Twin paradox explained for laymen

[PeroK]

@FactChecker another way to analyse this that like is as follows:

1) Pick any IRF in which the Earth is moving at some arbitrary speed $v$ and analyse the problem in that frame. Or:

2) A special case is to analyse the entire scenario in the traveller's oubound IRF. In this frame:

The Earth moves with constant speed $v = 0.8c$, say.

The traveller is stationary for the outbound leg and then moves at speed $V$, which can be calculated using velocity addition, during the second leg, and eventually catches up with the Earth. If you calculate things in this frame (purely for the inertial legs) then (as you must) you get the same answer. The Earth twin has aged 10 years and the traveller 6 years when they reunite.

In this frame, there is only inertial motion for both twins; the acceleration phase(s) can be neglected (as usual, assuming they are short and sharp), yet the twins age differently between their meetings.

Now, if you try to add a physical cause and effect for the acceleration phase, that must throw the calculations. If acceleration does anything it must do it in this IRF as well? Or, do something at least. But, it can't do anything because you've already got the right answer from the inertial phases alone.

 

[PAllen]

For those who insist on a pseudogravity approach, it is only applicable in coordinates for which the noninertial path has fixed position the whole time. It doesn’t apply in any inertial frame.

 

[pervect]

I see. I think you mean the greatest time among all paths between the two points, not just two paths. Comparing only two paths, it may be that neither is inertial.Suppose the traveling twin flies inertially to and from the far point and makes a fast, non-inertial turnaround. Also, suppose he is mistaken and attempts to use the SR equations to calculate the age of the stationary twin.

I'm not following. If he's mistaken, he gets the wrong answer. I'm not too inclined to go into this further, unless I can understand your motivation for sayin he's making mistakes.

Note that a person can tell if they are accelerating or not by physical experiments. It's not a matter of opinion, or convention. There are physical effects when one accelerates. To make a mistake about accelerating or not accelerating is to get the physics wrong. Perhaps that's your motivation for assuming he's making a "mistake"? If so, it is IMO misguided.

The idea that the acceleration itself causes the differential aging may be what's confusing you. Let's go back to the road trip analogy.

One driver takes a straight route, all of the time, and gets the shortest distance on his odometer.

The other driver travels in a straight line, "most of the time", but his course is off. He realizes this, so he makes a turn, correcting his course. The turn is sharp, it doesn't take him much time to make the turn. Then he travels in a straight line for the rest of the trip.

Travelling in a straight line "most of the time" simply is NOT good enough to have the shortest distance on the odometer. One has to travel in a straight line ALL the time, not just most of it.

One can say that if the angle of the course correction is small, while he'll drive further, it won't be too much further. The analogous space-time analogy to the angle of the turn is the total velocity change. This can be seen by drawing a space-time diagram. If the total velocity change is small, then there's not much differential aging. If there is a large change in the velocity, the space-time equivalent of a large angle, then there will be a large impact on the differential aging. The amount of time it takes to change the velocity is not critical to the aging calculation.

 

[PeterDonis]

I think you mean the greatest time among all paths between the two points, not just two paths. Comparing only two paths, it may be that neither is inertial.

This is a valid point. The correct statement is that, in flat spacetime, of all possible timelike paths between two fixed events that are timelike separated, the one with the longest elapsed time will be the inertial path.

 

[PeterDonis]

I'm not following.

See my post #179 just now. The correct general statement of the principle you are using is given there.

If you want to specialize that statement to just two paths, you have to also specify that one of the paths is inertial. If you have two paths and neither one is inertial, there is no general rule for which path will have the longer elapsed proper time; you have to look at the specific paths. I don't think you intended to discuss that case, but the way you worded your statement didn't rule it out.

If he's mistaken, he gets the wrong answer.

He means, if neither twin is inertial the whole time, then one twin will make a wrong prediction if he assumes that the other twin is inertial the whole time. Which, again, I don't think is what you intended, but your wording didn't rule it out.

 

[FactChecker]

I'm not following. If he's mistaken, he gets the wrong answer. I'm not too inclined to go into this further, unless I can understand your motivation for sayin he's making mistakes.

During any inertial-flight part of the traveler's trip, he is correct that the stationary twin is aging slower. With a high-acceleration quick turnaround, the inertial flight may be the vast majority of the trip. In that case, the traveling twin knows, correctly, that the stationary twin is aging slower during the vast majority of the trip. Yet, at the end, the stationary twin ends up older. So what would you say to the traveler as to why his turnaround caused the stationary twin to age so much more during the brief turnaround time to end up older?

PS. I am ok with this conversation ending here. I don't see any reason to continue it.

 

[jbriggs444]

During any inertial-flight part of the traveler's trip, he is correct that the stationary twin is aging slower. With a high-acceleration quick turnaround, the inertial flight may be the vast majority of the trip. In that case, the traveling twin knows, correctly, that the stationary twin is aging slower during the vast majority of the trip. Yet, at the end, the stationary twin ends up older. So what would you say to the traveler as to why his turnaround caused the stationary twin to age so much more during the brief turnaround time to end up older?

Emphasis mine.

Neither piece of knowledge is correct. Both are coordinate-dependent statements that are not correct in any larger sense.

 

[FactChecker]

Emphasis mine.

Neither piece of knowledge is correct. Both are coordinate-dependent statements that are not correct in any larger sense.

These phases of the flight are the basic SR situation of one observer traveling inertially versus a stationary observer. Each observer sees that time is passing slower for the other. Its validity is not open to question. It is fundamental SR.

 

[Sagittarius A-Star]

Neither piece of knowledge is correct. Both are coordinate-dependent statements that are not correct in any larger sense.

Coordinate-dependent statements can be correct or incorrect. They refer to the reference frame.

In their respective restframe, both twins can calculate the other twin's watch's (frame-dependent) tick-rate. They can integrate that tick-rate over the complete travel-time to calculate the frame-independent age-difference. Both calculations must give a consistent result.

 

[PeroK]

These phases of the flight are the basic SR situation of one observer traveling inertially versus a stationary observer. Each observer sees that time is passing slower for the other. Its validity is not open to question. It is fundamental SR.

This is not correct and is at the root of your problem. Time dilation is relative. In various other inertial frames the time dilation may be more or less for either twin. Time dilation is not differential ageing.

 

[A.T.]

Both are coordinate-dependent statements that are not correct in any larger sense.

Coordinate-dependent statements can be correct or incorrect. They refer to the reference frame.

In their respective restframe, both twins can calculate the other twin's watch's (frame-dependent) tick-rate. ...

Note that these frame-dependent calculations depend on frame conventions, while coordinate-independent statements do not.

 

[FactChecker]

This is not correct and is at the root of your problem. Time dilation is relative. In various other inertial frames the time dilation may be more or less for either twin. Time dilation is not differential ageing.

It is my understanding that all physical processes appear slower in an IRF that is moving wrt a stationary observer. Any physical process which can be thought of as a clock goes slower. That includes normal clocks, molecular processes, and the aging process.

 

[Vanadium 50]

It is my understanding that all physical processes appear slower in an IRF that is moving wrt a stationary observer.

There is your problem. There is no "moving" and "stationary" observer. "Stationary" is not a concept in relativity.

 

[PeroK]

It is my understanding that all physical processes appear slower in an IRF that is moving wrt a stationary observer. Any physical process which can be thought of as a clock goes slower. That includes normal clocks, molecular processes, and the aging process.

The physical processes are unaffected because inertial motion is relative. Neither twin is physically affected in any way by their relative motion.

 

[FactChecker]

There is your problem. There is no "moving" and "stationary" observer. "Stationary" is not a concept in relativity.

Right. Call them observer A and B if you prefer. All that is necessary is that they are at a fixed position in different inertial reference frames that are moving wrt each other. (This is not a problem with my statements. I used the terms "moving" and "stationary" to represent a typical situation.)

 

[jbriggs444]

Right. Call them observer A and B if you prefer. All that is necessary is that they are at a fixed position in different inertial reference frames that are moving wrt each other. (This is not a problem with my statements. I used the terms "moving" and "stationary" to represent a typical situation.)

No. That is not all that is necessary. The term "observer" carries more baggage than that.

 

[FactChecker]

The physical processes are unaffected because inertial motion is relative. Neither twin is physically affected in any way by their relative motion.

I should have said that any physical process in one IRF appears slower to an observer in a different IRF that is moving relative to the process IRF.

 

[FactChecker]

Then what would you say is happening during the inertial flight stages of the trip? What does each one think about the aging process of the other. If there is some difference between them, why?

 

[PeroK]

I should have said that any physical process in one IRF appears slower to an observer in a different IRF that is moving relative to the process IRF.

But that has no physical significance, so needs no physical cause. Proper time along a worldline is an invariant quantity. All observers agree on that. Time dilation is not invariant.

 

[Sagittarius A-Star]

But that has no physical significance, so needs no physical cause. Proper time along a worldline is an invariant quantity. All observers agree on that. Time dilation is not invariant.

Assume, the traveling twin just came back from Alpha Centauri and both twins are now sitting in a room on Earth with a constant distance of 1.5 meters from each other in their common restframe. Then their age difference is still frame-dependent.

Does the age difference in their common rest frame have no physical significance?

 

[PeroK]

Then what would you say is happening during the inertial flight stages of the trip? What does each one think about the aging process of the other. If there is some difference between them, why?

The inertial phases are physically indistinguishable. But, like the triangle analogy, if you join two lines at an angle they are longer than the direct line.

This is why utlimately it's about spacetime geometry; not about time dilation as a physical process with a cause.

 

[PeterDonis]

During any inertial-flight part of the traveler's trip, he is correct that the stationary twin is aging slower.

No, he isn't. All he can say is that in the inertial frame in which he is currently at rest, the stationary twin is aging slower. But this is a frame-dependent statement. Frame-dependent statements are not about actual real things; they're about calculated abstractions.

Each observer sees that time is passing slower for the other.

This is false. Each observer calculates that, in his current inertial rest frame, time is passing slower for the other. But that is not what each observer actually sees. What each observer actually sees is what I have been describing all along about Doppler shifts. In other words:

The traveling twin sees the stay-at-home twin's clock running slower than his until he turns around; then he sees the stay-at-home twin's clock running faster than his. The speed-up in the second part outweighs the slow-down in the first part, so when the twins meet up again the traveling twin has seen the stay-at-home twin's clock have more total elapsed time than his.

The stay-at-home twin sees the traveling twin's clock running slower than his for most of the time they are apart; then, not long before the twins meet again, the stay-at-home twin sees the traveling twin's clock speed up so it is running faster than his. But the slow-down in the first part outweighs the speed-up in the second part, so when the twins meet up again the stay-at-home twin has seen the traveling twin's clock have less total elapsed time than his.

The Doppler Shift Explanation page in the Usenet FAQ article that I linked to earlier describes this in somewhat more detail.

The crucial point here is that you have to distinguish the frame-dependent concept of "time dilation", which by itself cannot be used to make accurate predictions about differential aging, from the invariant concept of "directly seen Doppler shift/clock rate", which can be used to make accurate predictions about differential aging. But the latter is not the same as the former; the directly seen Doppler shift/clock rate factor is not the same as the calculated "time dilation" factor.

This is actually one of the limitations of the most common way of teaching SR, that it focuses on inertial frames and calculated frame-dependent quantities, and invites confusion of frame-dependent quantities with invariants.

I should have said that any physical process in one IRF appears slower to an observer in a different IRF that is moving relative to the process IRF.

No. What appears is what I described as seen above. There is no direct observable that corresponds to the frame-dependent calculated time dilation. (There can't be, because frame-dependent quantities can never be direct observables.)

 

[PeterDonis]

Then their age difference is still frame-dependent.

No, it isn't. The fact that they are at rest relative to each other is not frame-dependent; it is invariant. What you are calling the "age difference" can therefore be confirmed using round-trip light signals whose round-trip travel time, according to either twin's clock, will be unchanging and invariant. So the "age difference" can be expressed entirely in terms of invariants.

It is true that you could construct a frame-dependent "age difference" in some other frame by assigning coordinate times to various events on the two twins' worldlines; but these coordinate times would not correspond to any direct observables, since they would not match up with the actual readings on the twins' clocks or the information the twins could exchange using round-trip light signals between them.

 

[PeroK]

Assume, the traveling twin just came back from Alpha Centauri and both twins are now sitting in a room on Earth with a constant distance of 1.5 meters from each other in their common restframe. Then their age difference is still frame-dependent.

Does the age difference in their common rest frame have no physical significance?

I can answer that one tomorrow if no one else does in the meantime.

 

[MikeLizzi]

Then what would you say is happening during the inertial flight stages of the trip? What does each one think about the aging process of the other. If there is some difference between them, why?

I have not read every post by FactChecker, but I agree with this one.
Given two inertial observers, each must consider the other's clock to be running slower (or the same). Each must consider the other guy ages slower (or the same). That's basic SR.

Why can't people just agree on this?
The traditional Twins Paradox as described, an astronaut moving at relativistic speed wrt an inertial observer instantly changing velocity to one of relativistic speed in the opposite direction, is physically impossible. One should not be surprised to get impossible answers when applying the correct laws of physics to an impossible behavior.

 

[A.T.]

The traditional Twins Paradox as described, an astronaut moving at relativistic speed wrt an inertial observer instantly changing velocity to one of relativistic speed in the opposite direction, is physically impossible. One should not be surprised to get impossible answers when applying the correct laws of physics to an impossible behavior.

What "impossible answers"?

 

[MikeLizzi]

What "impossible answers"?

The impossible answer is that each twin considers the other to be younger.

 

[PeterDonis]

Given two inertial observers, each must consider the other's clock to be running slower (or the same). Each must consider the other guy ages slower (or the same). That's basic SR.

No, it isn't. All that "basic SR" says is that frame-dependent "time dilation" is symmetric; but frame-dependent "time dilation" is not a direct observable. "Ages slower" implies that there is a direct observable corresponding to "time dilation". There isn't.

Why can't people just agree on this?

Because it's wrong.

The traditional Twins Paradox as described, an astronaut moving at relativistic speed wrt an inertial observer instantly changing velocity to one of relativistic speed in the opposite direction, is physically impossible.

The traditional twin paradox does not require an instantaneous turnaround. That is an idealization. It is easy to set up a realistic scenario in which the elapsed time for the astronaut during turnaround is negligibly short compared to the elapsed times of the outbound and inbound inertial legs of his trip. The latter is really all that is required to simplify the calculations that show that the traveling twin has aged less when the twins meet again (i.e., to avoid having to make a more complicated computation of the actual elapsed time for the traveling twin during the turnaround).

 

[PeterDonis]

The impossible answer is that each twin considers the other to be younger.

Even the idealization in which the turnaround is instantaneous does not give that answer. See, for example, the discussion in this thread:

https://www.physicsforums.com/threads/potential-energy-formula-in-special-relativty.991687/

 

[MikeLizzi]

Even the idealization in which the turnaround is instantaneous does not give that answer. See, for example, the discussion in this thread:

https://www.physicsforums.com/threads/potential-energy-formula-in-special-relativty.991687/

Potential Energy formula? What's the purpose for introducing the potential energy formula into this thread? Are you saying the traditional method for solving the twins paradox in textbooks is wrong? Do you recognize that the traditional method gives an incompatible answer to the answer in your reference?

 

[Vanadium 50]

Right. Call them observer A and B if you prefer

And Observer B's clock is always slower?

You're trying to keep a very un-relativistic view. This will not work.

 

[PeterDonis]

Are you saying the traditional method for solving the twins paradox in textbooks is wrong?

What do you think the "traditional method" is? Can you give a reference? I suspect you are misunderstanding what the "traditional method" actually is.

 

[PeterDonis]

What's the purpose for introducing the potential energy formula into this thread?

Because one way of addressing the twin paradox is to adopt a non-inertial frame for the traveling twin, and in such a frame there will be a nonzero "pseudo-gravitational" potential energy difference during the turnaround.

I suggest that you read the Usenet Physics FAQ article on the twin paradox that was linked to earlier in this thread. You seem to be uninformed about the various possible ways of approaching it.

 

[MikeLizzi]

No, it isn't. All that "basic SR" says is that frame-dependent "time dilation" is symmetric; but frame-dependent "time dilation" is not a direct observable. "Ages slower" implies that there is a direct observable corresponding to "time dilation". There isn't.
Because it's wrong.
The traditional twin paradox does not require an instantaneous turnaround. That is an idealization. It is easy to set up a realistic scenario in which the elapsed time for the astronaut during turnaround is negligibly short compared to the elapsed times of the outbound and inbound inertial legs of his trip. The latter is really all that is required to simplify the calculations that show that the traveling twin has aged less when the twins meet again (i.e., to avoid having to make a more complicated computation of the actual elapsed time for the traveling twin during the turnaround).

Dropping the relevance of acceleration by making it negligibly short doesn't work. As the turnaround time gets smaller the magnitude of the acceleration gets bigger. You know that. The contribution of relative aging to the problem stays the same. Consider fuel consumption for the space trip. Coast at constant velocity wrt Earth to Alpha Centuri. No fuel consumed there. Neglect the trunaround because it is so small. Coast at constant velocity back to Earth. Fuel consumption = 0. Someone should tell NASA.

 

[PeterDonis]

Dropping the relevance of acceleration by making it negligibly short doesn't work.

Nobody is claiming that acceleration is not "relevant" simply because we idealize the turnaround to be instantaneous. In fact, the entire point of the other thread I linked to is that (as both my posts in the thread and the papers referenced show), even if we idealize the turnaround time as negligibly short for the traveling twin, we cannot ignore the time elapsed during the turnaround for the stay-at-home twin.

Neglect the trunaround because it is so small.

Nobody is claiming that the turnaround does not exist or can be neglected in all respects simply because we idealize it as being instantaneous. You are responding to a straw man.

I am beginning to think you are trolling.