There was a rather interesting announcement recently: three Danes calculated that the centre of the earth is 2.5 years younger than the crust ( U I Uggerhøj et al. The young centre of the Earth, European Journal of Physics (2016). DOI: 10.1088/0143-0807/37/3/035602 ). The concept is that from general relativity, the gravitational field of earth warps the fabric of space-time, thus slowing down time. This asserts that space-time is something more than a calculating aid and it brings up a certain logic problem. First, what is time and how do we measure it? The usual answer to the question or measurement is that we use a clock, and a clock is anything that has a change over a predictable period of time, as determined by some reference clock. One entity that can be used as a clock is radioactive decay and according to general relativity, that clock at the core would be 2.5 years younger than a clock on the surface; another is the orbit of the Earth around the star, and here the core has carried out precisely the same number of orbits as the crust. Where this becomes relevant is that according to relativity all clocks must behave the same way towards velocity, otherwise you could take your rocket ship and by comparing two different types of clocks you could measure your absolute velocity. So, does that mean gravitational time dilation is conceptually different from velocity time dilation? I believe this matters because it brings into question exactly what is space-time?
The above does not mean that time dilation does not occur. It is unambiguous. Thus we know that the muon travelling at relativistic velocities has its lifetime extended relative to a stationary one. If we assume that the process of decay is unaffected by the velocity, then the passage of time has to have slowed down. But that raises the question, is the assumption valid? An analogy might be, suppose I have a clock that is powered by a battery, and as the voltage drops, the clock slows. I would argue this is because the lower voltage is inadequate to keep the mechanism going at its previous rate, and not that time itself has slowed down.
Now, consider the mechanism of muon decay. If apparent mass increases according to velocity, why should not the rate of decay of a muon slow down, after all, it has accumulated more mass/energy so it is not the same entity? Is the accretion of mass equivalent to the change of gravitational potential?
Perhaps what relativity tells us is the rate at which clocks move indicates their altering the scale of the passage of time, rather than time itself slowing down. By that, I mean that when a clock hand completes one period, we say an hour has passed, but at relativistic speeds it might say that γ hours have passed per clock period, where γ = 1/√(1 – v2/c2). In terms of gravitational fields, it is not that time slows down, but rather clocks do, together with the rate of physical processes affected by the gravitational field.
That suggests we take our concept over to inertial motion. If a body travels near the velocity of light, then our equations tell us that time appears to dilate, but has time really slowed, or is it the process that leads to the decay that has slowed? Does it matter? In my opinion, yes, because it is through understanding that we are more likely to make progress into new areas.
The reason it is asserted that it is time itself that slows down comes from the principle of relativity, first (as far as I can tell) loosely stated by Galileo, used as the basis of his first law by Newton, and perhaps more clearly stated by Poincaré: the laws of physical phenomena must be the same for a fixed observer as for an observer who has uniform translational motion relative to him, so that we have not, nor can we possibly have, any means of discerning whether or not we are carried along in such motion. When added to the requirement from Maxwell that the velocity of light is a constant, we end up with Einstein’s relativity.
The question is, is the principle correct? It has to be in Galilean relativity, as it is the basis of Newtonian dynamics. If velocities are added vectorially, there is no option. But does it translate over into Einstein’s dynamics?
My argument is that it does not. There is an external fixed background, and that is the cosmic microwave background. The microwave energy comes almost uniformly from all directions, and through the Doppler shift one can detect an absolute velocity relative to it. (The accuracy of such determinations at present is not exactly high, but that is beside the point.) Very specifically, at 1977 our solar system was travelling with respect to this black body radiation at 390 +60 km/s in the direction 11.0+ 0.6 h right ascension and 6o +10 o declination. (Smoot et al., 1977, Phys Rev Lett. 39, 898 – 901). So we DO have the means of discerning whether or not we are carried along with such motion.
If we can measure an absolute velocity, it follows there is an absolute time, and as I have noted before, we can always measure when we are by determining the age of the Universe. Therefore I am reasonably confident in saying that the core of the Earth has aged at precisely the same rate as the crust once the Earth formed, and since there has not been complete mixing, it is more likely the core is older, as it on average would have accreted first. One the other hand, isotope decay there should have been held back by about two and a half years.