# Where s the moving train on the embankment?

• Grimble
In summary, the concept of relativity of simultaneity means that observers in different frames of reference will perceive events as occurring at different times. This applies to the scenario described, where observers on a train and on an embankment will see events as occurring at different times due to their relative velocities. This also means that there is no "neutral observer" as every observer has their own frame of reference. Additionally, each frame of reference is equally valid and there is no preference given to one over the other. Therefore, a "neutral observer" would see the two entities aligning with each other when A passes A', as described by Einstein in his thought experiment.
Grimble
http://img682.imageshack.us/img682/4396/movingtrain.jpg

How do these observers line up in relation to each other when A' passes A?

We know that from the train's reference frame B' will be adjacent to C and that from the embankment's frame C' will be adjacent to B, but as there is only one train and one embankment and as each has only a single physical existence and can only physically exist in one place at one time, how do they 'really' line up as they pass.

Now I can appreciate that time dilation and length contraction are perceived effects, distortions if you like due to the relative velocity of the participants, and that that perceived 'distortion' of time and space is reciprocal (as it must be, being due to their relative velocity).
And I can also appreciate that, to the observers in their reference frames those 'distortions' are the 'real' measurements they perceive; much as the pitch, of the sound of a passing car, being higher as it approaches and lower as it recedes, is real to an observer, whilst the actual pitch of the sound produced does not vary. It is once again an effect (albeit entirely different in nature) due to the relative velocity.

Now can we say that if we could calculate their relative positions, rather than 'observing them' from one or other of the reference frames, we would see them align, observer to observer?

Grimble

Last edited by a moderator:
You need to take into account relativity of simultaneity.

In the embankment frame, the train moves from left to right and is contracted by a factor of 1/2. The events "A' passes A" and "C' passes B" are simultaneous.

In the train frame, the embankment moves from right to left and is contracted by a factor of 1/2. The event "B passes C'" precedes the event "A passes A'", i.e. they are not simultaneous.

jtbell said:
You need to take into account relativity of simultaneity.

In the embankment frame, the train moves from left to right and is contracted by a factor of 1/2. The events "A' passes A" and "C' passes B" are simultaneous.

In the train frame, the embankment moves from right to left and is contracted by a factor of 1/2. The event "B passes C'" precedes the event "A passes A'", i.e. they are not simultaneous.

But in this scenario there are no 'lightning strikes' to associate simultaneity with either frame of reference, so why give preference to either?

Anyway, that apart, I am thinking of this as a 'thought experiment'.
We know that from the embankment's frame the train will be length contracted; and that from the train's frame the embankment will be length contracted; but those are two views/perceptions of one state of physical existence and unless we are venturing into the realms of multiple realities, only one set of physical relationships can exist.

Now it cannot be either of the above for that would give preference to one, so we need another view/reality and that can only be that neither is physically contracted i.e. the length contraction is an effect of their relative velocities.

This leaves us with the idea that, to a 'neutral observer', B lines up with B' and C lines up with C' when A lines up with A'.

And in fact, this is what Einstein describes in http://www.bartleby.com/173/9.html" and in the following paragraph where he writes
Let M' be the mid-point of the distance A —> B on the traveling train. Just when the flashes 1 of lightning occur, this point M' 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 M’ in the train did not possesses 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.
This is before he associates the relationship with reference to either of the parties and agrees with the fact that neither the train nor the embankment would experience any length contraction with reference to their own frame of reference.

I am trying to comprehend the physical relationship/juxtaposition of the two entities, not how they appear to each other.

PS I am not in any way denying the validity of all the experiments, and the fact that time dilation and length contraction are real and used everyday for GPS.

Grimble

Last edited by a moderator:
What do you mean by "neutral observer"? Every observer has some frame of reference. And observer moving with the train will see the situation completely differently form an observer on the embankment. And there are observers with non-zero speed relative to both train and embankment that would see the situation completely differently from either.

Grimble said:
But in this scenario there are no 'lightning strikes' to associate simultaneity with either frame of reference, so why give preference to either?
The lightning strikes are just meant to illustrate the relativity of simultaneity--they don't create it. No preference is given to either frame of reference--they are equally valid.

Anyway, that apart, I am thinking of this as a 'thought experiment'.
We know that from the embankment's frame the train will be length contracted; and that from the train's frame the embankment will be length contracted; but those are two views/perceptions of one state of physical existence and unless we are venturing into the realms of multiple realities, only one set of physical relationships can exist.
Every frame of reference will have its own space and time coordinates with with to describe the world. Each is perfectly valid.

Now it cannot be either of the above for that would give preference to one, so we need another view/reality and that can only be that neither is physically contracted i.e. the length contraction is an effect of their relative velocities.
What do you mean by 'physically contracted'? If you want an observer-independent way of describing things, you'll need to use space-time diagrams.

This leaves us with the idea that, to a 'neutral observer', B lines up with B' and C lines up with C' when A lines up with A'.
Huh? Please describe this 'neutral observer'. A lining up with A' is an event; so is B lining up with B', etc. The time order of those events depends on the frame of reference; no observer is 'neutral'.

And in fact, this is what Einstein describes in http://www.bartleby.com/173/9.html" and in the following paragraph where he writes
That quote has nothing to do with any mythical 'neutral' observer--it's just a description of M' and how an observer there is moving with the train.

Last edited by a moderator:
can only physically exist in one place at one time
A train exists during an extended period of time, not at one time. Each observer picks a different bunch of events from this extended existence and calls it "the train now". That's how it works, and I don't see how you could possibly come to grips with it or even ask the right questions if you don't draw the situation on a sheet of paper.

Doc Al said:
The lightning strikes are just meant to illustrate the relativity of simultaneity--they don't create it. No preference is given to either frame of reference--they are equally valid.

The above was in reply to my response to the following post :
jtbell said:
You need to take into account relativity of simultaneity.

In the embankment frame, the train moves from left to right and is contracted by a factor of 1/2. The events "A' passes A" and "C' passes B" are simultaneous.

In the train frame, the embankment moves from right to left and is contracted by a factor of 1/2. The event "B passes C'" precedes the event "A passes A'", i.e. they are not simultaneous.
So why are the two scenarios given that way round?

Grimble

Grimble said:
So why are the two scenarios given that way round?

That's just the way I happened to write them. Where I live, I don't have many opportunities to ride trains, so it's more common for me to be standing on the ground watching them go by, and that's the scenario I thought of first.

Ich said:
A train exists during an extended period of time, not at one time. Each observer picks a different bunch of events from this extended existence and calls it "the train now". That's how it works, and I don't see how you could possibly come to grips with it or even ask the right questions if you don't draw the situation on a sheet of paper.

I will do my best and draw some diagrams, but that may take me a day or so!

jtbell said:
That's just the way I happened to write them. Where I live, I don't have many opportunities to ride trains, so it's more common for me to be standing on the ground watching them go by, and that's the scenario I thought of first.

OK

I will do my best and draw some diagrams, but that may take me a day or so!
Only two: embankment frame and train frame. If you succeed, I bet you will answer the question yourself.
And don't draw fancy trains or something, a train in a spacetime diagram is two parallel lines, nothing more.

Doc Al said:
Every frame of reference will have its own space and time coordinates with with to describe the world. Each is perfectly valid.

Yes of course, I can see and acept that, but they are all different 'views' (i.e. space and time coordinates) of the same single world, that are dependent on the conditions under which they are viewed (measured).
And yes, of course they are all perfecly valid, for those conditions, but the conditions under which they are viewed do not change the way the molecules of either the train, or the embankment are put together.

What do you mean by 'physically contracted'? If you want an observer-independent way of describing things, you'll need to use space-time diagrams.

Thank you, yes, I will have a go!

Huh? Please describe this 'neutral observer'. A lining up with A' is an event; so is B lining up with B', etc. The time order of those events depends on the frame of reference; no observer is 'neutral'.

Sorry, please excuse my ignorance in choosing the way I express myself!
I believe I should have used the term "observer-independent"

That quote has nothing to do with any mythical 'neutral' observer--it's just a description of M' and how an observer there is moving with the train.

I'm sorry, I was reading it that, as Einstein was saying: "But the events A and B also correspond to positions A and B on the train." and: "Let M' be the mid-point of the distance A —> B on the traveling train." and: "Just when the flashes 1 of lightning occur, this point M' naturally coincides with the point M", he was, effectively describing an "observer-independent" view of the scenario...

Grimble

Grimble said:
Sorry, please excuse my ignorance in choosing the way I express myself!
I believe I should have used the term "observer-independent"

Grimble

There is no such thing in this scenario. Perhaps you are thinking of an observer relative to which the train and embankment have equal and opposite motion.

Matheinste.

may be, may be a 'neutral' observer has instant-vision.
(i.e. not an atomic observer, as usual, that depends on 'c' speed to ackowledge the events (and label time coordinate)).

Grimble said:
http://img682.imageshack.us/img682/4396/movingtrain.jpg

How do these observers line up in relation to each other when A' passes A?

We know that from the train's reference frame B' will be adjacent to C and that from the embankment's frame C' will be adjacent to B, but as there is only one train and one embankment and as each has only a single physical existence and can only physically exist in one place at one time, how do they 'really' line up as they pass.

Now I can appreciate that time dilation and length contraction are perceived effects, distortions if you like due to the relative velocity of the participants, and that that perceived 'distortion' of time and space is reciprocal (as it must be, being due to their relative velocity).
And I can also appreciate that, to the observers in their reference frames those 'distortions' are the 'real' measurements they perceive; much as the pitch, of the sound of a passing car, being higher as it approaches and lower as it recedes, is real to an observer, whilst the actual pitch of the sound produced does not vary. It is once again an effect (albeit entirely different in nature) due to the relative velocity.

Now can we say that if we could calculate their relative positions, rather than 'observing them' from one or other of the reference frames, we would see them align, observer to observer?

Grimble

The entire rod is shortened.

They will not line up if A does.

Last edited by a moderator:

Grimble said:
Yes of course, I can see and acept that, but they are all different 'views' (i.e. space and time coordinates) of the same single world, that are dependent on the conditions under which they are viewed (measured).
And yes, of course they are all perfecly valid, for those conditions, but the conditions under which they are viewed do not change the way the molecules of either the train, or the embankment are put together.

What experiment do you have to conclude this.

Time dilation and length contraction are in the mainstream logic.

Ich said:
Only two: embankment frame and train frame. If you succeed, I bet you will answer the question yourself.
And don't draw fancy trains or something, a train in a spacetime diagram is two parallel lines, nothing more.

So, in a spacetime diagram what method do you use for multiple observers in the same frame but at a distance?

So, in a spacetime diagram what method do you use for multiple observers in the same frame but at a distance?
Come on, the longest thread in PF history, and nobody bothered to explain the role of an observer in SR to you?
What changes if you introduce a gazillion observers hiding at every conceivable place?

Yes of course, I can see and acept that, but they are all different 'views' (i.e. space and time coordinates) of the same single world, that are dependent on the conditions under which they are viewed (measured).
And yes, of course they are all perfecly valid, for those conditions, but the conditions under which they are viewed do not change the way the molecules of either the train, or the embankment are put together.

cfrogue said:
What experiment do you have to conclude this.

Time dilation and length contraction are in the mainstream logic.

I'm sorry, but are you saying that the "way the molecules of either the train, or the embankment are put together" varies according to where they are referenced from, and therefore, if many observers are referencing them from different frames, that those molecules are arranged differently, and that we must therefore have multiple existences?

Can you point me to the experiments that lead one to conclude this?

And yes, of course TD and LC are real, I have never said they are not, but they are effects albeit ones that are real to those that experience them.

Consider, if you will, a rod at rest viewed by many observers in different frames moving with different velocities; which seems the more likely explanation:
1. that the rod has a separate existence in each frame of reference with a different length depending on the relative velocity
2. or, that the rod has one, unique existence that is measured differently from the different frames as a function of their individual velocities.

Surely the way to find the 'real' length of the rod would be to use an observer that was at rest relative to the rod, where the TD and LC, as a function of the velocity was 0? Would it not

Grimble

Grimble said:
Surely the way to find the 'real' length of the rod would be to use an observer that was at rest relative to the rod, where the TD and LC, as a function of the velocity was 0? Would it not

Grimble

Length contraction in SR is stress free, that is no distorting forces are involved, no moleclar changes. I am sure you already knew that.

As regards "real" length, I think what is usually said is that the rod length is maximal when measured in a frame in which it is at rest. Rest length.

Matheinste.

This is how I visualize the length contraction
The sketch is rather figurative and does not makes evident the mass growth with motion.
------------------------------

consider aaa...aaa this the initial 'atom' configuration with some spatial extention, then start to exert a steady force from left to right, beeing 'c' as the speed of transmission of the effect.
constant force implies crescent speed and sucessive length contraction
assume atom moving from left to rigth and letters a,b,c,d,...x,y represents crescent matter densities
we can observe a constant increase in the speed, and a constant decrease in length.
the times t0,.tn are from a lab clock (not within the particle)

t0 no force _aaaaaaaaaaaaaaaaaaaaaaaaa
t1 force >______bbbbaaaaaaaaaaaaaaaaa
t2 force >________cccccbbbbbaaaaaaaaaa
t3 force >____________dddddcccccbbbbba
t4 force >__________________eeeedddddcccccbbb
t5 force >______________________fffffeeeeedddddcccc
t6 force >____________________________gggggfffffeeeeedd
t7 force >____________________________________hhhhhgggggfffff
...
tn______________________________________________________________xxxyy

----------------------------
We must see it shrinking, otherwise we have to accept instant action at distance.
This is the Lorentz view. Neighbouring atoms adjust their sizes and positions to mantain the equilibrium (already preexistent) obeying electromagnetic laws.

The Einstein position on this issue is 'neutral' ( because of 'c' and definition of simultaneity we have to observe this effect) and said nothing about the underlying mechanism.
The Lorentz position on this issue is richer because he applyed Maxwell laws to an moving electron and showed that the configuration change and added and we are unable to measure the changes that happen to us, as observers.
Then MMX was negative as he said (it could be the cause of negative results of LIGO experiment)

----------
http://en.wikipedia.org/wiki/Lorentz-FitzGerald_contraction_hypothesis"
The Lorentz–FitzGerald contraction hypothesis, the more formal name for length contraction, was proposed by George Francis FitzGerald and independently proposed and extended by Hendrik Lorentz to explain the negative result of the Michelson–Morley experiment, which attempted to detect Earth's motion relative to the luminiferous aether.
After reading a paper by Heaviside that showed how electric and magnetic fields are affected by motion, FitzGerald hit on the idea that when a body moves through space its size changes due to its motion, and that this may explain Michelson and Morley's "null result". FitzGerald suggested the contraction in an 1889 letter to Science, but did not himself see the letter in print, and it attracted no notice until many years later. He did, however, describe the idea to his scientific friends, and Oliver Lodge mentioned it in print in 1892. Lorentz had hit on the idea independently in 1891 and in 1892 showed how such an effect might be expected based on electromagnetic theory and the electrical constitution of matter. ...This small change accounts for Michelson and Morley's negative result by making the source of light and the mirror draw closer together when the system is moving lengthwise.

http://en.wikisource.org/wiki/Electromagnetic_phenomena"

Last edited by a moderator:
I am on a spaceship and my brother is on another 5 light years away.
I set off towards him at 0.866c (instant acceleration)
Does the last post imply that, because of the force experienced, my atoms rearrange them selves and I become shorter?
Or is it my brother who experiences LC and become physically shorter? And if so, when does this happen?
If it happened when I accelerated it would constitute 'instant' action at a distance, would it not? Or does it take 5 years for the effect to be 'felt' by him?

LC is reciprocal so if my brother were instantly contracted, how long would it be before I was contracted in his frame? Surely it would take at least 5 years before he could be aware of it?

And so that would mean that when I accelerated he would immediately be half as big and half as far away, while I would still be the same size and distance away for him and would that be for 5 years or 2.5 years?

And if I accelerated equentl the distance between us halved, would that mean that we had traveled 2.5 light years in 0 time?

Hi Grimble,

you've been engaged in some extensive discussions, yet I see that you still struggle with the basic concepts. From my experience, this is because you haven't drawn spacetime diagrams. Really, that's all you have to do.
So please take my advice and come back with some diagrams before you ask further questions. There is no other way.

Grimble said:
I am on a spaceship and my brother is on another 5 light years away.
I set off towards him at 0.866c (instant acceleration)
Does the last post imply that, because of the force experienced, my atoms rearrange them selves and I become shorter?
Or is it my brother who experiences LC and become physically shorter? And if so, when does this happen?
If it happened when I accelerated it would constitute 'instant' action at a distance, would it not? Or does it take 5 years for the effect to be 'felt' by him?

LC is reciprocal so if my brother were instantly contracted, how long would it be before I was contracted in his frame? Surely it would take at least 5 years before he could be aware of it?

And so that would mean that when I accelerated he would immediately be half as big and half as far away, while I would still be the same size and distance away for him and would that be for 5 years or 2.5 years?

And if I accelerated equentl the distance between us halved, would that mean that we had traveled 2.5 light years in 0 time?

The example that I put forward is because we can not have 'instant action' at distance, and the existence of a rigid-body permits 'instant action' at distance.
There are presently more than one way to derive SR equations, being Lorentz AFAIK the first one to put them forward (LC,TL and Mass Increase), and he deserves to be appointed as the 'father of Relativity' (SR), but also others were getting closer (FitzGerald and Poincaré).
The solution of Einstein is simpler and did not needed to present a physical mechanism.

There is not such instant acceleration unless your spaceship has no mass.

First we need to settle: who is the observer (this observer has his rod and clock with which we make all the measurements)
If both actually shrink brings the multiple existences problem (a paradox). This leaves only 2 hypotheses: none or only one has actually to shrink.

The problem 'seems' the reverse one of the other but only the train has been accelerated previously, in relation to the embankment. Energy had been invested only in one object.
Previous history, what happened before the configuration you present, is relevant.

If both actually shrink depending on the observer brings the multiple existences problem (a paradox). This leaves only 2 hypotheses: none or one has actually shrinked.

The problem 'seems' the reverse one of the other but only the train has been accelerated, previously, in relation to the embankment. Energy had been invested only in one object.
Previous history, what happened before the configuration you present, is relevant because we need a non Gallilean reference frame to study the complete happening.

for simplicity
be it the train at rest : aaaaaaaaaaaa
be it the train at 0.866c : bbbbbb

lets draw the embankment in train (at rest) units:
A B C
aaaaaaaaaaaa - embankment observer rod = 1 embankment length= 1 train (at rest) length
bbbbbb - train passing by first event (A aligned)
______bbbbbb - train passing by second event (C aligned)

The length halved (LC) in relation to the rest position.
And the times? From the invariant c=dl/dt one concludes that doubles (TD) as it must vary in inverse relation of length variation.
We can blindly apply SR Lorentz relations and get the same results. But the evasion from paradoxes are more critical.

About the simetry of the experiment:
Supose that you are at CERN, accelerating protons, and watching the colisions.
The CERN is the lab, the observer.
The accelerated protons gain energie in relation to the other at rest.
Then they are aproching to colide but it is not a symetrical situation.
Some are heavier than the ones at rest. In terms of speed approach the situation is similar.
Which ones gained mass and get length contracted?
AFAIK It does not exist experimental basis contrary to the way I expressed the experiment.
See the train as the proton: first at rest in the lab, then the train (proton) gets accelerated, and finaly about to colide with other proton yet at rest in the embankment (our proton rod at rest)).
There is no symetry.
Concluding In the experiment we must consider the masses to became physically meaning.
This way I think that no paradox remains.

Concluding: In the experiment we must consider the masses to became physically meaning.
This way I think that no paradox remains unsolved and it is in accord with all the experiments that we have made until now.

Ich said:
A train exists during an extended period of time, not at one time. Each observer picks a different bunch of events from this extended existence and calls it "the train now". That's how it works, and I don't see how you could possibly come to grips with it or even ask the right questions if you don't draw the situation on a sheet of paper.

I'm unsure as to how to draw a spacetime diagram. From what I can determine it seems to be a Minkowski diagram?

http://img709.imageshack.us/img709/3476/spacediagram.jpg

Having tried to draw that I am unsure how to proceed, perhaps you will be good enough to guide me?

The one thing that does standout for me, is that from each frame of reference, when A' and A are adjacent, (and that is an event in any frame of reference?), considering only that frame of reference, the points B and C, B' and C' have the same relative spacetime displacement from the 'event' A' passes A?

Grimble

Last edited by a moderator:

Grimble said:
Consider, if you will, a rod at rest viewed by many observers in different frames moving with different velocities; which seems the more likely explanation:
1. that the rod has a separate existence in each frame of reference with a different length depending on the relative velocity
2. or, that the rod has one, unique existence that is measured differently from the different frames as a function of their individual velocities.
I vote for 3) The rod's length is different in different reference frames, not because it has a separate existence, but because length is frame dependent.

This concept isn't new to SR, in Newtonian physics many things are frame dependent. For example, the kinetic energy of the rod above is different in each reference frame.

Would you claim that the rod must have a separate existence in each reference frame because its energy is different in each frame in Newtonian physics? Would you ask how the rod "gained" or "lost" energy? The kinetic energy of the rod didn't change, it was always different in different reference frames.

Last edited by a moderator:
Grimble said:
I am on a spaceship and my brother is on another 5 light years away.
I set off towards him at 0.866c (instant acceleration)
Does the last post imply that, because of the force experienced, my atoms rearrange them selves and I become shorter?
Nope, you would be the same length you always were in that reference frame, which was always shorter than your length in your rest frame.
Or is it my brother who experiences LC and become physically shorter? And if so, when does this happen?
If it happened when I accelerated it would constitute 'instant' action at a distance, would it not?
Length contraction isn't an "action". An object's length is different in different reference frames now and yesterday. The length didn't change, it was always frame dependent.
And if I accelerated equentl the distance between us halved, would that mean that we had traveled 2.5 light years in 0 time?
Nope, but the time can be arbitrarily small. In accelerated reference frames, velocity isn't limited to c like it is in inertial reference frames.

Al68 said:
I vote for 3) The rod's length is different in different reference frames, not because it has a separate existence, but because length is frame dependent.

This concept isn't new to SR, in Newtonian physics many things are frame dependent. For example, the kinetic energy of the rod above is different in each reference frame.

Would you claim that the rod must have a separate existence in each reference frame because its energy is different in each frame in Newtonian physics? Would you ask how the rod "gained" or "lost" energy? The kinetic energy of the rod didn't change, it was always different in different reference frames.

No, the kinetic energy is a function of their relative velocity, just as LC and TD are functions of the relative velocity.

What do you mean by frame dependent? It has a nice sound to it and it is a nice easy image but what does it mean? How is something frame dependent?

Something may have different values in different frames, with things like kinetic energy or doppler effects we know why and how that works and we know, in each case, it is the view that changes not the object viewed.

I'm unsure as to how to draw a spacetime diagram. From what I can determine it seems to be a Minkowski diagram?
Yes.
Ok, you got the embankment right in the embankment's frame, and the train in the train's frame. Time and space in the embankment frame are called (t,x), in the train frame (t',x').
Now some hints for corrections. Please make sure you understand why it has to look different.
1. From the embankment' frame, the train moves to the right (+x). That means that the embankment moves to the left in the train's frame (-x).
2. The line C' must cross the line B at t=0 (they align when A meets A', as seen in the embankment frame).
2'. The line C must cross the line B' at t'=0 (they align when A meets A', as seen in the train frame).
(I hope you see that these are two different conditions, not contradicting each other.)
3. The speed is much closer to c than you've drawn it. Try to get the inclination of the lines right, this will become important.

Ich said:
Yes.
Ok, you got the embankment right in the embankment's frame, and the train in the train's frame. Time and space in the embankment frame are called (t,x), in the train frame (t',x').
Now some hints for corrections. Please make sure you understand why it has to look different.
1. From the embankment' frame, the train moves to the right (+x). That means that the embankment moves to the left in the train's frame (-x).
2. The line C' must cross the line B at t=0 (they align when A meets A', as seen in the embankment frame).
2'. The line C must cross the line B' at t'=0 (they align when A meets A', as seen in the train frame).
(I hope you see that these are two different conditions, not contradicting each other.)
3. The speed is much closer to c than you've drawn it. Try to get the inclination of the lines right, this will become important.

Hello, and thank you for your help in this forum.

I have tried to make the changes you describe but I seem to be getting in a bit of a muddle with them
Here is what I have done so far, but I must be getting confused somewhere - Help!
http://img19.imageshack.us/img19/6204/spdiagfig1.jpg
http://img191.imageshack.us/img191/6783/spdiagfig2.jpg

Grimble

Last edited by a moderator:
Not bad, but in Fig 2, the A' B' and C' lines should all be parallel to the ct axis, not the x axis. It might also help you to compare the two diagrams if you continued Fig 2 downwards below the x' axis to before the event where A meets C'.

Grimble said:
What do you mean by frame dependent? It has a nice sound to it and it is a nice easy image but what does it mean? How is something frame dependent?
A quantity is frame dependent if its value depends on the reference frame used, like kinetic energy, or length in SR.
Something may have different values in different frames, with things like kinetic energy or doppler effects we know why and how that works and we know, in each case, it is the view that changes not the object viewed.
Exactly. An object's length in SR is frame dependent, meaning it has a different value in different reference frames, but the object doesn't "change" just because we choose a different frame resulting in a different length.

Like you said, the kinetic energy of an object doesn't "change" just because it will have a different value if we choose a different reference frame. Same goes for length in SR.

OK, Grimble,

factor in DrGreg's comments and you're done with drawing.
There's one important thing I suspect you didn't consider:
The space points A,B,C,A',B',C' are actually lines in the diagram. You seemed to label certain events (i.e. points in the spacetime diagram) with these letters.
Do you see how (and why) these points are represented by lines?
That their intersection with the x/x'-axis selects 5 different events (one common to both intersections), and that we're talking about these different events when we talk about length contraction?

You should have some questions now, as to what you're supposed to be doing here. Ask them, otherwise I don't know where you're stuck.

DrGreg said:
Not bad, but in Fig 2, the A' B' and C' lines should all be parallel to the ct axis, not the x axis. It might also help you to compare the two diagrams if you continued Fig 2 downwards below the x' axis to before the event where A meets C'.

Like this?

http://img64.imageshack.us/img64/4666/28262050.jpg

Grimble

Last edited by a moderator:

• Special and General Relativity
Replies
21
Views
577
• Special and General Relativity
Replies
52
Views
5K
• Special and General Relativity
Replies
21
Views
950
• Special and General Relativity
Replies
11
Views
1K
• Special and General Relativity
Replies
12
Views
1K
• Special and General Relativity
Replies
58
Views
4K
• Special and General Relativity
Replies
88
Views
4K
• Special and General Relativity
Replies
20
Views
1K
• Special and General Relativity
Replies
16
Views
926
• Special and General Relativity
Replies
25
Views
789