A Derivation of the Quantum Phase by Armin Nikkhah Shirazi

Armin,

An absolutely fascinating essay. It's hard to believe that I'm the first to comment, but I guess there are a lot of essays to read. I have committed to read five a day. Of the five essays I read today, yours was by comparison, not only worth the time, but worth a second read and review. I'm sure I'll have more comments after I have time for a second read. I would also like to read your other essay from the nature of time contest, too.

Have a great day,

Dan

Dan,

Thank you for your kind remarks. I think the absence of comments in my forum reflects a combination of two factors: First, although I think to a physicist/mathematician the content of my essay should be fairly clear, I am not so confident that this is also the case for lay persons. Second, the ideas presented here are really unfamiliar (at least I have not seen them elsewhere) and it takes time to get used to them.

I am very glad to hear that you intend to review this essay, which is an excellent way to make the basic ideas seem less unfamiliar, and look forward to your questions, comments and objections.

Armin

Dear Armin Shirazi,

First I must mention that your essay technically is much better than some other essays I saw yesterday. However, some questions need clarification.

- ''all objects of atomic and nuclear proportion have in common is that, compared to objects on our scale, they are vastly more two-dimensional''.

It contradicts to experimental data. According to your theory, the interaction of micro-objects in a plane must be stronger than in third dimension because particles are flat and does not feel the third dimension. For example, the coherent beam of atoms or photons must have different properties in a plane (two dimensions) concerning a third dimension. The existence of a three dimensional nucleus as a sphere contradicts to your theory. Also, if nucleons were flat, they must interact in a plane stronger than in other dimensions that contradicts to experimental data.

- ''Photons exist in areatime. photons must be 2-dimensional entities''

Please read the Wikipedia_Photon: Rather, the photon seems to be a point-like particle since it is absorbed or emitted as a whole by arbitrarily small systems, systems much smaller than its wavelength, such as an atomic nucleus (10-15 m across) or even the point-like electron. Also, since photons must be 2-dimensional entities, they must have different properties in a plane conserning third dimension that contradicts to experimenal data.

Sincerely,

Constantin

Constantin,

Thank you for your objections. They illuminate where I need to express my ideas more clearly. I will attempt to give a thorough response.

You say:"It contradicts to experimental data."

The statement about smaller objects being more two-dimensional than larger objects of same shape was meant as a mathematical-not empirical-statement about the geometric properties of objects of different size. Mathematically, it seems to me hard to argue that if one takes the area-volume ratio as a parameter to compare relative dimensionalities (which I think from the context of my essay was clearly what I meant), smaller objects are indeed by this parameter more 2-dimensional than larger ones of same shape.

You say:"According to your theory, the interaction of micro-objects in a plane must be stronger than in third dimension because particles are flat and does not feel the third dimension."

I would be grateful if you could point me to any place in my essay where I mentioned anything about any kind of interactions. This essay is one of several that describe various aspects of this idea, and eventually the topic of interactions will need to be addressed as well, but I do not believe I did that here because that was outside the scope of the topic. In fact, in this paper there is not enough information to say anything specific about interactions. The idea that objects should interact more strongly in a plane than in the third dimension is yours, not mine.

You say "The existence of a three dimensional nucleus as a sphere contradicts to your theory."

Thank you for bringing up a point that evidently I did not make clear enough. When I claimed that smaller objects are more two-dimensional than larger ones of same shape, I meant that dimensionality in this specific sense (i.e. in terms of A/V) is something that takes on continuum of values, rather than 'quantized' ones (i.e. 1-D, 2-D etc.). In my example of a sphere of Bohr radius, I did not mean to say that it is two-dimensional (I would have then had to call it a 'disk') but, rather, that it *more* two-dimensional than a ball of radius 1 m by the amount indicated by the A/V parameter. Also, this argument was meant as nothing more than a motivation for axiom 1, which is really what should be attacked to destroy the idea.

You say: "Also, if nucleons were flat, they must interact in a plane stronger than in other dimensions that contradicts to experimental data."

As I was answering your objections, I just realized that a crucial concept which I did not sufficiently emphasize is bound to lead others to misunderstand this aspect of my idea. Thank you so much for bringing this to my attention!

When we actually 'measure' a nucleon (i.e. at that precise moment) its state collapses to an eigenstate. The 'collapse' is not well-understood, but I interpret this to mean that there is a brief moment where the state is not describable by a phase. One argument which may be enlisted in support of this view is that when we multiply the phase (and the rest of the wave function) by its complex conjugate to get a term proportional to its probability of occurrence, the phase disappears. Indeed, it is well known that a wavefunction uniquely specifies a state only up to a phase for this very reason. Of course, if we assume that during the measurement the phase disappears, than we must also assume that very shortly after the measurement, the phase has to reappear because the state spreads out in space again according to Schrodinger's equation. But the point is this: when we talk about the shape or dimensionality of nucleons, we talk about them usually as they are when we do a measurement on them, and when we do a measurement, if the phase presumably disappears, then the nucleon *at that moment* is not characterized by a phase, and hence not subject to the claims made in my essay. In short, at the moment it is 'measured', the nucleon exists in spacetime and, in particular, it is *not* flat (i.e. 2-dimensional), but 3-dimensional, much in agreement with your assertions. Again, I thank you for making me aware of this point which definitely needed further clarification. Please let me know if this makes things any clearer.

You say "Please read the Wikipedia_Photon: Rather, the photon seems to be a point-like particle since it is absorbed or emitted as a whole by arbitrarily small systems, systems much smaller than its wavelength, such as an atomic nucleus (10-15 m across) or even the point-like electron."

This is really another 'interaction' question, and my answer has to be again that in this paper there was not enough information provided to say anything specific about interactions. Just to be clear, I consider this a shortcoming of my argument, not a rebuttal to your objection. There is a follow-up paper (as yet not finished, unfortunately) which will hopefully provide more information on this. My original plan was to have all of the papers finished a 'go public' at the same time. Very regrettably I was not able to finish them all before the contest deadline, and taking taking advantage of this opportunity meant that it would force my hand before I was really ready. I can only request to bear with me until, hopefully very soon, the follow-up paper is finished so that there are actually specific ideas about interactions which can be evaluated.

You say: "Also, since photons must be 2-dimensional entities, they must have different properties in a plane conserning third dimension that contradicts to experimenal data."

I must admit that I'm not exactly sure what you mean. It seems to me that you are still thinking very much in terms of the classical trajectory picture. If so, please be aware that my framework makes no attempt to support such a picture for photons which is, indeed, contradicted by standard quantum theory. If I misunderstood your objection, please clarify.

Constantin, I appreciate that you took the time to evaluate the essay. My impression is that at least some of your objections arose because I presented only a part of my theory, and this incomplete picture can easily give rise to misunderstandings. Of course, it is my responsibility to present a complete picture, and I hope to have remedied this problem very soon. If you find further objections, please do not hesitate to let me know.

Dear Armin,

You wrote: ''I would be grateful if you could point me to any place in my essay where I mentioned anything about any kind of interactions''.

The absence of this conclusion in your theory is a flaw in your theory because it is logically self-evident. You wrote: In order to transition from three to two dimensions, a direction in space has to vanish. There is a way of postulating a scale at which space vanishes while area is preserved which avoids these difficulties: we assume that at that scale not only space vanishes, but spacetime itself is reduced by one dimension''. Therefore ''all objects of atomic and nuclear proportion have in common is that, compared to objects on our scale, they are vastly more two-dimensional''.

Consequently, if a direction in space has to vanish, it is self-evident that a particle can interact in two dimensions only, because one does not feel other dimensions. It is self-evident, it is a right logical conclusion and I'm surprised that you missed this inevitable conclusion in your theory. For example, imagine two one-dimensional objects (lines) in one dimensional space. They can interact one with another in one dimension only because they do not feel other dimensions. Please explain how these lines can interact in three-dimensions. Thus, since particles really do not interact in a plane, but in space, it is a evidence that the ''areatime'' theory is wrong.

''It seems to me that you are still thinking very much in terms of the classical trajectory picture''.

The classical trajectory picture appears as an inevitable consequence of our discussions about the shape or dimensions of elementary particles. According to quantum mechanics, a particle is smeared out over some region of space and its position and momentum is uncertain. Therefore it is senseless to discuss about the shape of a particle ''photons must be 2-dimensional entities'' because it leds to the classical trajectory picture. Another your proposition ''When I claimed that smaller objects are more two-dimensional than larger ones of same shape'' also contradicts quantum mechanics; particles cannot have shape (as a plane). Since a particle is smeared out over some region of spacetime then one is in three-dimensions always and therefore the notion of areatime is wrong. And the propositions ''Photons exist in areatime. photons must be 2-dimensional entities'' contradicts quantum mechanics.

Sincerely,

Constantin

Constantin,

I can see that there is a gap between what you think my theory says and what it actually says. It is my responsibility to make it very clear what it actually says, so I'll have a go at it.

You wrote: "The absence of this conclusion in your theory is a flaw in your theory because it is logically self-evident."

I'm not sure what you mean. What is 'it' that is logically self-evident? The absence of a conclusion (or rather, conclusive statement) about interactions? If that's what you meant, then I'll have to again request that you wait until the follow-up paper is finished. Or did you mean that the (necessity for?) interactions is logically self-evident? I don't think that interactions are logically forced upon the structure of quantum mechanics. There are such things as free particles, after all, and we could have lived in a universe in which that is the only kind. Please clarify what you meant if I did not address your comment.

You then quoted two passages out of my paper, connecting the antecedent to the subsequent by 'therefore', when in fact there was no such connection in my paper, thereby changing the meaning of the conjunction of the passages to an assertion which is not contained in my essay and furthermore seems so obviously false that you were "surprised" that I missed this "inevitable conclusion". In philosophical circles, this is called a straw man.

I'll give you the benefit of the doubt and assume that this came out of a genuine misunderstanding rather than bad faith, mainly because at this stage it is very easy to misunderstand this idea. So let me explain. As I mentioned in my previous post, this whole business about smaller objects being more two-dimensional than larger objects of same shape is merely a plausibility argument to motivate axiom 1. The key idea, and the one you really should focus on, is axiom 1. You assert that "if a direction in space has to vanish, it is self-evident that a particle can interact in two dimensions only, because one does not feel other dimensions". Agreed, but that is not what I claim. I specifically mentioned in my essay that positing that a direction in space vanishes poses difficulties because it conflicts with isotropy of space.

If you take axiom 1 as a given, however, it is not 'a direction in space' that vanishes in that postulated limit, but the volume element in question 'all at once' because the fundamental quantity that changes in that limit is spacetime, not space. Thus it also makes no longer any sense to talk of 'particles' in that limit or how they interact, and your objections about their interactions being preferential along a plane do not apply. That is because in that limit *they do not actually exist as particles*. Of course, we do know that particles exist and interact in space but, and this is the a crucial point I tried to emphasize in my previous response, *we know this as a result of measurements*, and if we assume that a measurement causes the phase to disappear (however briefly) then for that duration there actually is a particle in space (and spacetime) that is manifesting the properties that are being measured. This is actually quite consistent with the orthodox interpretation of QM, according to which a particle has no definite properties unless it is measured. The question of what a 'measurement' is from the perspective of this theory is addressed at least in some detail in the follow-up to this paper. I ask for your patience on these details until I get to finish my paper. In the meantime you may wish to read a related paper of mine which discusses this aspect from a more philosophical perspective:

"Ontology and the Wave Function Collapse" at

http://deepblue.lib.umich.edu/handle/2027.42/83153

You say "The classical trajectory picture appears as an inevitable consequence of our discussions about the shape or dimensions of elementary particles." I'm afraid that is incorrect. If photons really exist outside of spacetime in the manner specified in my paper, it can be perfectly sensible to talk about their shape and dimensionality without its 'inevitably' leading to photon trajectories in space. The events associated with the 'life' of a photon are its emission and absorption. Assuming that these count as measurements, what you have, according to this theory, are two events in spacetime related to each other by a distance in space ct and time interval t due to some process that occurs in areatime. No trajectory in space required, in fact if there were a trajectory it would contradict the notion that photons exist in areatime!

You say "According to quantum mechanics, a particle is smeared out over some region of space and its position and momentum is uncertain." If by 'uncertain', you mean 'not well defined' then I agree.

You say "Therefore it is senseless to discuss about the shape of a particle ''photons must be 2-dimensional entities'' because it leds to the classical trajectory picture."

Please see my above comment.

You say" Another your proposition ''When I claimed that smaller objects are more two-dimensional than larger ones of same shape'' also contradicts quantum mechanics; particles cannot have shape (as a plane). Since a particle is smeared out over some region of spacetime then one is in three-dimensions always and therefore the notion of areatime is wrong. And the propositions ''Photons exist in areatime. photons must be 2-dimensional entities'' contradicts quantum mechanics."

Again, you are confusing a mathematical observation with an empirical one. The mathematical statement that the A/V ratio of smaller objects is larger than that of larger objects of same shape is true independent of the laws of physics that govern our universe. It is true even though we cannot ascribe to quantum objects a definite shape. My theory attempts, in part, to provide an explanation for why we cannot do this. Let me also urge you once more to focus on the axioms of my theory (or the conclusions I draw from them), rather than the motivating arguments leading up to them.

Thanks again for taking the time to consider my ideas, I think that sparring with you is valuable training for future encounters with other skeptics.

Armin

Armin,

It is a good method to defend your essay by claiming that nobody can understand your unfinished theory. Meanwhile, my objections were correct because there is the main conclusion at the end of your essay: "The derivation implies that quantum objects actually exist in areatime". It is your words that: all objects of atomic and nuclear proportion have in common is that, compared to objects on our scale, they are vastly more two-dimensional. Therefore, at least partially, the essay contradicts to reality. Let the FQXi community sees, if the quantum particles are flat or not. The existence of head-on collisions proton-proton, electron-electron in colliders is a proof that quantum particles are not flat. The Compton scattering phenomenon is a proof that photons are not two-dimensional entities.

Armin, this proposition ''The classical trajectory picture appears as an inevitable consequence of our discussions about the shape or dimensions of elementary particles'' is true, because, if you'll try to see the shape, for it is necessary to localize a photon in a very small region of space with definite position - and it is an approach to classical picture. The macroscopic classical bodies only seem to have the ''definite'' positions and trajectories.

I finish here, since Armin does not recognize the logic, confuses readers and uses the opposing propositions; He wrote first in the essay that particles (photons) have the shape, then he says the opposite. He wrote first in the essay that quantum particles are flat, then he tries to show the opposite...

Sincerely,

Constantin

Armin,

I've had a chance to your essay a second time, but really haven't had a chance to study it. I have one question to start. You begin with the properties of the ratio of A to V, but then your first axiom relates quantities of spacetime U_4 in the limit as V approaches 0. Since the geometry of spacetime is different then the geometry of space, shouldn't V be in terms of the invariant interval such that:

[math]A/V \propto\ {(r^2-(ct)^2)}^{-1/2}[/math]

In other words, how do you know that time doesn't vanish also, since c approaches infinity at this scale. Doesn't it?

Dan

Constantin,

You wrote: "It is a good method to defend your essay by claiming that nobody can understand your unfinished theory."

I did not claim that"nobody" understands my essay, only that you misunderstood it. But, I don't blame you because this essay presents only part of the picture.

You wrote: "I finish here, since Armin does not recognize the logic, confuses readers and uses the opposing propositions;"

Fortunately, our exchange is publicly available so that readers can decide for themselves how accurate your characterizations are.

I thank you for the time you took to consider my essay and for making clear the dangers of presenting only a partial picture of a truly novel idea. My hope is that once the rest is in, this sort of problem will become moot.

Best,

Armin

Dan,

Before I start, let me thank you for making the extra effort of reading my essay a second time and for raising an interesting question.

There are two separate issues here:

First, I realize now that I used the same letter for two distinct concepts, which may cause confusion. Pardon me for that, I will attempt to clarify now:

The A/V ratio in the beginning was used as an argument to make axiom I seem more plausible. In this context, A refers to the surface area of a 3-D object, which naturally exists in spacetime.

After axiom I is introduced, the symbol A refers to a two-dimensional region in areatime within the limit specified by that axiom.

So, before going further in answering your question, I must specify the sense in which A is used. My impression is that since you used A in the context of the A/V ratio, you mean it in the surface area sense, so that will be sense in which I'll use it as well.

The second issue has to do with how to characterize the 'transition' from U_4 to U-3 in terms of the components of the volume element. It seems that you are saying that the occurrence of this transition should be independent of the inertial frame used (did I understand right?) and to make it so, one should use an expression for V in terms of the invariant interval. I admit that I need to think about this, I will get back to you soon.

Thanks again,

Armin

Armin

Irvin,

Yes, you where correct in the way in which you interpreted my correspondence. I was referring to A in the surface area sense, and believe that since you are working with quantities of spacetime in your axiom, you should also be using an expression for V in terms of the invariant interval. The important question is: As V of spacetime approaches zero does U_4 "transition" to U_3 or U_2 (which is 2-D space, with no time)?

Dan

Dear Sir,

The validity of a physical statement rests with its correspondence to reality. We do not see how this condition could be satisfied in your description of area-time.

You have correctly described the relationship of Area that is related to two dimensional fields and Volume that is related to three dimensional structures. Both are related to the radius r or rather d or 2r. When r is reduced, obviously both are proportionately reduced. But it does not make a sphere (a three dimensional structure) flat, i.e., a circle (a two dimensional structure). Appearance may or may not be reality. We have shown in our essay that what we see is not the same as what we measure. The difference can be shown mathematically as follows:

Write down the formula for the Volume and Surface Area of the Sphere. Here the numbers 4/3 and 4 respectively and pi are constants. The only variable is r. Both vary according to the variations of r. Thus, these variations are proportionate and depend upon the value of r.

Now divide both the formulae by 4 pi r^2.

The result: r/3 varies as one.

Or r varies as 3.

This means that for every increase of r by unity, circumference of the sphere increases by 3, whereas we know that it actually increases by pi or 3.141.... Since circumference of the sphere is related to the diameter of the cylinder containing the sphere, which is used to determine the values of the Volume and Surface Area of the sphere, it is also related to the Volume and Surface Area of the sphere. Thus, there is an anomaly. The other mathematical derivations of the values of the Volume and Surface Area of the sphere are also not strictly exact, but near approximations. Thus, the anomaly is not explained by these.

The anomaly is further reinforced by the size of the radius of atoms using a scanning tunneling microscope. On the periodic table of the elements, atomic radius size tends to increase when moving down columns (periods), but decrease when moving across rows (groups). While the increase in size with increase in period is understandable, the decrease in size with increase in group Number has not been satisfactorily explained. We explain those differently, which also solves the anomaly of pi vs 3 and derives the value of pi from fundamental principles.

We treat gravity not as a force that pulls, but a force that stabilizes - be it the atomic orbit or the planetary orbits. We also treat gravity not as a single force but as a composite force of 7, which we derive from fundamental principles. These 7 forces five rise to the 7 periods. Each atom also has these 7 varieties of gravity in it, which regulates its internal dynamics. Their inter-relationship is reveled from the inter-relationship of the energy levels of the s, p, d and f orbitals. As we have derived earlier, r varies as 3. The r is determined by these 7 forces collectively. Thus, the atom has a 7 x 3 = 21 layered structure. While this constitutes the nucleus, the electrons that confine these fall into a different category. The nucleus part is subject to fermionic rules of exclusion. But the electron orbits are subject to the bosonic principle of superposition. Thus, the bigger the atomic number, the bigger the force of confinement. The electron sea is responsible for our perception of the object. But since they do not have a fixed structure like the nuclear part, they are not apparent in measurement. This explains the ratio r varies with (21/7) 3. This also explains the perceived value of pi as (22/7) 3.141...

Regarding the other parts of your essay, we will comment separately.

Regards,

basudeba

Dear Armin,

Wisdom is more important than imagination is more important than knowledge for all the we know is just an imagination chosen wisely.

Please read Theory of everything at your convenience posted by me in this contest.

Who am I? I am virtual reality, I is absolute truth.

Love,

Sridattadev.

FYI: I responded to another gentleman "Basudeba", asking me to comment on part of your Essay. Therefore you may be interested. You can see my reply to your Essay under my Essay: By Russ Otter Subtext: Digital or Analog? Date of reply March 7th. To Dear Basudeba,

Your Essay is obviously brilliant, but it properly draws no critical conclusions, however it does open some doors...

Deep Congratulations on your outstanding detail and work,

Russ

Dear Sir,

We have replied to Mr. Russ Otter in his thread. Kindly see it there.

Regards,

basudeba.

Dear Armin,

Your essay offers a very creative idea, to try to understand the quantum phase from first principles. It is interesting to try to imagine "area without volume," where, as you put it, "space vanishes while area is preserved." It reminds me of the idea of compactification for higher dimensions, only applied to spacetime itself.

Best regards,

Paul

Dear Armin Nikkhah Shirazi,

I like your essay and I have a similar result. In my case I assume directly the periodicity as constraint (in your paper is $\tau_a$), which is nothing else that the de Broglie periodicity of fields. I show that this provides a remarkable matching with ordinary relativistic QM.

I hope you'll give a look to my essay [link:www.fqxi.org/community/forum/topic/901]link[\link].

Good luck,

Donatello

PS: you should give a look also to the concept of de Broglie phase harmony.