Relative Velocity Measurement – Frame and photon

[Pete]

First, post #53 clearly demonstrates I am talking about M' as stationary.

In post #59, you clearly acknowledge that the scenario is defined according to times in the rest frame of M.

Perhaps we need to readdress how you this scenario is described.

So:
We start with the conditions of rest M:

A and B are equidistant and stationary with respect to M. Lightning strikes at A and B simultaneously with M' passing M.
Lightning strike at A:
(x,t) = (-d,0)

Lightning strike at B:
(x,t) = (d,0)

M' passes M:
(x,t) = (0,0)​

OK? All the above is defined with M at rest.

Now, we switch to working in the rest frame of M':
You said: "...assume there were M' observers co-located at B and A when the lightning strikes occurred at A and B and call them A' and B'."
However, that sentence is inconsistent with your following analysis, which implies that A' meets A at the same time as B' meets B.
Perhaps you meant this:

assume there were M' observers co-located at A and B when M is co-located with M' and call them A' and B'.​

Does that sound reasonable? There are two immediate results of this change in the setup.
First, we're not assuming anything about the simultaneity of the lightning strikes.
Second, we immediately get the results you calculated:

When M and M' are co-located, the distance from M' to B' is d/λ and the distance from M' to A' is d/λ.
Obviously, if B' is located at a rest distance d/λ, then M could conclude B' and B are not co-located at the time of the strike since M would view B' at a distance of d/λ^2.

These statements are correct. Right?

Now, moving on:

To support Einstein’s conclusion that M' sees the light from B prior to A one of the following two possibilities must be true:
1. M' moves toward the lightning strike at B closing the distance for light to travel relative to the strike at A.
2. The strike at B occurs prior to the strike at A in the time coordinates of M'.

We know the first is not true, because M' is stationary, as you correctly point out:

Possibility 1
Since M' is stationary, it is not moving. A, B and M are moving relative to M'. Sure, B closes the distance to M' as the light travels toward M' but this has nothing to do with the distance light traveled in the frame of M'.

Possibility 2
Since, there are the observers B' and A' co-located at the lightning strikes at A and B, it is impossible there is any disagreement between the frames as to whether light is moving along the x-axis or not. Hence, for example, if B' claims lightning just struck, B will make the same claim as well. So, it cannot be claimed the lightning appears for one frame at some location while a co-located observer claims light is not at that location. Therefore, perhaps the time on the clock of B' will show an earlier time than the clock of A' for the light strike and this explains it. In other words, the light emitted from B' before it emitted from A'.

And now we see that the earlier assumption about simultaneity has come back to bite us.
You set up A' and B' so that A' meets A and B' meets B when M meets M'.
You assumed that this is also when lightning strikes A and lightning strikes B. Why?

 

[Pete]

Here's the bottom line, Jack.
With M' stationary:
If A' meets A when lightning strikes A, then A' meets A after M' meets M.
If A' meets A when M' meets M, then A' meets A before lightning strikes at A.

So, which is it in your scenario?
When is A' colocated with A? When the lightning strikes at A? Or when M is colocated with M'?

You can't have it both ways, unless you assume that the lightning strike is simultaneous with M passing M'.

 

[Jack_]

Yes, that's correct.
However, you are not being careful about which distances are rest distances in which frames.

The distance from A to M will be length contracted in the rest frame of M'.
The distance from A' to M' will be length contracted in the rest frame of M.

See? But perhaps we're still confused about the setup. Let's go back a few steps.

i dont care what happens when M is stationary.

We are working with M' stationary.

I cant understand why this is taking so long.

 

[Pete]

i dont care what happens when M is stationary.

See post 101

 

[Jack_]

See post 101

And now we see that the earlier assumption about simultaneity has come back to bite us.
You set up A' and B' so that A' meets A and B' meets B when M meets M'.
You assumed that this is also when lightning strikes A and lightning strikes B. Why?

Set this up for yourself. I works.

It is simple logic.

If a moving frame has a rod of d and a rest frame has a rod of length d/γ,

then the midpoints of the two rods and the endpoints will all co-locate simultaneously in the rest frame.

 

[Pete]

Set this up for yourself. I works.

It is simple logic.

If a moving frame has a rod of d and a rest frame has a rod of length d/γ,

then the midpoints of the two rods and the endpoints will all co-locate simultaneously in the rest frame.

Yes, you're setting this up so in rest frame M', A meets A' when M meets M' and B meets B'.
But this means that the lightning strikes at A after A meets A', and lightning strikes at B before B meets B'.
Why are you assuming that the lightning strikes occur at the same time as M meets M'?

Check it out for yourself when you go back to M stationary - where are A' and B' when M meets M'?

 

[Jack_]

Yes, you're setting this up so in rest frame M', A meets A' when M meets M' and B meets B'.

But this means that the lightning strikes at A after A meets A', and lightning strikes at B before B meets B'.

Check it out for yourself when you go back to M stationary - where are A' and B' when M meets M'?

Let's stay on task of the rods.

Do you agree with my statement yes or no.

 

[Pete]

Of course, Jack. You don't seem to be following what I'm saying.
Yes, if A' and B' are both d/λ from M', then A meets A' when M meets M' and B meets B'.
No, this doesn't follow from your initial setup of A meets A' when lightning strikes A, and B meets B' when lightning strikes B.


Look, the problem with your logic is this:
You start with these premises:

• In the rest frame of M, A and B are each a distance d either side of M and at rest with respect to M.
• In the rest frame of M, lightning strikes at A and at B simultaneously with M' passing M at velocity v.
• In the rest frame of M', A' and B' are at rest with respect to M'.
• In the rest frame of M', A passes A' at the moment that lightning strikes A.
• In the rest frame of M', B passes B' at the moment that lightning strikes B.

Right?
You then conclude that:

• In the rest frame of M', when M and M' are co-located, the distance from M' to B' is d/λ
• In the rest frame of M', when M and M' are co-located, the distance from M' to A' is d/λ

And these are wrong. They do not follow from the premises.
Why?
The logic you seem to be applying is this:

• In the rest frame of M', the distance from A to M (a moving rod) is length contracted to d/λ.
• therefore, when M and M' are co-located, the distance from A to M' is d/λ.
• therefore, when M and M' are co-located, the distance from A' to M' is d/λ.

The first two steps are correct. The last is not. Can you see why?
How do you conclude that the distance from A to M' when M meets M' is the same as the distance from A' to M'?
Is it because you assume that when M meets M', A meets A'?

Can you see that "A' meets A when lightning strikes A" does not imply "A' meets A when M' meets M"?

 

[Pete]

You know, I think this might come down to one question, Jack.

With M' stationary, how far does SR say that A is from M' when the lightning strikes A?

You know that A is d/λ from M because of length contraction.
But that doesn't help, does it? Because you don't know how far M is from M' when the lightning strikes.

 

[AlphaNumeric]

Can you see that you are assuming that when M and M' are co-located, A and A' are also co-located?

I'm not following this thread and haven't scrolled back from this 6th page but is this not the same mistake he was doing with me?

Frame 1 has points p and q
Frame 2 has points p' and q'
In Frame 1 coordinates (t,x) the difference p-q is a specified vector V = p-q
In Frame 2 coordinates (t',x') the difference p'-q' is a specified vector V = p'-q'

If they agree on the location of p and p', ie those are coincident it does NOT follow that they agree on the location of q and q'. They are NOT coincident.

 

[Pete]

Yes, it keeps coming back to simultaneity.
It is understandable. Simultaneity is deeply ingrained into our intuition, and people who are good intuitive thinkers can easily fall into traps of simultaneity when grappling with SR. To make things worse, good intuitive thinkers are sometimes disinclined to work through the drudgery of the formalism, which means that they are unlikely to recognize the traps they fall into.

I had the same problem as Jack when I first tried to understand relativity.

 

[Jack_]

Of course, Jack. You don't seem to be following what I'm saying.
Yes, if A' and B' are both d/λ from M', then A meets A' when M meets M' and B meets B'.
No, this doesn't follow from your initial setup of A meets A' when lightning strikes A, and B meets B' when lightning strikes B.


Look, the problem with your logic is this:
You start with these premises:

• In the rest frame of M, A and B are each a distance d either side of M and at rest with respect to M.
• In the rest frame of M, lightning strikes at A and at B simultaneously with M' passing M at velocity v.
• In the rest frame of M', A' and B' are at rest with respect to M'.
• In the rest frame of M', A passes A' at the moment that lightning strikes A.
• In the rest frame of M', B passes B' at the moment that lightning strikes B.

Right?
You then conclude that:

• In the rest frame of M', when M and M' are co-located, the distance from M' to B' is d/λ
• In the rest frame of M', when M and M' are co-located, the distance from M' to A' is d/λ

And these are wrong. They do not follow from the premises.
Why?
The logic you seem to be applying is this:

• In the rest frame of M', the distance from A to M (a moving rod) is length contracted to d/λ.
• therefore, when M and M' are co-located, the distance from A to M' is d/λ.
• therefore, when M and M' are co-located, the distance from A' to M' is d/λ.

The first two steps are correct. The last is not. Can you see why?
How do you conclude that the distance from A to M' when M meets M' is the same as the distance from A' to M'?
Is it because you assume that when M meets M', A meets A'?

Can you see that "A' meets A when lightning strikes A" does not imply "A' meets A when M' meets M"?

The distance of A' to M' is a rest d/λ. So I cannot see what that is false.

Can you see that "A' meets A when lightning strikes A" does not imply "A' meets A when M' meets M"?

I have not yet gotten to this proof.

I am still working with you on the basics which you appear to have down.

Would you now like me to proceed?

 

[Jack_]

You know, I think this might come down to one question, Jack.

With M' stationary, how far does SR say that A is from M' when the lightning strikes A?

You know that A is d/λ from M because of length contraction.
But that doesn't help, does it? Because you don't know how far M is from M' when the lightning strikes.

I have not yet approached this issue.
But, you are now onto it.

Do you agree when M' is co-located with M that A' is co-located wioth A and B' is co-located with B.

That is the issue right now.

 

[Jack_]

Yes, it keeps coming back to simultaneity.
It is understandable. Simultaneity is deeply ingrained into our intuition, and people who are good intuitive thinkers can easily fall into traps of simultaneity when grappling with SR. To make things worse, good intuitive thinkers are sometimes disinclined to work through the drudgery of the formalism, which means that they are unlikely to recognize the traps they fall into.

I had the same problem as Jack when I first tried to understand relativity.

LOLOL
I did not have a problem with simultaneity when I first learned SR.

Anyway, this experiment is where your logic is derived.

So, when you are ready to proceed let's see where we end up.

We will find out that Einstein took the M frame as the preferred frame for universal deductions.

 

[Jack_]

OK, here is where we are.

M has a midpoint M and two equadistant points A and B each a distance d from M.

M' has a midpoint M' and two equadistant points A' and B' each a distance d/γ from M'.

The logic of length contractions.

Assume M' is stationary and M is moving.

By length contraction, if M co-locates with M' then A co-locates with A' and M co-locates with B' from the rest frame M'.

 

[Pete]

LOLOL
I did not have a problem with simultaneity when I first learned SR.

Well, you clearly have a problem with it now, but I understand that you don't see it that way. It's not uncommon.

OK, here is where we are.

M has a midpoint M and two equadistant points A and B each a distance d from M.

M' has a midpoint M' and two equadistant points A' and B' each a distance d/γ from M'.

OK, so these are your starting premises?
You understand that this is not a consequence of "...assume there were M' observers co-located at B and A when the lightning strikes occurred at A and B and call them A' and B'"?

The logic of length contractions.

Assume M' is stationary and M is moving.

By length contraction, if M co-locates with M' then A co-locates with A' and M co-locates with B' from the rest frame M'.

Yes, that's correct.

 

[Jack_]

Well, you clearly have a problem with it now, but I understand that you don't see it that way. It's not uncommon.

OK, so these are your starting premises?
You understand that this is not a consequence of "...assume there were M' observers co-located at B and A when the lightning strikes occurred at A and B and call them A' and B'"?

Yes, that's correct.

OK, here we go.

The original experiment said, when M and M' are co-located, the lightning strikes A and B simultaneously.

We also have established, if M and M' are co-located, then A' is co-located with A and B' is co-located with B.

Do you agree so far yes or no.

 

[Pete]

OK, here we go.

The original experiment said, when M and M' are co-located, the lightning strikes A and B simultaneously.

...in the rest frame of M.

We also have established, if M and M' are co-located, then A' is co-located with A and B' is co-located with B.

...in the rest frame of M' only, and only if you explicitly place A' and B' each a distance d/γ from M'. Not if you place them to be colocated with A and B when the lightning strikes.

Do you agree so far yes or no.

With those qualifications, yes.

 

[Jack_]

...in the rest frame of M.

Are you claiming that co-location does not happen in M' with M? If so, you invalidate LT construction.

...
...in the rest frame of M' only, and only if you explicitly place A' and B' each a distance d/γ from M'.

With those qualifications, yes.

I want to make sure I can continue.

Are we in agreement?


I will prove in the frame of M', the strikes at A' and B' will occur simultaneously based on the machinery I developed above.

I just want to make sure you are here first.

 

[Pete]

Are you claiming that co-location does not happen in M' with M? If so, you invalidate LT construction.

I'm claiming that in the rest frame of M', we haven't yet decided if "when M and M' are co-located, the lightning strikes A and B simultaneously."

In the rest frame of M', M and M' are colocated at a particular time. We haven't established if that is at the same time as one or both lightning strikes.

I want to make sure I can continue.

Are we in agreement?

I want to be very explicit about what we are agreeing on.
You said:

We also have established, if M and M' are co-located, then A' is co-located with A and B' is co-located with B.

We only agree on that if A' and B' are each a placed at a distance d/γ from M'.
We do not agree on that if A' and B' are placed at A and B when lightning strikes.

I'm not sure which method you using to place A' and B', and I'm not sure that you understand that they are not equivalent.