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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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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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