The twin paradox is mutual

[worlov]

The time dilation in relativity is relative. Every observer sees that the clock of another moving observer slows down. However, the twin paradox shows that time can indeed slow down. The twin paradox is not mutual... But I think I have discovered the trick. Everything depends on who determines the distance of the trip. Does the twin who remained on Earth do that, then this twin ages faster. And vice versa: Does the travelling twin do that in his frame during the outward journey, then this twin ages faster. 

The difference is the length contraction. The twin who sees the route from another reference system sees this route shortened. Therefore, he needs less time to travel this route.

Best regards
Walter Orlov

[swansont]

2 hours ago, worlov said:

The time dilation in relativity is relative. Every observer sees that the clock of another moving observer slows down. However, the twin paradox shows that time can indeed slow down. The twin paradox is not mutual... But I think I have discovered the trick. Everything depends on who determines the distance of the trip. Does the twin who remained on Earth do that, then this twin ages faster. And vice versa: Does the travelling twin do that in his frame during the outward journey, then this twin ages faster. 

The difference is the length contraction. The twin who sees the route from another reference system sees this route shortened. Therefore, he needs less time to travel this route.

But that's true even for a one-way trip, in which the time dilation is indeed symmetric. If a rocket ship and earth start their clocks simultaneously (when they are co-located), each will see the other clock as running slow as the rocket ship goes to some destination. But an earthbound observer and the rocket observer agree that physics is working just fine on the trip. If the destination was 2 LY away according to the earth observer and gamma was 2, then the rocket observer will see the trip as lasting half the time as in the earth frame because the distance in that frame was 1 LY.  The physics of d = vt works exactly the same, as it must.  

The twin paradox is not mutual because once you accelerate you change your frame of reference. That breaks any symmetry you had. There are a number of threads where this is discussed and in which Janus gives excellent explanations of this phenomenon.

[worlov]

2 hours ago, swansont said:

If the destination was 2 LY away according to the earth observer and gamma was 2, then the rocket observer will see the trip as lasting half the time as in the earth frame because the distance in that frame was 1 LY.  The physics of d = vt works exactly the same, as it must.  

And that applies vice versa. If the destination was 2 LY away according to the rocket observer (the lower half of the picture), then the earth observer will see the trip 1LY long.

[studiot]

I can't honestly see anything objectionable in the OP so I have placed a +1 to counter the negative.

[michel123456]

5 hours ago, swansont said:

But that's true even for a one-way trip, in which the time dilation is indeed symmetric. If a rocket ship and earth start their clocks simultaneously (when they are co-located), each will see the other clock as running slow as the rocket ship goes to some destination. But an earthbound observer and the rocket observer agree that physics is working just fine on the trip. If the destination was 2 LY away according to the earth observer and gamma was 2, then the rocket observer will see the trip as lasting half the time as in the earth frame because the distance in that frame was 1 LY.  The physics of d = vt works exactly the same, as it must.  

The twin paradox is not mutual because once you accelerate you change your frame of reference. That breaks any symmetry you had. There are a number of threads where this is discussed and in which Janus gives excellent explanations of this phenomenon.

Actually it is called a "paradox" because it appears at first sight mutual. The paradox appears when both observers are mutually older than the other one. Once it has been explained by Janus that it is not mutual, the paradoxal effect disappear and becomes "normal".

The "normal" thing is that one observer is older than the other one.

[swansont]

2 hours ago, worlov said:

And that applies vice versa. If the destination was 2 LY away according to the rocket observer (the lower half of the picture), then the earth observer will see the trip 1LY long.

Why? We've already established that the rocket will see the distance as half of what the earth sees. It can't simultaneously be half and twice that value.

 

11 minutes ago, michel123456 said:

Actually it is called a "paradox" because it appears at first sight mutual. The paradox appears when both observers are mutually older than the other one. Once it has been explained by Janus that it is not mutual, the paradoxal effect disappear and becomes "normal".

The "normal" thing is that one observer is older than the other one.

Until the acceleration occurs, the two observers each think the other's clock is the one running slow. It is mutual up to that point. The apparent paradox is the naive expectation that it will continue afterwards.

[worlov]

1 hour ago, swansont said:

Why? We've already established that the rocket will see the distance as half of what the earth sees. It can't simultaneously be half and twice that value.

As I said, it depends on who determines the journey. 

In usual representation this makes the twin on earth. He chooses a star that rests in his frame. In his view, the traveling twin must fly the full length of the route. That's why the journey takes the longest. The traveling twin, however, sees the route shortened due to the length contraction. As a result, the journey takes shorter.

Now we let the traveling twin determine the destination of the journey. He finds an object, e.g. a meteroid, in the direction from the other side of the earth (see picture). This meteroid rests in the frame of the traveling twin. Together they fly relative to the earth (sun). From the perspective of the traveling twin, the earth should pass the full distance to the meteroid. That's why the journey takes the longest in his frame. However, because of the length contraction, the twin on Earth sees the meteroid closer. That's why the journey will be shorter for him.

In addition, the twin paradox is mutual.

[swansont]

19 minutes ago, worlov said:

As I said, it depends on who determines the journey. 

In usual representation this makes the twin on earth. He chooses a star that rests in his frame. In his view, the traveling twin must fly the full length of the route. That's why the journey takes the longest. The traveling twin, however, sees the route shortened due to the length contraction. As a result, the journey takes shorter.

The spaceship observer sees the distance as 1 LY. That's no different than before. The earth never gets to the destination, because the earth is not moving relative to the destination.

19 minutes ago, worlov said:

Now we let the traveling twin determine the destination of the journey. He finds an object, e.g. a meteroid, in the direction from the other side of the earth (see picture). This meteroid rests in the frame of the traveling twin. Together they fly relative to the earth (sun). From the perspective of the traveling twin, the earth should pass the full distance to the meteroid. That's why the journey takes the longest in his frame. However, because of the length contraction, the twin on Earth sees the meteroid closer. That's why the journey will be shorter for him.

However, this is a new measurement you have added to the problem. Such additions usually just complicate the situation.

 

[studiot]

27 minutes ago, swansont said:

The earth never gets to the destination, because the earth is not moving relative to the destination.

 

@worlov

Since you are not interested in my comments look very carefully at this one.

It contains the a most important piece of information.

[Markus Hanke]

11 hours ago, worlov said:

The difference is the length contraction.

The difference is the geometric length of the observers’ world lines, which connect the two events - and that length physically corresponds to what a clock travelling along that world line records. 

The longest possible world line between two given events is always a geodesic in spacetime - which physically corresponds to an inertial frame. However, an accelerating rocket does not trace out a geodesic, because it isn’t an inertial frame, due to the presence of proper acceleration. Therefore, the world line of the rocket is shorter, meaning less time is recorded by a co-moving clock; that is your time dilation. 

No complications need to come into this, just simply compare the geometric length of the world lines traced out by the two observers. You’ll find they are not equal. It’s that simple.

[worlov]

1 hour ago, swansont said:

However, this is a new measurement you have added to the problem. Such additions usually just complicate the situation.

It's not that easy either. What is the difference between these two cases purely practical? In the first case the traveling twin flies 1 light-year forth and back. His brother is getting older than him. In the second case the traveling twin flies a bit further, additionally 1 light-year, and back. His brother is getting younger than him...

 

37 minutes ago, studiot said:

swansont: "The earth never gets to the destination, because the earth is not moving relative to the destination."

@worlov

Since you are not interested in my comments look very carefully at this one.

It contains the a most important piece of information.

Of course, always the traveling twin flies. In the first case, his journey for the twin on earth takes the longest.

[studiot]

 

10 minutes ago, worlov said:

In the first case, his journey for the twin on earth takes the longest.

 

 

Did you not read the very short piece I referred to? The Earth twin doesn't go anywhere so makes no journey at all.

[worlov]

13 minutes ago, studiot said:

 

Did you not read the very short piece I referred to? The Earth twin doesn't go anywhere so makes no journey at all.

How long flies the traveling twin from the perspective of the twin on earth?

[koti]

I fail to see a paradox in the twin paradox. There are no contradictions and everything is logical as long as you apply SR correctly using 2 seperate inertial frames. It's annoying that a case which is perfectly logical, consistent and holds no contradictions is called a paradox. 

Edited June 12, 2018 by koti

[studiot]

3 hours ago, worlov said:

How long flies the traveling twin from the perspective of the twin on earth?

That is a strange answer to my question.

Anyway consider the following.

How can the Earth twin measure the speed of the traveller?

He can have previously measured the distance to the turnaround point by astronomical means.
That is he knows how far the target star is away.
He can set his clock to start when the traveller leaves and read it again when the traveller returns.

Thus he can calculate the speed as the distance divided by the double time in his system.

 

What about the traveller?

Well he can take a clock with him that starts as he leaves and is read again when he returns.
He will find this clock reads a different time from that of the Earth twin.
His reading however is the transit time in his system.

But what about the distance?

He has no means of measuring distance.

He has no means of directly measuring speed.

 

 

[Janus]

4 hours ago, koti said:

I fail to see a paradox in the twin paradox. There are no contradictions and everything is logical as long as you apply SR correctly using 2 seperate inertial frames. It's annoying that a case which is perfectly logical, consistent and holds no contradictions is called a paradox. 

It depends on what definition of "paradox" you use.  One definition is "a seemingly absurd or self-contradictory statement or proposition that when investigated or explained may prove to be well founded or true."

[worlov]

6 hours ago, studiot said:

What about the traveller?

Well he can take a clock with him that starts as he leaves and is read again when he returns.
He will find this clock reads a different time from that of the Earth twin.
His reading however is the transit time in his system.

But what about the distance?

He has no means of measuring distance.

He has no means of directly measuring speed.

The rocket can be built like a catamaran. In this way, the traveling twin can apply geometric parallax to determine the distance. And he will measure the time with his own clock. And calculate the speed from it. 

[studiot]

2 hours ago, worlov said:

The rocket can be built like a catamaran. In this way, the traveling twin can apply geometric parallax to determine the distance. And he will measure the time with his own clock. And calculate the speed from it. 

Over a journey distance of 5 light years from Earth?

No way.

[koti]

8 hours ago, Janus said:

It depends on what definition of "paradox" you use.  One definition is "a seemingly absurd or self-contradictory statement or proposition that when investigated or explained may prove to be well founded or true."

I wasn’t aware of multiple meanings of the concept of paradox. I was convinced it always involves self contradiction which the „twin paradox” clearly lacks. 

[swansont]

15 hours ago, worlov said:

It's not that easy either. What is the difference between these two cases purely practical? In the first case the traveling twin flies 1 light-year forth and back. His brother is getting older than him. In the second case the traveling twin flies a bit further, additionally 1 light-year, and back. His brother is getting younger than him...

No, that's not an accurate summary of the situation. There is no scenario in the standard formulation of the twin paradox where the earth-bound twin is younger at the end of the trip. 

59 minutes ago, koti said:

I wasn’t aware of multiple meanings of the concept of paradox. I was convinced it always involves self contradiction which the „twin paradox” clearly lacks. 

As with other so-called paradoxes it's because some information is missing in the original statement of the problem. The time dilation is symmetric while the twins are in inertial frames, and yet it's not symmetric in the final resolution. That's the paradox. What is missing is the realization that an acceleration is required, and the symmetry is broken. The rocket twin does not remain in the same inertial frame for the whole trip.

[koti]

44 minutes ago, swansont said:

As with other so-called paradoxes it's because some information is missing in the original statement of the problem. The time dilation is symmetric while the twins are in inertial frames, and yet it's not symmetric in the final resolution. That's the paradox. What is missing is the realization that an acceleration is required, and the symmetry is broken. The rocket twin does not remain in the same inertial frame for the whole trip.

Right. So as long as we approach this using two inertial frames and the symmetry is broken which is the only correct way to approach it, there is no paradox. „Twins age differently due to how the universe works” would be a better name for this implication of SR.