Isotropic and anisotropic propagation of light

[Aether]

Looks like your "simulation" program is all messed up. Here are the calculations for the case that you listed above in post #111, they show very clearly the phase dependency on v_z. Are you still having difficulties with elementary calculations? Better check that program of yours.

Your first four equations are the same as the ones that I gave in post #111 except for a difference in the signs on k and k'. The convention when dealing with waveguides is to lay them along the negative z-direction. The fifth equation seems to be missing a term, but that term is invariant over changes in v_z so it doesn't change the predicted outcome of the experiment.

The next term sin((k-k')z/2) modulates the amplitude of E_0, and the amplitude of the composite waveform is 2 E_0 sin((k-k')z/2). Since the composite waveform is demodulated at this point, the term sin((k+k')z/2-\omega t) has no further effect.

If we were to design a new experiment where the composite waveform is not demodulated, we would also need to transform the z and t coordinates.

 

[clj4]

Your first four equations are the same as the ones that I gave in post #111 except for a difference in the signs on k and k'. The convention when dealing with waveguides is to lay them along the negative z-direction. The fifth equation seems to be missing a term, but that term is invariant over changes in v_z so it doesn't change the predicted outcome of the experiment.

The next term sin((k-k')z/2) modulates the amplitude of E_0, and the amplitude of the composite waveform is 2 E_0 sin((k-k')z/2). Since the composite waveform is demodulated at this point, the term sin((k+k')z/2-\omega t) has no further effect.

If we were to design a new experiment where the composite waveform is not demodulated, we would also need to transform the z and t coordinates.

Do you have difficulty in terms of understanding the term "phase"? How far do you plan to take this embarassment? You have been told for months what the "phase" means in the Gagnon experiment : (k+k')z/2.
It is what appears in the same expression with \omega t, ok? The standard texbook thing.

 

[Aether]

Do you have difficulty in terms of understanding the term "phase"? How far do you plan to take this embarassment? You have been told for months what the "phase" means in the Gagnon experiment : (k+k')z/2.
It is what appears in the same expression with \omega t, ok? The standard texbook thing.

This is a phase-shift on the ~40GHz composite carrier-wave signal prior to demodulation. That high-frequency signal is filtered out by the double balanced mixer/demodulator, and it is irrelevant to the outcome of this experiment. We could detect the phase of the carrier wave using a synchronous demodulator, but then we would have to transform the z and t coordinates.

 

[clj4]

We could detect the phase of the carrier wave using a synchronous demodulator, but then we would have to transform the z and t coordinates.

The (z,t) have been transformed already, this is how the partial differential equation was obtained in first place. Give it up, it is getting embarassing.

 

[Aether]

In the http://imaginary_nematode.home.comcast.net/papers/Gagnon_et_al_1988.pdf" experiment, two waveguides are driven on one end by the same 40.16GHz sine-wave source, the two waveguides run parallel to one another along the negative z-axis, and the waves reflect back and forth within the waveguides at different pitch angles with the result that the waves emerging at the opposite ends of the two waveguides have traveled along paths having substantially different geometric length. We describe the total phase-angle traversed by a wave traveling through a first waveguide as k * z where k is the wave-number of the first waveguide, and z is the length of the first waveguide. The term "wave number" refers to the number of complete wave cycles of an electromagnetic field that exist in one meter of linear space, but because the waves in the waveguides reflect back and forth within the waveguide, there can be many more wavelengths stored within the waveguide than if the wave traveled along a straight line through the waveguide. Similarly, we describe the total phase-angle traversed by a wave traveling through a second waveguide as k' * z where k' is the wave-number of the second waveguide, and z is also the length of the second waveguide layed along the negative z-axis.

When the two waves emerge at the far end of the waveguides, a detector circuit is used to measure the differential phase of the two waves. To do this, the common-mode phase of the two signals is "rejected". On page 1769 of the Gagnon paper under section III. Experimental Analysis, the authors describe their detector circuit:

Signals from the two waveguides are recombined in a balanced mixer which gives a dc output proportional to their phase difference when the waveguide outputs are set near phase quadrature.

clj4, I figured out that the missing term in your fifth equation is just a sign. You could correct that equation by swapping the order of E_z and E'_z. The "dc output proportional to their phase difference..." that Gagnon refers to in the quote above is proportional to sin((k-k')z/2), where "there phase difference" refers to (k-k')z. The term that you refer to incorrectly as "the resultant phase measured by Gagnon" is actually the common-mode phase shift that is rejected by the balanced mixer. To demonstrate this, I have modeled a balanced mixer circuit in SPICE using the Micro-Cap 8.1.1.0 Evaluation Version which is freely available for download on the web. Anyone can download this circuit simulator free of charge and reproduce my results independently.

The attached file "BalancedMixerSchematic.jpg" shows a screen-shot of the schematic of the circuit used to simulate the output traces discussed below. The schematic shows three identical balanced mixer circuits driven by dual sine wave sources at a frequency of 40.16KHz (for convenience, I have simulated a 40.160KHz carrier wave rather than 40.160GHz; the principles are the same). The first circuit is driven by sine sources WG1 and WG2 with phase parameters PH=840 and 40 radians respectively. The blue trace on the "BalancedMixerOutput.jpg" plot corresponds to the simulated output of this circuit over a period of one second. The traces in this plot all start out on the left side at higher than normal voltages because the circuit parameters are undefined prior to T=0, and then they settle to nearly flat dc signals as time goes by. These voltages would settle a bit further if the simulation were run for a longer time.

The second (lower left) circuit is driven by sine sources WG3 and WG4 with phase parameters PH=840.7854 and 40.7854 radians respectively. The red trace on the "BalancedMixerOutput.jpg" plot corresponds to the simulated output of this circuit. The phases of the two sine sources have both been offset by +\pi/4. Since this is a common-mode phase shift, we see that the red trace settles to the same value of the blue trace so that there is no difference between the outputs of the two circuits once they have settled. This is what is expected, and if the simulation were run for a longer period the two traces would continue to converge on the same value. Conclusion: common-mode phase shifts do not affect the output of a balanced mixer circuit, by design.

The third (center right) circuit is driven by sine sources WG5 and WG6 with phase parameters PH=840.7854 and 39.2146 radians respectively. The green trace on the "BalancedMixerOutput.jpg" plot corresponds to the simulated output of this circuit. The phases of the first sine source has been offset by +\pi/4 (relative to PH=840), and the phase of the second sine source has been offset by -\pi/4 (relative to PH=40). Since this is a differential-mode phase shift, we see that the green trace settles to a substantially different value from the red and the blue traces. This is what is expected. Conclusion: differential-mode phase shifts do affect the output voltage of a balanced mixer circuit, by design.

GGT predicts common-mode phase shifts for the two waveguides, and this is simply not observable by means of the experiment described by Gagnon et al..

 

[clj4]

In the http://imaginary_nematode.home.comcast.net/papers/Gagnon_et_al_1988.pdf" experiment, two waveguides are driven on one end by the same 40.16GHz sine-wave source, the two waveguides run parallel to one another along the negative z-axis, and the waves reflect back and forth within the waveguides at different pitch angles with the result that the waves emerging at the opposite ends of the two waveguides have traveled along paths having substantially different geometric length. We describe the total phase-angle traversed by a wave traveling through a first waveguide as k * z where k is the wave-number of the first waveguide, and z is the length of the first waveguide. The term "wave number" refers to the number of complete wave cycles of an electromagnetic field that exist in one meter of linear space, but because the waves in the waveguides reflect back and forth within the waveguide, there can be many more wavelengths stored within the waveguide than if the wave traveled along a straight line through the waveguide. Similarly, we describe the total phase-angle traversed by a wave traveling through a second waveguide as k' * z where k' is the wave-number of the second waveguide, and z is also the length of the second waveguide layed along the negative z-axis.

When the two waves emerge at the far end of the waveguides, a detector circuit is used to measure the differential phase of the two waves. To do this, the common-mode phase of the two signals is "rejected". On page 1769 of the Gagnon paper under section III. Experimental Analysis, the authors describe their detector circuit:

clj4, I figured out that the missing term in your fifth equation is just a sign. You could correct that equation by swapping the order of E_z and E'_z. The "dc output proportional to their phase difference..." that Gagnon refers to in the quote above is proportional to sin((k-k')z/2), where "there phase difference" refers to (k-k')z. The term that you refer to incorrectly as "the resultant phase measured by Gagnon" is actually the common-mode phase shift that is rejected by the balanced mixer. To demonstrate this, I have modeled a balanced mixer circuit in SPICE using the Micro-Cap 8.1.1.0 Evaluation Version which is freely available for download on the web. Anyone can download this circuit simulator free of charge and reproduce my results independently.

The attached file "BalancedMixerSchematic.jpg" shows a screen-shot of the schematic of the circuit used to simulate the output traces discussed below. The schematic shows three identical balanced mixer circuits driven by dual sine wave sources at a frequency of 40.16KHz (for convenience, I have simulated a 40.160KHz carrier wave rather than 40.160GHz; the principles are the same). The first circuit is driven by sine sources WG1 and WG2 with phase parameters PH=840 and 40 radians respectively. The blue trace on the "BalancedMixerOutput.jpg" plot corresponds to the simulated output of this circuit over a period of one second. The traces in this plot all start out on the left side at higher than normal voltages because the circuit parameters are undefined prior to T=0, and then they settle to nearly flat dc signals as time goes by. These voltages would settle a bit further if the simulation were run for a longer time.

The second (lower left) circuit is driven by sine sources WG3 and WG4 with phase parameters PH=840.7854 and 40.7854 radians respectively. The red trace on the "BalancedMixerOutput.jpg" plot corresponds to the simulated output of this circuit. The phases of the two sine sources have both been offset by +\pi/4. Since this is a common-mode phase shift, we see that the red trace settles to the same value of the blue trace so that there is no difference between the outputs of the two circuits once they have settled. This is what is expected, and if the simulation were run for a longer period the two traces would continue to converge on the same value. Conclusion: common-mode phase shifts do not affect the output of a balanced mixer circuit, by design.

The third (center right) circuit is driven by sine sources WG5 and WG6 with phase parameters PH=840.7854 and 39.2146 radians respectively. The green trace on the "BalancedMixerOutput.jpg" plot corresponds to the simulated output of this circuit. The phases of the first sine source has been offset by +\pi/4 (relative to PH=840), and the phase of the second sine source has been offset by -\pi/4 (relative to PH=40). Since this is a differential-mode phase shift, we see that the green trace settles to a substantially different value from the red and the blue traces. This is what is expected. Conclusion: differential-mode phase shifts do affect the output voltage of a balanced mixer circuit, by design.

GGT predicts common-mode phase shifts for the two waveguides, and this is simply not observable by means of the experiment described by Gagnon et al..

Thank you for the disertation, this is a great example of GIGO. You know perfectly well that the term (k-k') is independent of v_z because v_z reduces trivially in the subtraction. So, there was no need of the above disertation.You are so stuck in the original description of the Gagnon experiment that you cannot even begin to understand that two waveforms can be SUBTRACTED as well as being added, generating the term sin((k+k')z/2-\omega*t) INSTEAD of the term sin((k-k')z/2). In the term sin((k+k')z/2-\omega*t) the phase (k+k')z/2 IS a linear function of v_z and is fully DETECTABLE (hint: you do not need to use the exact Gagnon setup for this, you can use a simple phase detector). If you continue to apply the original detection setup to the modified experiment don't be surprised that you are getting nonsensical results. (GIGO rules)
Since you wasted so much simulating the wrong thing try simulating the right thing:

Feed the sin((k+k')z/2-\omega*t) to a phase detector and try to separate the phase (k+k')z/2. Do you think you can handle this?Finally, the correct statement is that :

GGT predicts light speed anisotropy and also predicted a phase shift between the two waveguides but the Gagnon experiment detected a much smaller than predicted phase shift thus disproving the notion of light speed anisotropy. Period.

 

[Aether]

You are so stuck in the original description of the Gagnon experiment that you cannot even begin to understand that two waveforms can be SUBTRACTED as well as being added, generating the term sin((k+k')z/2-\omega*t) INSTEAD of the term sin((k-k')z/2).

The balanced mixer does subtract the waveforms, so I'm not sure what you are talking about.

In the term sin((k+k')z/2-\omega*t) the phase (k+k')z/2 IS a linear function of v_z and is fully DETECTABLE (hint: you do not need to use the exact Gagnon setup for this, you can use a simple phase detector).

To do this I would start by multiplying the two waveguide outputs together, and then I would rectify (maybe) and low-pass filter the product waveform. Common-mode phase would still drop out though. Do you have something else in mind? I'll simulate the circuit if you will describe it in sufficient detail.

If you continue to apply the original detection setup to the modified experiment don't be surprised that you are getting nonsensical results. (GIGO rules)

You agree that the original detection setup yields null results with GGT, but want to explore alternate setups? That's fine, I'll simulate the alternate setups if we can define what they are.

Since you wasted so much simulating the wrong thing try simulating the right thing:

Feed the sin((k+k')z/2-\omega*t) to a phase detector and try to separate the phase (k+k')z/2. Do you think you can handle this?

See above. I would start by multiplying the two waveforms together, and then rectify (maybe) and low-pass filter the result.

Finally, the correct statement is that :

GGT predicts light speed anisotropy and also predicted a phase shift between the two waveguides but the Gagnon experiment detected a much smaller than predicted phase shift thus disproving the notion of light speed anisotropy. Period.

GGT doesn't predict a phase-shift between the two waveguides (e.g., a differential phase shift) that is dependent on v_z; it predicts a common-mode phase shift that is dependent on v_z and that is not measurable.

Anyway, this is what the simulations will decide.

 

[clj4]

The balanced mixer does subtract the waveforms, so I'm not sure what you are talking about.

To do this I would start by multiplying the two waveguide outputs together, and then I would rectify and low-pass filter the product waveform. Common-mode phase would still drop out though. Do you have something else in mind? I'll simulate the circuit if you will describe it in sufficient detail.

You agree that the original detection setup yields null results with GGT, but want to explore alternate setups? That's fine, I'll simulate the alternate setups if we can define what they are.

See above. I would start by multiplying the two waveforms together, and then rectify and low-pass filter the result.

GGT doesn't predict a phase-shift between the two waveguides (e.g., a differential phase shift) that is dependent on v_z; it predicts a common-mode phase shift that is dependent on v_z and that is not measurable.

Anyway, this is what the simulations will decide.

This is getting embarassing. Do you understand that the signal that needs to be analyzed sin((k+k')z/2-\omega*t) and NOT sin((k-k')z/2). When you subtract k' from k the term in v_z cancels out.

 

[Aether]

This is getting embarassing. Do you understand that the signal that needs to be analyzed sin((k+k')z/2-\omega*t) and NOT sin((k-k')z/2).

I only know of two ways to get at the common-mode phase, I already described one. The other is to multiply the sum of the two waveguide outputs by a third waveform from the same signal generator. That won't yield a differential signal that is dependent on v_z either. What is your suggestion?

When you subtract k' from k the term in v_z cancels out.

Not if you use Gagnon's original Eq. (7) it won't. That is why I balked at their paper from the very beginning. Only now that Eq. (7) has been corrected, then "When you subtract k' from k the term in v_z cancels out". I would be thrilled to find a way to distinguish between GGT and SR+Einstein Sync. by experiment, but know that's not possible.

 

[clj4]

I only know of two ways to get at the common-mode phase, I already described one. The other is to multiply the sum of the two waveguide outputs by a third waveform from the same signal generator.

You need to get off the "common mode" first.
Secondly, you need to use a phase detector in order to measure the variation of the phase (k+k')L/2 with time as I showed you in the original attachment. I am attaching it again.
You can use any oscilloscope from the list below:
http://www.home.agilent.com/USeng/nav/-536902447.0/pc.html
One simple way is to turn on "jitter analysis mode" and let the oscilloscope accumulate the waveform resultant from the subtraction of the two waves. The "smearing" due to the change in phase over time will be maximum if you let the system run 6 hours since v_z varies from 0 to V_max depending on the Earth orientation. The oscilloscope will calculate with an incredible precision the variation of the phase during this time interval. You don't need to design any type of equipment, you just need to pick the appropriate oscilloscope from the list.

That won't yield a differential signal that is dependent on v_z either. What is your suggestion?

I suggest that you read the attachment. You are dealing with a simple sine wave, all you need to do is to measure the variation in phase.

Not if you use Gagnon's original Eq. (7) it won't. That is why I balked at their paper from the very beginning.

No, this is not why you balked . You balked for a zillion of reasons, over hundreds of posts. Now you have nothing to balk about since the solution to the partial differential equation has been corrected.

Only now that Eq. (7) has been corrected, then "When you subtract k' from k the term in v_z cancels out".

This is not true but it is not germaine to the discussion. In BOTH the corrected and uncorrected form of the Gagnon paper you eventually get the same thing in terms of dependency on v_z, the solutions look the same in both cases :

k=(omega*v_z)c^2+sqrt...
k'=(omega*v_z)c^2+sqrt...

If you subtract the wave vectors you get no dependency of v_z, if you add them you get the dependency. Therefore you need to subtract the waveforms. Obviously this is a red herring in the style of your previous persistent diversions.

I would be thrilled to find a way to distinguish between GGT and SR+Einstein Sync. by experiment, but know that's not possible.

Try to be honest for a while? Drop your bias that leads to your making embarassing never ending defenses? Since you "know that's not possible" professing that "you would be thrilled..." doesn't ring true at all. Besides , you have quite a few experiments that prove that light speed is not anisotropic that you have to contend with. Gagnon is just one of 10. And I think the physics community, much to your despair will continue producing such experiments and your declaring them invalid will not lead anywhere.

 

[Aether]

You need to get off the "common mode" first.
Secondly, you need to use a phase detector in order to measure the variation of the phase (k+k')L/2 with time as I showed you in the original attachment. I am attaching it again.
You can use any oscilloscope from the list below:
http://www.home.agilent.com/USeng/nav/-536902447.0/pc.html
One simple way is to turn on "jitter analysis mode" and let the oscilloscope accumulate the waveform resultant from the subtraction of the two waves. The "smearing" due to the change in phase over time will be maximum if you let the system run 6 hours since v_z varies from 0 to V_max depending on the Earth orientation. The oscilloscope will calculate with an incredible precision the variation of the phase during this time interval. You don't need to design any type of equipment, you just need to pick the appropriate oscilloscope from the list.

The attached diagram is from p. 3 of the datasheet for http://cp.literature.agilent.com/litweb/pdf/5988-5235EN.pdf" oscilloscope. To do a jitter analysis of a waveform, you need to generate a reference clock signal. This is why there are two waveguides in the Gagnon experiment; one waveguide represents the "data" signal and the other represents the reference "clock" signal. If you want to use the internal clock from the oscilloscope, then we will have to transform the coordinates of that clock signal along with those of the waveguides.

I suggest that you read the attachment. You are dealing with a simple sine wave, all you need to do is to measure the variation in phase.

To do that we need to have a reference clock signal, and the coordinates of that signal vary with v_z in exactly the same proportion as the data signal. This is "common-mode" phase shift.

No, this is not why you balked . You balked for a zillion of reasons, over hundreds of posts. Now you have nothing to balk about since the solution to the partial differential equation has been corrected.

What I'm balking at now is your claim that GGT predicts a phase-shift dependent on v_z that could be detected in an experiment if it existed.

This is not true but it is not germaine to the discussion. In BOTH the corrected and uncorrected form of the Gagnon paper you eventually get the same thing in terms of dependency on v_z, the solutions look the same in both cases :

k=(omega*v_z)c^2+sqrt...
k'=(omega*v_z)c^2+sqrt...

The falsified equations have a dependency on v_x that doesn't exist in the corrected equations.

If you subtract the wave vectors you get no dependency of v_z, if you add them you get the dependency. Therefore you need to subtract the waveforms. Obviously this is a red herring in the style of your previous persistent diversions.

Try to be honest for a while? Drop your bias that leads to your making embarassing never ending defenses? Since you "know that's not possible" professing that "you would be thrilled..." doesn't ring true at all. Besides , you have quite a few experiments that prove that light speed is not anisotropic that you have to contend with. Gagnon is just one of 10. And I think the physics community, much to your despair will continue producing such experiments and your declaring them invalid will not lead anywhere.

Please try to focus on the issue at hand. I have already shown how to simulate the theoretical waveguide outputs from the Gagnon experiment in SPICE, and we can use these to test any detector design we can think of. Now we need to show that the phase-shift that you are referring to can actually be detected using some real-world circuit.

 

[clj4]

The attached diagram is from p. 3 of the datasheet for http://cp.literature.agilent.com/litweb/pdf/5988-5235EN.pdf" oscilloscope. To do a jitter analysis of a waveform, you need to generate a reference clock signal. This is why there are two waveguides in the Gagnon experiment; one waveguide represents the "data" signal and the other represents the reference "clock" signal. If you want to use the internal clock from the oscilloscope, then we will have to transform the coordinates of that clock signal along with those of the waveguides.

To do that we need to have a reference clock signal, and the coordinates of that signal vary with v_z in exactly the same proportion as the data signal. This is "common-mode" phase shift.

This is just not true. Long term jitter is determined by recording over time ONE signal, which is the signal sin((k+k')L-omega*t). You do not need a second reference signal for long term jitter measurements, you simply compare the ONE signal against ITSELF over time (6 hrs as I told you).
Even if you insisted in feeding a reference signal , you could do this with sin(omega*t). Don't give me the story that "(z,t) need to be transformed in Earth frame" , they have already been transformed at the beginning of the Gagnon paper. All variables are calculated in Earth frame.

What I'm balking at now is your claim that GGT predicts a phase-shift dependent on v_z that could be detected in an experiment if it existed.

Yes, you have been trying different "balks" for hundreds of posts. Your latest ploy is the fact that you "don't know" how to measure the time varying phase of a sine signal.

The falsified equations have a dependency on v_x that doesn't exist in the corrected equations.

This is why I corrected the equations :-)

Please try to focus on the issue at hand. I have already shown how to simulate the theoretical waveguide outputs from the Gagnon experiment in SPICE, and we can use these to test any detector design we can think of. Now we need to show that the phase-shift that you are referring to can actually be detected using some real-world circuit.

Ok, GGT predicts a phase shift proportional to v_z.
Your last line of this emabarassing defense is that "it can't be measured" or "I don't know how to measure it". I gave you a suggestion, if you don't understand it (looks more like you are wishing it away) , it is your problem.

One more thing : please give up on the " z and t need to be transformed in the Earth frame, otherwise we cannot execute the measurement". They have already been transformed in the Earth frame from the beginning of the paper. All variables are computed in the Earth frame.

 

[Aether]

This is just not true. Long term jitter is determined by recording over time ONE signal, which is the signal sin((k+k')L-omega*t). You do not need a second reference signal for long term jitter measurements, you simply compare the ONE signal against ITSELF over time (6 hrs as I told you).
Even if you insisted in feeding a reference signal , you could do this with sin(omega*t). Don't give me the story that "(z,t) need to be transformed in Earth frame" , they have already been transformed at the beginning of the Gagnon paper. All variables are calculated in Earth frame.

To sample the "one signal" that you are talking about, you must provide a separate "clock" signal to trigger the sampling events. Each sample in the recorded data stream will have an implicit time coordinate that is determined by this clock signal. We can't use sin(omega*t) for this, but we could use sin(k*z-omega*t).

Yes, you have been trying different "balks" for hundreds of posts. Your latest ploy is the fact that you "don't know" how to measure the time varying phase of a sine signal.

Most if not all of my different balks will be shown to be valid ones once you finally understand that it is not possible to measure what you're assuming that you can measure.

This is why I corrected the equations :-)

You and gregory did do a good job with that.

Ok, GGT predicts a phase shift proportional to v_z.
Your last line of this emabarassing defense is that "it can't be measured" or "I don't know how to measure it". I gave you a suggestion, if you don't understand it (looks more like you are wishing it away) , it is your problem.

Your suggestion to use an oscilloscope wasn't helpful. Your suggestion for a reference clock signal modeled as sin(omega*t) is along the lines of what is needed if we adjust it to read sin(k*z-omega*t).

One more thing : please give up on the " z and t need to be transformed in the Earth frame, otherwise we cannot execute the measurement". They have already been transformed in the Earth frame from the beginning of the paper. All variables are computed in the Earth frame.

Ok. As long as z and t are treated the same with both the data and clock signals, then it is enough for now if we transform the k's properly.