Debate: Lorentz invariance of certain zero angles

Updated tracking list

1.0 Scenario (Complete)

1.1 - Coordinate dependence vs. coordinate independence (Resolved)
1.2 - Definition of rods T1 and T2 (Resolved)
1.3 - Definition of points A and B (Obsolete)​

2.0 Methodology (Active)

2.1 - Tach's proposed measurements (Active)

2.1.1 - Transverse doppler effect (Active)​

2.2 - Pete's proposed measurements (Pending)
2.3 - Measuring remote events using background Rods and Clocks (Pending)​

3.0 Calculations (not started)

4. Summary and reflection (not started)​

 

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Sure they can, this is the exact definition of TDE, the beam whose frequency is measured is aimed at 90 degrees wrt the line of sight.

 

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How can the laser photons be measured at O if no laser photons reach O?

 

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The same exact way Hasselkamp et al. measured a true TDE effect.

 

2.1.1 - Transverse doppler effect

Direct observation of the transversal Doppler-shift (pdf)
D. Hasselkamp, E. Mondry and A. Scharmann, 1979
Zeitschrift für Physik A Hadrons and Nuclei
Volume 289, Number 2, 151-155, DOI: 10.1007/BF01435932

That experiment involved a beam of excited hydrogen ions radiating light in all directions, not a laser.

The experimenters measured the frequency of light emitted from the ion beam at approximately 90 degrees to the ion velocity:

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In your methodology, the laser light can not be detected or measured at O, unless it is aimed so that the beam intersects O.

If the lasers are aimed so that the beam intersects O, then the transverse doppler effect due to the motion of the laser source can be measured at O.

 

If you ever looked at a laser beam, you never looked head on, right? You looked from the side, correct? You could still see it, isn't it? The reason that you see it is that, there are stray photons arriving at your eye. So, this is exactly the situation as in the Hasselkamp experiment, except that the ion source is replaced with a laser. If you do not want to use a laser, you can always replace it with a source of ions.

 

No, I can't see a laser beam from the side, unless it scatters off something such as dust in the air.
I have a laser pointer. I can see the red dot where the beam strikes the wall and scatters. I can not see the beam in the air.

This is your methodology. Do you want to replace your lasers with ion beams?

 

Well, I can.

Sure no problem.

 

Assuming that enough laser light does scatter from the air, the expected frequency of the scattered light received at O isn't simply a case of applying the transverse doppler effect.

Why don't you just attach a simple light source of known frequency to P?
The light that travels straight from P to O will be shifted by the transverse doppler effect.

OK, so now you have ion guns mounted on the wheel and on T2.
Ions are emitted from the guns at known velocity relative to the guns.
The ions emit light at a known frequency.
A detector at O measures the frequency of light received from the emitted ions.
You propose that those measurements can be used to draw conclusions about the motion of the ion guns.

Is that right?

 

Yes.

Yes, the detection of \(f=f_0/\gamma\) coming from both sources tells you that they are perpendicular on \(\vec{OP}\) (and parallel to each other. Can we move on to your method?

 

Yes, you're attaching a simple light source to P rather than the ion gun?

Is there still an ion gun on T2, or is it also a simple light source?

The doppler shift can potentially tell you about the direction of the velocities of P and the point on T2, but don't you also want to determine the orientation of T2?

 

either works

Let's stop wasting time, both lasers have been replaced by ion guns.

both guns point in the same direction , same sense

 

They work very differently.
A simple multidirectional light source on P, so that light from P goes directly to O, will be frequency shifted by the TDE depending only on the velocity of P.
Light from ions depends on the velocity of the ions, which is not the same as the velocity of P.
The wheel will be spraying ions like a sprinkler.
You'll have ions all over the place moving in different directions, not perpendicular to the direction from the ion to O, and it will be a real mess to analyse.

Sure,if that's what you want... but what I suggested was replacing them with simple multidirectional light sources, so you can ue the transverse doppler effect as you described.

I'm not sure what you mean.
Yes, both guns point in the same direction... but you're not measuring the direction they're pointing in, as far as I can tell.
You're measuring the direction of their velocity, or the direction of the velocity of the ions.

 

...which is the direction of \(\vec{v_P}\) and \(\vec{T_2}\).

 

What is?

 

The direction of the ion beams is the same direction as \(\vec{v_P}\) respectively \(\vec{T_2}\). How much more time do you plan to waste on this? Time to move to 2.2. Please get going on it.

 

No, that's not something that can be assumed.

I have no plans to waste time, and I do not appreciate the implication of that question.
I do intend to follow the process we agreed on, and establish shared understanding every step of the way.

I'm really struggling to understand exactly how you the methodology you describe is supposed to work.
I do not think that it will work in the way that you seem to think it will.

For example:

Consider the ion gun mounted on the wheel at P.
At some time t_0, it emits some ions. These ions move at some known speed parallel to \(\vec{v_p}(t_0)\), radiating light in all directions as they go.

It seems to me that the doppler shift at O of light from those ions will change as they travel. The angle between the ion velocity and the ion-observer line is only perpendicular at t_0.

So, does the observer at O measure the light from these ions continually as they travel, or only at t_0?

It seems that you want the observer to measure them continually, otherwise the ion gun would be redundant and you could just have a single light source at P, radiating light toward O.

But it also seems that you only want them measured at t_0, because that is the only time the doppler shift is purely transverse.​

Another example:

Consider the gun on T2.
In S, this gun is moving perpendicularly to the position vector of the gun, but it is aimed perpendicularly to the position vector of P.

It seems to me that due to aberration, the velocity of the ions emitted at a particular time will be in a different direction to where the gun is aimed, so measuring the direction of the ion velocity is not a substitute for measuring either the velocity or the angle of T2.​

Also, it is not at all clear what, if anything, is to be measured in any frame other than S, and how any such measurements will be analysed.

We can put 2.1 on hold while we address 2.2 if you like.

 

It is not assumed, it is by design. They point along the respective directions, I already explained this for the laser case.

This is false: the ion gun rotates with the wheel, its aim is always perpendicular onto the radius , so the ion beam is always parallel to the tangential velocity in the axle frame. You are getting confused by the fact that the beam is indeed not transverse in any other frame, like the ground frame. This is messing you up.

Continuously as they travel since the ion beam is always perpendicular on the line of sight. See above.

Correct, this is exactly what happens.

The shift is transverse at all times in the axle frame. You are getting confused by the fact that the beam is indeed not transverse in any other frame, like the ground frame. This is messing you up.

Well, I hope that the above clarifies things, so we can close it and move on to 2.2.

 

Tach, your methodology is not clear at all, and I'm uneasy about your impatience to move on. We agreed to conduct this debate in a spirit of mutual discovery.

Do you want to continue discussing it until we agree on how it works, or do you want to put it on hold while we discuss mine?

 

I explained it several times, I think that I have also cleared what I think is a misconception that you might have, why don't you think about it while we discuss your proposal?