Dilation and inertial frames

[victorqedu]

Twin A says: "Twin B travels away and ages slowly, then he travels back and ages slowly, all according to Lorentz equation."

Before reading further the reader may perhaps want to to try to think what twin B might say.

Twin B says:

"Twin A travels away and ages slowly, then he travels back and ages slowly, all according to Lorentz equation. In the middle a GR thing happens, which thing is fast aging of A"

Twin A's comment to the above: "I don't remember any fast aging of myself."

 

According to wikipedia example the Lorentz factor is calculated from the point of view of the stationary twin and is applied only to the space and time of the twin that accelerates..

http://en.wikipedia....pecific_example

This solves the standard twin problem and is even intuitive.

 

The question remains this:

Let's say that there are 2 ships.

Both are accelerating in opposite directions with a different acceleration for some time and then they return to the start point(still with asymmetric accelerations).

Accelerations are still instant.

Now I can't apply Lorentz factor.

How do I compute the age of the each twin?

[md65536]

Let's say that there are 2 ships.

Both are accelerating in opposite directions with a different acceleration for some time and then they return to the start point(still with asymmetric accelerations).

Accelerations are still instant.

Now I can't apply Lorentz factor.

How do I compute the age of the each twin?

Calculate it from the perspective of an additional observer that remains inertial.

In your example, you could still use "Earth" as the start/end point and an inertial observer. Calculate the aging of twin A relative to Earth. Do the same for B. Since A and B reunite at the start point (this is how you set it up, correct?), they do so "simultaneously" (according to anyone), A's and B's clocks can be meaningfully compared at that point.

Edited September 2, 2013 by md65536

[victorqedu]

Calculate it from the perspective of an additional observer that remains inertial.

In your example, you could still use "Earth" as the start/end point and an inertial observer. Calculate the aging of twin A relative to Earth. Do the same for B. Since A and B reunite at the start point (this is how you set it up, correct?), they do so "simultaneously" (according to anyone), A's and B's clocks can be meaningfully compared at that point.

This is a very simple solution.

And if the acceleration is not instant?

How will I quantify now the age of the twins?

[between3and26characterslon]

This is what wikipedia says:

Explanations put forth by Albert Einstein and Max Born invoked gravitational time dilation to explain the aging as a direct effect of acceleration.

http://en.wikipedia.org/wiki/Twin_paradox

 

I agree.

The pressure can't be the cause.

Otherwise a simply pressurized box with a clock inside will have a different time.

However, the question is how do I apply the Lorentz equation to the the special relativity to explain twins paradox?

I must apply for both twins, after they meet.

And twin A should say that B is younger.

And twin B should say that A is older.

 

I don't see this happening using Lorentz factor. If I use Lorentz factor than:

Twin A should say that B is younger.

Twin B should say that A is younger.

 

:bold mine:

 

You must NOT apply for both twins. It only works for an inertial observer, the twin that accelerates is not inertial.

 

http://www.einstein-online.info/spotlights/Twins

Edited September 3, 2013 by between3and26characterslon

[victorqedu]

:bold mine:

 

You must NOT apply for both twins. It only works for an inertial observer, the twin that accelerates is not inertial.

 

http://www.einstein-online.info/spotlights/Twins

 

I understand this now.

My last question remains:

If the acceleration is not instant how do I compute the age of the twins ?

[Iggy]

I understand this now.

My last question remains:

If the acceleration is not instant how do I compute the age of the twins ?

 

You use the relativistic rocket equation

[swansont]

This is a very simple solution.

And if the acceleration is not instant?

How will I quantify now the age of the twins?

 

You have to calculate the dilation for the whole path. Knowing the acceleration allows you to calculate the velocity, so this is solvable.

[victorqedu]

This is a great forum on all domain I posted.

Does this forum represents an educational institution?

[DimaMazin]

I have not read all the post from here http://www.scienceforums.net/topic/74683-acceleration-is-not-important-in-the-twin-paradox/.

But I think is counter productive to read it all.

My original post is solved, I understand it.

But bigger problems appeared now.

 

My next question is about the twin paradox - just the standard version, using just special relativity.

It seems to me that in that big post has been assumed something that has not been proved.

 

Einstein special relativity theory has just 2 postulates:

1) All laws are the same in the same inertial frame.

2) c is constant.

 

How do you conclude from these 2 postulates some asymmetry will make one twin older?

And how do you conclude that the twin that left the earth will be younger and not the other way?

 

I read how the Lorentz factor is derived and this is clear.

I even saw a few explanations of the twin paradox that are very nice. Here they are:

https://www.youtube.com/watch?feature=player_embedded&v=7ce970Pq82s

 

But all of them have the same problem.

If you watch from the other perspective you will see the same thing(the other twin will be younger)

 

I understand that one twin makes a U turn and changes direction.

But from the other twin perspective is the same symmetrical situation.

The only difference is the pressure of the acceleration felt only by one twin.

 

But I can't see how to fit this pressure in the 2 postulates stated.

Pressure it's self should not interfere at all with relativity.

So I can only conclude that the 2 twins will have the same age when they meet again?

I don't think so.

Can someone give some directions about this?

 

Then why Hafele–Keating experiment show that running clocks run slow?

Well, this is done in a gravity field. Maybe this is the answer.

 

 

There speeds work(for a slowing of time) relatively of center of the Earth,not gravitational field of Earth.Maybe relatively of gravitational fields of Earth and Sun.

[DimaMazin]

Somebody has wrongly understood me.The Earth is rotating.The Earth gravitational field is rotating with the Earth. But you should calculate a plane speed for a slowing of the plane time = speed of rotation of the atmosphere+speed of the plane in the atmosphere when the plane has eastern direction.

a plane speed for a slowing of the plane time=speed of rotation of the atmosphere - speed of the plane in the atmosphere when the plane has western direction.