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Thread: Einstein explains relativity to Newton.

  1. #201  
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    Quote Originally Posted by Jagella
    Quote Originally Posted by Myuncle
    This is to explain that the concept of unity you won't find it in reality, but only in your mind.
    Whoa! Finally somebody here besides myself shows some understanding of what math is: a language that's used to communicate ideas about how we humans describe quantity, order, shape, and size. It is a human invention just like electrical circuits. There's nothing absolute or universal about it.

    Quote Originally Posted by Myuncle
    So we all agree about math only because we want to make this world more comfortable, math it's nothing but an agreement.
    Speaking of minds, you must have been reading mine. I was going to reply to another member that any apparent objectivity in mathematics is actually agreement about how we apply its rules. If two Catholics agree that the pope is infallible, does that make the pope's infallibility an objective truth? No. Catholics are taught that the pope is infallible, and math students are taught that they can graph a function using rules created by Descartes in the Seventeenth Century. The common denominator (no pun intended) in both cases is agreement rather than objectivity.

    Quote Originally Posted by Myuncle
    The unpredictable factor is nothing new, we can't even calculate, with all the math that we have, exactly when an earthquake is going to strike, just to give you an example.
    We can calculate probabilities which, like much of statistics, are quite subjective. Anybody who claims that math is totally objective has never studied probability and statistics, or if they did, they must have been daydreaming.

    Jagella
    Good we agree Jagella, if I find only one person that agrees than I achieved my goal. You showed clearly you didn't come here to patronize, but to debate politely. The most beautiful thing about a forum and internet it's disagreeing politely. People can agree or disagree about anything as long as they are polite, which means: not to patronize, being rude, arrogant, doing sarcastic remarks, provoking, insulting, and taking things out of context. Only if you are open minded you can have a polite debate. I don't believe anyone is stupid in this world, stupidity is always mistaken for an untreated personality disorder or any other mental illness. But that's another subject...
    Can we find a unity in reality? Math is based on the concept of unity, and that unity is supposed to be identical to another unit. This is very practical and convenient for all of us, but can we find a unity identical to another in reality? No, only in our mind, in our imagination, in our subjectivity, in our concept. And this happens so quickly we don't even realize it. Is one banana identical to another banana? Only in our concept. Is one atom identical to another atom? Only in our imagination. Is one twin identical to his twin? Only in our thoughts. Math is very useful for us and for physics, who can deny this? It is objective if we agree and accept its rules.
    I am not one of those who think math it's the language of physics, I would rather say that math is the language of math, and physics is the language of physycs.
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  2. #202  
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    Quote Originally Posted by Myuncle
    The most beautiful thing about a forum and internet it's disagreeing politely. People can agree or disagree about anything as long as they are polite, which means: not to patronize, being rude, arrogant, doing sarcastic remarks, provoking, insulting, and taking things out of context.
    Really?

    You said this "I don't mean to be rude, but it seems you can't read properly, and you put in my mouth things I didn't say. "

    That was both ignorant and offensive, so you appear incapable of following your own guidleines.
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    I'm confused. If mathematics is not objective, then what would qualify to be called "objective"?

    If your definition of "objective" is so restrictive that nothing qualifies as such, then perhaps you are basing your conclusions on the wrong definition of the word.
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    Quote Originally Posted by Myuncle
    You showed clearly you didn't come here to patronize, but to debate politely.
    To be honest, Unc, I must admit that I did veer a bit into the belligerent side of this discussion, but I will make an effort to debate politely, as you say. What would any of us like to gain here? Discovering new truth or degrading our ideological opponents? I'll take the former.

    Quote Originally Posted by Myuncle
    I don't believe anyone is stupid in this world...
    To paraphrase Helena Rubinstein: “There are no stupid people, only dogmatic ones.” Our stubborn prejudices can close our minds to knowledge that, if only we were open to it, would change our lives for the better.

    Quote Originally Posted by Myuncle
    Is one banana identical to another banana? Only in our concept.
    Are you familiar with Plato's “universals”? A universal is an ideal form which has no physical existence but is an ideal. A “universal banana” might be what most people would think of an ideal banana: perfectly curved and yellow without blemish. I believe mathematical concepts may be similar to these universals in that one banana equals one banana, but in reality we know that bananas are different and cannot be truly equal. However, for practical purposes we know that bananas are similar enough that we can accept them as equal, and a customer at the supermarket will pay the same price for a banana as another customer pays for a different banana without complaining too much.

    Quote Originally Posted by Myuncle
    Math is very useful for us and for physics, who can deny this?
    That, we can all agree to.

    Jagella
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    Quote Originally Posted by salsaonline
    I'm confused. If mathematics is not objective, then what would qualify to be called "objective"?

    If your definition of "objective" is so restrictive that nothing qualifies as such, then perhaps you are basing your conclusions on the wrong definition of the word.
    Well, I hope you realize that nothing really needs to be objective for the word to have meaning. A "perfect wife" is meaningful enough even though there may be no perfect wives. "Objective" means without bias and true regardless of opinion. How can mathematics be objective when we all have biases and cannot know that it is universally true?

    I believe that this may not be an insurmountable problem. Mathematics has a "apparent" objectivity in that virtually all people find it useful and consistent. In many cases it has never been found to be wrong, so for practical purposes we can accept it as objective. Until somebody proves that assertions like 2 + 2 = 4 are not true, treating it as objective is fine at least as far as teaching the basic techniques and postulates are concerned.

    Nevertheless, I think it is misleading to insist that mathematics is objective in the full sense of the word. To do so constitutes adhering to an unprovable dogma which, as I hope you agree, has no place in science.

    Jagella
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    A few questions:

    One, do you really think anyone's opinion has any effect on "2+2=4"?

    Second, are you familiar with the term axiom?

    The two questions are related. Given the standard axioms (ZF set theory), 2+2=4 becomes a foregone conclusion and things like 2+2=5 can be shown to be contradictory.

    Also, why is your "mathematics is subjective" not unprovable dogma? Your opinion is at least as subjective as everyone else's. You still seem to think things like deciding to use 3.142 instead of 3.14 is somehow part of math, which, as has been pointed out, is confusing the tool and its use.
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    This will go on and on. Jagella you have been reduced to basically claiming everything is subjective. Do you believe ANYTHING exists outside your own experience?

    Tell us, without doubt, what you believe to be purely 100% objective that we can't contradict using the same all encompassing cop out that you are using? Are these letters real? your computer screen? The air you breathe?
    Does any of this exist atall!

    To try and say that a universal constant like PI, evident in natural structures here on earth and millions of light years away, is somehow a figment of the mind is no better than saying we have imagined hundreds of years of scientific progress and the universe actually follows no rules at-all. Because rules are subjective.

    Maybe you believe the only objective truth is "everything is subjective"?
    'Aint no thing like a chicken wing'
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    Quote Originally Posted by kojax
    If Jagella is a graphic designer, then it is likely that her field has a proprietary definition for the word "visualize", and he/she has made the mistake of forgetting that industry jargon definitions are not always universal to everyone. An easy mistake to make. Hardly worth 6+ pages of ridicule.
    As far as I know, there is no particular use of the word visualize that is peculiar to the graphic-design profession. Nevertheless, as a graphic designer I have been trained to understand how illustrations, animations, figures, and diagrams affect people. People react to and interpret visual media in many different ways. Based on the discussion on this thread, I can see that some mathematicians tend to interpret the visual aids used in teaching mathematics literally rather than as mere visual aids. For instance, a graphed curve is what a function looks like!

    Quote Originally Posted by kojax
    Actually it's not about the distance varying, but the speed. If your throwing speed is 30 mph (IE. you can throw a ball hard enough so that it's traveling at 30 mph when it leaves your hand), and your riding in a car at 60 mph and decide to throw a ball in front of you, the ball's total speed would be 90 mph.

    Light isn't like that. If you're traveling at .5 C and you shoot a laser beam in front of you, the laser beam doesn't travel at 1.5 C. It still travels at exactly C. Instead of it's total speed being higher, what will happen instead is that it's color will be closer to blue (higher frequency).
    Yes. When I stated that distance varies I meant that time varies.

    Anyway, the speed of light can be written as C = d / t where C is the speed of light, d is distance, and t is time. Of the three variables, we know that C and d are constant. If the speed of light cannot vary even if its source's frame of reference is moving, then time must vary from one frame of reference to another.

    Einstein had the advantage over Newton of knowing that the speed of light is constant. As you may know, this fact was discovered in 1887 by Albert Michelson and Edward Morley, long after Newton's time. I'm sure that Einstein would mention the Michelson-Morley experiment to Newton as the basis for knowing that the speed of light is constant.

    Jagella
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    Quote Originally Posted by Jagella
    I can see that some mathematicians tend to interpret the visual aids used in teaching mathematics literally rather than as mere visual aids. For instance, a graphed curve is what a function looks like!
    Are you being deliberately obtuse, or is their a simpler explanation?
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    Quote Originally Posted by harvestein
    This will go on and on. Jagella you have been reduced to basically claiming everything is subjective. Do you believe ANYTHING exists outside your own experience?

    Tell us, without doubt, what you believe to be purely 100% objective that we can't contradict using the same all encompassing cop out that you are using? Are these letters real? your computer screen? The air you breathe?
    Does any of this exist atall!

    To try and say that a universal constant like PI, evident in natural structures here on earth and millions of light years away, is somehow a figment of the mind is no better than saying we have imagined hundreds of years of scientific progress and the universe actually follows no rules at-all. Because rules are subjective.

    Maybe you believe the only objective truth is "everything is subjective"?
    I was thinking the same thing, but I think you said it better than I would have.

    Unless you're taking certain philosophy courses, teaching students "everything is subjective" would most certainly not be conducive to their learning.

    (Also, Jagella is wrong that d is constant in c = d/t. Only c is a constant. Length contraction and time dilation both occur.)
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    Quote Originally Posted by MagiMaster
    (Also, Jagella is wrong that d is constant in c = d/t. Only c is a constant. Length contraction and time dilation both occur.)
    I know that the length of an object traveling near the speed of light contracts, but you say the distance traveled contracts? Are you sure about that? The formula for length contraction is L' = L sqrt(1 - v^2 / c^2). If you substitute d / t for v, then
    L' = L sqrt(1 - (d^2/t^2) / c^2)

    If what you're saying is true, then at speeds near the speed of light a traveler's journey shortens.

    Jagella
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    Quote Originally Posted by Jagella

    If what you're saying is true, then at speeds near the speed of light a traveler's journey shortens.

    Jagella
    Which is precisely what is predicted by special relativity.
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    Yes, and that is relatively easy to illustrate.

    If you are travelling at 86.6% of c, then a journey of 5 light years should take you 5.77 years. But at that speed, gamma (the "relativistic change factor") is 2, which means it only takes you half that length of time to make the journey - you get there in only 2.88 years! This means the distance to your destination must have contracted from your point of view, from 5 light-years to 2.5 light-years, as that is the distance covered at 86.6% of c in 2.88 years!
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  14. #214  
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    Quote Originally Posted by Jagella
    Quote Originally Posted by MagiMaster
    (Also, Jagella is wrong that d is constant in c = d/t. Only c is a constant. Length contraction and time dilation both occur.)
    I know that the length of an object traveling near the speed of light contracts, but you say the distance traveled contracts? Are you sure about that? The formula for length contraction is L' = L sqrt(1 - v^2 / c^2). If you substitute d / t for v, then
    L' = L sqrt(1 - (d^2/t^2) / c^2)

    If what you're saying is true, then at speeds near the speed of light a traveler's journey shortens.

    Jagella
    The Michelson and Morley experiment you mentioned earlier is the one that lead Hendrik Lorentz to formulate Lorentz contraction, which is the theory that, not only does a person's perception of time change as they approach the speed of light, but also their perception of distance changes as well (though the change is determined by a different formula). Anyway, Lorentz contraction is also pretty essential to relativity.

    http://en.wikipedia.org/wiki/Lorentz_transformation


    Perceiving distances to be shorter would be a natural consequence of an object becoming shorter. Think of how triangulation works. You take two reference points a known horizontal distance apart, and measure the angle each of them perceives a distant object to be located at, and you can use that to calculate how far away it is. In a Lorentz contracted object, the apparent angles get screwed up because the lenses (or whatever other device you might use to measure those angles) are contorted.
    Some clocks are only right twice a day, but they are still right when they are right.
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    Quote Originally Posted by kojax
    Perceiving distances to be shorter would be a natural consequence of an object becoming shorter. Think of how triangulation works. You take two reference points a known horizontal distance apart, and measure the angle each of them perceives a distant object to be located at, and you can use that to calculate how far away it is. In a Lorentz contracted object, the apparent angles get screwed up because the lenses (or whatever other device you might use to measure those angles) are contorted.
    Also, I think here we have to acknowledge the difference between what we can observe as we travel at a high percentage of c, with what we can calculate about our situation, based on those observations.

    When travelling at a "relativistic" speed, your view of the universe around you is subject to both Doppler effect and the aberration of light. The Doppler effect is obvious - objects in your direction of travel are blueshifted and objects in the opposite direction are redshifted. The aberration of light, on the other hand, causes your field of view to expand - the faster you go, the more you see of what is around the sides and behind you! As you approach c, the whole sky seems to be concentrated into a small area in front of you, and objects in your direction of travel actually look to be further away!

    http://www.fourmilab.ch/cship/aberration.html

    But of course, if we could accelerate up to a relativistic speed, rather than simply using our view of the universe to work out the distance to our destination, we could simply calculate it. If we know how far away our destination was to begin with, and how fast we are moving towards it, we should know how long it will take to get there!

    If we subtract the effects of Doppler and aberration, we end up with a Lorentz contraction of the universe, in our direction of motion.
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    Quote Originally Posted by kojax
    The Michelson and Morley experiment you mentioned earlier is the one that lead Hendrik Lorentz to formulate Lorentz contraction, which is the theory that, not only does a person's perception of time change as they approach the speed of light, but also their perception of distance changes as well (though the change is determined by a different formula). Anyway, Lorentz contraction is also pretty essential to relativity.

    http://en.wikipedia.org/wiki/Lorentz_transformation


    Perceiving distances to be shorter would be a natural consequence of an object becoming shorter. Think of how triangulation works. You take two reference points a known horizontal distance apart, and measure the angle each of them perceives a distant object to be located at, and you can use that to calculate how far away it is. In a Lorentz contracted object, the apparent angles get screwed up because the lenses (or whatever other device you might use to measure those angles) are contorted.
    Thanks for that information. I think I did not use a wise choice of words earlier. Rather than my saying that distance is "constant," I should have described it as absolute.

    Well, I think I was only half wrong. Distance is absolute in your own frame of reference. If you accelerate changing your frame of reference, then your perception of distance changes in proportion to that acceleration. Is that correct?

    Also, is your perception of distance changing correct? That is, does distance really change, or just your perception of distance?

    Something you've said seems to be counterintuitive. You said: "Perceiving distances to be shorter would be a natural consequence of an object becoming shorter." If the "object" you are referring to is the observer, then I'd think that distances would seem to be longer rather than shorter as a result of contraction. If I shrink back to the size of that little boy I was 45 years ago, then my small apartment would seem to be the size of a cathedral.

    In any case, I'm not too familiar with relativistic distance. None of the books I've studied say much about it. I'll need to find a good book about relativity.

    Jagella
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    Quote Originally Posted by Jagella
    Quote Originally Posted by kojax
    The Michelson and Morley experiment you mentioned earlier is the one that lead Hendrik Lorentz to formulate Lorentz contraction, which is the theory that, not only does a person's perception of time change as they approach the speed of light, but also their perception of distance changes as well (though the change is determined by a different formula). Anyway, Lorentz contraction is also pretty essential to relativity.

    http://en.wikipedia.org/wiki/Lorentz_transformation


    Perceiving distances to be shorter would be a natural consequence of an object becoming shorter. Think of how triangulation works. You take two reference points a known horizontal distance apart, and measure the angle each of them perceives a distant object to be located at, and you can use that to calculate how far away it is. In a Lorentz contracted object, the apparent angles get screwed up because the lenses (or whatever other device you might use to measure those angles) are contorted.
    Thanks for that information. I think I did not use a wise choice of words earlier. Rather than my saying that distance is "constant," I should have described it as absolute.

    Well, I think I was only half wrong. Distance is absolute in your own frame of reference. If you accelerate changing your frame of reference, then your perception of distance changes in proportion to that acceleration. Is that correct?

    Yeah. That would be right. There's no "fact of the matter" about how far something is away from you. Observers in different reference frames may observe the distance to be longer or shorter than you do.

    Also, is your perception of distance changing correct? That is, does distance really change, or just your perception of distance?
    Yeah, it's just your perception. But, it's just like everything else in relativity: no one frame of reference is more accurate than any other. If they disagree, they are still both right. (Though they're never able to compare notes in a way that would enable them to become aware of that contradiction.)


    Something you've said seems to be counterintuitive. You said: "Perceiving distances to be shorter would be a natural consequence of an object becoming shorter." If the "object" you are referring to is the observer, then I'd think that distances would seem to be longer rather than shorter as a result of contraction. If I shrink back to the size of that little boy I was 45 years ago, then my small apartment would seem to be the size of a cathedral.

    In any case, I'm not too familiar with relativistic distance. None of the books I've studied say much about it. I'll need to find a good book about relativity.

    Jagella
    Oh. ... I think you're right. I get that backwards all the time.
    Some clocks are only right twice a day, but they are still right when they are right.
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    Quote Originally Posted by kojax
    Yeah, it's just your perception. But, it's just like everything else in relativity: no one frame of reference is more accurate than any other. If they disagree, they are still both right. (Though they're never able to compare notes in a way that would enable them to become aware of that contradiction.)
    If they did compare notes, then doing so would destroy relativity's stipulation of uniform motion, would it not?

    Quote Originally Posted by kojax
    Oh. ... I think you're right. I get that backwards all the time.
    Don't feel bad. It's easy for me to forget that the clock in my thought experiment is not measuring my time but my friend's time (see the thread “Time Dilation Thought Experiment.”).

    In any case, I have a length-contraction thread planned. I've come up with a thought experiment that I hope explains why a fast moving object gets longer for a person in its frame of reference.

    Jagella
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    Quote Originally Posted by Jagella
    In any case, I have a length-contraction thread planned. I've come up with a thought experiment that I hope explains why a fast moving object gets longer for a person in its frame of reference.
    But a fast moving object does not get longer for a person in its frame of reference. Nor does it get shorter for a person in its frame of reference. It stays the same length as it always was.
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    Quote Originally Posted by SpeedFreek
    Quote Originally Posted by Jagella
    In any case, I have a length-contraction thread planned. I've come up with a thought experiment that I hope explains why a fast moving object gets longer for a person in its frame of reference.
    But a fast moving object does not get longer for a person in its frame of reference. Nor does it get shorter for a person in its frame of reference. It stays the same length as it always was.
    Moreover, length is a maximum in the rest frame.
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    Quote Originally Posted by SpeedFreek
    Quote Originally Posted by Jagella
    In any case, I have a length-contraction thread planned. I've come up with a thought experiment that I hope explains why a fast moving object gets longer for a person in its frame of reference.
    But a fast moving object does not get longer for a person in its frame of reference. Nor does it get shorter for a person in its frame of reference. It stays the same length as it always was.
    Right. The length seems to change.

    Jagella
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  22. #222  
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    Quote Originally Posted by Jagella
    Quote Originally Posted by SpeedFreek
    Quote Originally Posted by Jagella
    In any case, I have a length-contraction thread planned. I've come up with a thought experiment that I hope explains why a fast moving object gets longer for a person in its frame of reference.
    But a fast moving object does not get longer for a person in its frame of reference. Nor does it get shorter for a person in its frame of reference. It stays the same length as it always was.
    Right. The length seems to change.
    Not to an observer in the frame of reference of the object concerned, it doesn't.

    However, the length of an object does contract when calculated from a different frame of reference. A different frame of reference can be a frame in motion in relation to the object, or a frame the object is in motion in relation to.
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    I think every new member should be forced to read the special relativity primer sticky when they join ( oh my , I'm starting to loose my patience just like DrR does ).

    Length , time and mass are 'variant' ( that means they change ) in special relativity. The only 'invariant' ( that means it doesn't change ) in SR is the speed of light.
    In other words, the object's length ( or passage of time, or that object's mass) may change when observed from another frame of reference according to the Lorentz transforms, BUT never when observed from the same reference frame.
    The speed of light, c , being invariant, will not change no matter what reference frame it is observed or measured from.
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    Yup, and it seems we might need to make it more clear as to why length, mass and time never change when observed from the same reference frame.
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    i sense that Jagella does not understand the meaning of the word relative.
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