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
Andy,
This is an interesting suggestion. I will give it a try.
Thanks.
Hou Ying Yau
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
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
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
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
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
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
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?
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
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?
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
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
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
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.
Dear Hou,
The atomic electron cloud in disk form is similar to disks near of some neutron stars.
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,
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
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 [math]R_1 [/math] and [math]N_1 [/math] was the quantity of people which gave you ratings. Then you have [math]S_1=R_1 N_1 [/math] of points. After it anyone give you [math]dS [/math] of points so you have [math]S_2=S_1+ dS [/math] of points and [math]N_2=N_1+1 [/math] is the common quantity of the people which gave you ratings. At the same time you will have [math]S_2=R_2 N_2 [/math] of points. From here, if you want to be R2 > R1 there must be: [math]S_2/ N_2>S_1/ N_1 [/math] or [math] (S_1+ dS) / (N_1+1) >S_1/ N_1 [/math] or [math] dS >S_1/ N_1 =R_1[/math] In other words if you want to increase rating of anyone you must give him more points [math]dS [/math] then the participant`s rating [math]R_1 [/math] 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.
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.