Lorentz transformation - Tilted Forum Project Discussion Community

vinaur · 02-17-2005, 10:39 AM

I'm doing a "little" english project on the theory of relativity (most likelly both special and general) and I came across this problem with Lorentz Transformation. The whole process is described right here. What I have problem with is arriving at equation #7a. Any help would be much appreciated. Thanks upfront.

fckm · 02-17-2005, 04:03 PM

in sentence {11}, he says to set t'=0, which results in the equation under sentence eleven.
He then uses this equation to transform a point in x to a point in x':
x=0 => x'=0
x=1 => x'=a(1-v^2/c^2)

thus

delta_x => delta_x'=a(1-v^/c^2)

By the way, how Englishy is this project going to be? From what I understand of general relativity, it's hard. Really hard. Unless you already have a background in tensor math, I think it will be much more difficult to follow the derivation than special relativity

Jrock · 02-17-2005, 07:00 PM

I'd be carefull about writing a science paper for english class. I have a friend who recently wrote a paper on string theory for his english class. He dumbed it down as much as he could, and it was still too difficult for the english professor to understand. As a result, he didn't get a very good grade. It's easy to pad out an english paper to the required length with equations, but your teacher probably wants words. But completely skipping the derivation leads to a different problem; you'll probably get marked off for not explaning where the equation comes from. You'll run into problems whether you derive it or not.

If you insist on writing about relitivity, I would focus on the more basic topics that can be explained without a lot of math. I'd focus mostly on the definition of an intertial reference frame and the invariance of the spacetime interval. That'll be enough to solve some of the relativity paradoxes well enough for an english class.

vinaur · 02-18-2005, 06:04 AM

Thank you for your responses. I do realize that deriving equations in an English paper is a bad idea, so I'm not going to do it. I'll be explaining the reasoning behind relativity, etc. My teacher is rather dumb so, I think she won't even really try to understand the paper.

As I have discovered yesterday, there is a mistake on the page that I linked to yesterday. It had some characters missing, like delta infront of x' on line 10 and that should be equal to I not 1. So here's the correct page (as much as I can tell).

Maybe it will help solve my problem by finding what I'm doing wrong. Here's what I do:

1) Set t' to 0 in equation #5 and solving for t: t=(bx)/(ac)

2) Substitute t in the other equation 5: x'=ax-(b^2*x)/(a)

3) Since v=(bc)/a we can do this: x'=ax-(b*v*x)/c

4)We can do the same thing again: x'=ax-(v^2*a*x)/c^2

5)Factor out ax: x'=a*(1-v^2/c^2)*x

So how do they get I to show up instead of 1??? Or is it a mistake in their text??

And why do they just get rid of x when they go to equation 7a. Wouldn't it become delta_x and then be replaced by I?

Thanks again.

BTW, I know this wasn't really necessary, but how do you like the pretty print for the equations? Click them if you haven't figured it out yet. could be useful for some more complex stuff.

shakran · 02-18-2005, 06:28 AM

if you already know your audience is dumb and won't understand what you are talking about, why are you talking about it? The quickest path to an F is to make your teacher feel like an idiot. . .

That said, if you have time grab A Brief History of Time by Hawking or Coming of Age in the Milky Way by Tim Ferris. Both books are VERY good at explaining complex subjects in ways that ordinary mortals like me can understand. They might give you ideas on how to approach your paper.

vinaur · 02-18-2005, 08:07 AM

The I serach project is supposed to allow you to research stuff that you are interested in and you want to learn more about. If I really have a hard time explaning relativity, then I might just switch to writing about Einstein's accomplishments. That way, I won't have to go as much in depth. Thanks for the comment though,

FngKestrel · 02-18-2005, 04:31 PM

You might want to use something a little more layman to describe relativity, like the Cartoon Guide to Physics. http://www.amazon.com/exec/obidos/AS...330488-1055024

Also recommeded is Einstein for Beginners:
http://www.amazon.com/exec/obidos/tg...glance&s=books

fckm · 02-19-2005, 08:24 AM

Um, I think that I is actually a 1. That's the only thing that makes sense to me right now.

Slavakion · 02-19-2005, 08:47 AM

Oh dear lord, my head asplode. What the hell is a Lorentz Transformation? From what I've gathered from Google, it measures time dilation/contraction. I won't see this until higher-level physics, right?

fckm · 02-19-2005, 09:01 AM

Um, if you're a physics major/engineer, you'll probably see this in freshman level physics. You're most likely to see it at the end of first or second semester mechanics. (Actually, my high school physics teacher was going to teach us special relativity, but then he had to go on paternity leave, so he never got around to it) The math is pretty simple, it's just conceptually difficult. If you ARE a physics major, and you haven't seen this yet, I would be.... concerned.

vinaur · 02-19-2005, 11:08 AM

Quote:

Originally Posted by Slavakion

Oh dear lord, my head asplode. What the hell is a Lorentz Transformation? From what I've gathered from Google, it measures time dilation/contraction. I won't see this until higher-level physics, right?

Lorentz Transformation is not that hard to understand if you read the first 20 pages or so of Einstein's Relativity: The Special and General Theory . I knew nothing of it, and yet I think I'm getting it now.

BTW, there is one thing that either I don't get or Einstein got it wrong. In Chapter 9 of his book, Einstein says that When you are moving towards one flash of lightning and are right in between the two when they strike, you will see one of them faster, hence ruining the concept of simultanity. However, if the law of propagation of light is taken into account, the two beams of light from the lightningsshould reach you at the same time no matter how fast you are travelling in any direction, as long as you are right inbetween the two when they strike, since the distance between you and the lightning has to decrease at a constant rate c.

Also, I could not find a good site where they explain how they arrived at the law of propagation of light. Does anyone know anything helpfull.

Oh, and thanks for all of your suggestions.

fckm · 02-19-2005, 08:17 PM

Light propagation comes out of Maxwell's equations, which describe the origins and interaction of Electric and Magnetic fields. Maxwell's equations led to the "discovery" of the Lorentz transformation. Newtonian mechanics are invarient under Galilean transformation, but Maxwell's equations are not. The Lorentz transformation was originally derived to create a coordinate transform that maintained the invarience of Maxwell's equations. It is considered the correct transform to apply because experimental obervation shows us that Maxwell's equations are indeed invarient under transformations between inertial reference frames.

Quote:

Events which are simultaneous with reference to the embankment are not simultaneous with respect to the train, and vice versa (relativity of simultaneity). Every reference-body (co-ordinate system) has its own particular time ; unless we are told the reference-body to which the statement of time refers, there is no meaning in a statement of the time of an event.

Quote:

We were led to that conflict by the considerations of Section 6, which are now no longer tenable. In that section we concluded that the man in the carriage, who traverses the distance w per second relative to the carriage, traverses the same distance also with respect to the embankment in each second of time. But, according to the foregoing considerations, the time required by a particular occurrence with respect to the carriage must not be considered equal to the duration of the same occurrence as judged from the embankment (as reference-body). Hence it cannot be contended that the man in walking travels the distance w relative to the railway line in a time which is equal to one second as judged from the embankment.

Here, he's speaking of time dilation, where time in one frame has a different meaning than time in another frame.

vinaur · 02-20-2005, 08:21 AM

This is what I was talking about in my post above:

Quote:

When we say that the lightning strokes A and B are simultaneous with respect to be embankment, we mean: the rays of light emitted at the places A and B, where the lightning occurs, meet each other at the mid-point M of the length A B of the embankment. But the events A and B also correspond to positions A and B on the train. Let M1 be the mid-point of the distance A B on the travelling train. Just when the flashes (as judged from the embankment) of lightning occur, this point M1 naturally coincides with the point M but it moves towards the right in the diagram with the velocity v of the train. If an observer sitting in the position M1 in the train did not possess this velocity, then he would remain permanently at M, and the light rays emitted by the flashes of lightning A and B would reach him simultaneously, i.e. they would meet just where he is situated. Now in reality (considered with reference to the railway embankment) he is hastening towards the beam of light coming from B, whilst he is riding on ahead of the beam of light coming from A. Hence the observer will see the beam of light emitted from B earlier than he will see that emitted from A. Observers who take the railway train as their reference-body must therefore come to the conclusion that the lightning flash B took place earlier than the lightning flash A. We thus arrive at the important result:

Events which are simultaneous with reference to the embankment are not simultaneous with respect to the train, and vice versa (relativity of simultaneity). Every reference-body (co-ordinate system) has its own particular time ; unless we are told the reference-body to which the statement of time refers, there is no meaning in a statement of the time of an event.

Was I right when I said that the two beams of light will still seem simultaneous to point M' even if it is moving towards one of them?

fckm · 02-20-2005, 09:41 AM

I believe you are wrong. Because the two events occur simultaneously in the frame of M, by the tenets of special relativity, there can be no causal relationship between them. In other words, you can't say that A caused B, or B caused A (Since the two events occur simultateously in frame M, it's impossible that one caused the other).
Causal relationships are preserved under transformation (this is a tautology, causation is defined that way), so that if A caused B, then A must occur before B in ALL reference frames. In order for this to occur, special relatvity tells us that (if A caused B), B must occur at least t=d/c seconds after A occurs (where d is the distance between the two and c is the speed of light). Since this problem states that A and B occur simultaneously in the M frame, then we can see that A and B do not have a causal relationship.
The causal relationship (t>=d/c) is the only time in special relativity where the order of the events is preserved under transformation. In all other cases, it is possible to find a frame M' where A occurs before B, or B occurs before A.
So in this case with the lightning, since in the M frame, A and B occur simultaneously, they do not have a causal relationship. Thus it is possible that in M', A occurs before B, or B occurs before A.

It's been a while since I've taken SR. Hopefully someone else will chime in and correct any mistakes I've made.

edit:spelling

vinaur · 02-21-2005, 07:12 AM

I think you misunderstood me there. What I was trying to get at is that the two beams of light will reach the moving object at the same time regardless of its speed, as long as the object was exactly inbetween the two lightnings when they hit. My reasoning is that, according to the law of propagation of light the speed of the light beam relative to the moviong object has to be c, therefore the distance between the object and either of the two light beams has to be decreasing at the same rate c. If the object is heading towars one of the beams, then it "slows down" the one it's heading towards, and "speeds up" the one it moving away from. So basically relative to both beams (taken at the same time) it is not moving.

So since the beams reach the person at the same time, Einsteins argument that time is different for two reference bodies is not supported.

I hope this is a bit clearer and I hope I'm not starting to bug you (or anyone else).

Paradise Lost · 02-21-2005, 04:47 PM

Just going by logic and without any pure mathematical knowledge of the subject, it
seems like, since you are moving at a constant speed, that when both strike, at time
t = 0, then, say you are 5 meters away from both bolts, moving at 5 m/s, you still are
getting closer to the one flash, or it gets closer to you quicker than the other flash,
albiet only 1.67x10^-8 seconds quicker.

But then again, this is in reference to you, although, in a theoretical set-up, there
would be no other reference other than empty space, which, I suppose, relative to
the empty space directly inbetween the beams, which I suppose also can be
considered at rest, the bolts would happen 'simultaneously.'

2nd Paragraph could be totally wrong.

Oh, and talk about physics questions anytime you want, I need more info
myself, and the more people talking, the more knowledge flowing.

fckm · 02-21-2005, 07:21 PM

Vinaur, I understand what you're saying. It's been too long since I've taken SR and I'm too lazy to do the math, so I didn't want to do it out explicity. I was trying to reformulate your question in such a way that I didn't have to do any math.

Anyway, maybe I am misunderstanding you, but:

Quote:

My reasoning is that, according to the law of propagation of light the speed of the light beam relative to the moviong object has to be c, therefore the distance between the object and either of the two light beams has to be decreasing at the same rate c. If the object is heading towars one of the beams, then it "slows down" the one it's heading towards, and "speeds up" the one it moving away from. So basically relative to both beams (taken at the same time) it is not moving.

Let's say that L1 is light 1, and L2 is light 2 and M' is a train, M the platform. Arrows show travel direction. If I'm standing on a platform, I see the following

Code:

                                 M'
*-->               *      <--^        <--*
L1     -d1-      M     -d2-              L2

where d1 and d2 are distances, and the ^ is the train. When I'm sitting on the platform, reading my newspaper, I look at L1 and L2, and the distance between me and L1 and L2 is decreasing at c. The train is moving toward me at .9c.

If I'm on the train, I see the following:

Code:

                 M            
*-->          *-->      ^       <---*
L1     -d1'-              M'  -d2'-  L2

If I'm on the train, I'm not moving anymore, so M' doesn't have an arrow. The platform is now moving toward me, and the two lights are still moving toward me. I've redefined some distances. d1' and d2' are the distance between me (on the train now), and the two lights. (If it helps, you can imagine that at this particular time, the train ^ and the platform M are at the same place in space. I can't draw it in ASCII like that, so this diagram will have to do.)

In Newtonian physics, the rate of chance of d1' is c+.9c, and the rate of change of d2' is c-.9c. However, this is false. Special relativity tells us that the rate of change of d1' and d2' are the same, the are both c.

Here's another illustration (from the point of view of sitting on the platform):

Code:

*        <--^          *
A            M'          B

At this point in time (t=0), M' is at the midpoint of AB. And at this point in time, light from A and B hit M' at the same time, From The Point of View of The Platform. (This is important)

However, 1) M' is moving. 2) It takes light some time to get from either A or B to the midpoint of AB. Therefore, at the time that the light is actually emited, the picture looks something like this:

Code:

*                      <--^         *
A     -d1-              M' -d2-  B

d1' > d2'
At this point, two lights are emitted, so the picture looks like this:

Code:

*-->                 <--^        <--*
L1          -d1-        M'   -d2-  L2

Remember now, from the frame of M', things look like this:

Code:

*-->                    ^           <--*
L1     -d1'-            M'    -d2'-    L2

In the frame of M', M' isn't moving, and L1 and L2 are moving. But remember, d1' and d2' decrease at the same rate, c. Also, d1' and d2' is the distance between the light and the train now.(we can now ignore the points A and B) This is what makes SR kooky. In the frame of M', since d1'>d2', and the distance is deceasing at the same rate, from the point of view of M', L2 will reach M' sooner than L1.

In the frame of the platform, since the platform is not moving with respect to A and B, the lights hit each other and the moving train simultaneously. From the frame of the train, L2 hits the train before L1. There is nothing wrong with this. The idea of simulataneity no longer exists in special relativity. Something which is simultaneous in one frame, is not simulateous in another frame.

Why my earlier reply talked about order and causality:
In the example above, we can see that in special relativity, order is not preserved! L1 and L2 hit at the same time in the frame of M, but L2 hit before L1 in the frame of M'. These events do not have an absolute order in which they occur!

However, what if I do something at point A which causes something else to occur at B? The philosophical implication is that no matter what frame I'm in, in order for A to cause B, A must always occur before B. But our example shows us that in general, order is not preserved in SR. Is there any way that order can be preserved?

To preserve Order (A before B) in SR, the condition is the following. Given events A and B and the distance between them D, A will always occur before B if and only if t, the time between A and B, is t>=D/c. Thus, this says that for A to cause B (A to occur before B) the time between evens A and B must be greater than or equal to the time it takes light to travel between A and B. This is the only case in SR where order is preserved. In all other cases, order is not preserved.

In the example with the train:
Since on the platform, A and B are seen to occur at the same time, then the events at A and B do not meet the criterea stated above for causation. (the time between A and B is not greater than or equal to D/c). Because A and B are not causally related, I can always find a frame where A occurs before B, and viceversa.

phew. that was a long post. If anyone finds any errors, please correct me.

vinaur · 02-21-2005, 09:34 PM

Wow, this is cool. I never thought of thinking about d1 and d2 being different at t=0 and the train ending up at the midpoint when the two light beams meet. Then the concept of simultanity does fly out the window (or does it...I would still argue that it holds true, but let's drop it).

Does anyone else out there think that there is something incorrect about SR. Even though it does make sense if you take it one step at a time, I still think there is something wrong. Maybe the law of propagationof light is wrong? just think of it, if it was, wouldn't it make stuff so much easier (on the daily basis anyway).

I was thinking, what if there was a way to measure the occurance of an event in a distance with something faster than the speed of light, then SR would be incorrect, wouldn't it??

BTW Thanks for you time and info fckm.

Yakk · 02-22-2005, 11:46 AM

Quote:

I was thinking, what if there was a way to measure the occurance of an event in a distance with something faster than the speed of light, then SR would be incorrect, wouldn't it??

Yes. Either that or incomplete -- the general ability to communicate faster than light leads to time travel (of information at least) under SR.

I find Light Cones help understanding relativity.

Divide the universe into 3 pieces.

The "past", which consists of time/space locations from which photons could have reached you.
The "future", which consists of time/space locations from which photons you could emit can reach.
And "elsewhere", which consists of the rest of the universe.

This can be described with 'light cone' diagrams. Here are two:
http://physics.syr.edu/courses/modules/LIGHTCONE/
http://en.wikipedia.org/wiki/Light_cones

If two things are "elsewhere" to each other, then they are unordered in time. Which comes first is a matter of frame of reference.

n0nsensical · 03-22-2005, 01:59 AM

Quote:

Originally Posted by vinaur

Does anyone else out there think that there is something incorrect about SR. Even though it does make sense if you take it one step at a time, I still think there is something wrong. Maybe the law of propagationof light is wrong? just think of it, if it was, wouldn't it make stuff so much easier (on the daily basis anyway).

It can be really difficult to wrap your head around it. It's taken me a few years of general physics classes to really start understanding it. So far no experiment has shown a flaw in the theory.

Quote:

Originally Posted by vinaur

Lorentz Transformation is not that hard to understand if you read the first 20 pages or so of Einstein's Relativity: The Special and General Theory . I knew nothing of it, and yet I think I'm getting it now.

BTW, there is one thing that either I don't get or Einstein got it wrong. In Chapter 9 of his book, Einstein says that When you are moving towards one flash of lightning and are right in between the two when they strike, you will see one of them faster, hence ruining the concept of simultanity. However, if the law of propagation of light is taken into account, the two beams of light from the lightningsshould reach you at the same time no matter how fast you are travelling in any direction, as long as you are right inbetween the two when they strike, since the distance between you and the lightning has to decrease at a constant rate c.

This would be true if the events did occur at the same time as the observer on the ground sees, however, the point is the two strikes of lightning actually occur at DIFFERENT TIMES in your frame of reference. So you do see one flash before the other one, and this doesn't contradict the light propagation law because all of the light IS approaching you at a constant speed; you see one before the other because that bolt struck first. The observer also sees that the light from one bolt reaches you before the other one, even though the events are actually simultaneous in the observer's frame, because you are moving in that frame.

The basic postulate of special relativity is really quite simple and intuitive: that laws such as Maxwell's are valid in every inertial frame of reference. Maxwell's laws predict that the speed of light is constant, specifically 3.0x10^8 m/s, so the speed of light must be 3.0x10^8 m/s in every inertial frame if this is correct. The Lorentz Transformations handily resolve the apparent contradictions when you assume this.

What vexed physicists before Einstein about Maxwell's equations was that they predicted a constant speed of light and even more, they predicted EXACTLY what the speed of light would be before it could be accurately found experimentally. However, they said nothing about speed relative to what, i.e. in which frame of reference. This is where the idea of the ether came in handy; the frame of the ether was assumed to be the frame in which this was the speed of light. Michelson and Morley then famously couldn't find the ether, which made things even more confusing.

Einstein's simple genius was to propose that that was the speed in EVERY frame, and all of the consequences of special relativity such as time dilation really come from that one idea.

02-17-2005, 10:39 AM	#1 (permalink)
vinaur Insane	Lorentz transformation I'm doing a "little" english project on the theory of relativity (most likelly both special and general) and I came across this problem with Lorentz Transformation. The whole process is described right here. What I have problem with is arriving at equation #7a. Any help would be much appreciated. Thanks upfront.

02-17-2005, 04:03 PM	#2 (permalink)
fckm Insane Location: Ithaca, New York	in sentence {11}, he says to set t'=0, which results in the equation under sentence eleven. He then uses this equation to transform a point in x to a point in x': x=0 => x'=0 x=1 => x'=a(1-v^2/c^2) thus delta_x => delta_x'=a(1-v^/c^2) By the way, how Englishy is this project going to be? From what I understand of general relativity, it's hard. Really hard. Unless you already have a background in tensor math, I think it will be much more difficult to follow the derivation than special relativity __________________ And if you say to me tomorrow, oh what fun it all would be. Then what's to stop us, pretty baby. But What Is And What Should Never Be.

02-18-2005, 06:04 AM	#4 (permalink)
vinaur Insane	Thank you for your responses. I do realize that deriving equations in an English paper is a bad idea, so I'm not going to do it. I'll be explaining the reasoning behind relativity, etc. My teacher is rather dumb so, I think she won't even really try to understand the paper. As I have discovered yesterday, there is a mistake on the page that I linked to yesterday. It had some characters missing, like delta infront of x' on line 10 and that should be equal to I not 1. So here's the correct page (as much as I can tell). Maybe it will help solve my problem by finding what I'm doing wrong. Here's what I do: 1) Set t' to 0 in equation #5 and solving for t: t=(bx)/(ac) 2) Substitute t in the other equation 5: x'=ax-(b^2x)/(a) 3) Since v=(bc)/a we can do this: x'=ax-(bvx)/c 4)We can do the same thing again: x'=ax-(v^2ax)/c^2 5)Factor out ax: x'=a(1-v^2/c^2)x So how do they get I to show up instead of 1??? Or is it a mistake in their text?? And why do they just get rid of x when they go to equation 7a. Wouldn't it become delta_x and then be replaced by I? Thanks again. BTW, I know this wasn't really necessary, but how do you like the pretty print for the equations? Click them if you haven't figured it out yet. could be useful for some more complex stuff. Last edited by vinaur; 02-18-2005 at 06:08 AM..*

02-19-2005, 08:24 AM	#8 (permalink)
fckm Insane Location: Ithaca, New York	Um, I think that I is actually a 1. That's the only thing that makes sense to me right now. __________________ And if you say to me tomorrow, oh what fun it all would be. Then what's to stop us, pretty baby. But What Is And What Should Never Be.

02-19-2005, 09:01 AM	#10 (permalink)
fckm Insane Location: Ithaca, New York	Um, if you're a physics major/engineer, you'll probably see this in freshman level physics. You're most likely to see it at the end of first or second semester mechanics. (Actually, my high school physics teacher was going to teach us special relativity, but then he had to go on paternity leave, so he never got around to it) The math is pretty simple, it's just conceptually difficult. If you ARE a physics major, and you haven't seen this yet, I would be.... concerned. __________________ And if you say to me tomorrow, oh what fun it all would be. Then what's to stop us, pretty baby. But What Is And What Should Never Be.

02-17-2005, 07:00 PM	#3 (permalink)
Jrock Upright	I'd be carefull about writing a science paper for english class. I have a friend who recently wrote a paper on string theory for his english class. He dumbed it down as much as he could, and it was still too difficult for the english professor to understand. As a result, he didn't get a very good grade. It's easy to pad out an english paper to the required length with equations, but your teacher probably wants words. But completely skipping the derivation leads to a different problem; you'll probably get marked off for not explaning where the equation comes from. You'll run into problems whether you derive it or not. If you insist on writing about relitivity, I would focus on the more basic topics that can be explained without a lot of math. I'd focus mostly on the definition of an intertial reference frame and the invariance of the spacetime interval. That'll be enough to solve some of the relativity paradoxes well enough for an english class.

02-18-2005, 06:28 AM	#5 (permalink)
shakran Tone.	if you already know your audience is dumb and won't understand what you are talking about, why are you talking about it? The quickest path to an F is to make your teacher feel like an idiot. . . That said, if you have time grab A Brief History of Time by Hawking or Coming of Age in the Milky Way by Tim Ferris. Both books are VERY good at explaining complex subjects in ways that ordinary mortals like me can understand. They might give you ideas on how to approach your paper.

02-18-2005, 08:07 AM	#6 (permalink)
vinaur Insane	The I serach project is supposed to allow you to research stuff that you are interested in and you want to learn more about. If I really have a hard time explaning relativity, then I might just switch to writing about Einstein's accomplishments. That way, I won't have to go as much in depth. Thanks for the comment though,

02-18-2005, 04:31 PM	#7 (permalink)
FngKestrel Junkie	You might want to use something a little more layman to describe relativity, like the Cartoon Guide to Physics. http://www.amazon.com/exec/obidos/AS...330488-1055024 Also recommeded is Einstein for Beginners: http://www.amazon.com/exec/obidos/tg...glance&s=books

02-19-2005, 08:47 AM	#9 (permalink)
Slavakion Mjollnir Incarnate Location: Lost in thought	Oh dear lord, my head asplode. What the hell is a Lorentz Transformation? From what I've gathered from Google, it measures time dilation/contraction. I won't see this until higher-level physics, right?

02-20-2005, 09:41 AM	#14 (permalink)
fckm Insane Location: Ithaca, New York	I believe you are wrong. Because the two events occur simultaneously in the frame of M, by the tenets of special relativity, there can be no causal relationship between them. In other words, you can't say that A caused B, or B caused A (Since the two events occur simultateously in frame M, it's impossible that one caused the other). Causal relationships are preserved under transformation (this is a tautology, causation is defined that way), so that if A caused B, then A must occur before B in ALL reference frames. In order for this to occur, special relatvity tells us that (if A caused B), B must occur at least t=d/c seconds after A occurs (where d is the distance between the two and c is the speed of light). Since this problem states that A and B occur simultaneously in the M frame, then we can see that A and B do not have a causal relationship. The causal relationship (t>=d/c) is the only time in special relativity where the order of the events is preserved under transformation. In all other cases, it is possible to find a frame M' where A occurs before B, or B occurs before A. So in this case with the lightning, since in the M frame, A and B occur simultaneously, they do not have a causal relationship. Thus it is possible that in M', A occurs before B, or B occurs before A. It's been a while since I've taken SR. Hopefully someone else will chime in and correct any mistakes I've made. edit:spelling __________________ And if you say to me tomorrow, oh what fun it all would be. Then what's to stop us, pretty baby. But What Is And What Should Never Be.

02-21-2005, 07:12 AM	#15 (permalink)
vinaur Insane	I think you misunderstood me there. What I was trying to get at is that the two beams of light will reach the moving object at the same time regardless of its speed, as long as the object was exactly inbetween the two lightnings when they hit. My reasoning is that, according to the law of propagation of light the speed of the light beam relative to the moviong object has to be c, therefore the distance between the object and either of the two light beams has to be decreasing at the same rate c. If the object is heading towars one of the beams, then it "slows down" the one it's heading towards, and "speeds up" the one it moving away from. So basically relative to both beams (taken at the same time) it is not moving. So since the beams reach the person at the same time, Einsteins argument that time is different for two reference bodies is not supported. I hope this is a bit clearer and I hope I'm not starting to bug you (or anyone else).

02-21-2005, 04:47 PM	#16 (permalink)
Paradise Lost "Afternoon everybody." "NORM!" Location: Poland, Ohio // Clarion University of PA.	Just going by logic and without any pure mathematical knowledge of the subject, it seems like, since you are moving at a constant speed, that when both strike, at time t = 0, then, say you are 5 meters away from both bolts, moving at 5 m/s, you still are getting closer to the one flash, or it gets closer to you quicker than the other flash, albiet only 1.67x10^-8 seconds quicker. But then again, this is in reference to you, although, in a theoretical set-up, there would be no other reference other than empty space, which, I suppose, relative to the empty space directly inbetween the beams, which I suppose also can be considered at rest, the bolts would happen 'simultaneously.' 2nd Paragraph could be totally wrong. Oh, and talk about physics questions anytime you want, I need more info myself, and the more people talking, the more knowledge flowing. __________________ "Marino could do it." Last edited by Paradise Lost; 02-21-2005 at 05:08 PM..

02-21-2005, 09:34 PM	#18 (permalink)
vinaur Insane	Wow, this is cool. I never thought of thinking about d1 and d2 being different at t=0 and the train ending up at the midpoint when the two light beams meet. Then the concept of simultanity does fly out the window (or does it...I would still argue that it holds true, but let's drop it). Does anyone else out there think that there is something incorrect about SR. Even though it does make sense if you take it one step at a time, I still think there is something wrong. Maybe the law of propagationof light is wrong? just think of it, if it was, wouldn't it make stuff so much easier (on the daily basis anyway). I was thinking, what if there was a way to measure the occurance of an event in a distance with something faster than the speed of light, then SR would be incorrect, wouldn't it?? BTW Thanks for you time and info fckm.