A Derivation of the Quantum Phase by Armin Nikkhah Shirazi

Hi Armin,

It's been a busy summer and I just had a moment to revisit your forum and the question to you that I addressed above. I have to admit to thinking about it from time to time, yet never gave it the attention it deserved. I'm glad to see that you have been working hard and plan to review the links you gave below. I believe your perspective may lead to new and useful understanding.

Best wishes,

Dan

Hi Armin,

As you were mentioned in the FQXi range of Forum updates, I arrived to read your essay.

It was however already on the first page that my attention was drawn to the essence of your work :

"The ratio of A/V becomes larger as the objects become smaller"

Here I would like to comment as follows (and I am not at all a mathematician so if I am wrong please react, I am sure that you will !!!)

Archimedes already made the formula's for the surface and the volume of a sphere:

A: surface : 4πr²

V: volume : 4/3 πr³

So the A/V ratio is : 3/r

This means that with EVERY sphere the A/V ratio is 3/r.

The size of r is a size to be accorded among us, if you take the size of r as a light year then the NUMBER of A/V is very little compared to the number of a millimetre, which doe not mean thet a dimension has been lost compared to the lightyear distance.

Any way I think you make an essential error in assuming that the A/V ratio is changing with lengths that we are assuming, a sphere will always be a sphere and his surface is made of a plane that has no thickness , so the essential ratio will always be the same, it is like going into a fractal, all the forms stay the same and the basic PROPORTIONS also.

My conclusion is that the assumption you make is wrong, dimensions are not diminishing at certain scales.

However I would like to draw your attention to the Planck scale of 10^-33cm, after this length we cannot measure any more and our universe becomes incomprehensible, In my essay I enter a non causal dimension called Total Simultaneity, but that does not matter now.

What I would like to indicate here is that the Planck scale is perhaps the only sc le that is a real limit to our 4D causal Universe.

However for your information there is an article in NEW SCIENTIST of 25 september 2010 entitled : DIMENSIONS VANISH IN QUANTUM GRAVITY, written by Rachel Courtland, Steven Carlip from the University of California (arxiv.org/abs/1009.1136v1) explains his view about a strange behaviour at small scales that fields ans particles start to behave as if space is one-dimensional, and explains that by the QUANTUM FOAM proposed by John Wheeler in the 1950s, so you see ther is nothing new under the sun.

Keep on thinking free

Wilhelmus

Dear All,

If we just observer a human life from pre conception, where the child is a dream of the parents, to how the child acquires knowledge of space and time as it grows and how eventually that being dies and looses the meaning of space and time again we would understand the universe. Answer lies with in us.

Singularity is not only relative infinity but it is also absolute equality,

Singularity is not only out there in the universe but also with in here in our hearts.

Love,

Sridattadev.

Hi Wilhelmus,

Thank you for taking the time to review my essay.

First, let me emphasize that the A/V argument was meant as a plausibility argument and not much more to make axiom I, which on its own is highly unfamiliar, more acceptable. The conclusions of my paper rest on the axioms, not on the plausibility argument.

Having pointed that out, let me now attempt to respond to your comments. I must admit that I did not exactly understand your objection, but I will attempt to further elaborate on the plausibility argument, taking your comments into account.

It is true that the A/V ratio is a dimensionful number, and as such its magnitude depends on the units used. However, I was comparing two different A/V ratios, not making a claim about a single A/V ratio without any context.

To make this explicit, I could have instead of the original wording in my paper explicitly used the ratio of the two A/V ratios of a ball with r=1m and r=10^-11m,

i.e. {(A/V)_r=10^-11} / {(A/V)_r=1} =10^11

This is a dimensionless number, completely independent of units (assuming that you use the units consistently of course). You can use light years or millimeters, but the number will remain the same. And it does tell you something absolute, namely, that the smaller ball has more area per volume than the larger ball or, conversely, that the smaller ball has less volume per area than the larger ball.

If I had made a claim about the A/V ratio of a single object, without comparing it to anything else, then I agree that would have been nonsense, because you can manipulate the magnitude by arbitrarily choosing units. But that is not what I did.

Think about it physically: The changing A/V ratio in conjunction with the fact that mass is expressible in terms of a volume density and not an area density is ultimately part of the reason that there are no basketball-sized dust grains floating in the air, or that we can't walk on water, like many small insects can.

As I perceive our world, its character does change with scale albeit not in a strictly proportional manner, and in my view a substantial factor is the changing A/V ratio of objects at different scales (although it is of course not all, e.g. the cancellation of electrical charges in macroscopic objects and the magnitude of the elementary charge are other very important factors).

I hope that you can now better understand my argument.

As for speculations about the Planck scale, my best understanding is that at best it is a heuristic guess. I have yet to see a substantial theoretical foundation other than it is obtained by combining the central constants of QM and GR, which is really merely a plausibility argument. The fallacy is to think that this necessarily means something. It could, but, absent any deeper reasons, it may not. Not every combination of constants has to signify something. Think of the Planck mass, for example.

I think a lot of people have a vested interest in it meaning something, and so it has taken a more important role than it perhaps deserves and people attribute to it the properties you mention without solid theoretical backing.

As for my views on Quantum Gravity, they are totally divergent from mainstream. If you wish to find out what they are, you are invited to read the follow-up paper to this, which can be found here:

http://hdl.handle.net/2027.42/83865

I regret that I can't just come out and say what my views are, because they are so unfamiliar that I would feel compelled to explain how I arrived at those views, which would take quite a bit of space. The paper, by proposing a novel interpretation of quantum mechanics, in effect does that.

I hope that I was able to address your comments. Should you have have any further suggestions, feel free to post.

Cordially,

Armin

A quick addendum because I realized that giving my Planck mass example without further elaboration may lead to misunderstanding.

Currently, the Planck mass has no known physical significance but that is most likely not what you will hear. What you will hear instead is that the Planck mass multiplied by c^2, which is the Planck energy, sets the scale at which we should expect new physics.

But notice, if we had discovered a quantum theoretically important object with Planck mass, we would have pointed out that this is the significance of the planck mass. Absent such discovery, we have to reframe any discussion about the significance of the Planck mass in terms of the Planck Energy.

To me, this is a little like going through a book with a algorithm (say pick every nth letter) and then discovering ex post facto that some of the letter combinations spell meaningful words. It could mean something, but it may (especially in this example, overwhelmingly likely) not.

This is the fallacy I was referring to. The theoretical reasoning backing the significance the of the Planck scale is to me little more than plausible dimensional analysis and it does not help that the Planck scale is many orders of magnitude beyond the access of experimental test.

Armin

Hi Armin,

Thanks for your reaction.

I still have some great problems with your A/V ratio and the implementation in your theory.

In your answer you indicate you do not take in view that the A/V ratio is only related to the OUTSIDE world, the internal ratio between surface of a sphere and its volume do have always the same constant whatever the scale of radius you are agreeing upon.

The size of the radius compared to the initial measure , for instance light year or meter, is decisive for the scale difference and so if the relative length of the most little length compared to the biggest is or can be negligible and even vanish(???) in your opinion, in my opinion it does not at all become negligable or certainly does not lead to a loss of a dimension, this is as I mentioned already before only a matter of scale (a mm is very little compared to a light year but does exist in his full length (immense compared to the Planck scale) in all its glory.

You use the word AXIOM in your essay and answer, an axiom is self evident, a logical statement that is "assumed" to be true, some points that you indicate in your essay leading to the assumption of your axiom:

"whether there exists a scale at which volume vanishes but area does not"

"by zero volume and finite area still exists in spacetime"

"any direction in space could vanish at that scale"

"there is a way of postulating a scale at which space vanishes while area is still preserved, --- we assume that at that scale not only space vanishes, but spacetime itself is reduced by one dimension"

"presuming the existence of a scale at which space but not the area vanishes etc"

Hereafter you introduce : "areatime" and you exprees the assumption as . AXIOM I

So I feel free not to accept these assumptions based on the arguments above , it is not scientific, because as you indicate yourself it is a SCALAR quantity, without putting constraints to its shape, and a shape is the same at EVERY scale (fractal). Creating axioms on this base is a misunderstanding.

I like your arguments on page 4, regarding the state of photons, though I do not accept your conclusion that they exist in the so called areatime. (se above).

All the math's will be all right but you loose me there, the main problem I have is your assumptions that lead to your axiom 1.

I was at the site handle.net but needed an extra code to enter that are only for the students of your university think.

You have my e-mail but here it is again : wilhelmus.d@orange.fr, I suppose you have the PDF text yourself , so if you want you can sent it, it is of course not a must, but I am interested.

Keep on thinking free

Wilhelmus.

Hi Sri,

Always a pleasure to read your posts from the hart, a singulairity in my opinion only exists in our consciousness, like infinities, our life-line is constituated here in the 4D causal universe and forms indeed the moments of our past that we are aware of (remember), there are an infinite number of moments that we are not "aware" of but our consciousness indicates that there is more .

If you read my essay, the explanations are given (also published on THE SCIENTIFIC GOD JOURNAL) but I remember you read it because your answering posts are known to me, I only put this info here so that our friend Armin will also read it.

keep on thinking free

Wilhelmus

Hi Wilhelmus,

This may be in part because English is not your native language, but I find it difficult to understand your comments.

Nevertheless, I will attempt once more to go through my argument step by step, highlighting where my best guess is as to where there might have been a misunderstanding. I know you said that you are not a mathematician but I'd like to ask you to *please* take the time and make the effort to work through the following simple algebraic argument. I will make it easy and go very slow.

Consider a ball, call it ball 1, of radius 1 meter, or

[math]r_1=1m[/math]

where the subscript 1 of r means that it is the radius of ball 1.

What is its radius in terms of light years? 1 light year, abbreviated by 1 ly , is the distance traveled by light in one year, and that is equal to 299792458 m which to keep it simple I will round up to 30000000 meters or 3 X10^8 m.

So the radius of ball 1 in terms of light years is

[math]r_1= 1m \times \frac{1 ly}{3\times10^8 m}\approx 3.33\times 10^{-9}ly[/math]

So far so good? Now, what is the radius in terms of millimeters? 1 meter is 1000 mm or 10^3 millimeters, therefore

[math]r_1=1m \times \frac{1000mm}{1m}=10^3mm[/math]

Now, the A/V ratio of ball 1, denoted by A_1/V_1, in terms of light years is:

[math]\frac{A_1}{V_1}=\frac{4 \pi r_1^2}{4/3 \pi r_1^3}=\frac{3}{r_1}=\frac{3}{3.33\times 10^{-9}ly}[/math]

When A_1/V_1 is expressed in terms of millimeters, it is

[math]\frac{A_1}{V_1}=\frac{4 \pi r_1^2}{4/3 \pi r_1^3}=\frac{3}{r_1}=\frac{3}{1000mm}[/math]

one possible interpretation of what you wrote is that you seem to think that I'm claiming that A_1/V-1 when expressed in terms of light years or in terms of millimeters is different because the units of measure are different.

If this is what you thought, then you have completely misunderstood my argument.

I totally agree that whether you express A_1/V-1 in ly or in mm it is one and the same. There is no difference because in what you units you express a quantity of length does not change that quantity of length in and of itself. By itself, A_1/V-1 doesn't really tell you anything.

So then, what is my argument?

It is based on this:

You have to compare the A/V ratio of ball 1 with the A/V ratio of another ball with a different radius.

This is the point I get the impression you've been missing.

Let me work through the details:

Consider a second ball, call it ball 2, of radius 10^{-11) (this is 10 picometers). Denoting the radius of ball 2 by r_2, this means

[math]r_2=10^{-11}m[/math]

In terms of light years, r-2 is

[math]r_2= 10^{-11}m \times \frac{1 ly}{3\times10^8 m}\approx 3.33\times 10^{-20}ly[/math]

In terms of millimeters, r_2 is

[math]r_2=10^{-11}m \times \frac{1000mm}{1m}=10^{-8}mm[/math]

The A/V ratio of ball 2, denoted by A_2/V_2, in terms of light years is:

[math]\frac{A_2}{V_2}=\frac{4 \pi r_2^2}{4/3 \pi r_2^3}=\frac{3}{r_2}=\frac{3}{3.33\times 10^{-20}ly}[/math]

A-2/V-2 expressed in terms of millimeters is

[math]\frac{A_2}{V_2}=\frac{4 \pi r_2^2}{4/3 \pi r_2^3}=\frac{3}{r_2}=\frac{3}{10^{-8}mm}[/math]

Do you follow so far? Again, I agree with you that this ratio, whether expressed in light years or in millimeters is exactly the same quantity.

But now we finally get to my argument:

Take the ratio of A_1/V-1 and A_2/V-2 in terms of light years:

[math]\frac{\frac{A_1}{V_1}}{\frac{A_2}{V_2}}=\frac{\frac{3}{r_1}}{\frac{3}{r_2}}=\frac{r_2}{r_1}=\frac{3.33\times 10^{-20} ly}{3.33\times 10^{-9}ly}=10^{-11}[/math]

Notice that this is a dimensionless number, the units cancel out.

Expressing the ratio of A_1/V-1 and A_2/V-2 in terms of millimeters:

[math]\frac{\frac{A_1}{V_1}}{\frac{A_2}{V_2}}=\frac{\frac{3}{r_1}}{\frac{3}{r_2}}=\frac{r_2}{r_1}=\frac{10^{-8} mm}{10^3 mm}=10^{-11}[/math]

Did you notice that this dimensionless number is the same as before? It did not matter whether we expressed the radii in terms of light years or in millimeters.

What does the dimensionless number 10^-11 tell us? It tells us that ball_1 has 10^-11 (or hundred billion times) fewer units of volume per unit of area than ball_2, ***regardless*** of what units you choose. You can choose light years, millimeters, inches, yards etc. the number 10^-11 will not change.

Also note that while to keep it simple I used the specific example of balls, the general fact that smaller objects have less volume per area than larger objects of same shape holds for any shape, as long as you use objects that have the same shape and you are consistent in your use of units.

I have attempted here to explain in painstaking detail what my argument is. If you still have trouble with it, I strongly advise you to carefully work through this argument again. I have it laid out in front of you as clearly as I could. Beyond that, I'm afraid I can't help you with understanding the A/V argument.

But let me now move on to the other parts of your comments. Does the A/V argument imply that there has to be some limit in which volume vanishes, since the smaller an object, the less volume per area it has? Absolutely not, this is why I call it a "plausibility argument". The purpose of a plausibility argument is to render something else that follows it more intuitive. It is *not* a proof. This is why axiom I had to be stated as an axiom, as opposed to, say a theorem.

You state that an axiom is, among other things, "self-evident". While this is part of the general definition of the word axiom, this is not the standard way in which the term is used in physics. The standard use of "axiom" in physics is simply as a formal assumption which requires no further justification. Although a plausibility argument may be given, a plausibility argument is too weak to qualify as a formal justification.

In fact, I challenge you to find anyone who is willing to claim that the axioms of standard quantum mechanics are self-evident. In case you need a refresher, you can find them stated here (NB. Postulates and axioms are used synonymously):

http://vergil.chemistry.gatech.edu/notes/quantrev/node20.html

You won't be able to find anyone who is willing to claim that the axioms or postulates of quantum mechanics are self-evident because they simply aren't. This is really a major part of the problem of the interpretation of quantum mechanics.

Your notion of an axiom was popular up until the beginning of last century when it was thought Euclid's derivation of his geometry proceeded from self-evident axioms and was considered a model for all other sciences to emulate. Alas, David Hilbert showed that Euclid's 'self-evident' axioms actually contained hidden assumptions, and given that it would not be difficult to find people who'd dispute that, say, the speed of light postulate or the principle of equivalence are self-evident, one can make a strong case that none of our fundamental physical theories at present are based on self-evident assumptions.

It may be possible in the future, if we ever obtain a complete understanding of fundamental processes and what they mean, to derive them from self-evident assumptions, but requiring that axioms be self-evident right now is making any approach at a more fundamental understanding unworkable. As mentioned, by your notion of an axiom, we would have to throw out standard quantum mechanics because it is not based on self-evident assumptions.

I did not really need to include the A/V argument in my paper because Axiom I, as stated before, by definition requires no further justification. Nevertheless, I decided to include it in the hope that Axiom I does not appear entirely unmotivated.

Finally, I think it is worthwhile to mention how the evaluation of a scientific argument works in the ideal case. If you are presented with a novel scientific idea, you should ideally evaluate it as follows:

1. you keep your skepticism about the assumptions but try to understand them the best you can

2. You examine the chain of reasoning that leads from the basic assumption to the conclusion.

3. You check whether there are any contradictions, non-sequiturs or other erroneous steps in this chain of reasoning, including the assumptions.

4. You check whether the conclusion fits what is already known, whether it contradicts any known experimental tests, whether it "seems right" etc.

***Only after you have gone through these steps*** do you decide whether to accept the assumptions or not.

You write " I feel free not to accept these assumptions based on the arguments above ...(the rest of the sentence I don't comprehend)" when the arguments you mentioned, to the best I could make out, were themselves based on a misunderstanding of the A/V argument and a misunderstanding of the notion of an axiom in physics, but not on the steps outlined above.

You are certainly welcome not to accept the assumptions, but then why did you bother to continue reading the paper? If you reject the assumptions without having gone through the process above, you are really done right there. We can at that point only agree to disagree. The only problem is that this sort of approach is a lot closer to dogma than to science.

As for your inability to download the paper, please try this url:

http://141.213.232.243/handle/2027.42/83865

go to the bottom of the page and click on "view/open". The paper is supposed to be publicly available. If it is not, I will check with the systems administrator.

Cordially,

Armin

Good afternoon Armin,

I appreciate very much your involvement in the subject we are discussing, perhaps I am ignorant about the basic physics you are implementing in your theory, but until now your answers , however clear, did not resolve my understanding, sorry for that.

I follow you 100% in the formula's comparing ball 1 and ball 2, the units of measurement are different and are comparable , different ratios can be compared, if they are brought back to the same unit of length (m), and a ly (light year)can be expressed in meters so, no problems at all., we are expressing comparable quantities.

Then you continue to calculate the ratio of A1/V1 between A2/V2, (so this is not the A/V ratio but a ratio between TWO A/V's) and end up with a dimensionless number 10^-11, of course this is pure logic because the comparable unit of quantity is then disappearing, but this dimensionless figure is ONLY valuable for the example as used in your example (ball 1 : 1ly and ball 2 : 10^-11m)

I noticed that you indicate : this dimensionless number is the same as whether we expressed the radii in terms of light year or in millimetres, of course we are not comparing aplles with pears, and the difference of A/V is for this specific example 10^-11, but ONLY for this specific one of ball 1 and ball 2, the number will change when we take two other balls : ball 1 :1 meter (10^3mmm and ball 2: 10 meters (10^4mm (A1/V1 : 3/1000 mm ; A2/V2 : 3/10.000mm )then the dimensionless number becomes 10. So you see that the dimensionless number is always changing with the volumes we are comparing.

What does this number tell us :

When you compare little ball with greater balls it tells us that the volume of the little bal is less compared with the greater ball (logic) and this is also true for its surface of course:

only the ratio of surface and volume is the same with EVERY ball, because it is a ball.

You say : Smaller objects have less volume per area then larger objects of the same shape.

HERE WE DO NOT AGREE,

as I indicated above (and you did the same yourself) the ratio of the surface and the volume of an object (no matter what is its shape) is always the same, the size of the object does not influence this ratio !!!

This means that even at the smallest scale the volume does not disappear!!!, your so called "plausibility argument" is wrong, and I think this is fundamental in your thinking,

The explanation of the word AXIOM I used came from Wikipedia. Your assumption by using the idea that volume is disappearing at small scales is in my view still wrong, so when the assumption is wrong the axiom is wrong. Axioms and postulates of QM have been tested scientifically and until now have confirmed the theory, of course there can happen other events that can change our point of view regarding QM.

I bothered to read your whole very interesting essay because of the fact that even when the first assumption is perhaps not right the rest of your thinking is very factual and promising,, as I noted before I like very much your photon/time treatment, and the idea that the smaller we go (for me the Planck length, see my essay) the less dimensions are involved made me think of John Wheeler (again see New Scientist of 25 september 2010) you can also see : Causal Dynamical Triangulation (Renate Loll, Utrecht University), Renormalisation Group Analysis, Horava Gravity, and of course String theory and LQG.

I will read your further writings and hope you will comment mine also.

Cordially and

Keep on thinking free

Wilhelmus

Hello Wilelmus,

Thanks, for the email regarding your discussion with Armin. Unfortunately, I have not had the pleasure to study Armin's new papers, but hope to very soon. I believe his perspective and framework is both novel and important and my views tend to be similar to his.

I believe your objection above is unfounded. You wrote: "... only the ratio of surface and volume is the same with EVERY ball, because it is a ball." This is an incorrect statement, conflicting with the correct statement from a previous post: "This means that with EVERY sphere the A/V ratio is 3/r." It is obvious that this last relation does not represent a constant (i.e. remains the same for every ball), but varies inversely proportional to r, which is the radius of the ball. As the radius of the ball, r, approaches zero, the ratio becomes very large, which implies that surface area dominates volume, which further implies that space is becoming more two dimensional.

I hope this helps,

Dan

Hi Wilhelmus and Dan,

First, Wilhelmus :

regarding the A/V ratio: I really couldn't put it better than Dan in explaining where your reasoning led you astray. Let me just for completeness point out one other sentence, you wrote: "..the size of the object does not influence this ratio". In the specific example of balls, the radius is an indicator of the size of an object. As you know, for a ball the A/V reduces to 3/r, so the size does influence the ratio.

Put conversely, your thinking would have been correct if the dimensionless ratio of two A/V's of any arbitrary sized balls were always the same, say 10^-11, but as you noticed yourself, it is different when you consider balls with other radii than the ones I chose. That means the A/V ratio changes with size.

I chose the specific two radii because I wanted to point out how much objects in the quantum regime are different from our everyday objects with respect to this parameter.

I read the wikipedia article and completely agree that in logic an axiom is assumed self-evident. But while logic is undoubtedly an element of physics, it is not the same as it. And that is really all I pointed out. It is not uncommon that the same term can have different meanings in different disciplines. The wikipedia article says something similar under the heading "other sciences" but their explanation strikes me as very vague and ultimately not effective. And yes, I agree with you that we have accepted the totally non-self evident axioms of standard quantum mechanics because they lead to a framework that as far as we can tell gives a correct description of the relevant regime.

Finally, thank you for explaining why you continued to read on even though you disagree with the first axiom. Your explanation tells me that you have a more open mind than some physicists with whom I have discussed my theory.

The photon/time treatment is more exhaustively discussed the paper that I submitted to the first FQxi essay contest on the nature of time, but that paper had some very minor errors which are fixed in the version available at

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

Are you able to access it?

Now, Dan

It is a pleasure to hear from you again. Since our last communication, I presented a poster of the follow-up paper at a conference on the foundations of quantum mechanics. The poster, which was meant to give a quick overview of the theory can also be found online at http://www.perimeterinstitute.ca/Events/Conceptual_Foundations_and_Foils_for_Quantum_Information_Processing/Contributed_Posters/

(scroll down to find my name). However, the poster contains a typo: Axiom V is actually

[math]\tau_A=\pm \frac{i\hbar}{mc^2}[/math]

The typo is apparently caused by their formatting program, it is not present in my own power point file. I tried to get them to change it, but so far without success (even though they tried). I think this is very unfortunate because I sensed that at the conference I was already being shoehorned into the crackpot category by several of the other participants, and the typo doesn't help matters. I also wished I had included in the 'Steps to quantum mechanics' the actual mathematical derivation. Evidently, several physicists came away with the impression that there were no equations in the derivation.

I also submitted the paper to two physics journals, unsuccessfully. In fact, one editor found it helpful to include an insult in his rejection. So, it is very refreshing to see someone who has the technical competence to do so display a willingness to seriously consider and examine these ideas.

I now tend to think that the while the paper format is the best medium to allow for a thorough examination of an argument, it may not be the most suitable for introducing what, if correct, may well be (setting all false modesty aside) a paradigm changing idea. For instance, I was criticized for introducing unfamiliar terms and symbols in my papers. This is certainly true, but in my view that is necessary because they are used to represent ideas that I have not previously encountered in the field. Instead of focusing on the symbols and terms, I wished the focus was on the ideas they represent.

Do you have any suggestions for how at least to get people in field interested in at least taking a look? It seems that as the more conventional channels for disseminating these ideas are closing for me, I am forced to consider less conventional ones.

If you have any questions once you do review the papers, please feel free to contact me.

Cordially,

Armin

A quick note: It has been some time since I thought about this paper and it occurred to me just now that it would be better to express axiom V not in terms of an equality but as a mapping. e.g.

[math]\tau_A \Rightarrow \pm \frac{i\hbar}{mc^2}[/math]

as the plus minus sign on only one side otherwise might strike some as nonsense. I may change the paper to reflect this, but I'll try to thoroughly review it first to see if I find any other problems.

Armin

Hi Armin, thanks Dan,

It is astonishing how an essential remark from Dan made me conscious of the fact that I was mixing up two ways of thinking :

1. The mathematical way of thinking about the A/V ratio, without giving a "length" to r, r can have now any length to be agreed upon, even a length under the Planck length, it is the length that we apply to r in our 4D causal universe that causes the effect you are using in your first axiom which brings me to :

2. the 4D causal way of treating mathematical formula's, where we "measure" objects relative to others and therefore agree on a specific distance the m. (and so also using the time dimension) In using this causal distance indeed you reach a length (relative to the m) at which the A/V ratio could be an indication of "losing dimensions".

So far so good, but I think we both are right, only I was mixing up abstract thinking (like going back in fractal world) with down to earth thinking in meters, sorry for the mess I made, but I am happy to have made the exercise (very egoistic isn't it?) your essay so is to me very inspiring Armin, sorry also for having asked for the second opinion of Daniel, but it helped very much as you can see, thanks again Dan for your precious time.

So okay Armin, we are lined up regarding the lower limit part of your theory, however I still would ask you two questions :

1. In my point of view the lower limit of our measurable universe is the Planck length (10^-35m), could it be the half length of the radius of a sphere before you loose a dimension ?

2. I agree with you that going to the lower limit there are going to happen things with our dimensions (see my essy, click on the word "my essay" in the answer to sri), but are such things also happening when we go to upper limits ? are we entering there in perhaps 5D universes ?, where is the upper limit, is it connected to the speed of light? Are we here touching the measurable limit of the shpere , read Bubble that is our universe, or do we need just an extra dimension (the fifth) to reach these other Bubbles ?

Interesting questions that I am thinking of.

Keep on thinking free

Wilhelmus

Hi Irvin,

It's good to hear from you. I empathize with your dilemma. I am an aspiring author also, and currently unpublished. From what I've read about the peer review process, it sounds like it can brutal.

I have a couple of suggestions that I hope will help. I'm not sure what journals to which you have submitted your papers, but you might contact Christian Corda, who was in the last essay contest. You can get his contact info from his forum thread. He is the Editor in Chief of the Hadronic Journal along with another cosmology journal. He seems like a genuinely nice person and should give you a fair chance and good feedback for improvement, if needed.

Secondly, another physicist, Amrit Sorli, who has posted quite a bit in the past on FQXI, has published his paper "Is Time an Illusion" at Physics Essays. Their URL address is http://physicsessays.org/

He and his co-author received some good press from this paper in such magazines as Scientific American, PhysOrg.com and BBC Focus. The only minor drawback to Physics Essays is that they insist that the paper be submitted in both English and French. I'm sure you could recruit someone to translate for you, if you don't know French. I know there are on-line companies that will do it for a fee.

Unfortunately, it seems there are too many closed minded journals and editors. Since your papers are uniquely creative, it makes them a target for criticism, rather than judged on their merit. Don't let two rejections hold you back. Submit them to as many journals as possible until you get someone to notice. Remember that Einstein's original paper wasn't taken seriously, until by happenstance, Max Planck read it and recognized its importance. Just think of it as the price you must pay, if you want to change the world.

Wishing you all the best,

Dan

Hi Wilhelmus and Dan,

First, Dan:

Thank you so much for your suggestions. You have mentioned venues that were not on my radar screen at all. Before I contact them, though, I will attempt to check how well they are generally regarded.

I should also mention that I was contacted by a publisher who has offered to publish the follow up paper as book (even though it is only 19 pages long?). Evidently, they go through university archives and check for theses that they wish to publish, at no cost to the author.

I checked and it appears that it is legitimate publisher, but that the quality of their publications is regarded by the academic community generally as low. This may not be too surprising considering that (they claim) they've published over a million titles (I seriously doubt that there even exist anything close to a million high quality science papers).

If all else fails, I may just go with them. In case you wish to find out more, I can forward you the email with the faq etc. if you like.

Thank you again for your suggestions.

Now, Wilhelmus:

I'm glad that the A/V issue got settled.

About your questions:

1. As I mentioned before, I am not convinced that the Planck scale is as significant as currently people think it is because, again, it lacks a solid theoretical foundation. Dimensional analysis based on a plausibility argument is not enough in my book to qualify as a solid theoretical foundation. This is not to say that I absolutely don't think nothing will happen at that scale, just that I am more skeptical than the rest of the physics community on this point.

As to what exactly happens at that limit, this is really the same astute question that Dan asked me a while back. You see, I only postulated that such a limit exists. I did not specify how it is actually approached, or how to mathematically carry out the operation of taking the limit. The reason I haven't done this is because I simply don't know how, other than that below the limit, the notion of space is postulated to be as imaginary as the notion of 4-space is to us. This is a very important subject and I strongly suspect that a detailed description can only be given in the context of quantum field theory, not plain quantum mechanics. Unfortunately, this is a subject on which I am still not well-versed. I can tell you however what my current train of thought is (subject to change as I get more educated): As before, I don't think that you "lose a dimension" (which implies that you modify the repository but ultimately still keep it) but that really spacetime vanishes, "all at once", as it where. The problem is, of course, that for any quantity involving finite distance this would prima facie conflict with relativity. So the idea is that instead of focusing on a particular volume element, you focus on a (quantum) object over a small interval of time (therefore you are considering a 4-dimensional object), and that the change at that limit is really a change in the object's behaviour, perhaps something analogous to a phase change (e.g. going from ice to liquid water). There is a very intriguing fact that quantum field theory is formally very closely analogous to thermodynamics.

A more visual analogy is as follows: Surely you have seen photomosaics (if not, you can see one here:

http://click7.org/image-mosaic-generator/?create

At a sufficient large magnification, all you see is a juxtaposition of pictures. But as you step back, you notice that all these pictures come together to form a bigger picture. My current working hypothesis is that the emergence of spacetime from areatime may have to be modeled as something similar, except that the component parts have one fewer dimension.

But, keep in mind, this is all speculation. I really don't know, and I don't have anything near a substantive quantitative model to back it up.

2. It appears to me to be more self-consistent that, yes, the process continues with increasingly larger scales, than that it stops at spacetime. I briefly alluded to that in my follow-up paper, noting that the fact that Dark Energy and Dark Matter are phenomena which are essentially "invisible" at our scale may be a hint. Also, I should mention that I have come up with a toy model, taking into account the additional dimension at larger scale and a simple modification of Newton's laws to take this and the changed dynamics to allow for stable orbits that seems to replicate and thereby give axiomatic underpinning of MOND. In case you're not familiar with it, MOND (Modified Newtonian Dynamics) was developed about 25 years ago by an Israeli Astrophysicist to explain the galactic rotation curves. It is strongly considered only by a about 1% of astrophysicists, in large part because it seems unmotivated physically, but also because it does not account for the dynamics of galaxy clusters very well(to learn more, google "Mond Pages").

However, I am nowhere near going public with this because I still need to learn a lot more about galactic dynamics and cosmology and because, once again, the ideas are so unfamiliar that it would permanently put me in the crackpot category.

Anyway, thanks for your comments.

My dear Armin,

It is increadible how our thinking is paralel, please if you want read my essay, the last remark Imade on the essay is indeed about the Planck length that I use as a limit to begin my "free thinking", ,The last results from the INTEGRAL point to a length of 10^-48m, I indicate here like you do yourself that it is not the exact length that is important but the fact that there is a limit, this limit is for me the border of the causal universe and the beginning of the Total Simultaneity (This is a different view of yours), I can start this free thinking because all physicists before me are doing the same, great example is string theory (I have immense doubts about that) and Loop Quantum Gravity 5a theory that I like). You talk about MOND , I fully agree with that , I too have great problems with black matter dark forces etc just to explain that the other 95% of the material around us that we don't understand and cannot observe obeys to same "laws" as the 5% we are aware of. You might be interested in the view of a countryman of mine Eric Verlinde, see http://fqxi.org:community:articles/display/132, he sees garvity emerging from a higher dimension and not as abasical force.(like image mosaic).

I hope you will take some time to read my essay and will be happy to read your comments on the thread there.

have a nice weekend and

keep on thinking free

Wilhelmus

Hi Wilhelmus,

Thank you for your comments and I regret that the comments I am giving below may be perceived by you as negative. I'd much rather say complimentary things, but on the other hand, I think it is important to give honest feedback.

First, about the limit. The notion of a limit is a very specific one. It implies a specific quantity with a specific magnitude, and typically also the variation in some quantity as the limit is approached. If you postulate a limit, you have to at least specify what it is a limit of. In my paper, I used axiom I as a mathematical expression to indicate, as specifically as I could, that the fundamental assumption is a limit on spacetime itself (i.e. a quantity that has dimensional units of L^3*T), and that this limit is approached by letting L^3 (*not* L, which is what you seem to be thinking) go to zero. This is very different from postulating that there is a minimum length or minimum time.

There are current modern theories that postulate that there exists a minimum length (such as LQG) but these theories can hide the difficulties that such postulated length or time limits pose by the fact that these limits are not measurable using current technologies. The theoretical difficulties that postulating such length/time limits pose are formidable and that is why such theories are presently regarded as little more than speculation (even though they are called "theories", they are more appropriately *highly speculative* theories, which is a *completely* different animal from our established theories like quantum mechanics and relativity).

To just give you a little bit of a taste, let me briefly review one major problem the assumption of a lower limit on length bring about: According to special relativity, if an object is moving relative to you, you will observe its length to be contracted (i.e. shorter)in its direction of motion as compared to an observer who is at rest relative to that object (assuming properly calibrated measurements). So if that object had (in its direction of motion relative to you) a minimum length, say 10^-48 m, in the frame of an observer at rest, then its length according to you (since its length is contracted) would be even shorter! But if it is a "minimum length" it can't be shorter by definition in any frame (including yours) for then it wouldn't be a minimum length. So either your assumption of a minimum length is wrong, or you have to change special relativity. Because special relativity is one of our best confirmed theories, people are very hesitant to change it, unless you can come up with a changed version that predicts something that you can measure and that is different from what special relativity predicts, do the experiment and show that your changed version gave the correct prediction, not special relativity.

So, you see, there are problems with assuming that there is a minimum length, and physicists who make this assumption typically try to find a way to solve these by proposing modifications to the established theories like special relativity, but this is like messing with the foundation of a house: If you change one thing, it will affect other things, and you will have to change other things, which in turn force you to still change other things and so on. And keep in mind, I have only told you of one problem, there are others. It is therefore not a trivial thing to postulate that there exists a minimum length scale.

Now I can tell you what my opinion is, and bear in mind, this is only a belief, not a scientific argument which I can back up with facts: In my opinion, there is no theoretical lower limit on length or time (i.e. L or T) but there is on spacetime (i.e. L^3T). If the amount of Energy in the universe is finite, there might be a lower practical limit on wavelength, or inverse frequency (because Energy and wavelength or inverse frequency have an inversely proportional relationship). So given, my opinion, I think we do have a substantial difference in our views about a minimum length.

Second, about your paper. I tried to read it, but once again it was difficult for me to understand it. As far as I could tell, you seem to have the notion of quantized world consisting essentially of discrete building blocks given by what you call the "wall of Planck", below which our usual notions of causality, time and distance disappear, something you call "total simultaneity".

This is not an uncommon view, I believe, but it is still regarded as highly speculative. Our two most fundamental theories of nature are General Relativity and Quantum Theory. According to General Relativity, Spacetime is a smooth manifold, which directly contradicts the postulated existence of discrete building blocks greater than zero size. According to quantum theory, while certain quantities are quantized (and are therefore added "blockwise") there is no indication in the theory of fundamental length and time scales. It is true that under certain circumstances, such as a particle in a box with impermeable walls, the theory does predict that there are regions where you will never locate a particle (which would seem like a quantized length scale), but that is a consequence of the setup of that particular situation, not a fundamental result of the theory.

So currently, our established theories do not support your notion. But they don't seem compatible with one another either, yet both describe nature excellently within their own domains. So, it would seem reasonable to assume that the two theories can be made compatible to one another by changing one or both, and some physicists have used this as a way to introduce notions similar to yours.

After reading your paper, I would like to give you, if I may, some constructive suggestions on how to write scientific arguments more effectively. I have found that what I am suggesting below helps me personally both in thinking about a problem and in presenting it two others.

1) Always keep in mind that your number one priority in presenting a scientific argument is to communicate your ideas as clearly as possible. You could have the best idea in the world, but if you communicate it in such a way that no one understands it, then nobody else will know. If you have a friend with similar interests you could ask him/her to read your piece and try to explain back to you what they understood you to say. This will tell you whether you communicated clearly or not.

2) Before you even write up your paper, formulate your argument in a bullet or numbered point format, making sure that each point logically follows from the previous ones. This will help both you and the reader of the paper that is based on the argument constructed in this way, to understand your chain of reasoning more clearly.

3) Avoid, as much as possible, introducing non-standard terms or notation. But sometimes it is unavoidable, in which case you should make absolutely sure that you have the terms defined clearly and explicitly immediately after you introduced them. If you don't do this, it will be a lot less likely that people will seriously consider your argument.

4) Avoid, as much as you can, reference to results of speculative theories of which you may have at best only a superficial understanding to justify results from your own arguments. I get a very strong impression that you take all these speculative theories' results at face value and then try to show that your own notions are consistent with these. Very frankly, I am not sure that you even realize that there is a big difference between established theories like relativity and quantum theory on the one hand, and highly speculative theories like String Theory, Loop Quantum Gravity, and Verlinde's Entropic Force Theory on the other. The reader will likely know that you are not a researcher in one of these fields, so your reliance on the conclusions of these, I think, will diminish, rather than augment your credibility.

I should emphasize, however, that point 4) does not necessarily apply to established theories like Relativity and quantum theory. If you come up with a novel idea that leads to the same result as one of these theories, then generally that is a strength. But you still want to convey that you have a much better than superficial understanding of these theories, and you want to convey this as precisely and clearly as you can. For better or for worse, this usually means that you want to convey this in the form of a mathematical equation that leads to a known result.

Again, I wished I could provide you with more positive feedback, but I hope that you will find my comments helpful in the spirit of constructive criticism.

Armin

Hello again,

There is something else I wanted to mention. You got several positive comments from other members on your essay. I think you should take the sincerity of at least some of the comments with some measure of skepticism because they were made during the time when voting on the essays still mattered. Especially the first comment is a blatant and disgusting attempt by its author to win a high rating from you. I don't know if he succeeded but I seriously doubt that his compliments for your essay were honest.

Armin