Do you ever ask yourself, what is the cause of . . . ? I think you cannot expect to make significant advances on what you are familiar with unless you can answer such questions. However, what I consider to be one of the more serious problems of modern physics is the belief that if you have an equation that accounts for observation, then the problem is solved. For only too many, physics IS mathematics, and everything about us is determined by mathematics. That is not a new thought; the Pythagoreans and devotees of Plato held this belief. That is why there were five elements (earth, air, fire, water, ether): there are five and only five “Platonic solids” in solid geometry. We all know how well that turned out. Now the mathematics are more complicated, but we get the same outcome: belief.
What has inspired this are my thoughts on Special Relativity. The question is, physically, what is the primary cause of what is happening, and what are the consequences? What we see mathematically is that to make correct calculations when motion approaches the velocity of light, we must alter the value of certain variables by multiplying or dividing by what is called the Lorentz contraction term. Thus if a rod is moving at a speed v approaching the speed of light c and is aligned in the direction of motion, then lengths in this direction will appear to be shorter by a factor of √(1 – v2/c2). The question then is, what is going on?
It is easy to derive this in terms of length contraction if we believe the speed of light is constant. If it is, following Feynman in “Six Not-so easy Pieces” then we can build a simple apparatus with two equal arms at right angles to each other. If we put mirrors on the end, and send light signals each way, and if the result must not be able to be used to measure the velocity of the instrument if it is moving without acceleration, then with a bit of algebra you find this only makes sense if the length in the direction of travel has contracted by the factor √(1 – v2/c2). That time must dilate by a factor of 1/√(1 – v2/c2) arises because if it did not, again you could work out the absolute velocity of your apparatus. The length contraction arises because light going there and back at right angles to the direction of motion has to travel along the hypotenuse of a right-angled triangle, which is perforce longer than the two arms. However, as Feynman notes, you can also get all of special relativity if you assume the mass increases by the “rest mass” being multiplied by 1/√(1 – v2/c2).
The length contraction is derivable, nevertheless it raises another interesting question: how does the length “know” to contract? The length of the space ship is possibly understandable, but the problem is it is also the length in whatever direction you are travelling. Alternatively, we could ask why does the time dilate? While the velocity of light must be constant, that does not explain why, because it does not relate the effect to anything external. As an example, in my cat paradox, if you are in a space ship raveling at almost light speed towards Epsilon Eridani, and if you fix the frame of reference as your ship, then it appears Epsilon Eridani is hurtling towards you, and you are stationary. Now, if you put v into the equations, it is Epsilon Eridani that suffers time dilation. Of course you can get around this, but my argument is every time you try, you do not use the space ship’s frame of reference.
Elsewhere, Patrice Ayme has argued that given time dilation, you also get a corresponding mass increase for a physical reason rather than a mathematical one (https://patriceayme.wordpress.com/2016/03/25/relativistic-mass-from-time-dilation/ ). If I have this right, the argument is that if time dilates, then collision of the object with “force carriers” is much less frequent and hence inertial mass is, or appears, higher. The logic of mass increase, however, also implies time dilation by a reverse logic.
So what is fundamental? The constancy of the speed of light? Or does that arise from the length/time dilation? Which is the chicken and which is the egg? One interesting fact is that you have to choose one to be fundamental, and the rest follows. You could start with the mass augmentation, and everything else follows from the usual relationships. The constancy of the speed of light is an attractive place to choose for its being fundamental because that arises essentially from Maxwell’s electromagnetic theory, namely c = 1/√(εμ), where ε and μ are the permittivity and permeability of space. If you choose that, then the equations of special relativity follow from Feynman’s argument about length contraction.
Furthermore, there is fairly clear evidence that the time dilation effect is real. Muons are generated by cosmic ray events in the upper atmosphere and they travel at relativistic velocities. Muons have a very short lifetime and if they were constrained to that lifetime without time dilation they could only travel so far before they decayed, but we know from observation that they can travel so much further. They can also travel so much further in particle accelerators, and this is only explicable in terms of their “clocks” that govern their decay rate are going slow, in accordance with relativity. Of course, their clocks might go slow because of mass augmentation.
So, what is the issue? For me, if length and time contraction are fundamental, in the case of my previous posts on a space ship going to Epsilon Eridani, all the space between the ship and Epsilon Eridani has to “know” to contract, otherwise a light beam from the ship to a mirror somewhere near Epsilon Eridani travelling at the same velocity as the ship would be a means of determining the ship’s velocity, which is allegedly forbidden. (One can always find the velocity by reflecting light from something fixed about Epsilon Eridani; the reason for having the mirror travelling at the same velocity is so there is nothing external to the frame of reference.) On the other hand, if the mass enhancement is the real cause, then the effect is a consequence of the energy poured into the entity during acceleration. Thus in one case, the effect is due to space “knowing what is coming”, the effect is non-local and only applies to the travelling object. By that, I mean if the fast moving ship overtakes a snail, the space on the path somehow distinguishes between them. (Mathematically, the distinguishing is trivial, but physically?) Why does the space light years away respond differently and correctly to two objects at the same time? If it is mass that is enhanced, the effect is due to the entity “recording what has been done to it” and the effect is local to it. By that I mean its clock will slow, and the distance will appear to contract. I know what I prefer, and as usual with me, it is not the same as what everyone else seems to think.