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January 21, 2018

CATEGORY:
The Nature of Time Essay Contest (2008)
[back]

TOPIC: A Derivation of the Speed of Light Postulate by Armin Nikkhah Shirazi [refresh]

TOPIC: A Derivation of the Speed of Light Postulate by Armin Nikkhah Shirazi [refresh]

The speed of light postulate, one of the two fundamental assumptions upon which the special theory of relativity (SR) is based, still seems as mysterious today as when it was first introduced. This paper presents a derivation of the postulate based on three axioms:1) A definition of motion in proper time that captures most of the mathematical aspects of SR except for the speed of light postulate itself, 2) An axiom concerning the nature of the existence of entities which do not age, and finally 3) an axiom which defines existence in a spacetime to be transitive. The second axiom is motivated by an apparent paradox inherent in the structure of SR, called the existence paradox, pertaining to entities which do not age. The duration of existence of such entities in their proper frame is precisely equal to zero, which is consistent with non-existence, and inconsistent with the empirical evidence for the existence of such entities. The resolution of this apparent paradox is guided by a quasi-philosophical principle, called the Principle of least Speciality. The second axiom presents a resolution to the existence paradox that follows this principle while at the same time providing the essence of the explanation for the speed of light postulate. Given the three axioms, it is straightforward to show that the speed of light postulate is a logical consequence. Furthermore, this framework implies a direct experimentally testable prediction that is, according to currently prevailing views, unexpected.

Armin Nikkhah Shirazi is a physics and philosophy student at the University of Michigan, Ann Arbor by day and a Midnight Pharmacist by night. One of his greatest passions is contemplating fundamental questions in a range of subjects. He is also an amateur pianist and composer, having composed over 75 musical works.

Being able to see my abstract as any other potentially interested reader will see it here has caused me to notice that it could easily give the impression that my derivation violates Occam's razor (i.e. one can reasonably ask why it is necessary to use three axioms to derive one postulate) and therefore be dismissed altogether.

I would like to take this space to explain why this impression is false. If one invests the time to read the paper, one will find that the derivation leads not just to the speed of light postulate, but to a framework that is equivalent to SR, with one exception: An unambiguous explanation for the speed of light postulate is built in that is completely absent in the standard formulation of SR, and this explanation leads to a definite experimental prediction which would be unexpected in the standard form. Therefore this derivation is not simply a tautological chain of reasoning presented from a novel starting point (which would violate Occam's razor), but really a "deeper" framework, provided the experimental prediction fails to be falsified (because the prediction is that of a null-result, it can never be be confirmed with absolute certainty).

I would like to take this space to explain why this impression is false. If one invests the time to read the paper, one will find that the derivation leads not just to the speed of light postulate, but to a framework that is equivalent to SR, with one exception: An unambiguous explanation for the speed of light postulate is built in that is completely absent in the standard formulation of SR, and this explanation leads to a definite experimental prediction which would be unexpected in the standard form. Therefore this derivation is not simply a tautological chain of reasoning presented from a novel starting point (which would violate Occam's razor), but really a "deeper" framework, provided the experimental prediction fails to be falsified (because the prediction is that of a null-result, it can never be be confirmed with absolute certainty).

Armin,

You are the first person who has welcomed some criticism that shows the strength of your character.

I think the lack of comments you have received is due to mathematical derivations. A real physics argument requires the reader to work through the derivations and is time consuming. Maybe our essays would have been discussed more if we avoided mathematics and wrote about the applications of LQG, string theory and the multiverse on human consciousness. Maybe we were mistaken and this contest had nothing to do with time.

Reading your essay reminded me of the Einstein-Lorentz clock I did find a video that explains it well:

http://www.learner.org/resources/series42.html#

It is episode 42, "The Lorentz Transformation" about 11:45 into the video. The series is very 80s and is an introduction to physics. You do have to register to watch the videos but it is free and requires only an email address.

The "photon clock" is a photon that is reflected between two mirrors. The clock is put in motion and an observer at rest views the path of the photon as the hypotenuse of a right triangle. Gamma is then derived using the Pythagorean theorem. Axiom I can be derived by the same argument. If you are using a similar Lorentz derivation it would seem C is fixed because the two mirrors are a fixed distance apart. Indeed you do need a proof for the "triangle becoming a line". I would start with the law of cosines and see where it took me.

In equation (1) you wrote V as the magnitude of a constant velocity. I think you were too careful here. V can be a vector because V^2 is the scalar (dot) product which gives a scalar. Similarly (1) can be rewritten so Vt is Vt^2 and a scalar product too.

Axiom II seems like a stretch but if it is true then Axiom III is possible, it looks identical to the Zeroth law of thermodynamics.

I found some mathematical steps hard to follow because my relativity is rusty. I had to remember that

dTau / dt = dt / gamma.

Photons are described in two extreme branches of physics, special relativity and quantum mechanics. Feynman does a great job explaining the photon and its properties:

http://vega.org.uk/video/subseries/8

Overall I found your essay very creative. I'm impressed that a double major working a midnight shift had the energy to write such a creative essay. I like that you are both mathematically and musically gifted like Einstein and Pythagoras. Good luck on your finals.

B^2

You are the first person who has welcomed some criticism that shows the strength of your character.

I think the lack of comments you have received is due to mathematical derivations. A real physics argument requires the reader to work through the derivations and is time consuming. Maybe our essays would have been discussed more if we avoided mathematics and wrote about the applications of LQG, string theory and the multiverse on human consciousness. Maybe we were mistaken and this contest had nothing to do with time.

Reading your essay reminded me of the Einstein-Lorentz clock I did find a video that explains it well:

http://www.learner.org/resources/series42.html#

It is episode 42, "The Lorentz Transformation" about 11:45 into the video. The series is very 80s and is an introduction to physics. You do have to register to watch the videos but it is free and requires only an email address.

The "photon clock" is a photon that is reflected between two mirrors. The clock is put in motion and an observer at rest views the path of the photon as the hypotenuse of a right triangle. Gamma is then derived using the Pythagorean theorem. Axiom I can be derived by the same argument. If you are using a similar Lorentz derivation it would seem C is fixed because the two mirrors are a fixed distance apart. Indeed you do need a proof for the "triangle becoming a line". I would start with the law of cosines and see where it took me.

In equation (1) you wrote V as the magnitude of a constant velocity. I think you were too careful here. V can be a vector because V^2 is the scalar (dot) product which gives a scalar. Similarly (1) can be rewritten so Vt is Vt^2 and a scalar product too.

Axiom II seems like a stretch but if it is true then Axiom III is possible, it looks identical to the Zeroth law of thermodynamics.

I found some mathematical steps hard to follow because my relativity is rusty. I had to remember that

dTau / dt = dt / gamma.

Photons are described in two extreme branches of physics, special relativity and quantum mechanics. Feynman does a great job explaining the photon and its properties:

http://vega.org.uk/video/subseries/8

Overall I found your essay very creative. I'm impressed that a double major working a midnight shift had the energy to write such a creative essay. I like that you are both mathematically and musically gifted like Einstein and Pythagoras. Good luck on your finals.

B^2

Hi Brian,

Thank you for your input and suggestions.

If I am not mistaken, Einstein himself used something like the photon clock to derive the Lorentz Transformations. The photon clock argument assumes the speed of light postulate and therefore I could not use it in my derivation. However, once the speed of light postulate is derived, then, it appears to me, one could use the photon...

view entire post

Thank you for your input and suggestions.

If I am not mistaken, Einstein himself used something like the photon clock to derive the Lorentz Transformations. The photon clock argument assumes the speed of light postulate and therefore I could not use it in my derivation. However, once the speed of light postulate is derived, then, it appears to me, one could use the photon...

view entire post

report post as inappropriate

Armin,

I was in the same situation of working full time while taking physics and math classes. Physics and non-physics classes should be weighted differently. Being a full time student in physics is like drinking from a fire hose.

Is the connection between axiom II and quantum the many worlds interpretation?

I'm not so certain that light doesn't have a gravitational field. We know from GR that light is influenced by gravity. Newton tells us that every action has an equal and opposite reaction. The rest mass of a photon is zero, however, the photon does have energy and momentum according to

P = h/lambda

E = hv

My QED and GR is not strong enough to tackle this problem head on but I have thought about it a lot too.

I was in the same situation of working full time while taking physics and math classes. Physics and non-physics classes should be weighted differently. Being a full time student in physics is like drinking from a fire hose.

Is the connection between axiom II and quantum the many worlds interpretation?

I'm not so certain that light doesn't have a gravitational field. We know from GR that light is influenced by gravity. Newton tells us that every action has an equal and opposite reaction. The rest mass of a photon is zero, however, the photon does have energy and momentum according to

P = h/lambda

E = hv

My QED and GR is not strong enough to tackle this problem head on but I have thought about it a lot too.

Armin,

An intriguing and well constructed essay. I think it is interesting how you explore the issue of light having zero spacetime interval.

Regards,

Paul

An intriguing and well constructed essay. I think it is interesting how you explore the issue of light having zero spacetime interval.

Regards,

Paul

Brian,

Yes, I agree that physics classes should have different weight.

wrt your question about axiom II and MWI, in a word, no.

Thank you for raising this issue. I think that conservation of momentum presents the toughest challenge to my idea.

Newton's third law generally does not hold in classical Electrodynamics. If you consider, for instance, two charges q1 and q2...

view entire post

Yes, I agree that physics classes should have different weight.

wrt your question about axiom II and MWI, in a word, no.

Thank you for raising this issue. I think that conservation of momentum presents the toughest challenge to my idea.

Newton's third law generally does not hold in classical Electrodynamics. If you consider, for instance, two charges q1 and q2...

view entire post

Hey Armin,

I have not replied sooner because I have been thinking a lot about this thread and I like where it is going. Your post has given me an idea for an experiment, but first I have one correction.

The full relativistic energy equation is:

E^2 = (M_o)^2 C^4 + P^2 C^2

The rest mass of the photon is zero so the first term above drops out reducing the equation...

view entire post

I have not replied sooner because I have been thinking a lot about this thread and I like where it is going. Your post has given me an idea for an experiment, but first I have one correction.

The full relativistic energy equation is:

E^2 = (M_o)^2 C^4 + P^2 C^2

The rest mass of the photon is zero so the first term above drops out reducing the equation...

view entire post

Hi Brian,

I have no more finals as of today, so I can once again delve into this issue.

Your statements about the relationship between mass and Energy are correct. I am not sure, but it seems to me that you made them in reference to my equivalence principle argument. If so, I should have perhaps pointed out that I was referring to inertial and gravitational rest mass.

This point can sometimes cause confusion because E=mc^2 actually refers to two distinct equations, one involving rest mass and its equivalent rest energy, and the other involving rest mass multiplied by the gamma factor and total energy. Let m_0 be the rest mass and m=gamma *m_0, then

E=(m_0^2 c^4+p^2c^2)^1/2

=(m_0^2 c^4+gamma^2 m_0^2 v^2 c^2)^1/2

=m_0 c^2 (1+gamma^2 (v^2/c^2))^1/2

=m_0 c^2 (1+gamma^2 beta^2)^1/2

=m_0 c^2 (1 +gamma^2 (1-gamma^-2))^1/2

=m_0 c^2 (1 +gamma^2-1)^1/2

=m_0 c^2 gamma

=mc^2

I wrote out all the intermediate steps because skipping steps when it is a pain to read the equations might not be such a great idea. If I misunderstood your point and you already knew this, I apologize, and ask that you tell me to which statement of my previous post you were referring.

I did make a careless statement when I said that the "binding energy is higher" when referring to the photon absorption scenario in my previous post. Since the mass of two particles when bound together is less than the sum of their separate masses, binding energy is negative, hence in that sense I should have actually said that the binding energy is less negative. The net effect, though, that an excited state of a system of bound masses should produce a stronger gravitational field than that of a system of less excited masses should still hold, though.

Also, when I mentioned that perhaps a change in "direction" of the photon might be considered a form of "momentum storage" I was referring to the fact that the direction is given by the wave vector, which is proportional to the photon's momentum. So I was thinking about something analogous to the magnetic force, which can only change the direction of a particle but never accelerate it in its direction of motion.

Interestingly, neutrino oscillations can be regarded as evidence for a finite neutrino mass by a simple argument very similar in spirit to the existence paradox: If neutrinos oscillate, then they must observe themselves to change in their proper frame, therefore they age, therefore they must travel at v

I have no more finals as of today, so I can once again delve into this issue.

Your statements about the relationship between mass and Energy are correct. I am not sure, but it seems to me that you made them in reference to my equivalence principle argument. If so, I should have perhaps pointed out that I was referring to inertial and gravitational rest mass.

This point can sometimes cause confusion because E=mc^2 actually refers to two distinct equations, one involving rest mass and its equivalent rest energy, and the other involving rest mass multiplied by the gamma factor and total energy. Let m_0 be the rest mass and m=gamma *m_0, then

E=(m_0^2 c^4+p^2c^2)^1/2

=(m_0^2 c^4+gamma^2 m_0^2 v^2 c^2)^1/2

=m_0 c^2 (1+gamma^2 (v^2/c^2))^1/2

=m_0 c^2 (1+gamma^2 beta^2)^1/2

=m_0 c^2 (1 +gamma^2 (1-gamma^-2))^1/2

=m_0 c^2 (1 +gamma^2-1)^1/2

=m_0 c^2 gamma

=mc^2

I wrote out all the intermediate steps because skipping steps when it is a pain to read the equations might not be such a great idea. If I misunderstood your point and you already knew this, I apologize, and ask that you tell me to which statement of my previous post you were referring.

I did make a careless statement when I said that the "binding energy is higher" when referring to the photon absorption scenario in my previous post. Since the mass of two particles when bound together is less than the sum of their separate masses, binding energy is negative, hence in that sense I should have actually said that the binding energy is less negative. The net effect, though, that an excited state of a system of bound masses should produce a stronger gravitational field than that of a system of less excited masses should still hold, though.

Also, when I mentioned that perhaps a change in "direction" of the photon might be considered a form of "momentum storage" I was referring to the fact that the direction is given by the wave vector, which is proportional to the photon's momentum. So I was thinking about something analogous to the magnetic force, which can only change the direction of a particle but never accelerate it in its direction of motion.

Interestingly, neutrino oscillations can be regarded as evidence for a finite neutrino mass by a simple argument very similar in spirit to the existence paradox: If neutrinos oscillate, then they must observe themselves to change in their proper frame, therefore they age, therefore they must travel at v

The last part of my previous post got somehow cut off, so here is the rest:

...therefore they must travel at v

...therefore they must travel at v

Hmmm,

it seems that this program does not like the "less than" sign, so here is yet another attempt to complete my post:

...therefore they must travel at v less than c, therefore they have mass.

I think you have an interesting idea there; if I understood you correctly you say that if the reaction products of the same fusion process exit a start at very different times, then this produce observable consequences in the star's gravitational field.

Let me think about this, I'll get back with you.

Armin

it seems that this program does not like the "less than" sign, so here is yet another attempt to complete my post:

...therefore they must travel at v less than c, therefore they have mass.

I think you have an interesting idea there; if I understood you correctly you say that if the reaction products of the same fusion process exit a start at very different times, then this produce observable consequences in the star's gravitational field.

Let me think about this, I'll get back with you.

Armin

Provocative paper and discussion! Very insightful ideas. I think your idea of existence in another continuum is intuitively very satisfying and has great potential. Here are a few questions and comments.

Armin, you state that photons exist in another continuum. You discuss "interactions" as events seperated in space by interval ct. This demonstrates a clear relationship between the two continua which is still difficult to characterize by your axioms. What is the intuitive nature of this relationship?

Also, your mention of the effects of gravitons on photons then assumes that gravitons also exist in the same continuum as photons. If these two "particles" do exist together then we would expect intuitively to see an effect of photons on gravitons. (I thought such an interaction has already been postulated from general relativity by Hawkins, etc? This would be most relevant at the beginning of the universe when photons are postulated to exist in "high density" without matter. I must check.) The lensing of light by massive bodies suggests a spatial location for this interaction. How can this be explained if photons do not exist over any point in space where this interaction would occur?

Lastly, what is the resultant intuitive explanation for the continuum of relative v from 0 to c (max) as related to c itself? This seems to me an equivalence principle in itself that begs an understanding.

Daniel

PS - Thanks for the acknowledgement!

Armin, you state that photons exist in another continuum. You discuss "interactions" as events seperated in space by interval ct. This demonstrates a clear relationship between the two continua which is still difficult to characterize by your axioms. What is the intuitive nature of this relationship?

Also, your mention of the effects of gravitons on photons then assumes that gravitons also exist in the same continuum as photons. If these two "particles" do exist together then we would expect intuitively to see an effect of photons on gravitons. (I thought such an interaction has already been postulated from general relativity by Hawkins, etc? This would be most relevant at the beginning of the universe when photons are postulated to exist in "high density" without matter. I must check.) The lensing of light by massive bodies suggests a spatial location for this interaction. How can this be explained if photons do not exist over any point in space where this interaction would occur?

Lastly, what is the resultant intuitive explanation for the continuum of relative v from 0 to c (max) as related to c itself? This seems to me an equivalence principle in itself that begs an understanding.

Daniel

PS - Thanks for the acknowledgement!

An updated version of this paper which contains some minor corrections can be found at

http://deepblue.lib.umich.edu/handle/2027.42/83152

report post as inappropriate

http://deepblue.lib.umich.edu/handle/2027.42/83152

report post as inappropriate

To anyone who is interested,

I think part of the reason this paper has been essentially ignored the last 3 years is because it must seem hard to see how one of the central assumptions, the one pertaining to the ontological status of photons, fits in with everything we know. recently posted a paper which gives a conceptual discussion of the framework which purports to help 'understand' what the formalism of quantum mechanics tells us about reality, and one of the important aspects of this is that the same assumption about photons is validated from a completely different perspective.

The paper is entitled "A Novel Way of `Understanding' Quantum Mechanics" and can be found either at Deep Blue, the University of Michigan repository at

http://hdl.handle.net/2027.42/86651

or at

http://www.vixra.org/abs/1110.0005

I appreciate any feedback. Thanks,

Armin

I think part of the reason this paper has been essentially ignored the last 3 years is because it must seem hard to see how one of the central assumptions, the one pertaining to the ontological status of photons, fits in with everything we know. recently posted a paper which gives a conceptual discussion of the framework which purports to help 'understand' what the formalism of quantum mechanics tells us about reality, and one of the important aspects of this is that the same assumption about photons is validated from a completely different perspective.

The paper is entitled "A Novel Way of `Understanding' Quantum Mechanics" and can be found either at Deep Blue, the University of Michigan repository at

http://hdl.handle.net/2027.42/86651

or at

http://www.vixra.org/abs/1110.0005

I appreciate any feedback. Thanks,

Armin

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