Is it really “time” that is dilating?

Question

Consider the following variation of the twin paradox:

A clock or a biological system ultimately is an electromagnetic system. First, let’s devise a new time measuring device. Imagine a tank of water with a spout on the bottom. The spout has a control mechanism that will release a single drop of water into a vacuum tube. At the bottom of the tube is a sensor that detects when the drop hits it. A wire connecting the sensor at the bottom with the spout control at the top then signals the spout to drop the next drop of water. The system is calibrated such that each drop measures precisely one second of time. Let’s refer to this time measuring device as a gravity clock.

Our gravity clock almost entirely eliminates EM from the timing mechanism (at the surface of the Earth the E&M component along the signal wire makes up 1.6e-8s (4.9/c) of each second).

Now empty the Universe save for 2 instances of Earth. On each of these Earths we place one normal clock (an EM clock) and one gravity clock. Both Earths are in the same inertial frame and all 4 clocks are synchronized.

We now attach rockets to one of the Earth’s and accelerate it and its clocks to near the speed of light.

It seems to me that the “time” dilation is caused by the longer round trip time of photons (or virtual photons) moving between charges. Since, the gravity clock (very nearly) eliminates electromagnetism from its timing mechanism, it will largely be unaffected by the shifting frame.

If the wandering Earth is returned to the stationary Earth (again at near the speed of light), then the two clocks on the stationary Earth will be still be in sync, and I suspect the gravity clock on the wandering Earth will largely be in sync with the stationary clocks (aside from the effect of the signal along wire), while the wandering electromagnetic clock will vary fully as predicted by the Lorentz transformation.

First, is there any reason to believe that this would not be the case; that the gravity clock would actually be affected in the same way as the EM clock?

If not, is it really accurate to describe this situation as “time” dilating (as opposed to say the animation rate of EM systems dilating)?

EDIT: Apologies for not noticing it earlier, but this question: (Time dilation only on electromagnetic force?) is essentially the same as mine. Although, I don't think either of the answers indicate whether any experiment has shown that a gravity clock is affected by "time" dilation.

Answer 1

In introductory courses on special relativity it's very common to use setups like light bouncing between two rockets or light travelling along a moving rocket. This works well in showing that time dilation and length contraction must happen, but it does tend to give the impression that it's all something to do with the propagation of light and this is most definitely not the case.

Many (most?) physical theories are based upon a fundamental symmetry of nature , and understanding this symmetry is the only way to really appreciate how the theory works. However this is a somewhat abstract approach and is usually not used in introductory courses. Whether this is a good thing or not is debatable, but it does lead to misconceptions like the one your question is based on.

In the case of SR the theory is based on Lorentz covariance or the invariance of the proper time. Suppose we have two spacetime points $(t_1, x_1, y_1, z_1)$ and $(t_2, x_2, y_2, z_2)$, and we set $\Delta t = t_2 - t_1$, $\Delta x = x_2 - x_1$, and so on. Then we define the proper time, $\tau$, by:

$$ c^2\Delta \tau^2 = c^2\Delta t^2 - \Delta x^2 - \Delta y^2 - \Delta z^2 $$

Special relativity is based on the symmetry that all observers in all inertial frames will calculate the same value for $\Delta \tau$. All the weird effects like time dilation and length contraction derive from this principle. I've demonstrated how to do this in my answer to How do I derive the Lorentz contraction from the invariant interval? so I won't go through it again here. The point is that none of the working involves light beams or any other form of electromagnetic radiation.

So your question is really based upon a misconception, and as such I can't answer it. The behaviour of any system such as your clock can be calculated just using Lorentz covariance, though since your example involves acceleration it gets a little more complicated. Acceleration can be described using special relativity - you'll sometimes hear claims that acceleration requires general relativity to explain it but this is not so. As it happens I've just done a related calculation in How long would it take me to travel to a distant star? It wouldn't be hard to extend this calculation to explain what happens in the twin paradox.

Answer 2

Preface

(styled as counterpoint to the answer given here earlier by John Rennie):

The pursuit of physics, being a human endeavor, is not immune to misconceptions, pitfalls, or disagreement about philosophic or epistemologic concepts and directions. Some of them are brought to prominence in the study and even the application of the theory of relativity.

Most glaring is perhaps the idea that anything of geometric of physical relevance might be defined or explained in terms of coordinates. But there are no coordinates "in nature"; therefore proper statements "about nature" cannot refer to coordinates either. On the other hand, the use of coordinates (or at least: good coordinates) and the corresponding use of arithmetic are of course effective and common techniques for solving physics problems. Einstein's struggles with this problematic are often discussed in relation to Einstein's "hole argument". Along the way Einstein expressed the foundational principle that

All our well-substantiated space-time propositions amount to the determination of space-time coincidences [such as] encounters between two or more recognizable material points.

(Arguably, the admissibility of "determination of space-time coincidences" of participants and by participants also implies admissibility of their determination of their non-coincidence.)

This principle is of course put into practice by Einstein's through-experimental definitions; most famously perhaps his (coordinate-free) definition of simultaneity. Of course, this definition explicitly deals with participants observing each other and judging coincidence (or non-coincidence) of observations. (This is even already apparent in Einstein's definition of synchronism (of 1905); especially regarding the requirement of transitivity.)

A related contentious issue is how far the contents and results of (S)RT would be attributable "to nature" (as its "universal properties") at all; or instead to ("conventional", "universally comprehensible") definitions introduced and followed by physicists. In Einstein's writings (directed to the broader public, but therefore surely no less scrupulous and decisive) we find the demand

We thus require a definition of simultaneity such that this definition supplies us with the method by means of which, in the present case, he can decide by experiment whether or not both the lightning strokes occurred simultaneously. As long as this requirement is not satisfied, I allow myself to be deceived as a physicist (and of course the same applies if I am not a physicist), when I imagine that I am able to attach a meaning to the statement of simultaneity. (I would ask the reader not to proceed farther until he is fully convinced on this point.)

Of course, what's required of one particular notion ("simultaneity") is to be demanded of all notions or quantities to be measured, such as "duration" (or more precisely: equailty of durations, or ratios of durations), "mutual rest" (a.k.a. "joint membership of participants in the same inertial frame") etc.; necessarily with the exception of the foundational ability to judge coincidence. Of course the corresponding required "methods" (or in the terminology of the 1905 article: "treatments") are generally stated as thought-experimental definitions.

In summary, relating to your question: It is certainly correct and commendable to approach and study (S)RT by means of thought experiments; you thereby stand in a proud tradition of physicists.

Concerning your specific proposed thought experiment:

[...] The system is calibrated such that each drop measures precisely one second of time.

Of course, this unit "second" has a particular definition referring to some very particular systems of electro-magnetic charges: "caesium 133 atom"s ...

Answer 3

Time dilation is not a consequence of motion impairing the mechanism of clocks. Time dimension is a property of the geometry of spacetime, and is symmetrical between any pair of inertial reference frames. It means that time interval between two events in a frame in which they are collocated is always less than the time interval between the same two events in a frame in which they occur in different places. Note that it is the actual interval that is different—it might be five seconds in one frame and twenty in another, and accurate clocks in either frame will indicate the interval correctly by ticking at a second per second.

In the frame of a high-speed muon, you might be time dilated by a factor of sixty, say, so that the interval between every second ticked off by your watch is a minute in the muon's frame. The half-hour TV programme you watch is thirty hours long in the muon frame. The interval between your birthdays is sixty years. A four-minute mile is a 240-minute mile. These effects are all due to the fact that the time axis in the frame of the Earth is tilted relative to the time axis in the frame of the muon—time dilation has nothing to do with the factors you suggested in your question.

Furthermore, your suggestion, if it were true, would lead to logical contradictions. Suppose on Earth we construct an apparatus that includes a bomb that would explode if two clocks became out of synch, one of the clocks being a light-clock and the other being the type of gravity clock that you imagine to be immune to relativistic effects. On Earth, where the clocks remain in synch, there would be no explosion. In the frame of a passing muon, the clocks, according to your suggestion, would become out of synch and the bomb would explode. You cannot have it both ways, so your suggestion must be false.