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Hello All,

I have been challenged by a friend to look into Gravitational waves and some questions he has about them -- but I have always been a slow starter. Took physics with SR in college, got my BSEE, happily can build analog circuitry of all kinds -- but found that certain questions about SR never did get answered by the Prof and have gnawed at me ever since. Now I accept SR by and large -- but don't really accept GR yet -- so gravity waves are still in the Poincaire electrical charge theory realm (and Feynman had some speculation too, if I remember correctly) for me. And I figure, I best resolve the simple issues first before tackling the bigger ones ... a physics oriented crowd has perhaps studied some experiment that I haven't and might already know which of a set of answers is a dead end... hopefully this thread will grow in knowledge and build toward my friends questions -- which intrigue me, and I hope -- you.

So here is a simple gedanken with inertial frames to begin the journey toward gravity. I am not good with Minowski 4 vectors, so -- if you don't use them thanks! -- but if you do, please be very clear what they mean.

I am envisioning a radar trap with a policeman. We can ignore the rotation of the Earth and gravity here. I am also envisioning a craft passing the policeman at c/2. Since we are with the policeman at the moment, he is our inertial frame. The craft is another inertial frame -- not accelerating nor decelerating. There is sufficient rest mass with both the policeman and the craft so that the radar gun he fires at the craft does not change the speed between them measurably.

Please correct any assertion that is clearly contradictory:

1. Since there are only two objects -- the policeman and the craft -- the speed measured by one ought to be the same as the speed observed by the other. There is no third body issue.

2. The policeman is firing a low wattage continuous wave radar gun. Eg: let's say 300MHz in his frame -- and he is aiming it at the craft passing him. At T=0 the craft is touching the gun, and thereafter it recedes directly away from the gun at a constant velocity V.

3. Older radar guns work on the Doppler effect (red shift/blue shift). Our police man is using one -- eg: Essentially, he is measuring the beat frequency of his outgoing wave with the incoming one -- and using that to determine the crafts speed. The craft -- for its part -- is made of a superconductor, and is acting as a perfect mirror nicely aimed to give the policeman an accurate reading.

4. Einstein believed in "photons" and the photoelectric effect. Hence, we may view (consistently for his thinking) the police man as ejecting photons with wavelength 1 meter, frequency 300Mhz (assuming c=3x10**8 exactly, otherwise -- scale accordingly for nice math.).

5. Using my old EE books on radiation, by Dr. Aziz Inan -- we can view this as a simplification of Maxwell's equation. We can treat the outgoing and reflected waves as a plane wave in the x direction. The boundary condition is that the perfect conductior has no E-field inside it (charge neutral superconductor) and its location is x=v*t. The resulting TE (transverse electric) then is zero at x=vt. When I solve Maxwell's equations this way, I arrive at a standing wave. The returning wave has the same amplitude as the outgoing one, and is 100MHz.

Now; Here's where my choose your poison/paradox/irritation begins.

I naively thought, since the original wave had a length 1M in the policeman's reference frame -- in the crafts frame it ought to have one of 1M / L, where L=sqrt( 1- v**2/c**2). Now that is clearly wrong. When I find the second place away from the reflector where no E-field exists by Maxwell's equations -- I come to the conclusion it is at 1.5Meters from the reflector in the police frame. now 1.5Meters/L = 1.7329Meter'.

Where the ' means the craft's meter stick. That answer looks right.

So, here's the first question: Since Einstein viewed photons as having energy E=hf; What is the proper way to balance Energy for a *single* photon? Upon reflection from a lossless mirror which has sufficient rest mass such that acceleration is negligible -- Maxwell's equations predict the reflected wave will have a lower frequency in the police man's reference frame. eg: the photon lost energy upon a lossless mirror. The loss depends on the velocity of the mirror, and nothing else.

In the reference frame of the craft -- the light does not know who (police or craft) is moving -- so being a good mirror -- the light is reflected and is the same color to the observer on the craft. ergo: No energy loss. The perspectives are at odds to each other -- so rather than believe the police unconditionally -- tear these to shreds:

1. proposition: Photons do not really have E=hf energy each -- that is just the energy they release to an electron during a reaction ejecting an electron from a photoconductor. Actual photons may have FRACTIONAL amounts more or less than hf.

2. proposition. Photons are not really individual (a variation of 1) -- if we take the extra time delay from when a the police gun is shut off to when the last of the light arrives back at the gun -- we will find that the lower energy returning photons last for just enough extra time that a the energy (assuming a CW wave and ignoring photons) balances out. Low power x longer time = higher powe x shorter time. (In fact it does balance out.)

3. What would you propose that completely explains the reconciling of the policeman's view -- and the crafts view?

I have been challenged by a friend to look into Gravitational waves and some questions he has about them -- but I have always been a slow starter. Took physics with SR in college, got my BSEE, happily can build analog circuitry of all kinds -- but found that certain questions about SR never did get answered by the Prof and have gnawed at me ever since. Now I accept SR by and large -- but don't really accept GR yet -- so gravity waves are still in the Poincaire electrical charge theory realm (and Feynman had some speculation too, if I remember correctly) for me. And I figure, I best resolve the simple issues first before tackling the bigger ones ... a physics oriented crowd has perhaps studied some experiment that I haven't and might already know which of a set of answers is a dead end... hopefully this thread will grow in knowledge and build toward my friends questions -- which intrigue me, and I hope -- you.

So here is a simple gedanken with inertial frames to begin the journey toward gravity. I am not good with Minowski 4 vectors, so -- if you don't use them thanks! -- but if you do, please be very clear what they mean.

I am envisioning a radar trap with a policeman. We can ignore the rotation of the Earth and gravity here. I am also envisioning a craft passing the policeman at c/2. Since we are with the policeman at the moment, he is our inertial frame. The craft is another inertial frame -- not accelerating nor decelerating. There is sufficient rest mass with both the policeman and the craft so that the radar gun he fires at the craft does not change the speed between them measurably.

Please correct any assertion that is clearly contradictory:

1. Since there are only two objects -- the policeman and the craft -- the speed measured by one ought to be the same as the speed observed by the other. There is no third body issue.

2. The policeman is firing a low wattage continuous wave radar gun. Eg: let's say 300MHz in his frame -- and he is aiming it at the craft passing him. At T=0 the craft is touching the gun, and thereafter it recedes directly away from the gun at a constant velocity V.

3. Older radar guns work on the Doppler effect (red shift/blue shift). Our police man is using one -- eg: Essentially, he is measuring the beat frequency of his outgoing wave with the incoming one -- and using that to determine the crafts speed. The craft -- for its part -- is made of a superconductor, and is acting as a perfect mirror nicely aimed to give the policeman an accurate reading.

4. Einstein believed in "photons" and the photoelectric effect. Hence, we may view (consistently for his thinking) the police man as ejecting photons with wavelength 1 meter, frequency 300Mhz (assuming c=3x10**8 exactly, otherwise -- scale accordingly for nice math.).

5. Using my old EE books on radiation, by Dr. Aziz Inan -- we can view this as a simplification of Maxwell's equation. We can treat the outgoing and reflected waves as a plane wave in the x direction. The boundary condition is that the perfect conductior has no E-field inside it (charge neutral superconductor) and its location is x=v*t. The resulting TE (transverse electric) then is zero at x=vt. When I solve Maxwell's equations this way, I arrive at a standing wave. The returning wave has the same amplitude as the outgoing one, and is 100MHz.

Now; Here's where my choose your poison/paradox/irritation begins.

I naively thought, since the original wave had a length 1M in the policeman's reference frame -- in the crafts frame it ought to have one of 1M / L, where L=sqrt( 1- v**2/c**2). Now that is clearly wrong. When I find the second place away from the reflector where no E-field exists by Maxwell's equations -- I come to the conclusion it is at 1.5Meters from the reflector in the police frame. now 1.5Meters/L = 1.7329Meter'.

Where the ' means the craft's meter stick. That answer looks right.

So, here's the first question: Since Einstein viewed photons as having energy E=hf; What is the proper way to balance Energy for a *single* photon? Upon reflection from a lossless mirror which has sufficient rest mass such that acceleration is negligible -- Maxwell's equations predict the reflected wave will have a lower frequency in the police man's reference frame. eg: the photon lost energy upon a lossless mirror. The loss depends on the velocity of the mirror, and nothing else.

In the reference frame of the craft -- the light does not know who (police or craft) is moving -- so being a good mirror -- the light is reflected and is the same color to the observer on the craft. ergo: No energy loss. The perspectives are at odds to each other -- so rather than believe the police unconditionally -- tear these to shreds:

1. proposition: Photons do not really have E=hf energy each -- that is just the energy they release to an electron during a reaction ejecting an electron from a photoconductor. Actual photons may have FRACTIONAL amounts more or less than hf.

2. proposition. Photons are not really individual (a variation of 1) -- if we take the extra time delay from when a the police gun is shut off to when the last of the light arrives back at the gun -- we will find that the lower energy returning photons last for just enough extra time that a the energy (assuming a CW wave and ignoring photons) balances out. Low power x longer time = higher powe x shorter time. (In fact it does balance out.)

3. What would you propose that completely explains the reconciling of the policeman's view -- and the crafts view?

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