How is twin paradox resolved in case of no/zero acceleration?

[lovetruth]

A does not kill B in A's frame.

A kills B, period.

A B or C can then each use their own frames to measure what happened.

In A's frame, A kills B. Thats the question, you can not change it.

I know the question looks insane as it involves killing. But I had no other option to demonstrate how weird things become when both the twins see themselves older.

The same weirdness will be encountered when twins exchange photos in which they both are present.

 

[Dale]

If twin A is on a bike while B is on ground.

HOLD ON! I think there has been a HUGE miscommunication here.

Everyone who is responding that the ages are relative is assuming that A and B are spatially separated as would be implied by your no-acceleration version of the twins scenario. It sounds like you are assuming that A and B are spatially close together.

There is no unique answer as to which of two spatially separated objects is older. The reason for that is because of the relativity of simultaneity (http://en.wikipedia.org/wiki/Relativity_of_simultaneity). Different frames will disagree on whether or not two events are simultaneous, so one frame may say A's 50th birthday on Andromeda was at the same time as B's 25th birthday on Earth, while someone else would say, no A's 50th birthday was a little bit earlier than B's 25th birthday.

If two objects are colocated then simultaneity is irrelevant and the relative age is an absolute quantity that all frames agree on.

 

[Doc Al]

In A's frame, A kills B. Thats the question, you can not change it.

It makes no sense to say 'in A's frame'. B is simply killed. The only question is when was he killed.

 

[lovetruth]

In every frame B is 25 years old when he dies. Of course, according to B-frame observers, A was only 12.5 years old when B was killed.

Why should B be 25 when he die in all frame? Why can't A be 50 when he kills in all frame. Your answer is biased.

 

[Doc Al]

Why should B be 25 when he die in all frame? Why can't A be 50 when he kills in all frame. Your answer is biased.

What do you mean? You said B is killed when he's 25, right? EVERYBODY must agree with that--we can just check the body. Relativity isn't that strange.

The part that's strange--until you get used to it--is how old A is when B is killed. According to A-frame observers, he's 50. But different observers will calculate different ages for A at the moment when B is killed. You seem to think that A 'really is' twice as old as B at all times for all observers. Not so.

Actually, your answer is biased. You think there's something special about A's frame.

 

[lovetruth]

It sounds like you are assuming that A and B are spatially close together.

Time Dilation depends only upon relative velocity and not on proximity. Why can't the path of observers cross if they are not accelerating.

 

[tiny-tim]

Why can't A be 50 when he kills in all frame.

If it's a knife, A is 50 when he kills in all frames.

If it's long-distance (which is what Doc Al was then talking about), then the words "when he kills" are ambiguous, they mean different things in different frames,

and that's how A can be 12.5 !

 

[Dale]

Time Dilation depends only upon relative velocity and not on proximity.

Time dilation is the rate of ageing, not the age. Those are two distinct concepts. Do you understand the difference?

 

[lovetruth]

What do you mean? You said B is killed when he's 25, right? EVERYBODY must agree with that--we can just check the body. Relativity isn't that strange.

I only said that A sees that B was 25 when he killed him. Why the act of being killed is same in all frame rather than the act of killing be same in all frame. I see prejudice in your view.

 

[tiny-tim]

Why the act of being killed is same in all frame rather than the act of killing be same in all frame. I see prejudice in your view.

Because "B dying" is unambiguous, it describes a unique event.

"A killing B" is ambiguuous, it describes an earlier event than B dying, doesn't it?

(and it describes a different event in different frames)

 

[rede96]

I don't know if this will help, but I found it useful to get my head around this problem.

Let’s say twin A and twin B are on earth, aged say 40. Twin B gets in his rocket ship and sets off for a round trip to the stars at some relativistic speed. Also, let’s say that B is traveling fast enough so A ages 40 years while B ages 10.

Imagine both twins have really powerful cameras that can see each other for the duration of B's round trip. They also keep their cameras recoding constantly. However, the twins don't actually see each other during the trip.

After 10 years, B turns around and returns to his twin, so 20 years have past for B for the round trip. When he gets back he finds that his brother died 40 years ago at age 80, but B is only 60. So 80 years have past where A was, but only 20 for B.

What happened?

B finds A's camera and sets both of them to watch together. What would he see? Oddly when he plays both videos back together at super fast forward speeds, for the first 10 years A's video shows B aging less and B's video shows A aging less at the same rate!

Then, after a time index of 10 years (When B turned around) B's camera showed something strange happen, A rapidly starts to age (It may happen instantaneously, I am not sure.) and he sees his twin die of old age, 80 years old. On A's camera he doesn't see this same effect for himself.So the point is that as twins are traveling wrt to each other, they will both see each other age slower, which is an effect of traveling through space time relative to someone else. It acts like a two-way time mask, which makes us see time in another frame pass at a slower rate and vise-versa.

However, when B breaks that symmetry of them both moving wrt to each other by turning around, common sense catches up and we get to see what has really been going on. And that is that A was indeed aging faster than B

 

[lovetruth]

Because "B dying" is unambiguous, it describes a unique event.

"A killing B" is ambiguuous, it describes an earlier event than B dying, doesn't it?

(and it describes a different event in different frames)

Nothing is ambiguous everything is certain. If A kills then B dies.

 

[lovetruth]

I don't know if this will help, but I found it useful to get my head around this problem.

Let’s say twin A and twin B are on earth, aged say 40. Twin B gets in his rocket ship and sets off for a round trip to the stars at some relativistic speed. Also, let’s say that B is traveling fast enough so A ages 40 years while B ages 10.

Imagine both twins have really powerful cameras that can see each other for the duration of B's round trip. They also keep their cameras recoding constantly. However, the twins don't actually see each other during the trip.

After 10 years, B turns around and returns to his twin, so 20 years have past for B for the round trip. When he gets back he finds that his brother died 40 years ago at age 80, but B is only 60. So 80 years have past where A was, but only 20 for B.

What happened?

B finds A's camera and sets both of them to watch together. What would he see? Oddly when he plays both videos back together at super fast forward speeds, for the first 10 years A's video shows B aging less and B's video shows A aging less at the same rate!

Then, after a time index of 10 years (When B turned around) B's camera showed something strange happen, A rapidly starts to age (It may happen instantaneously, I am not sure.) and he sees his twin die of old age, 80 years old. On A's camera he doesn't see this same effect for himself.


So the point is that as twins are traveling wrt to each other, they will both see each other age slower, which is an effect of traveling through space time relative to someone else. It acts like a two-way time mask, which makes us see time in another frame pass at a slower rate and vise-versa.

However, when B breaks that symmetry of them both moving wrt to each other by turning around, common sense catches up and we get to see what has really been going on. And that is that A was indeed aging faster than B

Read the title: No acceleration.

 

[Doc Al]

I only said that A sees that B was 25 when he killed him.

A obviously didn't personally kill B--they are a zillion miles apart. (Or are they? If you mean something else, define it exactly.)

Why the act of being killed is same in all frame rather than the act of killing be same in all frame.

Please describe exactly how B is killed. In fact, describe the entire scenario from the top.

I see prejudice in your view.

And I see ignorance in yours.

 

[harrylin]

Momentum is frame dependent but the application of Newtons law give same results in all frames. If bullet with 1 kgm/s will kill a person in one frame then, bullet with 0 kgm/s will kill the same person in another frame. All frames give same result.

But time dilation gives different result of a physical phenomena like ageing. The observation is affected by the choice of frame.

Let's see, we can directly transpose your Newtonian assertions on SR. then we get:

Time dilation is frame dependent but the application of SR gives same results in all frames. If a traveler is found to have aged more than another person when they meet up as measured in one frame then, the same traveler at 0 m/s will also be found to have aged more than that other person when they meet up as measured in another frame. All frames give same result.

Yes, that is correct, our example stood the test.
What matters here, is that we can only agree about when things happen nearby (at one place); how long ago things happened far away depends on our assumption of how fast we are moving, and in which direction.

Harald

 

[rede96]

Read the title: No acceleration.

Ok, I was waiting for that.

Imagine B doesn't turn around and simply switches off his camera. He sends a message to his twin to do the same. He is now 10 light years away from his twin, so the message takes 10 years to get back to A.

Then, sometime in the future, say another 10 years for B, B decides to return to A.

He still finds the same situation, A has been dead for 40 years, dying at age 80.
EDIT: Was a bit too quick on the post button there. Obviously, this is not the case as B has been away for 40 years. But the point is still relevant.

This time when he plays the camera, what does he see?

Firstly, A didn’t get the message to switch his camera off as he was dead.
Secondly, B sees exactly the same as the first scenario, where A is aging less than B and vise-versa. As the cameras were switched off with no acceleration taken place.

B's return to A in not important in this, as the cameras were only recording while they were in relative motion.

 

[Dale]

Nothing is ambiguous everything is certain. If A kills then B dies.

If A kills B while they are located next to each other then everyone will agree on their ages when B dies.

If A kills B while they are distant then everyone will agree on B's age when B dies, but they will disagree on A's age when B dies. The exact value of A's age when B dies is not a "physical fact" and it has no physical significance or consequences. It is a matter of "naming convention", just like left and right.

That is what the relativity of simultaneity means. That is one of the three key features of the Lorentz transform (time dilation, length contraction, relativity of simultaneity).

 

[San K]

in summary (does this sound ok?, though no detailed enough)

Twin paradox where twins meet

Is resolved by the fact that:

One (or even both in a more complex scenario) of them would have to undergo acceleration/deceleration and change/switch frames of reference to compare in the same frame of reference.

Twin paradox where twins do not meet

Is resolved by the fact that:

Both are in different frames of reference and not comparable.
Both are correct if they say the other aged faster because they both are right in their frame of reference/point of view.

one of them has to be brought into the frame of reference of the other (or both have to be bought to some same frame of reference) and the "apparent paradox" is resolved.There are no paradoxes (in life/science etc), it simply means our knowledge/information is incomplete...;)

 

[lovetruth]

A obviously didn't personally kill B--they are a zillion miles apart. (Or are they? If you mean something else, define it exactly.)

Please describe exactly how B is killed. In fact, describe the entire scenario from the top.

And I see ignorance in yours.

If A kills B while they are located next to each other then everyone will agree on their ages when B dies.

If A kills B while they are distant then everyone will agree on B's age when B dies, but they will disagree on A's age when B dies. The exact value of A's age when B dies is not a "physical fact" and it has no physical significance or consequences. It is a matter of "naming convention", just like left and right.

That is what the relativity of simultaneity means. That is one of the three key features of the Lorentz transform (time dilation, length contraction, relativity of simultaneity).

For people having difficulty how can A kills B(although i have told that A while ridding on a bike stabbed B ), I present you another version of the tale/question.

In A's frame, A is 50 while B is 25. B dies due to illness(choose your pick: cancer, aids, heart failure, infectious disease) or killed by someone else or killed himself(poison, bullet).
Q: In B's frame, at what age did B died and what was the age of A at the time of death of B?

 

[Dale]

In A's frame, A is 50 while B is 25. B dies due to illness(choose your pick: cancer, aids, heart failure, infectious disease) or killed by someone else or killed himself(poison, bullet).
Q: In B's frame, at what age did B died and what was the age of A at the time of death of B?

25 and 12.5

 

[San K]

If A kills B while they are distant

this can only happen if something is sent from A to B and the max speed it can be sent is speed of light. when accounted for that and transition to B's frame of reference all paradoxes/confusion disappears?

however if we were to take a case where A can kill B instantaneously from a distant:

would it work? i mean would the whole thing won't integrate into the theory of relativity. won't we have "mismatches" that cannot be explained?

 

[Dale]

this can only happen if something is sent from A to B and the max speed it can be sent is speed of light. when accounted for that and transition to B's frame of reference all paradoxes/confusion disappears?

Yes.

if we were to take a case where A can kill B instantaneously from a distant:

would it work? i mean would the whole thing won't integrate into the theory of relativity. won't we have "mismatches" that cannot be explained?

If you make an unphysical assumption you will get unphysical conclusions.

 

[lovetruth]

25 and 12.5

How you got these numbers?

 

[Dale]

A and B are perpetually inertial twins separated at age 0, correct? B is 25 when he dies in all frames. Therefore, since in A's frame A is 50 when B dies the time dilation factor is 2. 25/2 is 12.5 so A is 12.5 years old in B's frame when B dies.

 

[San K]

they don't disagree on their age, they disagree on their rate of ageing

(they don't disagree on their age because they can't make measurements at what they both agree is at the same time)

Well don't they disagree on both?

1. rate of aging
and
2. age

because for 2, so just need to bring them both into same frame of reference and compare.

they can make measurements by bringing them (stationary and moving twin) into the same frame of reference at a particular point in time.

both are correct and it depends upon who is brought into the frame of reference of who, or more generally, what frame of reference are they finally compared in?

i.e. whether the stationary Earth is accelerated to match the speed of the spaceship

or the spaceship is slowed down to (a stand-still) to match the speed of the spaceship

or some other common/same frame of reference

 

[tiny-tim]

Well don't they disagree on …
2. age

No!

… it depends upon who is brought into the frame of reference of who …

exactly! … so what are they disagreeing on?

 

[San K]

No!


exactly! … so what are they disagreeing on?

when they are in same frame of reference there is no disagreement.


however when they are in different frames of reference (speed) then

isn't there disagreement on both

1. rate of aging
2. age

however it certainly gets resolved when the bought on same frame of reference

for example there are twins A and B.

A says B is older, B says A is older

now both are correct, however if only one of them (A or B) is brought to the other's frame of reference...then in hindsight, we can say...who was correct...

i.e. we can make either of A or B to be correct, in a sense, depends upon who moves ...assuming...only one of them is allowed to "move" (back into others frame of reference)

 

[tiny-tim]

for example there are twins A and B.

A says B is older, B says A is older

now both are correct

yes

… , however if only one of them (A or B) is brought to the other's frame of reference...then in hindsight, we can say...who was correct...

no!

they were both correct …

you just said so yourself!​

 

[San K]

yes


no!

they were both correct …

you just said so yourself!​

they both are correct, when far...i.e. different frame of reference.

however when brought into same frame of reference...depending upon who was moved (taking a simple case) ...one of them will be older than other...

 

[tiny-tim]

they both are correct, when far...i.e. different frame of reference.

however when brought into same frame of reference...depending upon who was moved (taking a simple case) ...one of them will be older than other...

Yes, but they were still both correct …

where is the paradox? ​

 

[harrylin]

when they are in same frame of reference there is no disagreement.

In classical physics as well as in SR, they are always in the same reference system; as a matter of fact, they are always in an infinite number of reference systems.

Is that clear to you so that it's just a matter of formulation, or are you perhaps not familiar with the definitions of classical mechanics?

[...] i.e. we can make either of A or B to be correct, in a sense, depends upon who moves ...assuming...only one of them is allowed to "move" (back into others frame of reference)

Whatever inertial reference system you choose, the prediction will be the same.
For example:

1. As determined with a system in which the "stay-at-home" is always in rest (approximately):
- Nearly all the time the traveler's clock appears to be slowed down due to speed.

2. As determined with a system in which the traveler is in rest during the first leg:
- Nearly all the time the stay-at-home's clock appears to be slowed down due to motion.
- during the second leg the traveler appears to move much faster than the stay-at-home, and his clock appears to be much more slowed down.

Calculation shows - as it ought to be - that the results of both descriptions are the same.

Harald

 

[D H]

Twin paradox where twins do not meet

Is resolved by the fact that:

Both are in different frames of reference and not comparable.
Both are correct if they say the other aged faster because they both are right in their frame of reference/point of view.

No!

Special relativity uses the same concept of a reference frame as does Newtonian mechanics. Reference frames extend to infinity. An object can be described from the perspective of any frame of reference, but the object isn't "in" anyone of those frames (to the exclusion of others).

As far as the resolution of the paradox, what paradox? There is only an apparent paradox that results from the erroneous thinking that because A sees himself as being older than B then B must necessarily see herself as being younger than A. There is no paradox here; there is only erroneous thinking.