A Derivation of the Quantum Phase by Armin Nikkhah Shirazi

Hi Wilhelmus,

I did not know that this was your first attempt at writing an essay. When I first started out, my very first essay that expressed my ideas would have been subject to the exact same criticism that I gave you and probably a lot more, so don't feel bad. This is something that takes a lot of practice. My ideas have gone through many, many drafts and the version here is very different from my first few attempts, and the journey (to write better scientific essays) is still far from over for me, and in fact may never end.

Now, about your question: I basically just wrote out Axiom I in words, and (sorry I should have explained this) I used the capital letters L and T to indicate the dimensional units. So L^3*T is just the dimensionality of U_4, just as L^3 is the dimensionality of V.

If you recall, I was arguing in my essay that our current view is that as we consider a volume element to go to zero, everything (including spacetime) is assumed to go to zero. You won't usually see this assumption stated this way, but you can realize this indirectly, because our description of particles as point-like implies this. Point-like particles are zero-dimensional.

So I wanted to make clear that I was assuming something fundamentally different, namely that even after a volume element goes to zero "something" remains: it is not spacetime but areatime. That means that even in the limit in which there is no more space (V=0), there is a non-zero quantity of something, and this has, of course, a magnitude attached to it.

Ok, so why not introduce a length limit? Well, first, as mentioned before the introduction of such a limit brings along with it a host of known problems that physicists are still grappling with. But apart from that it is really not necessary, because I postulated that the shape of this quantity of areatime is variable.

Here is an analogy with volume (because volume is easier to visualize than areatime): Suppose you have a cube with side 1m, and just for the sake of argument, let's say that the volume of this cube constituted a limit, but that its shape was allowed to remain variable. It's volume is 1m^3, but you can still avoid going below this limit at very small distance scales, as long you can compensate along the other directions. So, for example, you can flatten one side to 10^-49 m, but if the product of the other two sides is larger than 10^49 m^2, the volume is still above that limit. So you see, I can limit xyz without limiting x, y or z individually if I am allowed to keep the shape variable. This is something I explicitly assumed for the postulated limit.

Also, I still get a sense that there is a very important aspect of special relativity (SR) that you may not have realized, so let me point it out.

Recall that one of the postulates of SR is that all inertial frames are equivalent. There is no such thing as an "absolute" inertial frame of an observer in spacetime. This implies that it is perfectly acceptable to consider there to exist frames that are arbitrarily close to the speed of light. Let us consider a frame that was in motion relative to the earth at 99.999999999999% the speed of light (i.e.v=0.999999999999999c) . The diameter of the earth is 12, 756 km but, to keep it simple, let's round this down to 10,000 km 10^4 km, which is 10^7m (remember, this is relative to an observer frame who is stationary with respect to earth). What is the diameter of earth in the frame of the moving observer?

Using the Length contraction formula, we get:

[math]L'=L*\sqrt{1-\frac{v^2}{c^2}}=10^7m *\sqrt{1-0.99999999999999^2}\approx 10^7m*10^{-7} m=1m[/math]

In the moving frame, the earth would be contracted to about a 1 m diameter along the direction of relative motion. What is the point of this example? It is this: There was nothing special about this frame. I could have chosen a frame that was going faster by adding fortynine 9's to the percent figure of this moving frame. In this other moving frame, the diameter of the earth would be contracted to 10^-49 m. And again, there is nothing special about this frame. It is *extremely* close to the speed of light relative to us, but it is just as good as your rest frame. If you think that this speed is unrealistically fast for any actual object, you are still thinking inadvertently in terms of absolute frames.

So you see, the problem with Special relativity postulating a length limit is actually worse than my previous explanation may have given you to believe.

But as I said before, it is possible that such a length limit does exist, but then special relativity (and actually General Relativity and Quantum theory in their present form) have to be changed. And a lot of researchers in fundamental physics try to do just that.

If you really wish to continue your development in this area and have your views seriously considered, then you will have to seriously study the subject matter. There is an excellent web resource for aspiring theoretical physicists that was created by your own countryman Gerardus 't Hooft. It can be found here:

http://www.staff.science.uu.nl/~hooft101/theorist.html

Good luck and best wishes,

Armin

The formula did not come out right, here is another attempt:

[math]

L'=L*\sqrt{1-\frac{v^2}{c^2}}=10^7m *\sqrt{1-0.99999999999999^2}\approx 10^7m*10^{-7} m=1m

[/math]

If this doesn't come out right either, you can just paste the equation below into any online latex editor (google) to see what it looks like

L'=L*\sqrt{1-\frac{v^2}{c^2}}=10^7m *\sqrt{1-0.99999999999999^2}\approx 10^7m*10^{-7} m=1m

Armin

Dear Armin,

Thanks a lot for your help, the site of 't Hooft is very very good, I am going to study it.

What you indicate with the SR and the observer that is going almost at the speed of light is clear to me, it explains that we are have to regard it as "local" velocities, the subjects do not perceive their relative lengnth or volume if you want that is realtive to other observers who are speeding at even more as the speed of light (see for example the CMBR , the origin of this is about 45 billion lightyears away and is speeding at (much) more as the speed of light from us, but perhaps I am just simplifying here too much.

I come back to you

best regards

Wilhelmus

To anyone who is interested,

I'd like to mention that I recently posted a paper which gives a conceptual discussion of the framework that I have been working on, and which is hopefully accessible even to those who only understand the basics of quantum mechanics.

It is entitled "A Novel Way of `Understanding' Quantum Mechanics"

It can be found either at Deep Blue, the University of Michigan repository at

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

or at

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

I appreciate any feedback. Thanks

Hi Armin,

I read your article twice now, but the way you are treating TIME is difficult to accept forme, on the other hand you come back to the A/V ratio, that I accept now if you apply it to the scale of our material universe (not in the mathematical way like in Fractals wher you infinitely up and down without any dimension lost or gained). I left also a post on Deep Blue, but I am not sure that it went all right.

Just a thought :

Imagine:

1. a point in an endless universe, no time needed

2. two points in an endless universe : time needed (reference of point a and b, and the time needed to go from a to b, at any possible velocity)

My opinion is that time is emerging so there is no difference in atwo dimensional world with the time in a three dimensional world, you even rotate by a quarter of a circle, really I lost you there totally, perhaps I am not intelligent enough.

best regards and

think free

Wilhelmus

Hi Wilhelmus,

Thank you for your response. I am using the concept of time as it is used in relativity, but I apply it to areatime. The concept of time in relativity is counterintuitive and even today, there are still many people who do not accept it. As you know, it distinguishes between the concept of coordinate time and proper time, where the proper time is proportional to the distance or interval in spacetime. Because this simple if counterintuitive conception of time explains lot of facts about our worlds with very few additional assumptions ,I do believe that relativity provides a correct description of nature and that includes the way it treats the concept of time.

Really, I have the impression that your problem is with the concept of time as it is used in relativity. I would advise you to first learn it thoroughly, and then if you still do not accept it, at least you know exactly what it is that you are rejecting. If you take this advice and then appreciate how many seemingly disconnected facts about nature suddenly fit together just with this conception, whereas otherwise they would seem to be totally unrelated, you may just change your mind and choose not to reject it.

Armin

Hi Armin,

As far as I see it, I have no problem at all understanding time in relativity, it is that I have a problem in understanding your text on page 5 and 6 :

* you are making a difference in the "nature" of time in three dimensions and that in two dimensions, of course it is difficult to design a twodimensional clock, but I think that is not neccecerry because time is "emerging" (in my point of view) and in fact not existing (see also Julian Barbour's PLATONIA : "There is no passage of time, merely a set of unconnected instants, or "nows", In my essay it is the consciousness that is able to form these lines), so in fact from my point of view you are treating time as if it is a real dimension that is changing when the number of dimensions are changing (like in your A/V ratio .

* "Hypothetical objects in areatime cannot have a spacetime history", I understand your view, it is as if the point in the two dimensions becomes a line in the three dimensions (beginning of your text), this is a good mathematical way of representing the extra's that are appearing when you are adding a dimension, only time cannot be treated like thet (I think, and also others) The symmetry you are adding on page 6, by comparing the proper time Ta in areatime with the proper time T of an observer in spacetime and the transformation you think is needed to arrange this idea , including the so called "perpendicularity" (I think you took that from the fact that when adding a dimension the line that was the point is penrpendicular on the point with reference to the x and y axes) but I really doubt this view also because of the reasons that I mentioned above.

* Your idea of actualisation with regard to these diminishing dimensions is very understandable, an endless quantity of possibillities is "falling down" to one (like in a FEYNMAN diagram), but this way of visualisation is not nececerrily the base of a new theory I think. You mention (page 11) "the collapse process is in fact the mechanism by which all of spacetime emerges from spacetime". In fact this is the essence of your view of reality, mathematically it "seems" at the first sight all right, but try to dig deeper and you will see that every comparision has its "LIMITS", it is at these limts,in my humble opinion, that your theory differs in essence with mine, this is not bad at all , because we all are thinking in areas where nor you nor me can do and repeat experiments, you may think that you are more scientific because of the fact that you know more formula's, I fully agree with that, but it is not my goal to become also a "specialist", however I learn each day, and I hope you do too.

keep on thinking free

Wilhelmus

Hi Wlhelmus,

On your first point, again I have the impression that the difficulty is with exactly understanding what the concept of proper time in relativity is.

Let me state it explicitly:

In special relativity, in cartesian coordinates, the spacetime interval

[math]

ds^2

[/math] is defined as

[math]

ds^2=c^2dt^2-dx^2-dy^2-dz^2

[/math]

(you can also flip the signs,but that is irrelevant here). Notice that the time here is *not* the proper time, it is called the coordinate time.

The proper time

[math]

d\tau^2

[/math]

is defined as

[math]\frac{ds^2}{c^2}

[/math]

so that we can express the proper time also as

[math]

c^2d\tau^2=c^2dt^2-dx^2-dy^2-dz^2

[/math]

For areatime, the analogous proper time

[math]c^2d\tau_A^2

[/math]

is

[math]

c^2d\tau_A^2=c^2dt^2-dx^2-dy^2

[/math]

do you see that they are different? Also, because spacetime in Special relativity does not have a Euclidean geometry you cannot directly compare dx and dy in spacetime with areatime.

so the argument is that because you cannot use

[math]ds_A^2=c^2d\tau_A^2

[/math]

to measure distances in spacetime, you cannot age along

[math]d\tau_A^2

[/math]

in spacetime. Conversely, if something ages along

[math]d\tau_A^2

[/math]

it cannot age along

[math]d\tau^2

[/math]

and since no time is passing for it in spacetime, it cannot have a spacetime history in its frame (It can have an areatime history in its frame, though).

I believe that to someone who understands relativity this argument should be obvious, which is why I only put it in words in my paper. Also, Julian Barbour's conception of time is by no means generally accepted. I would say that his is also what I previously referred to as a "highly speculative theory", but special relativity is not.

As for the visualization *It is only an analogy*. Quantum Mechanics has something very similar, it is called the wave function collapse, and it has been an open problem for the last 80 years or so to understand what it means, and whether it even actually occurs. I am not aware that anyone has tried to connect the wave function collapse to the collapse in terms of the analogy. Please be clear that the actual mechanism I propose for the wave function collapse is different from the analogy. I have the impression you have confused my analogy with the actual explanation I propose.

(Also, a Feynman diagram has nothing to do with the wave function collapse, it is simply a diagram that visually depicts certain equations that model interactions between particles).

Yes, I do try to continually learn, and I would like to suggest the advice that I have tried to follow myself, which is to try to make sure that one really understands the concepts one mentions, because if you use them differently from the way they are normally used it becomes difficult to communicate with others. Also, some people when they notice that someone totally uses terms differently from the way they are normally used will stop taking seriously what that person says. In an ideal world, people would be more patient, but I have experienced myself that the real world is not like that.

Armin

Hi Armin,

thank you for your "clarifications".

In SR the flow of time is a. relative to the mass and b. dependant on the relative velocity of subjects. I never met the so called areatime that you introduce (logic because it is your idea). Your formula's above are clear the difference is the dz^2, simply because you treat a dimension less in your so called areatime.

However the essence of your theory is the A/V ratio , this subject we treated together and I understand now your point of view, only I still think that you are mixing up mathematical approach and the material approach. In your exemple you begin with a sphere, but you can also take a cube I think, the surface of a cube is 6 x a^2, the volume a^3, so the mathematical ratio of A/V is always 6/a, whatever cube you take, this A/V ratio becomes very little when we go to the material universe and agree upon a "length". then you can go up and down in the ratio, if I take the Planck length as the minimal length where our physical laws are still working then you get an A/V ratio of 6/ root of hG/2pi c^2 = 6/1.6x10^-35m. In my opinion that is the minimal A/V ratio (as for now) call it the Planck A/V ratio. In my opinion this is the ratio where causality disappears, the arrow of time is no longer valuable, you say that there disappears only one dimension and you enter in your areatime, you still accept time and so the a

sorry hit a wrong button, so I continue :

you still accept the arrow of time, which I don't.

Both our views are as I think not compatible, but we both are exploring our own "new" reality, I am happy to discuss with you and really it gives me lots of thoughts, there is still one thing that I would like to mention : take a look at the fractal universe, there you can go infinitely up and also down, without loosing or gaining any dimensions, it is in my opinion a typical mathematical universe, where ratio's are fix, so please understand that only when you inroduce a specific "agreed upon" length the ratios are also taking values that are taking avery minimal and also maximal size, it is these "relative" sizes that you and I use to explain our ideas.

best regards and

think FREE

Wilhelmus

Hi Wilhelmus,

You said:

"In SR the flow of time is a. relative to the mass and b. dependant on the relative velocity of subjects."

Roughly speaking yes, but that applies to coordinate time. I am referring to **proper time** in my paper. Proper time is invariant, it is proportional to the invariant interval.

Please, Wilhelmus, I almost have the impression that you are taking my suggestion to study physics as an insult, it is not meant as such. It is meant to help you communicate your ideas more effectively and also to help avoid elementary misunderstandings when reading someone else's work. You don't need to be a "specialist" in relativity or quantum mechanics but you do need to have at least a minimum background if you want to hold an in-depth discussion about these topics. The difference between coordinate time and proper time is something that is taught early on in relativity. If you don't understand the difference, you cannot claim that you understand relativity.

You said:"I never met the so called areatime that you introduce."

Well, the term is mine, but the idea of a 2+1 spacetime is not new, in fact often toy models in general relativity use this to simplify some of the mathematical difficulties to study certain situations. See for example http://books.google.com/books/about/Quantum_Gravity_in_2+1_Dimensions.html?id=C0_HROt5D8YC

You said:"Your formula's above are clear the difference is the dz^2, simply because you treat a dimension less in your so called areatime."

The difference is actually more subtle: You see, because areatime is postulated to be the lower limit, you *cannot* directly relate dx in areatime to dx in spacetime or dy in areatime to dy in spacetime. What that means is that it is not just that the z-direction vanishes, but that spacetime "as a whole" is replaced by areatime. So, strictly speaking, I should have labeled the dx and dy in the formula above for areatime with a subscript A.

You said:"However the essence of your theory is the A/V ratio."

No, the essence of my theory is its axioms. I am really surprised that you are saying this after I've been explaining several times that the A/V ratio is a **plausibility argument**. Therefore it cannot be the essence of my theory.

You said: In your exemple you begin with a sphere, but you can also take a cube I think, the surface of a cube is 6 x a^2, the volume a^3, so the mathematical ratio of A/V is always 6/a, whatever cube you take, this A/V ratio becomes very little when we go to the material universe and agree upon a "length". then you can go up and down in the ratio, if I take the Planck length as the minimal length where our physical laws are still working then you get an A/V ratio of 6/ root of hG/2pi c^2 = 6/1.6x10^-35m. In my opinion that is the minimal A/V ratio (as for now) call it the Planck A/V ratio.

if you want to posit a rigid cubic lattice as the lower limit of spacetime, you have to explain how the symmetries of spacetime are preserved, for instance how you address the length contraction problem (remember, I mentioned before that loop quantum gravity has essentially the same problem)

You said:"you still accept the arrow of time, which I don't."

I accept the definition of proper time, as defined in the theory of relativity. The arrow of time is a separate problem that is not addressed in my papers.

You said: "Both our views are as I think not compatible, but we both are exploring our own "new" reality, I am happy to discuss with you and really it gives me lots of thoughts."

Think about this: Who are you creating your theory for? If it is just for yourself, then you don't need to study relativity or quantum mechanics, you can make up whatever you want.

But I get the impression that you want to share your theory with others and get them to consider it seriously. In order for that to happen, you have to be aware of what has been done already. The reason is that otherwise it could happen very easily that your theory conflicts with things that we have already observed to be different and then your theory is shown to be wrong.

If you don't study the subject matters i.e. relativity and quantum mechanics, you won't know all the observations you have to make sure your theory agrees with. Also, it is only through the study of these subject matters that you gain an appreciation for what creating a new theory actually entails. For example, can you state what experiment can be performed to test whether your theory is correct?

You said:"take a look at the fractal universe, there you can go infinitely up and also down, without loosing or gaining any dimensions, it is in my opinion a typical mathematical universe, where ratio's are fix, so please understand that only when you inroduce a specific "agreed upon" length the ratios are also taking values that are taking avery minimal and also maximal size, it is these "relative" sizes that you and I use to explain our ideas."

I see no physical motivation for introducing fractal dimensions into my idea. Also, at this point I do have a self-contained model. What is needed at this stage is peer criticism, which has been very difficult for me to obtain.

I hope that you do take my advice seriously. Read again what `t hooft says in the introduction of his theoretical physicist page. I wish you good luck in your endeavor.

Armin

Thank you Armin for the exhaustive reply,

perhaps I am more a philosopher as a scientist.

Yes I want to discuss my ideas with others in order to know if I am just crazy or perhaps trying to find new solutions in science, that untill now seems to be stuck.

No my ideas cannot be tested , just like the 10 dimensions of string theory and so on, only my idea is simpler.

Axioms are starting points that can be choosed personnally, I have other axioms as you have, but that gives us stuff to discuss. As a matter of fact I think that each human being has his own unique reality with his own axioms, this is what makes our world interesting but also dangerous, becuase every human also has the tendancy to think that he has the only TRUTH, I don't.

Of ciurse you too have different ideas as the scientific world around you, that is a good thing, but be carefull that you do not get chained in your own ideas that is why I always end my posts with :

keep on thinking free

Wilhelmus

Hi Wilhelmus,

You said:"perhaps I am more a philosopher as a scientist."

I like to think of myself in similar terms.

You said:"Yes I want to discuss my ideas with others in order to know if I am just crazy or perhaps trying to find new solutions in science, that untill now seems to be stuck."

I don't think your ideas are crazy, but I do think that in order to be able to be considered as solutions for some of the current problems they will have to be stated in much greater detail and expressed more precisely. And ideally they should make testable predictions.

You said"Axioms are starting points that can be choosed personnally, I have other axioms as you have, but that gives us stuff to discuss. As a matter of fact I think that each human being has his own unique reality with his own axioms, this is what makes our world interesting but also dangerous, becuase every human also has the tendancy to think that he has the only TRUTH, I don't."

Indeed, I agree with you that each of us has his own frame through which to perceive reality and that there is a real danger of mistaking that with an absolutely correct frame.We need to be as vigilant as you are about that.

You said:" Of ciurse you too have different ideas as the scientific world around you, that is a good thing, but be carefull that you do not get chained in your own ideas that is why I always end my posts with :

keep on thinking free"

Well, while I did spend a lot of time thinking about these ideas, this is part of what is required to develop them into full-fledged theories. But now that the basic version of my theory is out I want to work on some other ideas I have as well. I will very shortly post a paper abut the difference between the concept of mass in quantum theory and in general relativity which is directly related to the dimensional theory, and then I have three other papers in preparation (over the next few months) which deal with completely different topics in fundamental physics and philosophy of physics.So yes, I am trying not to chain myself to just one set of ideas.

Armin

Hi again Armin,

It is true that you can give the most grounded answers when you are aware of all the details that are hided behind the essence of a question, the dnager is also to get lost in the details, so in this area of time (21th century) it is quite impossible to know all the details just as it was in 18th century, that is the reason that I am not diving into text books but when I don't understand an expression (sometimes these scientists talk abrakadabra) I go first to Wikipedia an study the thing, it is together with Google a treasure of knowledge. Also I think that just by not loosing yourself in details can reveal the essence that is important for my way of constructing and understanding the "reality".

I hope really that you keep me informed of your future papers, I just bumpted in your latest paper by accident during my search for truth, therefore my e-mail address is

wilhelmus.d@orange.fr

keep on thinking free

and best regards

Wilhelmus

ps

congratulations with your continued presence on the home page, forum updates, it seems that your ideas have sense (like mine , I also was about 7 weeks there), gives a good feeling isn't it ?)

wilhelmus