1. Sep 7, 2009

### dwspacetime

hello everyone i am new here. i have been to some websites about relativity but still kind of suspicious about it. here i have a problem. could anyone give me a mathematical answer. by the way this is not a homework. i am not a student.

say we have a railroad from point A to point B and the length btw A and B is L=ct. c is the speed of light. now we have 2 trains, train1 and train2 pass point A towards point B at midnight or at time 0 oclock. train1 travels at v=c/2 relative to point A and train2 travels at v=3c/4 relative to train A. if there is a person at point B, when will he see train2. and why? thanks.

Last edited: Sep 7, 2009
2. Sep 7, 2009

### Al68

Assuming the person is at rest with the track, and L is the proper distance between points A and B, train2 will reach him at L/0.909c. The velocity of train2 relative to the track is (v1+v2)/(1+v1v2/c^2)=0.909c.

If, for example, L= 1 light second, then train2 will reach him when his clock reads 1.1 seconds.

3. Sep 7, 2009

### dwspacetime

thanks AL68. how did you get the equation. if you know a link please let me know. but i am still confused about time travel. people say if someone travels very fast away from earth, when he comes back he will be younger than his twin brother. but his twin brother also travels very fast away from his spaceship on the earth. why not his twin brother is younger?

4. Sep 7, 2009

### JesseM

The time dilation equation only works in inertial frames, that is, the frames of observers who don't accelerate...whichever twin turns accelerates to move toward his brother after they've been moving apart for a while, he didn't remain in one inertial frame so he can't assume that his twin's aging will be given by plugging his relative velocity at different moments into the time dilation formula, and in fact the twin that accelerated will always be the one that's younger when the two reunite. Lots of different perspectives on this problem can be found at this twin paradox page. And for a good intro text on relativity in general, you could read http://www.oberlin.edu/physics/dstyer/Einstein/SRBook.pdf [Broken].

Last edited by a moderator: May 4, 2017
5. Sep 7, 2009

### dwspacetime

thanks JesseM

sorry you said one of them will be younger? i dont understand. both of them accelerates in the exact same way to and away from each other in opposite directions i think. my intuition just tells me something is wrong here which i dont what it is. i will read more. is there any prove the speed of light is always c nomatter what?

6. Sep 7, 2009

### Al68

http://en.wikipedia.org/wiki/Special_relativity. Look under "Composition of Velocities".

7. Sep 7, 2009

### Al68

The standard SR equations are only valid in inertial reference frames. The earth twin is stationary in an (approximately) inertial reference frame, while the ship's twin is not. Simply put, an inertial reference frame is one in which if you let an object go, it will remain stationary in the frame if no forces act on it. This is not true of the ship's accelerated frame. So while it is true that the earth had coordinate acceleration relative to the reference frame in which the ship is "stationary", earth had no proper acceleration, ie in any inertial reference frame. Relative to any inertial reference frame, the ship, but not earth, accelerated.
No. But there is overwhelming evidence that it's always c relative to any inertial reference frame.

Last edited by a moderator: Sep 7, 2009
8. Sep 7, 2009

### JesseM

The initial acceleration is irrelevant to the problem, it makes no difference whether the initial departure point consists of them starting out at rest next to each other and then accelerating away, or just crossing paths while moving at constant velocity. What's important is which one accelerates to turn around after they have been moving apart for awhile after the departure point, so that the distance between them begins to decrease after it has been increasing for a while, and eventually they can reunite and compare ages.

The fact that the one whose worldline contains a "bend" midway between the departure point and the reunion point always ends up being younger is closely how it works with distances along spatial paths, where if you have two paths between a pair of points in 2D space, and one is a straight line between those points while the other is bent, then the bent path will always have a greater length since a straight line in 2D is the shortest distance between points. Similarly, in spacetime a "straight line" (constant velocity) path between two events always has the greatest amount of "proper time" (time as measured by a clock that moves along that path). I expanded on this analogy a bit in this thread:
Depends what you mean by that. In SR the coordinates of different inertial frames are related by the "Lorentz transformation", which says that if an arbitrary event has coordinates x,t in one inertial frame, then the coordinates x',t' of the same event in a different inertial frame moving at speed v relative to the first will be:

$$x' = \gamma * (x - vt)$$
$$t' = \gamma * (t - vx/c^2)$$
with $$\gamma = 1/\sqrt{1 - v^2/c^2}$$

It's possible to prove that, given this coordinate transformation, if something has a coordinate speed of c in one frame, it will have a coordinate speed of c in any other frame. However, it's another matter to demonstrate that if different observers construct physical coordinate systems out of grids and rulers and clocks at rest relative to themselves, then the readings on one physical coordinate system will be related to the readings on another by this transformation. It can be shown that this will be true if all the fundamental laws of physics (which govern the behavior of physical rulers and clocks along with everything else) have a property called "Lorentz-symmetry", which means the equations are such that if you write them down in one frame and then do a Lorentz transformation on them to see what the correct equations would be in another frame, the equations look exactly the same in both frames; so far, all the fundamental laws of physics which have been discovered so far do have this property. Also, tests which have tried to look for variations in the speed of light when it is measured in different directions (and measured at different points in the Earth's orbit) have failed to find any such variations. All of this is empirical evidence though, there's no way to prove relativity must be correct in a non-empirical way (the same is true of any other statement about the laws of physics of course).

9. Sep 7, 2009

### dwspacetime

wow thank you guys. just came back from gym.

10. Sep 7, 2009

### dwspacetime

i have another question before i read on. sorry if the answer is in the links you told me. say there are only two balls in the universe, ballA and ballB with nothing. suddenly two of them accelerat away from each other. how can you tell which one is accelerating. i mean which one gets the force from God. if you say ballA is at rest, to me ballA must be in a system that is at rest and there must be no relative movement between ballA and the system. but what is the system? the empty space? say i am ballA or ballB. do i feel a force that pushs me to accelerate? but what does that mean feeling a force?

11. Sep 7, 2009

### JesseM

Think of what happens when you accelerate in a car--you get pushed back against the seat. Acceleration causes you to experience G-forces, even in empty space free of any actual gravity. So, whichever ball accelerates, someone traveling along with it will experience G-forces, while someone traveling along with a ball that doesn't accelerate will feel weightless in SR.

12. Sep 7, 2009

### dwspacetime

ok. same situation only 2 balls in the universe. they remain relatively motionless. you think they are at rest? wait. God can make them both accelerating in the same manner. but they are accelerating away from what? so my question is is there an system independent of matter. or the empty space is matter.

13. Sep 7, 2009

### JesseM

Acceleration doesn't need to be "away from" anything physical, even with only a single ball in flat spacetime, it's defined as accelerating if the laws of physics as seen by an observer on the ball would be different from those that apply in inertial reference frames (including the fact that an accelerometer which measures G-forces should always give a reading of zero when it's at rest in an inertial frame).

14. Sep 7, 2009

### dwspacetime

well. i have to say i am not satisfied with your answer this time JesseM. I will put this question aside for now. if there is one ball only in the space, when its speed changes from 0 to none 0. it is moving away from a system whose v=0 obviously. the system may not have anything physical. well it does not make 100% sense to me. we may not have an answer now or we may have an answer somewhere already.

15. Sep 7, 2009

### JesseM

If it helps, you can talk about various inertial coordinates in empty space even if there are no physical objects at rest in these systems. So if the ball changes velocity, there will have been some inertial frame where it was previously at rest but it is now moving. On the other hand, there will be a different inertial frame where it was initially in motion, and the change in velocity brought it to rest. In relativity the laws of physics work exactly the same in all inertial frames so there is no basis for preferring any one frame over the others, which means there is also no notion of absolute rest or absolute motion, all statements about rest vs. motion are relative to an arbitrary choice of reference frame.

16. Sep 7, 2009

### dwspacetime

i think i understand what you said. my concern if the space itself is matter. in a absolute empty space with nothingness in it it seems there is no differece of anywhere in the space. and it is emptyness anywhere. if a ball moves from v=a to v=b. its position changes from where it was when v=a to where its v=b. the position when its v=a can't be anywhere like a space with nothing in it. it must be that particular location and this should not change if we take out the ball out of the space if we can.

if we observe the only 2 balls in the space accelerate away from each other and if we for some reason say one is at rest or in a constant speed while the other is accelerating. there must be a difference btw the way the balls change their positions. but to what reference frame? if we use either of the ball as reference frame we can't tell which one is accelerating. so the referenc frame must not be any of the balls but something independent of them . what is that? the nothingness space? you see my point?

17. Sep 7, 2009

### atyy

JesseM said with respect to an inertial frame.

I don't think it's too cheating to think of an inertial frame as a system of rulers and clocks "stationary" wrt to each other, where "stationary" is defined by some conventions involving light being sent back and forth from different points on the various rulers.

Less cheating is to say that to define an inertial frame we use light - the electromagnetic field - which *is* a form of "matter" - so an inertial frame is defined wrt to "matter" and not "nothingness".

18. Sep 12, 2009

### dwspacetime

that is a very good book. i mean relativity for questioning mind. i am halfway through. just finished chapter 9. do they teach this in high school. i didnt learn it when i was in high school.

19. Sep 12, 2009

### Cleonis

The thing is, your question comes from a widespread deficiency in special relativity introductions. In my opinion all introductions to special relativity are wrongfooting the reader. (Yeah, that's a big claim, let's see if I can back that up.)

By implication relativistic physics attributes physical properties to space. (Well, the arena of relativistic physics is referred to as spacetime, but that's not my emphasis now.) By implication relativistic physics assumes that any matter or energy located in space is subject to the phenomenon of inertia. Since inertial mass cannot be its own source of inertia the existence of inertia must be a property of space. Peculiarly, this implicit assumption is rarely or never made explicit. In fact, many introductions cloud the issue. Many introductions shift the attention away from space, by emphasizing the aspect that 'Special relativity has done away with the ether'.

Actually, what special relativity abandoned was the following aspect of ether theories: in ether theories it is assumed that objects located in the ether have particular velocity to the ether. One may be unable to determine that velocity, but it is assumed that 'velocity relative to the ether' does exist. What Special relativity has abandoned precisely is the concept of attributing a velocity vector to ether, or equivalently, what is abandoned is the concept of a velocity vector for velocity of an object relative to the ether.

The twin scenario illustrates the things that special relativity does use: the traveling twin travels a longer pathlength, which corresponds to a smaller amount of proper time elapsing. This difference in pathlength effect is a property of space!

If you are pushed by something pushing against you, or you are pulled by some string, then you can certainly feel that, and an accelerometer will give a reading. What is sensed is acceleration with respect to space. Special relativity does use acceleration vectors that represent acceleration relative to space There is a crucial distinction here; relativistic physics has - as a matter of principle - no such thing as a velocity vector relative to space. What relativistic physics does have (as a fundamental necessity) is an acceleration vector relative to space

The contrast with classical physics couldn't be bigger. In classical physics velocity is a derivative of position, and acceleration is a derivative of velocity; not just mathematicaly, but also in physical interpretation. Not so in relativistic physics. While you cannot have velocity relative to spacetime, you can and do have acceleration relative to spacetime.

The problem with introductions to special relativity is that the authors are leaving out essential information. All novices are puzzled and start asking the same questions that you do. You have been wrongfooted.

Cleonis

Last edited: Sep 12, 2009
20. Sep 12, 2009

Nope.