Twin Paradox

[Xamonas Chegwé]

I was trying to think of a way of doing away with the acceleration, as it just complicates the matter.

Of course it does! But, just because it's complicated, doesn't mean it's wrong! And it certainly doesn't mean that it should be disregarded!

If the twins were atomic stopwatches, and one was passing the stationary one at a high speed, when they were both set to start, then the moving one goes a million miles at high speed, and meets an identical stopwatch moving at the same speed in the opposite direction. At the instant that they pass, the elapsed time is synchronised to the returning stopwatch, using radio.
So now, the second stopwatch returns to the stationary one, and the elapsed time is compared.

OK. A is stationary. B is moving away from A at constant velocity. C is moving towards A at constant velocity and passes B at some point.

All three are in relative motion and no two are accelerating with respect to each other. This is NOT a rephrasing of the twins paradox precisely because it does not involve travel to and from a distant point and the inevitable acceleration that that must entail (in order to change direction).

So what you have done, is removed any acceleration from the experiment.

Precisely. You've just ignored the bit you don't get and hoped it went away! And as a result, you are no longer describing the same experiment, or any analogue of it!

Which stopwatch would show the greater elapsed time?

Irrelevant, for the reasons given in my last comment.

The moving stopwatch should show the time of the outward trip, plus the time of the return trip, which should be identical, and the total should be equal to the elapsed time of a two million mile trip at high speed, with no acceleration involved.
Would it be any different, to the "stationary" stopwatch time?

It sounds complicated, but it would be quite easy to set up, once we are doing regular flights to Mars.

...and quite pointless in terms of investigating the twins paradox!

So long as you get two flights that cross, you could easily do it.

Removing acceleration from GR makes about as much sense as removing cheese from cheese on toast! ie. none!

[Xamonas Chegwé]

You might find this wiki article useful in terms of understanding what is meant by inertial and non-inertial frames of reference. Especially the section I've linked to.

https://en.wikipedia.org/wiki/Philosoph ... ationalism

[Xamonas Chegwé]

It can be held that any object, even one that appears to be accelerating, can be considered stationary. However, the curvature of spacetime is such that an accelerating object will experience force - this force could be considered to be that of its own acceleration, the gravitational force of the universe accelerating relative to it, or the result of not following the local geodesic - all three are equivalent and indistinguishable (by GR).

[mistermack]

If we replace the human twins by 2 identical sub-atomic particles with a known half-life before decaying, the experiment can actually be done. If one sample is stationary relative to an observer who times the decays, and another sample is accelerated to near light speed in a cyclotron, the stationary observer observes a lengthened decay time of the moving particle by exactly the amount predicted by the Lorenz formula.

When a particle is accelerated, it experiences a slowing of time, in the same way as when it is in a strong gravitational field.
When it's in a cyclotron, it's accelerated to a high speed, and it also has a strong constant acceleration towards the centre of rotation, as in a centrifuge.
So you would expect the one in the cyclotron to decay slower.

[JimC]

If we replace the human twins by 2 identical sub-atomic particles with a known half-life before decaying, the experiment can actually be done. If one sample is stationary relative to an observer who times the decays, and another sample is accelerated to near light speed in a cyclotron, the stationary observer observes a lengthened decay time of the moving particle by exactly the amount predicted by the Lorenz formula.

When a particle is accelerated, it experiences a slowing of time, in the same way as when it is in a strong gravitational field.
When it's in a cyclotron, it's accelerated to a high speed, and it also has a strong constant acceleration towards the centre of rotation, as in a centrifuge.
So you would expect the one in the cyclotron to decay slower.

And in any situation where the twins start off stationary with respect to each other, and later one of them is travelling at an appreciable fraction of the speed of light, acceleration has also be involved. One of the twins, the one in the spacecraft, will experience a force (indistinguishable from a gravitational field), the one left behind will not.

[Xamonas Chegwé]

If we replace the human twins by 2 identical sub-atomic particles with a known half-life before decaying, the experiment can actually be done. If one sample is stationary relative to an observer who times the decays, and another sample is accelerated to near light speed in a cyclotron, the stationary observer observes a lengthened decay time of the moving particle by exactly the amount predicted by the Lorenz formula.

When a particle is accelerated, it experiences a slowing of time, in the same way as when it is in a strong gravitational field.
When it's in a cyclotron, it's accelerated to a high speed, and it also has a strong constant acceleration towards the centre of rotation, as in a centrifuge.
So you would expect the one in the cyclotron to decay slower.

And in any situation where the twins start off stationary with respect to each other, and later one of them is travelling at an appreciable fraction of the speed of light, acceleration has also be involved. One of the twins, the one in the spacecraft, will experience a force (indistinguishable from a gravitational field), the one left behind will not.

Further to this, you CAN argue that either of the twins is stationary. But, in order for the travelling twin to be thus, the entire universe must be accelerating in the opposite direction. This causes a distortion of spacetime in his vicinity and means that he is not following the geodesic (path of least resistance) and so he will still experience an identical force to that which he would experience from acceleration. Similarly, when he reaches his destination, the entire universe would then need to brake and accelerate in the opposite direction.

The experienced force, in a sense, causes the time dilation. Because that force is the result of spacetime distortion. Whether that distortion is caused by the mass of a nearby body (gravity) or by the rocket's thrusters is immaterial. The twin remaining on Earth does not experience that force and so, does not experience time dilation - except for the relatively slight, constant amount caused by the Earth's gravity and motion around the Sun, etc.

[Xamonas Chegwé]

If you want a shot at understanding relativity - especially general relativity - you have to understand the Maths behind it. I recommend this book. It begins with an assumption of no university-level mathematics and introduces the required concepts as it proceeds. Be warned though, it took me months to get through the GR parts! But they were months well-spent in terms of (approaching) understanding this fascinating subject.

[Xamonas Chegwé]

If we replace the human twins by 2 identical sub-atomic particles with a known half-life before decaying, the experiment can actually be done. If one sample is stationary relative to an observer who times the decays, and another sample is accelerated to near light speed in a cyclotron, the stationary observer observes a lengthened decay time of the moving particle by exactly the amount predicted by the Lorenz formula.

When a particle is accelerated, it experiences a slowing of time, in the same way as when it is in a strong gravitational field.
When it's in a cyclotron, it's accelerated to a high speed, and it also has a strong constant acceleration towards the centre of rotation, as in a centrifuge.
So you would expect the one in the cyclotron to decay slower.

Precisely. The acceleration is what causes the time dilation. An object in circular motion experiences constant acceleration merely to continue spinning at the same speed. This is because its natural path is to follow the geodesic - ie. to continue on its current trajectory - which would send it flying in a straight line out of the circular path - like a ball released by a bowler. It is only the injection of force that prevents this from happening and changes its path - in the cyclotron, this force is electromagnetic; for the bowler, it is the pressure of his fingers on the ball - and any change of course is an acceleration.

[mistermack]

It's fine to put it down to acceleration causing the slowing of time.
Except that Special Relativity says that it doesn't.

According to the clock hypothesis, which is a basic assumption of SR, acceleration does not cause time dilation. And that has been verified experimentally, both for lateral and transverse acceleration :

The clock hypothesis states that the extent of acceleration doesn't influence the value of time dilation. In most of the former experiments mentioned above, the decaying particles were in an inertial frame, i.e. unaccelerated. However, in Bailey et al. (1977) the particles were subject to a transverse acceleration of up to ∼1018 g. Since the result was the same, it was shown that acceleration has no impact on time dilation.[27] In addition, Roos et al. (1980) measured the decay of Sigma baryons, which were subject to a longitudinal acceleration between 0.5 and 5.0 × 1015 g. Again, no deviation from ordinary time dilation was measured.[29]

The clock hypothesis is an assumption in special relativity. It states that the rate of a clock doesn't depend on its acceleration but only on its instantaneous velocity. This is equivalent to stating, that a clock moving along a path P measures the proper time, defined by:

The clock hypothesis was implicitly (but not explicitly) included in Einstein's original 1905 formulation of special relativity. Since then, it has become a standard assumption and is usually included in the axioms of special relativity, especially in the light of experimental verification up to very high accelerations in particle accelerators.

This is why I was looking at ways to take acceleration out of the experiment, to see what was happening without acceleration complicating it.

I think I get what they are saying, about the twins being in different frames. It's not very well explained, that's all.
An observer who is STATIONARY in one frame, will observe a slower clock, that is stationary in any frame moving relative to him.
But any observer who is stationary in the moving frame, will see his own clock as normal, and the clock in the original frame as slowed.

So, when they are saying that the moving twin is changing frames, what they mean is that he is changing the frames that he is stationary in. Which is actually the same thing as saying that he is accelerated.
They are really talking about the same thing, expressed differently.
If you change the frame that you are stationary in, you have accelerated.

So in the twin paradox, the twin that goes and comes back has been existing as stationary, in frames in which time runs slower, as observed from his starting and finishing frame.
The twin that stayed put, has stayed as stationary in the same frame of reference, so his time hasn't dilated.

[mistermack]

Further to this, you CAN argue that either of the twins is stationary. But, in order for the travelling twin to be thus, the entire universe must be accelerating in the opposite direction. This causes a distortion of spacetime in his vicinity and means that he is not following the geodesic (path of least resistance) and so he will still experience an identical force to that which he would experience from acceleration. Similarly, when he reaches his destination, the entire universe would then need to brake and accelerate in the opposite direction.
.

I don't think that stands up. For the entire universe to accelerate in the opposite direction, and one twin to remain still, there would need to be a gigantic increase in momentum, whereas we know that momentum has to be conserved.

In fact, what happens is that the universe DOES accelerate in the opposite direction, but only enough to balance the momentum of the moving twin. Which is like shooting a bullet from the Moon. (ignoring the Moon's gravity, for argument's sake)
The Moon gets shoved one way, and the bullet the other. But the effect on the Moon could never be detected.
But when you scale that up to the size of the Universe, compared to a twin, the effect would be almost a perfect zero.

[mistermack]

I was trying to think of a way of doing away with the acceleration, as it just complicates the matter.

Of course it does! But, just because it's complicated, doesn't mean it's wrong! And it certainly doesn't mean that it should be disregarded!

If the twins were atomic stopwatches, and one was passing the stationary one at a high speed, when they were both set to start, then the moving one goes a million miles at high speed, and meets an identical stopwatch moving at the same speed in the opposite direction. At the instant that they pass, the elapsed time is synchronised to the returning stopwatch, using radio.
So now, the second stopwatch returns to the stationary one, and the elapsed time is compared.

OK. A is stationary. B is moving away from A at constant velocity. C is moving towards A at constant velocity and passes B at some point.

All three are in relative motion and no two are accelerating with respect to each other. This is NOT a rephrasing of the twins paradox precisely because it does not involve travel to and from a distant point and the inevitable acceleration that that must entail (in order to change direction).

So what you have done, is removed any acceleration from the experiment.

Precisely. You've just ignored the bit you don't get and hoped it went away! And as a result, you are no longer describing the same experiment, or any analogue of it!

Which stopwatch would show the greater elapsed time?

Irrelevant, for the reasons given in my last comment.
Removing acceleration from GR makes about as much sense as removing cheese from cheese on toast! ie. none!

On further reading of the Wiki page, it says this :

Eventually, Lord Halsbury and others removed any acceleration by introducing the "three-brother" approach. The traveling twin transfers his clock reading to a third one, traveling in the opposite direction. Another way of avoiding acceleration effects is the use of the relativistic Doppler effect (see What it looks like: the relativistic Doppler shift below).

Removing acceleration from GR makes about as much sense as removing cheese from cheese on toast! ie. none!

More tea, milord?

[Xamonas Chegwé]

Interesting. The way it was explained to me (many years ago) it was all about the acceleration. The three brother approach appears to remove the acceleration but I would argue that there is still implicit acceleration included. The synchronisation of the brothers' clocks as they swap over can be considered to be an instantaneous change of velocity, and hence an acceleration - even though neither brother technically changes their velocity, the time measurement does. In other words, it's a clever fudge.

There is no absolute present, so one can only validly synchronise timepieces when they are at the same point in space. This means that the only way to compare the times of two observers in different inertial frames twice is to do so when they return to the same point in space. To do so, one or both must undergo acceleration. The third brother complicates things but I am still pretty much convinced that it is the changeover that causes the effect.

[Xamonas Chegwé]

I have thought further upon this.

The fundamental difference between the two twins (or three brothers) is that one of them exists solely within a single frame, whereas the other(s) occupy, at various times, two separate frames (plus, in the paradox as originally described, an infinite number of transitional frames during the deceleration/re-acceleration between the two).

The human beings/spaceships serve merely as timepieces in the paradox. They may as well be clocks as people. They serve merely as a measure of elapsed time in the story. But either way, the direction of travel changes and this causes the paradox - without it, the twins would never meet again and could not compare watches. Whether twin B is one person (or actually twins!) is irrelevant - the second timepiece must change frames in order for the paradox to work.

Where I am confuzzled is on the subject of energy. The paradox, as originally stated, requires an injection of energy to reverse the direction of travel of twin B (the moving one). The three brothers version appears not to require this - unless it occurs during the transfer of information - passing the reading on one clock to an object that is moving relative to you at close to the speed of light can't be cheap at BT rates!