Three Questions On Special Relativity

Question

Twins Paradox

Using the simplified version of the paradox, where acceleration to near light speed and the turning of the spaceship are almost instantaneous, the paradox is completely symmetrical - in that the observer on earth would see the clock on the spaceship running slow and the observer on the spaceship would see the clock on earth running slow - by the same factor.

That implies both of the following:

• The observer on the spaceship would age slower than the observer on earth
• The observer on earth would age slower than the observer on the spaceship

So at the heart of the paradox, there is a contradiction, as given above. Contradictions always mean that an axiom is in error, as in proof by contradiction - start by assuming a false axiom is true and then show it leads to a contradiction to obtain a proof.

Surely, in this case, the axiom in error is: 'the speed of light is constant for all observers regardless of motion'?

No Absolute Frame Of Reference

• According to astronomers, space is expanding
• Nothing cannot expand, hence space must be something, IE, space must be aether
• Hence there must be an absolute frame of reference, IE the aether.

On the Mickelson-Morely experiment, they assumed that the lack of aether drag meant that there was no aether. Surely, the correct deduction was that the lack of aether drag meant that aether existed, but caused no drag?

Eternalism

SR implies eternalism, IE: the past and future are as real as the present (eg: the Andromeda Paradox or Einstein's train thought experiment both imply this).

But imagine the earth when the dinosaurs were wandering around on it. The future being real at that time implies that homo sapiens were real at that time also. But 65 million years of genetic mutations must take place before humans can be real.

So I cannot see how 'future real' could be possible?

Answer 1

On these three questions

Twins Paradox

Surely, in this case, the axiom in error is: 'the speed of light is constant for all observers regardless of motion'?

However the assumption in error is that "the acceleration to near light speed and the turning of the spaceship are almost instantaneous" in reality, because this acceleration can't be instantaneous and acts on only one of the twins, it introduces an asymmetry that leads to the resolution of the twin paradox.

No Absolute Frame Of Reference

As the aether couldn't be detected and has no influence on matter, it fell out of favour after 1905. The Michelson-Morley experiment showed that the aether didn't exist or that it was moving with the earth. The second possibility has been considered by physicists but rejected by most.

There are still some modern aether theories, but these bear little resemblance to the ones of the 19th Century. See Problems of partial aether dragging and aether theories

Eternalism

This part of the question seems to be getting too philosophical for Physics Stack Exchange and it's recommended that you try a Philosophy forum.

Answer 2

Twin Paradox,

It does appear nonsensical when one encounters the idea for the first time that time dilation is symmetrical. However, the mystery clears up when you understand it properly to be the result of the relativity of simultaneity. Let me try an analogy to explain it. Suppose you are on one train passing another slowly at a metre per second. Every ten meters along the train you are passing is a person holding a clock, and each of the clocks is set to be one second ahead of the clock before it. You pass the first clock at t=0. This is what you see unfold...

As you pass the second clock it says t=11s while your clock says t=10s

As you pass the third clock it says t=22s while your clock says t=20s

As you pass the fourth clock it says t=33s while your clock says t=30s

And so on.

So it appears to you and to the people on the other train that your clock is running slow.

Now, imagine that behind you on your train are people at 10m intervals also holding clocks, each being set 1s ahead of yours. Imagine what the person at the front of the other train sees as she passes all the clocks in your train.

As she passes the second clock it says t=11s while her clock says t=10s

As she passes the third clock it says t=22s while her clock says t=20s

As she passes the fourth clock it says t=33s while her clock says t=30s

And so on

It seems to her and to the people on your train that her clock is running slow.

And so you, see that both you and the person on the other train can believe your respective clocks are running slow, when in fact it is simply that the other clocks with which they are being compared are out of synch.

It is exactly the same in SR. The key point to remember in SR is that you never compare one moving clock with one stationary one- you cannot, because they are never together more than an instant. Instead you compare a moving clock to first one and then another clock set a distance apart in the stationary frame, and it is the fact that those clocks have a sloping plane of simultaneity in the other frame that causes the time dilation effect.

Absolute Frames

If you wish you can call space an absolute frame. The point you have failed to understand is not that you cannot define an absolute frame, but that calling it absolute makes it no different to any other apart from in name. The laws of relativity still apply.

Eternalism

It is naive to believe that SR implies some kind of eternalism. SR simply means that different reference frames use a different value of t to label the present.