Debate: Lorentz invariance of certain zero angles

[Pete]

Because the velocity of the ions is a prototype for the tangent to the wheel in P.

The velocity of P is a prototype for the tangent to the wheel at P. Using the ions doesn't seem to add anything except potential confusion.

Yes, the observation is done in O, I have already explained that. I have also explained why I am using moving ions as a prototype of the velocity.The observation is, again, of the TDE in O.

You don 't seem to have understood the question.
Does the observer at O look at the T1 ion beam only where it leaves the gun?
Or does the observer at O look at any other part of the T1 ion beam?

The observer at O will measure a transverse doppler effect for light directly emitted from T1 and from P, so what extra information is provided by the ion beam?

This is false, in my scenario, the experiment is about the velocity of the ions.

OK, but it's a step removed from the point of the debate... so you'll have to demonstrate that the ion beam velocities match the vectors of interest.

I could do that, the guns make it more interesting as explained.

More interesting, more complex, more confusing, and less relevant to the point of the debate.
Is that what you want?

 

[Tach]

Does the observer at O look at the T1 ion beam only where it leaves the gun?
Or does the observer at O look at any other part of the T1 ion beam?

Neither. The observer looks in a direction perpendicular to the ion beam, as such, his line of sight intercepts the ion beam along the line OP.

More interesting, more complex, more confusing, and less relevant to the point of the debate.

It is not more confusing and not less relevant. You need to try harder to understand it.

Is that what you want?

yes

 

[Pete]

Neither. The observer looks in a direction perpendicular to the ion beam, as such, his line of sight intercepts the ion beam along the line OP.

Aha!
Thank you, that's one part that hasn't been clear.

It is not more confusing and not less relevant. You need to try harder to understand it.

I disagree regarding confusion and relevance, and suggest that you could try harder to explain your thoughts. But lets not go down the path of bickering.

This discussion is exhausting and its becoming difficult to maintain interest, so we'll work with your methodology as proposed.
It will take a while... I think you are making a number of assumptions that I don't accept at face value. They will need to be sorted out as we go.

In particular, you seem to be assuming that:

• The direction of the ion velocity (which determines the doppler shift) is the same as the orientation of the ion beam (which is the tangent vector of interest).
• The observer already knows the magnitude of the ion beam velocity. This isn't necessarily a problem in S, but might cause issues in S'

Also, you haven't described how this setup is going to work in S'.
Is there an observer at O' also making frequency measurements?

 

[Tach]

Aha!
Thank you, that's one part that hasn't been clear.

Good. I made it clear about three times before but it is ok that now you agree.

I disagree regarding confusion and relevance, and suggest that you could try harder to explain your thoughts. But lets not go down the path of bickering.

It would help if you did not try so hard to find fault where there isn't any. So , let's move quicker.

In particular, you seem to be assuming that:

• The direction of the ion velocity (which determines the doppler shift) is the same as the orientation of the ion beam (which is the tangent vector of interest).

• 
  
  It is not an assumption, it is by design.
  
  

  [*]The observer already knows the magnitude of the ion beam velocity.

  
  Of course he does, otherwise the experiment would be meaningless. Like I said, this is tailored exactly from the Hasselkamp experiment (or, if you wish, from the earlier experiment on Ives and Stilwel)
  
  

  This isn't necessarily a problem in S, but might cause issues in S'

Not at all, if you know the speed in S and you know S' speed wrt to S , you know the speed in S'.

Also, you haven't described how this setup is going to work in S'.
Is there an observer at O' also making frequency measurements?

Yep, except that he will not be observing a TDE but an arbitrary Doppler effect.

 

[Pete]

It is not an assumption, it is by design.

I disagree. We'll see when we do the calculations.

Of course he does, otherwise the experiment would be meaningless.

He knows the magnitude of the ion velocity relative the ion gun.
Not necessarily relative to S.

Not at all, if you know the speed in S and you know S' speed wrt to S , you know the speed in S'.

I suspect it will cause problems. We'll see when we do the calculations.

Yep, except that he will not be observing a TDE but an arbitrary Doppler effect.

So how does the observer at S' compare the angles?
Does he assume that equal doppler shift implies equal velocity (magnitude and direction)?

And how does the O' observer relate the velocity of the T1 ion beam to the orientation of T1?
Does he assume it is the same?

If so, you'll have to support that assumption at some stage?

 

[Tach]

I disagree. We'll see when we do the calculations.


He knows the magnitude of the ion velocity relative the ion gun.
Not necessarily relative to S.

Like I said, it is a simple problem of velocity composition.

So how does the observer at S' compare the angles?
Does he assume that equal doppler shift implies equal velocity (magnitude and direction)?

Nope, equal velocity+equal Doppler shift => equal angles, exactly like the equal TDE=> equal angles (90 degrees).

If so, you'll have to support that assumption at some stage?

I will , don't worry.

 

[Pete]

Like I said, it is a simple problem of velocity composition.

The whole exercise is a simple problem of geometry, which makes the whole experimental measurement of doppler shifted radiation from the ion-beam redundant.
But we'll work it out anyway.

Nope, equal velocity+equal Doppler shift => equal angles, exactly like the equal TDE=> equal angles (90 degrees).

So you allow the velocity magnitude to be calculated theoretically, but you insist the angle has to be measured through doppler shift of the ion beam.
Why not just calculate the angle as well?

 

[Tach]

So you allow the velocity magnitude to be calculated theoretically,

There is no argument about speed composition, so I see no problem with that.

but you insist the angle has to be measured through doppler shift of the ion beam.

I do not "insist", I see this as a practical way of doing the angle measurement experimentally, especially since the measurements need to be executed precisely and by arbitrary remote observers in motion wrt the experimental setup. Certainly more practical than running after the wheel with protractors.

 

[Pete]

I do not "insist", I see this as a practical way of doing the angle measurement experimentally, especially since the measurements need to be executed precisely and by arbitrary remote observers in motion wrt the experimental setup. Certainly more practical than running after the wheel with protractors.

My point is that practicality is not relevant to this discussion, since we're not actually going to do the experiment.
Everything we do in this thread is theoretical.
So, since we agree on the theoretical basis, why not just calculate the velocity vectors?
In fact, we have to do that anyway in order to calculate the doppler shift measured by the observers... and then we'll go backward to calculate the velocity vector given the measured doppler shift.
Why insist on remote observers doing practical experiments?
Why not just use the agreed theoretical foundation of SR to calculate the velocity vectors?

But whatever. You insist on a remote observer doing something 'practical', so be it.

I also find it odd that you think using a protractor to measure an angle is less practical than setting up ion beams and measuring frequencies... But, this is an irrelevant sidetrack.

We have agreed on enough. We don't need to agree on philosophical elements.

Shall we calculate your measurements first, or mine?

 

[Tach]

My point is that practicality is not relevant to this discussion, since we're not actually going to do the experiment.
Everything we do in this thread is theoretical.
So, since we agree on the theoretical basis, why not just calculate the velocity vectors?

We will do that.

In fact, we have to do that anyway in order to calculate the doppler shift measured by the observers... and then we'll go backward to calculate the velocity vector given the measured doppler shift.

The other way around, knowing the velocity vector we will calculate the Doppler shift. remember, we know the velocity in frame S.

Why insist on remote observers doing practical experiments?
Why not just use the agreed theoretical foundation of SR to calculate the velocity vectors?

This is precisely what we will do, using the speed composition laws. It is nice to have a means of testing the theory in practice and measuring TDE is a very elegant way of doing just that.

Shall we calculate your measurements first, or mine?

Do you agree with my methodology? I agree with yours, so, if you agree with mine, why don't you go ahead.

 

[Pete]

We will do that.



The other way around, knowing the velocity vector we will calculate the Doppler shift.

Exactly! Knowing the magnitude and angle of the velocity vector, we will calculate the doppler shift.
... and then use the doppler shift to calculate the angle.

This is precisely what we will do, using the speed composition laws.

Agreed.

It is nice to have a means of testing the theory in practice and measuring TDE is a very elegant way of doing just that.

Perhaps, but this thread is not about testing SR, and we're not planning on doing anything in practice.
So it adds nothing to this debate except unnecessary complexity.

Do you agree with my methodology? I agree with yours, so, if you agree with mine, why don't you go ahead.

Do you mean go ahead with my methodology?
We both need to work through both methodologies.

 

[Tach]

Exactly! Knowing the magnitude and angle of the velocity vector, we will calculate the doppler shift.
... and then use the doppler shift to calculate the angle.


Agreed.

Excellent.

Do you mean go ahead with my methodology?
We both need to work through both methodologies.

No, if you agree with my methodology, we can move on to the calculations.

 

[Pete]

We already know the velocity angle in order to figure the doppler shift, then we use the doppler shift to calculate the velocity angle.
Excellent.

Yes, we can move on to calculations. We both need to do calculations for both methodologies.
You suggested that I "go ahead."
Did you mean that I go ahead with the calculations for my methodology?
Or that I go ahead with the calculations for your methodology?

 

[Tach]

We already know the velocity angle in order to figure the doppler shift, then we use the doppler shift to calculate the velocity angle.
Excellent.

Nope, you still got it wrong, You know that the angles are the same (90 degrees) in S frame. This allows you to calculate the Doppler shift.
Frame S' is another story, you claim that the angles aren't equal, I will prove the other way.

Yes, we can move on to calculations. We both need to do calculations for both methodologies.
You suggested that I "go ahead."
Did you mean that I go ahead with the calculations for my methodology?
Or that I go ahead with the calculations for your methodology?

I suggested that you do your calculations for your method.
I will do the calculations for my method.
Then, we will compare notes. Ok?

 

[Pete]

Nope, you still got it wrong, You know that the angles are the same (90 degrees) in S frame. This allows you to calculate the Doppler shift.

So why do you want to know the doppler shift when what we're interested in is the angles?

Frame S' is another story, you claim that the angles aren't equal, I will prove the other way.

We'll see. You haven't adequately described your methodology for S', but I'm sure it will become clear as we go.

I suggested that you do your calculations for your method.
I will do the calculations for my method.
Then, we will compare notes. Ok?

I've had another look at the agreed protocol:

1. Tach and Pete will individually prepare calculations for the results of each measurement.
2. When we both indicate readiness, the two analyses will be posted at around the same time.
3. The analyses should be posted directly in the thread if at all possible. If either poster needs to use an off-site document, they should ask first and explain why.
4. We will then discuss any discrepancies (one at a time) between the analyses, using sufficient mathematical rigor to resolve them.

So that's what we'll do.
We'll both prepare analyses for both methodologies.
When we're both ready, we'll post them up and go from there.

OK?

 

[Tach]

So why do you want to know the doppler shift when what we're interested in is the angles?

Because the Doppler shift will give you the angles in the other frames. I have already explained that earlier, why are we going in circles?

We'll see. You haven't adequately described your methodology for S', but I'm sure it will become clear as we go.

Rest assured that it will.

I've had another look at the agreed protocol:


So that's what we'll do.
We'll both prepare analyses for both methodologies.
When we're both ready, we'll post them up and go from there.

OK?

OK. I will upload mine on the google server because it will contain a lot of math and pictures so I am more confortable preparing and previewing it off - line. I suggest that you upload yours as well. When we are ready, we unveil the documents simultaneously. OK?

 

[Pete]

Because the Doppler shift will give you the angles in the other frames.
I have already explained that earlier, why are we going in circles?

We're going in circles because I can't make sense of your explanations.

Do you mean that the doppler shift at O can be used to determine angles in S'?
If so, you haven't explained how.
Do you mean that the doppler shift at O' can be used to determine angles in S'?
If so, then we first need to calculate the doppler shift at O'... which we can do if we first calculate the angles in S'.

OK. I will upload mine on the google server because it will contain a lot of math and pictures so I am more confortable preparing and previewing it off - line. I suggest that you upload yours as well. When we are ready, we unveil the documents simultaneously. OK?

OK. I'll probably need a few days.

 

[Tach]

We're going in circles because I can't make sense of your explanations.

You sometimes accept it and than you revert to non-accepting the explanation, this is why we are going in circles.

Do you mean that the doppler shift at O can be used to determine angles in S'? If so, you haven't explained how.

I did, see here again.

Do you mean that the doppler shift at O' can be used to determine angles in S'?

Yes, I have already told you that several times.

If so, then we first need to calculate the doppler shift at O'... which we can do if we first calculate the angles in S'.

No, be patient and I'll show you how it is done.

 

[Pete]

You sometimes accept it and than you revert to non-accepting the explanation, this is why we are going in circles.

I accepted parts of it. But parts have changed.
I still can't make sense of a cohesive whole.

I did, see here again.

No, that doesn't relate doppler shift at O to angles in S', it relates doppler shift at O' to angles in S'.

Yes, I have already told you that several times.
No, be patient and I'll show you how it is done.

You're supposed to explain your approach in the methodology section.
This is why it's so hard to make sense of your explanations.
I feel like I'm trying to read your mind.

Please, tell me what factors you plan to use to calculate the doppler shift at O'?

 

[Tach]

I accepted parts of it. But parts have changed.
I still can't make sense of a cohesive whole.


No, that doesn't relate doppler shift at O to angles in S',

This is not what I said, what I said is equal Doppler shift in S'+equal velocities in S' => equal angles in S'. How I calculate the Doppler shift in O' is going to become apparent when I upload the detailed math description. You haven't done yours, I am going to assume that you will have the mathematical backup, until then I can wait. Can you please do the same and wait?

it relates doppler shift at O' to angles in S'.

Exactly what is asked for: equal velocity in S'+equal Doppler shift in S' => equal angles in S', exactly like the equal TDE in S=> equal angles (90 degrees) in S.

Please, tell me what factors you plan to use to calculate the doppler shift at O'?

Why don't you wait until I put together the mathematical formalism for you?