Time-like or Space-like Events: Analyzing the Train Diagram

[John232]

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.

Someone could take two particles that are entangled, and then change the spin of one of them, and the other particle would change its spin instantly faster than the speed of light. Then your "reality" would depend on how fast of a transmission you observed it with. Someone observing it with a string of thread would see it differently than someone with a camera, or even with someone with an entanglement experiment.

 

[Michael C]

https://www.physicsforums.com/attachment.php?attachmentid=44643&stc=1&d=1330706663

Adel, I'm going to stick to the train frame and give some names to things so we can be clear about what we are discussing:

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?

 

[ghwellsjr]

Adel, I'm going to stick to the train frame and give some names to things so we can be clear about what we are discussing:

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?

Are you doing this for his original scenario in post #1 or for the one in post #22? Or are they supposed to be the same or related in some way?

 

[Adel Makram]

Adel, I'm going to try to explain what time-like and space-like 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 even at the origin. Then we can use the Lorentz transformation in a simple way to understand these terms.

First off, time-like simply means that the time coordinate is greater than the spatial coordinate. Space-like simply means that the spatial coordinate is greater than the time coordinate. Light-like simply means that both coordinates are equal.

So if we look at the simplified Lorentz transform, we see:

t' = γ(t-xβ)
x' = γ(x-tβ)

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 this 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(t-xβ) ? γ(x-tβ)

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/√(1-β²)

Therefore, we can remove γ from our conditional statement without effecting the evaluation of the condition:

t-xβ ? x-tβ

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 ill-defined 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.

Thank u for your care to clarify things for me. But my scenario is different from just assigning events to different coordinates in different frames. I posted here a clear detailed diagram and calculation based on my idea. Even from the diagram it is clear that A and B are still spacelike for the train observer because the source is put near to A than B which means that Signal must reaches B in no later than a signal would have taken to reach B coming from A. But how about the math! I see no contradictory to insert ∆t``= (AB`)/c and equating it with ∆t`= (AB`v/c2)/(1-(v2/c2)) can you? In other words, if A and B are spacelike for the train observer, why the math of LT allows the time difference between receiving signal at both ends to equal the time difference a light signal would take to reaches B from A?

 

[Adel Makram]

Adel, I'm going to stick to the train frame and give some names to things so we can be clear about what we are discussing:

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?

yes correct

 

[nitsuj]

Someone could take two particles that are entangled, and then change the spin of one of them, and the other particle would change its spin instantly faster than the speed of light. Then your "reality" would depend on how fast of a transmission you observed it with. Someone observing it with a string of thread would see it differently than someone with a camera, or even with someone with an entanglement experiment.

& 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.

 

[ghwellsjr]

Thank u for your care to clarify things for me. But my scenario is different from just assigning events to different coordinates in different frames. I posted here a clear detailed diagram and calculation based on my idea. Even from the diagram it is clear that A and B are still spacelike for the train observer because the source is put near to A than B which means that Signal must reaches B in no later than a signal would have taken to reach B coming from A. But how about the math! I see no contradictory to insert ∆t``= (AB`)/c and equating it with ∆t`= (AB`v/c2)/(1-(v2/c2)) can you? In other words, if A and B are spacelike for the train observer, why the math of LT allows the time difference between receiving signal at both ends to equal the time difference a light signal would take to reaches B from A?

Could you explain what the single and double back quotes mean?

 

[Michael C]

Adel, I'm going to stick to the train frame and give some names to things so we can be clear about what we are discussing:

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?

yes correct

Without using any relativistic calculations it's easy enough to see that this is impossible. Just put a mirror at A.

But you seem to be claiming that relativistic calculations show this to be possible. In order to understand your argument I need more explanation. In the PDF you just attached, what exactly do you mean by t`<sub>a</sub> and AB` ? In what frame of reference are you doing your calculations?

 

[Fredrik]

Apologies if this has all been sorted out. I haven't read all the posts after my previous one.

OK, so can this time difference allows a timelike separation between A and B if a signal would take off from A to reach B?

It only makes sense to ask about the separation between A and B if they are events. If they are, then the separation is determined from the sign of
$$-(t_A-t_B)^2+(x_A-x_B)^2.$$ If we define
$$x=\begin{pmatrix}t_A-t_B\\ x_A-x_B\end{pmatrix},\qquad\eta=\begin{pmatrix}-1 & 0\\ 0 & 1\end{pmatrix}$$ we have
$$-(t_A-t_B)^2+(x_A-x_B)^2=x^T\eta x.$$ A Lorentz transformation is defined as a linear transformation that preserves $x^T\eta x$, so
$$-(t_A-t_B)^2+(x_A-x_B)^2=x^T\eta x=x'^T\eta x'=-(t_A'-t_B')^2+(x_A'-x_B')^2.$$
So the separation is clearly the same in all inertial frames.

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?

Here A and B have two different meanings in the same sentence. You need to make up your mind if you want them to be events on locations on the ground.

 

[Adel Makram]

Without using any relativistic calculations it's easy enough to see that this is impossible. Just put a mirror at A.

But you seem to be claiming that relativistic calculations show this to be possible. In order to understand your argument I need more explanation. In the PDF you just attached, what exactly do you mean by t`<sub>a</sub> and AB` ? In what frame of reference are you doing your calculations?

I know that it is impossible from the diagram and the experiment setup. So the physics says it is impossible but the math says it is possible!

Even from the diagram it is clear that A and B are still spacelike for the train observer because the source is put near to A than B which means that Signal must reaches B in no later than a signal would have taken to reach B coming from A.

AB` means the distance between A & B in the train
ta` is the time when A received the signal from the source
All calculations are done in the train rest frame

 

[Adel Makram]

Could you explain what the single and double back quotes mean?

Δt` is the difference in time of receiving the light signals at A and B
Δt`` is the time that would have been taken by a light signal emitted from A to reach B

Thanks,,,

 

[Fredrik]

I know that it is impossible from the diagram and the experiment setup. So the physics says it is impossible but the math says it is possible!

Only if you're doing the math wrong.

AB` means the distance between A & B in the train

Have you read any of my posts? I've been telling you lots of times that there's no such thing as a distance between A and B in the train's rest frame, if A and B are events that are simultaneous in the ground's rest frame.

 

[Michael C]

AB` means the distance between A & B in the train
ta` is the time when A received the signal from the source
All calculations are done in the train rest frame

OK. I imagine that v is the velocity of the train relative to the ground?

Please could you explain the reasoning behind the first step in your PDF, where you state that:

t`_{a} = \frac{(\frac{1}{2}AB`)-vt`a}{c}

 

[ghwellsjr]

All calculations are done in the train rest frame

Then why is there a "v" in the calculations and in your diagrams?

The speed of the light source has no bearing on anything except maybe to determine its location at the time it emits a flash which means you could analyze your scenario with the location of the light source as a variable instead of the way you are doing it, correct? Then instead of something special happening at v/c=0.618, it would happen at some position of the light source, correct? And then you could tell us what that location is and you could show us what the something special is, correct? Why don't you do that?

 

[John232]

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."

It happens when particles split apart, their brother particle continues to have a link with the other particle it was joined with. So, they are like blood brothers for life. I think the mention of the indefinite qualities was only referring to the uncertainty principle. But looking further on the same page, "When a measurement is made and it causes one member of such a pair to take on a definite value (e.g., clockwise spin), the other member of this entangled pair will at any subsequent time[7] be found to have taken the appropriately correlated value (e.g., counterclockwise spin)." This is saying that it will happen at any subsequent time. It takes on a definite value when one of the particles are measured, that without measurement would be uncertain. The spins of the two particles would always be the opposite of the other. Then it would only be a matter of turning a clockwise spin of particle into a 1 and a counterclockwise spin into a 0 to gain 1 bit of information that is FTL, more bits would require more particles spins being measured and the tricky part would be haveing them have the same common ancestor. So then it would not be very feasible technology, unless computers could be fed these particles over the internet, even then it wouldn't make much of a difference since light can travel around the world many times in a secound.

 

[Adel Makram]

OK. I imagine that v is the velocity of the train relative to the ground?

Please could you explain the reasoning behind the first step in your PDF, where you state that:

t`_{a} = \frac{(\frac{1}{2}AB`)-vt`a}{c}

v is the velocity of the train relative to the ground, yes. But it is also the velocity of a source put in the ground moving with -v relative to the train if the location of that source coincides with the point of the source in the train at the beginning of the experiment. This I missed to mentioned at the PDF. So the light emitted from a source in the ground corresponding to a point in the train near A than B.
This also gives the answer to your second question. That is when the ground source coincides with the midpoint of the train relative to the ground observer, their light signal would reach A and B at the same time relative to him. It must coincides too with the center of the train relative to the train observer ( because the world lines of the source and the midpoint of the train coincide in all FORs) So ta` is the time recorded by the train observer when the light strikes A and tb` has the same meaning for B

 

[Adel Makram]

Then why is there a "v" in the calculations and in your diagrams?

The speed of the light source has no bearing on anything except maybe to determine its location at the time it emits a flash which means you could analyze your scenario with the location of the light source as a variable instead of the way you are doing it, correct? Then instead of something special happening at v/c=0.618, it would happen at some position of the light source, correct? And then you could tell us what that location is and you could show us what the something special is, correct? Why don't you do that?

v is the velocity of the train relative to the ground, yes. But it is also the velocity of a source put in the ground moving with -v relative to the train if the location of that source coincides with the point of the source in the train at the beginning of the experiment. That is I missed to mention in the PDF. So the light emitted from a source in the ground corresponding to a point in the train near A than B.

So when the ground source coincides with the midpoint of the train relative to the ground observer, their light signal would reach A and B at the same time relative to him. It must coincides too with the center of the train relative to the train observer ( because the world lines of the source and the midpoint of the train coincide in all FORs) So ta` is the time recorded by the train observer when the light strikes A and tb` has the same meaning for B

 

[ghwellsjr]

You only addressed my first question and you didn't even answer it:

All calculations are done in the train rest frame

Then why is there a "v" in the calculations and in your diagrams?

v is the velocity of the train relative to the ground, yes. But it is also the velocity of a source put in the ground moving with -v relative to the train if the location of that source coincides with the point of the source in the train at the beginning of the experiment. That is I missed to mention in the PDF. So the light emitted from a source in the ground corresponding to a point in the train near A than B.

My question was: why, since "all calculations are done in the train rest frame" do you need "v" in those calculations?

So when the ground source coincides with the midpoint of the train relative to the ground observer, their light signal would reach A and B at the same time relative to him. It must coincides too with the center of the train relative to the train observer ( because the world lines of the source and the midpoint of the train coincide in all FORs) So ta` is the time recorded by the train observer when the light strikes A and tb` has the same meaning for B

Isn't it the case that the source of light emits a single flash at an instant of time? If this is true, why do you care where the source moves to after the flash has occurred? Couldn't the flash be emitted by a flash bomb that ceases to exist once it is set off? And if this is true, why do you care about its state of motion prior to it being set off?

Please answer the rest of my questions:

The speed of the light source has no bearing on anything except maybe to determine its location at the time it emits a flash which means you could analyze your scenario with the location of the light source as a variable instead of the way you are doing it, correct? Then instead of something special happening at v/c=0.618, it would happen at some position of the light source, correct? And then you could tell us what that location is and you could show us what the something special is, correct? Why don't you do that?

I think if you actually do what I'm suggesting, that is, break your scenario into two parts, one for the train with the flash occurring at a specific point and one where the speed of the ground observer determines where that point is, you will discover that at your special speed of 0.618, the flash actually occurs at location A and for higher speeds, it occurs to the right of A. But I don't know, because I still cannot figure out the second part of your scenario.

You still have not told us where the train observer is located on the train or where the ground observer is located with respect to the light source.

 

[Michael C]

v is the velocity of the train relative to the ground, yes. But it is also the velocity of a source put in the ground moving with -v relative to the train if the location of that source coincides with the point of the source in the train at the beginning of the experiment. This I missed to mentioned at the PDF. So the light emitted from a source in the ground corresponding to a point in the train near A than B.

It's important to remember this: what the source of the light signal does after emitting the signal is irrelevant to the course of the light flash that has already been emitted. The light source could be on the train and the experiment would work just the same way: all that matters is the space-time location of the source at the moment when the signal is fired.

All that you are doing in saying that the source is on the ground is keeping a record in the ground frame of the spatial position of the event "light signal is fired". I'll call this "position p" in the ground frame.

This also gives the answer to your second question. That is when the ground source coincides with the midpoint of the train relative to the ground observer, their light signal would reach A and B at the same time relative to him.

You have to be very careful here. We can distinguish 4 events:

Event 1: light flash is emitted.
Event 2: the middle of the train coincides with "position p" in the ground frame.
Event 3: the light reaches A
Event 4: the light reaches B

In the ground frame, events 2, 3 and 4 are simultaneous. In the train frame, they aren't: they happen in the order 3,2,4.

It must coincides too with the center of the train relative to the train observer ( because the world lines of the source and the midpoint of the train coincide in all FORs)

The two world lines meet at event 2, but I don't see where this helps us in the train frame: in this frame (as remarked above) this is not simultaneous with either event 3 or 4.

So ta` is the time recorded by the train observer when the light strikes A and tb` has the same meaning for B

Yes, but that doesn't explain your first equation.

 

[Adel Makram]

​

You have to be very careful here. We can distinguish 4 events:

Event 1: light flash is emitted.
Event 2: the middle of the train coincides with "position p" in the ground frame.
Event 3: the light reaches A
Event 4: the light reaches B

In the ground frame, events 2, 3 and 4 are simultaneous. In the train frame, they aren't: they happen in the order 3,2,4.
The two world lines meet at event 2, but I don't see where this helps us in the train frame: in this frame (as remarked above) this is not simultaneous with either event 3 or 4.

You are right I made my calculation based on Events 2 & 3 and Events 2 & 4 are simultaneously. So how the wrong math leads to the correct LT?

Thanks,,,

 

[ghwellsjr]

Please don't ignore my response to you on the previous page. And don't expect any of us to figure out what the solution to your problem is until you tell us what your problem is. We can't read your mind.

 

[nitsuj]

Then it would only be a matter of turning a clockwise spin of particle into a 1 and a counterclockwise spin into a 0 to gain 1 bit of information that is FTL, more bits would require more particles spins being measured and the tricky part would be haveing them have the same common ancestor.

lol, yea, not quite "only a matter of".

To your point of the "common ancestor", I think you're missing the significance of this with regard to FTL information "transmission". If I give you a box, And you travel away from me to the other side of the world, and you open the box and find half a banana and deduce I have the other half that is not FTL transfer of information...

 

[Adel Makram]

Please don't ignore my response to you on the previous page. And don't expect any of us to figure out what the solution to your problem is until you tell us what your problem is. We can't read your mind.

Really I don`t. I am making up my mind but a bit slowly

 

[Adel Makram]

My question was: why, since "all calculations are done in the train rest frame" do you need "v" in those calculations?

Isn't it the case that the source of light emits a single flash at an instant of time? If this is true, why do you care where the source moves to after the flash has occurred? Couldn't the flash be emitted by a flash bomb that ceases to exist once it is set off? And if this is true, why do you care about its state of motion prior to it being set off?.

Firstly, I do not need it from the point of view of the train observer. But mathematically, I need a correlative tool with the ground frame so as to compare what will be the expected difference in time between A&B with an expected difference if light would have been emitted from A to B as a function of v! Exactly like the derivation of LT. so if every observer observes sequences related to light transmission from his frame point of view no LT would had ever come!

Secondly, this math could be considered as follow: The ground observer calculate what the train observer would see. So he must includes v

I think if you actually do what I'm suggesting, that is, break your scenario into two parts, one for the train with the flash occurring at a specific point and one where the speed of the ground observer determines where that point is, you will discover that at your special speed of 0.618, the flash actually occurs at location A and for higher speeds, it occurs to the right of A. But I don't know, because I still cannot figure out the second part of your scenario.

If the flash occurs at A, the light takes the same time to reach B that the source takes to reach the mid-point. In this case the v/c=0.5

You still have not told us where the train observer is located on the train or where the ground observer is located with respect to the light source.

There are 2 train observers at A and B
But there is just one ground observer to observe all events from the point where midpoint of the train coincides with the source

 

[Adel Makram]

You only addressed my first question and you didn't even answer it:

My question was: why, since "all calculations are done in the train rest frame" do you need "v" in those calculations?

Isn't it the case that the source of light emits a single flash at an instant of time? If this is true, why do you care where the source moves to after the flash has occurred? Couldn't the flash be emitted by a flash bomb that ceases to exist once it is set off? And if this is true, why do you care about its state of motion prior to it being set.

Yes I guess that if all calculations would be done by the ground observer expecting what the train observer would see, this can also solve the problem raised up by Michel in my calculation that the events of receiving lights by A and the source reaching the midpoint of train are not simultaneous relative to the train observer but they are relative to the ground one!

 

[Michael C]

​

You are right I made my calculation based on Events 2 & 3 and Events 2 & 4 are simultaneously. So how the wrong math leads to the correct LT?

It doesn't! Your results for t`<sub>a</sub> and t`_b are incorrect.

There's a simple relation between t`a and t`b which you can use to check your result. I'll label with "C" the place on the train from where the light flash starts. It's clear that the distances add up like this:

CA`+ CB` = AB`

CA` is t`_{a}c and CB` is t`_{b}c, so:

t`_{a}c + t`_{b}c = AB`

and therefore:

t`_{a} + t`_{b} = \frac{AB`}{c}

Since t`_{a} and t`_{b} are both positive (light isn't going backwards in time!), it's clear that their difference can never exceed \frac{AB`}{c}.