The Poynting vector has a problem in the nearfield of a dipole source. It can be shown that by setting the wave equation equal to a oscillating charge, that the transverse electric field component is generated outside the source at about 1/4 wavelength and launches waves both toward and away from the source, whereas the other components: longitudinal electric field and transverse magnetic field.are created at the source and propagate away from the source. The problem with using the Poynting vector in the nearfield is that it hides the fact that some of the energy is going back into the source and some is propagating away from the source, which cancel, creating no net energy flow in the nearfield, but energy flow in the farfield. Whereas in reality there is energy flow in the nearfield if one isolates each the individual field component terms, which can be done with a suitable dectector. Analyzing the individual field terms shows that the speed of the fields are instantaneous in the nearfield and reduces to about the speed of light in the farfield, at about 1 wavelength from the source. This corresponds to the phase speed, group speed, and information spees. Since the energy is proportional to the square of the field, then the energy is propagating at the group speed, which as I mentioned is instantaneous in the nearfield and reduces to about the speed of light in the farfield, at about 1/4 wavelength from the source. For more information see my paper:
This is very interesting work. I should point out, though, that the Poynting vector does describe the near-field energy flow. The mistake some investigators make is to assume there is a radiation energy flow distinct from the total energy flow. They calculate a Poynting vector based only on the far-field terms which ignores the near-field effects you describe.
The speed of light is not a constant as once thought, and this has now been proved by Electrodynamic theory and by Experiments done by many independent researchers. The results clearly show that light propagates instantaneously when it is created by a source, and reduces to approximately the speed of light in the farfield, about one wavelength from the source, and never becomes equal to exactly c. This corresponds the phase speed, group speed, and information speed. Any theory assuming the speed of light is a constant, such as Special Relativity and General Relativity are wrong, and it has implications to Quantum theories as well. So this fact about the speed of light affects all of Modern Physics. Often it is stated that Relativity has been verified by so many experiments, how can it be wrong. Well no experiment can prove a theory, and can only provide evidence that a theory is correct. But one experiment can absolutely disprove a theory, and the new speed of light experiments proving the speed of light is not a constant is such a proof. So what does it mean? Well a derivation of Relativity using instantaneous nearfield light yields Galilean Relativity. This can easily seen by inserting c=infinity into the Lorentz Transform, yielding the GalileanTransform, where time is the same in all inertial frames. So a moving object observed with instantaneous nearfield light will yield no Relativistic effects, whereas by changing the frequency of the light such that farfield light is used will observe Relativistic effects. But since time and space are real and independent of the frequency of light used to measure its effects, then one must conclude the effects of Relativity are just an optical illusion.
Since General Relativity is based on Special Relativity, then it has the same problem. A better theory of Gravity is Gravitoelectromagnetism which assumes gravity can be mathematically described by 4 Maxwell equations, similar to to those of electromagnetic theory. It is well known that General Relativity reduces to Gravitoelectromagnetism for weak fields, which is all that we observe. Using this theory, analysis of an oscillating mass yields a wave equation set equal to a source term. Analysis of this equation shows that the phase speed, group speed, and information speed are instantaneous in the nearfield and reduce to the speed of light in the farfield. This theory then accounts for all the observed gravitational effects including instantaneous nearfield and the speed of light farfield. The main difference is that this theory is a field theory, and not a geometrical theory like General Relativity. Because it is a field theory, Gravity can be then be quantized as the Graviton.
Lastly it should be mentioned that this research shows that the Pilot Wave interpretation of Quantum Mechanics can no longer be criticized for requiring instantaneous interaction of the pilot wave, thereby violating Relativity. It should also be noted that nearfield electromagnetic fields can be explained by quantum mechanics using the Pilot Wave interpretation of quantum mechanics and the Heisenberg uncertainty principle (HUP), where Δx and Δp are interpreted as averages, and not the uncertainty in the values as in other interpretations of quantum mechanics. So in HUP: Δx Δp = h, where Δp=mΔv, and m is an effective mass due to momentum, thus HUP becomes: Δx Δv = h/m. In the nearfield where the field is created, Δx=0, therefore Δv=infinity. In the farfield, HUP: Δx Δp = h, where p = h/λ. HUP then becomes: Δx h/λ = h, or Δx=λ. Also in the farfield HUP becomes: λmΔv=h, thus Δv=h/(mλ). Since p=h/λ, then Δv=p/m. Also since p=mc, then Δv=c. So in summary, in the nearfield Δv=infinity, and in the farfield Δv=c, where Δv is the average velocity of the photon according to Pilot Wave theory. Consequently the Pilot wave interpretation should become the preferred interpretation of Quantum Mechanics. It should also be noted that this argument can be applied to all fields, including the graviton. Hence all fields should exhibit instantaneous nearfield and speed c farfield behavior, and this can explain the non-local effects observed in quantum entangled particles.
*More extensive paper for the above arguments: William D. Walker and Dag Stranneby, A New Interpretation of Relativity, 2023: http://vixra.org/abs/2309.0145
Hi Tim, My research shows that the speed of light is not a constant, and if this is true, then Relativity can not be correct, because it is a core premise of the theory. Keep in mind it is not possible to prove a theory with experiments, because there may be other reasons for the effects being observed. But a theory can absolutely be disproved by just one experiment, and my experiment showing light does not propagate at constant speed can absolutely disprove Relativity. The rest of my arguments are an attempt to address what this means since all of modern physics depends on Relativity. Regarding your questions. Again there may be other reasons for the effects observed in the experiments you mentioned, so they do not prove Relativity. The Michelson Morley experiment showed that farfield light propagates at the same speed for different inertial frames. But this experiment did not measure the speed of light. Whereas I have with the experiment shown in my paper and it shows different speeds in the nearfield and the farfield.
No problem, Tim. I appreciate your feedback and comments. My sense is that fields and action-at-a-distance are mathematically equivalent if properly done, and it's more of a philosophic preference which you want to use. I like the fields approach because it promises to show the exact evolution of cause and effect across space and time. But there are times where an action-at-a-distance approach may be the better way to solve particular problems.
I have reached out to some of the action-at-a-distance proponents who argue that there are testable differences in their interpretation to see if we can agree on some tests in the arena of near-field wireless which is an area with which I'm more familiar than measuring magnetic forces.
The Poynting vector has a problem in the nearfield of a dipole source. It can be shown that by setting the wave equation equal to a oscillating charge, that the transverse electric field component is generated outside the source at about 1/4 wavelength and launches waves both toward and away from the source, whereas the other components: longitudinal electric field and transverse magnetic field.are created at the source and propagate away from the source. The problem with using the Poynting vector in the nearfield is that it hides the fact that some of the energy is going back into the source and some is propagating away from the source, which cancel, creating no net energy flow in the nearfield, but energy flow in the farfield. Whereas in reality there is energy flow in the nearfield if one isolates each the individual field component terms, which can be done with a suitable dectector. Analyzing the individual field terms shows that the speed of the fields are instantaneous in the nearfield and reduces to about the speed of light in the farfield, at about 1 wavelength from the source. This corresponds to the phase speed, group speed, and information spees. Since the energy is proportional to the square of the field, then the energy is propagating at the group speed, which as I mentioned is instantaneous in the nearfield and reduces to about the speed of light in the farfield, at about 1/4 wavelength from the source. For more information see my paper:
https://arxiv.org/abs/physics/0603240
The consequences of these results are discussed in my YouTube video presentation, and the paper it is based on:
*YouTube presentation: https://www.youtube.com/watch?v=sePdJ7vSQvQ&t=0s
*Based on this paper:
http://vixra.org/abs/2309.0145
Here is our most recent paper which experimentally demonstrates an EM pulse propagates instantaneously in the nearfield:
*Electromagnetic pulse experiment paper: https://www.techrxiv.org/doi/full/10.36227/techrxiv.170862178.82175798/v1
This is very interesting work. I should point out, though, that the Poynting vector does describe the near-field energy flow. The mistake some investigators make is to assume there is a radiation energy flow distinct from the total energy flow. They calculate a Poynting vector based only on the far-field terms which ignores the near-field effects you describe.
The speed of light is not a constant as once thought, and this has now been proved by Electrodynamic theory and by Experiments done by many independent researchers. The results clearly show that light propagates instantaneously when it is created by a source, and reduces to approximately the speed of light in the farfield, about one wavelength from the source, and never becomes equal to exactly c. This corresponds the phase speed, group speed, and information speed. Any theory assuming the speed of light is a constant, such as Special Relativity and General Relativity are wrong, and it has implications to Quantum theories as well. So this fact about the speed of light affects all of Modern Physics. Often it is stated that Relativity has been verified by so many experiments, how can it be wrong. Well no experiment can prove a theory, and can only provide evidence that a theory is correct. But one experiment can absolutely disprove a theory, and the new speed of light experiments proving the speed of light is not a constant is such a proof. So what does it mean? Well a derivation of Relativity using instantaneous nearfield light yields Galilean Relativity. This can easily seen by inserting c=infinity into the Lorentz Transform, yielding the GalileanTransform, where time is the same in all inertial frames. So a moving object observed with instantaneous nearfield light will yield no Relativistic effects, whereas by changing the frequency of the light such that farfield light is used will observe Relativistic effects. But since time and space are real and independent of the frequency of light used to measure its effects, then one must conclude the effects of Relativity are just an optical illusion.
Since General Relativity is based on Special Relativity, then it has the same problem. A better theory of Gravity is Gravitoelectromagnetism which assumes gravity can be mathematically described by 4 Maxwell equations, similar to to those of electromagnetic theory. It is well known that General Relativity reduces to Gravitoelectromagnetism for weak fields, which is all that we observe. Using this theory, analysis of an oscillating mass yields a wave equation set equal to a source term. Analysis of this equation shows that the phase speed, group speed, and information speed are instantaneous in the nearfield and reduce to the speed of light in the farfield. This theory then accounts for all the observed gravitational effects including instantaneous nearfield and the speed of light farfield. The main difference is that this theory is a field theory, and not a geometrical theory like General Relativity. Because it is a field theory, Gravity can be then be quantized as the Graviton.
Lastly it should be mentioned that this research shows that the Pilot Wave interpretation of Quantum Mechanics can no longer be criticized for requiring instantaneous interaction of the pilot wave, thereby violating Relativity. It should also be noted that nearfield electromagnetic fields can be explained by quantum mechanics using the Pilot Wave interpretation of quantum mechanics and the Heisenberg uncertainty principle (HUP), where Δx and Δp are interpreted as averages, and not the uncertainty in the values as in other interpretations of quantum mechanics. So in HUP: Δx Δp = h, where Δp=mΔv, and m is an effective mass due to momentum, thus HUP becomes: Δx Δv = h/m. In the nearfield where the field is created, Δx=0, therefore Δv=infinity. In the farfield, HUP: Δx Δp = h, where p = h/λ. HUP then becomes: Δx h/λ = h, or Δx=λ. Also in the farfield HUP becomes: λmΔv=h, thus Δv=h/(mλ). Since p=h/λ, then Δv=p/m. Also since p=mc, then Δv=c. So in summary, in the nearfield Δv=infinity, and in the farfield Δv=c, where Δv is the average velocity of the photon according to Pilot Wave theory. Consequently the Pilot wave interpretation should become the preferred interpretation of Quantum Mechanics. It should also be noted that this argument can be applied to all fields, including the graviton. Hence all fields should exhibit instantaneous nearfield and speed c farfield behavior, and this can explain the non-local effects observed in quantum entangled particles.
*YouTube presentation of above arguments: https://www.youtube.com/watch?v=sePdJ7vSQvQ&t=0s
*More extensive paper for the above arguments: William D. Walker and Dag Stranneby, A New Interpretation of Relativity, 2023: http://vixra.org/abs/2309.0145
*Electromagnetic pulse experiment paper: https://www.techrxiv.org/doi/full/10.36227/techrxiv.170862178.82175798/v1
Dr. William Walker - PhD in physics from ETH Zurich, 1997
Hi Tim, My research shows that the speed of light is not a constant, and if this is true, then Relativity can not be correct, because it is a core premise of the theory. Keep in mind it is not possible to prove a theory with experiments, because there may be other reasons for the effects being observed. But a theory can absolutely be disproved by just one experiment, and my experiment showing light does not propagate at constant speed can absolutely disprove Relativity. The rest of my arguments are an attempt to address what this means since all of modern physics depends on Relativity. Regarding your questions. Again there may be other reasons for the effects observed in the experiments you mentioned, so they do not prove Relativity. The Michelson Morley experiment showed that farfield light propagates at the same speed for different inertial frames. But this experiment did not measure the speed of light. Whereas I have with the experiment shown in my paper and it shows different speeds in the nearfield and the farfield.
No problem, Tim. I appreciate your feedback and comments. My sense is that fields and action-at-a-distance are mathematically equivalent if properly done, and it's more of a philosophic preference which you want to use. I like the fields approach because it promises to show the exact evolution of cause and effect across space and time. But there are times where an action-at-a-distance approach may be the better way to solve particular problems.
I have reached out to some of the action-at-a-distance proponents who argue that there are testable differences in their interpretation to see if we can agree on some tests in the arena of near-field wireless which is an area with which I'm more familiar than measuring magnetic forces.