Temporal distortion along train DURING Acceleration

In summary, the conversation discusses the concept of born rigid motion and its effects on time in both the stationary frame of reference and the frame of reference of an accelerating train. The train's rear clock appears to tick faster than the front clock in the stationary frame, and this is due to the higher coordinate acceleration of the train's tail. However, in the train's frame of reference, the clocks remain in sync. The conversation also mentions the importance of drawing a space-time diagram to better understand the situation.
  • #1
davidong3000
43
0
During acceleration,

will the train's rear clock appear to tick faster than the train's front clock from stationary frame of reference ?

I am asking because i don't see how else the train's rear clock would read farther into the future than the train front clock. Either the rear clock would appear to speed up or the front clock appear to slow down or both.

2nd question: if yes to above, will the train's rear clock tick faster than stationary clock from stationary frame of reference during acceleration?
 
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  • #2
davidong3000 said:
During acceleration,

will the train's rear clock appear to tick faster than the train's front clock from stationary frame of reference ?

I am asking because i don't see how else the train's rear clock would read farther into the future than the train front clock. Either the rear clock would appear to speed up or the front clock appear to slow down or both.

2nd question: if yes to above, will the train's rear clock tick faster than stationary clock from stationary frame of reference during acceleration?
Please have a critical look at
arXiv.org > physics > physics/0609118

Physics, abstract
physics/0609118


Radar echo, Doppler Effect and Radar detection in the uniformly accelerated reference frame


Subj-class: General Physics

The uniformly accelerated reference frame described by Hamilton, Desloge and Philpott involves the observers who perform the hyperbolic motion with constant proper acceleration gi. They start to move from different distances measured from the origin O of the inertial reference frame K(XOY), along its OX axis with zero initial velocity. Equipped with clocks and light sources they are engaged with each other in Radar echo, Doppler Effect and Radar detection experiments. They are also engaged in the same experiments with an inertial observer at rest in K(XOY) and located at its origin O. We derive formulas that account for the experiments mentioned above. We study also the landing conditions of the accelerating observers on a uniformly moving platform.
 
  • #3
davidong3000 said:
During acceleration,

will the train's rear clock appear to tick faster than the train's front clock from stationary frame of reference ?

I am asking because i don't see how else the train's rear clock would read farther into the future than the train front clock. Either the rear clock would appear to speed up or the front clock appear to slow down or both.

2nd question: if yes to above, will the train's rear clock tick faster than stationary clock from stationary frame of reference during acceleration?

Given that a train approximates "Born rigid motion" which can be roughlly described as keeping the distance between the head of the train and the tail of the train constant, and that there is some inertial "station frame" that represents the station that the train is pulling away from, the following remarks are true:

1) The tail of the train has a higher coordinate acceleration than the head of the train as viewed in the station frame

2) The tail of the train also has has a higher proper accelration as read out on an acclerometer traveling with the train.

3) The head and tail of the train appear, as a result, to get closer to each other in the station frame. The statement about the "distance being the same" applies not to the station frame, but the "train frame".

3) The point of view of the train is NOT an inertial frame, but an accelerated coordinate system. This is the point of view in which the head of the train has a clock which appears to tick faster than the tail.

See http://www.mathpages.com/home/kmath422/kmath422.htm for more details about born rigid motion, or any of the several recent posts on the forum talking about this topic.

It is very helpful to draw a space-time diagram for the situation, because there are several different coordinate systems and attendent notions of simultaneity in this problem.
 
  • #4
pervect said:
Given that a train approximates "Born rigid motion" which can be roughlly described as keeping the distance between the head of the train and the tail of the train constant, and that there is some inertial "station frame" that represents the station that the train is pulling away from, the following remarks are true:

1) The tail of the train has a higher coordinate acceleration than the head of the train as viewed in the station frame

2) The tail of the train also has has a higher proper accelration as read out on an acclerometer traveling with the train.

3) The head and tail of the train appear, as a result, to get closer to each other in the station frame. The statement about the "distance being the same" applies not to the station frame, but the "train frame".

4) The point of view of the train is NOT an inertial frame, but an accelerated coordinate system. This is the point of view in which the head of the train has a clock which appears to tick faster than the tail.

Pervect,

Regarding 1 & 3, I'm good there.

Regarding 2, I don't see why the train would note any accelrational differential along its length. The train doesn't appear to change at all per the passengers as it transitions frames. From the embankment, what you say would makes sense to me. But from the proper vantage of the train, I don't understand your point there?

Regarding 4, the 1st sentence looks good. However it seems that during acceleration, clocks drop out of sync only per the embankment vantage, not the train vantage. Or did I misunderstand your point there maybe?

pess
 
  • #5
pess5 said:
Pervect,

Regarding 1 & 3, I'm good there.

Regarding 2, I don't see why the train would note any accelrational differential along its length. The train doesn't appear to change at all per the passengers as it transitions frames. From the embankment, what you say would makes sense to me. But from the proper vantage of the train, I don't understand your point there?

The "proper acceleration", which one feels, can be derived from the coordinate aacceleration via a formula. The key point is that when the velocity is zero, the two concepts are the same. I.e. in a frame in which you start out at rest, your coordinate acceleration is your proper acceleration.

Given that you've already accepted the point that the coordinate accelerations of the two trains are not equal, you should therefore already be convinced that the proper accelerations are not equal either, for the proper acceleration is the same as the coordinate acceleration when the trains are not moving, and you've already accepted that the coordinate acceleration of the two trains are not equal.

The formula for correcting coordinate acceleration into proper accelration when one is moving is given at

http://en.wikipedia.org/wiki/Hyperbolic_motion_(relativity)

One can also see that the accelerations are different by looking at the space-time diagram (more below).

Regarding 4, the 1st sentence looks good. However it seems that during acceleration, clocks drop out of sync only per the embankment vantage, not the train vantage. Or did I misunderstand your point there maybe?

pess

It's very difficult to accurately describe the situation in words. I really don't know what you mean by "drop out of sync". What exact experiment do these words represent? I can't tell. Describing an experiment in exacting detail would be time consuming, and probably not all that enlightening.

Thats why I strongly recommend looking at a space-time diagram, such as the one at http://www.mathpages.com/home/kmath422/Image5456.gif. (This is an image from the page on Born rigid motion webpage, BTW). If you don't understand space-time diagrams, now is a great time to learn :-)

A space-time diagram is just a diagram of a collection of "events". Every different event in space-time has its own unique point. For a problem with 1 spatial and 1 time dimension, a space-time diagram can conveniently be drawn as a 2 d diagram. Several different space-time diagrams may represent the same physical situation, because the labels (coordinates) assigned to specific events in space-time depend on the point of view (POV) of the observer.

In this particular space-time diagram the POV of the diagram is the station frame. The red line segment on this diagram represents two points on the train "at the same time" as judged in the non-inertial train frame. The path of the train on the diagram can be seen to be a hyperbola (the mathematical analysis justifies this).

The horizontal red line segment represents the train "at rest" at the station.

The next horizontal red line segment above the first one represents the two ends of the train a short time later after the train has pulled away from the station. These two points are simultaneous in the "train frame", but you can see they are not simultaneous in the station frame.

Lines of simultaneity for the station frame would be represented on the diagram by horizontal lines.

A line of simultaneity for an observer is just a set of points that are regarded as happening "at the same time".

You can see that the lines of simultaneity for the "train frame" all pass through one point, a "pivot point". This is a consequence of the hyperbolic motion. To really see why this happens, you'd need to do some math.

Finally, as far as acceleration goes. You can see that the hyperbola on the left has a greater second derivative (curvature) than the hyperbola on the right. This means that the train on the left is accelerating harder than the one on the right.

At t=0 in the station frame, both frames have not yet started moving, so that their "felt" accelerations will be equal to their coordinate accelerations. Because we demand that the trains stay the same distance away from each other, the train on the right must accelerate less to maintain this distance.

This is related to Bell's spaceship paradox http://en.wikipedia.org/wiki/Bell's_spaceship_paradox
 
  • #6
pervect said:
The "proper acceleration", which one feels, can be derived from the coordinate aacceleration via a formula. The key point is that when the velocity is zero, the two concepts are the same. I.e. in a frame in which you start out at rest, your coordinate acceleration is your proper acceleration.

A space-time diagram is just a diagram of a collection of "events".

OK Pervect. I know Minkowski worldlines fairly well, so I'll crawl in my hole eventually here and think on it. The web links look good too. Thanx much, highly appreciated. I'll come back & bug you if I get stumped anywhere.

pess
 

1. How does acceleration affect temporal distortion along a train?

Acceleration can cause a change in the perception of time for observers on a moving train. As the train accelerates, the passengers inside may experience a shift in their perception of time due to the change in velocity. This can result in either an apparent slowing down or speeding up of time, depending on the direction of acceleration.

2. Is there a difference in temporal distortion between acceleration and deceleration?

Yes, there can be a difference in temporal distortion between acceleration and deceleration. As mentioned, acceleration can cause a change in the perception of time for observers on a moving train. However, deceleration can also have an effect on temporal distortion, as it involves a change in velocity. The specific impact on temporal distortion may vary depending on the magnitude and direction of the deceleration.

3. Can temporal distortion along a train during acceleration be measured?

Yes, temporal distortion can be measured using various methods such as clocks or physiological responses. However, the results may differ depending on the specific circumstances and factors involved, such as the speed of the train, the duration of acceleration, and the individual's perception of time.

4. Does the length of the train affect temporal distortion during acceleration?

The length of the train may have an impact on temporal distortion during acceleration. As the train accelerates, the change in velocity may not be consistent throughout the entire length of the train. This can result in varying degrees of temporal distortion for passengers in different sections of the train.

5. How does the speed of the train impact temporal distortion during acceleration?

The speed of the train can have a significant effect on temporal distortion during acceleration. Generally, the faster the train is moving, the greater the change in velocity and the stronger the impact on the perception of time. This can result in a more noticeable temporal distortion for passengers on a high-speed train compared to a slower-moving train.

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