Age of Universe relative to what?

[my_wan]

Not t=0, but Δt=0 for photons moving in the +x direction. That is a synchronization convention corresponding to an infinite one way speed of light in the +x direction.

Still not sure why you used any variable t at all, except as implied by the RPM.

Regarding the rest of your post, fine there is not a peak brightness, but there is still a brightness as a function of the RPM and you calculate the corresponding "measurement" of the one way speed of light from that function.

But you are ignoring the paucity of required variables and instead using "as a function of: as if the variables of the function justify your statement independent of what the variables entail.

The calculation you use to obtain the value of c depends not only on the measured brightness v RPM function but also on the assumed geometry of your device at different speeds (which is coordinate dependent).

No, it gets the same result no matter which geometry or coordinate choice you use. Hence it is coordinate independent, and synchronization conventions are themselves a form of coordinate choice in which you still get coordinate independent speeds. You CANNOT get any speed other than c by any coordinate or synchronization choice for exactly the same reason you cannot make 1 inch bigger by calling it 2.54 cm.

Yet you still misrepresent the measurement itself. The variables consist of RPM, 1 meter, and 1 cm, from which all else is a purely Newtonian space and defines all variables. Not even the intrinsic brightness of the light source makes any difference, so long as it's constant. The measured brightness v RPM function is insufficient, and requires a divergence of that function to a reference function taken from the variables above.

And Most Importantly:
Changing the geometry does NOT have any effect on the measured speed of light!

I have gone to great lengths to provide multiple reasons why in multiple different logical frameworks to make it clear. Yet your response contains no attempt at justification beyond a repeat of the same claims. It would be helpful if some explanation beyond the claim itself was provided, as well as more justification for the denial of my point. A mere repeat of claims gives me no basis for intuiting what you might see wrong with my rebuttal, formulating a better explanation, or having any clue whatever why extensive and multiple explanations are rebutted with a mere repeat of a claim.

So the same brightness v RPM curve can be made to fit any one-way speed of light under an appropriate choice of coordinates.

Absolutely not. This is the entire point of me obtaining a coordinate independent result from a coordinate choice that many consider incompatible with the curved geometry of the relativity of rigidity.

You CANNOT get any other speed of c or (an)isotropy of c by choosing different coordinate choices or synchronization conventions unless something is wrong with SR, without breaking the legitimate transforms. Breaking legitimate transforms is tantamount to claiming 2 inches cannot possibly be bigger than 2.54 cm, or that object A is bigger than itself. Relativity maintained this by the simply principle that the order of events could not be causally reversed.

You have no obligation to agree, but if you have an argument that is valid I really want to hear it rather than a repeat of claims. If your argument is sound enough I will gladly say: "Oops, you win", but it has to be presented.

 

[Dale]

synchronization conventions are themselves a form of coordinate choice in which you still get coordinate independent speeds.

This is eggregiously false. A speed is some |Δx/Δt|. If you have two different synchronization conventions then they will in general disagree about the Δt and therefore about the speed.

And Most Importantly:
Changing the geometry does NOT have any effect on the measured speed of light!

Sure it does. If the tube is not straight then you will get a different brightness/RPM curve for each possible speed of light compared to the same curves if it is straight. As you have pointed out many times, the "pure geometry" is what does everything in this device. Change the geometry and you change the measurement. You cannot have it both ways, you cannot claim that the geometry does everything for you and that the geometry doesn't have any effect.

I will tell you what. If you would find it convincing then why don't you mathematically derive your brightness v RPM curve for your straight tube under the standard "global t" for two or three possible different values of the one way speed of light. I will do the same for a different synchronization convention (similar to post 105, but not that extreme) and show how the different geometry of the new synchronization convention gives the same brightness v RPM curves for different values of the one way speed of light.

 

[my_wan]

Sure it does. If the tube is not straight then you will get a different brightness/RPM curve for each possible speed of light compared to the same curves if it is straight. As you have pointed out many times, the "pure geometry" is what does everything in this device. Change the geometry and you change the measurement.

But changing the geometry entails changing t at each point along the curve. Hence t is what changes with respect to the coordinate choice rather than the measurement outcome itself. This claim is so simplistic as to be tantamount to saying changing your velocity changes your measurement of c. That's not right either for the exact same reason, because changing your velocity changes the t interval over your path relative to the path associated with your initial velocity.

Only in the experimental case described the change in coordinates did not correspond to any physical changes to the system whatsoever, for any given reference data point to empirical data point pairs.

It's this simple: You can change t over some space of empirical events and all you have to do to keep measurement physically consistent, i.e., not "change the measurement" outcome, is change where that event was in relation to when that event was. Hence the outcome is no longer tied to how you choose to define t or the space. For inertially flat space you merely have to keep the same relative relation between space and time to avoid changing the measurement. Which is why when to changed t in your coordinate choice you had to change the definition of the geometry itself in order to keep a constant c. Which is why it is equivalent to, and does not change the measurement, as a result of this coordinate transform.

It's the same basic inverse space/time relation both SR and GR depend on. When you travel from Earth to some station 1 light hour away from Earth in 10 minutes it's not because you exceeded light speed. For you it's because the station was positioned much closer to Earth that is was from the Earth frame. From the Earth frame you got there at a much later t and your apparent t is attributed slow clocks on your ship. Space and time covary to maintain c. Hence when you relabeled t in the experiment you had to relabel spatial coordinates as though it was a curved geometry to keep the exact same resulting measurement in a system which no actual physical changes occurred. Only your coordinates did.

I repeated it so many ways because I am at a loss as to how SR, much less GR, can be comprehended without knowing this already.

 

[Dale]

But changing the geometry entails changing t at each point along the curve.

Of course, that is what a synchronization convention is.

This claim is so simplistic as to be tantamount to saying changing your velocity changes your measurement of c. That's not right either for the exact same reason, because changing your velocity changes the t interval over your path relative to the path associated with your initial velocity.

That is true only for the Einstein synchronization convention. The rest of your comments similarly apply only to a coordinate system established using the Einstein synchronization convention.

I repeated it so many ways because I am at a loss as to how SR, much less GR, can be comprehended without knowing this already.

Perhaps you don't realize it, but there are many quantities which are independent of the coordinate system and many which are dependent on the coordinate system. The one way speed of light is one of the coordinate dependent types.

 

[my_wan]

Of course, that is what a synchronization convention is.

That is true only for the Einstein synchronization convention. The rest of your comments similarly apply only to a coordinate system established using the Einstein synchronization convention.

So you have just claimed that purely Newtonian mechanics with purely Galilean transforms assumes the Einstein synchronization convention. That wasn't a question.

Perhaps you don't realize it, but there are many quantities which are independent of the coordinate system and many which are dependent on the coordinate system. The one way speed of light is one of the coordinate dependent types.

Yet again I'm left with nothing but a repeat of a raw authoritative claim, with that authority backed up with a maybe I don't realize I have 10 toes to match my 10 fingers.

 

[Dale]

Yet again I'm left with nothing but a repeat of a raw authoritative claim, with that authority backed up with a maybe I don't realize I have 10 toes to match my 10 fingers.

I assume that is a strangely worded request for references.

The best reference is Zhang, "Special Relativity and Its Experimental Foundations". E.g. Section 1.3.2 "we want to stress here is that only the two-way speed, but not the one-way speed, of light has been already measured in the experimental measurements, and hence the isotropy of the one-way velocity of light is just a postulate. ... a more general postulate, a choice of the anisotropy of the one-way velocity of light, together with the principle of relativity, would give the same physical predictions."

Since the more general postulate would give the same physical predictions, any experimental result which is predicted with an isotropic one-way speed of light equal to c is also predicted with an anisotropic one-way speed of light not equal to c.

See also Edwards, Am. J. Phys. 31 (1963), pg 482, which is the original source for the relevant section of Zhang.

 

[my_wan]

I assume that is a strangely worded request for references.

It was a reference to the authoritative (lacking content) rebuttal, so you have deferred the same. I have repeatedly asked for an explanation rather than raw claims. However, I will run with this.

The best reference is Zhang, "Special Relativity and Its Experimental Foundations". E.g. Section 1.3.2 "we want to stress here is that only the two-way speed, but not the one-way speed, of light has been already measured in the experimental measurements, and hence the isotropy of the one-way velocity of light is just a postulate. ... a more general postulate, a choice of the anisotropy of the one-way velocity of light, together with the principle of relativity, would give the same physical predictions."

Noted: You address the red letters next, but before I respond to that let me quote you on what lead us here.

OK, so you agree that the spatial shape of the device depends on your coordinate choice.
[...]
The point is that you made an assumption ("global t") and the thing you said you were measuring depends on that assumption.
[...]
The point is that you made an assumption ("global t") and the thing you said you were measuring depends on that assumption.

To this I give an extensive explanation for why coordinate choices have no physical meaning and CANNOT give physical predictions. Only you claimed it does in post #142. Yet you finished the same post by saying differing synchronization convention gives the same brightness v RPM curves for different values of the one way speed of light.

Are here we are a step back, with me saying same physical predictions and you effectively claiming a coordinate choice changes the predicted speed of light. Does changing from feet to inches make my house 12x bigger? Yet here you are quoting from external sources exactly what I've been saying.

Since the more general postulate would give the same physical predictions, any experimental result which is predicted with an isotropic one-way speed of light equal to c is also predicted with an anisotropic one-way speed of light not equal to c.

Exactly, because you are not describing a differing theory, only a differing coordinate choice. Insisting that the anisotropic coordinate transform entails a directional speed of light is exactly like insisting that the $k_e$ of a pair of meteors MUST be located only at the first meteor if you choose a coordinate with an origin at the second meteor. That BS. It's the same BS that got physics in trouble with Newtonian aether theories to begin with.

Now, when I said "Changing the geometry does NOT have any effect on the measured speed of light!", you responded with "Sure it does." Post #142. Yet you say in the same post "...different geometry of the new synchronization convention gives the same brightness v RPM curves for different values of the one way speed of light." So let's take your differing c as somehow physically meaning, however absurd it may to to assign physical significance to a coordinate choice. What in fact your claim entails is that my coordinate choice gives the proper speed of light, whereas yours gives an invalid speed of light. Why, exactly because SR is constructed in such a way that c is constant under Galilean kinematics. In fact, as I'll show, your curved geometry defined this way is off by $c'\theta = \frac{c}{1 + \beta \: cos\theta}$.

See also Edwards, Am. J. Phys. 31 (1963), pg 482, which is the original source for the relevant section of Zhang.

So let's look at where it is the formula I just gave and Edwards paper operate with came from, called the Sagnac effect. Let's look at where this anisotropy from a rotating frame and see where it comes from.
Noninvariant one-way speed of light and locally equivalent reference frames
Found. Phys. Lett. 10, 73-83 (1997).

Using 3 points, $i = (1,2,3)$, in the full rotation of a frame then $t_{0i} = t_i F_1(v,a)$. For light propagating in the opposite direction as the rotation distance is smaller by $L_0 - x = \omega R(t_{02} - t_{01})$, such that $L_0 - x = c(t_{02} - t_{01})$. This gives us $t_{02} - t_{01} = \frac{L_0}{c(1 + \beta)}$. The RHS is you standard one way light speed transform, inverted for the opposite direction.

Here, since this clearly indicates that this one way speed is defined by $t_{02} - t_{01}$, and t has no a priori meaning whatsoever, not that it can't be measured but none whatsoever, then neither does $t_{02} - t_{01}$ or your one way speed. So does this mean this effect cannot be measured. No! That is exactly what the Sagnac effect is! This effect must also be accounted for in GPS synchronization, Y. Saburi et al., IEEE Trans. IM25, 473 (1976).

Does this mean this correction makes my coordinate choice wrong without this correction and yours correct? No, as demonstrated by A. Dufour and F. Prunier, J. de Phys. 3, 153 (1942). So by insisting that the effect makes the anisotropy of c it describes as physically meaningful beyond a simple coordinate choice and that it is not a measurable effect means both such claims are wrong.

So when you introduce this curved geometry you are merely relabeling t in (x,y,z,t) into a non-Galilean standard whereupon you are required to change the effective positions of (x,y,z) accordingly such that it is nothing more than an equivalent coordinate relabeling of (x,y,z,t). Yet insist that in some undefined way this coordinate relabeling is physically meaningful. It's only physically meaningful in the same way that a house plan using feet and inches will not work if interpreted to mean meters and centimeters. Attempting to do so has measurable effects. We lost a Mars probe this way.

 

[Dale]

It was a reference to the authoritative (lacking content) rebuttal, so you have deferred the same. I have repeatedly asked for an explanation rather than raw claims.

That is a pretty absurd complaint. I have given you many explanations. The mere fact that you disagree with the explanations given doesn't negate the fact that you have been given explanations.

Noted: You address the red letters next, but before I respond to that let me quote you on what lead us here.

My statements that you highlighted in red are all correct. This goes back to my comment in post 144. You seem unable to distinguish between coordinate dependent and coordinate independent quantities.

To this I give an extensive explanation for why coordinate choices have no physical meaning and CANNOT give physical predictions. Only you claimed it does in post #142. Yet you finished the same post by saying differing synchronization convention gives the same brightness v RPM curves for different values of the one way speed of light.

Are here we are a step back, with me saying same physical predictions and you effectively claiming a coordinate choice changes the predicted speed of light.

Coordinate choices change coordinate dependent quantities like the one-way speed of light. Coordinate choices do not change coordinate independent quantities like the outcome of some physical experiment. The outcomes of physical experiments can be used to calculate other values which have some specific meaning, but that calculation, in general, depends on the coordinates used.

The outcome of a physical experiment is the output of some specific measuring device, like the number of ticks of a clock, or, in this case, the voltage on a CCD. That is a coordinate independent quantity. However, the equation which relates the voltage on the CCD to the one way speed of light is coordinate dependent.

As Zhang said, the Edwards simultaneity convention (in which the one way speed of light may range from 1/2 c to infinity), is compatible with relativity. This means that anything which can be predicted (e.g. the voltage on your CCD) using the one-way speed of light = c can also be predicted using the one-way speed of light = 9000 c.

Now, when I said "Changing the geometry does NOT have any effect on the measured speed of light!", you responded with "Sure it does." Post #142. Yet you say in the same post "...different geometry of the new synchronization convention gives the same brightness v RPM curves for different values of the one way speed of light."

Yes, do you understand now? The brightness v. RPM is the coordinate independent outcome of the physical experiment, the one way speed of light is a value calculated from that physical experiment under a set of assumptions, one of those assumptions being the value of the one way speed of light.

Let this sink in for a bit. If you are still doubtful then I would recommend that we actually work through the problem together, as I suggested in post 142. Calculate the brightness v RPM curve that would indicate a one-way velocity of c and 2c using standard synchronization and then I will show how those same curves can indicate one-way velocities of 10 c and 20 c using a different synchronization convention.

 

[my_wan]

That is a pretty absurd complaint. I have given you many explanations. The mere fact that you disagree with the explanations given doesn't negate the fact that you have been given explanations.

I don't see them, in spite of my long winded explanations.

My statements that you highlighted in red are all correct. This goes back to my comment in post 144. You seem unable to distinguish between coordinate dependent and coordinate independent quantities.

Yet what your are calling the coordinate dependence of one-way light speeds is a product of using one coordinate choice to describe the system and another coordinate choice to characterize the consequences. You are mixing and matching coordinate choices to to justify the claims.

Coordinate choices change coordinate dependent quantities like the one-way speed of light. Coordinate choices do not change coordinate independent quantities like the outcome of some physical experiment. The outcomes of physical experiments can be used to calculate other values which have some specific meaning, but that calculation, in general, depends on the coordinates used.

Here you have made a valid direct distinction coordinate choices an physical outcomes. Why then when I said:

And Most Importantly:
Changing the geometry does NOT have any effect on the measured speed of light!

Sure it does.

So when I make a claim about measured outcomes you get to reject it by injecting a coordinate choice. Yet you get to defend that rejection by claiming coordinate choices do not change measured outcomes. Come on now, this is getting absurd beyond reason.


The outcome of a physical experiment is the output of some specific measuring device, like the number of ticks of a clock, or, in this case, the voltage on a CCD. That is a coordinate independent quantity. However, the equation which relates the voltage on the CCD to the one way speed of light is coordinate dependent.

As Zhang said, the Edwards simultaneity convention (in which the one way speed of light may range from 1/2 c to infinity), is compatible with relativity. This means that anything which can be predicted (e.g. the voltage on your CCD) using the one-way speed of light = c can also be predicted using the one-way speed of light = 9000 c.

Yes, do you understand now? The brightness v. RPM is the coordinate independent outcome of the physical experiment, the one way speed of light is a value calculated from that physical experiment under a set of assumptions, one of those assumptions being the value of the one way speed of light.

How is it that I have assumed a one way light speed when in fact the assumption labels it infinite though we know it is certainly not? Therefore the only assumption is that the assumption that was made is going to be empirically wrong. This resolves your next suggestion. If the brightness v. RPM is, as you admit here, a coordinate independent outcome then so is the speed of light. I'll explain in detail in the following response.

Let this sink in for a bit. If you are still doubtful then I would recommend that we actually work through the problem together, as I suggested in post 142. Calculate the brightness v RPM curve that would indicate a one-way velocity of c and 2c using standard synchronization and then I will show how those same curves can indicate one-way velocities of 10 c and 20 c using a different synchronization convention.

So what are are saying is that because you can choose a coordinate choice that is inconsistent with $L_0$ as defined by another coordinate choice it proves the one-way speed c is coordinate dependent, in spite of the fact that it cannot represent any experimental outcome?

Let's look at the brightness v. RPM issue. You have chosen a curved geometry where t is non-uniform, though $L_0$ which defines the diameter of the rotating system is still assumed to be $L_0 = L_1$. This mixing of coordinate choices is the reason the factor $c'\theta = \frac{c}{1 + \beta \: cos\theta}$, in which your one-way speed claim depends, occurs.

Thus the fatal flaw in your argument that the one-way speed is coordinate dependent is that you have not shown it was dependent on your coordinate choice, but rather that your coordinate choice differed from a differing coordinate choice. If we restrict the coordinate choice to your curved coordinates alone, then $L_0 \neq L_1$, since $L_0 = L_1$ is inconsistent with the coordinate choice you made.

Once you adjust $L_1$ to properly represent the diameter that your own coordinate choice dictates then brightness v. RPM once again give a constant c without the $c'\theta = \frac{c}{1 + \beta \: cos\theta}$ correction factor. You cannot use one coordinate choice to describe the system and another to define define the consequences and then claim the difference was the result of your particular coordinate choice.

 

[Dale]

I don't see them, in spite of my long winded explanations.

See posts 58, 77, 96, 105, 119, 125, 131, 138, 142, and 146, all of which contained explanations of one or more of the issues here. Clearly you don't agree with any of the explanations, but they are there.

Yet what your are calling the coordinate dependence of one-way light speeds is a product of using one coordinate choice to describe the system and another coordinate choice to characterize the consequences. You are mixing and matching coordinate choices to to justify the claims.

This is not true at all. Show exactly where I did that.

So when I make a claim about measured outcomes you get to reject it by injecting a coordinate choice. Yet you get to defend that rejection by claiming coordinate choices do not change measured outcomes. Come on now, this is getting absurd beyond reason.

I thought that was clear already. What you are claiming in that quote to be a measured outcome is not, in fact, the outcome of a physical experiment, but a coordinate dependent calculation from from the outcome. Different coordinate systems will agree that the brightness v. RPM curve is the same, but they will not agree about what speed of light produced that curve. So the speed of light is a coordinate dependent value, and you merely measure the value you assumed in the calculation.

How is it that I have assumed a one way light speed when in fact the assumption labels it infinite though we know it is certainly not?

We don't know it is certainly not infinite. We assume it is not.

If the brightness v. RPM is, as you admit here, a coordinate independent outcome then so is the speed of light. I'll explain in detail in the following response.

So what are are saying is that because you can choose a coordinate choice that is inconsistent with $L_0$ as defined by another coordinate choice it proves the one-way speed c is coordinate dependent, in spite of the fact that it cannot represent any experimental outcome?

Let's look at the brightness v. RPM issue. You have chosen a curved geometry where t is non-uniform, though $L_0$ which defines the diameter of the rotating system is still assumed to be $L_0 = L_1$. This mixing of coordinate choices is the reason the factor $c'\theta = \frac{c}{1 + \beta \: cos\theta}$, in which your one-way speed claim depends, occurs.

Thus the fatal flaw in your argument that the one-way speed is coordinate dependent is that you have not shown it was dependent on your coordinate choice, but rather that your coordinate choice differed from a differing coordinate choice. If we restrict the coordinate choice to your curved coordinates alone, then $L_0 \neq L_1$, since $L_0 = L_1$ is inconsistent with the coordinate choice you made.

Once you adjust $L_1$ to properly represent the diameter that your own coordinate choice dictates then brightness v. RPM once again give a constant c without the $c'\theta = \frac{c}{1 + \beta \: cos\theta}$ correction factor. You cannot use one coordinate choice to describe the system and another to define define the consequences and then claim the difference was the result of your particular coordinate choice.

I have not made any claims about $L_0$ or $L_1$ or any $\theta$ to my knowledge. Please define your terms and show mathematically how I have said any of that.

Again, I recommend that you actually go through the exercise of analyzing your device using the standard synchronization convention and show the predicted brightness curve, and I will analyze it using a different synchronization convention, and show how the same brightness curve is compatible with a different velocity of light.

I think that the reason you hesitate to do so is that you realize that the math will back me up.

 

[my_wan]

I have not made any claims about $L_0$ or $L_1$ or any $\theta$ to my knowledge. Please define your terms and show mathematically how I have said any of that.

If you have a curved geometry between where the light enters and exits the hollow the distance $L_0$ most certainly cannot represent the diameter that is valid for a Galilean frame. The only really important variables I use is RPM and diameter. So you tell me what effect you think your coordinate has on $L_0$, the total distance from one end to the other?

Again, I recommend that you actually go through the exercise of analyzing your device using the standard synchronization convention and show the predicted brightness curve, and I will analyze it using a different synchronization convention, and show how the same brightness curve is compatible with a different velocity of light.

First off what synchronization convention? I have merely used one tape measure to measure the distance across the spinning device (diameter), and one clock to measure RPM.

Second you speak as though I am predicting a brightness curve. I am making no such predictions. I am measuring, not predicting.

I think that the reason you hesitate to do so is that you realize that the math will back me up.

So why then do you need to pretend a measurement is a prediction? If the logic of this accusation held couldn't you be accused of the same thing with this conflation between prediction and measurement?

Let's consider a simplistic system in which we can capture the requisite physics with a minimum of variables. The simplest I can think of is a version of the ladder paradox. Only in this case the ladder is point-like and the barn is rotating. Hence we can break it down to a single event system and ask if the particle makes it through both barn doors. Hence for any given speed of the particle there is a maximum RPM in which the particle can possibly make it through both barn doors. For simplicity assume the doors are 1 meter apart and are 1 cm^2 squares. This captures the mechanics, without the specifics of the actual experiment, perfectly.

 

[PhilDSP]

The experiment in post #50 would be interesting if it was performed with all the necessary control conditions. But it could wind up being very difficult to interpret the results. For one thing the holes would act as waveguides and drag the EM waves along in a velocity dependent fashion, wouldn't they? The disk would need to be thinner than the wavelength of the light otherwise.

 

[Dale]

If you have a curved geometry between where the light enters and exits the hollow the distance $L_0$ most certainly cannot represent the diameter that is valid for a Galilean frame. The only really important variables I use is RPM and diameter. So you tell me what effect you think your coordinate has on $L_0$, the total distance from one end to the other?

Is $L_0$ the distance that the light travels or is it the length of the tube at some specific instant in time? If it is the distance that the light travels, then that is the same under different synchronization conventions. If it is the length of the tube then it is different under different synchronization conventions.

First off what synchronization convention? I have merely used one tape measure to measure the distance across the spinning device (diameter), and one clock to measure RPM.

The synchronization convention where the spinning device is straight.

Second you speak as though I am predicting a brightness curve. I am making no such predictions. I am measuring, not predicting.

So why then do you need to pretend a measurement is a prediction?

Because you are not measuring the one way speed of light, you are measuring a brightness v RPM curve. You are then interpreting that measurement as indicative of some specific one way speed of light.

The way you make that interpretation is by taking your geometry and predicting what the brightness v RPM curve should look like for a variety of different values of the one way speed of light. You described the process quite well in your post 139.

Let's consider a simplistic system in which we can capture the requisite physics with a minimum of variables. The simplest I can think of is a version of the ladder paradox. Only in this case the ladder is point-like and the barn is rotating. Hence we can break it down to a single event system and ask if the particle makes it through both barn doors. Hence for any given speed of the particle there is a maximum RPM in which the particle can possibly make it through both barn doors. For simplicity assume the doors are 1 meter apart and are 1 cm^2 squares. This captures the mechanics, without the specifics of the actual experiment, perfectly.

I am certainly willing to consider a simplified version. Compared to your post 113 it seems that you are essentially removing the tube walls, or turning the tube wall into a big cylinder. Are you still considering the light to be tightly collimated as it enters the opening, or are you thinking of the "door" as a spherical source now?

 

[my_wan]

If you think of the tube as as merely a pair of openings, like a variation of the Fizeau-type experiment, the $L_0$ is merely the distance between the opening. I have no idea why you would specify at some particular instant because it is constant. Even if you assume it relativistically changes with differing RPM is is still constant at a given RPM.

Unlike some Fizeau-type experiments it is mechanistically bound like in http://arxiv.org/abs/1103.6086 such that geometry, not synchronization, determines mutually open light paths. Also unlike previous methods no comparison to a return path is needed, such that the path is not closed. Which was the issue with the referenced experiment.

The synchronization convention where the spinning device is straight.

Due to the mechanical constraints that is a pure coordinate choice issue which does not require any synchronization assumptions that are not bound to geometry. The usual Fizeau-type experiments, like above, requires the assumption that whatever relational variation between space and time was not washed out by closing the path, since it was not a velocity being measured but rather a differential in a path pair plus a return path pair. That leaves only pure coordinate choices by which to maintain any argument.

The main point being, not that you can't define a differing coordinate choice, but that physical laws play no role in either validating or invalidating either choice. Not as a result of an inability to measure a difference, but rather that the difference has no physical meaning whatsoever.

I am certainly willing to consider a simplified version. Compared to your post 113 it seems that you are essentially removing the tube walls, or turning the tube wall into a big cylinder. Are you still considering the light to be tightly collimated as it enters the opening, or are you thinking of the "door" as a spherical source now?

Yes, the tube walls are of little importance so long as the opening are mechanically tied and the only light exiting the cylinder to be detected must pass though the cylinder. In this way, if you want to impose a different geometry, it is sufficient to consider just the opening at each end. Nor does it matter how distant the light sources or even the distance of the detector on the other side of the apparatus. $L_0$, the distance between the openings, is what determines how much light gets to the detector if all else is equal. Collimated light has certain practical advantages, but strictly speaking that doesn't even matter in general. Just stick with Collimated light for simplicity.


For conceptual purposes a highly idealized variation of the so called ladder paradox is useful. For conceptual purposes we can treat the photon like a very tiny bullet with a relativistic velocity. What we are asking then the given some velocity of the bullet what is the maximum RPM at which this bullet can pass through a hollow pipe without reflections off the internal walls. What we know about the ladder paradox is that its solutions in all cases entails the same outcome we would expect if no purely relativist frame dependent distortions of geometry was involved.

You have objected that by introducing these frame dependent distortions that it entails a differing speed of light. I have rebutted by pointing out that the differing light speed has been obtained by selecting a differing globally non-uniform frame (coordinate choice) and then relating that back to a globally uniform Galilean lab frame which does not account for the variations in spatial intervals your transforms of time intervals entails. A valid specification of velocity cannot involve relating it back to a global Galilean lab frame that is not globally used in defining the geometry of the space. Thus using an unused coordinate choice to make claims about a coordinate choice that was used.

Nonetheless, this objection of yours does appear to be worth quantitatively working through. The standard formalism involves rotating the angle or path the particle takes through the relativistically squashed hole. An alternative to relativistic rotation, given a point sized object, is to simply have the distant exit (detector) hole lag behind. Of course any such relativistic lag must make synchronization assumptions Galilean transforms neither require nor necessarily deny a priori. It is this property of Galilean transforms, that does not alone a priori require consistency with SR synchronization conventions, that in principle gives the purely Galilean initial assumptions an advantage. Even though, given what we empirically do know, the lack of a priori consistency is effectively moot.

 

[my_wan]

The experiment in post #50 would be interesting if it was performed with all the necessary control conditions. But it could wind up being very difficult to interpret the results. For one thing the holes would act as waveguides and drag the EM waves along in a velocity dependent fashion, wouldn't they? The disk would need to be thinner than the wavelength of the light otherwise.

The waveguide issue is not such a problem in itself if the walls are recessed, like in a barn, or otherwise non-reflective. A possibly bigger issue for accuracy is edge dispersion due to the uncertainty principle. Essentially the hole may have to be big enough to minimize such path uncertainties. I haven't completely thought every issue that hasn't been brought up here, but controlling for them doesn't appear to be a major issue.

 

[Dale]

I have no idea why you would specify at some particular instant because it is constant. Even if you assume it relativistically changes with differing RPM is is still constant at a given RPM.

That is true only under synchronization conventions where the one way speed of light is isotropic. Under other conventions length contraction is also not isotropic and therefore the geometry changes over time.

Due to the mechanical constraints that is a pure coordinate choice issue which does not require any synchronization assumptions that are not bound to geometry. ...

The main point being, not that you can't define a differing coordinate choice, but that physical laws play no role in either validating or invalidating either choice. Not as a result of an inability to measure a difference, but rather that the difference has no physical meaning whatsoever.

I basically agree with this. Coordinate choices have little physical meaning other than convenience and convention, the one-way speed of light is an artifact of the coordinate choice, therefore the one-way speed of light has little physical meaning.

Just stick with Collimated light for simplicity.

Sounds good to me.

I have rebutted by pointing out that the differing light speed has been obtained by selecting a differing globally non-uniform frame (coordinate choice) and then relating that back to a globally uniform Galilean lab frame which does not account for the variations in spatial intervals your transforms of time intervals entails. A valid specification of velocity cannot involve relating it back to a global Galilean lab frame that is not globally used in defining the geometry of the space.

Coordinate transformations are completely legitimate. There is nothing wrong with specifying one coordinate system in terms of a specific transform from another coordinate system. See post 105. This is very standard in both SR and GR.

Nonetheless, this objection of yours does appear to be worth quantitatively working through.

I am glad you think so, I will look forward to seeing the result.