i am just starting to learn about relativity. One of the first big concepts the book teaches is time dilation and one of the first examples is the one many of you probably have heard of the two spacecraft moving very fast and one emitting and receiving the photon. ( it is also the example used on wiki). Anyway, it just shows that the photon takes longer to come back from the perspective of the other spacecraft as it has a bigger distance to accomplish and c is constant. The book then proceeds to directly apply the lorentz coefficient to other situations where light is not even mentioned. My question is thus: what if we were in total darkness and no photon was emitted? Would the length of the spacecraft still differ from observer to observer?
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3If a tree falls in a forest and no one is around to hear it, does it make a sound? – Dmitry Brant Oct 31 '16 at 03:31
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7I think the downvotes are unkind. SR is frequently taught to undergrads using light clocks and it's a common confusion that the propagation of light somehow causes time dilation. Anthony is far from the first student to be misled in this way. – John Rennie Oct 31 '16 at 07:06
4 Answers
The principles of special and general relativity do not depend on exactly how we test them, but in physics they are worth very little until we do test them, no matter how we do it it.
As an example, the chair in your room is also there at night. If you fall over it in the dark, you have tested that it is still there, even though you can't see it.
We have tested general relativity in the darkness of space, and it works fine. Photons are the easiest things to use, as they are easily made at any frequency and energy level, They are easily detected and timed, and so almost every test uses them, offhand I can't think of a test, even testing for gravitional waves, that does not need electromagnetic methods of testing.
Now that we have tested them, we know the lengths are related in their sizes in the way Einstein predicted they would be.
Time dilation is often taught to undergraduates using light clocks like the one you describe. It's taught this way because it's easy for beginners to understand, but the problem is that it can give beginners the idea that time dilation is related to the way light propagates, and this is not the case. Time dilation is a consequence of the geometry of spacetime. If you're interested to pursue this further have a look at What is time dilation really?
The point is that since time dilation is not caused by the way light travels it is unaffected by whether light is present or not. For example we see the lifetime of atmospheric muons increased by time dilation even though beams of light play no role in this process.
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"we see the lifetime of atmospheric muons increased" You don't see anything like that. What you see is the lifetime of some muons drastically decreased as they bump into an obstacle and their speed instantaneously changes from almost c to zero: http://www.physics.rutgers.edu/ugrad/389/muon/muon-rutgers.pdf "In order to measure the decay constant for a muon at rest (or the corresponding mean-life) one must stop and detect a muon, wait for and detect its decay products, and measure the time interval between capture and decay." – Pentcho Valev Oct 31 '16 at 07:40
Yes. Relativity and what would happen to light does not depend on whether or not there actually is light. If you drop a rock, gravity makes it fall, but there is still gravity if you don't drop a rock.
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It follows from Einstein's 1905 (false) constant-speed-of-light postulate that a clock runs slower than a clock in a different reference frame only insofar as the measurements are done in the second clock's system. The presence or absence of light is irrelevant but still the effect is illusory in the sense that, if the measurements are done in the first clock's system, it is the second clock that proves slower. Such a symmetrical illusion, a valid consequence of the light postulate, would have been fatal for Einstein's relativity (the theory is obviously "not even wrong") if Einstein had not abused logic, that is, if he had not derived from the light postulate something that does not follow from it. In 1905 Einstein defined one of the clocks as moving, the other as stationary, and informed the world that the moving clock is slow while the stationary one is FAST:
http://www.fourmilab.ch/etexts/einstein/specrel/www/ ON THE ECTRODYNAMICS OF MOVING BODIES, A. Einstein, 1905: "From this there ensues the following peculiar consequence. If at the points A and B of K there are stationary clocks which, viewed in the stationary system, are synchronous; and if the clock at A is moved with the velocity v along the line AB to B, then on its arrival at B the two clocks no longer synchronize, but the clock moved from A to B lags behind the other which has remained at B by tv^2/2c^2 (up to magnitudes of fourth and higher order), t being the time occupied in the journey from A to B."
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