# Multiplet paradoxes

I have been roaming around threads on PF and there are certain things on which there is no consensus. I would appreciate some expert opinion on the follows...

1. Are all effects of relativity Viz. Time Dilation and Length Contraction real or apparent? And if some are real and others are apparent, which is the factor differentiating between them?

2. Does acceleration cause time dilation? For example, If one of the two twin clocks is accelerated to certain distance and brought back in perfectly symmetrical way, without any constant velocity period, will it accumulate less time?

3. Can two clocks, in uniform relative motion, be synchronized?

A

## Answers and Replies

I believe its:
1) Real, for those 2. Others are still debated ie mass
2) Yes. GPS takes this into account.
3) Yes. uniform motion can also viewed as 2 stationary clocks from thier view.

I think he means that the two clocks are moving relative to eachother in question 3.

3) If 2 clocks are not stationary too each other then they can have the same start times, but because they experience time at different rates the 2 clocks can not stay synchronised for both frames.

I believe its:
1) Real, for those 2. Others are still debated ie mass
2) Yes. GPS takes this into account.
3) Yes. uniform motion can also viewed as 2 stationary clocks from thier view.

1) Why is the relativistic effect on mass debated for being real or apparent?
2) I thought so, yet the thing is this:
Acceleration is not relative but absolute, because, one can measure his own acceleration by a simple accelerometer. Now, acceleration of a body, which is a determinable quantity should give a unique time dilation effect, and not different effects for different observers. However, using Lorentz transforms, we will get different values for different observers. Thus, the case with GPS is different, I think.

3) If 2 clocks are not stationary too each other then they can have the same start times, but because they experience time at different rates the 2 clocks can not stay synchronised for both frames.

So, we can not speak about synchronization, when two such clocks are in relative motion with each other, right?

Last edited:
1) I have not really looked into this part much but it has to do with how the equation p=gamma*m*v is interpreted.

2) Just because someone knows they are being accelerated does not mean that they will not feel the relativistic effects. This will still yield "different effects for different observers" if the observers are not in the same frame together, because they have velocity to add to the acceleration.

3) It is actually possible to synchronize 2 clocks (in different frames) for just 1 frame, but the other frame will see the clocks as unsynced.

2) My question is, As acceleration is absolute, the relativistic effects relevant to the acceleration should also be absolute (and not relative), but you see, the sentence "relativistic effects should not be relative" it self is self contradicting! Thus, if acceleration is absolute (and not relative), why should it contribute to relativistic effects at all?

3) Do we always need synchronized clocks to compare accumulated time of two clocks? I mean, If we make to read two clocks "zero" at some arbitrary instant, can't we compare two clocks after some particular event to compare their respective accumulated time?

2) I think the confusion is in the term relative and relativity. The real back bone is that light has a constant velocity in all frames. This is why even though everyone knows who is accelorating there are still the relativistic effects ( times dilation ect.) caused by the inability of light to travel at other speeds in a vacum.

3) Sure we can, and relativity tells us by how much those 2 clocks will be out of sync.

3. Can two clocks, in uniform relative motion, be synchronized?
Sure they can - it is a requirement for GPS to work.
Just remember that one of the clocks must be set to run fast (or slow) wrt time in its own local reference frame, meaning it will be out of synch with its own local time.

2) I think the confusion is in the term relative and relativity. The real back bone is that light has a constant velocity in all frames. This is why even though everyone knows who is accelorating there are still the relativistic effects ( times dilation ect.) caused by the inability of light to travel at other speeds in a vacum.

The confusion is even profound for me ...
See, currently there are so many threads on twin paradox, and we are not able to reach to a consent that what is role of acceleration in the solution. Some posts describe convincing math, but it's very hard to take any physical meaning out of it. Well the point about isotropy of light is taken. Now analyze this... As speed of light is same for all observers in relative motion or not, is it not the same for all accelerating objects as well (because, though he is accelerating, at any particular arbitrary instant he should have only one unique velocity)? And if so, he will surely realize isotropy of the light speed. In such a case, how is there any symmetry break, even if the accelerating observer knows that he is accelerating? the time dilation will still be relative, and it should not be possible for any observer to accumulate different elapsed time!

Further, the acceleration is realized by inertial force to the observer (or accelerometer). What if the whole universe is moving in opposite direction, in which case, the observer would feel the same amount of acceleration even if he is at absolute rest. Then, how is the acceleration absolute and not relative?

3) Sure we can, and relativity tells us by how much those 2 clocks will be out of sync.
Sure they can - it is a requirement for GPS to work.
Just remember that one of the clocks must be set to run fast (or slow) wrt time in its own local reference frame, meaning it will be out of synch with its own local time.

Point taken, but I was wondering that they would no longer be identical clocks then, as, in rest frame, they will be off sync!!!

Further, the acceleration is realized by inertial force to the observer (or accelerometer). What if the whole universe is moving in opposite direction, in which case, the observer would feel the same amount of acceleration even if he is at absolute rest. Then, how is the acceleration absolute and not relative?

Acceleration is always felt by the accelerated, if the universe accelerates toward you, you will not feel acceleration. Just as if I accelerate toward you, you will not feel acceleration.

Acceleration is always felt by the accelerated, if the universe accelerates toward you, you will not feel acceleration. Just as if I accelerate toward you, you will not feel acceleration.
Well, I think you misinterpreted it, or I made it less clear.
Acceleration is realized (or felt) by the force of inertia. And Einstein showed inertial force to be equivalent to gravitation. Now, If the whole universe accelerates towards me, the resultant effect of change in gravitation should make me feel something. But, As I could not decide wether it is gravity or inertial force, I am bound to think that I am accelerated, and the whole universe has not moved (accelerated) towards me, but I am the one who has accelerated. Ditto for accelerometer.

In such a scenario how is the acceleration absolute?

Dale
Mentor
2020 Award
Absolute means frame-invariant, relative means frame-variant. In any reference frame (including the non-inertial reference frame where the universe is accelerating and the accelerometer is at rest) the proper acceleration of the accelerometer is the same. Therefore the proper acceleration is frame-invariant or absolute.

Absolute means frame-invariant, relative means frame-variant. In any reference frame (including the non-inertial reference frame where the universe is accelerating and the accelerometer is at rest) the proper acceleration of the accelerometer is the same. Therefore the proper acceleration is frame-invariant or absolute.

Exactly, thus, the proper acceleration, which is absolute, will not infer the observer (or accelerometer), wether he is moving or the universe, No?

(including the non-inertial reference frame where the universe is accelerating and the accelerometer is at rest)
That does not seem to follow logic.
If reference frame has an accelerometer that is at rest as in indicating no acceleration, doesn’t that define the frame as an “inertial reference frame” and not a “non-inertial reference frame”?

Now, If the whole universe accelerates towards me, the resultant effect of change in gravitation should make me feel something.
...
In such a scenario how is the acceleration absolute?
I think the problem boils down to the fact that the entire universe can not accelerate towards you. Conservation of momentum prevents that. Also gravity is not the only type of acceleration. Although it is true that a change in gravity is a change in acceleration.

I think the problem boils down to the fact that the entire universe can not accelerate towards you. Conservation of momentum prevents that. Also gravity is not the only type of acceleration. Although it is true that a change in gravity is a change in acceleration.

Well, we don't need to accelerate the whole universe for that. Only acceleration of just the surroundings of the observer imparting most of the gravitational effects would be sufficient for the observer. Yes, gravity is not the only type of acceleration, but It was only meant to explain the situation. You can take any arbitrary situation and any arbitrary acceleration. My point is, even acceleration can be indistinguishable, and can not necessarily infer that the one who feels acceleration is necessarily the one moving. In case of gravity example, the one feeling gravitational acceleration may be at rest and the surroundings may be moving.

Dale
Mentor
2020 Award
That does not seem to follow logic.
If reference frame has an accelerometer that is at rest as in indicating no acceleration, doesn’t that define the frame as an “inertial reference frame” and not a “non-inertial reference frame”?
No, an accelerometer is at rest in a reference frame if and only if the first time derivative of its position is 0. This is irrespective of the acceleration measured by the accelerometer. An inertial reference frame is one where any accelerometer at rest in the frame would read 0.

Consider, for example, a ring-type space station rotating to achieve artificial gravity. An accelerometer attached to the space station is at rest in the station's frame, but it reads a non-zero value indicating that the station's frame is non-inertial.

Dale
Mentor
2020 Award
Exactly, thus, the proper acceleration, which is absolute, will not infer the observer (or accelerometer), wether he is moving or the universe, No?
That is correct. The term "moving" is relative (frame variant), so it is only meaningful to speak of whether or not something is moving in a particular reference frame.

That is correct. The term "moving" is relative (frame variant), so it is only meaningful to speak of whether or not something is moving in a particular reference frame.

That also means, (as we have agreed upon before in the accelerating universe/gravity case), that just because one feels acceleration does not mean he is accelerated, the situation 'can' be the other way around. And if such is the case, how can acceleration break the symmetry. The physical meaning of the symmetry breaking is that, as one can decide he is accelerating and not the other twin, only his clock will slow more and not the stationary twin's clock. However, even though acceleration is "absolute", It does not necessarily impart the observer any information as to he is moving or not, thus can not slow the clocks in asymmetrical way.

Last edited:
Dale
Mentor
2020 Award
First, I strongly dislike the acceleration-based explanation of the twin "paradox".

Second, you need to distinguish between coordinate acceleration and proper acceleration. Coordinate acceleration is the second time derivative of position in some reference frame. It is relative and mathematical. Proper acceleration is what is measured by an accelerometer. It is absolute and physical.

Thus, if two bodies have different proper acceleration (accelerometer reading) then they are not symmetrical in an absolute physical sense, despite the mathematical coordinate symmetry that can be constructed through careful choice of non-inertial reference frames.

No, an accelerometer is at rest in a reference frame if and only if the first time derivative of its position is 0. This is irrespective of the acceleration measured by the accelerometer. An inertial reference frame is one where any accelerometer at rest in the frame would read 0.

Consider, for example, a ring-type space station rotating to achieve artificial gravity. An accelerometer attached to the space station is at rest in the station's frame, but it reads a non-zero value indicating that the station's frame is non-inertial.
It is not that simple, a rotating framework is not a single reference frame – different parts have reference frames changing vectors wrt other parts of the same framework.