expands in Betty’s world therefore it would be fitting for time and distance to expand together. After all, both Betty and Bill used exactly the same equations to arrive at their conclusions, even though the terms were swapped, except for the terms in the gamma factor of course.

    So for the sake of the story, when time expands, so does time.

    You might object that “time and space are different” and therefore Betty’s equations are illegal. But she is just unconventional, that’s all. She was quite tall too....about 2/300,000,000 light-seconds in her heels.

    Is there an experiment that defines the difference between space and time? And if not, how can we reject the possibility of Betty’s world? I am guessing that wavelength shifts, time dilation and even field differences could be equally explainable by a reconciled world view between Betty and Bill.
    ***********************************************

    The end.
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  24. #23  
    Moderator Moderator Markus Hanke's Avatar
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    Quote Originally Posted by HAL ON EARTH View Post
    Is there an experiment that defines the difference between space and time? And if not, how can we reject the possibility of Betty’s world?
    Because in Betty's world the laws of gravity would be very different.
    Gravity as we experience it is only possible in a universe with 3+1 macroscopic dimensions - any other mix of dimensions, and we would get completely different gravity laws.
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    I’m having trouble uploading equations onto this site, which is a pity. I have a really entertaining take on the Michelson-Morley experiment, with many equations.
    Look, you are really wasting your time. We know that SR is a correct and valid description of inertial frames just as it is, because there is a huge body of evidence that tells us that much. SR is not just based on Michelson-Morley, but on a body of evidence which spans pretty much most disciplines of physical sciences. You should also not forget that SR is only a special case of the much more comprehensive theory of General Relativity, which is in and of itself very well verified by experiment and observation. You will not find any contradictions in either by positing weird and strange scenarios, many have tried this, and they have all failed, because those scenarios are always based on a failure to correctly understand the laws of relativity. There are no contradictions, the theory is perfectly consistent.
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  26. #25  
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    Quote Originally Posted by HAL ON EARTH View Post
    I’m having trouble uploading equations onto this site, which is a pity.
    LaTeX. Or images.

    But you are wasting your time. The only people who think there is something wrong with special relativity are those who don't understand it. Luckily, most of them realise that the problem is in their understanding and keep working at it until they understand. A small minority seem to suffer from something like Dunning-Kuuger syndrome and come to forums like this to waste their time.

    It is a bizarre form of self delusion, "I have spotted this trivial error that the greatest minds have overlooked for the last hundred years!!1!".

    Yes, of course you have.
    Without wishing to overstate my case, everything in the observable universe definitely has its origins in Northamptonshire -- Alan Moore
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    I don't know...you guys think I'm claiming an error, not a contradiction. Big difference. Contradictions happen all the time in quantum theory, and I hope you don't claim to understand that.
    A contradiction can be resolved with a new approach that strengthens the existing, by all accounts, very nice theory.
    It is telling that there is no experiment that can determine the diffference between space and time.
    Oh, you think you know how Betty's world would operate with regard to gravity? You must be kidding yourself. I certainly don't claim to know.
    Don't be surprised if currently unexplainable phenomena in life sciences ends up supporting the idea that time and space is isotropic. That is my final word, but thanks for your opinions anyway.
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    Quote Originally Posted by HAL ON EARTH View Post
    Contradictions happen all the time in quantum theory, and I hope you don't claim to understand that.
    There are no contradictions in QM either - where did you get that impression ?
    In any case, that is besides the point because we are talking about relativity here, not QM.

    It is telling that there is no experiment that can determine the diffference between space and time.
    I told you otherwise. Swapping space and time will result in different physical laws.

    Oh, you think you know how Betty's world would operate with regard to gravity? You must be kidding yourself.
    Yes, we know. The laws of gravity are a direct consequence of space-time geometry. This is actually very well understood.
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    There are no contradictions in QM either - where did you get that impression ?
    Well, they seem strange enough to qualify as contradictions. Pass.
    Swapping space and time will result in different physical laws
    I won't argue, but Betty's world is an abstraction, a kind of mirror inverted scenario. Her world is different, but it won't change our laws. How different? I don't claim to know the difference between space and time. Betty's world is like a reflection, but her world's laws still have to comply with ours in inverse.

    I haven't set out to disprove Einstein or any such nonsense. By 'contradiction' I mean more of a paradox.

    Visualise yourself in a small bubble of spacetime (stationary). You exchange signals with a person in a large bubble (moving). The signal takes longer to enter and pass through the large bubble because the space has expanded. Therefore, the person in the large bubble will see your signal as blue-shifted because, by relativity, the wavelengths are more frequent- more of them fit into the large bubble.

    I find this visualisation helpful in remembering the right order of time dilation, the right order of the Doppler effect...and even in general relativity by extension. If nothing else, my conceptualisation helps me to visualise what actually happens, even if the theory underpinning it seems wrong.

    I will take a nap now.
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  30. #29  
    Brassica oleracea Strange's Avatar
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    Quote Originally Posted by HAL ON EARTH View Post
    By 'contradiction' I mean more of a paradox.
    Paradoxes are not contradictions. They are things that appear (naively) to be contradictory but when properly analysed turn out to be fully consistent with the theory.
    Without wishing to overstate my case, everything in the observable universe definitely has its origins in Northamptonshire -- Alan Moore
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  31. #30  
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    Quote Originally Posted by HAL ON EARTH View Post
    but her world's laws still have to comply with ours in inverse.
    No they don't. I really don't know where you get that idea from ? If you swap space and time you get something completely different from our universe.

    Visualise yourself in a small bubble of spacetime (stationary). You exchange signals with a person in a large bubble (moving). The signal takes longer to enter and pass through the large bubble because the space has expanded. Therefore, the person in the large bubble will see your signal as blue-shifted because, by relativity, the wavelengths are more frequent- more of them fit into the large bubble.
    I don't really get this scenario. Whether the signal will appear red or blue shifted depends first and foremost upon the direction of motion relative to the wave front of the light, and does not have anything to do with expanding space...? There is no expansion of space happening here.
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    Paradoxes are not contradictions. They are things that appear (naively) to be contradictory but when properly analysed turn out to be fully consistent with the theory.
    Point taken. Let's investigate how things appear....

    [If you swap space and time you get something completely different from our universe.
    Well, OK, but I think you are taking this idea "literally". If I asked you to measure all distances in units of time and to measure all time in units of distance you should expect exactly the same results, but you might call those results by a different name. It may not be reality as we know it, but it is a valid view. How valid? You can look at a panoramic scene directly or change the view by looking at the same panoroma reflected in a mirror. One view is "real" and the other is an abstraction. However, both views need to be symmetrical. When both views are symmetrical, we have a thing called "reality". It just so happens that if you want to find symmetry in relativity, even though you will use exactly the same equations, you end up calling the result in the "abstract" view by a different "name". I have shown by example that the different name is "distance expands and time contracts". The exact opposite result from the real world. But they are symmetrical. It's really that simple. It's a paradox because it seems contradictory.

    [Whether the signal will appear red or blue shifted depends first and foremost upon the direction of motion relative to the wave front of the light, and does not have anything to do with expanding space...? There is no expansion of space happening here
    Most textbooks couch signal exchanges in terms of moving bodies travelling away from the observer or vice versa. This creates complications due to the Doppler effect. It's a pain. So let's change the scenario and have the two bodies always in close proximity.

    A peer reviewed physics expert wrote a book "Explorations in Mathematical Physics". He shows why moving clocks do not always run slowly

    Do moving clocks always run slowly?

    The point is, if the spacetime bubble (as I'm calling it) is a speeding satellite revolving very closely around a fixed observer then any signals exchanged will comply with the bubble size law.
    1. The satellite will perceive signals sent by the observer as blue-shifted
    2. The oberver will perceive signals sent by the satellite as red-shifted.

    This is amazing to consider: If they are broadcasting TV signals to each other, then the oberver will see the satellite's inhabitant as not only red-shifted but also in slow motion! Conversely, the satellite guy will see the observer in BLUE tones and in fast motion! You see, the signals travel in and through different sized spacetime bubbles. By definition, a larger bubble needs to accomodate more wavelengths, which in the frame of the large bubble will be perceived as more frequent.

    In general relativity, by Einstein's principle of equivalence clocks run slower on large masses relative to clocks on smaller masses. Gravity is equivalent to acceleration (except the directions are different but that is not relevant). Can you see how SR and GR so easily connect? I think it is interesting to consider Einstein's early idea that a body's "relativistic mass" increased by the gamma factor. I've just assumed, by my silly and controversial logic, that the fabric of time and space for that body increases by the same amount.

    I simply cannot believe I am the only person on Earth to have thought of these ideas.
    Last edited by HAL ON EARTH; August 7th, 2012 at 10:29 PM. Reason: BLUE AND RED
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    I simply cannot believe I am the only person on Earth to have thought of these ideas.
    You're not. The reason you don't hear about the others is that these ideas are wrong, and so sink slowly back into the oblivion they deserve. Along with their ideaees.
    Its the way nature is!
    If you dont like it, go somewhere else....
    To another universe, where the rules are simpler
    Philosophically more pleasing, more psychologically easy
    Prof Richard Feynman (1979) .....

    Das ist nicht nur nicht richtig, es ist nicht einmal falsch!"
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  34. #33  
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    Quote Originally Posted by HAL ON EARTH View Post
    If I asked you to measure all distances in units of time and to measure all time in units of distance
    Why would you propose to measure time in meters and distance in seconds ? How many seconds is London away from Singapore ? How many meters does it take to fly to Paris ?
    This is just completely meaningless.

    but it is a valid view.
    See above.

    This creates complications due to the Doppler effect.
    I am not aware of any "problems" with that. It is a very straightforward calculation.

    This is amazing to consider: If they are broadcasting TV signals to each other, then the oberver will see the satellite's inhabitant as not only red-shifted but also in slow motion! Conversely, the satellite guy will see the observer in BLUE tones and in fast motion!
    This will depend on the directions of motion, but is essentially correct. This is just standard SR. I just don't know what that has to do with "space-time bubbles", because under SR we always work in Minkowski space, and no changes in the space-time metric occur.

    Can you see how SR and GR so easily connect?
    Yes of course - SR is just a special case of GR for inertial frames.
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  35. #34  
    Forum Freshman HAL ON EARTH's Avatar
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    I simply cannot believe I am the only person on Earth to have thought of these ideas. You're not. The reason you don't hear about the others is that these ideas are wrong, and so sink slowly back into the oblivion they deserve. Along with their ideaees.
    I assume you are not a scientist.

    Why would you propose to measure time in meters and distance in seconds ? How many seconds is London away from Singapore ? How many meters does it take to fly to Paris ?
    This is just completely meaningless
    I propose it to see what happens when we don't care about what we want to see.

    Been watching the Olympics lately? What does winning by 2/50ths of a second mean to you? What is a light-year, a distance or a time? Was there a famous experiment that proves it either way? Our conventions for time and space are just that, conventions. It's not always easy to grasp intuitively.

    This creates complications due to the Doppler effect. I am not aware of any "problems" with that. It is a very straightforward calculation.
    The Doppler "problem" just makes calculating shifts harder, is what I mean. Obviously (or not) if a light source speeds away from you the light will appear to shift toward the red end of the spectrum. Then ***news flash***you need to calculate how much that shift is reversed by the time dilation effect, according to SR. It's a drag. It's much easier to isolate the phenomenon when the two bodies remain in very close proximity.

    I just don't know what that has to do with "space-time bubbles", because under SR we always work in Minkowski space, and no changes in the space-time metric occur
    It is possible spacetime bubbles co-exist with Minkowski space. The physics of spacetime is not a closed subject. Perhaps the "metric" is ultimately a matter of viewpoint. Hopefully spacetime bubble theory is entirely consistent with relativity theory, and that length contraction co-existing with length expansion is just a paradox.
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  36. #35  
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    What does winning by 2/50ths of a second mean to you?
    It means someone arrived 2/50s of a second earlier than someone else ( =measurement of time in seconds )

    What is a light-year, a distance or a time?
    A measurement of distance in meters.

    Our conventions for time and space are just that, conventions.
    Yes, conventions for time and space, but not conventions to mix them around as you please. Because you can't.

    Then ***news flash***you need to calculate how much that shift is reversed by the time dilation effect, according to SR.
    Yes...but why would that be a problem ? Because you find it too hard ? Would you like me to show you the calculations ?

    It is possible spacetime bubbles co-exist with Minkowski space. The physics of spacetime is not a closed subject. Perhaps the "metric" is ultimately a matter of viewpoint. Hopefully spacetime bubble theory is entirely consistent with relativity theory, and that length contraction co-existing with length expansion is just a paradox.
    On what do you base this opinion ? Do you have any references, or can you present any maths ?
    Things like Doppler shift are easily treated under the rules of SR without needing to resort to unproven concepts like "space-time bubbles".
    In case you are interested - the bubble model has been extensively worked on ( see "Alcubierre Metric" ), and found to have a number of very ugly problems. Also, it is definitely not compatible with SR but needs the full GR treatment.
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  37. #36  
    Forum Freshman HAL ON EARTH's Avatar
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    In case you are interested - the bubble model has been extensively worked on ( see "Alcubierre Metric" ),
    Nah, it's not like that. Too weird. I'll call it a sphere instead.

    Glad you understood the news flash. I wasn't trying to be rude.

    The Doppler effect obstructs the knowledge that a signal takes longer to enter and leave the proprietary dimensions of that which I term a sphere of spacetime. (Proprietary is the original and correct term, by the way. Proper is physics slang). A rapidly rotating satellite, in close proximity to a relatively fixed observer, receives more wavelengths from the observer per unit of the (stationary) observer's proprietary time. That’s because the signal covers more “distance” from the observer's view.

    This means by the time the first wavelength has entered and left the moving body's proprietary dimensions many extra wavelengths would have entered the body's sphere. These extra wavelengths all need to be registered in a comparitively longer proprietary time from the observer's perspective, so they must appear more frequently in the sphere's frame.

    You create a long wavy line in the sand, and imagine its moving. It represents the constant speed of light. At different points you draw a circle around the line. The larger the circle, the more waves that fit into the circle. If you imagine the circle is moving away from the line, for each moment in time there are fewer new waves entering the circle, because each new wave has an extra distance to travel, so there is a delay. Hence the frequency will lessen for the circle. But its easier to imagine the circle when fixed, as per the fixed distance between a satellite and a stationary observer.

    On what do you base this opinion ? Do you have any references, or can you present any maths ?
    I am still forming the theory, and collecting data.

    A proprietary set of dimensions for time and distance can be likened to a sphere. I’m willing to let this sphere be subjective in nature. Voila. That’s one way it can co-exist in Minkowski space.

    "What is a light-year, a distance or a time?" You said: A measurement of distance in meters
    And this leads me to suggest that time and distance are also subjective. A light-year is ALSO a time. It’s the time it takes light to travel a zillion metres. Your choice to call it a distance is purely subjective.

    My choice to mess around with the terms for space and time is also subjective. When the maths for the subjective method squares up with the maths for the objective method, what is left? You can lambast it...but

    ....you have to admit, even if this story seems crazy, the spacetime sphere hypothesis is not contradicted by the phenomenon of light frequencies received in different sized spheres (or frames of reference). I therefore claim that as the first piece of evidence for the theory.
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    I assume you are not a scientist.
    Whether I am or I am not does not change the status of your ideas. Oblivion
    Its the way nature is!
    If you dont like it, go somewhere else....
    To another universe, where the rules are simpler
    Philosophically more pleasing, more psychologically easy
    Prof Richard Feynman (1979) .....

    Das ist nicht nur nicht richtig, es ist nicht einmal falsch!"
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    Forum Freshman HAL ON EARTH's Avatar
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    Not totally necessarily true. Because it doesn't upgrade the status of your opinion to fact.
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    Forum Freshman HAL ON EARTH's Avatar
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    Markus Hanke said: [QUOTE][SR is not just based on Michelson-Morley, but on a body of evidence which spans pretty much most disciplines of physical sciences./QUOTE]
    I begin with MM because it was the mother of all subsequent experiments.

    Some comments. How subjective must physics be if one insists a light-year can only be a measure of distance? Is time and distance a fact? A fact is defined as a phenomenon agreed upon by competent observers. For example, is "red" a fact? Red is associated with a wavelength of light. But that same wavelength may appear blue to competent observers in a different frame. Can we say with certainty that time and distance are not different aspects of the same thing (Minkowski), as red and blue are not different aspects of the same wavelength?

    Your earlier matrix (Markus Hanke) is correct as long as you accept its correctness is valid in one viewpoint. If you called the "t" term "s" (for distance) and the x, y, and z terms stood for time, would the matrix be wrong? You implied it would be wrong because a new physics would result...but it is not wrong notionally. And notionally the the two matrices must cancel each other out.

    The gamma factor is derived from the Pythagoras Theorem. We use a right triangle with "time" on one side of the hypotenuse and "distance" on the other. When you swap your view (i.e. terms ONLY, not the values) you get an opposite but symmetrical result. If we can't claim length contraction we are still left with a diagonal path that apparently expands in...what? Call it a parallel type of spacetime, which I concede may be subjective.

    To create an expanding spacetime sphere you start with the radius. What is expanding? It's the double diagonal path between two mirrors. So we can use either of these equations. radius t.gif radius diagonal path.gif


    When the speed of the moving frame is zero r =2. When the speed is 0.6 of c, the r=2.5. Divide the initial radius by the subsequent radius 2/2.5 = 0.8. This is the gamma factor. In this case, the sphere's volume volume of sphere.gif

    has increased by about 1.953 times. This is exactly the magnitude demanded to accommodate the required increase in frequency of light to enter and leave the sphere (or circle).

    I trust this maths help you to visualise my ideas....which need more crash testing obviously. But that's science.
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    How subjective must physics be if one insists a light-year can only be a measure of distance?
    The accepted definition of light year is quite clear ( quote Wikipedia article ) :

    A light-year, also light year or lightyear (symbol: ly), is aunit of length equal to just under 10 trillion kilometres (or about 6 trillion miles). As defined by the International Astronomical Union (IAU), a light-year is the distance that light travels in a vacuum in one Julian year.[1]


    Can we say with certainty that time and distance are not different aspects of the same thing (Minkowski),
    You can consider them different aspects of space-time if you so wish, but that does not mean you can swap them around arbitrarily.

    Your earlier matrix (Markus Hanke) is correct as long as you accept its correctness is valid in one viewpoint.
    It's correct because we can compare its prediction against experiments, and find that it gives the right numbers. In all experiments.

    You implied it would be wrong because a new physics would result...but it is not wrong notionally. And notionally the the two matrices must cancel each other out.
    Why don't you show us ?
    Besides, it is pretty obvious to everyone that our world has more than 1 spatial dimension.


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    It might be fitting to conclude this thread on a note of philosophy.

    Good old Wikipedia says defining time in a manner applicable to all fields without circularity has consistently eluded scholars.

    Distance is experienced in intervals of time. We need to operate on the concept of simultaneity to take two points and compare them. Simultaneity is relative, so distance is too. Relative to what? Relative to time? What’s time?....a circular argument. A light year is therefore, despite what Wikipedia says, fitting to be considered as a year. If the distance light travels is completed... it took a year, regardless of which calendar you use. If the distance the little hand moves around the clock equals one revolution, a minute has expired.

    As humanity has failed to define time, we therefore have failed to define the difference between time and distance. So why don’t we let a computer decide? A computer operates on values, not symbols. It doesn’t matter what you call the values if the output is the same....or even inverted.

    If you retain the parallel meaning of the symbols without changing the values you have not “arbitrarily” changed the symbols. You have deliberately changed them to obtain an exactly inverted result. You will just have to take it on trust that reality will still be there.

    Would you like me to post a document in a new thread to show you what I mean? I’m ready to write it up for entertainment purposes.
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  43. #42  
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    Quote Originally Posted by HAL ON EARTH View Post
    A light year is therefore, despite what Wikipedia says, fitting to be considered as a year.
    That is just your personal opinion. The official definition does not agree.

    If the distance light travels is completed... it took a year, regardless of which calendar you use
    That is correct only for an observer at rest - you seem to be forgetting that.

    As humanity has failed to define time, we therefore have failed to define the difference between time and distance.
    That is just weird.

    It doesn’t matter what you call the values if the output is the same....or even inverted.
    Well, maybe then you can try to invert all the 1s and 0s in the binary code of some arbiterary application - do you think it will still execute ?

    You will just have to take it on trust that reality will still be there.
    Take on trust ? Not exactly very scientifc.

    Would you like me to post a document in a new thread to show you what I mean? I’m ready to write it up for entertainment purposes.
    Do that, just for entertainment...
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    Forum Freshman HAL ON EARTH's Avatar
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    Firstly, the Lorentz transformation is

    Attachment 1000,
    Attachment 1003,
    Attachment 1002,
    t equation.gif


    I need to supply the alternative LT in another post, due to web file limits, apparently. Then I will comment. Hope the equations come out.
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    Forum Freshman HAL ON EARTH's Avatar
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    alt x equation.gif alt t equation.gif


    The proposed alternative Lorentz transformation equations are child's play. I've skipped the y and z as they are the same, and not necessary in a 2D Michelson-Morley experiment. (And I've having trouble with the latex application). We can't visualise 3D time, but we can give it a notional existence.

    As you can see, I've subsituted the first and fourth equations with the above two, which are "mirrored". Only the terms have been changed.

    Why should we expect a different result? I have only changed the names of what we are observing. I am not, as you may believe, changing any VALUES, just the names of those values.

    Similarly, I can change the name of what I observe to be "time". For example, I can measure time as the number of centimeters a clock's hand travels around the face. It is unconventional, but not illogical.

    A light year is therefore, despite what Wikipedia says, fitting to be considered as a year.
    That is just your personal opinion. The official definition does not agree.
    Officialdom! You have seen how easy it is to measure time in centimeters, see above.

    If the distance light travels is completed... it took a year, regardless of which calendar you use That is correct only for an observer at rest - you seem to be forgetting that.
    I will also forget that distance too is only correct for an observer at rest. See my point?

    As humanity has failed to define time, we therefore have failed to define the difference between time and distance. That is just weird
    Glad you agree.

    It doesn’t matter what you call the values if the output is the same....or even inverted. Well, maybe then you can try to invert all the 1s and 0s in the binary code of some arbiterary application - do you think it will still execute
    Of course it will execute if the code is in the same order. I'm only changing the NAMES.

    If we change the names in a novel, the plot stays the same. E.g. the plot leads to the moral "crime never pays". However, when we change the names for the Lorentz transform (which is ALL I've done) the plot changes. It's like the novel leading to "crime ALWAYS pays". In the LT transform, we end up with a changed story, i.e. time contraction with length expansion, not the conventional time expansion with length contraction.

    My point is, how are we supposed to know the "correct" LT if mere convention is our only guide? Did Lorentz just take a lucky guess?

    I understand your point that the conventional version is supported by empirical evidence. But you should question exactly what that evidence is definitely showing.
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    Why should we expect a different result? I have only changed the names of what we are observing. I am not, as you may believe, changing any VALUES, just the names of those values.
    Can you write down the full transformation in the notation I have used in post 2, so that we can make a direct comparison. Only in that way we can see what exactly it is you are relabelling.
    I will then perform a sample calculation for you using your own matrix, just to see what happens.

    Officialdom! You have seen how easy it is to measure time in centimeters, see above.
    If you like it or not, the official definition is the one used in science. You are free to reject it, just do not expect anyone to take your rejection seriously.
    And no, you can't measure time in meters. In fact, in terms of dimensional analysis your formula for t' yields a dimension of seconds-meters^2/seconds, which is undefined and completely meaningless.

    I will also forget that distance too is only correct for an observer at rest. See my point?
    I don't know what that means. We were talking about the light year, and how that relates to time. I do not see the connection to your comment.

    Glad you agree.
    Do you understand "that is just weird" as agreement ?
    That's just weird !

    Of course it will execute if the code is in the same order. I'm only changing the NAMES.
    Wait a minute now - your original contention was that you can replace time by space and vice versa. That is not relabelling, because space and time dimensions aren't the same thing, as explained to you numerous times.
    Relabelling means choose a different name for time, and choose a different name for space. The dimensionality still needs to be 3 spatial + 1 temporal, no matter what you call those coordinates.

    And in case you don't believe that : stand up from your chair. Take a step back. Take a step to your left. Wait 10 seconds.
    There you go ! I just proved to you that there are indeed 3 spatial and 1 temporal dimensions. It is really that simple.

    My point is, how are we supposed to know the "correct" LT if mere convention is our only guide? Did Lorentz just take a lucky guess?
    He didn't. It is the only possible transformation in Minkowski space which preserves the same speed of light for all observes, i.e. ensures that Maxwell's equations of electromagnetism are the same in all reference frames.
    In other words - it is based on observation and experiment.

    I'll wait for your transformation matrix, and then we can also see what happens to Maxwell's equations in your model.

    But you should question exactly what that evidence is definitely showing.
    See above. Within SR it shows that the speed of light is the same in all frames, and that Maxwell's equations are valid for all observers.
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    Having problems working with equation files...

    I should distinguish between distance and space.
    Q: what does the infinity of space mean if time flows in only one direction?
    Hypothesis: time = distance ; space = time + distance

    I therefore hypothesise the existence of 3D time.

    The matrix can be written as (g = gamma; b = beta )

    cx g -bg 0 0
    t -bg g 0 0
    y 0 0 1 0
    z 0 0 0 1

    Here, the time dimensions are t, y and z.

    Naturally everything in the conventional matrix agrees with the evidence.
    The alternative matrix may strike you as artificial or bogus. Perhaps its like stating "light is both a particle and a wave". So I'm hypothesising a similar duality exists in nature, with regards to dimensions.

    Would this matrix ruin Maxwell's equations? Can you assist?
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    I'll move this thread to New Hypothesis and Ideas for the time being. Might be heading further down though...
    Disclaimer: I do not declare myself to be an expert on ANY subject. If I state something as fact that is obviously wrong, please don't hesitate to correct me. I welcome such corrections in an attempt to be as truthful and accurate as possible.

    "Gullibility kills" - Carl Sagan
    "All people know the same truth. Our lives consist of how we chose to distort it." - Harry Block
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    I'll move this thread to New Hypothesis and Ideas for the time being. Might be heading further down though.
    OK. Here is my take on what is accepted, and my commentary follows.

    Accepted:

    Distance is a measurement between two simultaneous points in time.
    Therefore we can't measure distance without time.

    An interval is a measurement between two simultaneous points in distance. (The distance between two markings on a clock's face needs to exist simultaneously).
    Therefore we can't measure time without distance.

    Commentary:

    Regard time and distance as equal partners of space, and swap the terms to change your view. An island that is three hours away by boat is both a distance and a time. Changing the view does not change the fact.

    In the matrix, two symbols are swapped. I am guessing it only changes our view of what we measure.

    But if Maxwell's equations are destroyed then I'm prepared to learn why.
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    Accepted:

    Distance is a measurement between two simultaneous points in time.
    Therefore we can't measure distance without time.

    An interval is a measurement between two simultaneous points in distance. (The distance between two markings on a clock's face needs to exist simultaneously).
    Therefore we can't measure time without distance.
    Interesting how you get things completely backwards.
    Its the way nature is!
    If you dont like it, go somewhere else....
    To another universe, where the rules are simpler
    Philosophically more pleasing, more psychologically easy
    Prof Richard Feynman (1979) .....

    Das ist nicht nur nicht richtig, es ist nicht einmal falsch!"
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    Quote Originally Posted by HAL ON EARTH View Post
    cx g -bg 0 0
    t -bg g 0 0
    y 0 0 1 0
    z 0 0 0 1
    Ok, so you are using the same LF matrix, but you are now working on a manifold with 1+3 dimensions instead of 3+1 dimensions.

    So I'm hypothesising a similar duality exists in nature, with regards to dimensions.
    I very much doubt that. Like stated on several occasions already, spatial and temporal dimensions behave differently and are not freely interchangeable.

    Would this matrix ruin Maxwell's equations? Can you assist?
    The matrix is the same is the standard LF transformation matrix. What you have done is turn 3+1 into 1+3 dimensions; consider the differential form of the Maxwell equations ( in normal 3+1 dimensions )





    and of course



    The very first problem you now have is that the curl operator is only defined for at least 3 spatial dimensions, so the above equations cannot even be completely re-written in a 1+3 space. The next thing is that the divergence operator then would ( presumably ) only act on the spatial part of the vectors, so all you are left with is




    and therefore




    which is basically meaningless, but in any case has no resemblance whatsoever to the original Maxwell equations.

    So, to make a long story short - this whole thing in nonsense.
    Last edited by Markus Hanke; August 11th, 2012 at 05:34 AM.
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    Quote Originally Posted by HAL ON EARTH View Post
    I'll move this thread to New Hypothesis and Ideas for the time being. Might be heading further down though.
    OK. Here is my take on what is accepted, and my commentary follows.

    Accepted:

    Distance is a measurement between two simultaneous points in time.
    No. There is no such thing as absolute simultaneity, for events separated by space. There is no such thing as two simultaneous points in time that are separated by distance - there will always be frames of reference where those events were not simultaneous.
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    Quote Originally Posted by HAL ON EARTH View Post
    Accepted:

    Distance is a measurement between two simultaneous points in time.
    Therefore we can't measure distance without time.

    An interval is a measurement between two simultaneous points in distance. (The distance between two markings on a clock's face needs to exist simultaneously).
    Therefore we can't measure time without distance.
    This is not how distance and interval is defined. The general definition is done via the line element, integrated along the curve you want to measure, like so :



    So yes, obviously you can very easily measure time without distance, and also distance without time.
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    Interesting how you get things completely backwards.
    Maybe not backwards in the way you imagine.
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    Like stated on several occasions already, spatial and temporal dimensions behave differently and are not freely interchangeable.
    They are not interchangable. It is hard to explain. By analogy, the verb "swimming" is not quite interchangeable with the noun "swimming" in the manifold of grammar. Both are totally different. A video of swimming is temporal, while a photo is spatial. Yet both require the existence of the other in their own contexts.

    The very first problem you now have is that the curl operator is only defined for at least 3 spatial dimensions, so the above equations cannot even be completely re-written in a 1+3 space.
    Nice work. But yes, it's not logical. This is due to trying to re-write it in 1 + 3 space. It can't be done. You have tried to give time and distance each other's meaning but you can't because you are confined to one manifold. The best you can do is "pretend" time=distance in name only, and use the standard Lorentz transformation matrix. That's why I think Maxwell's equations remain in the same form.

    No. There is no such thing as absolute simultaneity, for events separated by space. There is no such thing as two simultaneous points in time that are separated by distance - there will always be frames of reference where those events were not simultaneous.
    I think this is irrelevant. But anyway, let's use the idea of "agreement" instead, because I am talking about one frame of reference only. For example:

    To measure an agreed length of distance you need two observers with synchronised (agreeing) light-clocks at each end.

    To measure an agreed interval of time you need an agreed length of distance (see above)

    Think of the distance between two mirrors in a light-clock as ALSO the period of time between two mirrors. They are interchangeable and equal in ONE frame of reference.

    So yes, obviously you can very easily measure time without distance, and also distance without time.
    I'm having a big problem accepting this, due to above. A moving train requires the front and back ends to be recorded against synchronised time-clocks. So an agreed length requires an agreed time reading. Therefore measuring a time requires a length! Doesn't the distance between the markings on a dial for 12:00 o'clock and 6:00 o'clock mean anything to you? If it's a digital clock, ditto the distance travelled by an electron.

    So, to make a long story short - this whole thing in nonsense
    Well, maybe. I'll re-read your mathematical treatment and argument. But in the meantime we should consider one example of empirical support for an expanding time and distance model. Namely, a sphere that grows in volume by the gamma factor will accomodate EXACTLY the right frequency of externally originating wavelengths required in SR. (P.S. external= origin in a different frame). To arrive at a sphere, find the double diagonal path in Pythagoras' theorem and use it as the radius.

    If you want to know what happens between an orbiting body and a stationary body, convert each body to a sphere and you immediately know what the end result should be. If you introduce gravity you need to consider mass in a separate calculation, but you immediately visualise that a larger sphere should have more gravitational energy, and more gravity means slower clocks. More gravity means external signals appear more frequent, so now you have a mnemonic device for remembering this.

    This conclusion may be disputed by some. But it seems nicely symmetrical with Einstein's early idea that relativistic mass increases by the same gamma factor that expands the sphere.
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    Quote Originally Posted by HAL ON EARTH View Post
    They are not interchangable. It is hard to explain.
    Yet that is what you have done in post 46 - you turned 3+1 space-time into 1+3 time-space (?!).

    Nice work. But yes, it's not logical. This is due to trying to re-write it in 1 + 3 space.
    Yes, because that is what you asked me to check - refer to post 46.

    Think of the distance between two mirrors in a light-clock as ALSO the period of time between two mirrors. They are interchangeable and equal in ONE frame of reference.
    Well, you can either measure the distance with a ruler, or you can measure the time with a clock. You can't measure time with a ruler, or distance with a clock. It makes no sense, and is meaningless, because they are not the same thing ! In fact, the time in this scenario is actually dependent on the medium of propagation - swap the vacuum for glass, and it's no longer the same.

    I'm having a big problem accepting this, due to above. A moving train requires the front and back ends to be recorded against synchronised time-clocks. So an agreed length requires an agreed time reading. Therefore measuring a time requires a length!
    That makes no sense - there is no such thing as agreed length and agreed time, because both change if you travel at relativistic speeds. Why are you making your own life so hard ? SR provides a very simple relationship between those two frames, don't complicate things by requiring "agreed" measurements and "synchronised" clocks. None of this is needed to determine relative velocity, and relative velocity is the only thing two inertial observers can agree on.

    But in the meantime we should consider one example of empirical support for an expanding time and distance model.
    When the speed is 0.6 of c, the r=2.5. Divide the initial radius by the subsequent radius 2/2.5 = 0.8. This is the gamma factor.
    This is from post 39. I think you are getting something seriously mixed up here - for v = 0.6c the gamma factor is

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    I'll answer your questions backwards.
    I think you are getting something seriously mixed up here - for v = 0.6c the gamma factor is
    ...1.25
    My physics coordinator once told me the same thing. I use the gamma symbol to mean gamma "factor". You elect to divide it by 1 to get 1/0.8 = 1.25. So a sphere that is 1.25 times "expanded in distance" (so to speak) is 1.25 times "expanded in time". Alternatively a sphere that is 0.8 times "slower in distance" is 0.8 times "slower in time". This might make more sense as I answer your questions.

    That makes no sense - there is no such thing as agreed length and agreed time, because both change if you travel at relativistic speeds.
    I am not talking about relativistic speeds here. Maybe you assumed so because I use light-clocks. I am only referring to inertial frames. I want to arrive at a definition of agreed length and agreed time. That's how measurements of agreed length and time can agree. Inertial observers (e.g. stationary observers in the same room) must agree on the same length and time.

    Well, you can either measure the distance with a ruler, or you can measure the time with a clock. You can't measure time with a ruler, or distance with a clock. It makes no sense, and is meaningless, because they are not the same thing ! In fact, the time in this scenario is actually dependent on the medium of propagation - swap the vacuum for glass, and it's no longer the same.
    Ah...maybe this is the source of all the confusion. I should have anticipated this.

    You measure the distance with a ruler, but to measure the ruler itself you need to simultaneously agree in time where the start and the end of the ruler is . You might think you don't need any kind of clock, but the ruler might undergo thermal expansion or contraction, for example. So you use the best synchronised vacuum encased light-clocks money can buy. Next, you lay out one of the light-clocks against the ruler and use the distance between the two mirrors as a ruler itself. You can rely on light's constancy to give you an accurate reading. So that's how you measure distance with a clock! You need time. It's a bit of a circular argument because the mirrors themselves might expand or contract. But what can you do? It's the best way we know to arrive at an agreed length. Alternatively we can rely on a piece of metal stored in a Swiss bank for a meter. But how was that length first derived? etc etc

    Furthermore, if you wanted to check the frequency of that Swiss metal's atomic vibration to confirm its accuracy, you could check it against a clock. If not, which length of metal do you choose?

    Yet that is what you have done in post 46 - you turned 3+1 space-time into 1+3 time-space (?!).
    Yes, because that is what you asked me to check - refer to post 46.
    I plead guilty as charged. I sent you off on a wild goose chase. Nevertheless I was genuinely interested if it could be possible. Because you had relied on an assumed intrinsically theoretically measurable difference between distance and time (which I interpret as a kind of scientific faith)I wondered if the Lorentz transform really did hold the key. I agree the LT requires length contraction to support the constancy of c. But can you see what this rationale is based on? Both length and time are vulnerable to the earlier circularity I identified. For in inertial frames how do you initially determine an agreed length (for distance) if you rely on a light-clock, and likewise how do you initially determine the distance between two mirrors (or the distance of earth's orbit etc etc) if you rely on a ruler?

    I think the anwer is you rely on some convention. And that is why I think length contraction is a length contraption.

    Why did I bother with all this you ask? Because I needed an excuse to use that one liner.
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    Quote Originally Posted by HAL ON EARTH View Post
    You measure the distance with a ruler, but to measure the ruler itself you need to simultaneously agree in time where the start and the end of the ruler is .
    No you don't, you only agree on two points in space.

    You might think you don't need any kind of clock, but the ruler might undergo thermal expansion or contraction, for example.
    That's nonsense, nowhere was there any mention of changes in temperature etc. What is this about ? I think you are clutching at straws now.
    You only need two points in space, all other things being equal.

    But what can you do? It's the best way we know to arrive at an agreed length.
    If you just let go of your notions about "agreed" measurements, you will not have any of these problems !
    I really don't get you.

    But can you see what this rationale is based on?
    The rationale is simply based on an experimental observation - that Maxwell's equations hold in all reference frames. The mathematical formulation for this very simple principle is the Lorentz-Fitzgerald transformation.

    For in inertial frames how do you initially determine an agreed length (for distance) if you rely on a light-clock, and likewise how do you initially determine the distance between two mirrors (or the distance of earth's orbit etc etc) if you rely on a ruler?
    You fix the measurement in one frame ( doesn't matter which one ) - it is then uniquely determined in all other inertial frames through LF.
    You are right, the definition in the original frame is simply convention ( the meter could just as well be twice as long without changing any laws ), however, the way to go from one into another frame is not convention, but a physically very real effect.

    I use the gamma symbol to mean gamma "factor".
    You cannot just arbitrarily change the meanings of scientifically well defined terms - the Gamma factor is the Gamma factor, and not its inverse. If you mean its inverse, then write 1/gamma, but don't change accepted meanings for basic terms.
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    No you don't, you only agree on two points in space.
    You used the word "agree". In space you can exchange signals to determine relative distance and position. Signals take time. Once agreement is established the two points in "space" are taken for granted. Afterwards, sure, you only need to use the previously agreed points. But they had to be agreed upon in the first place, and that required simultaneity.

    That's nonsense, nowhere was there any mention of changes in temperature etc. What is this about ? I think you are clutching at straws now.
    You only need two points in space, all other things being equal.
    Just trying to clarify a principle. Yes, sure, all things being equal...but before you got the initial agreement you stated was necessary in your first answer, you needed to confirm the reality of the length. Otherwise you are talking about a theoretical length, in which case you need to equally acccept a theoretical time.

    If you just let go of your notions about "agreed" measurements, you will not have any of these problems !
    I really don't get you.
    Agreement is the basis of evidence. But if you mean I should let go of my notion of always "having to confirm a length in terms of time" I already do, after the initial measurements have been synchronised and confirmed. Afterwards, we just use the units operationally as granted.

    The rationale is simply based on an experimental observation - that Maxwell's equations hold in all reference frames. The mathematical formulation for this very simple principle is the Lorentz-Fitzgerald transformation
    Yes, we can create equations that hold in all reference frames. If you merely call the terms of those equations by each other's names they will also hold (of course). So we make a choice about whether to call a cycle of reflection the "distance" a photon travels or the "time" it takes. To help in that decision we choose 3 +1 space and get confirmation for that. Neatly, that stops us from claiming a light clock that is laid parallel (not perpendicularly , as conventionally shown)to the direction of motion contracts in time. Instead we claim the light clock contracts in distance, and are careful to mean the distance travelled by the photon and not the time it takes.
    the way to go from one into another frame is not convention, but a physically very real effect.
    Yes, clocks really do slow down on satellites. Length contraction is much less tangible because of the problem of frame dependence. I searched the internet and found a professor of physics who claimed length contraction is a fact, not theory. I won't embarrass him by naming him. Newton's laws were held as fact for centuries. But we have the internet today. I found a Professor Robert J. Buenker who asserts length expansion, not contraction, occurs on satellites. The article is " The Global Positioning System and the Lorentz transformation".
    See http://redshift.vif.com/JournalFiles...F/V15N3BU1.pdf

    You cannot just arbitrarily change the meanings of scientifically well defined terms - the Gamma factor is the Gamma factor, and not its inverse. If you mean its inverse, then write 1/gamma, but don't change accepted meanings for basic terms.
    OK, I should qualify my usage. But I have shown how the accepted gamma and its inverse can support an arguably isotropic model. I then ask: what can this model predict? How useful is it?
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    I searched the internet and found a professor of physics who claimed length contraction is a fact, not theory. I won't embarrass him by naming him.
    This has already been adressed multiple times :

    1. Length contraction and time dilation are the same effect. If you accept time dilation you need to accept length contraction as well, they cannot be separated. The alternative is only that you reject both.
    2. The reality of length contraction can quite simply be confirmed by observing the outcome of certain particle accelerator experiments. The easiest is the collision of heavy gold ions, such as here :

    RHIC | Physics of the Relativistic Heavy Ion Collider

    Observe how the ions are length contracted into flattened disks - the outcome of the collision ( i.e. the resulting plasma and particles ) would be very different if those ions were in fact spheres at the time of collision. In other words, they don't just look contracted, they behave as flattened disks as well, which is not possible if this was only an apparent effect.

    The article is " The Global Positioning System and the Lorentz transformation".
    See http://redshift.vif.com/JournalFiles...F/V15N3BU1.pdf
    This is not a source of valid, peer-reviewed scientific data, but a privately operated anti-relativity site. I am not sure what quoting such a source says about your own intentions and agenda - I sincerely hope you only quoted this because you don't know any better. In any case, the article is full of errors and failures to understand basic principles of relativity. What I find the most worrying is that the paper you referenced in not listed in Prof Buenker's official list of publications :

    Buenker Group

    Prof Buenker, who is a real person at said university, does not perform any research into relativity per se, and no publications dealing with GPS are listed, according to this university's website.

    what can this model predict? How useful is it?
    You tell us. It's your model, and in my mind it is still meaningless, and makes no testable, unique predictions that are of any scientific value.
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    So Professor Buenker turns out to be Professor Bunkum? I'll accept that.

    Suppose I also accept all the very strong evidence you supply. Then I can't help suspecting that length contraction exists with either an anomaly or just a happy model in my mind that is just a coincidence.

    The anomaly in my mind is why the sphere model successfully predicts

    1. The correct frequency of externally originating signals (i.e. light) in both inertial and non-inertial frames

    2. Time dilation because the diagonal path is "real" and space/distance expands. Signals really do travel a longer distance to complete a cycle

    3.That gravitational energy is greater in larger spheres for a given mass (which seems intuitively neat).

    And really interesting to me is what I referenced in post #31.

    4. Moving clocks in different frames do NOT always run slowly from the view of the other frame. Is this correct? The author seems respectable though the reference is not peer reviewed. It implies the inertial frame will see the non-inertial frame's clock to run slowly, and contrawise the non-inertial frame will see the inertial frame's clock to run fast. All in real time for a close orbit situation. This suggests simultaneity. Is this consistent with special relativity?

    My only agenda is to understand this stuff.
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  62. #61  
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    Quote Originally Posted by HAL ON EARTH View Post
    4. Moving clocks in different frames do NOT always run slowly from the view of the other frame. Is this correct? The author seems respectable though the reference is not peer reviewed. It implies the inertial frame will see the non-inertial frame's clock to run slowly, and contrawise the non-inertial frame will see the inertial frame's clock to run fast. All in real time for a close orbit situation. This suggests simultaneity. Is this consistent with special relativity?
    How can it suggest simultaneity if the clock in the non-inertial frame is running slower and the clock in the inertial frame is running faster? How can both observers agree on the time/distance between two events?
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  63. #62  
    Moderator Moderator Markus Hanke's Avatar
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    Quote Originally Posted by HAL ON EARTH View Post
    1. The correct frequency of externally originating signals (i.e. light) in both inertial and non-inertial frames
    A rapidly moving sphere is length contracted along the axis of the velocity vector, and becomes an elipsoid with the volume



    and thus



    Whereas on the other hand the frequencies in relativistic Doppler shift behave as



    How do you explain this to be the same ?

    2. Time dilation because the diagonal path is "real" and space/distance expands. Signals really do travel a longer distance to complete a cycle
    This I don't understand at all, it makes no sense. In any case, since the sphere is contracted those 'signals' ( whatever they are ) actually have less distance to cover.

    3.That gravitational energy is greater in larger spheres for a given mass (which seems intuitively neat).
    How do you define "gravitational energy" here ?
    If the mass stays constant and the volume increases, the energy density, and thus the gravitational field strength, decreases.

    4. Moving clocks in different frames do NOT always run slowly from the view of the other frame. Is this correct? The author seems respectable though the reference is not peer reviewed. It implies the inertial frame will see the non-inertial frame's clock to run slowly, and contrawise the non-inertial frame will see the inertial frame's clock to run fast.
    Yes, the source is trustworthy, but your conclusion is not quite right - who sees what between inertial and non-inertial frames is very complex, and depends on many factors such as acceleration, gravitational fields etc etc. There is no generic answer, and in any case this is not within the realm of SR, but GR.
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  64. #63  
    Forum Freshman HAL ON EARTH's Avatar
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    These are elegant equations, but the sphere I'm describing retains its shape i.e. is not length contracted. It is a subjective sphere with interesting parallels. It takes some explaining, if you are willing to entertain a situation I invented:


    See the diagram. orbiting light clock.jpg

    Each broken line of the inner circle represents the "top" mirrors of 8 stationary light clocks. The centre lines represent the straight path taken by a photon, but you can't see the "bottom" mirrors here, which are obscured by the tiny writing "stationary light clock" (centre of diagram). But you know they are there. Also, assume the 8 light-clocks are synchronised and don't interfere with each other.

    Next we look at the top broken circle. Here, each broken line stands for the "top" mirror of a single moving light-clock that is orbiting the 8 stationary light-clocks. I have allowed the "bottom" mirror to share each stationary light-clock's "top" mirror, but actually there should a very small separation between the two. I should have drawn them better. You can imagine they are almost touching, which is why you only see one mirror.

    So we have the photon in the orbiting mirrors taking a double diagonal path, forming the zig zag star pattern. Contra wise, each photon's path in the 8 stationary light-clocks is a straight line.

    The experiment

    Each light-clock also sends a (separate) signal to the other frame when the "proper" photon in its own frame completes a cycle. In this way signals are exchanged between "inner" and "outer" light-clocks, each signal being activated by a single cycle of reflection respectively. I have drawn the mirrors so that each of the 8 stationary light-clocks are matched exactly with the changing position of the orbiting light-clock. The set up in the experiment is such that the right orbiting speed is coordinated with the required positions.

    Let's look at the orbiting frame first. Because the orbiting frame's cycles are less frequent it sends signals to the stationary frame less frequently, as it must wait longer for the zig zag path to be completed. A less frequent signal implies a longer wavelength. So each stationary mirror receives signals less frequently, which must be "red-shifted" compared to the signal frequency in its own frame.

    On the other hand, each cycle in the stationary mirror is more frequent than the cycles in the orbiting frame's light-clock, because the photon's path is a shorter straight line. So a higher frequency of signals will be sent, meaning more signals fit between the orbiting mirrors than what the "proper" photon registers within the same mirrors. Hence the orbiting mirrors will receive a relatively higher frequency of signals, meaning they are "blue-shifted".

    Can you confirm your understanding or objections so far, before I respond to your other questions?
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  65. #64  
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    [QUOTE=SpeedFreek;344220]
    Quote Originally Posted by HAL ON EARTH View Post
    How can it suggest simultaneity if the clock in the non-inertial frame is running slower and the clock in the inertial frame is running faster? How can both observers agree on the time/distance between two events?
    Good question. Can two clocks joined at the hip, each ticking at their own rate, agree to disagree?
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  66. #65  
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    Quote Originally Posted by HAL ON EARTH View Post
    Good question. Can two clocks joined at the hip, each ticking at their own rate, agree to disagree?
    This isn't the same scenario, because two clocks joined together are always in the same frame of reference, and will thus agree ( even if they tick at different rates ).

    These are elegant equations, but the sphere I'm describing retains its shape i.e. is not length contracted.
    I don't understand - I have already shown you that length contraction is a real physical effect, i.e. no sphere will retain its rest-shape when travelling at relativistic velocities.

    Can you confirm your understanding or objections so far, before I respond to your other questions?
    I don't think I get your reasoning - why would anything be red or blue-shifted ? All that changes is the time between two signals, but the signals themselves do not change their wavelengths.
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  67. #66  
    Forum Freshman HAL ON EARTH's Avatar
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    Markus Hanke

    Originally Posted by HAL ON EARTH
    Good question. Can two clocks joined at the hip, each ticking at their own rate, agree to disagree?



    This isn't the same scenario, because two clocks joined together are always in the same frame of reference, and will thus agree ( even if they tick at different rates ).
    It is still interesting. One clock is stationary while the other clock is orbiting around it. The separation could be only the width of an electron. You can re-define “joined” as connection by a “live” communication link. Thus both clocks communicate in “real time”. The stationary clock sees the orbiting clock as running slow, while the orbiting clock sees the stationary clock as running fast. Thus they can both agree to disagree. See Do moving clocks always run slowly? which is a valid source.

    I don't understand - I have already shown you that length contraction is a real physical effect, i.e. no sphere will retain its rest-shape when travelling at relativistic velocities.
    Bear with me. The hypothetical sphere has different “physical” properties. It is something like the fabric of spacetime, rather than the shape of mass. I’ve seen the photograph of the flattened particle in the accelerator. I asked myself “is it a photograph of contracted distance or a contracted moment in time? (Tricky) And, what would we look like to the particle if it photographed us? (Answer: we don’t know)

    I don't think I get your reasoning - why would anything be red or blue-shifted ? All that changes is the time between two signals, but the signals themselves do not change their wavelengths.
    It is problematic to state “all that changes is the time between two signals”. I don’t think you can distinguish between “a signal” and “a signal itself” where time is concerned. I offer three scenarios.

    Assumptions: Signal = photon. A signal is both a particle and a wave. Frequency= number of wavelengths AND/OR number of particles. Light-clock= clock. One clock is orbiting a stationary clock of negligible separation in distance. Both clocks transmit photons to each other, synchronised with a parallel photon’s cycle of reflection. The "frequency" of a photon is measured as the number of cycles of reflection within a mirror system.

    Scenario A
    If the number of signal wavelengths stays the same, the number of particles must stay the same. For this to happen would require length contraction in the orbiting clock. Whether this contraction is in time or distance, I don’t know. If the contraction is in time the photon in the orbiting clock should retain the same frequency as the photon in the stationary clock, and the apparent distance travelled by the photon between the two mirrors in the orbiting clock expands from the view of the stationary clock.

    But if the contraction is in distance, the frequency will also stay the same and the apparent time it takes for the photon to travel between the two mirrors from the stationary view expands.

    Either way, if the frequency stays the same, and the two clocks are joined by a “live” communication link (i.e. exchange of signals) courtesy of negligible separation, this implies NO effects of time dilation (or length contraction) will be observed.

    Why not? Suppose each sent signal is synchronised with a physical action. If the frequency is unchanged the accompanying physical actions must also remain unchanged, else they fall out of synch. So the rates of time between the two clocks would always agree, courtesy of their negligible separation.

    The above scenario seems to be forbidden in special relativity.

    Scenario B
    On the other hand, if the apparent distance a photon travels between the mirrors in the orbiting clock expands, then the frequency of photons measured as each cycle of reflection from the stationary view must be less. Therefore the stationary clock must receive fewer signals, and fewer signals means a lower frequency of photons, and a lower frequency of photons must mean a lower frequency of visible light i.e. red-shifted. This is also observed in the Doppler Effect.

    Moreover, if each signal is synchronised with a physical action both clocks will view each other as time distorted i.e. the orbiting clock will appear slow to the stationary clock, and the stationary clock will appear fast to the orbiting clock.

    Scenario B seems to comply with special relativity. It is also supported by a valid source shown previously.

    So how will lengths be measured by each clock? The stationary clock should see the orbiting clock as length contracted. Surely the orbiting clock cannot see the stationary clock as length contracted too? As the stationary clock sees the orbiting clock as slow, and the orbiting clock sees the stationary clock as fast, shouldn’t this symmetry be equally applicable? I.e. the orbiting clock should look shortened, while the stationary clock should look lengthened?

    Scenario C
    Each photon has its own wavelength regardless of the frame of reference . The word “frequency” should not be taken literally.(I don’t accept this view, and it conflicts with the Doppler Shift evidence).

    Conclusion: I favour scenario B. If this is accepted, I should then show how spheres can also describe what is going on, and discuss any conflict with accepted theory.
    Last edited by HAL ON EARTH; August 15th, 2012 at 10:29 AM.
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  68. #67  
    Moderator Moderator Markus Hanke's Avatar
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    One clock is stationary while the other clock is orbiting around it.
    Even if they are close together they still would not be in the same frame - in fact, the orbiting clock would be non-inertial, strictly speaking.

    Bear with me. The hypothetical sphere has different “physical” properties. It is something like the fabric of spacetime, rather than the shape of mass. I’ve seen the photograph of the flattened particle in the accelerator. I asked myself “is it a photograph of contracted distance or a contracted moment in time? (Tricky) And, what would we look like to the particle if it photographed us? (Answer: we don’t know)
    That wasn't a photograph, only a computer animation. The point was that the ion behaved like a flattened disk during the collision. We can tell the difference by the collision products, i.e. the quark plasma and the decay particles.

    The "frequency" of a photon is measured as the number of cycles of reflection within a mirror system.
    Actually no, the frequency of a photon depends only on its energy / momentum : Photon - Wikipedia, the free encyclopedia
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  69. #68  
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    One clock is stationary while the other clock is orbiting around it.
    Even if they are close together they still would not be in the same frame - in fact, the orbiting clock would be non-inertial, strictly speaking.
    Yes I know. Nevertheless it is very interesting to consider a very close proximity between clocks. For entertainment, imagine you were the size of the moon having a conversation with a normal person. By the time a nerve signal did its thing in your giant head the normal person might have perceived several of your minutes in one second.

    That wasn't a photograph, only a computer animation. The point was that the ion behaved like a flattened disk during the collision. We can tell the difference by the collision products, i.e. the quark plasma and the decay particles.
    Again, it is interesting to ask generally "is it a snapshot of distances, or a snapshot of time?". It might sound silly. What does time look like? Just take a photo then look at the image. It has more than one dimension when frozen in a snapshot.

    The "frequency" of a photon is measured as the number of cycles of reflection within a mirror system. Actually no, the frequency of a photon depends only on its energy / momentum : Photon - Wikipedia, the free encyclopedia
    Yes, but I'm talking about relative frequency. The relative energy and relative momentum of a photon will change when considered in a different frame. If not, a light-clock would not slow if it carried the same relative energy and relative momentum
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  70. #69  
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    Quote Originally Posted by HAL ON EARTH View Post
    If not, a light-clock would not slow if it carried the same relative energy and relative momentum
    Time dilation is not just an apparent effect related to how we "see" clocks - it is time itself which slows down.
    How do we know this ? Consider a particle called a "muon" - these particles are products of high-energy collisions high up in our atmosphere. They are very massive, and as such their lifetime is very short, in fact it is so short that normally it would decay before it can reach the surface of the earth ( about half way through the atmosphere ), even at velocities near the speed of light.
    However, we do in fact detect such muons here on the surface - and relativity provides a simple explanation, namely that time is dilated for the particle because it moves at high speed, and thus its lifetime is sufficiently extended to reach the surface of the earth before it decays. This is physical fact, so time dilation isn't just apparent, it's physically quite real in all frames of reference - both the muon and the earth-bound observer agree that the particle reaches the surface. The observer sees this as a result of time dilation, the muon sees it as a result of the atmosphere being length contracted, but it is the same effect. Both agree on the final outcome.
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    Time dilation is not just an apparent effect related to how we "see" clocks - it is time itself which slows down.

    If we accept time dilation and length contraction are the same effect, then we may agree about the sphere model.

    As I proposed in the orbiting light-clock experiment ( Scenario B in Post 66), an orbiting body might see us as time contracted, contrary to how we see the orbiting body. The evidence is the "live" exchange of signals, due to the negligible separation. Suppose the interval between each signal sent (which is coordinated with a cycle of reflection) measures each body's "Proper Space" (to coin a phrase) respectively. The "PS" is the apparent distance between the mirrors in both proper frames. The orbiting body's relative "PS" expands while the stationary body's relative "PS" contracts.

    We can still accept length contraction as fact because length contraction is just another view of time dilation. We can't "see" length contraction, but we can experience the reality of time dilation or time contraction via the signal exchanges, depending on the frame.

    In the end, the sphere is "subjective" because it paints a picture of "proper spacetime" expansion for moving bodies, relative to stationary bodies. It is "proper" because it is only true for one's frame; therefore it is subjective. But it is also "real" because it accommodates the correct relativistic wavelength frequencies, as I suggested in Scenario B.

    So I'd be happy to accept the reality of length contraction in parallel with the reality of a subjective "proper spacetime" sphere. I don't think I've broken any rules of special relativity. Earlier, it seemed to me that length contraction was at odds with localised sphere expansion, but length contraction is objective while "Proper Space" expansion is subjective.
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  72. #71  
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    Quote Originally Posted by HAL ON EARTH View Post
    I don't think I've broken any rules of special relativity.
    No, you're just making your life harder than it needs to be
    Relativity alone already provides a sufficient explanation for all phenomena mentioned, so I don't see why you would need to suggest sphere's of "proper space-time" and things like that. SR is fine just as it is, and very well tested experimentally.
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  73. #72  
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    SR is fine just as it is, and very well tested experimentally
    Sure, SR is fine as it is. It just depends on what you want to show.... Thanks for your point of view.
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  74. #73  
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    EDIT : Please ignore. I made an error, this post was not meant to be here. My apologies.
    Last edited by Markus Hanke; August 21st, 2012 at 12:54 PM.
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