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FQXi FORUM
June 20, 2013

CATEGORY: FQXi Essay Contest - Spring, 2012 [back]
TOPIC: Newtonian Potential and the Einstein Equivalence Principle by Colin Walker [refresh]

Author Colin Walker wrote on Jun. 15, 2012 @ 12:22 GMT
Essay Abstract

An object in a gravitational field has an associated velocity from the Einstein equivalence principle. Do these velocities add relativistically when objects merge? This possibility leads to a reconsideration of the nature of gravitational potential energy.

Author Bio

I received a B. Math in 1970 from the University of Waterloo. I am retired after solving a lot of equations.

Download Essay PDF File

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Vladimir F. Tamari wrote on Jun. 16, 2012 @ 09:17 GMT
Hello. The equivalence principle equates gravity with acceleration. Here you define a "velocity" of an object with gravitational potential. What if the object experiences thrust and changes its velocity? I am a bit confused. Can you please provide a non-mathematical explanation of the key points of your interesting essay? Thanks.

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Author Colin Walker replied on Jun. 17, 2012 @ 01:43 GMT
Hi Vladimir

Perhaps I can clarify.

Classical gravitational potential can be linked to general relativity

through escape velocity. Einstein was pleased, as he should have been,

to find that the Schwarzschild solution to his field equations gave a

radial escape velocity exactly matching the classical calculation.

Unfortunately, it is the equality of escape velocities that betrays

general relativity's incompletely relativistic origins.

It is important to note that attention in the paper is restricted

to this problem of determining a radial escape velocity This allows

a metric to be associated with the revised potential energy, calculated

by a multiplicative process to match the expected relativistic redshift.

There is an assumption that only gravity (or an equivalent acceleration)

is being considered.

The two processes to be compared can be summarized as follows:

(A) Classical potential energy -> classical escape velocity -> GR metric

(B) Einstein field equations -> Schwarzschild solution -> GR metric

vs

(a) Revised potential energy -> revised escape velocity -> exponential metric

(b) Einstein-???????? equations -> ?????????? solution -> exponential metric

The essay presents (a) to be compared with (A). It begs the question, "what

is (b)?".

By the way, Hamilton and Lisle's River Model of Black Holes (ref 7) gives

an excellent (and entertaining) explanation of the rather obscure but very useful Gullstrand-Painleve coordinates, although I am arguing against black holes.

Hope this helps

Colin

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Vladimir F. Tamari wrote on Jun. 17, 2012 @ 02:54 GMT
Thanks Colin

This is certainly helpful - I should have read your paper more carefully. The reference you gave and your work shows that GR can be reformulated in simpler and more useful ways. I was led to something like this conclusion although in a qualitative way, inspired by Eddington's suggestion regarding a refractive index of a gravitational field where light bends accordingly. After trying to fit in various mechanistic concepts together I concluded that twisting of a space lattice element defines gravitational potential (see my Beautiful Universe pdf ) I was happy to read that twisting is a factor in the metric proposed in your ref [7] . Many thanks.

Vladimir

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Author Colin Walker wrote on Jun. 27, 2012 @ 15:36 GMT
On rereading the essay, I found a point in the Introduction that is needlessly complicated and confusing. The values of z_1 and z_2 referred to after equation (1) were supposed to be defined explicitly as approximations carried over from the derivation of the Einstein equivalence principle (EEP). At least, that was my intention at the time. It may not be obvious that I had assumed z_1 = -v_1 / c and z_2 = -v_2 / c which are approximations. However it would have been far less complicated to formulate the EEP with exact relativistic expressions in the first place.

The exact forms for z_1 and z_2, which can be taken from equation (1), obey the product rule exactly. In retrospect, I should have gone back and started with exact expressions instead of approximations for photon energy and redshift in the EEP. I was concentrating on making a connection to the original EEP and did not see exact expressions as advantageous. Note 2 at the end of the essay is unnecessary since z_1 and z_2 can be taken as exact from the EEP.

Bottom line: z_1 and z_2 can be assumed to be exact expressions for relativistic redshift, not approximations as I had originally intended.

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Vladimir F. Tamari replied on Aug. 22, 2012 @ 01:02 GMT
I could not comment on the exact point you made in your last post, but its wonderful how over time we get to understand our own theories (and sometimes those of others) better and better. Good luck with your researches!

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Pentcho Valev wrote on Jun. 28, 2012 @ 12:06 GMT
Colin,

You write in your essay: "Let us follow the steps of the derivation in the accelerated system which is undergoing uniform acceleration g in the upward direction to mimic gravity. The time required for radiation emitted downward to travel a distance h to meet the rising measurement system is h/c, where c is the speed of light. In that time, the measurement system has acquired a velocity v = gh/c upward."

So if v is low enough, the measured (shifted) frequency is f'=(c+v)/(lambda)=f(1+v/c) and the relativistic corrections are negligible. On the other hand, we have f'=c'/(lambda) where c' is the measured speed of light. It follows that the speed of light varies with the speed of the measurement system (in other words, with the speed of the observer): c'=c+v. Do you agree?

Pentcho Valev pvalev@yahoo.com

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Author Colin Walker replied on Jun. 28, 2012 @ 20:22 GMT
Hi Pentcho,

The Newtonian part of me wants to say yes, but I must say no - I disagree. You have assumed the constancy of wavelength lambda instead of constancy of the speed of light. You can see it in your second equation for frequency which should say f'=c'/(lambda'), referring to an altered wavelength.

You and Newton selected the constancy of wavelength, while Einstein in special relativity selected the speed of light. For the purpose of the essay, I am following special relativity.

Colin

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Pentcho Valev replied on Jun. 28, 2012 @ 22:44 GMT
Colin,

Let us consider the Doppler shift (moving observer) for ANY waves (not just light waves). Initially the observer is stationary and measures the speed of the waves to be c, the frequency f and the wavelength L. Then the observer starts moving towards the wave source with speed v and now measures the frequency to be f'=(c+v)/L. For all waves other than light waves the moving observer also measures the speed of the waves to be c'=c+v and the wavelength L'=L. Only in the case of light waves the situation should be different: the moving observer should measure the speed of the waves to be c'=c and the wavelength to be L'=cL/(c+v). Isn't that suspicious? How can the motion of the observer change the wavelength?

Note that special relativity admits that an observer in the frame of the source measures the frequency with which the light waves hit the moving observer to be f'=(c+v)/(lambda), the speed of the light waves relative to the moving observer to be c+v and the wavelength to be L. That is, according to the observer in the frame of the source, the moving observer CANNOT and DOES NOT change the wavelength.

Pentcho Valev pvalev@yahoo.com

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Pentcho Valev replied on Jun. 29, 2012 @ 11:36 GMT
Colin,

If you want to be an Einsteinian and not a Newtonian, you should be teaching that, in a gravitational field, the speed of light varies twice as fast as the speed of cannonballs (Newton's emission theory predicts an identical accceleration for photons and cannonballs):

http://arxiv.org/pdf/gr-qc/9909014v1.pdf

Steve Carlip: "It is well known that the deflection of light is twice that predicted by Newtonian theory; in this sense, at least, light falls with twice the acceleration of ordinary "slow" matter."

http://www.mathpages.com/rr/s6-01/6-01.htm

"Specifically, Einstein wrote in 1911 that the speed of light at a place with the gravitational potential phi would be c(1+phi/c^2), where c is the nominal speed of light in the absence of gravity. In geometrical units we define c=1, so Einstein's 1911 formula can be written simply as c'=1+phi. However, this formula for the speed of light (not to mention this whole approach to gravity) turned out to be incorrect, as Einstein realized during the years leading up to 1915 and the completion of the general theory. (...) ...we have c_r =1+2phi, which corresponds to Einstein's 1911 equation, except that we have a factor of 2 instead of 1 on the potential term."

http://www.speed-light.info/speed_of_light_variable.htm

"Einstein wrote this paper in 1911 in German. It predated the full formal development of general relativity by about four years. You can find an English translation of this paper in the Dover book 'The Principle of Relativity' beginning on page 99; you will find in section 3 of that paper Einstein's derivation of the variable speed of light in a gravitational potential, eqn (3). The result is: c'=c0(1+phi/c^2) where phi is the gravitational potential relative to the point where the speed of light co is measured......You can find a more sophisticated derivation later by Einstein (1955) from the full theory of general relativity in the weak field approximation....For the 1955 results but not in coordinates see page 93, eqn (6.28): c(r)=[1+2phi(r)/c^2]c. Namely the 1955 approximation shows a variation in km/sec twice as much as first predicted in 1911."

Pentcho Valev pvalev@yahoo.com

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Armin Nikkhah Shirazi wrote on Jul. 1, 2012 @ 15:21 GMT
Hi Colin,

I had previously written a comment, but somehow it disappeared, so here it is again. I just wanted to mention that I like the fact that you are making a definite prediction in your paper. Have you thought about presenting your results at some astronomy conferences, in order for people to become aware of it and perhaps be induced to look of the second-order effect you are predicting?

Armin

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Anonymous replied on Jul. 3, 2012 @ 17:41 GMT
Hi Armin

I was hoping to accomplish something similar here, and I thank the organizers of the contest for the opportunity.

From what I have seen, there is already interest among specialists in high precision experiments with the focus on discriminating between general relativity (tensor) and Brans-Dicke (scalar-tensor) theories. The target of experimentors will naturally be the second-order term in the Schwarzschild expansion since this could falsify general relativity as it is currently understood. The adjustable parameter in Brans-Dicke makes it a rather elusive thing to pin down in comparison with the exponential metric.

Whatever the result, a second-order test of general relativity would be historic and is feasible within the decade.

Colin

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Author Colin Walker wrote on Jul. 4, 2012 @ 00:52 GMT
My essay presents the revised classical part of a theory of gravitation without its modern counterpart. It is possible that the revised modern theory can be taken from general relativity's exponential map. Given my limited facility with the mathematics involved (or even the terminology), a suggestion on how to proceed is presented as a problem.

The first possibility to investigate would be an exponential map of the Riemannian metric. I don't really know what this means. If it means that the exponential metric and the Schwarzschild metric are related through an exponential map, then the revised modern theory might only involve a minor modification to general relativity. A simple analogy to an exponential map in one dimension is 1-x -> exp(-x). This is precisely the sort of difference that exists between corresponding terms in the metrics.

The problem is this: Equation (9) for the exponential metric changes to the Schwarzschild metric when sigma is substituted for sigma-with-the-squiggle-on-top. Are the two versions of equation (9) related by an exponential map? If so, can the exponential map be used to make comparable first-order predictions?

I would like to have a better idea if this will work, and I suspect some readers might be able to see a way, if it is possible. When a similar question was posted to the newsgroup sci.physics.research last year it was rejected as too speculative but the moderator did tell me "the short answer is yes", the metrics are related by an exponential map. I was satisfied with that, as I probably would not understand the long answer, and did not send the post to s.p.foundations where it should have gone in the first place.

General relativity has no adjustable parameters, but I wonder if it has another solution from the exponential map corresponding to the classical revision proposed in the essay.

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James Lee Hoover wrote on Jul. 11, 2012 @ 18:34 GMT
Colin,

I am also dealing with gravity but w/o your math skills.

"It is likely that a relic of Galilean relativity remains in the modern theory of gravitation."

Galilean relativity states that the fundamental laws of physics are the same in all inertial frame.

I don't have the math skills to follow your explanation. What is the evidence that this "relic" find its way into the modern theory?

Jim

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Author Colin Walker replied on Jul. 13, 2012 @ 17:59 GMT
Hi Jim

The "relic" is the classical notion from Galilean relativity that velocities add. I think if you understand two points, you will see what I am getting at.

In the essay, I have followed Einstein's original derivation of the equivalence principle by presenting approximations, which are actually very useful in seeing that small changes in gravitational potential, redshift and velocity (as discussed in the Introduction) are all equivalent. The first point to recognize is that Newtonian potential energy is obtained by adding small changes in potential, or equivalently, velocity or redshift.

The second thing to recognize is that special relativity combines velocities and redshifts through a process of multiplication, not addition.

The first point is also the main point of evidence, such as it is. Newtonian potential essentially adds velocities classically. General relativity has embedded the same assumption as Newton regarding the additive nature of gravitational potential energy. This includes producing the same expression for radial escape velocity, which can exceed the speed of light. The classical assumption has led to concepts like black holes, which are highly problematic. These difficulties are resolved by treating potential energy in the same way that special relativity treats redshift and forming it through a process of multiplication, not addition.

I suppose this is evidence only if you are skeptical of black holes. Eddington thought that there ought to be a law of nature to prevent their existence and that their possibility almost reduces general relativity to absurdity. I suggest that general relativity gives absurd results in strong fields because of the classical assumption that potential energy is additive, and that the law of nature which prevents gravitational black holes is multiplication given by special relativity.

Here is a long-winded example of relativistic velocity "addition" (more properly called "composition") as a setup to a quip from Eddington. Let us suppose that a stationary observer is standing by a railway track and I have passed by on a railcar at a speed the observer and I agree is v. Suppose I manage to throw a radiating object forward at a speed v by my reckoning relative to the moving railcar. Classically the velocity of the object away from the stationary observer is expected to be 2v, but special relativity claims it is less, and that no speed can exceed c. Radiation measured by the stationary observer is redshifted by an amount predicted by special relativity.

"We used to think that if we knew one, we knew two, because one and one are two. We are finding that we must learn a great deal more about 'and'." - Arthur Stanley Eddington

Colin

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Bentley Jarvis wrote on Jul. 16, 2012 @ 02:17 GMT
Colin please contact Bjarvis@faculty.ocadu.ca

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Author Colin Walker replied on Jul. 17, 2012 @ 23:57 GMT
Hi Bentley (Old friend, been a while)

I tried to contact you, but no reply.

Here is my email, cw47xyz at google.com which I should have included in the essay.

Colin

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Vijay Mohan Gupta wrote on Aug. 2, 2012 @ 18:52 GMT
Dear Colin,

I read your interesting essay and appreciate your depth of understanding of mainstream physics and maths. I seek your assisstance as guide to help me with PicoPhysics .

Thanks and Regards,

Vijay Gupta

905-771-0024

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Author Colin Walker replied on Aug. 4, 2012 @ 02:17 GMT
Hi Vijay

I am afraid my knowledge of both subjects is limited and rather specialized, but I think we share some similar intuitions.

From what I have read so far of Picophysics, it is you who could be a guide in investigating the realm of the infinitesimal. I will keep an eye out for problems that might benefit from your approach.

Colin

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Gurcharn Singh Sandhu wrote on Aug. 24, 2012 @ 07:29 GMT
Dear Colin,

I have read your essay and I appreciate your viewpoint. Your essay is excellent and I wish you good luck in the contest.

Of course, all authors in this contest cannot agree on any one point of view. I believe various contributions from many like-minded authors can definitely make a difference in the emergence of a consolidated un-orthodox viewpoint needed to remove some of the major weaknesses, contradictions and fantasies from current Physics.

You are also requested to read and comment my essay titled "Wrong Assumptions of Relativity Hindering Fundamental Research in Physical Space".

Best Wishes

G S Sandhu

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James Putnam wrote on Aug. 24, 2012 @ 19:35 GMT
Colin Walker,

While just reading your interesting essay I came across your support for:

"It can be seen that potential energy calculated by the rule of redshifts is a nite positive quantity and con rms the postulate, a corollary of Mach's principle, that the kinetic energy gained in free fall can be no greater than the rest energy."

In my own essay I give the same conclusion, I think. I say I think because perhaps you might feel otherwise. I calculate gravitational potential energy with the solution that it is equal to mc^2. I must point out though that while I use Einstein's form of rest energy expression from his kinetic energy equation, I do this because readers are familiar with it. His kinetic energy equation is not the form that I use in my own work. Just giving you a heads-up that I do not accept the theory of relativity in case that matters to you. I will continue to study your essay. Thank you for submitting it.

James

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Author Colin Walker replied on Aug. 26, 2012 @ 23:19 GMT
Hi James,

You have come up with a number of really interesting relations starting with eq (8). Correcting the problems at the start pointed out by Anne Smith on June 21 in your essay - ie. consistent sign in eqs (4) and (5) and changing the limits in the integral on the right hand side of eq (7) to use infinity instead of 0 (being careful with the sign again), you get what I call in my essay the Schwarzschild "scale factor" if you factor out the speed of light C.

I recognize your expression (8) as tangential velocity of light in a gravitational field according general relativity. See An Exact Solution at mathpages.com near the end of the article. The variation radially is different (the square of the scale factor) so it would be a gyroscope-like effect happening at right angles to what would be expected. Curious.

Colin

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James Putnam replied on Aug. 27, 2012 @ 23:25 GMT
Colin Walker,

Thank you for reading my essay. I need to look back at your essay and think about what you have said. As a help to me, I would appreciate learning your response to this: All theories that closely mimic the patterns in empirical evidence will have equations that look anaogous. In my case, if the idea that mass is the inverse of the acceleration of light within one photon length of the particle is not held as valid then the rest of my equations are only loose mimics of the correct theory's equations.

I hold that mass must be a definable property. It must be definable in the same terms as is the empirical evidence from which its existence was inferred. That is why I define its units in terms of meters and seconds. I see no way to avoid this except by making a guess that mass is a property on par with distance and duration. That it must have its own indefinable units. I wonder if this second choice is one that you prefer.

I will look into your essay again to see if the answer is there. Thank you for your message.

James

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Author Colin Walker replied on Aug. 29, 2012 @ 00:45 GMT
Hi James

My essay avoids dealing with the concept of mass because only the free-fall problem is considered. Different masses are taken to fall at the same rate. Mass seems to be quite peculiar.

As to whether I prefer mass to have its own independent units, I have been borrowing general relativity's answer, "yes". According to M.G. Bowler in his 1976 book Relativity and Gravitation, another unit besides length and time is required to specify the contortions of dimensions in general relativity as a gauge theory. Bowler takes mass as a third independent unit.

Classical approaches seem to have great difficulty accounting for the difference between radial and transverse physical quantities. The attached table shows by dimensional analysis how physical quantities vary radially and transversely in a gravitational field under the assumptions of general relativity according to Bowler. All the differences between radial and transverse quantities come from an assumption that length is contracted radially, but not transversely. This curvature theory does not rule out another table in another theoretical framework.

Colin

attachments: gravtab.pdf

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Author Frank Martin DiMeglio wrote on Aug. 25, 2012 @ 20:30 GMT
Colin, the key is that F=ma is fundamentally demonstrated given the fundamental equivalency and balancing of inertia and gravity in conjunction with instantaneity and the fact that gravity cannot be shielded. Here we have equivalent and balanced attraction and repulsion, true/real quantum gravity, instantaneity, the union of gravity and electromagnetism, fundamental and balanced force/energy, and fundamental (and fundamentally balanced/stabilized) distance in/of space.

Do you not agree that -- at least theoretically -- this is our dream list for the unification that we (and yourself) seek?

This is space that is invisible, not visible, and visible in a fundamentally balanced fashion. And this actually occurs.

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Author Colin Walker replied on Aug. 26, 2012 @ 23:21 GMT
Hi Frank,

Yes, it is looking like all of that has to be there. Sounds kind of Newtonian, which is perhaps a Utopian ideal.

Colin

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Frank Martin DiMeglio replied on Sep. 16, 2012 @ 01:48 GMT
Colin, how could we grow and become other than we are if such a unification could not and did not actually exist? We couldn't. My essay proves that this unification actually and theoretically is real/true. This is because the self represents, forms, and experiences a comprehensive approximation of experience in general by combining conscious and unconscious experience.

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Armin Nikkhah Shirazi wrote on Aug. 26, 2012 @ 03:10 GMT
Hi Colin,

I know that you are to some extent already familiar with my ideas on how they attempt to make sense out of quantum mechanics, and thought you'd be interested in the context that my essay provides for how it might help us understand how general relativity and quantum mechanics fit together.

I'd be particularly interested in your perspective on the restriction on the domain of validity the idea presented in my paper imposes on general relativity, and appreciate any constructive criticism.

All the best,

Armin

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Author Colin Walker replied on Aug. 26, 2012 @ 23:25 GMT
Hi Armin,

Good to see your entry. The dimensional aspect of your idea is really intriguing. I have yet to give a your essay a good read, so I will comment later.

By the way, Simon and Mark Newstead want to experiment with "weighing" light in their essay about electromagnetic radiation, in case you missed it.

Colin

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Author Colin Walker replied on Aug. 27, 2012 @ 17:46 GMT
Oops, that's Stephen Newstead, not Simon.

Colin

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Armin Nikkhah Shirazi replied on Sep. 5, 2012 @ 08:43 GMT
Hi Colin,

I read the paper, but I must admit that my belief is that massless objects really are fundamentally different from massive objects. I give them credit for proposing an experiment and also emphasize that my perspective is colored by how I arrived at many of my ideas. If you care to understand better what I mean, take a look at my submission 4 years ago to the first fqxi contest, which might seem slightly bizarre without the benefit of knowing about the dimensional theory in hindsight

the original essay is here:

http://fqxi.org/community/forum/topic/329

while one that contains some minor corrections can be found here:

http://hdl.handle.net/2027.42/83152

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Hoang cao Hai wrote on Sep. 19, 2012 @ 14:53 GMT
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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Vladimir F. Tamari wrote on Sep. 29, 2012 @ 08:59 GMT
Hello. This is group message to you and the writers of some 80 contest essays that I have already enjoyed reading, rating and in most cases commenting on.

This year I feel proud that the following old and new online friends have accepted my suggestion that they submit their ideas to this contest. Please feel free to read, comment on and rate these essays (including mine) if you have not already done so, thanks:

Why We Still Don't Have Quantum Nucleodynamics by Norman D. Cook a summary of his Springer book on the subject.

A Challenge to Quantized Absorption by Experiment and Theory by Eric Stanley Reiter Very important experiments based on Planck's loading theory, proving that Einstein's idea that the photon is a particle is wrong.

An Artist's Modest Proposal by Kenneth Snelson The world-famous inventor of Tensegrity applies his ideas of structure to de Broglie's atom.

Notes on Relativity by Edward Hoerdt Questioning how the Michelson-Morely experiment is analyzed in the context of Special Relativity

Vladimir Tamari's essay Fix Physics! Is Physics like a badly-designed building? A humorous illustrate take. Plus: Seven foundational questions suggest a new beginning.

Thank you and good luck.

Vladimir

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Member Benjamin F. Dribus wrote on Oct. 2, 2012 @ 15:41 GMT
Dear Colin,

This is an interesting and important topic. It reminds me of two "somewhat related" ideas I read about recently:

1. The first is from a post-doc of my acquaintance, Se-Jong Kim, who wrote some papers on velocity addition in relativity that relates this to quantum information theory via a group-like algebraic structure called a "loop."

2. The second appears in papers by Piret Kuusk about "geodesic multiplication" in general relativity and possible connections to quantum gravity. The algebraic structure involved is called the "local geodesic loop" and is similar to the structure of the velocity-addition problem.

From reading your paper, I know that neither of these topics is exactly what you are discussing, but there may be interesting analogies. I don't see an email address on your paper, but if you email me, I'd be glad to send you copies of these papers. My email address is on my essay here). Take care,

Ben

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Author Colin Walker replied on Oct. 3, 2012 @ 20:03 GMT
Hi Ben

Both of the ideas you mention look highly relevant. It is exciting to think there might be a quantum aspect to the problem - with loops too!

I have sent you an email and look forward to reading the papers.

Thank you very much for your interest.

Colin

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Sergey G Fedosin wrote on Oct. 4, 2012 @ 09:53 GMT
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
$R_1$
and
$N_1$
was the quantity of people which gave you ratings. Then you have
$S_1=R_1 N_1$
of points. After it anyone give you
$dS$
of points so you have
$S_2=S_1+ dS$
of points and
$N_2=N_1+1$
is the common quantity of the people which gave you ratings. At the same time you will have
$S_2=R_2 N_2$
of points. From here, if you want to be R2 > R1 there must be:
$S_2/ N_2>S_1/ N_1$
or
$(S_1+ dS) / (N_1+1) >S_1/ N_1$
or
$dS >S_1/ N_1 =R_1$
In other words if you want to increase rating of anyone you must give him more points
$dS$
then the participant`s rating
$R_1$
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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