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We've seen by experiment that the speed of light c appears to be constant for each observer (leading to all well-known consequences of relativity).

I'm wondering if this appearance of constancy of c might be due to the observer's way of measuring it: All observers are bound to compare c to something else which itself is also based on c. A clock based on a photon bouncing between two mirrors (and taking the time it takes to bounce) for instance uses that speed of the photon to measure everything. A clock like a watch based on springs uses tension forces buried in the spring material (electromagnetic forces are based on c). Quartz crystal oszillators, sand clocks (hourglasses), water clocks — all facilitate some mechanism like friction or piezoelectricity which fundamentally are electromagnetism.

Nevertheless it is said that the time appears to be going slower, not just all clocks we can build.

My questions now are:

Is there a reasoning (which I just didn't find in my research) why the time as a whole is supposed to be influenced by relativity, not just all events based on the forces based on c? Maybe there even is a word or a term to google for in order to find more about this?

I understand that physicists managed to unite three of the four basic forces, wrapping up electromagnetism with the strong and the weak force. I guess then that these additional two forces also are based on c. Is there any such connection of c to the remaining force, the gravitation?

I could understand that if all existing forces are hinged on c then there is no real difference between saying "all clocks we can build are going slower" and "the time itself is going slower".

Alfe
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    "it is said that the time appears to be going slower, not just all clocks we can build." As Feynman said (and I think he was quoting someone) "a complete conspiracy is a law of nature." To draw any meaningful distinction between time itself going slower, and clocks going slower, there would have to be some process in nature that would let you make a clock which dilates differently to everything else. So far, despite much searching, nothing of that sort has been found. All of the known force laws predict the exact same time dilation as electricity and magnetism. – Michael Oct 21 '13 at 13:38
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    You can build "clocks" around radioactive decay. http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/muon.html I suppose that doesn't change the question though, since nuclear forces can be unified with electromagnetic. – Nicolas Oct 21 '13 at 13:43
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    So I take it that there also have aspects been found which indicate that also the gravitation's speed is depending on c? Feynman's quote is a nice way to put the thought. Are there mathematical or otherwise computational ways of handling things which use this different view? Or is the difference too academic to be pragmatic? – Alfe Oct 21 '13 at 13:45
  • @Nicolas, yes, we receive radiation on the surface of the earth which is composed of particles which should not have survived through their voyage due to them being very short-lived (when stationary). The explanation for this is that they experience time dilation, so I guess that counts as a "clock" based on decaying particles (I'm not sure whether strong or weak force is their incentive, though). Stays the question about gravitation; do we have clocks based solely on that? (I. e. without using the other forces as well as pendulum clocks do.) – Alfe Oct 21 '13 at 13:53
  • @Alfe well obviously planet orbits look like such clocks, but I'm waaaay too uneasy with general relativity to post anything definitive. – Nicolas Oct 21 '13 at 14:02
  • Right, Nicolas. Stupid me. I could have thought of them myself. – Alfe Oct 21 '13 at 14:09
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    @Nicolas: Only the weak force has been unified with electromagnetism. If you choose a nucleus that alpha decays, then your radioactive clock is purely based on the strong nuclear force. –  Oct 21 '13 at 20:57
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    What a nice question. –  Oct 21 '13 at 21:13
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    "Or is the difference too academic to be pragmatic?" So far it's a philosophical difference, and physicists have not yet found a way to tell them apart. Physics is grounded on what we can sense. Also, you question about grav waves and $c$: we have not yet detected these waves directly, but calculations assuming they run at $c$ give excellent agreement with the witnessed "spin down" of the Hulse-Taylor Binary Pulsar. So there's a great deal of tested theory that indirectly rests on the two concepts being the same, not only clock rates. – Selene Routley Oct 22 '13 at 01:37

2 Answers2

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There is a general class of experiments called clock comparison experiments. Two of the earliest with high precision were Hughes 1960 and Drever 1961; they're collectively known as "the Hughes-Drever experiment," described here. The idea is to take two clocks that operate on different physical principles, leave them side by side, and see if they measure time differently. Hughes-Drever was not actually exactly of this form, but it can be indirectly interpreted as being of this form. Mattingly 2005 has a survey of such experiments in section 5.2. If any such experiment gave a non-null result, it would tell us that there was a problem with our traditional interpretation of relativity, exactly as suggested in the question.

References

Drever, R. W. P. (1961). "A search for anisotropy of inertial mass using a free precession technique". Philosophical Magazine 6 (65): 683–687.

Hughes, V. W.; Robinson, H. G.; Beltran-Lopez, V. (1960). "Upper Limit for the Anisotropy of Inertial Mass from Nuclear Resonance Experiments". Physical Review Letters 4 (7): 342–344.

Mattingly, 2005 "Modern Tests of Lorentz Invariance", Living Rev. Relativity 8, (2005), 5, http://relativity.livingreviews.org/Articles/lrr-2005-5/fulltext.html

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I'm wondering if this appearance of constancy of c might be due to the observer's way of measuring it

Yes, of course it is.

Now, the two-way speed of light is measured with one clock but the one-way speed of light measurement requires two spatially separated clocks that must by synchronized according to some convention.

For Einstein synchronization, the spatially separated clocks are synchronized with light pulses and, thus, the measured one-way speed of light is guaranteed to be c.

Your question is quite insightful and you get to the heart of the fact that, in SR, time is a coordinate and thus, in some sense, arbitrary.

On the other hand, there is, in SR, an invariant proper time that is not arbitrary.

Alfred Centauri
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