
#19
Mar212, 09:22 AM

P: 249

In the orignal post it sounded like A and B where two seperate places outside of the train. So then if you put two objects at a location down the track they would appear to come closer together as the train moved down the track. I was trying to say that the track itself would become shorter from the frame of reference of the train while it was moveing, not longer.




#20
Mar212, 09:41 AM

P: 163

In other words, if the train observer emits a light signal from A once A happens, can that signal reaches B before or at the same time when B happens? 



#21
Mar212, 09:44 AM

PF Gold
P: 4,533

If you use a distance in the ground frame of 1 (using compatible units like seconds and lightseconds and where c=1 and speeds are expressed as beta which is v/c) and you set the first event at the origin (all components equal zero), then as you increase beta from 0 to almost 1, the value of the reciprocal of gamma goes from 1 to almost 0 and the absolute value of the time coordinate of the transformed event goes from 0 to almost infinity. At some particular value of beta, these other two values will become equal. This value of beta is 0.618034 and the reciprocal of gamma is 0.786151 and the time component is 0.786151. But what does this mean? Nothing at all. In order to compare a length of an object in one frame to its length in another frame, you have to do it when the events at both ends of the object have the same time component. Clearly, in your discovery, those two events do not have the same time component (one end is at the origin with time equal to zero and the other end has a time component of 0.786151) and so the length component, which will be equal to gamma or 1.272020, is not the correct length to use. What you have to do is pick another value of time for the second event in the original frame such that the value of the time component of transformed event is zero. This is very easy to do when you normalize the problem as I have, you just set the time component to the value of beta. So if you set the time component for the second event to 0.618034 (with x equal to 1) then the transformed time component is 0 and the distance component is 0.786151 (the reciprocal of gamma). Of course, if you wanted to use any other distance, you would multiply beta by the distance to get the correct time component to use and then the transformed distance would be the original distance divided by gamma. So the bottom line is that in order to see what length anything is in any frame, you have to make sure the time components at both ends are equal. The corollary to this is that if you want to see what a time interval is in any frame, you have to make sure the spatial components are the same at both events. Now it should be pretty obvious that there cannot be a single pair of events for which both of these conditions are satisfied, that is, you cannot use the same two events in any frame to know both the length and time intervals in any other frame. 



#22
Mar212, 09:56 AM

P: 163

Please refer to the attached diagram
Suppose that a light source is put near the A end of the train so as to be seen simultaneously at A & B for a ground observer. It will be definitely seen at A before B for the train observer. Now can this time difference allows a timelike separation? http://www.physicsforums.com/attachm...1&d=1330703748 



#23
Mar212, 10:05 AM

P: 132

In order to make sense of your example, we need to be clear as to whether we are talking about an event or the location of this event in a particular frame. By using "A" and "B" both for events and for "the 2 train ends", we end up in confusion. 



#24
Mar212, 10:26 AM

P: 1,098

lol too hippy, well in that context your scenario is too trippy. the measure of length & time (dimensions) are defined by c, why do you mention the speed of sound? If you want to define "reality" as a measure of sound then I'd say yes. But that is a stupid definition. In physics I find it is better defined as everything that is physical, from the perspective of measurement. "Fundamental Interaction" is limited by c (i assume). In "reality" spacetime is a continuum of fundamental interaction. 



#25
Mar212, 10:36 AM

P: 163

http://www.physicsforums.com/attachm...1&d=1330705974
Here is my calculation This can be also considered as simple derivation of Lorentz transformation up to the equation (i) Now no worries to assign A and B to whether events or train ends as long as we are talking from the perspective of the train rest frame the second image is more clear and accurate http://www.physicsforums.com/attachm...1&d=1330706663 



#26
Mar212, 11:23 AM

PF Gold
P: 4,533





#27
Mar212, 11:26 AM

P: 132

 the distance between the two ends of the train in a certain frame  the distance between the locations where the two events occur in a certain frame. If you could type your argument in a post, complete with explanations of the steps, it would be easier to see what is going on. 



#28
Mar212, 11:32 AM

PF Gold
P: 4,533





#29
Mar212, 11:56 AM

P: 163

Thank you 



#30
Mar212, 12:25 PM

PF Gold
P: 4,533

Adel, I'm going to try to explain what timelike and spacelike mean, and why if two events have one type of likeness in one frame, they have the same type of likeness in all frames. Again, I'm going to use compatible units where the value of c=1 and I'm going to align the first event at the origin. Then we can use the Lorentz transformation in a simple way to understand these terms.
First off, timelike simply means that the time coordinate is greater than the spatial coordinate. Spacelike simply means that the spatial coordinate is greater than the time coordinate. Lightlike simply means that both coordinates are equal. So if we look at the simplified Lorentz transform, we see: t' = γ(txβ) x' = γ(xtβ) What we want to do is compare the values of these two equations for different values of β, where β can range from 1 to +1 (but not including those values). So we compare like the following where the calculation of the new time coordinate, t', is on the left and the calculation of the new space coordinate, x', is on the right (the question mark can be replaced with =, <, or > depending on our evaluation): γ(txβ) ? γ(xtβ) Now we note that γ is a function of β but for all values of β, γ is a positive number equal to 1 or greater than 1: γ = 1/√(1β^{2}) Therefore, we can remove γ from our conditional statement without effecting the evaluation of the condition: txβ ? xtβ Next we rearrange the terms so that the t factors are on the left and the x factors are on the right: t+tβ ? x+xβ Now we factor out the common terms: t(1+β) ? x(1+β) Now since β can have a range of 1 to +1 but not including those numbers, the factor 1+β has a range of 0 to 2, not including those nuimbers. Therefore we can divide out the (1+β) factor without changing the evaluation of the condition: t ? x What does this mean? It means what everyone has been telling you: If t>x in one frame, t'>x' in any other frame, no matter what the value of β is. If t=x in one frame, t'=x' in any other frame, no matter what the value of β is. If t<x in one frame, t'<x' in any other frame, no matter what the value of β is. So no amount of coming up with specific scenarios, especially illdefined ones, can produce an example that will violate the conclusion that whatever likeness two events have in one frame, they have the same likeness in any other frame. It's kind of a waste of time to try to decipher your scenarios and point out where your confusion is so that you will accept our critiques of what you are doing. My single most important advice to you is to learn what an event is, how to define a scenario in ONE frame, not two like you have been doing, and then use the Lorentz Transform to see what that scenario looks like in another frame. 



#31
Mar212, 12:32 PM

P: 249





#32
Mar212, 01:07 PM

P: 132

IN THE TRAIN FRAME A and B are the two ends of the train. C is the point somewhere between them where there is a light source. p is the event "a light signal is emitted at C". q is the event "the light signal from C reaches A". r is the event "the light signal from C reaches B". What you seem to be claiming is that it could be possible to send a light signal from A after event q that will reach B before event r. Am I correct? 



#33
Mar212, 01:17 PM

PF Gold
P: 4,533





#34
Mar212, 01:17 PM

P: 163





#35
Mar212, 01:25 PM

P: 163





#36
Mar212, 02:03 PM

P: 1,098

& classical physics has left the building. (not that I think this is incompatible with classical physics) IIRC there is no information exchanged in that scenario, ie no "break" in causality / faster than c. Not sure I subscribe to the scenario you describe with changing spin. A NYSE trader would love that kinda communication speed advantage, let alone any wireless communications company. It is a "state" that the particle is in, I guess there can be a "clone" particle of sorts that share indefinite properties (specifically a state); as wiki says "...which is indefinite in terms of important factors such as position,[5] momentum, spin, polarization, etc." "Entanglement" is misleading. Really this is not much different than "distant star" scenario we were discussing above. With theory, we can measure, calculate values & make predictions. I hope someone who knows more can correct me on this if wrong, but there is no change in state of either particle, merely the values become mostly definitive/determined. 


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