Similar to the Einstein train experiment

[PAllen]

Ok, here's a new set of numbers, slight variation because I have B' and C synch clocks when coincide. Suppose when B' and C are coincident, they synch clocks to 0. They are moving past each other at .6c. Let's use c=1 for easier numbers. At his moment of passing C announces: the beam emitted to the right when light struck when I passed your front is 'now' 20 units (it would be, say, light seconds) away. [edit: and C would know this because the lightning struck 20 seconds ago, by their clock] This means C is referring to the event on light's history that C labels as (x,t)=(20,0). B' would find that this moment on the light's history is given by:

t' = γ (t-vx/c^2) = (1.25) ( 0 - .6 * 20) = -15
x' = γ(x-vt) = (1.25) (20 - .6*0) = 25

So, if B' know the light was at (x',t') = (25,-15), then now, for B' it is at (x',t')=(40,0) just by light propagation. So these are the two relevant events per B' : B''s view of the event C calls 'where the light is now', and B's view of what he calls where the light is now. Two different events.

To see what C says, we run this backwards. First, transform (25,-15) back just for kicks:

t = γ (t' + vx/c^2) = (1.25) (-15 + .6 *25) = 0
x = γ (x' + vt') = (1.25) (25 + .6 * (-15)) = 20

as expected. Now, C's view of what B' calls where the light is now:

t = (1.25) (0 + .6 *40) = 30
x = (1.25) (40 + .6 *0) = 50

Note:

- This second event per C is consistent with light propagation for our c=1 convention
- Both B' and C agree on the time ordering (which came first) of these two events on the light's history

 

[ghwellsjr]

Ok, here's a new set of numbers, slight variation because I have B' and C synch clocks when coincide.

And here's a new set of diagrams.

Suppose when B' and C are coincident, they synch clocks to 0. They are moving past each other at .6c. Let's use c=1 for easier numbers. At his moment of passing C announces: the beam emitted to the right when light struck when I passed your front is 'now' 20 units (it would be, say, light seconds) away. [edit: and C would know this because the lightning struck 20 seconds ago, by their clock] This means C is referring to the event on light's history that C labels as (x,t)=(20,0).

B' would find that this moment on the light's history is given by:

t' = γ (t-vx/c^2) = (1.25) ( 0 - .6 * 20) = -15
x' = γ(x-vt) = (1.25) (20 - .6*0) = 25

So, if B' know the light was at (x',t') = (25,-15), then now, for B' it is at (x',t')=(40,0) just by light propagation.

So these are the two relevant events per B' : B''s view of the event C calls 'where the light is now', and B's view of what he calls where the light is now. Two different events.

To see what C says, we run this backwards. First, transform (25,-15) back just for kicks:

t = γ (t' + vx/c^2) = (1.25) (-15 + .6 *25) = 0
x = γ (x' + vt') = (1.25) (25 + .6 * (-15)) = 20

as expected.

Same as the first diagram.

Now, C's view of what B' calls where the light is now:

t = (1.25) (0 + .6 *40) = 30
x = (1.25) (40 + .6 *0) = 50

Note:

- This second event per C is consistent with light propagation for our c=1 convention
- Both B' and C agree on the time ordering (which came first) of these two events on the light's history

 

[Whatifitaint]

No. Simple. Again.

Thanks, please let me turn this into logical statements. Please explain why this logic that I learned is false.

Let statement P = B' and C are colocated.

Let statement Q = the lightning flash is located at A in the space-time of C.

Then, we have C claiming,

Special relativity \Rightarrow P \rightarrow Q.

Since you said no, we have B' claiming

Special relativity \Rightarrow P \rightarrow \neg Q.

This is called a contradiction.

Can you please show me where this is wrong?

 

[Whatifitaint]

Ok, here's a new set of numbers, slight variation because I have B' and C synch clocks when coincide.


Suppose when B' and C are coincident, they synch clocks to 0. They are moving past each other at .6c. Let's use c=1 for easier numbers. At his moment of passing C announces: the beam emitted to the right when light struck when I passed your front is 'now' 20 units (it would be, say, light seconds) away. [edit: and C would know this because the lightning struck 20 seconds ago, by their clock] This means C is referring to the event on light's history that C labels as (x,t)=(20,0). B' would find that this moment on the light's history is given by:

t' = γ (t-vx/c^2) = (1.25) ( 0 - .6 * 20) = -15
x' = γ(x-vt) = (1.25) (20 - .6*0) = 25

So, if B' know the light was at (x',t') = (25,-15), then now, for B' it is at (x',t')=(40,0) just by light propagation. So these are the two relevant events per B' : B''s view of the event C calls 'where the light is now', and B's view of what he calls where the light is now. Two different events.

To see what C says, we run this backwards. First, transform (25,-15) back just for kicks:

t = γ (t' + vx/c^2) = (1.25) (-15 + .6 *25) = 0
x = γ (x' + vt') = (1.25) (25 + .6 * (-15)) = 20

as expected. Now, C's view of what B' calls where the light is now:

t = (1.25) (0 + .6 *40) = 30
x = (1.25) (40 + .6 *0) = 50

Note:

- This second event per C is consistent with light propagation for our c=1 convention
- Both B' and C agree on the time ordering (which came first) of these two events on the light's history

I agree with everything above.

Even though this is a little different, it has the same issue in it.

C observer view of now and lightning at A when the clocks are synched,

t = γ (t' + vx/c^2) = (1.25) (-15 + .6 *25) = 0
x = γ (x' + vt') = (1.25) (25 + .6 * (-15)) = 20

B' frame calculations of the C observer view of now and lightning location in C frame coordinates when the clocks are synched.

t = (1.25) (0 + .6 *40) = 30
x = (1.25) (40 + .6 *0) = 50

It is correct, that C will see the lightning strike at x=50 when t=30 with t=30 from the new clock sync, which is in the future for C. That is perfectly true. But, that is not the correct now in the C frame.

What I am saying is that is it okay for SR to get the wrong answer for C frame "now" of the location of the lightning strike when the clocks are synched?

Again,

C frame "now" at the clock sync,
t = γ (t' + vx/c^2) = (1.25) (-15 + .6 *25) = 0
x = γ (x' + vt') = (1.25) (25 + .6 * (-15)) = 20

B' claim of C frame "now" at the clock sync
t = (1.25) (0 + .6 *40) = 30
x = (1.25) (40 + .6 *0) = 50

 

[PAllen]

Thanks, please let me turn this into logical statements. Please explain why this logic that I learned is false.

Let statement P = B' and C are colocated.

ok

Let statement Q = the lightning flash is located at A in the space-time of C.

Already a big mistake pointed out many times. This statement has no meaning. You need to add, for example, "located at A per C at Cs time t0". Otherwise it has exactly the content of "how high is up?".

Thus all the rest is completely meaningless.

Then, we have C claiming,

Special relativity \Rightarrow P \rightarrow Q.

This is independently false, as has also been pointed out multiple times. Two co-located observers disagree on where something else is unless their state of motion is the same. Here it is not, so P->Q is simple a totally false statement in SR.

Since you said no, we have B' claiming

Special relativity \Rightarrow P \rightarrow \neg Q.

This is called a contradiction.

Can you please show me where this is wrong?

Everywhere. Further, this has been all explained before.

 

[PAllen]

What I am saying is that is it okay for SR to get the wrong answer for C frame "now" of the location of the lightning strike when the clocks are synched?

Two observers in relative motion disagree on "now"

Again,

C frame "now" at the clock sync,
t = γ (t' + vx/c^2) = (1.25) (-15 + .6 *25) = 0
x = γ (x' + vt') = (1.25) (25 + .6 * (-15)) = 20

B' claim of C frame "now" at the clock sync
t = (1.25) (0 + .6 *40) = 30
x = (1.25) (40 + .6 *0) = 50

No, B' claim of C frame light "now" is (25,-15). (30,50) is C's description of B' claim of the light "now". Each has their own label for these two different events. B' would agree that C would consider (25,-15) [C now per B'] to be (20,0) [C now per C].

Again:

At colocation, there are two separate events:

- where the lightning is now per C
- where the lightning is now per B'

Each (B' and C) have labels for both of these events. Each agrees with how the other would label both of these events. Each agrees with the order of these events - the first one above occurs earlier than the second in the light's history. I really don't see how this is so confusing once you accept relativity of simultaneity.

 

[PAllen]

B' frame calculations of the C observer view of now and lightning location in C frame coordinates when the clocks are synched.

t = (1.25) (0 + .6 *40) = 30
x = (1.25) (40 + .6 *0) = 50

This is a key error. This is C's view of the event B' calls "where the light is now". B' would agree that this is how C would label this event. It corresponds to the event B' labels as (40,0).

 

[Whatifitaint]

Two observers in relative motion disagree on "now"


No, B' claim of C frame light "now" is (25,-15). (30,50) is C's description of B' claim of the light "now". Each has their own label for these two different events. B' would agree that C would consider (25,-15) [C now per B'] to be (20,0) [C now per C].

Again:

At colocation, there are two separate events:

- where the lightning is now per C
- where the lightning is now per B'

Each (B' and C) have labels for both of these events. Each agrees with how the other would label both of these events. I really don't see how this is so confusing once you accept relativity of simultaneity.

I am sorry, I am not following you. You wrote Two observers in relative motion disagree on "now" I completely agree with this, but this has nothing to do with what I said. I totally agree with you that each frame will have a different interpretation of now for any given event. But, if C claims "now" is this (0,t) for an event at the clock sync, and B' translates to determine the C frame "now" of that event at clock sync, that is what I did, is it okay to get the answer wrong. Please note that I am not comparing prime coordinates to unprimed coordinates. I am comparing unprimed coordinates to B' calculated unprimed coordinates.


Above you wrote,
1) This means C is referring to the event on light's history that C labels as (x,t)=(20,0). B' would find that this moment on the light's history is given by:
t' = γ (t-vx/c^2) = (1.25) ( 0 - .6 * 20) = -15
x' = γ(x-vt) = (1.25) (20 - .6*0) = 25

You also wrote,
2) No, B' claim of C frame light "now" is (25,-15).

Please note you said (25,-15) are unprimed coordinates in (2) and primed coordinate in (1).

Look, I really only want a simple answer and then I am finished.

Is it okay for lorentz transforms to get the B' calculation as the wrong answer for the C frame now of the lightning location at the clock sync in the C frame coordinates. This is the experiment you set up.

If it is not OK, then please simply show how B' calculates the correct answer of the "now" of the lightning location of (20,0,0) with t=0 based on its "now" of the lightning location at the clock sync in the C frame. In other words, translate the "now" location of the lightning in B' to the correct "now" in the C frame coordinates using the lorentz transforms.

 

[PAllen]

I am sorry, I am not following you. You wrote Two observers in relative motion disagree on "now" I completely agree with this, but this has nothing to do with what I said. I totally agree with you that each frame will have a different interpretation of now for any given event. But, if C claims "now" is this (0,t) for an event at the clock sync, and B' translates to determine the C frame "now" of that event at clock sync, that is what I did, is it okay to get the answer wrong. Please note that I am not comparing prime coordinates to unprimed coordinates. I am comparing unprimed coordinates to B' calculated unprimed coordinates. Above you wrote,
1) This means C is referring to the event on light's history that C labels as (x,t)=(20,0). B' would find that this moment on the light's history is given by:
t' = γ (t-vx/c^2) = (1.25) ( 0 - .6 * 20) = -15
x' = γ(x-vt) = (1.25) (20 - .6*0) = 25

You also wrote,
2) No, B' claim of C frame light "now" is (25,-15).

Please note you said (25,-15) are unprimed coordinates in (2) and primed coordinate in (1).

Look, I really only want a simple answer and then I am finished.

Is it okay for lorentz transforms to get the B' calculation as the wrong answer for the C frame now of the lightning location at the clock sync in the C frame coordinates. This is the experiment you set up.

If it is not OK, then please simply show how B' calculates the correct answer of the "now" of the lightning location of (20,0,0) with t=0 based on its "now" of the lightning location at the clock sync in the C frame. In other words, translate the "now" location of the lightning in B' to the correct "now" in the C frame coordinates using the lorentz transforms.

There are no wrong answers from the Lorentz transform. There are two events, each with two labels (per B', per C).

- Where the light is now per B' is labeled (40,0) by B' and (50,30) by C.
- Where the light is now per C is labeled (25,-15) by B' and (20,0) by C.

The Lorentz transform takes each of these labels into the other: (40,0) <-> (50,30) ; (25,-15) <-> (20,0). I showed every one of these transforms, both directions (4 of them).

 

[Whatifitaint]

This is a key error. This is C's view of the event B' calls "where the light is now". B' would agree that this is how C would label this event. It corresponds to the event B' labels as (40,0).

These are your calculations based on the B' interpretation, not the other way around. Please read your post. I agree C will calculate this as the B' now in the future. But, this is in the future for C since t=0 and for this x=50 and t=30. t=30 is not the now for C at the clock sync.

This discussion is about the correct "now" for the location of the lightning in the C frame at the clock sync. t=0 is the now for the C frame as you made for this experiment. The lightning is at (20,0,0) with t=0. That is what you did.

So, when t'=0 at the clock sync for B', does B' get the correct "now" of (20,0,0) with t=0 for C of the lightning location?

That is the physical reality of your experiment at the clock sync.

 

[PAllen]

So, when t'=0 at the clock sync for B', does B' get the correct "now" of (20,0,0) with t=0 for C of the lightning location?

That is the physical reality of your experiment at the clock sync.

t'=t=0 only at the single event of colocation. For every other location except the origin (as it were), t' different from t.

 

[PAllen]

So, when t'=0 at the clock sync for B', does B' get the correct "now" of (20,0,0) with t=0 for C of the lightning location?

Per B', the event of "what C calls where the light is now" is (25,-15). t'=0 does not apply to this event. Anyone (B' or C) can use the Lorentz transform (as I explicitly showed) to go from (x',t')=(25,-15) to (x,t)=(20,0). No other transform is relevant, or meaningful. These are the two observer's labels for the same event.

 

[Whatifitaint]

Per B', the event of "what C calls where the light is now" is (25,-15). t'=0 does not apply to this event. Anyone (B' or C) can use the Lorentz transform (as I explicitly showed) to go from (x',t')=(25,-15) to (x,t)=(20,0). No other transform is relevant, or meaningful. These are the two observer's labels for the same event.

Okay, is it the physical reality of your proposed experiment above when the clocks sync, C says the lightning strike is at (20,0,0) with t=0?

Is this the undisputed physical reality of C?

 

[PAllen]

Okay, is it the physical reality of your proposed experiment above when the clocks sync, C says the lightning strike is at (20,0,0) with t=0?

Is this the undisputed physical reality of C?

Yes (well, undisputed physical reality is too strong - it is philosophy, but let's not quibble). And B' says the what C is calling (20,0) is (25,-15). And B' says that at t'=0, the lightning is at (40,0). And C says this event B' is referring to is at (50,30).

Though colocated, and though synching clocks, the only event for which B' and C agree on the "now" of is the moment and location of their passing.

 

[ghwellsjr]

Is this the undisputed physical reality of C?

The undisputed physical reality of C (and B') can be shown on any spacetime diagram. It shows what each observer sees on their own clocks when various things happen to them. It's very important for you to realize that no observer can see light as it propagates away from them. Neither B' nor C can tell where the light is at any given moment except when it reaches them unless they make an assumption or follow a convention. What they have to do is allow the light to reflect off a distant object and wait for the reflection to return to them. Then they assume according to Einstein's second postulate and his convention that the light took the same amount of their own time to get to the distant object as it took for the reflection to get back to them and this allows them to calculate according to their own time when the reflection occurred. Since moving observers have clocks that run at different rates and because they may be at different locations when the light reaches them, they're going to get different answers for when the reflections occurred. There's no physical reality beyond this.

Let's go back to my example of the train with the black locomotive, C' and the red caboose, B', traveling at 0.6c past the blue ground observer, C. I've marked in some of the times for the caboose's dots from the train's rest frame so that the dots are at the same times as the Coordinate Times. Don't worry about the fact that the dots all end in .5 for the red caboose, B':

Now I want to go back to the original spacetime diagrams and add in how each observer measures the time of the "event" of just the flash of light going off to the left and arriving at various locations. I have added in an object shown as a small black circle, at the location of these "events" in order to provide a reflection, shown as a thin black line, back to the observers and I have extended the progress of the observers so that they can detect the reflection of the light.

Here's the rest frame of the blue ground observer, C, showing how he determines the time of the reflection event that is simultaneous with when the red caboose, B', reaches him:

The reflection event occurs at the Coordinate Time of 10 usec but neither observer can see this. The blue ground observer, C, measures the time according to his clock when the original flash occurred at his time 0 usec and he sees the reflection at his time 20 usec so he averages these two numbers (adds them and divides by two) to get 10 usec as the determined time of when the reflection event occurred according to his clock when the red caboose, B', reached him.

The red caboose, B', does the same thing except that he averages the time when the original flash of light passed him, 7.5 usec, and the time the reflection reached him, 32.5 usec, and determines that the reflection occurred at 20 usecs according to his clock. So he doesn't agree that that particular reflection occurs when he passes the blue ground observer, C. I have shown how the red caboose, B', makes this determination using the rest frame of the blue ground observer, C, but we can transform to the rest frame of the red caboose, B', and see that his determination now matches that of the Coordinate Time of his rest frame:

Now we can put another reflecting object in the path of the light at the point where this reference frame determines that the light is when the red caboose, B', and the blue ground observer, C, pass each other:

Here you can see how the red caboose, B', averages the time when the original flash passed him, 7.5 usec, and the time the reflection gets to him, 17.5 usec, and determines that the reflection occurred at 12.5 usec, the same as the Coordinate Time of his rest frame says it happened.

On the other hand, the blue ground observer, C', does the same thing except he averages 0 usec and 12.5 usec and determines that the reflection occurred at 6.25 usec according to his own clock, so he disagrees with the red caboose observer that the reflection is simultaneous with their passing.

But we can transform back to the rest frame of the blue ground observer, C', and see that the Coordinate Time of 6.25 usec is when the reflection occurred according this frame and we see that the red caboose, B', still makes the same determination as he did in his own rest frame:

So now do you understand how Special Relativity determines the undisputed physical reality of both observers and that it is different because they are using different clocks and making their observations at different places and at different times?

 

[Whatifitaint]

Yes (well, undisputed physical reality is too strong - it is philosophy, but let's not quibble). And B' says the what C is calling (20,0) is (25,-15). And B' says that at t'=0, the lightning is at (40,0). And C says this event B' is referring to is at (50,30).

Though colocated, and though synching clocks, the only event for which B' and C agree on the "now" of is the moment and location of their passing.

Okay, I like your change to sync the clocks. I did not think of it and that is very good.

So, what we have for the laws of physics at the clock sync is both C and B' are co-located and the lightning is located at (20,0,0) in the coordinates of the C frame with t=0 because of the clock sync.

The lorentz transforms are required to preserve all truths/laws of physics after the transformation otherwise we have a cpt violation.

Please correct me if I am wrong.

So, after taking the above facts, we must see after the lorentz transforms only evidence that both clocks are synced to 0 and that B' and C are co-located since that was the input to the lorentz transforms functions.

However, after transformation, we find based on your calculations that t=30 in the C frame and the lightning is at (50,0,0). So, the lightning is not at (20,0,0) in the coordinates of the C frame and with t=30, B' and C are not co-located.

But, prior to the transformation B' and C a co-located and the lightning is at (20,0,0) in the coordinates of the C frame.

How did the lorentz transforms preserve the truths of physics based on the above?

 

[PAllen]

So, after taking the above facts, we must see after the lorentz transforms only evidence that both clocks are synced to 0 and that B' and C are co-located since that was the input to the lorentz transforms functions.

However, after transformation, we find based on your calculations that t=30 in the C frame and the lightning is at (50,0,0). So, the lightning is not at (20,0,0) in the coordinates of the C frame and with t=30, B' and C are not co-located.

But, prior to the transformation B' and C a co-located and the lightning is at (20,0,0) in the coordinates of the C frame.

How did the lorentz transforms preserve the truths of physics based on the above?

This is getting pointless. No matter what I say or how I word it, you state that I said something completely different from what I said.

There is nothing correct about your reasoning above. There is no sequence of transforms that goes from (20,0) to (30,50). These are C's coordinates for two completely different events. C has these labels for these two events. B' has the labels (25,-15) and (40,0) for these same two events. You keep wanting to merge these separate events and create a contradiction. That is totally absurd. They both agree these are two separate events, the transforms work in both directions as I've shown in multiple posts:

(25,-15) <-> (20,0)
(40,0) <-> (50,30)

All of this is consistent with - and computed from - the assumption that both are colocated at the event they both call (0,0). But for any distance away, they disagree on what 'now' is.

 

[Whatifitaint]

This is getting pointless. No matter what I say or how I word it, you state that I said something completely different from what I said.

There is nothing correct about your reasoning above. There is no sequence of transforms that goes from (20,0) to (30,50). These are C's coordinates for two completely different events. C has these labels for these two events. B' has the labels (25,-15) and (40,0) for these same two events. You keep wanting to merge these separate events and create a contradiction. That is totally absurd. They both agree these are two separate events, the transforms work in both directions as I've shown in multiple posts:

(25,-15) <-> (20,0)
(40,0) <-> (50,30)

All of this is consistent with - and computed from - the assumption that both are colocated at the event they both call (0,0). But for any distance away, they disagree on what 'now' is.

Here is your statement above,

There is nothing correct about your reasoning above. There is no sequence of transforms that goes from (20,0) to (30,50).


Here is your post #31.

t = γ (t' + vx/c^2) = (1.25) (-15 + .6 *25) = 0
x = γ (x' + vt') = (1.25) (25 + .6 * (-15)) = 20

B' frame calculations of the C observer view of now and lightning location in C frame coordinates when the clocks are synched.

t = (1.25) (0 + .6 *40) = 30
x = (1.25) (40 + .6 *0) = 50

How are you following the logic of your own posts?

But, what I want to get to is whether the lorentz transforms preserves the truths of physics for this case

 

[Dale]

But, what I want to get to is whether the lorentz transforms preserves the truths of physics for this case

Yes.

Also, here is PAllen's actual post 31, which you misquoted:

Ok, here's a new set of numbers, slight variation because I have B' and C synch clocks when coincide.


Suppose when B' and C are coincident, they synch clocks to 0. They are moving past each other at .6c. Let's use c=1 for easier numbers. At his moment of passing C announces: the beam emitted to the right when light struck when I passed your front is 'now' 20 units (it would be, say, light seconds) away. [edit: and C would know this because the lightning struck 20 seconds ago, by their clock] This means C is referring to the event on light's history that C labels as (x,t)=(20,0). B' would find that this moment on the light's history is given by:

t' = γ (t-vx/c^2) = (1.25) ( 0 - .6 * 20) = -15
x' = γ(x-vt) = (1.25) (20 - .6*0) = 25

So, if B' know the light was at (x',t') = (25,-15), then now, for B' it is at (x',t')=(40,0) just by light propagation. So these are the two relevant events per B' : B''s view of the event C calls 'where the light is now', and B's view of what he calls where the light is now. Two different events.

To see what C says, we run this backwards. First, transform (25,-15) back just for kicks:

t = γ (t' + vx/c^2) = (1.25) (-15 + .6 *25) = 0
x = γ (x' + vt') = (1.25) (25 + .6 * (-15)) = 20

as expected. Now, C's view of what B' calls where the light is now:

t = (1.25) (0 + .6 *40) = 30
x = (1.25) (40 + .6 *0) = 50

Note:

- This second event per C is consistent with light propagation for our c=1 convention
- Both B' and C agree on the time ordering (which came first) of these two events on the light's history