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FQXi FORUM

July 4, 2015

CATEGORY:
FQXi Essay Contest - Spring, 2012
[back]

TOPIC: Taking the Mechanics out of Space-Time and Putting it Back Into Quantum Mechanics by Randy Wayne [refresh]

TOPIC: Taking the Mechanics out of Space-Time and Putting it Back Into Quantum Mechanics by Randy Wayne [refresh]

One of the basic postulates of fundamental physics that is ingrained in our thinking is that the photon is an elementary particle that can be represented as a mathematical point, with spin-1, but without radial extension. According to General Relativity, gravity influences the motion of light, not by acting on light itself, but by directly acting on a dynamic four-dimensional space-time continuum through which the point-like photon passively propagates. Here I present an alternative explanation of the effect of gravity on light based on the rotational as well as translational motions of the photon. By taking the mechanics out of the description of space-time, and putting it back into the quantum mechanics of light, I show that the deflection of starlight, the experimentum crucis in favor of General Relativity over Newtonian mechanics, can be explained using Newton’s Law of Gravitation, Euclidean space and Newtonian time. This treatment has the advantage over General Relativity in encompassing the dynamical properties of photons that were neither known to Newton nor employed by Einstein. This interpretation, which is also applicable to the understanding of gravitational lensing, the Global Positioning System, the gravitational red shift, and black holes, may lead to a deep or “ultimate” understanding of the nature of reality.

Randy Wayne earned a PhD in Plant Cell Biology at the University of Massachusetts. Wayne is an Associate Professor in the Department of Plant Biology at Cornell University. He is a biophysical plant cell biologist known for his work on membrane biology, cell motility, and how plant cells perceive and respond to light and gravity. More recently, he has been working on the physical nature of light and gravity from the unique perspective of a biophysical plant cell biologist. He is the author of "Light and Video Microscopy" and "Plant Cell Biology: From Astronomy to Zoology," both published by Elsevier.

Dear Randy Wayne,

You've chosen a very significant topic, of obvious importance to both physics and biology. I agree with your insistence on finite size, non-zero momentum and ever-present spin that represents rotational motion.

I further agree with your equipartition of rotational and translational energy, and call your attention to the reduced equation [ curl C ~ p ] in my essay, The Nature of the Wave Function, where curl C is the rotational circulation of the C-field and p is the particle momentum. Observe that, as in your model, the rotational term on the left balances the translational term on the right. If I may suggest it, the photon 'particle' plus the local 'wave' component -- always present -- might be analogous to your 'composite' photon. I did not find an exact description of the composition of the photon and I hope you might consider the C-field as the second component in your model.

I am extremely impressed with your derivation of the 'double deflection' which appears to be unique. Congratulations.

I hope you will read my essay in the context of your own and will comment on my thread.

Best of luck in the contest,

Edwin Eugene Klingman

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You've chosen a very significant topic, of obvious importance to both physics and biology. I agree with your insistence on finite size, non-zero momentum and ever-present spin that represents rotational motion.

I further agree with your equipartition of rotational and translational energy, and call your attention to the reduced equation [ curl C ~ p ] in my essay, The Nature of the Wave Function, where curl C is the rotational circulation of the C-field and p is the particle momentum. Observe that, as in your model, the rotational term on the left balances the translational term on the right. If I may suggest it, the photon 'particle' plus the local 'wave' component -- always present -- might be analogous to your 'composite' photon. I did not find an exact description of the composition of the photon and I hope you might consider the C-field as the second component in your model.

I am extremely impressed with your derivation of the 'double deflection' which appears to be unique. Congratulations.

I hope you will read my essay in the context of your own and will comment on my thread.

Best of luck in the contest,

Edwin Eugene Klingman

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Dear Edwin Eugene Klingman,

Thank you for your comment and I enjoyed your essay on the Nature of the Wave Function. I also wish you good luck in the essay contest.

The best published exposition of my model of the photon (mutatis mutandis) is in Appendix II (A Microscopist's Model of the Photon) of my book, "Light and Video Microscopy" (Elsevier, 2009), which you can preview for the most part using Google Books. Your model and my model of light describe a photon that has extension (a fundamental aspect of reality) and spin (a physical and real rotational motion).

We differ in that you describe the photon as an elementary particle (a one-body problem with its physical wave), and I describe the photon as a composite particle (spin 1 boson) composed of two conjugate particles (spin 1/2 fermions), one composed of matter and the other composed of antimatter. The two conjugate particles oscillate both longitudinally and rotationally.

Since I ascribe a positive mass to matter and a negative mass to antimatter, the total mass of the photon in free space is zero. In order for their angular momenta add up to h-bar, the two conjugate particles must rotate with opposite senses. Since a composite particle composed of conjugate particles of positive and negative mass would accelerate to an infinite velocity, I assign an equal and opposite charge to each conjugate particle to restrain the velocity of the midpoint of the congugate photon to the speed of light (thanks to the electrical permittivity and magnetic permeability of the vacuum).

The combination of charge and mass in the moving particles produces a linearly polarized electric field as well as a "circular" magnetic field (or circulation) as in your model. However, in my model of the complex photon, various combinations of mass and charge are allowed, the only restraint being that the combination must produce a mass-less and neutral composite photon. Thus the composite photon can be made out of conjugate particles with (+m+q) and (-m-q) or conjugate particles with (+m-q) and (-m+q). (Note that the positive signs in front of the mass and charge are not reproduced in this thread and are assumed). Consequently, my model of the photon allows for the possiblity of a composite photon with a right-handed magnetic field (circulation) or a left-handed magnetic field (circulation) whereas your model predicts exclusively a left handed circulation.

It would be wonderful to see your wave function applied to each of the conjugate particles as well as the sum of the two. The wave equation for the magnetic field (circulation) would have to take into consideration the the velocities (and accelerations) of the conjugate particles oscillating in three dimensions as well as the drift velocity of the particles. So far, this has been beyond my level of competence. Again, I wish you well with the essay contest.

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Thank you for your comment and I enjoyed your essay on the Nature of the Wave Function. I also wish you good luck in the essay contest.

The best published exposition of my model of the photon (mutatis mutandis) is in Appendix II (A Microscopist's Model of the Photon) of my book, "Light and Video Microscopy" (Elsevier, 2009), which you can preview for the most part using Google Books. Your model and my model of light describe a photon that has extension (a fundamental aspect of reality) and spin (a physical and real rotational motion).

We differ in that you describe the photon as an elementary particle (a one-body problem with its physical wave), and I describe the photon as a composite particle (spin 1 boson) composed of two conjugate particles (spin 1/2 fermions), one composed of matter and the other composed of antimatter. The two conjugate particles oscillate both longitudinally and rotationally.

Since I ascribe a positive mass to matter and a negative mass to antimatter, the total mass of the photon in free space is zero. In order for their angular momenta add up to h-bar, the two conjugate particles must rotate with opposite senses. Since a composite particle composed of conjugate particles of positive and negative mass would accelerate to an infinite velocity, I assign an equal and opposite charge to each conjugate particle to restrain the velocity of the midpoint of the congugate photon to the speed of light (thanks to the electrical permittivity and magnetic permeability of the vacuum).

The combination of charge and mass in the moving particles produces a linearly polarized electric field as well as a "circular" magnetic field (or circulation) as in your model. However, in my model of the complex photon, various combinations of mass and charge are allowed, the only restraint being that the combination must produce a mass-less and neutral composite photon. Thus the composite photon can be made out of conjugate particles with (+m+q) and (-m-q) or conjugate particles with (+m-q) and (-m+q). (Note that the positive signs in front of the mass and charge are not reproduced in this thread and are assumed). Consequently, my model of the photon allows for the possiblity of a composite photon with a right-handed magnetic field (circulation) or a left-handed magnetic field (circulation) whereas your model predicts exclusively a left handed circulation.

It would be wonderful to see your wave function applied to each of the conjugate particles as well as the sum of the two. The wave equation for the magnetic field (circulation) would have to take into consideration the the velocities (and accelerations) of the conjugate particles oscillating in three dimensions as well as the drift velocity of the particles. So far, this has been beyond my level of competence. Again, I wish you well with the essay contest.

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Hi Randy,

Thanks for your response. You note that I "describe the photon as an elementary particle (a one-body problem with its physical wave)". I'm not sure I would characterize it as a 'particle' so much as a 'localized energy density' that is represented by a Poynting vector. It is the momentum of the photon (however constituted) that sources the C-field circulation. This gravito-magnetic (C-field) circulation due to the photon momentum is *in addition to* the electro-magnetic circulation due to the charge.

Thanks for the additional details of your photon model. I intend to give some consideration to your model.

Edwin Eugene Klingman

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Thanks for your response. You note that I "describe the photon as an elementary particle (a one-body problem with its physical wave)". I'm not sure I would characterize it as a 'particle' so much as a 'localized energy density' that is represented by a Poynting vector. It is the momentum of the photon (however constituted) that sources the C-field circulation. This gravito-magnetic (C-field) circulation due to the photon momentum is *in addition to* the electro-magnetic circulation due to the charge.

Thanks for the additional details of your photon model. I intend to give some consideration to your model.

Edwin Eugene Klingman

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In case it was not clear from my above comment, the left-handed C-field circulation is due to the photon momentum, and is independent of the electro-magnetic (B-field) circulation which in your model is induced by charges. I am uncertain how to handle your negative mass -- my first inclination would be to avoid negative momentum.

Edwin Eugene Klingman

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Edwin Eugene Klingman

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Dear Randy Wayne!

I am sorry. I apologize for my poor English.

Very interesting read your article.

In my article, I show that negative mass(energy) provides an explanation for dark matter and dark energy.

Article : Negative mass and negative energy

Computer simulation on negative mass

If you read my essay, I will be very happy^^*

Have a Nice day!

--- Hyoyoung Choi

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I am sorry. I apologize for my poor English.

Very interesting read your article.

In my article, I show that negative mass(energy) provides an explanation for dark matter and dark energy.

Article : Negative mass and negative energy

Computer simulation on negative mass

If you read my essay, I will be very happy^^*

Have a Nice day!

--- Hyoyoung Choi

report post as inappropriate

For the observation or evidence of negative mass(energy)

In 1998, an observation by both the HSS team and SCP team obtained a negative mass density from inspected field equations over 70years.(field eq. has a Lamda=0)

SCP(Supernova Cosmology Project) team : If Lamda=0, Omega_M= - 0.4(±0.1)

http://arxiv.org/abs/astro-ph/9805201 refer to 7P

HSS(The High-z Supernova Search) team : If Lamda=0, Omega_M = - 0.38(±0.22)

http://arxiv.org/abs/astro-ph/9805201 refer to 14P

However, the two teams which judged that negative mass and negative energy level could not exist in our universe based on "the problem of the transition of the energy level of minus infinity" and they instead revised the field equation by inserting the cosmological constant.

We must to know that not the equation has disposed the value, but our thought disposed the value.

Moreover, we considered vacuum energy as the source of cosmological constant Lamda, but the current result of calculation shows 10^{120}, which is unprecedented even in the history of Physics.

However, if "the problem of the transition of the energy level of minus infinity" does not occur, and thus negative and positive mass can coexist, what would happen?

It is well known that a cosmological constant can respond to the negative mass density.

p_{eff} = -Lamda/4piG

Lamda is positive, so p_{eff} is negative.

Please view to my article and simulation video

report post as inappropriate

In 1998, an observation by both the HSS team and SCP team obtained a negative mass density from inspected field equations over 70years.(field eq. has a Lamda=0)

SCP(Supernova Cosmology Project) team : If Lamda=0, Omega_M= - 0.4(±0.1)

http://arxiv.org/abs/astro-ph/9805201 refer to 7P

HSS(The High-z Supernova Search) team : If Lamda=0, Omega_M = - 0.38(±0.22)

http://arxiv.org/abs/astro-ph/9805201 refer to 14P

However, the two teams which judged that negative mass and negative energy level could not exist in our universe based on "the problem of the transition of the energy level of minus infinity" and they instead revised the field equation by inserting the cosmological constant.

We must to know that not the equation has disposed the value, but our thought disposed the value.

Moreover, we considered vacuum energy as the source of cosmological constant Lamda, but the current result of calculation shows 10

However, if "the problem of the transition of the energy level of minus infinity" does not occur, and thus negative and positive mass can coexist, what would happen?

It is well known that a cosmological constant can respond to the negative mass density.

p

Lamda is positive, so p

Please view to my article and simulation video

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Dear Hyoyoung Choi,

I think that your thoughts on negative mass are very reasonable and well presented in your essay. Good luck in the contest. Your graphics were also very illustrative. Physics requires that some quantities be positive and some be negative. It seems to me that having positive and negative mass, along with positive and negative charge, and north and south magnetism provides the more realistic and testable symmetry than asserting that mass can only be positive and introducing the negative sign in terms of time (e.g. Feynman's idea that antimatter is equivalent to matter going backwards in time). I have recently published a couple papers on negative mass in the Turkish Journal of Physics (Thermodynamics of Negative Mass and Thermodynamics of Positive Mass). In one paper (Negative Mass and Antimatter), I identify negative mass with antimatter.

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I think that your thoughts on negative mass are very reasonable and well presented in your essay. Good luck in the contest. Your graphics were also very illustrative. Physics requires that some quantities be positive and some be negative. It seems to me that having positive and negative mass, along with positive and negative charge, and north and south magnetism provides the more realistic and testable symmetry than asserting that mass can only be positive and introducing the negative sign in terms of time (e.g. Feynman's idea that antimatter is equivalent to matter going backwards in time). I have recently published a couple papers on negative mass in the Turkish Journal of Physics (Thermodynamics of Negative Mass and Thermodynamics of Positive Mass). In one paper (Negative Mass and Antimatter), I identify negative mass with antimatter.

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Dear Randy Wayne!

I am sorry. I apologize for my poor English.

Thank you very much!

I am glad to read your paper ("Symmetry and the order of events in time. A proposed identity of negative mass with antimatter")

I really happy because of read your paper!

I have a background paper on my essay.

=======

We set up each model from the birth of universe to the present, and calculated gravitational potential energy using computer simulation in each level.

As a result, we could verify that "pair creation model of negative energy and positive energy" explains inflation of the early universe and decelerating expansion, and present accelerating expansion in time series.

This simulation is showing incredible results.

It not only explains the total energy of the universe, flatness, and the essence (Total zero energy, pair creation of negative energy and positive energy) of the process of birth of the universe, but it explains inflation, decelerating expansion in the early stage, accelerating expansion in the late stage, and dark matter through the only term, negative energy. Moreover, this negative energy is one that is essentially required by the law of energy conservation.

Paper : The change of Gravitational Potential Energy and Dark Energy in the Zero Energy Universe.

http://vixra.org/abs/1110.0019

=========

Have a nice day!

--- Hyoyoung Choi

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I am sorry. I apologize for my poor English.

Thank you very much!

I am glad to read your paper ("Symmetry and the order of events in time. A proposed identity of negative mass with antimatter")

I really happy because of read your paper!

I have a background paper on my essay.

=======

We set up each model from the birth of universe to the present, and calculated gravitational potential energy using computer simulation in each level.

As a result, we could verify that "pair creation model of negative energy and positive energy" explains inflation of the early universe and decelerating expansion, and present accelerating expansion in time series.

This simulation is showing incredible results.

It not only explains the total energy of the universe, flatness, and the essence (Total zero energy, pair creation of negative energy and positive energy) of the process of birth of the universe, but it explains inflation, decelerating expansion in the early stage, accelerating expansion in the late stage, and dark matter through the only term, negative energy. Moreover, this negative energy is one that is essentially required by the law of energy conservation.

Paper : The change of Gravitational Potential Energy and Dark Energy in the Zero Energy Universe.

http://vixra.org/abs/1110.0019

=========

Have a nice day!

--- Hyoyoung Choi

report post as inappropriate

Dear

Very interesting to see your essay.

Perhaps all of us are convinced that: the choice of yourself is right!That of course is reasonable.

So may be we should work together to let's the consider clearly defined for the basis foundations theoretical as the most challenging with intellectual of all of us.

Why we do not try to start with a real challenge is very close and are the focus of interest of the human science: it is a matter of mass and grain Higg boson of the standard model.

Knowledge and belief reasoning of you will to express an opinion on this matter:

You have think that: the Mass is the expression of the impact force to material - so no impact force, we do not feel the Higg boson - similar to the case of no weight outside the Earth's atmosphere.

Does there need to be a particle with mass for everything have volume? If so, then why the mass of everything change when moving from the Earth to the Moon? Higg boson is lighter by the Moon's gravity is weaker than of Earth?

The LHC particle accelerator used to "Smashed" until "Ejected" Higg boson, but why only when the "Smashed" can see it,and when off then not see it ?

Can be "locked" Higg particles? so when "released" if we do not force to it by any the Force, how to know that it is "out" or not?

You are should be boldly to give a definition of weight that you think is right for us to enjoy, or oppose my opinion.

Because in the process of research, the value of "failure" or "success" is the similar with science. The purpose of a correct theory be must is without any a wrong point ?

Glad to see from you comments soon,because still have too many of the same problems.

Regards !

Hải.Caohoàng of THE INCORRECT ASSUMPTIONS AND A CORRECT THEORY

August 23, 2012 - 11:51 GMT on this essay contest.

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Very interesting to see your essay.

Perhaps all of us are convinced that: the choice of yourself is right!That of course is reasonable.

So may be we should work together to let's the consider clearly defined for the basis foundations theoretical as the most challenging with intellectual of all of us.

Why we do not try to start with a real challenge is very close and are the focus of interest of the human science: it is a matter of mass and grain Higg boson of the standard model.

Knowledge and belief reasoning of you will to express an opinion on this matter:

You have think that: the Mass is the expression of the impact force to material - so no impact force, we do not feel the Higg boson - similar to the case of no weight outside the Earth's atmosphere.

Does there need to be a particle with mass for everything have volume? If so, then why the mass of everything change when moving from the Earth to the Moon? Higg boson is lighter by the Moon's gravity is weaker than of Earth?

The LHC particle accelerator used to "Smashed" until "Ejected" Higg boson, but why only when the "Smashed" can see it,and when off then not see it ?

Can be "locked" Higg particles? so when "released" if we do not force to it by any the Force, how to know that it is "out" or not?

You are should be boldly to give a definition of weight that you think is right for us to enjoy, or oppose my opinion.

Because in the process of research, the value of "failure" or "success" is the similar with science. The purpose of a correct theory be must is without any a wrong point ?

Glad to see from you comments soon,because still have too many of the same problems.

Regards !

Hải.Caohoàng of THE INCORRECT ASSUMPTIONS AND A CORRECT THEORY

August 23, 2012 - 11:51 GMT on this essay contest.

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Dear Randy,

I do not understand why in your formula (8) there is not total kinetic energy but only 1/4 of it? In theory of gravitation in kinetic energy also rest energy is included which is absent in your calculation.

Sergey Fedosin

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I do not understand why in your formula (8) there is not total kinetic energy but only 1/4 of it? In theory of gravitation in kinetic energy also rest energy is included which is absent in your calculation.

Sergey Fedosin

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Dear Sergey,

The orbital energy is only composed of the total kinetic energy and the total gravitational binding energy when the orbiting body is a translating corpuscle (or cannonball or planet) whose translational kinetic energy is equal to (or approximated by) its total kinetic energy. This is true of a Newtonian light corpuscle and using the total kinetic energy in this formula would give a "single deflection."

When some of the total kinetic energy (like in a rotating photon or a bullet) is involved in rotational motion, then the rotational kinetic energy component must be subtracted from the photon's or the bullet's total kinetic energy when determining the orbital energy.

In the case of a photon whose total energy is known and that has a spinning motion, we only use the translational part of the total kinetic energy when we calculate the orbital energy. If we assume that the total kinetic energy is equipartioned between the translational energy and the rotational energy, only one half of the total kinetic energy should be used to calculate the orbital energy. This results in a "double deflection." The fact that Eddington observed a "double deflection" can be interpreted to mean that the photon is not just a spin-1 geometrical point, but a real entity with extension and rotational motion. This is consistent with the interpretation of the selection rules of atomic spectra proposed by Arnold Sommerfeld.

By assuming that the photon has mechanical properties like translational motion and rotational motion, there is no need to look at space and time as a four-dimensional spacetime continuum which has the property of being able to be warped by matter.

Thanks for your question and I hope that this explanation helps.

Thanks,

Randy

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The orbital energy is only composed of the total kinetic energy and the total gravitational binding energy when the orbiting body is a translating corpuscle (or cannonball or planet) whose translational kinetic energy is equal to (or approximated by) its total kinetic energy. This is true of a Newtonian light corpuscle and using the total kinetic energy in this formula would give a "single deflection."

When some of the total kinetic energy (like in a rotating photon or a bullet) is involved in rotational motion, then the rotational kinetic energy component must be subtracted from the photon's or the bullet's total kinetic energy when determining the orbital energy.

In the case of a photon whose total energy is known and that has a spinning motion, we only use the translational part of the total kinetic energy when we calculate the orbital energy. If we assume that the total kinetic energy is equipartioned between the translational energy and the rotational energy, only one half of the total kinetic energy should be used to calculate the orbital energy. This results in a "double deflection." The fact that Eddington observed a "double deflection" can be interpreted to mean that the photon is not just a spin-1 geometrical point, but a real entity with extension and rotational motion. This is consistent with the interpretation of the selection rules of atomic spectra proposed by Arnold Sommerfeld.

By assuming that the photon has mechanical properties like translational motion and rotational motion, there is no need to look at space and time as a four-dimensional spacetime continuum which has the property of being able to be warped by matter.

Thanks for your question and I hope that this explanation helps.

Thanks,

Randy

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After studying about 250 essays in this contest, I realize now, how can I assess the level of each submitted work. Accordingly, I rated some essays, including yours.

Cood luck.

Sergey Fedosin

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Cood luck.

Sergey Fedosin

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If you do not understand why your rating dropped down. As I found ratings in the contest are calculated in the next way. Suppose your rating is and was the quantity of people which gave you ratings. Then you have of points. After it anyone give you of points so you have of points and is the common quantity of the people which gave you ratings. At the same time you will have of points. From here, if you want to be R2 > R1 there must be: or or In other words if you want to increase rating of anyone you must give him more points then the participant`s rating was at the moment you rated him. From here it is seen that in the contest are special rules for ratings. And from here there are misunderstanding of some participants what is happened with their ratings. Moreover since community ratings are hided some participants do not sure how increase ratings of others and gives them maximum 10 points. But in the case the scale from 1 to 10 of points do not work, and some essays are overestimated and some essays are drop down. In my opinion it is a bad problem with this Contest rating process. I hope the FQXI community will change the rating process.

Sergey Fedosin

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Sergey Fedosin

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Dear Randy Wayne,

A very impressive essay. Thank you for contributing it.

I hope you can read my essay "Rethink the Double Slit Experiment," which also discuss the scattering of particle with space time.

Yours,

Ke Xiao

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A very impressive essay. Thank you for contributing it.

I hope you can read my essay "Rethink the Double Slit Experiment," which also discuss the scattering of particle with space time.

Yours,

Ke Xiao

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Dear Randy Wayne,

I have read your essay and I am surprised that it is languishing relatively low down in the ratings with few comments. Perhaps because of your biologist biography. Or maybe because you are questioning the curvature of space-time from the outset. It was very readable until the maths (which I'll admit I skimmed over, -my loss.)

You are making a very important point that curved space-time is not necessary to account for the observations that have been made.I don't feel sufficiently knowledgeable to evaluate the model you put forward. However I'm thinking that though it might account for the observation of gravity I don't really understand how it could also give rise to the experienced force of gravity, but maybe that is a different consideration.

I also say that curvature of space-time is not foundational in my essay. My suggestion is that apparent curvature is due to an affect upon the 'pre-space-time' environment, due to unaccounted for motion of the masses (not the nature of individual photons alone).Though my very brief mention of Joy Christian's recent work and Roger Penrose' quaternion description of the light Cone was indicating that the way in which light propagates through the 'pre-space' time environment has a very important part to play in what space-time reality is observed where and when.

It was interesting to read your point of view. Regards Georgina

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I have read your essay and I am surprised that it is languishing relatively low down in the ratings with few comments. Perhaps because of your biologist biography. Or maybe because you are questioning the curvature of space-time from the outset. It was very readable until the maths (which I'll admit I skimmed over, -my loss.)

You are making a very important point that curved space-time is not necessary to account for the observations that have been made.I don't feel sufficiently knowledgeable to evaluate the model you put forward. However I'm thinking that though it might account for the observation of gravity I don't really understand how it could also give rise to the experienced force of gravity, but maybe that is a different consideration.

I also say that curvature of space-time is not foundational in my essay. My suggestion is that apparent curvature is due to an affect upon the 'pre-space-time' environment, due to unaccounted for motion of the masses (not the nature of individual photons alone).Though my very brief mention of Joy Christian's recent work and Roger Penrose' quaternion description of the light Cone was indicating that the way in which light propagates through the 'pre-space' time environment has a very important part to play in what space-time reality is observed where and when.

It was interesting to read your point of view. Regards Georgina

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Dear Georgina,

Thank you very much for your surprise that I am sitting in the back of the "science bus"...perhaps as a result of my biologist biography.

Thanks,

randy

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Thank you very much for your surprise that I am sitting in the back of the "science bus"...perhaps as a result of my biologist biography.

Thanks,

randy

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It might also have just been chance. As there are so many entries this year. I wonder what is most influential on potential readers choice?...Title, abstract, biography, topic, appearance eg. size of text or number of formulae, prior acquaintance with author, or similar ideas, public profile, participation, reciprocation, current ranking, other's comments?It could be useful information! (Some competitors have complained about perceived social influences upon an essay's ranking.) Whatever the reason its a pity you didn't get more feedback : )

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