# When the station comes to the train?

1. Nov 13, 2005

### Macro

The very desciption of Space-Time being only Relative
Concepts is not what Einstein proported. He thought
about calling it the opposite - "invariance theory."

It ought to be known that relatives owe their
existence to absolutes. They coexist.
You don't want disagreement mentors?
Then delete me!!! :!!)

"When the station comes to the train."
But clearly only the train moves through space to
get closer to the station - not the other way around.
One motion is a relative and it owes its existence to
another which is not.

Relatives are not the absolutes in themselves.
Relatives are not what they are proported to be.

2. Nov 13, 2005

### JesseM

When Einstein said he wished it had been called "invariance theory", he was talking about quantities that do not vary by reference frame, like the speed of light, the proper time along a worldline, the rest mass of an object, and so on. In contrast, sublight velocities always depend on your reference frame, so they are not invariant. If you pick a frame where the station is moving while the train is at rest, you'll get exactly the same answers to frame-invariant questions, such as the time on the train's clock at the moment it passes the station's clock. So, this frame is just as valid as a frame where the train is moving and the station is at rest, according to relativity.

3. Nov 13, 2005

### Macro

I understand that all frames are valid. What I am saying
is that moving through space isn't exactly the same as
not. After all, only one clock will slow down for the Twins.

Mitch Raemsch

4. Nov 13, 2005

### JesseM

These two statements are inconsistent, since the whole point of different "frames" is that they disagree about who is "moving through space" and who is at rest (for example, in the train's rest frame the train is at rest while the station is in motion). If they are all equally valid, that means there can be no objective truth about this question.
If both twins are travelling at constant velocity, it's not true that "only one clock will slow down"--in each twin's frame, the other twin's clock slows down, and both these perspectives are equally valid. It is only when one twin accelerates to turn around relative to the other, and thus switches from one inertial frame to another, that the symmetry is broken, and in this case whichever twin accelerated will be the one whose clock reads less time when they reunite (if it was the earth-twin who accelerated to catch up with the travelling twin while the travelling twin continued on at constant velocity, then it would be the earth-twin who was younger when they reunited, for example).

Last edited: Nov 13, 2005
5. Nov 13, 2005

### Macro

You lost the argument. :!!)
What does acceleration do to the clock?
What are accelerating frames but ones where time and space are
changing.

Only one Twins clock goes slow. Its called the Transverse Doppler Effect and
I say it is soley due to motion through space.

Mitch Raemsch

6. Nov 13, 2005

### JesseM

Acceleration doesn't do anything per se, it's more a geometric issue--if you have two points in spacetime and you draw two worldlines between them, one straight and the other bent (ie a worldline of an object whose velocity was not constant), you will always find that the bent worldline has a shorter proper time (time as measured by a clock that travels along that worldline) than the straight one. This is analogous to the fact that if you draw two points on a piece of paper, then a straight line between the points will always have a shorter length than a bent one.

Technically, if you know the velocity as a function of time v(t) of a clock in a given inertial reference frame, then to find the total time elapsed on the clock between two times in the frame's coordinate system $$t_0$$ and $$t_1$$, you do the integral $$\int_{t_0}^{t_1} \sqrt{1 - v(t)^2/c^2} \, dt$$ (because at any given moment, if the clock's velocity at that moment is v then it must be ticking at $$\sqrt{1 - v^2/c^2}$$ the normal rate in that frame, so you just integrate this to get the total time elapsed on the clock). You will find that if you evaluate this integral for two clocks that depart each other and reunite, it is always true that the result is longer for the clock that had a constant v(t) then the one that had a changing v(t), which is just another way of saying that the clock that accelerates will have elapsed less time.
Special relativity only says that the laws of physics work the same in all inertial frames, not in accelerating frames (for example, in accelerating frames it's possible for objects to be moving faster than c). Any textbook on SR will tell you this, and Einstein restricted the two postulates of SR to non-accelerating frames in his original 1905 paper.
You're wrong, and you are misunderstanding the most basic idea of what "relativity" is all about. It is easy to see by using the Lorentz transform (which tells you how to translate between different frame's coordinate systems) that the slowdown effect is perfectly symmetrical, and that each observer will say that the other observer's clock is the one that slows down. It might help you to look at an example I provided on the thread an illustration of relativity with rulers and clocks, showing how if you have two rulers sliding alongside each other at constant velocity with clocks placed at regular intervals along each one, in each ruler's frame it will be the other ruler's clocks that are running slow, and yet this does not lead to any inconsistencies in what the different frames predict about what two clocks read at the moment they pass each other. The specific numbers I used for the ruler-markings and clock times in that example were taken from the Lorentz transform.

I have no idea why you think the transverse doppler effect would contradict this symmetry--as explained here, the transverse doppler effect has to do with what an observer sees using light-signals when an object is moving along a straight line that does not cross his own position. As long as both the observer and the object are moving inertially, their view of each other will also be symmetrical--we can do a numerical example of this if you like. Also, note that what an observer sees using light-signals is different from what he says is "really" going on in his own frame--for example, if you're coming towards me I will see your clock running fast due to the doppler effect, even though your clock is really running slow in my frame (the time-coordinates between successive ticks of your clock are longer than normal in my coordinate system, but since you're moving towards me each successive tick happens at a closer distance to me, so the light from each tick takes less time to reach me than the last one and thus your clock appears sped-up when I look through my telescope at you approaching).

Last edited: Nov 14, 2005
7. Nov 14, 2005

### Macro

I'll say what Einstein wouldn't say: There is a fastest time corresponding to moving slowly through space.
Moving faster slows time as does a gravity field.
Remove both motion through space and gravity as best as you can and you have a "fastest time." It's an absolute.

Move or enter gravity and it becomes a relative.
Time is both an absolute and a relative.
The relatives owe their existence to an absolute.

Hope you like this! :tongue:

8. Nov 14, 2005

### JesseM

Einstein never said that. Perhaps you got the idea of "slower motion through space = faster motion through time" from Brian Greene's account of relativity (which is discussed on this thread), but most physicists don't think of relativity that way, and in any case Greene was only talking about moving faster or more slowly through space relative to a particular reference frame, there is no absolute truth about who is moving faster or slower through space. edit: never mind, I thought you wrote "I'll say what Einstein would say" when you actually wrote "I'll say what Einstein wouldn't say".
Look Macro, are you trying to promote your own theories here, or are you actually claiming that there is an absolute truth about who is moving faster through space and whose clock is ticking slower in relativity as understood by mainstream physicists? Because I can assure you that as physicists understand relativity, there is no absolute truth about these things, the answer will depend on which reference frame you choose.

Last edited: Nov 14, 2005
9. Nov 15, 2005

### Macro

All I am saying is that everything is moving through space in one form or another.

Just because you know Einstein's ideas doesn't make you anybody Jesse. You've learned Relativity by wrote. I have learned it by my own understaning. One is better than the other!!! :tongue2:

No absolute truth Jesse?
Then you can't be absolutely sure now can you?

10. Nov 15, 2005

### JesseM

Then I'll repeat my question from the other thread:
Now you're just being insulting. And why do you say you've "learned relativity by your own understanding", when the ideas you are promoting contradict relativity? Don't you really mean that "your own understanding" has led you to disbelieve relativity?
Uh, I'm not saying there is "no absolute truth" in some general philosophical sense, I'm just saying that within the theory of relativity there is no absolute truth about whose velocity is larger, different reference frames will give different answers and in relativity they are all treated as being equally valid (because all the known laws of physics work exactly the same in each frame). There is certainly an absolute truth about plenty of other things in relativity, like the proper time along a given worldline which will be the same in all reference frames, so I'm not saying there are no absolute truths about physics (or reality) in general, nor am I claiming to be absolutely sure that relativity is correct--thus your retort above "No absolute truth Jesse? Then you can't be absolutely sure now can you" is misguided.

And like I said above, it's certainly possible that in some untestable philosophical sense there could be an absolute truth about whose velocity is larger, although I don't see any need for such a belief. If you want your ideas to go beyond philosophy, you have to propose an experiment that would determine which of two objects has a greater speed through space.

Last edited: Nov 15, 2005