# Debate:Lorentz invariance of certain zero angles

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2.2 Pete's proposed measurements

I do not understand how you propose that the remote observer (comoving with the axle) measures the co-planarity of the two remote vectors $$\vec{v_t}$$ and $$\vec{T_2}$$ in your proposal.
$$\vec{v_t}$$ and $$\vec{T_2}$$ are not mentioned in my proposal, so I don't understand what you don't understand.
Look at your own definitions. $$\vec{v_t}$$ is your $$\vec{v_P}$$. $$\vec{T_2}$$ is your own $$\vec{T_2}$$.
$$\vec{T_2}(t,l)$$ was defined as the position vectors of the elements of T2 in S.
You seem to be using $$\vec{T_2}$$ to refer to a displacement vector parallel to T2 in S.
Can we please stick to consistent labels?

But that's a side issue. In my methodology post, I'm not proposing any measurements on T2.

I propose to measure the angle between $$\vec{v_p}(t)$$ and $$\hat{D_p}(t)$$, when t=0, and between $$\vec{v_p}'(t')$$ and $$\hat{D_p}'(t')$$ at the t' of the transformed event of P at t=0.

$$\hat{D_p}(t)$$ and $$\hat{D_p}'(t')$$ are unit displacement vectors tangent to the wheel at P in S and S' at times t and t' respectively.

Actually they are. I would like you to describe exactly how you plan to use "rods and clocks" or "remote detectors", whichever you prefer in order to measure the fact that $$\vec{T_2}$$ is parallel to $$\vec{v_P}$$. Even in the axle frame , where you know that they are parallel, you are still forced to do a remote measurement.

Rods and clocks:
An inertial reference frame is a conceptual, three-dimensional latticework of measuring rods set at right angles to each other with clocks at every point that are synchronised with each other...

So, the coordinates of any event can be determined by noting which clock is at the location of the event, and the time on that clock when the event occurs.

The event coordinates can then be used to determine other measurements.
For example, the position and orientation of an object at a particular time can be measured by noting which clocks are coincident with the object when they read that particular time.

Personally, I prefer the implicit use of the rods and clocks latticework, but I did suggest a more direct (but cumbersome) measurement in my first methodology post:

The angle between $$\vec{v_p}(t)$$ and $$\hat{D_p}(t)$$ can be directly measured with a protractor as the angle between:
• The path followed by an inertial object that is moving with P at the instant of interest, and
• A rod at rest that that is coincident with a straight rod tangent to the wheel at P at the instant of interest

To explain further:
Construct a background canvas, parallel to the XY plane, at rest in S.
• Attach a marker to rod T1 at the point that touches P.
The marker attached to T1 will mark on the canvas a physical line that matches the direction of $$\vec{v_p}(0)$$.
• Attach markers along the length of T1 that mark the canvas only at t=0
The resulting mark is a straight line that matches the direction of $$\hat{D_p}(0)$$
• The angle between the two lines is the angle between $$\vec{v_p}(0)$$ and $$\hat{D_p}(0)$$

The same process works in S':
Construct a background canvas, parallel to the XY plane, at rest in S'.
Let $$t'_0$$ be the time in S' when P touches T1.
• Attach a marker to rod T1 at the point that touches P.
The marker attached to T1 will mark on the canvas a physical line that matches the direction of $$\vec{v_p}'(t'_0)$$.
• Attach markers along the length of T1 that mark the canvas only at t'=$$t'_0$$
The resulting mark is a straight line that matches the direction of $$\hat{D_p}'(t'_0)$$
• The angle between the two lines is the angle between $$\vec{v_p}(t'_0)$$ and $$\hat{D_p}(t'_0)$$

2.2 Pete's proposed measurements

I propose to measure the angle between $$\vec{v_p}(t)$$ and $$\hat{D_p}(t)$$, when t=0, and between $$\vec{v_p}'(t')$$ and $$\hat{D_p}'(t')$$ at the t' of the transformed event of P at t=0.

Why only at t=0? You should be measuring at any t, there is nothing special about t=0. Why do you keep referring to t=0? As such, t' is the transform fo $$t \ne 0$$ .

$$\hat{D_p}(t)$$ and $$\hat{D_p}'(t')$$ are unit displacement vectors tangent to the wheel at P in S and S' at times t and t' respectively.

...where t should be arbitrary, there is nothing special about t=0.

Rods and clocks:
An inertial reference frame is a conceptual, three-dimensional latticework of measuring rods set at right angles to each other with clocks at every point that are synchronised with each other...

So, the coordinates of any event can be determined by noting which clock is at the location of the event, and the time on that clock when the event occurs.

The event coordinates can then be used to determine other measurements.
For example, the position and orientation of an object at a particular time can be measured by noting which clocks are coincident with the object when they read that particular time.

This is all good and fine in theory but how do you plan to do this practically? No experiment that I know of sets an "array of rulers and clocks".

Personally, I prefer the implicit use of the rods and clocks latticework, but I did suggest a more direct (but cumbersome) measurement in my first methodology post:

The angle between $$\vec{v_p}(t)$$ and $$\hat{D_p}(t)$$ can be directly measured with a protractor as the angle between:

How do you place this "protractor"? Do you plan t attach an observer to the rim of the wheel? Also, how would the remote observer(s) like the one on the ground read that protractor?

• The path followed by an inertial object that is moving with P at the instant of interest, and
• A rod at rest that that is coincident with a straight rod tangent to the wheel at P at the instant of interest

To explain further:
Construct a background canvas, parallel to the XY plane, at rest in S.

The wheel is rotating wrt S, so, do you plan to stick a "canvas" to the wheel, rotating with the wheel or do you plan to stick a "canvas" to the axle?

• Attach a marker to rod T1 at the point that touches P.
The marker attached to T1 will mark on the canvas a physical line that matches the direction of $$\vec{v_p}(0)$$.

• Why the fixation with t=0, again?
The marker will mark on the "canvas" the trajectory of the tip (or just a point on the vector) of the vector $$\vec{v_p}(0)$$. Not very interesting. What you want, is the direction of $$\vec{v_p}(t)$$
for arbitrary t.

[*]Attach markers along the length of T1 that mark the canvas only at t=0
The resulting mark is a straight line that matches the direction of $$\hat{D_p}(0)$$
[*]The angle between the two lines is the angle between $$\vec{v_p}(0)$$ and $$\hat{D_p}(0)$$

There is nothing special about t=0. Also, it isn't clear how you plan to attach a marker to the velocity vector $$\vec{v_p}$$.

The same process works in S':
Construct a background canvas, parallel to the XY plane, at rest in S'.
Let $$t'_0$$ be the time in S' when P touches T1.
• Attach a marker to rod T1 at the point that touches P.
The marker attached to T1 will mark on the canvas a physical line that matches the direction of $$\vec{v_p}'(t'_0)$$.
• Attach markers along the length of T1 that mark the canvas only at t'=$$t'_0$$
The resulting mark is a straight line that matches the direction of $$\hat{D_p}'(t'_0)$$
• The angle between the two lines is the angle between $$\vec{v_p}(t'_0)$$ and $$\hat{D_p}(t'_0)$$

Same objections as above. As an aside, using "markers" and "canvases" is hardly an option ever considered in experimental physics, so there is no way you could ever run your proposed experiment.

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Why only at t=0? You should be measuring at any t, there is nothing special about t=0. Why do you keep referring to t=0? As such, t' is the transform fo $$t \ne 0$$ .

...where t should be arbitrary, there is nothing special about t=0.
t=0 is when T1 is tangent to P.
It's an easy special case, that I believe will be enough to show that the angle of interest is zero in S, and non zero in S'.

As such, t' is the transform fo $$t \ne 0$$ .
I can't tell what you mean here.
T1 is tangent to the wheel at P at t=0 in S, and at t'= some non zero value in S'.

This is all good and fine in theory but how do you plan to do this practically? No experiment that I know of sets an "array of rulers and clocks".
Good and fine in theory is exactly what we need.
We are not planning to do this in practice.
This is a theoretical exercise, conducted solely in the abstract on Sciforums.

How do you place this "protractor"?
Exactly as you would normally use a protractor.

Do you plan to attach an observer to the rim of the wheel?
No
Also, how would the remote observer(s) like the one on the ground read that protractor?
They would walk over to the canvas and measure the angle between the lines.

The wheel is rotating wrt S, so, do you plan to stick a "canvas" to the wheel, rotating with the wheel or do you plan to stick a "canvas" to the axle?
The S canvas is at rest in S. It's simply a backdrop, it doesn't need to be stuck to anything.

The marker will mark on the "canvas" the trajectory of the tip (or just a point on the vector) of the vector $$\vec{v_p}(0)$$.
I'm not sure what you mean.
You seem to imply that $$\vec{v_p}(0)$$ has a trajectory, which doesn't make sense to me.
$$\vec{v_p}(0)$$ is the instantaneous velocity of P at t=0.
It doesn't have a trajectory.
$$\vec{v_p}(0)$$ is parallel to the y-axis, and the marker draws a line parallel to the y-axis.

Not very interesting. What you want, is the direction of $$\vec{v_p}(t)$$ for arbitrary t.
The same process could be done for any t.
But the rod T1 is in the scenario specifically for the case of t=0, and sticking to t=0 keeps things easier, so we might be done before next Christmas.

t=0 is when T1 is tangent to P.
It's an easy special case, that I believe will be enough to show that the angle of interest is zero in S, and non zero in S'.

Ok, this is a simplification since it deals only with a very restrictive case but if you want to run it this way, I have no objection.
I object though to your method since it is unimplementable. By contrast, the method that I suggested is fully implementable, it can be viewed as a direct implementation of the Hasselkamp experiment, with one ion source attached to the rim (pointing in the direction of the tangential speed $$\vec{v_P(0)}$$) and the other one representing the tangent to the rim $$\vec{T_1}$$ direction moving with velocity $$\vec{v_P(0)}$$ in the vertical direction according to your specification . We compare their respective frequencies as observed in frame S (anchored to the wheel axle) at t=0, when their positions are coincident in S and we compare them again in S'. So, I suggest that we combine our methods into a single method. OK?

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I object though to your method since it is unimplementable.
Can you explain your objection more?
Remember that we're not actually going to implement it.
It's enough that we can predict the results.
I think that we're focusing entirely too much on implementation, and it's bogging down the discussion.

All we really need to do in this section is sufficiently identify the vectors that define the angles of interest.

By contrast, the method that I suggested...
...isn't yet well defined, but that's not the current topic of discussion.

So, I suggest that we combine our methods into a single method. OK?
No, I think we're measuring different things.

Can you explain your objection more?
Remember that we're not actually going to implement it.
It's enough that we can predict the results.
I think that we're focusing entirely too much on implementation, and it's bogging down the discussion.

You cannot rely on plots drawn on paper to measure angles between moving parts.
The measurement approach needs to be meaningful, not just some pie in the sky.

All we really need to do in this section is sufficiently identify the vectors that define the angles of interest.

We just did that, we just reached an agreement of what is being measured.

...isn't yet well defined, but that's not the current topic of discussion.

I think it is, if you need to discuss more we can reopen the discussion.

No, I think we're measuring different things.

No we are not measuring different things, I just agreed with your definition of measurement. See the previous post.

You cannot rely on plots drawn on paper to measure angles between moving parts.
The measurement approach needs to be meaningful, not just some pie in the sky.
You can read a protractor by looking at it.
If plots drawn on paper accurately capture the angles of interest, then you can use them to measure the angles.
Post 63 sets out exactly how the vectors of interest are captured as lines than can be measured with a protractor at the observer's leisure.

We just did that, we just reached an agreement of what is being measured.
Then we're done with this section.
The measurement I propose is the angle between $$\vec{v_p}(t)$$ and $$\hat{D_p}(t)$$, when t=0, and between $$\vec{v_p}'(t')$$ and $$\hat{D_p}'(t')$$ at the t' of the transformed event of P at t=0.

If we agree that this is sufficient definition to calculate a result, then we can move on.

That's all I intended the methodology section to address anyway... the detailed implementation of practical measurement technique is only confusing things.

I think it is, if you need to discuss more we can reopen the discussion.
Yes, I intend to.

You can read a protractor by looking at it.

The wheel is turning wrt the axle at high speed, there is no way of setting remotely the protractor, let alone reading it.

If plots drawn on paper accurately capture the angles of interest, then you can use them to measure the angles.

But they don't. You can't expect any precision of measurement from dragging markers on paper.

Post 63 sets out exactly how the vectors of interest are captured as lines than can be measured with a protractor at the observer's leisure.

I am not buying any of the above. This is not how things are measured experimentally, especially when we have much higher precision methods.

Then we're done with this section.
The measurement I propose is the angle between $$\vec{v_p}(t)$$ and $$\hat{D_p}(t)$$, when t=0, and between $$\vec{v_p}'(t')$$ and $$\hat{D_p}'(t')$$ at the t' of the transformed event of P at t=0.

OK.

If we agree that this is sufficient definition to calculate a result, then we can move on.

That's all I intended the methodology section to address anyway... the detailed implementation of practical measurement technique is only confusing things.

We will move on when we have the method of measurement agreed on. So far we agreed on what we measure, not on how we measure.

The wheel is turning wrt the axle at high speed, there is no way of setting remotely the protractor, let alone reading it.
The protractor is used to measure the angle between the lines on the canvas.

But they don't. You can't expect any precision of measurement from dragging markers on paper.
In this abstract discussion, the markers can be as precise as we want them to be.

I am not buying any of the above. This is not how things are measured experimentally, especially when we have much higher precision methods.
Tach, this is an abstract discussion.
We're not actually planning practical experiments.

We will move on when we have the method of measurement agreed on. So far we agreed on what we measure, not on how we measure.
I maintain that it doesn't matter.
If we agree on the vector definition, then we can calculate the angle between them.

But, if we really must have experimental measurements, and if the protractor measuring lines on canvas is too hard, then for my measurements I'm going to stick with measuring event coordinates using the rods-and-clocks framework.

The protractor is used to measure the angle between the lines on the canvas.

In this abstract discussion, the markers can be as precise as we want them to be.

Tach, this is an abstract discussion.
We're not actually planning practical experiments.

I maintain that it doesn't matter.
If we agree on the vector definition, then we can calculate the angle between them.

But, if we really must have experimental measurements, and if the protractor measuring lines on canvas is too hard, then for my measurements I'm going to stick with measuring event coordinates using the rods-and-clocks framework.

No, it doesn't work this way, So far I have agreed to all your formulations, this time you will need to agree to my method of measurement.

We need to mutually agree on how we will proceed.

Do you have a problem with using the rods and clocks framework to identify event coordinates?

We need to mutually agree on how we will proceed.

Do you have a problem with using the rods and clocks framework to identify event coordinates?

Yes, I do. I insist on using a measuring way that we can really implement experimentally. In the end, it is experiments that decide which theory is correct and which one is false. So, if, in the end we still disagree, my method gives you an easy way to decide, in effect is nothing but Hasselkamp's setup on a turntable. I will consider using my method and your method but not your method to the exclusion of mine.

Yes, I do. I insist on using a measuring way that we can really implement experimentally.
I don't think so. Not unless you have some ion beams handy, along with all the other engineering required to set up a relativistic rolling wheel.

In the end, it is experiments that decide which theory is correct and which one is false.
In the case of this debate, we agree that special relativity is a correct theory.
The disagreement is over the predictions of that theory in a specific scenario.

I will consider using my method and your method but not your method to the exclusion of mine.
Yes, that's what we agreed to in the proposal.

So, are we all clear on my methodology?

2.0 Methodology
S' is a reference frame boosted relative to S by velocity v along the x-axis.

In both S and S', I propose to measure the angle between the instantaneous orientation of wheel element P and the instantaneous velocity of wheel element P, at the time when P is in contact with T1.

The instantaneous velocity of P in S is already given by $$\vec{v_p}(t)$$, and by the appropriately transformed $$\vec{v'_p}(t')$$ in S'.
If necessary, the instantaneous velocity of P can be explicitly measured by measuring the displacement over time of an inertial object that is moving with P at the instant of interest.

The instantaneous orientation of wheel element P is given by any displacement vector tangent to the wheel at P at the given instant.
Let $$\hat{D_p}(t)$$ be the unit displacement vector tangent to the wheel at P in S at time t.
Let $$\hat{D'_p}(t')$$ be the unit displacement vector tangent to the wheel at P in S' at time t'.
If necessary, whether a given displacement vector is tangent to the wheel can be tested in at least two ways:
• A displacement vector is tangent to the wheel at a given point at a given instant if it is a scalar multiple of the displacement between two points on a straight rod tangent to the wheel at that point at that instant.
• A displacement vector is tangent to the wheel at a given point at a given instant if and only if there is no other point on the wheel at that instant such that the displacement between the given point and the other point is a scalar multiple of the displacement vector.

The angle between the instantaneous orientation of P and the instantaneous velocity of P is given by the angle between the two defined vectors, that is:
• The angle between $$\vec{v_p}(t)$$ and $$\hat{D_p}(t)$$ in S.
• The angle between $$\vec{v'_p}(t')$$ and $$\hat{D'_p}(t')$$ in S'.

So, are we all clear on my methodology?

Not exactly, the angles were supposed to be measured at t=0 in S as per your latest change. Right?
Also, I want to make sure that both measurement methods (mine and yours) are spelled out in the methodology.

Not exactly, the angles were supposed to be measured at t=0 in S as per your latest change. Right?
Yes that's what I have in my original methodology post.
The same to any point on the wheel at any time, of course... but T1 is set up for point P at t=0.
Also, I want to make sure that both measurement methods (mine and yours) are spelled out in the methodology.

The direction of the ion beams is the same direction as $$\vec{v_P}$$ respectively $$\vec{T_2}$$.
No, that's not something that can be assumed.
It is not assumed, it is by design. They point along the respective directions
It is given that in S, they ion guns are aimed parallel to $$\vec{v_P}$$ and the rod T2.
But I don't accept your general assumption that the direction of the ion beams is the same as the direction in which the guns are aimed.

The relationship holds for the gun at P in S, but I don't think it holds for the gun on T2, and not for either gun in S'.

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.
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.
I don't think you understand what I'm saying. I think you are confusing the motion of the ion gun with the motion of the ion beam.

This diagram shows an element of the ion beam in S, a short time after it was emitted:

This element was emitted from the ion gun at t=0.
It is moving parallel to the y-axis.
It is emitting light in all directions.

Some of the light emitted from this ion beam element reaches the observer at O.
That light will be doppler shifted, depending on the angle between the ion beam element's velocity and the line from O to the ion beam element.

That angle is not a right angle, except at the instant the ion beam element is emitted from the gun.

I think your measurement technique needs a complete rethink.
It does not match up well with the Hasselkamp experiment.

Hasselkamp et al were measuring the transverse doppler shift of light emitted from moving ions that were emitted from a stationary gun, ie they were interested in the velocity of the ions.

But you are trying to measure the velocity of the gun.

In the Hasselkamp experiment, light was emitted directly from the moving objects of interest.

In your measurements, the moving objects of interest at the point P and the rod T2, so you should have light emitted directly from them. This is where you started with the lasers. The only problem was that you had them pointing the wrong way.

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Yes that's what I have in my original methodology post.
The same to any point on the wheel at any time, of course... but T1 is set up for point P at t=0.

It is given that in S, they ion guns are aimed parallel to $$\vec{v_P}$$ and the rod T2.
But I don't accept your general assumption that the direction of the ion beams is the same as the direction in which the guns are aimed.

The relationship holds for the gun at P in S, but I don't think it holds for the gun on T2,

We are not using T2, remember. Besides, the relationship holds, but that is besides the point.

and not for either gun in S'.

That remains to be seen. This is part of your belief, for the time being all that we need to agree on is the guns parallel to $$\vec{v_P(0)}$$ and $$\vec{T_1}$$ at t=0 in S only

I don't think you understand what I'm saying. I think you are confusing the motion of the ion gun with the motion of the ion beam.

Actually I do understand very well.

This diagram shows an element of the ion beam in S, a short time after it was emitted:

This element was emitted from the ion gun at t=0.
It is moving parallel to the y-axis.
It is emitting light in all directions.

Some of the light emitted from this ion beam element reaches the observer at O.
That light will be doppler shifted, depending on the angle between the ion beam element's velocity and the line from O to the ion beam element.

That angle is not a right angle, except at the instant the ion beam element is emitted from the gun.

Yes, this is the time t=0 that we agreed earlier that is the only time we take the measurements. At t=0, the beam is perpendicular on the line of sight.

I think your measurement technique needs a complete rethink.
It does not match up well with the Hasselkamp experiment.

I do not think so at all, see above.

Hasselkamp et al were measuring the transverse doppler shift of light emitted from moving ions that were emitted from a stationary gun, ie they were interested in the velocity of the ions.

But you are trying to measure the velocity of the gun.

This is incorrect, Hasselkamp was trying to measure a pure TDE and I am not trying to measure the velocity of the gun, I am using the TDE measurements from the two guns to show that the vectors $$\vec{v_P(0)}$$ and $$\vec{T_1}$$ are parallel at t=0 in S.

In the Hasselkamp experiment, light was emitted directly from the moving objects of interest.

In the Hasselkamp experiment light is emitted by the ions, I simply added a motion to the gun emitting the ions.

In your measurements, the moving objects of interest at the point P and the rod T2, so you should have light emitted directly from them. This is where you started with the lasers. The only problem was that you had them pointing the wrong way.

I don't think so, see above.

We are not using T2, remember.
Wait...
My measurements are separate to your measurements.
Decisions we make about one set of measurements don't have to affect the other set.

Yes, this is the time t=0 that we agreed earlier that is the only time we take the measurements. At t=0, the beam is perpendicular on the line of sight.
I'm still having difficulty following your line of thought. Please bear with me. You may need to repeat yourself. I apologize, but I really want to be clear on this before we go forward.

Consider for the moment only the ions emitted at t=0 from the gun on P.
Those particular ions travel up, parallel to the y-axis.
Light from those ions begins to arrive at O from t=r/c.
Does the observer measure light emitted from those ions only when it first arrives, or does it continue to measure the light from those particular ions as they travel?

Earlier, you said they would be monitored continually as they travel.
If they are only monitored when the first arrive, then why is the ion gun even necessary? Why not have the observer just monitor light emitted directly from P?

This is incorrect, Hasselkamp was trying to measure a pure TDE and I am not trying to measure the velocity of the gun, I am using the TDE measurements from the two guns to show that the vectors $$\vec{v_P(0)}$$ and $$\vec{T_1}$$ are parallel at t=0 in S.
$$\vec{v_p}(0)$$ is the velocity of a gun, not of the ion beam.

In the Hasselkamp experiment light is emitted by the ions, I simply added a motion to the gun emitting the ions.
That's not simple at all. It changes the nature of the experiment.

Wait...
My measurements are separate to your measurements.
Decisions we make about one set of measurements don't have to affect the other set.

I am not using T2 either. I don't need it. Though, if I want to, I can use it as well and still prove my point.

I'm still having difficulty following your line of thought. Please bear with me. You may need to repeat yourself. I apologize, but I really want to be clear on this before we go forward.

Consider for the moment only the ions emitted at t=0 from the gun on P.
Those particular ions travel up, parallel to the y-axis.
Light from those ions begins to arrive at O from t=r/c.
Does the observer measure light emitted from those ions only when it first arrives, or does it continue to measure the light from those particular ions as they travel?

Only when they fist arrive, i.e. only the light from the ions that emitted the light at t=0.

Earlier, you said they would be monitored continually as they travel.

...if I wanted to use a gun mounted on T2. I can still do that and I can still prove my point right but I gave up on this part in order to align my conditions precisely with yours.

If they are only monitored when the first arrive, then why is the ion gun even necessary? Why not have the observer just monitor light emitted directly from P?

Because T1 is moving on the vertical, the gun is moving with it.

$$\vec{v_p}(0)$$ is the velocity of a gun, not of the ion beam.

Yes, no question. What's the point? The second gun ions describe the direction of $$\vec{v_P}$$, exactly the way the laser was doing it before. Since you objected to the laser being observed at right angle, I just replaced the laser with an ion gun.

That's not simple at all. It changes the nature of the experiment.

Just enough to make it very interesting. Much better than playing with protractors and markers.

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I am not using T2 either. I don't need it. Though, if I want to, I can use it as well and still prove my point.
OK, just so long as I know what you're doing.

Now I'm not sure of the purpose of the ion guns.

Because T1 is moving on the vertical, the gun is moving with it.
There are two ion guns, right?
Is the ion gun on P necessary, since the observer is only observing the light from the ions emitted at P, not anywhere else on the beam?
Why not just have light emitted directly from P?

Same for the ion gun on T1. Does the observer measure the ion beam at any point other than at the ion gun?
If not, then why not just have light emitted directly from T1?

Yes, no question. What's the point?
The point is that the Hasselkamp experiment was about the velocity of the beam, but this scenario is about the velocity of the guns, or rather their point of attachment.
So, why not ditch the guns, and just attach simple light sources to P and T1?

OK, just so long as I know what you're doing.

Now I'm not sure of the purpose of the ion guns.

There are two ion guns, right?
Is the ion gun on P necessary, since the observer is only observing the light from the ions emitted at P, not anywhere else on the beam?
Why not just have light emitted directly from P?

Because the velocity of the ions is a prototype for the tangent to the wheel in P. Besides, I like the idea of generalizing the hasselkamp experiment to rotating platforms and the second gun just does that.

Same for the ion gun on T1. Does the observer measure the ion beam at any point other than at the ion gun?
If not, then why not just have light emitted directly from T1?

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.

The point is that the Hasselkamp experiment was about the velocity of the beam, but this scenario is about the velocity of the guns, or rather their point of attachment.

This is false, in my scenario, the experiment is about the velocity of the ions. The fact that the ion gun is also moving in the same exact direction as the beam does nothing else than a speed composition.

So, why not ditch the guns, and just attach simple light sources to P and T1?

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

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