Consistency of the speed of light

[Hans de Vries]

Lorentz versus Mansouri-Sexl

And here's the program to test Lorentz transform versus Mansouri-Sexl:

// Persistence Of Vision raytracer version 3.5 file.

#include "colors.inc"
//===================================================================================================
//
//                  LORENTZ VERSUS MANSOURI-SEXL SIMULATOR
//
//===================================================================================================
//
//
//    A laser gives a lightpulse downwards vertically in the rest frame. The laser can be made to 
//    co-move width the moving frame so that it will stay at the same position in the moving frame.
//
//    --------------------------------------------------------------------------------------------
// 
//    The moving frame is plotted in a two dimensional X,Y loop.
//
//    The reversed transforms are calculated back into the rest frame, from there a traceback is
//    made to the opening of the laser. If we are inside the laser radius and inside the pulse time
//    the a pixel is plotted with an intensity calculated from the phase of the laser at the time
//    of the emmision.  
//
//    For each X,Y location tested we test both in front and behind the mirro since each location
//    can have light directly from the laser or indirectly from the mirror. Values found behind the
//    mirror are reflected back and mixed with the direct light. 
//
//    --------------------------------------------------------------------------------------------
//
//    The Plot pulse macro has as inputs:                
//
//    1)  T:  the time in the moving frame. 
//    2)  V:  the speed of the moving frame
//    3)  The transformation, 1=Lorentz, 2=Mansouri-Sexl.
//
//    There are two calls of this macro at the end of the program, one for Lorentz and the other
//    for Mansouri-Sexl 
//
//    --------------------------------------------------------------------------------------------
//
//    The program uses spheres to draw pixels, When the X_delta and Y_delta values are made lower
//    it will draw less but bigger speres and visa versa.
//
//===================================================================================================
//===================================================================================================
//                  PLOT AREA DEFINITION
//===================================================================================================

#declare  X_min        =  -2.00;                  // leftmost  X position
#declare  X_max        =   2.00;                  // rightmost X position
#declare  X_delta      =   0.01;                  // step size

#declare  Y_min        =  -1.00;                  // Bottum    Y position  
#declare  Y_max        =   1.00;                  // Top       Y position
#declare  Y_delta      =   0.01;                  // step size

#declare  Y_mirror     =   Y_min;                 // Y location of the mirror   
#declare  C            =   1.00;                  // normalized speed of light
cylinder  {<X_min-0.1, Y_min-0.05, -0.1>,< X_max+0.1, Y_min-0.05, +0.1 >, 0.05 pigment {OldGold} }
cylinder  {<X_min-0.1, Y_max+0.05, -0.1>,< X_max+0.1, Y_max+0.05, +0.1 >, 0.05 pigment {OldGold} }
//===================================================================================================
//
//                  PLOT LASER PULSE MACRO
//
//===================================================================================================

#declare  Lorentz_Transform      =   1;
#declare  MansouriSexl_Transform =   2;#macro plot_laser_pulse ( T, V, Transform_Method ) //===================================================================================================
//                  LASER DEFINITIONS
//===================================================================================================

#declare  laser_radius =   0.20;
#declare  pulse_start  =  -2.50;
#declare  pulse_end    =   2.00;
#declare  Frequency    =   (2*3.141592) * 5;

#declare  Xi_laser     =  -1.00;                  // Initial Position of laser
#declare  Vx_laser     =   V;                     // Horizontal speed of laser

#declare  gamma        =   1/sqrt(1-V*V/(C*C)); 
union {//===================================================================================================
//                  X LOOP
//===================================================================================================

  #declare      X = X_min;
    #while     (X < X_max)//===================================================================================================
//                  Y LOOP
//===================================================================================================

     #declare   Y = Y_min;    // two times for mirroring  
      #while   (Y < Y_max) //===================================================================================================
//                  FOWARD AND REFLECTED PULSE LOOP
//===================================================================================================

     #declare  Forward_Pulse_Visible    = 0;
     #declare  Reflected_Pulse_Visible  = 0;
          

     #declare   Mirror = 0;    // loop exectuted two times for mirroring  
      #while   (Mirror < 2)

       

     #if (Transform_Method = Lorentz_Transform)
     
     // -------------------------------------------------------------------------------
     //             Lorentz Transform                                      
     // -------------------------------------------------------------------------------
     //
     //         T   = gamma*( T' - V*X'/(C*C) );
     //         X   = gamma*( X' - V*T');
     //         Y   = Y;
     //
     // ----------- Reverse Lorentz Transform ------------------------------------------
     //

     #declare   T1  = gamma*( T + V*X/(C*C) );
     #declare   X1  = gamma*( X + V*T);

     #end     #if (Transform_Method = MansouriSexl_Transform)

     // -------------------------------------------------------------------------------
     //             Mansouri Sexl Transform                                            
     // -------------------------------------------------------------------------------
     //
     //         T   = T'/gamma;
     //         X   = gamma*( X' - V*T');
     //         Y   = Y';
     //
     // ----------- Reverse Mansouri Sexl Transform -----------------------------------
     //

     #declare   T1  = T*gamma;
     #declare   X1  = X/gamma  + V*T/gamma;

     #end
     // -------------------------------------------------------------------------------
     //             Mirror Y
     // -------------------------------------------------------------------------------
     //
     
     #declare  Y1 =   Y;
     #if    (  Mirror = 1 )
     #declare  Y1 =   Y_mirror*2 - Y1;  // mirror if photon has passed mirror
     #end         
     

     // -------------------------------------------------------------------------------
     //             Traceback to laser opening
     // -------------------------------------------------------------------------------
     //

     #declare   T_1  = T1 - (Y_max-Y1)/C;
     
     #declare   X_1  = X1 - Xi_laser - Vx_laser * T_1;       

     
     // -------------------------------------------------------------------------------
     //             Test and Calculate Pixel_Intensity
     // -------------------------------------------------------------------------------
     //

     #if         ( T_1       >= pulse_start )
      #if        ( T_1       <  pulse_end   )
       #if       ( abs(X_1)  <= laser_radius )

        #if      ( Mirror  =  0)
         #declare  Forward_Pulse_Visible   = 1;
         #declare  Forward_Phase           = sin(Frequency*T_1); // Phase of light emmited at T_1
        #end

        #if      ( Mirror  =  1)
         #declare  Reflected_Pulse_Visible = 1;
         #declare  Reflected_Phase         = sin(Frequency*T_1); // Phase of light emmited at T_1 
        #end

        #end
      #end
     #end

//===================================================================================================
//                  END MIRROR LOOP
//===================================================================================================

    #declare  Mirror = Mirror+1;
   #end

     // -------------------------------------------------------------------------------
     //             Test and plot
     // -------------------------------------------------------------------------------
     //
     //

    #declare Pixel_Intensity = 0; 

    #if    ( Forward_Pulse_Visible   = 1)
    #declare Pixel_Intensity = 1/2 + Forward_Phase/5; 
    #end
    
    #if    ( Reflected_Pulse_Visible = 1)
    #declare Pixel_Intensity = 1/2 + Reflected_Phase/5; 
    #end

    #if    ( Forward_Pulse_Visible + Reflected_Pulse_Visible = 2)
    #declare Pixel_Intensity = 1/2 + Forward_Phase/5 + Reflected_Phase/5; 
    #end

    
    #if      ( abs(Pixel_Intensity) > 0)
    #object   {sphere  { <0,0,0>,X_delta pigment { rgb (Pixel_Intensity) } translate <X,Y,0> } }
    #end//===================================================================================================
//                  END Y LOOP
//===================================================================================================
         
    #declare  Y = Y + Y_delta;
   #end

//===================================================================================================
//                  END X LOOP
//===================================================================================================

  #declare    X = X + X_delta;
 #end

//===================================================================================================
//                  END PLOT LASER PULSE MACRO
//===================================================================================================

}
#end//===================================================================================================
//                  CALL LASER PULSE PLOT MACRO
//===================================================================================================
  object {plot_laser_pulse (1.00, -0.50, 1)   translate <0.00, 0.00, 0.00> }    // Lorentz Transform
//object {plot_laser_pulse (1.00, -0.50, 2)   translate <0.00, 0.00, 0.00> }    // Mansouri Sexl Transform//===================================================================================================
//                  Light source and Camera definition
//===================================================================================================

light_source { < 0,    0,-40.0> color red 2 green 2 blue 2 }                                     camera {
    
     location <  0,       0,     -10  >     // 
     sky      <  0.00,    0.00,  -1.00>
     look_at  <  0.00,    0.00,  -0.25>
     angle 26

}

Writen in the 3D raytracing Povray language which is simple
to follow and gives a very powerful visualization environment.

http://www.povray.org/

You can download and install the program for free here.

http://www.povray.org/download/

Then just copy and paste my program and click the RUN button.

Regards, and have fun, Hans

 

[Hans de Vries]

Program to test theLorentz transform versus Mansouri-Sexl

Here is the result for the Lorentz transform:

(A laser gives a light pulse downwards vertically in the rest frame.
There's a mirror at the bottom which reflects the light back.)Regards, Hans

 

[Hans de Vries]

Program to test theLorentz transform versus Mansouri-Sexl

And here is the result for the Mansouri-Sexl transform.The Lorentz transform is correct because of non-simultaneity. The light front
has traveled further at the left side of the image as compared to the right side.

The wave front has rotated as a result.

One day you'll appreciate non-simultaneity and Special Relativity as effects
perfectly predictable from classical physics and the classical wave function. Regards, Hans.

 

[gregory_]

The Lorentz transform is correct because of non-simultaneity. The light front has traveled further at the left side of the image as compared to the right side.

I feel you are misunderstanding something here. Those pictures are interesting, but prove neither theory correct. They just show the same situation with different "slices" through the events because of the differring simultaneity convention. The events themselves are unchanged.

One day you'll appreciate non-simultaneity and Special Relativity as effects perfectly predictable from classical physics and the classical wave function.

I realize you are speaking to Aether, but maybe I can help here.

Let's be frank: There are many compelling reasons to choose special relativity over the "generalized Galilean transforms". SR has a much stonger predictive power leading to a less ad hoc theory. Having the physics maintain the same form in all inertial frames is an incredible symmetry, so much so that it often allows us to solve problems in our head that we'd need to spend hours on if forced to do in just one particular frame. These are all good reasons, but "incorrectness of predictions by generalized Galilean transforms" can not be added to this list as a reason to disregard them.

If this is not obvious to you, let me explain why. (Because I "choose" to use SR over GGT, this may sound like a harsh view of them (sorry Aether), but may make it easier for mainstream followers such as Hans and myself understand.) Here goes:

In SR it is often convenient to do the calculations for an experiment in a particular frame (sometimes even changing frames several times). But we do realize that if we forced ourselves to do the calculations in just one particular frame that we'd still get the same predictions for the experiment, correct?

If two theories have exactly the same physical laws in one frame and are individually mathematically self consistent, then their predictions for experiments will always match. In this case the matching frame is just choosing some arbitrary frame in SR and labelling it the "aether frame". In this frame both theories have the same physical laws and therefore give the same predictions for all experiments.

What do the laws of physics look like in other frames? Honestly, we could choose any coordinate system (inertial or not) as long as we transformed the coordinates back into the "standard frame", did the calculations, then transformed back. Or, we could try to transform the equations into the coordinate system itself. If we use the lorentz transformations, we get back the same form (which is why we use them). Use another transform and we get something horrid looking, but we must still realize that it is correct (all predictions will match experiment still... mathematically it is still equivalent to SR).

The generalized Galilean transformations "mimic" SR in the sense that we still restrict ourselves to inertial frames (for this discussion I will define an inertial coordinate system as one in which a freely moving body moves at a constant velocity). It turns out that being an inertial coordinate system is fairly restrictive and the only freedoms we have are: origin, axis placement, and simultaneity convention.

If you were not expecting that last one, even after the previous explanation, I suggest you sit down and fiddle with it for awhile until you realize why this is. Changing the simultaneity convention may change the velocity of objects in that coordinate system, but the velocity of a freely moving object is still constant.

In summary, yes there are compelling reasons to choose Lorentz transformations over generalized galilean transformations. "Unfortunately" experimental proof is not one of them.

I hope that was helpful.

===========================
So, clj4 and Hans, please answer the following:

Question #1] Do you agree that one-way velocity cannot be defined independent of a coordinate system?

if not
Question #2] In my explanation of why experiments cannot distinguish between "Generalized Galilean transformations / coordinate systems" and "Lorentz Transformations / Special Relativity's" definition of the one way speed of light, which parts do you disagree with and why?

Thank you.

 

[Aether]

Because I "choose" to use SR over GGT, this may sound like a harsh view of them (sorry Aether), but may make it easier for mainstream followers such as Hans and myself understand.)

Choose any coordinate system you like, just don't tell me that mine is ruled out by experiment.

 

[Aether]

And here's the program to test Lorentz transform versus Mansouri-Sexl:

Writen in the 3D raytracing Povray language which is simple
to follow and gives a very powerful visualization environment.

http://www.povray.org/

You can download and install the program for free here.

http://www.povray.org/download/

Then just copy and paste my program and click the RUN button.

Regards, and have fun, Hans

Thank-you Hans, this is great! However, you don't seem to have defined an experiment yet. You'll need to at least place two clocks along the x-axis with one corresponding to the oscillator that is generating the waves, and the other corresponding to a wave phase detector. This second clock/oscillator is always going to be synchronized in such a way that the experiment can't distinguish between our choice of coordinate system. If you leave this second clock/oscillator out, you haven't got a real experiment yet. I want to see you calculate the phase difference (at one point along the x-axis) between this wave and a reference clock/oscillator of the same frequency, or at least show both the time and phase of the wave at some fixed point along the x-axis.

 

[Hans de Vries]

Those pictures are interesting, but prove neither theory correct. They just show the same situation with different "slices" through the events because of the differring simultaneity convention. The events themselves are unchanged.

That's exactly the point. There is only one reality! All reference frames
are just slices through the one and only reality. The way you slice is
determined by the way you define simultaneity.

One can not arbitrarily choose this however. Nature has it's preferred
way to define simultaneity. Happily enough in such a way that everything
looks and feels the same independent of the reference frame.

(Life on earth, with its intricate balances, doesn't end when the Milkyway
has rotated 180 degrees and we go in the other direction)

Let's be frank: There are many compelling reasons to choose special relativity over the "generalized Galilean transforms". SR has a much stonger predictive power leading to a less ad hoc theory. Having the physics maintain the same form in all inertial frames is an incredible symmetry, so much so that it often allows us to solve problems in our head that we'd need to spend hours on if forced to do in just one particular frame. These are all good reasons, but "incorrectness of predictions by generalized Galilean transforms" can not be added to this list as a reason to disregard them.

...

In summary, yes there are compelling reasons to choose Lorentz transformations over generalized galilean transformations. "Unfortunately" experimental proof is not one of them.

As long as nature manages to avoid us from detecting a preferred
background, which it does with an incredible precision, there is
a good reason to prefer Lorentz Transforms. So it's more the absence
of proof which makes other transformations less interesting.

If someone devices an apparatus which reliably gives us a speed relative
to a background, only then it becomes necessary to modify the Lorentz
transformations by an ever so small amount reflecting the non-isotropic
effects which one needs for such a detection.

So, clj4 and Hans, please answer the following:

Question #1] Do you agree that one-way velocity cannot be defined independent of a coordinate system?

You pose this question in such a way that one must agree always
No coordinate system = no speed.

if not
Question #2] In my explanation of why experiments cannot distinguish between "Generalized Galilean transformations / coordinate systems" and "Lorentz Transformations / Special Relativity's" definition of the one way speed of light, which parts do you disagree with and why?
Thank you.

Mathematically one is free to use any arbitrary non-isotropic transfor-
mation, but for it to make sense to use such a transformation you want
to see some physical effect based on the non-isotropy. Like a meter
which reliably gives you the speed relative to the background.

No meter ==> Stick to Lorentz.
Got a meter ==> Tiny modification to Lorentz if based on tiny effect.

In the latter case off course you've found the background, which is then
the principle frame of interest.Regards, Hans

 

[Aether]

That's exactly the point. There is only one reality! All reference frames are just slices through the one and only reality. The way you slice is determined by the way you define simultaneity.

OK.

One can not arbitrarily choose this however. Nature has it's preferred way to define simultaneity.

Isn't it really your view that nature does not have any locally preferred way to define simultaneity (that we know of), hence "relativity of simultaneity"?

As long as nature manages to avoid us from detecting a preferred
background, which it does with an incredible precision, there is
a good reason to prefer Lorentz Transforms. So it's more the absence
of proof which makes other transformations less interesting.

OK, less interesting to you, fine.

If someone devices an apparatus which reliably gives us a speed relative to a background, only then it becomes necessary to modify the Lorentz transformations by an ever so small amount reflecting the non-isotropic effects which one needs for such a detection.

You could always choose to ignore a locally preferred frame (even if you had a device to detect one) for many purposes, and still use the Lorentz transforms as they are.

Mathematically one is free to use any arbitrary non-isotropic transformation...

When someone (falsely) claims that the Mansouri-Sexl transforms are ruled out by experiment they are seeking (wrongly) to deny this freedom.

...but for it to make sense to use such a transformation you want to see some physical effect based on the non-isotropy. Like a meter which reliably gives you the speed relative to the background.

I don't disagree, but that's a different issue entirely. If we could all agree on these last two statements, then we could end this discussion until such time as I (or someone else) predict(s) some physical effect like you're talking about. How can I come in here and predict such a physical (e.g., measurable) effect if we don't agree on these last two statements? Any subsequent (false) claim(s) that one-way speeds are measurable in a coordinate independent way contradicts the first of these last two statements, and would start this discussion all over again. What exactly is it that you are disagreeing with me about then?

 

[my_wan]

https://www.physicsforums.com/showpost.php?p=941417&postcount=205"

I think you refuse to accept that nature doesn't provide for observing such a measurement because it is all you have.

You have this backwards. It is clj4 who has refused (so far) to accept this. Anyone else?

Retraction; blame it on tired eyes with a long post. It has forced me to review in much more depth than I wanted to.

clj4 was correct. The bicycle wheel clitches it. There are several litmus test I use to judge a set of ideas. They review as follows.

This postulate has so far proven to be consistent with experiment, but so too has "...an ether theory taking into account time dilation and length contraction but maintaining absolute simultaneity...". No experiment has ever been able to distinguish between these two points of view, and if one ever does it could only favor the ether view.

I don't have any problem with an ether theory in general that is empirically equivalent to SR. They aren't even that difficult to produce. Absolute simultaneity? No because that is not empirically equivalent. Upon review LET fails also.

any claim that the constancy of the one-way speed of light is an empirically determined fact is false.

My initial reaction was if a particular ether theory at some level stated this in an unobservable way, so what simply divorce from it in deriving the formulism. Upon review it can't be an unobservable.

Aether is used as shorthand for both a rarified gas (which is not how I am using it), and a locally preferred frame (which is how I am using it).

Locally preferred frame? That was an automatic failure fairly early in your post. Maybe if it referred to a very limited case it was worth overlooking for the moment. Upon review your seem to be attaching that to a redefinition of simultainelity and the one way light speed. This destroys the empirical equivalence to SR.

I predicted that the paper of Gagnon et al. wouldn't hold up to careful scrutiny, and I further predict that anyone who doesn't heed this lesson and produces a work in contradiction to the principles that we are discussing will fail.

If it were in fact empirically equivalent as you claimed it couldn't fail. You've also just predicted that SR will fail. By any scientific definition these aren't even predictions, they are opinions. I can tune in Art Bell for all those I want.

The dead horse statement means to to refuse to believe the horse, i.e. idea, theory, etc. is dead so you keep trying to ride it.

My concerns about your bias stands. It appears to me as if you loaded a set of preconcieved notions onto an ill defined ether fitted some data and ran with it. I'm not asking you to give up. Perhaps there's something to the way it makes so many concepts fit so well. However you do need to review your biases and look for ways they may have been imposed improperly. If you claim your not biased your either superhuman or deluded.

and if one ever does it could only favor the ether view.

Pure unadulterated bias.

 

[Aether]

I don't have any problem with an ether theory in general that is empirically equivalent to SR. They aren't even that difficult to produce. Absolute simultaneity? No because that is not empirically equivalent. Upon review LET fails also.

My initial reaction was if a particular ether theory at some level stated this in an unobservable way, so what simply divorce from it in deriving the formulism. Upon review it can't be an unobservable.

Locally preferred frame? That was an automatic failure fairly early in your post. Maybe if it referred to a very limited case it was worth overlooking for the moment. Upon review your seem to be attaching that to a redefinition of simultainelity and the one way light speed. This destroys the empirical equivalence to SR.

The issue of the coordinate-system dependence of speed measurements is distinct from local Lorentz symmetry violations. We are only talking about coordinate-system dependence of speed measurements at the moment (e.g., assuming perfect Lorentz symmetry).

If it were in fact empirically equivalent as you claimed it couldn't fail. You've also just predicted that SR will fail. By any scientific definition these aren't even predictions, they are opinions. I can tune in Art Bell for all those I want.

The GGT/RMS transforms are empirically equivalent to SR, but they weren't properly applied by Gagnon et al.. When properly applied (and assuming perfect Lorentz symmetry), they always predict the same outcome for experiments as SR.

The dead horse statement means to to refuse to believe the horse, i.e. idea, theory, etc. is dead so you keep trying to ride it.

My concerns about your bias stands. It appears to me as if you loaded a set of preconcieved notions onto an ill defined ether fitted some data and ran with it. I'm not asking you to give up. Perhaps there's something to the way it makes so many concepts fit so well. However you do need to review your biases and look for ways they may have been imposed improperly. If you claim your not biased your either superhuman or deluded.

Please see post #94 for a reference to Y.Z. Zhang, Special Relativity and its Experimental Foundations, World Scientific (1997); http://www.worldscibooks.com/physics/3180.html. Also, please take a look at the three Mansouri-Sexl papers cited elsewhere in this thread. These are the references that I am relying on. Please let me know if you have any problem with them.

Pure unadulterated bias.

Please see post #114. This discussion has been on-going for more than six months, and I have modified my views as appropriate when others have made good points.

 

[clj4]

The GGT/RMS transforms ... but they weren't properly applied by Gagnon et al..

This is your OPINION. You have to prove it , so far you haven't done so. This is the work that you promised to do a few posts ago (post 179). Correct?

 

[Aether]

This is your OPINION. You have to prove it , so far you haven't done so. This is the work that you promised to do a few posts ago. Correct?

I'm still waiting for you to respond to post #187. It appears that $$\omega$$ may have a completely different meaning in Eq. (7) as it does in Eq. (6). In Eq. (6) I interpret it to correspond to the common driving frequency $$\omega=\omega_1+\delta$$, but for $$v=0$$ Eq. (7) reduces to the standard wave number transform equation where $$\omega$$ is the cutoff angular frequency for a waveguide having a null wavenumber.

 

[clj4]

I'm still waiting for you to respond to post #187. It appears that $$\omega$$ may have a completely different meaning in Eq. (7) as it does in Eq. (6). In Eq. (6) I interpret it to correspond to the common driving frequency $$\omega=\omega_1+\delta$$, but for $$v=0$$ Eq. (7) reduces to the standard wave number transform equation where $$\omega$$ is the cutoff angular frequency for a waveguide having a null wavenumber.

I didn't see it but I thought that I made it clear that I will not accept any "made up" formulas. So you will need to rederive things from base principles, i.e. by solving eq (5). I am tired of finding the errors in your specious arguments.

 

[clj4]

It is a clear error on whose part? The boundary conditions on the waveguide "require the tangential component of the electric field in the laboratory frame to vanish at the waveguide walls", and this identifies

$$\omega_c=\omega_{10}=\frac{\pi c_0}{a}=\frac{2\pi c_0}{\lambda}$$,​

so:

$$\frac{\omega_c}{c_0}= \frac{2\pi}{\lambda}=k^0$$,​

which corresponds to the timelike component of a wave 4-vector $$k^\mu$$ and that transforms like $$t$$, right?

Wrong. For the simple reason that $$omega$$ has dimensions of 1/t.

 

[Aether]

Wrong. For the simple reason that $$omega$$ has dimensions of 1/t.

Here's Eq. (7):

$$k_g=-\frac{\omega}{c}\frac{v_z}{c}+\frac{1}{c}[\omega^2(1-\frac{v_x^2}{c^2})-\omega_c^2(1-\frac{v_x^2}{c^2}-\frac{v_z^2}{c^2})]^{1/2}$$.​

I can rewrite it like this:

$$k_g=-(\frac{\omega}{c})\frac{v_z}{c}+[(\frac{\omega}{c})^2(1-\frac{v_x^2}{c^2})-(\frac{\omega_c}{c})^2(1-\frac{v_x^2}{c^2}-\frac{v_z^2}{c^2})]^{1/2}$$​

Now, look at the wave 4-vector: http://teachers.web.cern.ch/teachers/archiv/HST2002/Bubblech/mbitu/wave_4.htm.

 

[clj4]

Here's Eq. (7):

$$k_g=-\frac{\omega}{c}\frac{v_z}{c}+\frac{1}{c}[\omega^2(1-\frac{v_x^2}{c^2})-\omega_c^2(1-\frac{v_x^2}{c^2}-\frac{v_z^2}{c^2})]^{1/2}$$.​

I can rewrite it like this:

$$k_g=-(\frac{\omega}{c})\frac{v_z}{c}+[(\frac{\omega}{c})^2(1-\frac{v_x^2}{c^2})-(\frac{\omega_c}{c})^2(1-\frac{v_x^2}{c^2}-\frac{v_z^2}{c^2})]^{1/2}$$​

Now, look at the wave 4-vector: http://teachers.web.cern.ch/teachers/archiv/HST2002/Bubblech/mbitu/wave_4.htm.

Great, look at formula (28), shows pretty clearly the rules for transforming $$\omega$$.
Look, if you want to refute this paper then you would need to do it as if you wrote a refutation to Physical Review A. You cannot grasp at straws, you must write a self consitent counter. I have given you a lot of help, I am quite interested in the result but it needs to be derived in a rigurous manner.

 

[gregory_]

clj4, you have not answered my two questions.
Please reread this post if necessary:

https://www.physicsforums.com/showpost.php?p=942326&postcount=214

Hans has already responded to my questions and agrees with the mathematical results of the transforms (and strongly agrees that there are good reasons to abandon GGT even if experimental disproof is not one of them). I would still be interested to hear your response as well.

Until we have agreed on such basic concepts, delving into the details of other papers can not be fruitful.

 

[clj4]

clj4, you have not answered my two questions.
Please reread this post if necessary:

https://www.physicsforums.com/showpost.php?p=942326&postcount=214

Hans has already responded to my questions and agrees with the mathematical results of the transforms (and strongly agrees that there are good reasons to abandon GGT even if experimental disproof is not one of them). I would still be interested to hear your response as well.

Until we have agreed on such basic concepts, delving into the details of other papers can not be fruitful.

This thread has been opened between me and "aether" in order to use LateEx to finish some calculations started on a different website. If you are willing to help "aether" in his calculations, you are welcome. Otherwise, your posts will not be read.

 

[gregory_]

I have shown why the paper is wrong.
I have asked very simple questions of you. This is not an unreasonable request.


Please read my post:
https://www.physicsforums.com/showpost.php?p=942326&postcount=214
and answer these questions:

Question #1] Do you agree that one-way velocity cannot be defined independent of a coordinate system?

Question #2] In my explanation of why experiments cannot distinguish between "Generalized Galilean transformations / coordinate systems" and "Lorentz Transformations / Special Relativity's" definition of the one way speed of light, which parts do you disagree with and why?

So, clj4, please stop avoiding them and answer the questions.
The other posters debating on this subject have already been nice enough to answer.
Thank you.

 

[clj4]

I have shown why the paper is wrong.
I have asked very simple questions of you. This is not an unreasonable request.


Please read my post:
https://www.physicsforums.com/showpost.php?p=942326&postcount=214
and answer these questions:

Question #1] Do you agree that one-way velocity cannot be defined independent of a coordinate system?

Question #2] In my explanation of why experiments cannot distinguish between "Generalized Galilean transformations / coordinate systems" and "Lorentz Transformations / Special Relativity's" definition of the one way speed of light, which parts do you disagree with and why?

So, clj4, please stop avoiding them and answer the questions.
The other posters debating on this subject have already been nice enough to answer.
Thank you.

You haven't shown one thing. Slogans don't prove things, calculations do.
If you want to refute the Gagnon paper, then you need to do the calculations.

 

[clj4]

I have shown why the paper is wrong.
I have asked very simple questions of you. This is not an unreasonable request.


Please read my post:
https://www.physicsforums.com/showpost.php?p=942326&postcount=214
and answer these questions:

Question #1] Do you agree that one-way velocity cannot be defined independent of a coordinate system?

Question #2] In my explanation of why experiments cannot distinguish between "Generalized Galilean transformations / coordinate systems" and "Lorentz Transformations / Special Relativity's" definition of the one way speed of light, which parts do you disagree with and why?

So, clj4, please stop avoiding them and answer the questions.
The other posters debating on this subject have already been nice enough to answer.
Thank you.

You haven't shown one thing. Slogans and declarations don't prove things, calculations do.
If you want to refute the Gagnon paper, then you need to do the calculations or find yourself another thread. Now, if you's excuse us, "Aether" , Hans and myself have work to do. With math and programs, not with empty slogans.

 

[gregory_]

You cannot dismiss it that easily.

BY DEFINITION special relativity and theories invoking GGT agree on the physical laws in one inertial frame. (Do you deny this?) Thus they predict the same results for all experiments BY DEFINITION.

My questions are quite reasonable and I wish you would just answer them (as they are not complicated questions).

Question #1] Do you agree that one-way velocity cannot be defined independent of a coordinate system?

Question #2] In my explanation of why experiments cannot distinguish between "Generalized Galilean transformations / coordinate systems" and "Lorentz Transformations / Special Relativity's" definition of the one way speed of light, which parts do you disagree with and why?

So, clj4, please stop avoiding them and answer the questions.
The other posters debating on this subject have already been nice enough to answer.
Thank you.

 

[clj4]

You cannot dismiss it that easily.

BY DEFINITION special relativity and theories invoking GGT agree on the physical laws in one inertial frame. (Do you deny this?) Thus they predict the same results for all experiments BY DEFINITION.

Well, looks like the Gagnon experiment flies in the face your statement above. So, please spare us the slogans, start explaining which equation in the Gagnon paper is wrong and why, or get off this thread.

 

[gregory_]

Are you denying that by definition special relativity and theories invoking GGT agree on the physical laws in one inertial frame?


My questions are quite reasonable and I wish you would just answer them (as they are not complicated questions).

Question #1] Do you agree that one-way velocity cannot be defined independent of a coordinate system?

Question #2] In my explanation of why experiments cannot distinguish between "Generalized Galilean transformations / coordinate systems" and "Lorentz Transformations / Special Relativity's" definition of the one way speed of light, which parts do you disagree with and why?

So, clj4, please stop avoiding them and answer the questions.
The other posters debating on this subject have already been nice enough to answer.
Thank you.

 

[clj4]

Are you denying that by definition special relativity and theories invoking GGT agree on the physical laws in one inertial frame?

Sure, I'll answer in excruciating detail after you explain in mathematical terms where is the Gagnon paper wrong (while you are at it, maybe you show us how the editors of Physical Review also missed the "errors" in the Krishner paper on the same subject - one way light speed measurement).
Once you understand these papers, perhaps you'll understand how the Mansouri-Sexl parametrization works so there might not be any need for me to answer any questions. In reading and understanding the papers you will be getting the answers to your slogans (they are slogans because for the time being you don't understand what you are saying).

 

[gregory_]

Sure, I'll answer in excruciating detail after you explain in mathematical terms where is the Gagnon paper wrong

Okay. But I expect you to keep your word.

Gagnon himself was an author of a later publication where he retracted and stated:
"A modified Lorentz theory (MLT) based on the generalized Galilean transformation has recently received attention. ... Several typical experiments are analyzed on this basis. The results show that emperical equivalence between MLT and special relativity is still maintained to second order terms."
Foundations of Physics Letters, v 1, Dec 1988, p 353-72


Now read https://www.physicsforums.com/showthread.php?p=943637#post943637" and answer my questions here:

Question #1] Are you denying that by definition special relativity and theories invoking GGT agree on the physical laws in one inertial frame?

Question #2] Do you agree that one-way velocity cannot be defined independent of a coordinate system?

Question #3] In my explanation of why experiments cannot distinguish between "Generalized Galilean transformations / coordinate systems" and "Lorentz Transformations / Special Relativity's" definition of the one way speed of light, which parts do you disagree with and why?

 

[clj4]

Okay. But I expect you to keep your word.

Gagnon himself was an author of a later publication where he retracted and stated:
"A modified Lorentz theory (MLT) based on the generalized Galilean transformation has recently received attention. ... Several typical experiments are analyzed on this basis. The results show that emperical equivalence between MLT and special relativity is still maintained to second order terms."
Foundations of Physics Letters, v 1, Dec 1988, p 353-72


Now read https://www.physicsforums.com/showthread.php?p=943637#post943637" and answer my questions here:

Question #1] Are you denying that by definition special relativity and theories invoking GGT agree on the physical laws in one inertial frame?

Question #2] Do you agree that one-way velocity cannot be defined independent of a coordinate system?

Question #3] In my explanation of why experiments cannot distinguish between "Generalized Galilean transformations / coordinate systems" and "Lorentz Transformations / Special Relativity's" definition of the one way speed of light, which parts do you disagree with and why?

Doesn't look like a retraction, he spends 20 pages to retract? Amazing. Why didn't you come straight out to say that you know of a retraction? Why all the game-playing? What does he say in the rest of the paper? Can u produce the full paper, not some selective quoting? Put it up on a website for a few hours so we can download it and see the full paper.

Did Kirshner retract as well? Now that we know about your surprise witnesses , let's have them all out at the same time.

 

[gregory_]

Put it up on a website for a few hours so we can download it and see the full paper.

That would be copyright violation. And the paper is long because they analyze MANY experiments to conclude that no variation to second can be found.


Now, I expect you to keep your word.
Read the https://www.physicsforums.com/showpost.php?p=942326&postcount=214" and answer my questions here:

Question #1] Are you denying that by definition special relativity and theories invoking GGT agree on the physical laws in one inertial frame?

Question #2] Do you agree that one-way velocity cannot be defined independent of a coordinate system?

Question #3] In my explanation of why experiments cannot distinguish between "Generalized Galilean transformations / coordinate systems" and "Lorentz Transformations / Special Relativity's" definition of the one way speed of light, which parts do you disagree with and why?


These questions will help focus on what we do and do not agree on. This can only help the discussion. So please stop avoiding them.

 

[clj4]

That would be copyright violation. And the paper is long because they analyze MANY experiments to conclude that no variation to second can be found.


Now, I expect you to keep your word.
Read the https://www.physicsforums.com/showpost.php?p=942326&postcount=214" and answer my questions here:

Question #1] Are you denying that by definition special relativity and theories invoking GGT agree on the physical laws in one inertial frame?

Question #2] Do you agree that one-way velocity cannot be defined independent of a coordinate system?

Question #3] In my explanation of why experiments cannot distinguish between "Generalized Galilean transformations / coordinate systems" and "Lorentz Transformations / Special Relativity's" definition of the one way speed of light, which parts do you disagree with and why?


These questions will help focus on what we do and do not agree on. This can only help the discussion. So please stop avoiding them.

Not if you put it up for 1hr. "aether" has done that and I did so as well.
The paper , please. Also, how about Kirshner? Kirshner (1990) quotes Gagnon (August 1988 ) as reference 15. Could it be that they did not know about the Dec 1988 "retraction". Did Kirshner retract at some later time?
Let's have it all on the table.

 

[gregory_]

Not if you put it up for 1hr. "aether" has done that and I did so as well.

I don't have an electronic copy, I merely have access to it in the library. I would have to scan each page in and post each page separately. Besides not having a scanner, this seems like the wrong order to approach things here. We should agree on the basics and build our way up.

If we try to do it the other way (paper by paper) we will never come to agreement. If I personally found the specific error in Gagnon's paper, would you even believe me? This will be a never ending discussion unless we agree on the basics first.

So please, in the interest of furthering our understanding of each other's stance on these issues, please read https://www.physicsforums.com/showpost.php?p=942326&postcount=214" and answer my questions here:

Question #1] Are you denying that by definition special relativity and theories invoking GGT agree on the physical laws in one inertial frame?

Question #2] Do you agree that one-way velocity cannot be defined independent of a coordinate system?

Question #3] In my explanation of why experiments cannot distinguish between "Generalized Galilean transformations / coordinate systems" and "Lorentz Transformations / Special Relativity's" definition of the one way speed of light, which parts do you disagree with and why?

 

[clj4]

I don't have an electronic copy, I merely have access to it in the library. I would have to scan each page in and post each page separately. Besides not having a scanner, this seems like the wrong order to approach things here. We should agree on the basics and build our way up.

If we try to do it the other way (paper by paper) we will never come to agreement. If I personally found the specific error in Gagnon's paper, would you even believe me?

Sure, if you do your calculations correctly. This is what you were asked all along. And, if you want to be thorough , find the error in Kirshner as well. It is only two papers, that's all.

 

[my_wan]

I will do a full review of my own set of litmus test. A general description of what parameters can and cannot transform in an unobservable manner could prove a very valuable piece of work in itself. It could also provide a very straightforward method of defining the emperical difference between any competing theory as well as any obscure test of SR not already tested. Before I leave this thread I want to give you a thought experiment to consider.

Using simultaneity and SR to measure distance.
Two telescopes A and B are pointed at a cepheid variable recording unique identifiable events. A is stationary relative to the cepheid. B in the vicinity of A is moving toward the cepheid at the velocity v. Given that the cepheid has sufficient distance even a small v can produce a shortening of relative distance of several light seconds.
For A d = d
For B d' = $$\gamma$$d
Now we simply compare by how much A and B disagree on when a unique event occurred on the cepheid plug in the known $$\gamma$$ and solve for d.

Question;
Why would the failure of this experiment not present a problem for simultaneity as dfined by SR?

 

[litlbunny]

It is the convention used for the synchronization of clocks which determines the outcome of a one-way speed of light measurement. If you postulate that the speed of light is isotropic, then clocks are synchronized by Einstein's convention, and...voila...all subsequent experiments measure a constant speed of light. That does not constitute experimental proof that the speed of light is constant; it is not possible to ever prove that by experiment. It is possible to disprove it upon the identification of a locally preferred frame, but that hasn't been done yet, and maybe it never will be.

What would each of you say if I told you with absolute certainty that the speed of light can be tested and proven to reach every observable angle by doing one simple experiment within a 3 dimensional mathematical formula?

However, after the initial experimental success with reference to a single “explosion of light” the experiment, as it is expanded, would prove several of the theories that I have seen argued/discussed within this thread, that each of them would become less believable?

Would any of you be interested in testing out this simple experiment to prove it to yourself? If you agree to do this experiment I must warn you, you will need to create a computer program in which to measure this experiment, and follow the guidelines I will be suggesting. If you agree to both of those requirements, would you like me to explain how?

Because the experiment I will be suggesting is not within “normal” theoretical teaching, I will not be able to post the experiment parameters within this forum, unless the moderators of this forum will allow for a little latitude with regards to a experimental suggestion. If not however, I could send you the “How To” in a PM

If you are interested either respond here or through a private PM.

 

[gregory_]

Sure, if you do your calculations correctly. This is what you were asked all along. And, if you want to be thorough , find the error in Kirshner as well. It is only two papers, that's all.

Only two papers. I will hold you to that.

Okay, I spent time on the Gagnon paper. The error is fairly obvious, but I wasted hours brushing up on this and that in order to feel confident enough to state it here.

The error is this: electrodynamics cannot be formulated with Maxwell's equations alone. It is Maxwell's equations (how the fields interact and are produced by the sources) _AND_ Lorentz's force law (how the fields act back on the sources). Gagnon used the transformed Maxwell's equations from reference 9 without using the transformed Lorentz force law. Reference 9 doesn't calculate it, so they must have (incorrectly) assumed that it retained the same form. This is incorrect.

Lorentz force law:
$$K^\mu = q n_\nu F^{\mu \nu}$$
where K is the Minkowski force, q the charge, n the proper velocity, F the field tensor.

Reference 9 chose the components of the covarient field tensor to define the electric and magnetic fields (instead of the contravarient field tensor, which is why the two source dependent Maxwell's equations come out horrid while the non-source dependent ones come out fairly clean). So we need to rewrite the equation to depend on that, as well as depend on the contravarient proper velocity (corresponds to the physical velocity as opposed to the covarient proper velocity).

$$K^\mu = q (g_{\nu a} n^a) (g^{\mu b}F_{b c}g^{c\nu})$$

Rearranging and noting that $$g^{c\nu} g_{\nu a} = \delta^c_{\ a}$$ we have:

$$K^\mu = q n^a g^{\mu b}F_{b a}$$

Let's move to another frame and see how the dependence of the force on the fields and the velocity changes. (I'll use a bar to denote quantities in this other frame.)

Of course we still have $$\bar{K}^\mu = q \bar{n}^a \bar{g}^{\mu b}\bar{F}_{b a}$$ but this will correspond to the same dependence on the velocity and fields ONLY if $$g^{\mu b}=\bar{g}^{\mu b}$$. In special relativity, the metric is frame independent, so the force law maintains the same form (as expected). However, this is not true for GGT. In GGT the metric is frame dependent and thus the Lorentz force law changes form when we change frames (the metric is worked out in reference 9, so you can calculate the horrid form of the Lorentz force law using GGT if you so wish).

How does this affect Gagnon's paper? It means the boundary conditions they invoke when solving for the fields in the wave-guide are not correct. So their calculations are flawed right at the beginning.

EDIT: changed kronecker delta symbol for clarity

 

[gregory_]

It took me awhile to figure out what the other paper was (apparrently you made a small typo above?). I assume the next paper is:
Test of the isotropy of the one-way speed of light using hydrogen-maser frequency standards
Krisher, T.P.; Maleki, L.; Lutes, G.F.; Primas, L.E.; Logan, R.T.; Anderson, J.D.; Will, C.M.
Physical Review D (Particles and Fields), v 42, n 2, 15 July 1990, p 731-4

I'll take a look at it.


As a side note, I tried to look up that Gagnon paper where he contradicts and says that no effect to second order should be seen according to GGT. The library records show it should be there, but the first three volumes of Foundations of Physics Letters are missing. So I can't even read the whole article myself. Oh well. I guess it doesn't matter now anyway.