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Thread: Unifying Space and Time

  1. #1 Unifying Space and Time 
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    My understanding is that Space and Time are manifestations of the same underlying phenomenon -in the same way as time only has meaning when a distance is measured also distance only has meaning when the time taken to measure it is accounted for (unless there are other workable theories that Space and Time are independent phenomena that interact with each other.....)

    Now it has occurred to me that in the same way that a "distance" between points in "Space" can be calculated by the square root of the sum of the squares of the distances along the x,y and z axes then (since this last example is only approximate anyway) it should be equally valid and predictive to include the time dimension in the framework .

    So my first stab is that the distance in Spacetime from the origin to a point(x,y,z t) could be the square root of the sum of the squares of those attributes (is that the right mathematical term?).

    Now I can see straight away the the time units and the space units cannot be seconds and metres.Both have to be expressed in a way that is common to both.(unless metres and seconds can both be tied down to a common unit)


    Is there a unit that can be applied equally to all 4 Space Time axes? What about the light nano second(or something even smaller) ? or the smallest known frequency connected to the smallest known object of known spacial dimension?



    If this unit was applicable to all 4 axes would the distance in SpaceTime as calculated by ,say the square root of the sum of the roots as measured along the 4 axes give a usable or predictive result?

    Would it be possible to represent acceleration using this kind of a graph?


    Last edited by geordief; January 12th, 2014 at 09:55 AM.
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    Quote Originally Posted by geordief View Post
    My understanding is that Space and Time are manifestations of the same underlying phenomenon
    They are aspects of the same manifold, so yes.

    Now it has occurred to me that in the same way that a "distance" between points in "Space" can be calculated by the square root of the sum of the square of the distances along the x,y and z axes then (since this last example is only approximate anyway) it should be equally valid and predictive to include the time dimension in the framework .
    Indeed. What you end up with is called a metric; for example, the metric for flat Minkowski space-time is



    So my first stab is that the distance in Spacetime from the origin to a point(x,y,z t) could be the square root of the sum of the square of those attributes (is that the right mathematical term?).
    Close enough - you have the basic idea

    Is there a unit that can be applied equally to all 4 Space Time axes?
    Yes, the standard is to use the meter. Look at the above metric - the time coordinate is not just t, but actually ct - giving this a dimension of meter. We are thus talking about distances between events in space-time.

    Would it be possible to represent acceleration using this kind of a graph?
    Of course. A uniformly moving observer traces out a straight trajectory in space-time. An accelerated observer traces out a curved trajectory. Counterintuitively, it is always the inertial ( i.e. uniformly moving ) observer who traces out the longest world line between given events; that's because the time coordinate has opposite sign to the spatial coordinates.


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  4. #3  
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    Welcome to Special Relativity
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    that makes no sense, you can't measure events that way, you will get paradoxes.
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  6. #5  
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    Quote Originally Posted by 514void View Post
    that makes no sense, you can't measure events that way, you will get paradoxes.
    No, you don't.
    There are no paradoxes in relativity, just people's misunderstandings of it.
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    I am confused.
    what happens when an accelerated observer goes a really long route?
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  8. #7  
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    Quote Originally Posted by 514void View Post
    I am confused.
    what happens when an accelerated observer goes a really long route?
    He will measure a really long proper time, as you would expect.
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    nahh, i mean he takes the same amount of time as the straight trajectory guy, but just goes really far.

    thats allowed with acceleration right?
    or does it have to go in a straight line too?
    Last edited by 514void; January 22nd, 2014 at 08:38 AM.
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  10. #9  
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    Quote Originally Posted by 514void View Post
    nahh, i mean he takes the same amount of time as the straight trajectory guy, but just goes really far.
    Yes, that's because he is accelerated, and hence goes faster. Also, the proper times won't agree between these observers.
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    is that after they arrive at the same point at the same time?
    I would of thought that their "clocks" would show the same time.
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    Quote Originally Posted by 514void View Post
    is that after they arrive at the same point at the same time?
    I would of thought that their "clocks" would show the same time.
    This is one of the effects of relativity - the amount of proper time recorded depends on the clock's velocity profile, which means that these two clocks will not agree. See here : Time dilation - Wikipedia, the free encyclopedia
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    the minkowski is a resultant vector of space and time - itself derived from motion.

    a better 'tensor' would be space and motion. but motion is about traversing space. a redundant 4th term?
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    Is it at all possible that an infinitesimally tiny (and universal ) spacetime interval could be used as a "unit" for spacetime?

    I mean a pair of events that occurred in or around the nucleus of an atom for example.

    Would that work and would it have any extra utility to using the meter? (or is that just what the meter is anyway? Does the "meter" explicitly measure a spacetime interval -or is it just implicit as I have assumed )
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    The meter measures distances in space (not time).

    You might be thinking of natural units (in contrast to our arbitrary, man-made ones): Natural units - Wikipedia, the free encyclopedia
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    No I wasn't thinking of natural units (I don't even begin to understand them even if I have often heard them referred to).

    It just ocurred to me that whenever they try to measure time or weight they always seem to gravitate to the extremely tiny (eg atomic clocks) and I thought perhaps a unit of spacetime might also benefit from being extremely accurate and based on the infinitesimally small.

    But it is also to do with trying to fix in my own mind the nature of spacetime as opposed to "space and time" .

    Since the Minkowski axes describe points(events I suppose) in Spacetime then I surmise that the 3 spatial axes are also really spacetime axes.

    I am not sure whether these representations are meant to be merely predictive or whether they are supposed to be "true" (I think they are true and so I tend to believe that spacial distances are really spacetime distances -and that "t" is never zero)

    Maybe I am being too abstract (or maybe the maths are just too hard for me!) .
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  17. #16  
    Brassica oleracea Strange's Avatar
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    Quote Originally Posted by geordief View Post
    Since the Minkowski axes describe points(events I suppose) in Spacetime then I surmise that the 3 spatial axes are also really spacetime axes.
    Well, there are four space-time axes: 3 space and 1 time. That's why it is called space-time!
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    nonsense
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    Quote Originally Posted by Strange View Post
    The meter measures distances in space (not time).
    Actually, that isn't quite the whole story; the choice of units is really largely arbitrary. For example, instead of using a "t" coordinate for time, you could use a "ct" coordinate ( as Taylor does in "Spacetime Physics" ), thereby using the meter to consistently measure distances between events in space-time. Likewise, you could choose a coordinate system that measures spatial distances in seconds. The conversion factor is always the speed of light c, which conveniently contains both meters and seconds
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  20. #19  
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    Is the omnipresence of "c" in these equations an acknowledgement that it the speed of light that governs the processes of transformation of information so that it could really be called the "speed of information" ?.

    Also I am trying to imagine what you would see if you had a direct video cam of a far away planet with events taking place on it and which you (the observer) were approaching at a relatavistic speed.

    Would these events appear speeded up and what would be the highest "fast forward" effect be as your approach speed reached (almost) the speed of light?

    I think I am right (but am prepared to be mistaken) that if the same planet was receeding at the same speeds (and you were able to view events on it) then the events (say a colony on said planet) would appear in slow motion to the receeding observer.
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    a moving charge experiences force.
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  22. #21  
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    Quote Originally Posted by geordief View Post
    Is the omnipresence of "c" in these equations an acknowledgement that it the speed of light that governs the processes of transformation of information so that it could really be called the "speed of information" ?.
    You could picture c as being the conversion factor between space and time; different observers see different length and different times, yet the relation between them remains constant - c.

    Also I am trying to imagine what you would see if you had a direct video cam of a far away planet with events taking place on it and which you (the observer) were approaching at a relatavistic speed.
    You may wish to take a look at these animations : Visualization of special relativity

    Would these events appear speeded up and what would be the highest "fast forward" effect be as your approach speed reached (almost) the speed of light?
    If both frames can be considered approximately inertial, then both observers would see the other one time dilated. If gravity and acceleration are present also, things become more complicated.

    I think I am right (but am prepared to be mistaken) that if the same planet was receeding at the same speeds (and you were able to view events on it) then the events (say a colony on said planet) would appear in slow motion to the receeding observer.
    Yes, and the same vice versa ( if they are approximately inertial ).
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    a force very similar to a centripetal force.
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  24. #23  
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    Quote Originally Posted by Markus Hanke View Post



    Would these events appear speeded up and what would be the highest "fast forward" effect be as your approach speed reached (almost) the speed of light?
    If both frames can be considered approximately inertial, then both observers would see the other one time dilated. If gravity and acceleration are present also, things become more complicated.

    I think I am right (but am prepared to be mistaken) that if the same planet was receeding at the same speeds (and you were able to view events on it) then the events (say a colony on said planet) would appear in slow motion to the receeding observer.
    Yes, and the same vice versa ( if they are approximately inertial ).
    I seem to discern that it makes no difference whether the observer is approaching the planet (at relatavistic speed) or whether he is receding from it at the same speed. He will only see events moving there more slowly - not more quickly.

    And it seems to me that there are probably no circumstances in which an observer can view events occurring on another moving Frame of Reference and see them as "speeded up" or "fast forwarded". That never , ever happens does it?

    If I am right here I wonder is this a common misapprehension or would I be one of the first to fall down this particular rabbit hole? (thinking that events might seem "speeded up" in the way they are when you fast forward a film )?
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  25. #24  
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    Quote Originally Posted by geordief View Post
    I seem to discern that it makes no difference whether the observer is approaching the planet (at relatavistic speed) or whether he is receding from it at the same speed. He will only see events moving there more slowly - not more quickly.
    Yes, correct. In this scenario it is only the magnitude of the relative velocity that is important.

    That never , ever happens does it?
    Not if the motion is purely inertial. It is however possible to get such an effect if one of the observers is accelerated in the right way.

    If I am right here I wonder is this a common misapprehension or would I be one of the first to fall down this particular rabbit hole?
    Ha ha, no, you aren't the first one, it is very common ( because it is counterintuitive )
    If you have two inertial frames A and B in relative motion, then A will see B time dilated, but B will see A also time dilated in the exact same way - that is what it means for the frames to be symmetric. Many people have difficulty wrapping their heads around this when they start to learn about relativity; it's pretty natural, I should think.
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  26. #25  
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    Quote Originally Posted by Markus Hanke View Post
    Quote Originally Posted by geordief View Post
    I seem to discern that it makes no difference whether the observer is approaching the planet (at relatavistic speed) or whether he is receding from it at the same speed. He will only see events moving there more slowly - not more quickly.
    Yes, correct. In this scenario it is only the magnitude of the relative velocity that is important.
    I think it's important not to confuse time dilation with the Doppler effect. The Doppler effect does depend on the direction of the relative velocity, not just the magnitude. The Doppler effect is what the observer sees with regards to relative velocity, not the time dilation. In the case of gravitation or acceleration, the time dilation is what the observe sees if there is no relative motion and therefore no Doppler effect. In the case of relative motion as well as gravitation or acceleration, then there is both the Doppler effect and the time dilation to consider.

    In the case of relative inertial motion, time dilation corrects for the amount of time it takes for light to travel the change in distance due to the relative motion. It is not what the observer sees. What the observer sees also includes the amount of time it takes for light to travel the change in distance due to the relative motion, which corresponds to the Doppler effect.
    There are no paradoxes in relativity, just people's misunderstandings of it.
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    Quote Originally Posted by KJW View Post
    I think it's important not to confuse time dilation with the Doppler effect. The Doppler effect does depend on the direction of the relative velocity, not just the magnitude. The Doppler effect is what the observer sees with regards to relative velocity, not the time dilation. In the case of gravitation or acceleration, the time dilation is what the observe sees if there is no relative motion and therefore no Doppler effect. In the case of relative motion as well as gravitation or acceleration, then there is both the Doppler effect and the time dilation to consider.

    In the case of relative inertial motion, time dilation corrects for the amount of time it takes for light to travel the change in distance due to the relative motion. It is not what the observer sees. What the observer sees also includes the amount of time it takes for light to travel the change in distance due to the relative motion, which corresponds to the Doppler effect.
    True of course, though probably not what geordief was aiming at
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  28. #27  
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    Quote Originally Posted by Markus Hanke View Post
    True of course, though probably not what geordief was aiming at
    Geordief did use the words "see events", and I feel that this should be taken at face value because to assume otherwise would be to assume that geordief has a level of understanding that is inconsistent with the question being asked, and because the distinction between time dilation and the Doppler effect is a very significant potential source of confusion with regards to a correct understanding of relativity.
    There are no paradoxes in relativity, just people's misunderstandings of it.
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    Quote Originally Posted by KJW View Post
    the distinction between time dilation and the Doppler effect is a very significant potential source of confusion
    You're probably right - I didn't really consider that.
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    Last edited by geordief; January 27th, 2014 at 09:29 AM.
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    Wasn't sure whether to start a new thread as all my questions seem to be of a similar level of knowledge so far.

    I spend a fair bit of time these past weeks scratching my head and trying to visualise scenarios in Relativity

    So this is my latest question.

    Suppose you are an observer in a "stationary" spacecraft with a lightbeam/mirror setup.You emit a light beam and it is reflected back to the source by a mirror .

    Then the spacecraft is accelerated in a direction perpendicular to direction of the light beam.

    What happens to the light beam?

    Does it still travel perpendicular to the direction of acceleration?

    I understand light has no mass so I am prepared for it to be unaffected by the acceleration but I also know that it can be bent around massive objects and so perhaps it will in this case also be bent since gravity and acceleration seem to be indistiguishable .

    I hope my scenario was realistic.
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    Quote Originally Posted by geordief View Post
    Does it still travel perpendicular to the direction of acceleration?
    The ray of light becomes "bent" as seen from the perspective of a stationary, outside observer. Like so :

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    What about for the observer who is accelerated along with the spacecraft? Does the light also bend for him ? (That would be an unpleasant incident.) Does it remain straight because they are both subject to the same conditions?

    I have another ,very theoretical question I have been thinking about (well it just crossed my mind is what I should say).

    There is no privileged frame of reference I understand but is it possible to create a scenario in which there are ,say "n" observers in "n" frames of references each with multiple and possibly interreacting or chain reacting views of what the other observers "see".

    This is a very half baked idea and I hope it is not "true" or consequential as it would seem to make things more complicated but it does slightly put me in mind of the "extra dimensions" I have heard talk about -the way they are so small that they are unnoticed..
    Last edited by geordief; January 27th, 2014 at 12:21 PM.
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  34. #33  
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    Quote Originally Posted by geordief View Post
    Suppose you are an observer in a "stationary" spacecraft with a lightbeam/mirror setup.You emit a light beam and it is reflected back to the source by a mirror .

    Then the spacecraft is accelerated in a direction perpendicular to direction of the light beam.

    What happens to the light beam?

    Does it still travel perpendicular to the direction of acceleration?

    I understand light has no mass so I am prepared for it to be unaffected by the acceleration but I also know that it can be bent around massive objects and so perhaps it will in this case also be bent since gravity and acceleration seem to be indistiguishable .

    I hope my scenario was realistic.
    Problems like this are best considered in an inertial frame relative to which the observer is accelerating. One examines the light-path in this inertial frame of reference. Then one examines how the light-path in the inertial frame appears in the accelerated frame of reference. In the accelerated frame of reference, the light-path will bend away from the direction of acceleration. If the spacecraft is accelerating upward at 9.8m/sē, then one has replicated the downward bending of the light-path in earth's gravity. Thus we have the equivalence principle between gravity and accelerated frames of reference.
    There are no paradoxes in relativity, just people's misunderstandings of it.
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