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"Consequently, light itself prevents charged particles from moving faster than the speed of light."

 
Xenus 
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"Consequently, light itself prevents charged particles from moving faster than the speed of light."
When resolving why electrons can never beat the speed limit set by light, it might be best to forget about time. Thanks to insight from studying movement inside a biological cell, it seems that light itself -- not the relativity of time -- may be the traffic cop, according to a Cornell University biologist.

Any space with a temperature above absolute zero consists of photons. As a result of the Doppler effect, the moving electron experiences the photons crashing into the front of it as being blue-shifted, and the photons colliding with the back of it as being red-shifted. Since blue-shifted photons exert more momentum than red-shifted photons, the photons themselves exert a counterforce on the moving electron, just as the cytoplasm in a cell exerts a viscous force on the moving organelles. The viscous force that arises from the Doppler-shifted photons prevents electrons from exceeding the speed of light, according to Randy Wayne, associate professor of plant biology.

Wayne's research, "Charged Particles Are Prevented From Going Faster Than the Speed of Light by Light Itself: A Biophysical Cell Biologist's Contribution to Physics," appears in the November 2010 issue of Acta Physica Polonica B.

On determining whether electrons can surpass the speed of light, Albert Einstein's special theory of relativity contends that electrons are prevented from exceeding the speed of light as a result of the relativity of time. But Wayne contends that Einstein didn't take the environment through which the electrons move into account.

"Given the prominence of viscous forces within and around cells and the experience of identifying and quantifying such resistive forces, biophysical cell biologists have an unique perspective in discovering the viscous forces that cause moving particles to respond to an applied force in a nonlinear manner," he explained.

[link to www.physorg.com]

There are 2 interesting implications to this, one that people are finally beginning to understand that time does not exist, that it is nothing more than a measurement of motion and change. And that living cells and the universe have a lot more in common than you would think.

At the first IEEE International Workshop on Plasma Cosmology held in La Jolla, California, in 1989, Hannes Alfvén reported:

The same basic laws of plasma physics hold from laboratory and magnetospheric heliospheric plasmas out to interstellar and intergalactic plasmas.

In order to understand the phenomena in a certain plasma region, it is necessary to map not only the magnetic but also the electric field and the electric currents.

Space is filled with a network of currents which transfer energy and momentum over large or very large distances. The currents often pinch to filamentary or surface currents. The latter are likely to give space, as also interstellar and intergalactic space, a cellular structure.

A number of plasma phenomena, like double layers, critical velocity, pinch effect, and the properties of electric circuits, are of decisive importance. The phenomena mentioned have been known for decades (or even more than a century), but up to now they have almost systematically been ignored in cosmic physics. If they are taken into account, not only interplanetary space but also interstellar and intergalactic space must have a cellular structure.

[link to www.plasma-universe.com]

Cellular structure with the ability to communicate between cells with radio waves and other EM frequencies. Just like living cells inside our body. Maybe it's time we re-defined what living means.
Smilin' Irish Eyes

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Re: "Consequently, light itself prevents charged particles from moving faster than the speed of light."
Maybe it is just because it is early, but I'm not sure I understand.

The Z pinch affects the speed of light because of cellular structure?

sie youtheman
Common sense in an uncommon degree is what the world calls wisdom. -- Samuel Taylor Coleridge

In seeking wisdom thou art wise; in imagining that thou hast attained it - thou art a fool. -- Lord Chesterfield
Xenus  (OP)

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Re: "Consequently, light itself prevents charged particles from moving faster than the speed of light."
The speed of charged particles seems to be governed by light itself and light travels through the medium of space. That what they call a vacuum even though it's not really one. There is always matter and energy in space, there is no nothing anywhere. So logically, the speed of light should be governed by the medium it travels through, just like sound and light on Earth. There have been many reported observations of light traveling faster then our accepted theory of the limits of the speed of light. This can be explained by the medium it travels through. Astronomers assume that the speed of light is a constant because we assume that space is empty and the same everywhere.

A perfect vacuum would be one with no particles in it at all, which is impossible to achieve in practice.
[link to en.wikipedia.org]
Anonymous Coward
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Re: "Consequently, light itself prevents charged particles from moving faster than the speed of light."
Very cool theory, thanks for posting this!
Anonymous Coward
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11/22/2010 07:46 AM
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Re: "Consequently, light itself prevents charged particles from moving faster than the speed of light."
I wish I could understand any of that. It sounds really cool.
Anonymous Coward
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11/22/2010 07:47 AM
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Re: "Consequently, light itself prevents charged particles from moving faster than the speed of light."
The speed of charged particles seems to be governed by light itself and light travels through the medium of space. That what they call a vacuum even though it's not really one. There is always matter and energy in space, there is no nothing anywhere. So logically, the speed of light should be governed by the medium it travels through, just like sound and light on Earth. There have been many reported observations of light traveling faster then our accepted theory of the limits of the speed of light. This can be explained by the medium it travels through. Astronomers assume that the speed of light is a constant because we assume that space is empty and the same everywhere.

A perfect vacuum would be one with no particles in it at all, which is impossible to achieve in practice.
[link to en.wikipedia.org]
 Quoting: Xenus 


C is nothing but an approximation

There are no true "laws of physics ", only principles of nature that constrain physical events. These principles change with our ability to observe at wider scales- smaller, larger, faster, slower, colder, hotter.

An example - protons were recently discovered to be 4% smaller than thought.

Time dilation ?

Twins paradox ?

Ok, stand next to me and travel in a circle , with a diameter of 1 ' at " C ", for 1 year ( by your measurement )

Now stop.

How old are you compared to me ?

Did you age slower in the same neighborhood ?

Or do you believe time dilation to occur only while traveling in a straight line ?
Xenus  (OP)

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11/22/2010 07:51 AM
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Re: "Consequently, light itself prevents charged particles from moving faster than the speed of light."
And as smart as Einstein was, he can easily be wrong, he was human as we all are. He made his theories based upon the information he had at the time. We now know a lot more about space and the plasma that fill over 99% of the visible universe. These particles are everywhere, they may seem low density for the most part, but that is only from our viewpoint and relative scale. If we could see the atomic structure of atoms at their scale, there would vastly be more space between them than actual matter (the atoms). But yet things are solid.

He spent his final years trying to make it all fit together, but he didn't have all the pieces so he could not, he knew this. The technology at the time simply could not provide all the required information.
Anonymous Coward
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Re: "Consequently, light itself prevents charged particles from moving faster than the speed of light."
And as smart as Einstein was, he can easily be wrong, he was human as we all are. He made his theories based upon the information he had at the time. We now know a lot more about space and the plasma that fill over 99% of the visible universe. These particles are everywhere, they may seem low density for the most part, but that is only from our viewpoint and relative scale. If we could see the atomic structure of atoms at their scale, there would vastly be more space between them than actual matter (the atoms). But yet things are solid.

He spent his final years trying to make it all fit together, but he didn't have all the pieces so he could not, he knew this. The technology at the time simply could not provide all the required information.
 Quoting: Xenus 


I agree.

I always did have some questions about Al's logical deduction and powers of reasoning.



Let's have some OJ ,lol.



He was dying of terminal cancer when this video was made. I've never seen a man so happy to " die ". He knew that he was about to receive an answer to a question that's been asked for all " time ".
BRIEF AND TO THE POINT

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11/22/2010 08:06 AM
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Re: "Consequently, light itself prevents charged particles from moving faster than the speed of light."
oxymoran1564
Poor people do poor people things, and rich people do rich people things.

You cannot legislate the poor into prosperity by legislating the wealthy out of prosperity.

What one person receives without working for, another person must work for without receiving.

The government cannot give to anybody anything that the government does not first take from somebody else.

When half of the people get the idea that they do not have to work because the other half is going to take care of them, and the other half gets the idea that it does no good to work because somebody else is going to get what they work for, that my dear friend, is the beginning of the end of any nation.

You cannot multiply wealth by dividing it!

when you rob Paul to give to Peter ... ... ... you will always get Peters support!

:Brieffromnativea:
Xenus  (OP)

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Re: "Consequently, light itself prevents charged particles from moving faster than the speed of light."
bump
Xenus  (OP)

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11/22/2010 02:36 PM
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Re: "Consequently, light itself prevents charged particles from moving faster than the speed of light."
bump

For the peak crowd.
Smilin' Irish Eyes

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11/22/2010 08:43 PM
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Re: "Consequently, light itself prevents charged particles from moving faster than the speed of light."
shakeit Bump for the night crowd.
Common sense in an uncommon degree is what the world calls wisdom. -- Samuel Taylor Coleridge

In seeking wisdom thou art wise; in imagining that thou hast attained it - thou art a fool. -- Lord Chesterfield
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11/23/2010 12:51 AM
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Re: "Consequently, light itself prevents charged particles from moving faster than the speed of light."
hf
RandyWayne

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Re: "Consequently, light itself prevents charged particles from moving faster than the speed of light."
I thank the many people who have commented on the press release. I would like to make a single response to a number of posts on the following websites:
[link to www.physorg.com]
[link to www.parascientifica.com]
[link to www.physicsforums.com]
[link to 204.74.214.194]
[link to www.talk-polywell.org]
[link to www.stumbleupon.com]

I think you will see that I have definite and convincing responses to the comments that challenge my theory:
There have been a number of comments that relate to the suggestion that the reason that charged particles cannot exceed the speed of light is because the mass becomes infinite. Currently, major proponents of Einstein’s Special Theory of Relativity claim that mass is not velocity-dependent but invariant. For example, N. David Mermin writes in, It’s About Time. Understanding Einstein’s Relativity (Princeton University Press, Princeton, NJ, 2005, see p. 153):
“As so defined, the mass of a particle continues to be an inherent property of the particle, having nothing to do with how fast the particle might be moving in other collisions in which it might subsequently find itself. It is an invariant, independent of frame of reference. If there were a particle whose mass were not invariant, then we could distinguish one inertial frame from another by performing in each frame a low-velocity collision that determined the mass of the particle. (In the early days of relativity, it was sometimes the practice to give a different relativistic definition of mass that made the mass of a particle depend on its velocity. Compensating changes were made in relativistic definitions of energy and momentum so that those expressions were the same as those we shall now construct. Today, however, the mass of a particle is always defined to be independent of its velocity.)”
In the following pages of chapter eleven, Mermin explains that while the mass is invariant, at speeds close to the speed of light, the relativistic momentum is velocity dependent as a result of the relativity of time and the necessity of using the time as reckoned in the particle’s inertial frame of reference. I want to be clear that I think that it is neither the relativity of mass nor the relativity of time that prevents charged particles from exceeding the speed of light. I claim that it is the counterforce provided by the Doppler-shifted photons that prevent charged particles from exceeding the speed of light. The only time that is relevant is that reckoned by the observer doing the experiment (not the time of the particle in the experiment nor the time of an non-existent aether).
There have been a number of comments that suggest that light/photons/electromagnetic waves are mass-less and thus do not have momentum. They do. J. H. Pointing described light pressure in The Pressure of Light (Society for Promoting Christian Knowledge, London, 1910). Here at Cornell University, E. F. Nichols and G. F Hull measured the pressure of radiation (Physical Review 17: 26-50, 91-104, 1903). In 1908, Johannes Stark characterized the momentum of photons as h⁄λ (J. Stark, Neue Beobachtungen an Kanalstrahlen in Beziehung zur Lichtquantenhypothese, Verh d. Deuschen Physicalischen Gesellschaft 10:713-725, 1908) and in 1917 Einstein used the momentum of photons to craft his Quantum Theory of Radiation and Atomic Processes (A. Einstein, 1917, in The World of the Atom, eds. H.A. Boorse, L. Motz, Basic Books, New York 1966, p. 888-901). The Compton and Inverse Compton effects are best described by the exchange of momentum between photons and charged particles. I want to be clear in stating that light/photons/ electromagnetic waves have momentum.

I also refer you to my book, Light and Video Microscopy (Elsevier Academic Press, Amsterdam, 2009 where all royalties go to Habitat for Humanity) in which I describe the use of optical tweezers to probe the mechanical nature of cells (p. 199). In the appendix of this book, I present a model of the photon (pp. 277-284). In this model, the photon, which has momentum, is not an elementary particle, but a composite made of two particles such that the sum of the masses equal zero.
There have been a number of comments that the interaction between a photon and an atom is conservative and that the particle should not change its velocity after the interaction. This is only true under the assumption that there is no friction. I think I have clearly showed that, as a result of the Doppler effect, at any temperature greater than absolute zero, the radiation that particles move through will result in a counterforce, friction, a viscous force or a dissipation of energy; however you wish to quantify it. Book One of the Principia, which presents Newton’s Three Laws, assumes that there is no friction. Book Two, which is, rarely read, cited or contemplated, discusses that in the real world there is friction that must be taken into consideration. If Book Two had not been forgotten, it would have served as the basis for understanding motion at velocities close to the speed of light. Some comments state that according to my analysis, all particles will slow down and according to my theory, Newton’s First Law would not be absolutely correct. I believe that Newton’s First Law is only absolutely valid at absolute zero, which is unattainable according to the Third Law of Thermodynamics ( [link to th-www.if.uj.edu.pl] reference 131). Some comments state that according to my theory particles could exceed the speed of light at absolute zero. My theory however, is based on the Laws of Thermodynamics that state that absolute zero is unattainable.
There are comments that my theory applies only to electrons. This is not true it applies to any charged particle, any particle that is composed of charged quarks, and any neutral particle that has a magnetic moment (neutron or neutrino (footnote 132 in [link to th-www.if.uj.edu.pl] That is, it applies to any particle that interacts with electromagnetic radiation.

There have been comments concerning the fact that I am a biologist and that I am using that experience to help me see physics differently. In order to find more information of the historical and productive relationships between biology, chemistry and physics, I refer you to my book: Plant Cell Biology from Astronomy to Zoology (Elsevier Academic Press, Amsterdam, 2009—all royalties go to the Profile in Courage Award given by the John F. Kennedy Library Foundation) and to my paper on charged particles ( [link to th-www.if.uj.edu.pl]

There have been comments on the impact factor of the journals that published my work. If you are wondering why my paper on why charged particles cannot go faster than the speed of light was not published in the Annalen der Physik, the journal that published Einstein’s Special Theory of Relativity and the first journal I submitted my manuscript to, I give you the editor’s review:
Dear Prof. Wayne,

I have discussed you papers with some collegues. It seems to us that the derivations seem correct. We nevertheless prefer not to publish the articles in Annalen der Physik. We suggest to publish them in a different more suitable journal.

Best wishes

Bernhard Kramer
(11/5/08)

Annalen der Physik also rejected my manuscript on the relativity of Simultaneity (which was recently published in the African Physical Review [link to www.aphysrev.org] Here is their response:

Dear Professor Wayne,
I am sorry but this manuscript -- like previous ones submitted to Annalen -- is not acceptable for publication in this journal. You must know that SRT has been treated in numerous theoretical papers and books, and confirmed in many experiments beyond any doubt. I enclose two papers published by us in 2005 which may be of interest for you. Hence I do not see any need for a discussion like the one you are providing.
Best regards
Ulrich Eckern
Editor in Chief
(9/26/09)

I suggested to the editor that the real value of science, according to Richard Feynman, is the freedom to doubt.

I have been called a crank and a crackpot. “The Crackpot Index,” was published by the mathematical physicist John Baez (1998) as an instrument to provide “A simple method for rating potentially revolutionary contributions to physics ( [link to math.ucr.edu] and, in an article commemorating the 100th anniversary of Einstein’s Theory of Special Relativity, theoretical physicist Clifford M. Will (in Einstein 1905-2005, Poincare ́ Seminar 2005, Birkha ̈user Verlag, Basel, 2006) wrote, “we see that the theory has been so thoroughly integrated into the fabric of modern physics that its validity is rarely challenged, except by cranks and crackpots ( [link to physics.wustl.edu] I assure you that I am neither a crackpot nor a crank.

Cornell University and the person in the Press Relations Office who wrote the press release and well as Acta Physica Polonica B and the reviewers of my paper have been attacked in various posts. It is possible that given the probability of being attacked for supporting and publishing something so different they have showed courage and a certain amount of charity. I thank them.
Xenus  (OP)

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11/29/2010 06:12 PM
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Re: "Consequently, light itself prevents charged particles from moving faster than the speed of light."
I thank the many people who have commented on the press release. I would like to make a single response to a number of posts on the following websites:
[link to www.physorg.com]
[link to www.parascientifica.com]
[link to www.physicsforums.com]
[link to 204.74.214.194]
[link to www.talk-polywell.org]
[link to www.stumbleupon.com]

I think you will see that I have definite and convincing responses to the comments that challenge my theory:
There have been a number of comments that relate to the suggestion that the reason that charged particles cannot exceed the speed of light is because the mass becomes infinite. Currently, major proponents of Einstein’s Special Theory of Relativity claim that mass is not velocity-dependent but invariant. For example, N. David Mermin writes in, It’s About Time. Understanding Einstein’s Relativity (Princeton University Press, Princeton, NJ, 2005, see p. 153):
“As so defined, the mass of a particle continues to be an inherent property of the particle, having nothing to do with how fast the particle might be moving in other collisions in which it might subsequently find itself. It is an invariant, independent of frame of reference. If there were a particle whose mass were not invariant, then we could distinguish one inertial frame from another by performing in each frame a low-velocity collision that determined the mass of the particle. (In the early days of relativity, it was sometimes the practice to give a different relativistic definition of mass that made the mass of a particle depend on its velocity. Compensating changes were made in relativistic definitions of energy and momentum so that those expressions were the same as those we shall now construct. Today, however, the mass of a particle is always defined to be independent of its velocity.)”
In the following pages of chapter eleven, Mermin explains that while the mass is invariant, at speeds close to the speed of light, the relativistic momentum is velocity dependent as a result of the relativity of time and the necessity of using the time as reckoned in the particle’s inertial frame of reference. I want to be clear that I think that it is neither the relativity of mass nor the relativity of time that prevents charged particles from exceeding the speed of light. I claim that it is the counterforce provided by the Doppler-shifted photons that prevent charged particles from exceeding the speed of light. The only time that is relevant is that reckoned by the observer doing the experiment (not the time of the particle in the experiment nor the time of an non-existent aether).
There have been a number of comments that suggest that light/photons/electromagnetic waves are mass-less and thus do not have momentum. They do. J. H. Pointing described light pressure in The Pressure of Light (Society for Promoting Christian Knowledge, London, 1910). Here at Cornell University, E. F. Nichols and G. F Hull measured the pressure of radiation (Physical Review 17: 26-50, 91-104, 1903). In 1908, Johannes Stark characterized the momentum of photons as h⁄λ (J. Stark, Neue Beobachtungen an Kanalstrahlen in Beziehung zur Lichtquantenhypothese, Verh d. Deuschen Physicalischen Gesellschaft 10:713-725, 1908) and in 1917 Einstein used the momentum of photons to craft his Quantum Theory of Radiation and Atomic Processes (A. Einstein, 1917, in The World of the Atom, eds. H.A. Boorse, L. Motz, Basic Books, New York 1966, p. 888-901). The Compton and Inverse Compton effects are best described by the exchange of momentum between photons and charged particles. I want to be clear in stating that light/photons/ electromagnetic waves have momentum.

I also refer you to my book, Light and Video Microscopy (Elsevier Academic Press, Amsterdam, 2009 where all royalties go to Habitat for Humanity) in which I describe the use of optical tweezers to probe the mechanical nature of cells (p. 199). In the appendix of this book, I present a model of the photon (pp. 277-284). In this model, the photon, which has momentum, is not an elementary particle, but a composite made of two particles such that the sum of the masses equal zero.
There have been a number of comments that the interaction between a photon and an atom is conservative and that the particle should not change its velocity after the interaction. This is only true under the assumption that there is no friction. I think I have clearly showed that, as a result of the Doppler effect, at any temperature greater than absolute zero, the radiation that particles move through will result in a counterforce, friction, a viscous force or a dissipation of energy; however you wish to quantify it. Book One of the Principia, which presents Newton’s Three Laws, assumes that there is no friction. Book Two, which is, rarely read, cited or contemplated, discusses that in the real world there is friction that must be taken into consideration. If Book Two had not been forgotten, it would have served as the basis for understanding motion at velocities close to the speed of light. Some comments state that according to my analysis, all particles will slow down and according to my theory, Newton’s First Law would not be absolutely correct. I believe that Newton’s First Law is only absolutely valid at absolute zero, which is unattainable according to the Third Law of Thermodynamics ( [link to th-www.if.uj.edu.pl] reference 131). Some comments state that according to my theory particles could exceed the speed of light at absolute zero. My theory however, is based on the Laws of Thermodynamics that state that absolute zero is unattainable.
There are comments that my theory applies only to electrons. This is not true it applies to any charged particle, any particle that is composed of charged quarks, and any neutral particle that has a magnetic moment (neutron or neutrino (footnote 132 in [link to th-www.if.uj.edu.pl] That is, it applies to any particle that interacts with electromagnetic radiation.

There have been comments concerning the fact that I am a biologist and that I am using that experience to help me see physics differently. In order to find more information of the historical and productive relationships between biology, chemistry and physics, I refer you to my book: Plant Cell Biology from Astronomy to Zoology (Elsevier Academic Press, Amsterdam, 2009—all royalties go to the Profile in Courage Award given by the John F. Kennedy Library Foundation) and to my paper on charged particles ( [link to th-www.if.uj.edu.pl]

There have been comments on the impact factor of the journals that published my work. If you are wondering why my paper on why charged particles cannot go faster than the speed of light was not published in the Annalen der Physik, the journal that published Einstein’s Special Theory of Relativity and the first journal I submitted my manuscript to, I give you the editor’s review:
Dear Prof. Wayne,

I have discussed you papers with some collegues. It seems to us that the derivations seem correct. We nevertheless prefer not to publish the articles in Annalen der Physik. We suggest to publish them in a different more suitable journal.

Best wishes

Bernhard Kramer
(11/5/08)

Annalen der Physik also rejected my manuscript on the relativity of Simultaneity (which was recently published in the African Physical Review [link to www.aphysrev.org] Here is their response:

Dear Professor Wayne,
I am sorry but this manuscript -- like previous ones submitted to Annalen -- is not acceptable for publication in this journal. You must know that SRT has been treated in numerous theoretical papers and books, and confirmed in many experiments beyond any doubt. I enclose two papers published by us in 2005 which may be of interest for you. Hence I do not see any need for a discussion like the one you are providing.
Best regards
Ulrich Eckern
Editor in Chief
(9/26/09)

I suggested to the editor that the real value of science, according to Richard Feynman, is the freedom to doubt.

I have been called a crank and a crackpot. “The Crackpot Index,” was published by the mathematical physicist John Baez (1998) as an instrument to provide “A simple method for rating potentially revolutionary contributions to physics ( [link to math.ucr.edu] and, in an article commemorating the 100th anniversary of Einstein’s Theory of Special Relativity, theoretical physicist Clifford M. Will (in Einstein 1905-2005, Poincare ́ Seminar 2005, Birkha ̈user Verlag, Basel, 2006) wrote, “we see that the theory has been so thoroughly integrated into the fabric of modern physics that its validity is rarely challenged, except by cranks and crackpots ( [link to physics.wustl.edu] I assure you that I am neither a crackpot nor a crank.

Cornell University and the person in the Press Relations Office who wrote the press release and well as Acta Physica Polonica B and the reviewers of my paper have been attacked in various posts. It is possible that given the probability of being attacked for supporting and publishing something so different they have showed courage and a certain amount of charity. I thank them.
 Quoting: RandyWayne


The only "crackpots" are those who take scientific theories and turn them into beliefs, disregarding observations and new data. Of course they wouldn't accept anything that challenges theories which have been the basis of their life's work, because it would mean they spent their lives doing something based upon a false theory.
Anonymous Coward
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11/29/2010 07:15 PM
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Re: "Consequently, light itself prevents charged particles from moving faster than the speed of light."
I would say this guys needs some sort of experiment to validate his hypothesis, Like Einstein showed very ellegantly the curving of star light during an eclipse. Purely theoretical work will alwais be looked at with the appropriate skepticism.
Anonymous Coward
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11/29/2010 09:29 PM
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Re: "Consequently, light itself prevents charged particles from moving faster than the speed of light."
I have proposed an experiment in the Acta Physica Polonica B paper that can distinguish between my theory and the Special Theory of Relativity. Since the photon density is greater at higher temperatures, the velocity-dependent counterforce that results from the Doppler effect at a given velocity will also be greater. Therefore the impulse needed to accelerate an electron to a given velocity will be greater in an accelerator at 300 K than in an accelerator at 3 K.

According to the Special Theory of Relativity, there will be no effect of temperature on the impulse needed to accelerate an electron to a given velocity.
RandyWayne
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11/29/2010 09:30 PM
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Re: "Consequently, light itself prevents charged particles from moving faster than the speed of light."
I have proposed an experiment in the Acta Physica Polonica B paper that can distinguish between my theory and the Special Theory of Relativity. Since the photon density is greater at higher temperatures, the velocity-dependent counterforce that results from the Doppler effect at a given velocity will also be greater. Therefore the impulse needed to accelerate an electron to a given velocity will be greater in an accelerator at 300 K than in an accelerator at 3 K.

According to the Special Theory of Relativity, there will be no effect of temperature on the impulse needed to accelerate an electron to a given velocity.

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