Age of Universe relative to what?

[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.