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Einstein's thought experiment about the speed of light

  1. Apr 7, 2014 #1
    Please excuse this question from a lay person but if I don't ask I will never know.
    I know that the speed of light is a constant, that no matter how fast an object travels, light travels away from that object at the same speed. Hence nothing can travel at or faster than the speed of light, time dilution, etc., etc.

    What I don't understand is how Einstein, in his famous "thought experiment", could infer that the speed of light is constant and that he could "never catch up with it". How could he infer that simply from a thought experiment with no physical measurement of the speed of light available to him. Or is the thought experiment just a metaphor?

  2. jcsd
  3. Apr 7, 2014 #2


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    Could you please describe that famous "thought experiment"? It's dangerous to assume that other people read the same thing as you do, into that description. It's a sure recipe for confusion.
  4. Apr 8, 2014 #3


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    I'm not sure about Einstein's personal motivations. But from the standpoint of history, what happened is that the "what if" experiments were just exploring the logical consequences of certain assumptions. It was the agreement of the results of those logically derived consequences with experiments that convinced people that relativity was a good description of the world.
  5. Apr 8, 2014 #4
    Good point. The thought experiment I was alluding to went something like this (or at least that is how I remember it):

    Einstein imagined he was "running" alongside a speeding object traveling at the speed of light but no matter how fast he traveled he could not catch up with the object. Hence you can't travel as fast as light. I just can't imagine how one could come to such an insight simply via such a though experiment.

    I may not have the details of the thought experiment exactly right but I believe that is the gist of it in several books written for laymen.
  6. Apr 8, 2014 #5
    Maxwell's equations (mid to late 19th Century) derive the speed of light. All you need to do is understand that these Laws work regardless of where you are, and whether is is summer or winter. You understand, I assume, that any two points in Earth's orbit separated by 6 months have the velocity of the Earth (and hence us) opposite (relative to the Sun). Maxwell's equations say that regardless of summer or winter, the speed of light is c. I am no historian of Einstein's theoretical development, but I understand for a long time before he published the Special Theory, he believed that physics must be frame invariant. There are plenty of publications preceeding his discovery. He 'just' took what was being discussed and accepted it and then figured out what the logical results of those assumptions are. I doubt if the "eureka" moment was with a thought experiment with him running anywhere. He used his thought experiments to explain his ideas, not form them (afaik).
  7. Apr 8, 2014 #6
    Maybe this will help:
    Traveling with the speed of light to “freeze” the wave (Einstein’s thought experiment) is equivalent to having the temporal period of the wave to be infinite, i.e., having the time set still, time lapse = 0. One is left with a spatial period, the wavelength, which amounts to a standing wave. However, because it is a traveling wave, taking away the temporal aspect of the wave, the wavelength will be nil too, which means there would not be a wave. Therefore, the wavelength, the spatial aspect of the wave, or the concept of length, distance, should be nil. Mathematically, this amounts to zero divided by zero, which leads to unity, and preserves the propagation velocity of the wave being c. The consequence is that the metric at c is annihilated.
  8. Apr 8, 2014 #7


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    What had happened in the scientific community around that time is that the speed of light had already been physically measured, and the measurements showed that the speed of light was constant. Other scientists were trying to figure out ways that the measurements were wrong. Einstein simply tried to figure out what it would mean theoretically if the measurements were right. So he started his thought experiments from the assumption that the speed of light is invariant, based on accepting the existing measurements at face value.
  9. Apr 8, 2014 #8
    I remember having read in an excellent article by Demetrios Christodoulou once, that one must view the speed of light as playing the role of infinite speed, a speed that can never be reached.

    Indeed, if you define the speed as rapidity http://en.wikipedia.org/wiki/Rapidity, the hyperbolic angle that differentiates two frames of reference in relative motion, you immediately see that for low speeds this rapidity is made approximately equal to your everyday usual speed as you measure it with a speedometer, whereas for the speed of light it is infinite.
  10. Apr 8, 2014 #9
    Interesting. That makes sense.
  11. Apr 8, 2014 #10
    Ah! I didn't know that the speed of light was already shown to be constant. That explains things.

    I can also understand why other scientists were trying to prove the measurements were incorrect - because it intuitively makes no sense that it should be true.

    (and maybe future scientists will prove it untrue despite our multiple proofs and evidence to the contrary. It wouldn't be the first time accepted scientific facts were shown to be wrong because of an erroneous assumption. I'm not saying it is wrong, just that if nobody thinks outside the box, then what is outside the box remains invisible. Spoken as someone who has not yet even learned what is in this box).
  12. Apr 8, 2014 #11


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    I think if you read the beginning of Einstein's 1905 paper in which he introduced Special Relativity, you might get an idea of what was going through his mind and what was important to him as he tried to persuade the scientific community of his revolutionary ideas.

    No one doubted that the measured speed of light was a constant but you have to realize that any measurement of the speed of light must of necessity involve a two-way or round trip measurement in which you have a light source co-located with a timing device and a remote mirror.

    Virtually everyone at the time believed that light was an undulation of a fixed "ether" through which the surface of the earth was traveling at some unknown speed and which would vary throughout the day and throughout the seasons which should have caused the two-way measurements to vary but since they didn't, Lorentz and others concluded that rulers and clocks must vary as the surface of the earth moved through the ether in such a way as to make the measurements constant. This would mean that the light took more time to travel one way to the mirror than it took for the light to get back.

    That explanation worked but Einstein figured out that if you assumed that the light took the same amount of time to get to the mirror as it took to get back, and if you assumed that those rulers and clocks were legitimate measurements of distances and time, then this new explanation would also work but it would be simpler than an explanation that relied on an ether that was fixed in some unknown state.

    Of course, this meant that time and space were now relative to the observer and the rest is history.
  13. Apr 8, 2014 #12
    And would I be wrong to think that combining space and time was an "assumption" made to explain things as they appeared to be? In which case without that underlying assumption (or if it is wrong) all that followed would fall apart?

    Probably best to ignore my ramblings until I find out more about proof of the notion of space time other than as a way to make subsequent theories plausible. After all, I should learn more before I speak.
  14. Apr 8, 2014 #13


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    As a starting point, a theory has to be based on assumptions. Then the theory can be tested to see if its predictions also comport with reality, which in the case of Special Relativity, it does.

    I don't think you have the right viewpoint on "proof" and it's not a matter of whether theories are "plausible" in the way I think you mean. It's only a matter of whether the theory continues to be supported by more and more rigorous tests. And in the case of Special Relativity versus Lorentz's ether theories (plural, because they kept changing), it's a matter of which one is simpler. It's a lot more convenient to treat any inertial state as one in which rulers and clocks make legitimate measurements than to presume that there exists only one inertial state for which they are legitimate, especially when it is impossible to identify that inertial state.
  15. Apr 8, 2014 #14


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    The combining of space and time into a single space-time came after Einstein had developed and published Special Relativity. Einstein didn't need it for SR, and to this day it's possible to teach SR (although it is bad pedagogy) without combining space and time; all that happens is that your equations are less pretty.

    The modern concept of space-time was developed by Minkowski to provide a cleaner mathematical structure around Einstein's original development of Special Relativity.

    This cleaner mathematical structure in turn made the development of General Relativity possible, but not as an assumption - instead it allowed the use of mathematical tools which made the analysis of gravitation as curvature more tractable.
  16. Apr 8, 2014 #15
    Thank you both for your patience and time. I truly appreciate appreciate it as I try to understand. I should read up a lot more before I shoot off my mouth again.

    As for theories, I know what you mean and how they are developed and proven. I was just attempting to unsuccessfully verbalize the intangible or illusive difference between theories and the how of things. I realize that reasons may not be part of what physics is about, but something in me wants to understand the how of what makes things behave the way they do.

    I should probably stop here, but I can for instance conceive of 2 (or 5) theories that could satisfactorily explain a set of facts including subsequent predictions based on the theories. But in my mind, though they may explain one or more ways these measured facts "could" occur, they may not be the way they really did. Because of that, subsequent new facts may force a modification or even a complete throwing out of the accepted theories. That would be the expected path of the progress of physics but it leaves a sour taste in my mouth because the early efforts seem to be directed towards providing possibilities rather than explanations. And the simpler more elegant one may not necessarily be the real one.

    I am surely expressing myself poorly and may gropping for something more philosophical than physics, but my layman's interest in physics stems from a desire to understand the how of things in the observable universe while modern physics provides me with theories - often requiring suspension of common sense - of possible how's to satisfy obscure derived mathematical formulas rather than explain the reasons why things behave the way they do.

    I was going to delete all the above and stop irritating you all but since I wrote it I'll leave it. You may just ignore what I wrote. After all, what do I know?
  17. Apr 8, 2014 #16


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    The purpose of this forum is to help people learn relativity, not to promote new alternatives. I think if you learn Special Relativity, you will lose interest in any other explanation you might now think is better.
  18. Apr 8, 2014 #17


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    It's hard to tell what you mean... Do you mean for example, that the theory of natural selection provides possibilities for explaining how all animals have evolved. But we have not yet comprehensively catalogued how every single animal evolved at every stage?
  19. Apr 8, 2014 #18


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    Einstein made two assumptions, usually called the two postulates: 1) the laws of physics are the same in all inertial frames 2) the speed of light in vacuum is the same in all inertial frames. These two assumptions lead to all of special relativity. However, there are alternative sets of assumptions that can get you to the same physics, so I don't think that I would say that "all that followed would fall apart".

    The combination of space and time is a result of the postulates, not it's own assumption.
  20. Apr 8, 2014 #19


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    I don't think that will ever happen. Consider Newtonian physics. New facts have shown that Newtonian physics is wrong, it makes predictions that are demonstrably wrong. So, has Newtonian physics been completely thrown out? No! Go to any introductory physics course and you will see that Newtonian physics is alive and well.

    How can that be when we know from experiment that it is wrong? The reason is that new data can never invalidate a theory in the regime where previous experiments have demonstrated it's validity. All new data can do is place limits on the domain of validity for a theory. Hence, Newtonian mechanics is and always will be valid in the classical domain. Similarly, relativity is and always will be valid in the relativistic domain. Future students will still need to learn Einstein, just as current students still need to learn Newton.
  21. Apr 8, 2014 #20
    No, I just mean that the natural selection does not require the suspension of common sense to believe in it.

    But then, common sense is not always right either.
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