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Hou Yau: on 10/2/12 at 18:33pm UTC, wrote Sergey, Thank you for taking time to rate our essays. I noticed a...

Sergey Fedosin: on 10/2/12 at 13:58pm UTC, wrote After studying about 250 essays in this contest, I realize now, how can I...

Sergey Fedosin: on 9/26/12 at 14:39pm UTC, wrote Dear Hou, The atomic electron cloud in disk form is similar to disks near...

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CATEGORY: Questioning the Foundations Essay Contest (2012) [back]
TOPIC: Is There Really No Reality Beneath Quantum Theory? by Hou Ying Yau [refresh]

Author Hou Ying Yau wrote on Aug. 10, 2012 @ 16:41 GMT
Essay Abstract

The standard interpretation (Copenhagen interpretation) of quantum mechanics asserts that reality does not exist when we are not observing. Is it really true that there has no reality beneath quantum mechanics? Here, we demonstrate a possibility that the quantum wave can have a real physical origin other than the probabilistic interpretation.

Author Bio

I am an independent researcher whose main interest is in fundamental physics. Before submitting to this contest, I sent an older version of this essay to one of the physics journals for review. Two of the reviewers find the paper interesting and suggest only minor revisions. Although the third and final fourth reviewers have not recommended publication, their comments do not include technical errors that disprove the idea. Depending on the outcome of this contest, my plan is to re-submit an updated version of this essay to another journal after gathering more feedbacks.

Angel Garcés Doz wrote on Aug. 10, 2012 @ 22:28 GMT
Dear, Hou-Ying Yau. The so-called virtual particles can not be observed, since, otherwise, would be "real"

But these virtual particles, not observable, are the foundation of ad-hoc method of renormalization, which leads to the unwanted infinities. It contradicts the Copenhagen interpretation, since no observable particles, not real, according to this interpretation, are what determine all calculations, and therefore are real deterministically. Excellent, your point of view. One of the keys, I agree: the loss of information of a system that deep down, most likely, is not as indeterministic as presented now by the quantum theory.

It is possible that the interference of measurement or observation, with a local system disturbs a unitary space-time-energy, non-local, because in reality the space-time-energy would be a continuous quantized, not separable.

The information he lost to the observer causes. This appears to the observer probabilistic knowledge, but this does not mean that there is no underlying reality independent of the observer, as evidenced by the existence of unobservable particles, but that influence the so-called "real" world. For example, the effect Cassimir, measured experimentally

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Author Hou Ying Yau replied on Aug. 11, 2012 @ 03:36 GMT
Dear Angel,

Thank you for your feedback. As you have mentioned, the process described in the new model may remind us of the virtual states that exists only for a limited time. In the quantum theory, virtual particles do not have a permanent existence; they arise from fluctuations of vacuum energy, and can be understood as a manifestation of time-energy uncertainty principle. Unlike the virtual particle, a normalized field in our new model always has sufficient energy for one particle to appear. The energy in this system is real which surface to the observational level as a real quantized oscillator (or particle). It appears at a location and can jump to other locations depending on the probability distribution. The world line in this case is real. Thank you for pointing out the similarity and differences between the virtual particle and the real quantized particle in our approach.

Hou-Ying Yau

Edwin Eugene Klingman wrote on Aug. 11, 2012 @ 03:01 GMT
Dear Hou Ying Yau,

You have picked an important topic and generated a new approach. I agree that the properties of an uncharged particle include 4-momentum, time and space, and I agree that the particles are physically real and localizable. In my approach, (The Nature of the Wave Function), I do not focus on the Planck scale. You discuss whether the amplitude of the matter waves can have a physical interpretation related to the principles of space-time relativity. I first assume 'flat space' and then I apply the weak field equation of general relativity to arrive at a wave function for non-relativistic QM. Unlike you, I have not considered information loss. Although our approaches are somewhat different, we both agree there *is* reality beneath quantum theory.

I am happy to see yet another essay that accepts the reality of the particle and a physical significance for the wave function. Both theory and recent experiments seem to be pointing this way.

Best of luck in the essay contest.

Edwin Eugene Klingman

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Author Hou Ying Yau replied on Aug. 11, 2012 @ 05:54 GMT
Dear Edwin,

I am also glad to see someone sharing very similar idea about reality for the wave function. Interestingly, we both begin with the belief that matter wave can be real and can be related to relativity. Of course, there are other ideas that shares the same belief, such as the use of Ricci flow by Carrol, Isidro et al. Although the approaches are different, it is only my opinion that there may be one advantage: If matter wave has properties that are directly related to relativity, it may be easier to resolve some of the differences between quantum theory and general relativity.

The deterministic system proposed in this model is at the Planck scale. In a conference I recently attended, it was pointed out during discussion that the formulation of this model actually allows starting at different energy level. I choose to start at the Planck scale because of the information loss theory developed from holographic principle. However, it does not eliminate the possibility of starting the theory at other energy level.

I also hope you best of luck in the contest.

Hou-Ying Yau

Ted Erikson wrote on Aug. 13, 2012 @ 20:06 GMT
1st timer submission, not yet submitted, while reviewing selected works for adding End Notes.

You are off the deep end in math and more abreast of present day physics.. Good Luck!

Impressed by considering the 4 parameters, E, p, t, and x to uncover determinism in quanta.

Simply, mass and energy, respectively, as the inscribed sphere, tangent to the face of a regular tetrahedron where sphere and tetrahedron have equal surface-to-volume ratios at ANY size, e.g. equivalent "activity" as free energy , unbounded as size approaches zero. Conclusion, birth and death via the angular frequency proportional to E.

Comment? (may use in end notes)

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Author Hou Ying Yau replied on Aug. 14, 2012 @ 03:40 GMT
Hi Erikson,

I hope you best of luck in the essay contest as well. Without knowing much detail of your proposal, I think I will have to skip commenting the end note.

Sincerely,

Hou-Ying Yau

James Dunn wrote on Aug. 14, 2012 @ 18:49 GMT
I assert that there is a fundemental causal entity from which all of physics is built.

http://fqxi.org/community/forum/topic/1368

As such, a virtual quantum particle might be akin to a Non-Relativistic system of an observable relativistic particle.

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Hou Ying Yau replied on Aug. 15, 2012 @ 04:00 GMT
James,

Thanks for sharing the information. I will take a look.

Hou-Ying Yau

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Jayakar Johnson Joseph wrote on Aug. 19, 2012 @ 06:08 GMT
Dear Hou Ying Yau,

Uncertainty principle on quantum mechanics reveals the inconsistency of observables for the observer that evolves from the assumed discrete point-like particles nature of the universe. Thus we may think of the universe is having consistency in continuum and fluidity, in that quantization of string dynamics may resolve paradox.

With best wishes,

Jayakar

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Hou Ying Yau replied on Aug. 20, 2012 @ 17:17 GMT
Dear Jayakar,

Thanks for sharing the information. Unlike the string theory approach, we hope to demonstrate a possibility that there can be a more fundamental deterministic system underlying quantum theory. Although the quantized particle is point like, we believe it can contain information through its vibrations in space and time. It is a new approach but we hope may provide a link between qunatum theory and relativity; and explain some of the fundamental questions in quantum theory.

Sincerely,

Gilbert

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Anton W.M. Biermans wrote on Aug. 22, 2012 @ 02:53 GMT
Hou-Ying Yau,

If we can consider the continuous exchange of virtual particles like photons and gravitons between real particles as observation interactions, if we can say that particles by interacting observe one another, then they certainly exist, to each other, even if we are not observing them.

The question as to whether there is an underlying reality, beneath quantum mechanics is in fact the question whether there exists an absolute, objectively observable reality even if we might not be able to observe it objectively, undistorted by out observation interaction. The problem is that if we live in a universe which creates itself out of nothing, without any outside interference, and this universe is to obey the conservation law according to which what comes out of nothing, should add to nothing, then it cannot be ascribed particular properties as a whole since this would violate conservation laws. This means that a Self-Creating Universe has no physical reality as a whole: if in a SCU particles have to create themselves, each other, then particles and particle properties must be as much the product as the source of their interactions, the consequence of which is that an observation interaction necessarily affects the observed.

If, as I argue in my essay ('Einstein’s error'), at the most fundamental level (quantum level) we cannot divide events in cause and effect in a SCU, then in such universe the speed of light doesn't refer to a velocity but to a property of spacetime, which is something else entirely. In a SCU there's nothing weird or paradoxical about the EPR 'paradox': experimental proof of the validity of the EPR 'paradox' in fact indicates that we do live in a SCU.

Anton

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James Putnam replied on Aug. 22, 2012 @ 03:11 GMT
Anton W.M. Biermans,

"The problem is that if we live in a universe which creates itself out of nothing, without any outside interference, and this universe is to obey the conservation law according to which what comes out of nothing, should add to nothing, then it cannot be ascribed particular properties as a whole since this would violate conservation laws. This means that a Self-Creating Universe has no physical reality as a whole: if in a SCU particles have to create themselves, each other, then particles and particle properties must be as much the product as the source of their interactions, the consequence of which is that an observation interaction necessarily affects the observed.

If, as I argue in my essay ('Einstein’s error'), at the most fundamental level (quantum level) we cannot divide events in cause and effect in a SCU, then in such universe the speed of light doesn't refer to a velocity but to a property of spacetime, which is something else entirely. In a SCU there's nothing weird or paradoxical about the EPR 'paradox': experimental proof of the validity of the EPR 'paradox' in fact indicates that we do live in a SCU."

Why does "a universe which creates itself out of nothing, without any outside interference, and this universe is to obey the conservation law according to which what comes out of nothing, should add to nothing, then it cannot be ascribed particular properties as a whole since this would violate conservation laws."

In a self creating universe: You get the conservation law out of nothing? Presumably then: You can get anything, maybe even everyting, out of nothing. Is that your starting point?

James

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Anton W.M. Biermans replied on Aug. 24, 2012 @ 04:01 GMT
James

Reason says that what comes out of nothing should add to nothing, so conservation laws in physics are the expression of this rational 'belief'. A SCU is a perpetuum mobile which yields as much as it cost: nothing. Only if we believe that there is a God who created the universe (which I don't) such conservation laws do not hold.

The insight that the universe (with us inside of it) doesn't exist as a whole, has no reality as 'seen' from without, so to say, may be hard to accept as we seem to crave an absolute kind of existence, wishing for Someone in Whose eyes we exist, for our existence to transcend the universe itself, to be immortal, as if we have a gene that encodes a longing for God.

Alas, it is this wish which confuses the mind of even physicists which think themselves to be atheist but are not as long as they cling to causality like kids to their mother's skirts.

Anton

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James Putnam replied on Aug. 24, 2012 @ 04:30 GMT
Anton,

James

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Peter Jackson wrote on Aug. 24, 2012 @ 16:34 GMT
Dear Hou-Ying

Beautifully written, well argued and agreeable. I too have determined an entirely deterministic interpretation of QM, including the Copenhagen interpretation. If a lens is part of the process of detection, prior to conversion and interpretation, then if there is no lens there can be nothing to interpret.

Bohr told Heisenberg, when he was about to fail his thesis, that he must learn how a lens worked before he could talk sense about physics. Perhaps we misinterpret and he actually did so!?

You've certainly earned a good score and I hope you do well. I'd also be very interested in how you view my own approach to what is essentially the same subject, deriving SR from QM with a few tweaks to interpretation of both.

Best wishes

Peter

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Author Hou Ying Yau replied on Aug. 27, 2012 @ 15:40 GMT
Peter,

Thank you for your kind comments. Your essay is very well written and deserves the high rating score. I will take a closer look.

Sincerely,

Hou Ying Yau

Andy S. wrote on Aug. 30, 2012 @ 01:14 GMT
Dear Yau,

I am also an independent researcher with some interests in emergent quantum mechanics (EQM). The bounded Hamiltonian and constraint equation you proposed are different from typical. How do you see they can relate to EQM?

Best Wishes

Andy

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Author Hou Ying Yau replied on Aug. 30, 2012 @ 03:54 GMT
Andy,

The deterministic system I used as the starting point is quite different from the one proposed in emergent quantum mechanics. The new system has real physical vibrations. As you have mentioned, the Hamiltonian is bounded versus the unbounded one in EQM. The Einstein mass-energy relation is the constraint in the new model. Although the approaches are different, the idea of determinism is the same. The use of information loss to explain the transition to a quantized field is an inspiration from EQM.

Sincerely,

Hou Ying Yau

Andy S. replied on Aug. 31, 2012 @ 19:48 GMT
Dear Yau

My point is that there may be connections between your Hamiltonian and the EQM pre-quantization equation. There are mnany cases that two seeminly different approaches are ultimately found related. Heisenberg and Schrodinger formulation look different when they first developed but they both describe the quantum system. Worth look deeper?

Andy

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Author Hou Ying Yau wrote on Sep. 2, 2012 @ 03:15 GMT
Andy,

This is an interesting suggestion. I will give it a try.

Thanks.

Hou Ying Yau

Andy S. wrote on Sep. 3, 2012 @ 23:15 GMT
Hou Yau,

The development of the Dirac equation because of the initial problem with Klein Gordon equation is another example. The equation was thought to have negative energy problem. Your model has some improvements that there are some observable observable at low energy level.

Andy

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Author Hou Ying Yau wrote on Sep. 4, 2012 @ 04:14 GMT
Andy,

There may be difficulties comparing a bounded equation with an unbounded equation. However, you pointed out an interesting example that Klein Gordon equation was first thought of having the difficulties of negative energy solution.

Hou Ying Yau

Marcoen Cabbolet wrote on Sep. 9, 2012 @ 20:02 GMT
Hello Hou Ying Yau,

Your essay opens with the following statement: "The standard interpretation (Copenhagen interpretation) of quantum mechanics asserts that reality does not exist when we are not observing."

Is that really so?

Does the Copenhagen Interpretation really imply that an electron doesn't exist in absence of observation? Or does the Copenhagen Interpretation only imply that the electron has no properties like position and momentum in absence of observation? Note that the fact that the electron has no position does not imply that the electron does not exist.

What is your position on this?

Best regards, Marcoen

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Author Hou Ying Yau replied on Sep. 10, 2012 @ 18:44 GMT
Dear Marcoen,

The Copenhagen Interpretation definietly describes what happens when we make a measurement. There is reality when an observation is made. However, what happens when we are not observing? Is there reality? The interpretation seems very vague. Many ideas have been associted with it but they can be very different or even sometimes opposing by different authors.

Rather than trying to interpretate what the mathematical formulation of quantum mechanics really mean when there is no observation, I tried a simple assumption that matter at rest can have vibrations in proper time. The non-interacting system we studied generates the same properties we expect in quantum theory. The world line of the paticle is real in the model.

Sincerely,

Hou Ying Yau

Donatello Dolce wrote on Sep. 17, 2012 @ 15:36 GMT
Hi Yau,

I can see interesting overlaps between your and my essay Elementary Time Cycles. In particular, starting from 2009, I have demonstrated mathematically in several peer reviewed papers how relativistic QM can be formally obtained from what you call "displacement" and I call space-time periodicity. In my papers I also interpret my results in terms of 't Hooft determinism and Elze's stroboscopic quantization.

I hope you will enjoy my essay.

Regards,

Donatello

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Author Hou Ying Yau wrote on Sep. 19, 2012 @ 15:29 GMT
Dear Donatello,

Thanks for sharing the essay with me. It is interesting we both get the results of the relativistice quantum mechancis but with different models. (I believe you use an unobservable extra dimension to present periodicity while the vibrations in my system are real.) I also started a number of years ago and similar results were presented in a 2007 pre-print. I have some questions about your idea which I will post on your blog soon.

Best of wishes

Hou Yau

Hoang cao Hai wrote on Sep. 19, 2012 @ 15:58 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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Sergey G Fedosin wrote on Sep. 21, 2012 @ 16:33 GMT
Dear Hou,

In the book: The physical theories and infinite nesting of matter. Perm, 2009-2012, 858 p. ISBN 978-5-9901951-1-0 the electron in atom has form a disk cloud. Then it seems that the Wave Function gives concentration of electron substance in the cloud. What do you think about it?

Sergey Fedosin

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Hou Ying Yau wrote on Sep. 23, 2012 @ 01:00 GMT
Dear Sergey,

Thanks for sharing the information. It will require some time to understand fully. At a first glance, is it reasonable to use the properties of a star to compare with the electron? Please correct me if I misunderstand your idea.

Sincerely,

Hou Ying Yau

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THOMAS GARCIA wrote on Sep. 23, 2012 @ 11:54 GMT
From: Thomas Garcia (On the Nature of Time)

Dear Hou.

When I try to download your essay, it fails after 1 second. Tried it 3 times. Any idea what I might be doing wrong?

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Hou Ying Yau replied on Sep. 24, 2012 @ 15:47 GMT
Dear Thomas,

I opened the file from the link and it look OK. Sometimes could be bad connection. I will e-mail a copy to your address.

Thanks.

Hou Yau

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Thomas Garcia replied on Sep. 26, 2012 @ 14:16 GMT
Dear Hou-Ying Yao,

I was finally able to download your essay and I read it through. To me, it is wonderfully written,concise yet complete. The math is beyond me, however,so I cannot dispute any of it. I freely accept it as correct.

Your essay essentially says to me that we may infer there is an aspect of reality that should be further reviewed. I feel sure, like you, that such research is needed.

My status as a layperson allows me only a superficial review of it, though, so I will refrain from commenting on it in depth.

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Member Benjamin F. Dribus wrote on Sep. 24, 2012 @ 01:16 GMT
Dear Hou,

I have now had a chance to read your essay, and I do find this idea interesting. I was going to point out to you Donatello Dolce's and Edwin Klingman's essays as others you might be interested in looking at, but it seems they have already contacted you! Let me itemize a few remark and questions:

1. A very important point you make is that any such wave must interact with spacetime itself (top of page 2). This seems like a statement of background independence.

2. I am not quite sure what mechanism selects the Planck scale as being special in your approach. As far as I can tell, you are not suggesting that the manifold structure of spacetime breaks down at the Planck scale, since the underlying waves are still defined at that scale. How does nature "know" that "quantization" is supposed to occur at this scale?

3. Although you discuss Lorentz transformations, I am still a little worried about this. A Planck volume in one frame of reference won't be a Planck volume in another frame. It seems that what appears to be a vacuum at the observable level in one frame might appear to contain energy in a sufficiently boosted frame. This is the sort of problem the developers of deformed special relativity (DSR) were thinking about.

4. It does seem as though you might get the appearance of nonlocality from this approach, since waves interfering mostly below the observable threshold could produce correlated observable interactions at a few distant points with nothing but "vacuum" in between.

Anyway, I enjoyed reading your essay; it gave me some interesting new food for thought. Take care, and good luck with the contest!

Ben

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Author Hou Ying Yau replied on Sep. 24, 2012 @ 21:29 GMT
Dear Ben,

Thank you for your remarks and comments. I hope some of the information will be useful. Here are some of my responses:

1. Yes, the theory proposed is background independence. In fact, the quantized vibration should affect the surrounding space-time geometry which I hope to prove is the same for a point mass in relativity.

2 & 3. This s a good point. The formulation of this model actually allows starting at different energy level. It is chosen to start at the Planck scale because of the information loss theory first developed from holographic principle. However, it does not forbid starting the analysis at other energy level. In fact, it may even be better for presentation to analyze the system in a box as shown in a preprint arXiv:0706.0190 [physics.gen-ph] and not starting at Planck scale. (Something that I am reconsidering for my next presentation.) This may avoid the confusion you have stated in 3.

4. The model seems to have non-local features that hopefully can help explain some of the questions in quantum mechanics.

Best wishes for you in the contest.

Hou Yau

Sergey G Fedosin wrote on Sep. 26, 2012 @ 14:39 GMT
Dear Hou,

The atomic electron cloud in disk form is similar to disks near of some neutron stars.

Sergey Fedosin

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Sergey G Fedosin wrote on Oct. 2, 2012 @ 13:58 GMT
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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Author Hou Ying Yau replied on Oct. 2, 2012 @ 18:33 GMT
Sergey,

Thank you for taking time to rate our essays. I noticed a substantial drop in my ranking. Your comments and feedback why such extremely low rating will be helpful. Is there technical error? or difference in opinion because of the point patricle suggested in my essay and yours that the particle has a radius?

Sincerely,

Hou Yau

Hoang cao Hai wrote on Oct. 3, 2012 @ 04:31 GMT
DEAR TO Hou Ying Yau

as well as ALL THE AUTHORS AND READERS WAS INTEREST.

Today, I am finished reading all of the essays in this topic.

First of all, thanks again to FQXi and the donors has facilitated for us to have the opportunity get contribute to science.

Next, would like to express to other author by the thanks for the comments that you have contributed to give me, and sincere apologies to those of you that I do not have specific feedback for your essay.The reason that is because:

The placing for issues and measures to solve for the problems of your offer is completely different from mine, so I can not comment when we do not have the same views on one matter, the purpose is to avoid the discussion became conflict of ideologies,it is will not be able to solve the problem which we are interested.

The end, I hope that : we ( who want the human to put their faith in science) will have the same fear: to someday,every people told each other that:

WAIITING FOR SCIENCE HELPS IS VERY LONGTIME,

LET PRAY TO GOD OR A CERTAIN DEITY SOMETIMES EVEN FASTER !

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Sergey G Fedosin wrote on Oct. 4, 2012 @ 07:10 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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Hoang cao Hai wrote on Oct. 10, 2012 @ 16:34 GMT
Dear Hou Yau

In fact history has shown: the vast majority of the changes are important are due to those who are considered "unprofessional".

Maybe it's because : those who are the "professional" too believe in what is there, so did not see the irrationality of them.

Be very careful when using mathematics, it is actually a "magic wand" but it can not think for you, if you "accidentally" steer the wrong way, then it will "squared" to your consequences.

Regards.

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Jeff wrote on Mar. 28, 2013 @ 03:10 GMT
Hou Yau,

Great paper, really thought provoking. I have some questions:

1) You point out that your theory does not predict precisely where in a fixed volume a particle may appear; additionally, we also can't predict exactly what kind of particle may appear (ie how does nature choose between two different particles of identical mass, for instance an electron vs a positron)

2) Your theory relies on the fact that mass can only materialize in discrete quanta, but does not suggest why this would be so.

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