B Twin paradox explained for laymen

[Tony Wright]

Yes, I understood the purpose of MM to show that light speed is not related to a stationary medium as sound is. My question about fixed points in space was different but irrelevant because the behaviour of time in the twin paradox is due to acceleration which I now realize is absolute, not relative like constant motion. So the asymmetry necessary for time dilation arises from the fact that the acceleration experienced by the departing twin is far greater than that of the remainer who is standing on the earth, and this effect is due directly to the mass of the Earth and not to the gravity associated with it.
You say that Einstein’s view of relative motion was never conclusively proved and that gives me the courage to mention what may be another unproven aspect. The speed of light emission is well known but how can the related tenet, that its speed at reception is also c be proved? If I throw a ball to a moving person they receive it at a different speed (even in vacuum with no friction). I don’t want to appear heretical enough to deny the accepted view but would like to know how it Is supported. I immediately think of unlikely observations such as the measurement of incoming light speed from two supernovae which are known to be in relative motion and using two or more receptors.

 

[Sagittarius A-Star]

and this effect is due directly to the mass of the Earth

No.

The speed of light emission is well known but how can the related tenet, that its speed at reception is also c be proved?

The emission theory was disproved in 1913 by de Sitter from Doppler red- and blue-shift timing observations of spectroscopic double stars:

Willem de Sitter's argument against emission theory. According to simple emission theory, light moves at a speed of c with respect to the emitting object. If this were true, light emitted from a star in a double-star system from different parts of the orbital path would travel towards us at different speeds. For certain combinations of orbital speed, distance, and inclination, the "fast" light given off during approach would overtake "slow" light emitted during a recessional part of the star's orbit. Thus Kepler's laws of motion would apparently be violated for a distant observer.

Source:
https://en.wikipedia.org/wiki/De_Sitter_double_star_experiment

 

[PeroK]

You say that Einstein’s view of relative motion was never conclusively proved and that gives me the courage to mention what may be another unproven aspect. The speed of light emission is well known but how can the related tenet, that its speed at reception is also c be proved? If I throw a ball to a moving person they receive it at a different speed (even in vacuum with no friction). I don’t want to appear heretical enough to deny the accepted view but would like to know how it Is supported. I immediately think of unlikely observations such as the measurement of incoming light speed from two supernovae which are known to be in relative motion and using two or more receptors.

Nothing in physics is proven, in a sense. We have models of nature that are used to predict the outcomes of experiments. Some models may be preferred to others because of simplicity. SR is the simplest way to model the phenomena we test - for example in particle collisions at CERN etc.

The theory of SR has its place at the centre of the theory of high-energy interactions between particles. The idea that there is still some debate about whether the whole thing is some untested hypothesis is nonsensical. You are 115 years too late.

In the last 115 years the behaviour of light has been studied and tested exhaustively. There is no room for experimental doubt on these basic questions. You are really asking whether in the last 115 years no ne has got round to testing a basic premise of SR?

Finally, the idea that the debate today is still about time dilation and can time really be like that is long out of date. Physics has moved a long way since 1905.

You may as well go down to your local hospital, find a heart surgeon and ask: have you really tested that the heart pumps blood round the body? I've been reading some 13th century medical texts that cast doubt on this. I just want to be sure that you have tested this.

 

[PeterDonis]

the asymmetry necessary for time dilation arises from the fact that the acceleration experienced by the departing twin is far greater than that of the remainer who is standing on the earth, and this effect is due directly to the mass of the Earth and not to the gravity associated with it.

There are several errors here.

First, acceleration in itself does not affect clock rates; there is no time dilation due to acceleration.

Second, the departing twin can be in free fall for almost all of his trip--the only time he has to experience acceleration is when he turns around. (And in fact, there are versions of the scenario where even the turnaround does not require acceleration: for example, the traveling twin could pass close enough to some large, distant planet or star to "slingshot" around it and be heading back towards Earth, and stay in free fall the whole time.) So it is not true to say that the acceleration of the traveling twin is "far greater" than that of the twin who remains on earth.

Third, gravitational time dilation is due to differences in gravitational potential. It is not due to "gravity" in the sense of "acceleration due to gravity", yes, but it is also not due "directly" to mass.

 

[FactChecker]

CAUTION: I see that experts are skeptical of this post, so it may be misleading. Sorry.

As a layman I find resolution of the twin paradox in terms of physics difficult. Given the observation of time dilation by astronauts on their return to Earth I can only approach it by means of the thought experiment In which the Earth is removed and the twins perform the same relative movements outside of any gravitational fields apart from their own. Because their motions, including acceleration, constant motion or inertial motion and deceleration away and then towards each other are mutual, or reciprocal, I cannot envisage any time dilation.

You are only looking at the math in a very limited extent of taking a derivative wrt a reference frame that may, or may not, be accelerating. But given an inertial reference frame, there is a set of defined paths in space-time that are unaccelerated and it is clear that the twin that turns around is not taking such a path, whereas the stationary twin is. So the situation of the twins is not symmetric, even in a purely mathematical sense. The mathematics does work out for the traveling twin to be younger, even staying within SR.
There is a physical rationalization (within GR?) for the traveling twin seeing the stationary twin aging very fast during the turn-around. The traveling twin experiences acceleration during the turn-around which is equivalent to there being a gravitational field pulling [EDIT] toward away from the stationary twin. The farther away the stationary twin is, the greater the speedup of his aging. Therefore, the turn-around has a much greater aging effect than the opposite acceleration/deceleration effects when the trip starts and ends with the twins near each other. (This all matches the SR calculations.)

i would be very grateful for any comments on my analysis so that I can move on and start to understand other concepts of relativity.

Regardless of whether you completely understand the twins paradox, you should continue on. There is a lot to think about that has nothing to do with the twins paradox.

 

[PeroK]

There is a physical rationalization (within GR?) for the traveling twin seeing the stationary twin aging very fast during the turn-around. The traveling twin experiences acceleration during the turn-around which is equivalent to there being a gravitational field pulling toward the stationary twin. The farther away the stationary twin is, the greater the speedup of his aging. Therefore, the turn-around has a much greater aging effect than the opposite acceleration/deceleration effects when the trip starts and ends with the twins near each other.

It's none of these things. It's simple flat spacetime geometry. It's really no more mysterious than Pythagoras' theorem.

 

[Sagittarius A-Star]

which is equivalent to there being a gravitational field pulling toward the stationary twin.

I think it should say: "which is equivalent to in this frame everywhere being a pseudo-gravitational field pulling toward the traveling twin."

The "stationary" twin is in free fall towards the traveling twin (= only coordinate-acceleration of the stationary twin).

 

[FactChecker]

It's none of these things. It's simple flat spacetime geometry. It's really no more mysterious than Pythagoras' theorem.

When something is true, there may be many ways to intuit it. There may be a simple mathematical calculation or it may just be compatible with other things.

 

[PeroK]

When something is true, there may be many ways to intuit it. There may be a simple mathematical calculation or it may just be compatible with other things.

The problem with "something weird happens during acceleration" is that you can remove all of the acceleration from the scenario.

 

[Sagittarius A-Star]

that you can remove all of the acceleration from the scenario.

You can also keep all of the acceleration in the scenario. I see no problem with this. SR is fine dealing with accelerated reference frames.

 

[PeroK]

You can also keep all of the acceleration in the scenario. I see no problem with this. SR is fine dealing with accelerated reference frames.

That's not the point. If acceleration were the "cause", then you couldn't remove it. You can always keep extraneous factors in the scenario.

 

[FactChecker]

That's not the point. If acceleration were the "cause", then you couldn't remove it. You can always keep extraneous factors in the scenario.

It is good to know that things are compatible, regardless of what you use for a proof.

(FYI. I do not think that there is a purely mathematical definition of an inertial reference frame that would allow one to distinguish between the two twins. There would need to be some way of identifying which was doing the traveling. That requires a (mathematically) arbitrary reference point. Otherwise, a purely mathematical approach makes the situation of the twins completely symmetric. )

 

[Sagittarius A-Star]

That's not the point. If acceleration were the "cause", then you couldn't remove it. You can always keep extraneous factors in the scenario.

1) In the rest frame of the stationary twin, acceleration of the traveling twin is no direct "cause". "Gamma" depends only directly on velocity.

2) In the rest frame of the traveling twin, pseudo-gravitational time-dilation is part of the "cause", besides the "Gamma" of the "stationary" twin.

Often, the turn-around is described as instantaneously. Then in the rest frame of the traveling twin, the wristwatch of the stationary twin makes a jump to a later time instead of a continuous change to that time. The acceleration is not left out, but only hidden in a "dirac delta function".

 

[Vanadium 50]

None of that is correct. You can set this up entirely with people looking at clocks through windows without anyone accelerating.

 

[Sagittarius A-Star]

None of that is correct. You can set this up entirely with people looking at clocks through windows without anyone accelerating.

You can always redefine the scenario, for example to a triplet scenario. But you don't have to.

 

[PeterDonis]

I do not think that there is a purely mathematical definition of an inertial reference frame that would allow one to distinguish between the two twins.

Certainly there is. In any scenario where the traveling twin has to undergo nonzero proper acceleration to turn around, his worldline has nonzero path curvature. The mathematical definition of an inertial frame specifies that worldlines with constant spatial coordinates have zero path curvature (that's what "inertial" means), so it is impossible to find an inertial frame in which the traveling twin has constant spatial coordinates for the entire trip.

 

[PeterDonis]

1) In the rest frame of the stationary twin, acceleration of the traveling twin is no direct "cause". "Gamma" depends only directly on velocity.

2) In the rest frame of the traveling twin, pseudo-gravitational time-dilation is part of the "cause", besides the "Gamma" of the "stationary" twin.

Note that these two statements are compatible with different definitions of what a "cause" can be.

In 1), the acceleration of the traveling twin is an invariant, so this statement is compatible with a definition of "cause" which requires any possible "cause" to be an invariant.

In 2), the pseudo-gravitational time dilation is not an invariant (it vanishes in the stay at home twin's rest frame), so this statement is not compatible with a definition of "cause" which requires any possible "cause" to be an invariant.

Physically, only invariants correspond to observable quantities, and it seems like anything that could be a "cause" should be an observable quantity, so only the first statement would be compatible with what seems like a physically reasonable definition of "cause".

 

[Sagittarius A-Star]

Physically, only invariants correspond to observable quantities, and it seems like anything that could be a "cause" should be an observable quantity, so only the first statement would be compatible with what seems like a physically reasonable definition of "cause".

The nonzero path curvature of the worldline of the traveling twin is invariant. In the rest frame of the stationary twin it appears as an acceleration (not influencing time-dilation). In the rest frame of the traveling twin, it appears as pseudo-gravity (influencing time-dilation).

 

[FactChecker]

Certainly there is. In any scenario where the traveling twin has to undergo nonzero proper acceleration to turn around, his worldline has nonzero path curvature. The mathematical definition of an inertial frame specifies that worldlines with constant spatial coordinates have zero path curvature (that's what "inertial" means), so it is impossible to find an inertial frame in which the traveling twin has constant spatial coordinates for the entire trip.

Using only the relative positions of the twins, one can not mathematically define which is moving, which is accelerating, etc. There must be a definition of "inertial" or "stationary" using some external or mathematically arbitrary reference. Which reference frame is defined as "inertial" must be based on physics and has associated consequences.

 

[PeterDonis]

The nonzero path curvature of the worldline of the traveling twin is invariant.

Yes.

In the rest frame of the stationary twin it appears as an acceleration

As coordinate acceleration, yes.

(not influencing time-dilation)

Not directly, but indirectly it does. The traveling twin's coordinate acceleration changes his velocity in the stationary twin's rest frame, which does affect the traveling twin's time dilation. See below.

In the rest frame of the traveling twin, it appears as pseudo-gravity

Basically, yes. But see below.

(influencing time-dilation)

The stationary twin's pseudo-gravitational time dilation in the traveling twin's rest frame is due to the stationary twin's position (at much higher "altitude" than the traveling twin). But if you are going to call that an influence of path curvature, manifesting as pseudo-gravity, on time dilation, it is not direct, only indirect. So in both cases (traveling twin in stationary twin's rest frame, or stationary twin in traveling twin's rest frame), the path curvature of the traveling twin's worldline does affect time dilation, but only indirectly.

 

[Sagittarius A-Star]

The stationary twin's pseudo-gravitational time dilation in the traveling twin's rest frame is due to the stationary twin's position (at much higher "altitude" than the traveling twin). But if you are going to call that an influence of path curvature, manifesting as pseudo-gravity, on time dilation, it is not direct, only indirect. So in both cases (traveling twin in stationary twin's rest frame, or stationary twin in traveling twin's rest frame), the path curvature of the traveling twin's worldline does affect time dilation, but only indirectly.

I think, the influence of pseudo-gravitational potential-difference on time dilation is directly. But that's no problem, because time dilation (tickrate-ratios at a certain instance of time) is frame-dependent. Only the end-result (age-difference when meeting the 2nd time) is absolute. The influence of pseudo-gravitational potential-differences on that is only indirectly. The age difference depends, amoung others, on the pseudo-gravitational time-dilation, integrated over the turnaround-time.

 

[PeterDonis]

I think, the influence of pseudo-gravitational potential-difference on time dilation is directly.

"Pseudo-gravitational potential difference" is not the same as "path curvature". The latter is the invariant, and, as I said, it affects time dilation indirectly, and does so in both frames. So there is no need to point to any frame-dependent quantity like "pseudo-gravitational field" as a cause of time dilation; the invariant, path curvature, works fine as a cause in any frame.

time dilation (tickrate-ratios at a certain instance of time) is frame-dependent

Under this definition of "time dilation" (which I have no issue with, but not everyone is careful about using the term only with this definition), it doesn't need to have a cause, because frame-dependent things don't need causes. Only invariant things, like the age difference of the twins when they meet again, need to have causes.

 

[Sagittarius A-Star]

Under this definition of "time dilation" (which I have no issue with, but not everyone is careful about using the term only with this definition)

That's right. For example in the English Wikipedia they define time dilation as a difference in elapsed time, measured by two clocks (due to velocity or gravitational potential difference), and in the German Wikipedia that processes in a physical system tick slower relative to the observer, if the system is moving relative to the observer.

 

[robphy]

From a geometric viewpoint,
time-dilation compares
the measurer's t-component of the 4-velocity of the measurer [which is 1, since 4-velocities are unit vectors]
with
the measurer's t-component of the 4-velocity of an astronaut [which is what the measurer measures as the elapsed time between two ticks (marked by events) of the astronaut's clock].

These are equal only for the Galilean spacetime used in PHY 101: measurer measures \Delta t = 1.
In special relativity, measurer measures \Delta t \geq 1 (since \gamma=\cosh\theta \geq 1).. this is time dilation.
In Euclidean geometry (by analogy), \Delta t \leq 1 (since \cos\phi \leq 1.
See the diagrams below.

From this viewpoint, the key idea is that:
the general situation is that \Delta t \ne 1
and that the Galilean case is the exceptional case [not typical case].

It seems to me that the root of time-dilation is that the real spacetime we live in isn't Galilean...
but is pseudoriemannian with a Minkowski signature [for dilation].
Once this is realized, there's no need to include gravity or acceleration etc...
unless you want to calculate specific elapsed times.
Including them probably clouds the real issue above.

Our low-relative-speed lifestyles have led to our "common sense" Galilean notions of time.
Using https://www.desmos.com/calculator/wm9jmrqnw2
for Special Relativity (E=1), Galilean (E=0), and Euclidean (E=-1)...

\quad

\quad

The bottom line is to calculate the elapsed time along different worldlines from event O to event Z.
The general case is that they are different.

 

[Sagittarius A-Star]

but is pseudoriemannian with a Minkowski signature [for dilation].
Once this is realized, there's no need to include gravity or acceleration etc...
unless you want to calculate specific elapsed times.
Including them probably clouds the real issue above.

That's all fine, if you teach relativity to physics students. But the OP asks for a laymen explanation of the typical "twin paradox" scenario and states wrongly, that a scenario without real gravity would be symmetrically.

I think, for laymen an explanation with 4-vectors and 4D-spacetime may be too difficult to understand. An explanation comparing the empirical viewpoint of both twins maybe didactically better for an explanation to laymen.

And the asymmetry, related to tick-rates, can be explaind by the fact, that in the inertial frame of the "stationary" twin the tick-rate of the other twin's wristwatch can be calculated as only velocity-dependent effect, while in the accelerated frame of the "travelling" twin also pseudo-gravitational potential difference influences the tick-rate of the other twin's wristwatch.

The OP came to the wrong idea, that real gravitation is needed to break the symmetry of the typical "twin paradox" scenario. I can understand why, because at gravitational time-delation, both twins agree on, whose wristwatch ticks slower and whose faster. But in reality in this case, the symmetry breaking of tick-rates does not come from real gravitation, but from pseudo-gravitational potential-difference in one of the rest frames. So in some sense, the OP was close to this real explanation of the needed asymmetry.

 

[Nugatory]

because at gravitational time-delation, both twins agree on, whose wristwatch ticks slower and whose faster.

However, the amount by which the ages differ is a function of the amount of time the traveller spends coasting and is independent of the duration and magnitude of the pseudo-gravitational time dilation at turnaround.

 

[Sagittarius A-Star]

However, the amount by which the ages differ is a function of the amount of time the traveller spends coasting and is independent of the duration and magnitude of the pseudo-gravitational time dilation at turnaround.

That's right, because the pseudo-gravitational time dilation relates to the fast tick-rate of the stationary twin's wrist watch while the turnaround und not to the tick-rate of the traveling twin's wrist watch, which stays "normal" in his frame. And the integral of the pseudo-gravitationally time dilated tick-rate over the turnaround-time is pre-defined in the scenarion, as the acceleration of the traveller's frame shall change his velocity in the stationary twin's frame from +v to -v in a certain approximate distance.

 

[PeroK]

That's right, because the pseudo-gravitational time dilation relates to the fast tick-rate of the stationary twin's wrist watch while the turnaround und not to the tick-rate of the traveling twin's wrist watch, which stays "normal" in his frame. And the integral of the pseudo-gravitationally time dilated tick-rate over the turnaround-time is pre-defined in the scenarion, as the acceleration of the traveller's frame shall change his velocity in the stationary twin's frame from +v to -v in a certain approximate distance.

Suppose the traveller takes two stopwatches on the journey. The first watch stays on for the whole journey (including the several acceleration phases). The second watch is switched on only during the inertial phases of the motion, and is stopped during the acceleration phases.

If we assume that the acceleration phases are short (they can, theoretically, be made arbitrarily short), then the two watches show approximately the same time on return the Earth. They may, for example, differ by a few minutes if the acceleration phases lasted only a few minutes.

Given that the second watch was switched off during the critical acceleration phases, how do you explain this? Using your pseudo-gravitational explanation?

 

[Sagittarius A-Star]

Given that the second watch was switched off during the critical acceleration phases, how do you explain this? Using your pseudo-gravitational explanation?

You find the answer already in my posting #57. Let me summarize it: The pseudo-gravitational time dilation relates to the stationary twin's watch tick-rate (in the rest frame of the traveling twin) and not to the tick-rate of the travelling twin's watch.

While the inertial phases, the stationary twin's watch ticks slow (1/"Gamma"), and while the short turn-around phase, the stationary twin's watch ticks very fast (over-compensating the slow tick-rates of the inertial phases), all in the rest frame of the traveling twin.

 

[Sagittarius A-Star]

@PeroK : see also the following "twin paradox" description in the middle of the linked page:

https://en.wikisource.org/wiki/Translation:Dialog_about_Objections_against_the_Theory_of_Relativity