How does a physical system evolve under acceleration?

[geordief]

Full disclaimer :I have be thinking about those twins...

 

When the accelerated twin speeds off  his internal system must evolve (as does the watch in the cabin)

When they are actually under acceleration is there (in their own frame of reference) any  change in the perceived passage of time ?

 

None because the perceiver is accelerating at the same rate as the watch? 

 

What about the "view" from the the unaccelerated frame of reference of the other twin?

 

It cannot see but can it deduce that em signals (within the cabin)are being red shifted in one direction and blueshifted in the other?

 

Would that have the effect of slowing down all  interactions between all parts of the physical system?

 

If so ,would it be of any consequence that particular interactions were mediated by blueshifted signals  rather than red?

 

Is the red/blue shift aspect  just part of the overall curvature of the light (and em) signals in the cabin?

Edited April 28 by geordief

[Genady]

As you were writing that post, you were an accelerating observer, according to the equivalence principle. The ISS, for example, is a nonaccelerating one. Here are all your answers.

[swansont]

The twins paradox typically idealizes the accelerations; the clocks are set equal after the space twin is up to speed, and the turnaround takes negligible time. The only importance of the acceleration is that it shifts the space twin into a different inertial frame.

A rotating system is accelerating, and a clock in that system would tick at a rate depending on the instantaneous speed. The same would apply to a clock under continuous linear acceleration.

[geordief]

1 minute ago, swansont said:

The twins paradox typically idealizes the accelerations; the clocks are set equal after the space twin is up to speed, and the turnaround takes negligible time. The only importance of the acceleration is that it shifts the space twin into a different inertial frame.

A rotating system is accelerating, and a clock in that system would tick at a rate depending on the instantaneous speed. The same would apply to a clock under continuous linear acceleration.

I was interested in a possible mechanism whereby this could be observed(or , rather  modeled in real time.)

An observer in the  rest frame against which the acceleration takes place only interacts when the accelerated body and it "share the same event" or perhaps is close enough for a signal to be sent and returned.

 

And any observer in the accelerated frame will see the time involved in any interactions as  the proverbial "one second per second".

What about my musing in the OP  that the interactions in any system under acceleration  will(unobservably) be altered in regards to the time between them because the em radiation involved in interactions (I think) travels in a curved path and is affected by blue /red shift? 

I think I am trying to see what actually happens(or should happen)  without it being possible to verify by real time measurements.

1 hour ago, Genady said:

As you were writing that post, you were an accelerating observer, according to the equivalence principle. The ISS, for example, is a nonaccelerating one. Here are all your answers.

When the twins separate ,they could do so from a nonaccelerating point in space and time.

Have  I replied appropriately to your post?

[Genady]

2 hours ago, geordief said:

When the twins separate ,they could do so from a nonaccelerating point in space and time.

This is how the "twins' paradox" is usually set up.

[swansont]

2 hours ago, geordief said:

I was interested in a possible mechanism whereby this could be observed(or , rather  modeled in real time.)

An observer in the  rest frame against which the acceleration takes place only interacts when the accelerated body and it "share the same event" or perhaps is close enough for a signal to be sent and returned.

There were Mössbauer experiments done with rotors - the emission/absorption moves out of resonance as you increase the rotation speed.

citations 82-84 in https://en.m.wikipedia.org/wiki/Tests_of_general_relativity

 

[geordief]

7 hours ago, Genady said:

This is how the "twins' paradox" is usually set up.

Sorry ,didn't see your post.

Well I had been thinking about the twins but I was interested generally in an accelersted system ,biological or mechanical.

I was thinking how ,in a rocket that was accelerating a beam of light would ,to a  person on board  to bend.

And so it seemed to me that ,since all(I think) interactions between objects inside the rocket  would depend upon the em forces then those forces would similarly be bent.

 

So I was wondering if  the distortion of the em field inside the accelerating rocket might be responsible for time slowing as compared to the unaccelerated frame of reference of the stay at home twin (not on Earth but somewhere really unaccelerated  like ,as per your example  in the ISS as a close approximation)

If light is curved in an accelerated  frame would that  have a bearing on the way that objects inside that  accelerated frame interact with each other?

If they interact less  with each other that would mean that they (ie the system as a whole)age less,mightn't  it?

Am I wrong to see a connection between em radiation and the forces that cause interactions between objects(it would hardly be the first time I have been wrong in  our discussions!)

[pzkpfw]

You may be looking for: from the equivalence principle, clocks at the tip and base of an accelerating rocket will measure different times.

[Genady]

1 minute ago, geordief said:

Sorry ,didn't see your post.

Well I had been thinking about the twins but I was interested generally in an accelersted system ,biological or mechanical.

I was thinking how ,in a rocket that was accelerating a beam of light would ,to a  person on board  to bend.

And so it seemed to me that ,since all(I think) interactions between objects inside the rocket  would depend upon the em forces then those forces would similarly be bent.

 

So I was wondering if  the distortion of the em field inside the accelerating rocket might be responsible for time slowing as compared to the unaccelerated frame of reference of the stay at home twin (not on Earth but somewhere really unaccelerated  like ,as per your example  in the ISS as a close approximation)

If light is curved in an accelerated  frame would that  have a bearing on the way that objects inside that  accelerated frame interact with each other?

If they interact less  with each other that would mean that they (ie the system as a whole)age less,mightn't  it?

Am I wrong to see a connection between em radiation and the forces that cause interactions between objects(it would hardly be the first time I have been wrong in  our discussions!)

It is wrong to assume that physical processes during acceleration are responsible for the time dilation. Time dilation is a geometrical rather than a physical effect. It is caused by the geometry of Minkowski spacetime.

Let me describe the "twin's paradox" when nothing happens during an "acceleration".

There is a clock located at 4 lh (light-hours) from Earth which is synchronized with the clock on Earth. Let's call this point in space, T. A ship moves with the speed 0.8c past the Earth. At the moment when a clock on the ship passes the clock on Earth, it is set to whatever is the time on Earth. Let's say, 10:00. 

The ship reaches the point T in 4/0.8=5 hours in the Earth time. The clock in T, which is synchronized with the clock on Earth, shows 10:00+5=15:00 when the clock on the ship passes it. However, the clock on the ship shows at this exact point in spacetime, i.e., as the two clocks are side-by-side, 10:00+3=13:00, because the time dilation factor for the speed of 0.8c is 0.6, and thus the trip to the point T takes 5*0.6=3 hours in the ship time.

At the same exact point in spacetime, another ship passes the point T, going toward the Earth with the speed 0.8c. They grab the ship's clock and take it back to Earth. This trip back takes the same 5 hours in the Earth time and the same 3 hours in the ship time. 

So, when the clock returns to Earth, the clock on Earth shows 10:00+5+5=20:00, while the returned clock shows 10:00+3+3=16:00. Done.

[geordief]

7 hours ago, Genady said:

It is wrong to assume that physical processes during acceleration are responsible for the time dilation. Time dilation is a geometrical rather than a physical effect. It is caused by the geometry of Minkowski spacetime.

Let me describe the "twin's paradox" when nothing happens during an "acceleration".

There is a clock located at 4 lh (light-hours) from Earth which is synchronized with the clock on Earth. Let's call this point in space, T. A ship moves with the speed 0.8c past the Earth. At the moment when a clock on the ship passes the clock on Earth, it is set to whatever is the time on Earth. Let's say, 10:00. 

The ship reaches the point T in 4/0.8=5 hours in the Earth time. The clock in T, which is synchronized with the clock on Earth, shows 10:00+5=15:00 when the clock on the ship passes it. However, the clock on the ship shows at this exact point in spacetime, i.e., as the two clocks are side-by-side, 10:00+3=13:00, because the time dilation factor for the speed of 0.8c is 0.6, and thus the trip to the point T takes 5*0.6=3 hours in the ship time.

At the same exact point in spacetime, another ship passes the point T, going toward the Earth with the speed 0.8c. They grab the ship's clock and take it back to Earth. This trip back takes the same 5 hours in the Earth time and the same 3 hours in the ship time. 

So, when the clock returns to Earth, the clock on Earth shows 10:00+5+5=20:00, while the returned clock shows 10:00+3+3=16:00. Done.

I was going to argue my point further  but I now see that the ship could also be traveling at a snail's pace  over a longer time and we would  get the same time dilated result.

Correct?

What difference ,I now wonder  if any  would it make if the ship was to add acceleration to its velocity?

Would that increase  the time dilation?

I  mean its average velocity was the same  but it kept accelerating and decelerating  linearly all the time..

Would it  just make the velocity picture more detailed(the ship travels further)?

 

Edited April 29 by geordief

[Genady]

43 minutes ago, geordief said:

I was going to argue my point further  but I now see that the ship could also be traveling at a snail's pace  over a longer time and we would  get the same time dilated result.

Correct?

Yes. The time dilation does not happen at some event or events along the ship's worldline, but rather accumulates along the entire worldline.

You can have a wild worldline with accelerations, decelerations, turning back and forth, etc., like this, for example:

 

You divide that line into infinitesimal straight segment. On each segment, the proper time of the traveler is \[d \tau^2 = dt^2-dx^2\]. Then you integrate, \[\int{d \tau}\] to obtain the total time of the travel on the traveler's clock.

43 minutes ago, geordief said:

What difference ,I now wonder  if any  would it make if the ship was to add acceleration to its velocity?

Would that increase  the time dilation?

I  mean its average velocity was the same  but it kept accelerating and decelerating  linearly all the time..

Would it  just make the velocity picture more detailed(the ship travels further)?

Just a matter of calculation, see above.

Edited April 29 by Genady

[geordief]

32 minutes ago, Genady said:

Yes. The time dilation does not happen at some event or events along the ship's worldline, but rather accumulates along the entire worldline.

You can have a wild worldline with accelerations, decelerations, turning back and forth, etc., like this, for example:

 

You divide that line into infinitesimal straight segment. On each segment, the proper time of the traveler is

dτ2=dt2−dx2

. Then you integrate,

∫dτ

to obtain the total time of the travel on the traveler's clock.

 

Just a matter of calculation, see above.

If we had a snail's pace (with no extra acceleration or deceleration)  the difference in the clocks would be similar or identical but  ,as an example it could be a billion years as against a billion and one years , depending on a great  distance and a slow speed.Make sense?  

It only stands out as remarkable when the speeds are relativistic.

[swansont]

58 minutes ago, geordief said:

If we had a snail's pace (with no extra acceleration or deceleration)  the difference in the clocks would be similar or identical but  ,as an example it could be a billion years as against a billion and one years , depending on a great  distance and a slow speed.Make sense?  

It only stands out as remarkable when the speeds are relativistic.

Driving across the US and back at highway speeds accumulates a couple of nanoseconds of time dilation. Most can ignore it, but if you’re transporting an atomic clock (as part of a calibration effort) you have to account for it. The quality of the clock matters, too.