Dilation and inertial frames

[victorqedu]

Hello.

 

Relativity is not very clear to me and I will a question as simple as posible.

Ship A and B are moving towards eatch other with very high speeds.

First problem is how do I decide witch ship is in the inertial frame?

 

The question appeared because of this deduction:

From A's point of view B's clock is running slowly. As I think From A's point of view he is the inertial frame.

From B's point of view A's clock is running slowly. As I think From B's point of view he is the inertial frame.

The problem appears when they meet(they stop for a coffe break )

When they stop whos clock is behind?

 

Thank you.

[swansont]

Both are in inertial frames, that simply means there is no acceleration. Both think they are at rest and the other ship is moving. Both will think the other's clock is running slow. The problem is completely symmetrical in this regard.

[Delta1212]

They didn't start next to each other, so they won't agree on when they started moving with respect to each other, and thus will both believe that the other's clock is behind.

[md65536]

They didn't start next to each other, so they won't agree on when they started moving with respect to each other, and thus will both believe that the other's clock is behind.

True, but with a "coffee break" they're both together in a common frame, and they'll be able to say for certain that one clock is ahead of the other, or that the two clocks are in sync.

 

(Actually "together" is the important part for agreement, they will agree on whose clock is faster even if they just pass through the same point. They'll agree at that moment.

 

Actually... "together" OR "relatively at rest in a common inertial frame" is good enough for agreement.)

 

When they stop whos clock is behind?

 

It depends on previous conditions which you didn't specify (when and how were the clocks reset or last synchronized, and/or what were the spacetime paths that each took before getting onto their inertial collision-course trajectories). You've set it up so that A and B are symmetrical, so assuming that everything else is set up symmetrically (paths, synchronization method, whatever), then their clocks will be the same when they meet. Or you could set it up so that one of their clocks is faster (a necessarily asymmetrical setup).

 

Note that if they meet/collide at a given point, the result will be the same whether they come to rest in a frame that averages their velocities, or if they come to rest in A's frame, or in B's frame. All 3 cases will give the same answer for "whose clock is faster?" given some particular starting conditions.

Edited August 28, 2013 by md65536

[victorqedu]

If in the beginning the clock are sinchronized and if they fly in a straight line aproaching eatch other then witch clock will be ahead?

I believe the answer is that they will be synchronized.

But why?

 

If from A's point of view B's clock is running slowly.

And if from B's point of view A's clock is running slowly.

They when they meet it should be a paradox because A will say that his clock is ahead and B will say that his clock is ahead.

But these 2 statements can't be true at the same time.

 

It looks like there is something fundamental about the theory of relativity that I don't see yet.

Edited August 28, 2013 by victorqedu

[Klaynos]

They are moving together in frame c.

 

If they meet (come to a stop in frame c) for some of the journey neither frames a or b are inertial,they are accelerating, you'd need to know the nature of this acceleration to make further comments.

[victorqedu]

Both ships are stopping instantly.

So everything about them is simetrical.

In this situation how do I solve the paradox?

[Klaynos]

Both ships are stopping instantly.

So everything about them is simetrical.

In this situation how do I solve the paradox?

Stopping instantly isn't physically possible so any conclusion you form will be useless. If the system is symmetric in frame c then the clocks will agree in frame c.

[victorqedu]

Theoreticaly you can asume that they stop instantly.

But let's assume that they stop in a simetric acceleration.

 

You have exposed the problem as if both ships are in the same frame - c.

My question would be how do I solve the paradox described?

 

If from A's point of view B's clock is running slowly.

And if from B's point of view A's clock is running slowly.

They when they meet it should be a paradox because A will say that his clock is ahead and B will say that his clock is ahead.

But these 2 statements can't be true at the same time.

Edited August 28, 2013 by victorqedu

[Klaynos]

From c's point of view both clocks are running slow by the same degree thus if they symmetrically accelerate into c's frame at every moment c will see both clocks being equally slow all the way to stationary relative to c.

[victorqedu]

So there are 3 points of view. A, B and C.

From C point of view both clocks are moving slow at the same rate. A ship and B ship will stop and both clocks will show the same time.

But from A point of view B's running slower. And when A and B meet B's clock should be behind.

A and C POV's are not in agreement.

Where is the mistake?

[swansont]

So there are 3 points of view. A, B and C.

From C point of view both clocks are moving slow at the same rate. A ship and B ship will stop and both clocks will show the same time.

But from A point of view B's running slower. And when A and B meet B's clock should be behind.

A and C POV's are not in agreement.

Where is the mistake?

 

The mistake is in the unspoken assumption that there is an objectively correct time, rather than time being relative to your frame.

[J.C.MacSwell]

So there are 3 points of view. A, B and C.

From C point of view both clocks are moving slow at the same rate. A ship and B ship will stop and both clocks will show the same time.

But from A point of view B's running slower. And when A and B meet B's clock should be behind.

A and C POV's are not in agreement.

Where is the mistake?

Did A and B both agree to the synchronization according to C? Because neither would agree on that unless starting from rest in C's frame. If they did, they would see a very non symmetric acceleration and speed paths of themselves vs the other, such that the clocks would only be considered synchronized at the start and at the end and never agreeing in between. Only C would see the paths as symmetric and the clocks continuously in synch..

[victorqedu]

This is what I understood:

 

When A and B are travelling at high constant speed twoards eatch other then A will see B's clock running slow and viceversa.

Next they start to decelerate.

As a consequence of the deceleration A will se how B's clock is starting to move faster and faster until B's clock will catch up with A clock.

As a consequence of the deceleration B will se how A's clock is starting to move faster and faster until A's clock will catch up with B clock.

When they meet both clocks will move at the same rate because they are in the same frame o reference.

Because the deceleration is the same for A and B the clocks will show the same time when they meet.

 

Is this correct?

 

But if :

- A will feel no acceleration(constant speed)

and

- B would decelerate until it will be in the same frame of reference with A.

 

The one that decelerates will bave the clock behind when they meet?

Could I say that accelleration compresses space and slows time?

And since only B will feel the pressure of the aceeleration only his frame will have slow time.

Edited August 28, 2013 by victorqedu

[md65536]

If in the beginning the clock are sinchronized and if they fly in a straight line aproaching eatch other then witch clock will be ahead?

I believe the answer is that they will be synchronized.

But why?

 

If from A's point of view B's clock is running slowly.

And if from B's point of view A's clock is running slowly.

They when they meet it should be a paradox because A will say that his clock is ahead and B will say that his clock is ahead.

But these 2 statements can't be true at the same time.

 

It looks like there is something fundamental about the theory of relativity that I don't see yet.

Yes, it's "relativity of simultaneity" that you're missing.

 

You've set it up so that they're symmetrical (what A sees of B is exactly what B sees of A).

Yes, each measures the other's clock running slowly, and when they meet the clocks are the same. The solution to that paradox is that they don't measure their "starting time" as simultaneous. Observer A measures that B started earlier, and B measures that A started earlier. They don't agree on the simultaneity of their starting.

 

As others have pointed out, for an observer C who observes the symmetry, A and B start simultaneously.

The one that decelerates will bave the clock behind when they meet?

Could I say that accelleration compresses space and slows time?

And since only B will feel the pressure of the aceeleration only his frame will have slow time.

No... acceleration doesn't affect a local ideal clock.

If they meet at a point and then enter a common inertial frame, it doesn't matter whose frame that is, the result will be the same. That is, if they come together and A instantly accelerates to match B, or if B instantly accelerates to match A, the result will be the same.

 

We kind of got into a big argument about all this in another thread, so I'll just point out: "Which observer accelerates" makes a big difference while A and B are apart.

[pantheory]

Both are in inertial frames, that simply means there is no acceleration. Both think they are at rest and the other ship is moving. Both will think the other's clock is running slow. The problem is completely symmetrical in this regard.

 

This would be true for Special Relaivity, right? For General Relativity if both ships were within a system with a common center of gravity, and one ship was moving faster than the other relative to the same common center of gravity of the field, its time would be more dilated. Also if one ship was closer to that center or gravity, then that ship would have more time dilation (time moving slower) than the other ship -- unless one ship was moving relative to the center of gravity of both, while the other was closer to the center of gravity but not moving relative to it, whereby the time dilation of both might balance out between them, right? -- time for both being somewhat dialated.

 

A little convoluted but correct, no?

 

From the OP question "When they stop whos clock is behind?"

 

The aswer, I believe, would require General Relativity and the answers to the above questions concerning distances and velocities relative to a common center of gravity. Then calculations may be needed for an answer.

Edited August 29, 2013 by pantheory

[victorqedu]

 

We kind of got into a big argument about all this in another thread, so I'll just point out: "Which observer accelerates" makes a big difference while A and B are apart.

 

 

Where is this thread?

From the OP question "When they stop whos clock is behind?"

 

I would like to make abstraction of general relativity for now.

[swansont]

This would be true for Special Relaivity, right?

Yes, That's implied by the mention of inertial frames of reference.

 

For General Relativity if both ships were within a system with a common center of gravity, and one ship was moving faster than the other relative to the same common center of gravity of the field, its time would be more dilated. Also if one ship was closer to that center or gravity, then that ship would have more time dilation (time moving slower) than the other ship -- unless one ship was moving relative to the center of gravity of both, while the other was closer to the center of gravity but not moving relative to it, whereby the time dilation of both might balance out between them, right? -- time for both being somewhat dialated.

 

A little convoluted but correct, no?

 

From the OP question "When they stop whos clock is behind?"

 

The aswer, I believe, would require General Relativity and the answers to the above questions concerning distances and velocities relative to a common center of gravity. Then calculations may be needed for an answer.

Im GR you no longer have the symmetry present in the OP. Clocks deeper in a gravitational potential will tick slower. But for clocks at the same potential you can probably ignore GR and space will locally be flat, so it looks like a SR problem.

[md65536]

Where is this thread?

http://www.scienceforums.net/topic/74683-acceleration-is-not-important-in-the-twin-paradox/

 

Note that it is 20 pages long and I don't think full agreement was ever reached, and the title of the thread was admitted to be misleading and incorrectly worded, so hopefully it doesn't cause more confusion than good!

[victorqedu]

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.

 

Maybe swansont was right. I can explain this only with general relativity.

As I think to this problem it seems to me that acceleration is the key and the explanation can be done only with general relativity.

After all gravity produces acceleration.

And maybe acceleration alone produces space time deformation.

[swansont]

The asymmetry is that you can tell when you are accelerating. It's not pressure, it's that you are no longer in an inertial frame of reference.

 

The Hafele-Keating experiment showed a combination of kinematic and gravitational time dilation.

[victorqedu]

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

The asymmetry is that you can tell when you are accelerating. It's not pressure, it's that you are no longer in an inertial frame of reference.

The Hafele-Keating experiment showed a combination of kinematic and gravitational time dilation.

 

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.

[swansont]

The twins paradox occurs because you have violated the assumption that you are in an inertial frame. The twin that accelerates changes from one frame to another. You can't just use the Lorentz factor to resolve this.

[victorqedu]

Then what should I use to solve it?

Or what should I read?

I found the best example on wikipedia.

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

 

This is a very good explanation.

However I can't apply this sollution when both twins are accelerating.

So let's say that there are 2 ships A and B

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).

How do I compute now the age of the each twin?

I understand now that acceleration is not the main cause for the time dilation.

Acceleration just "pushes" one twin in another inertial frame.

From here one all time is different between the 2 twins.

So time doesn't just dilates while accelerating, it is dilating when the acceleration has stopped and when the speed is constant because of the different frame of inertia.

Edited September 1, 2013 by victorqedu

[Toffo]

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.

 

 

 

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."

Edited September 1, 2013 by Toffo