Yes, another question on relativity - the amatuer kind. I'll break my question into parts so you can point out where I am wrong in my assumptions.

Assume a train with a single carriage is heading East at a speed close to speed of light - say 0.8c.

1) inside the carriage is a system of interaction consisting of 2 devices that emitt and receive light pulses to and from each other continuosly.

2) one device is place at the front of the carriage. The other device is placed at the end of the carriage. Since the train is heading East, both devices are considered to be moving along in the same direction - East.

3) the device at the front of the carriage will receive the light pulse emitted from the device at the end at a longer time - say X times longer than compared to when the train is stationary.

4) the device at the end of the carriage will receive the light pulse emitted from the device at the front of the carriage at a shorter time - say Y times shorter than compared to when the train was stationary.

5) Is X equals to Y?
If no, why?
If yes, then can it be considered that the slowing down in one direction was compensated with the speeding up in the other direction?
If yes again, then how does the system as a whole experience the effect of slowing down (is "time-dilation" the appropriate term to use here?)

6) If the both the devices were placed in North-South positions instead while the train continues heading East, will the system of interaction experience the effect of relativity?

7) What is the fundamental level of interaction in nature? Is it quantum interaction?

8) At the fundamental level of interaction, are there directions involved - uni-directional, bi-directional, multi-directionals or no directions at all?

9) IF there are directions at the fundamental level of interaction, how do they affect the consequences of relativity?

10) Does the direction of a moving frame of reference affect the consequences of relativity? If yes, how?

That's pretty much what I'm trying to understand. Intuition tells me the principle of relativity makes sense. However, I'm trying to picture in my mind some of the related concepts like the actual physical effect of time-dilation.

Originally posted by 1119
3) the device at the front of the carriage will receive the light pulse emitted from the device at the end at a longer time - say X times longer than compared to when the train is stationary.
No. The two devices have zero relative velocity. They are in the same reference frame. They see each other as they would always see each other -- Newton's laws hold.

This is an example of the Galilean equivalence principle: if you put an experiment in a box, and send it flying off at any speed you'd like, nothing inside the box can ever detect the 'absolute' motion of the box, without looking outside. No matter how fast the train is moving to some arbitrary outside observer, things happen in the train precisely the same way you're familiar with. Since the two devices on your train are moving with zero relative velocity, everything looks exactly the same (Newtonian) inside the train, no matter what velocity the train has relative to some other object.
If yes again, then how does the system as a whole experience the effect of slowing down (is "time-dilation" the appropriate term to use here?)
The system doesn't. Inside the train, everything seems perfectly normal. Any observer inside the train sees things acting just like Newton was right all along. An observer outside the train, however -- someone standing on the side of the tracks as the train whizzes by at 0.8c -- would measure that the train's length is foreshortened, and would measure that the train's internal experiments are running slow, as compared to an identical experiment sitting beside him on the side of the tracks.
6) If the both the devices were placed in North-South positions instead while the train continues heading East, will the system of interaction experience the effect of relativity?
As you can probably answer yourself now -- no. Nothing inside the train ever experiences any kind of relativistic effect, since the relative velocities of all the things inside it are zero. Relativity only comes into play when you consider outside observers moving at high relative velocities.
7) What is the fundamental level of interaction in nature? Is it quantum interaction?
There are four fundamental forces that we know about so far -- strong, weak, electromagnetic, and gravity. The strong, weak, and electromagnetic interactions are all understood from a quantum mechanical view; gravity is not (yet). No one's quite sure exactly what gravity is just yet, nor if it will ever be demonstrated to be "the same" as the other three forces.
8) At the fundamental level of interaction, are there directions involved - uni-directional, bi-directional, multi-directionals or no directions at all?
I'm not sure exactly what you mean. If you're asking "are there high relative velocities in the subatomic domain, and does relativity accurately describe them?" the answer is yes.
9) IF there are directions at the fundamental level of interaction, how do they affect the consequences of relativity?
Relativity predicts that an observer with a high relative velocity to some object will measure (compared to an identical object in his own frame of reference) the object as being foreshortened, as having an increased mass, and as if its physical processes are running slowly. This means that when you whirl particles around in a particle accelerator, they behave as if they were more massive -- you have to use stronger magnets (much stronger!) to keep the more massive particles in the machine. They behave as if their "clocks" are running slowly -- unstable particles appear to decay much more slowly when moving at a high relative velocity. Since we can't really measure a "size" of a subatomic particle, foreshortening has not, AFAIK, been directly measured. However, all three effects (time dilation, mass increase, and foreshortening) are all results of the same simple coordinate transform. If even one of the effects happens, the other two must happen, as well.
10) Does the direction of a moving frame of reference affect the consequences of relativity? If yes, how?
Yes. Relativity is only concerned with the parallel component of the velocity vector. This means that if something is coming right at you with velocity 0.8c, you'll see all the effects I've mentioned. If however the object is going at right angles to you, so that it has no component of velocity at all in your direction, you won't see any of the effects.

- Warren

Relativity only comes into play when you consider outside observers moving at high relative velocities.


chroot,

Thanks for the lengthy reply. I think I have a better picture of it now. A few additional questions:

a) From the quote above, I get the impression that without outside observers, the effects of Relativity does not exist. Am I wrong?

b) If so, then is time-dilation an actual physical effect in the absolute sense or is it only an effect to the extent that an outside observer is there to acknowledge it?

c) If an astronaut were to journey into space for about 30 years (in his frame of reference), roughly 50 years would have passed on Earth. If he returns and stays on Earth, his peers would have aged more than him. In this case, time-dilation seems to be an actual physical effect that continue to exist even after his frame of reference stopped moving. How do I reconcile the role of observer with the seemingly continuing effect of Relativity in this case?

Originally posted by 1119
a) From the quote above, I get the impression that without outside observers, the effects of Relativity does not exist. Am I wrong?
Without two observers in relative motion, relativistic effects are not seen. This is why it's called relativity.
b) If so, then is time-dilation an actual physical effect in the absolute sense or is it only an effect to the extent that an outside observer is there to acknowledge it?
There is no "absolute sense," which is why it's called relativity. Relativity deals with two observers in relative motion. If there is only one observer, there is no one around to see any relativistic effects.
c) If an astronaut were to journey into space for about 30 years (in his frame of reference), roughly 50 years would have passed on Earth. If he returns and stays on Earth, his peers would have aged more than him. In this case, time-dilation seems to be an actual physical effect that continue to exist even after his frame of reference stopped moving. How do I reconcile the role of observer with the seemingly continuing effect of Relativity in this case?
This is called the "Twin Paradox," and is really not a paradox at all. It's actually just a really good introductory problem to special relativity, and is analyzed by many an undergraduate physics student every year.

The moving twin follows a fundamentally different path through spacetime, because the moving twin fires rocket engines, feels forces and accelerations, and changes directions halfway through his journey. He is not following the "natural" path through spacetime. A "natural" path, without any sort of forces or accelerations, is called a geodesic. Geodesics are the paths followed by baseballs in free-fall, by the earth orbiting the sun, and so on. The moving twin doesn't follow a geodesic (and all observers will agree on that). Now, a geodesic is not only the "natural" path, it's the easiest path. It doesn't take any work at all to travel on a geodesic; it takes work to travel on any other path.

Relativity also defines another concept, called the interval. An interval is the distance between two points in spacetime (which are called events). For example, two events might be your office at 5 pm and your dinner table at 7 pm. Between these two points in spacetime you can define an interval of some characteristic length, L. Calculating the interval is not challenging: it is just

(dL)² = (dt)² - (dx)² - (dy)² - (dz)²

in which dt is the difference in time between two events, and dx, dy, and dz are the spatial separation between two events. Your intellectual hackles may get raised immediately -- I said "dt is the difference in time between two events" -- but I didn't say whose watch measures that time!

The trick about relativity is that all observers will always agree on the length of an interval. They will not agree on the individual components.

The leads to the conclusion that the moving twin's proper time is actually less than the stationary twin's proper time. All observers will agree on that!

I'm not really interested in writing a whole essay on all of the nuances, so I'll just point you to an excellent site:

http://math.ucr.edu/home/baez/physics/Relativity/SR/TwinParadox/twin_paradox.html

which will almost certainly answer any further questions you have.

- Warren

Thanks for the link, chroot. Will definitely look it up. Much appreciate.