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  • Post #61

Dear Florin,

you wrote:

"I did not mean solipsism as a negative term. In fact, from standard QM, not only solipsism makes perfect sense, but it is hard to contradict".

All philosophical considerations could be considered as abstract, too. So also solipsism. Some of these considerations are consistent and could be hard to contradict just like in maths, some could be inconsistent or merely incomplete just like in maths (see therefore Joe Christian's attempt or the event-based simulation concept i gave a link to at the essay-page of Lev Goldfarb). Whether they are consistent or not with our independent external reality, they remain abstract as long as they cannot be linked to human experience. But if they can be linked to human experience, they "only" make sense in a human's internal framework just like the english language does, as long as you do not assume the value of the term "sense" to be independent of conscious considerations.

In respect to the latter sentence, you are - from my position - absolutely right with your statement that the language of maths has universal independent existence. And my position is, as you have maybe already understood, that i cannot know for sure out of my limited knowledge, if maths has indeed universal independent existence or not; independent in the sense that its existence does not depend on my considerations of making sense or not for this existence.

Even if it would exist independently, i don't think that it has the omnipotent power to divide what can and does exist in general and what does not. In respect to the latter question (omnipotent power or not), it seems to me that your claim not to be a philosopher could indeed be true. I conclude that from the following words you wrote:

"Why is this physics and why it is not subjective? Because all the 3 principles are validated by all experiments performed to this date. In my heuristic rule I am asking for the differences between math and reality. This means that whatever differences are found (the 3 principles so far) they have to pass all past, present, and future experimental tests. This is why this is ultimately objective physics and not subjective philosophy. In computers there is the GIGO principle: garbage in, garbage out. If the 3 principles are invalidated by experiments, they are the garbage in and the conclusions will only be the garbage out. Next, the 3 principles generate mathematical consequences and they have already proven a large chunk of the necessity of our universe. By a leap of faith now, I am speculating that ALL core characteristics of our universe will be obtained in this way. If true, this will mean that our universe cannot be except in the way it is: it has uniqueness and this is big. If true then we have mathematically succeeded in proving that there is no God. God's hands were tied at the moment of creation and he had no freedom into creating this universe, the blue print for the universe was already there just like the value of pi.".

This is an absolutely legitimate scientific thread. I do not criticize this thread. But i am strongly convinced that an (computer-like) exclusively deterministic-based proof can't prove the exclusiveness of determinism. That's the position of mine.

Dear Stefan,

Thank you for the opportunity to present my ideas and I think we are in agreement now. The journey was not easy, but this made the ending that much more valuable. The problem is that outside math and physics, the potential for miscommunication is large. However, mathematical and physics ideas are never born in a vacuum and they are always surrounded by fuzzy philosophical considerations. Pure results without the surrounding philosophical cloud are dry, abstract, and boring.

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  • Post #63

The noncommutative coordinate terms do not involve the gravitational constant G. They are as such not due to the classical gravity field.

LC

Lawrence,

Is it not true that non-commutativity of the space-time coordinates occurs at the Plank length scale? And the Plank length is proportional with sqrt(G), and therefore G does enter the picture.

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  • Post #65

Dear Florin,

thank you also for the possibility to exchange our standpoints and lines of reasoning. Maybe our arguments could lead others to one or another considerable conclusion, too, independent in which direction. I enjoyed the exchange and wish you all the best at FQXi contest.

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  • Post #66

The gravitational constant does lurk in the wings of course, but it is not a scale factor which determines the strength of an induced field by noncommutative coordinates. Noncommutative geometry is of course stronger the smaller the region one looks at. If you look up to equation 12 the commutation of q and q' is

[q, q'] = ħ^2∂_{[p}A_{p']}.

For |q| = |q'| = L_p = sqrt{Għ/c^3} we have the magnitude of the B_q field is G/c^3 which is pretty small. For the commutation in the momenta

[p, p'] = ħ^2∂_{[q}A_{q']},

where for |p| = |p'| = P_p = sqrt{ħc^3/G} there is the field B_p which is appreciable. This is the gauge-like field on the Dirac matrix element. The magnitude of the momentum coordinate commutator is going to scale as (L_p/L). For the Compton wavelength 10^{-11}cm this factor is about 10^{-22}. Converting the commutator of momenta into energy units then on this scale the energy associated with this field is about 10^5ev, which is about the mass of an electron. So the mass of an electron might be due to the effect of noncommutative coordinates (induced by Planck scale physics) which bottles up a massless particle.

Lawrence B. Crowell

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  • Post #67

As a point of clarification, at the opening I said the gravitational constant is not a determinant of the strength of the induced field. I probably should have better said it does not scale things as a G&M/M (& = delta) for &M a fluctuation in a mass that is ~ L_p.

LC

Lawrence,

Thanks for your answers. I re-read your paper and now I have another question. You state that the length does not matter at the critical point in RG. But this is kind of backwards: if the physics is the same at different scale, then of course the length is irrelevant. So my question is: why is the relevant physics the same at different scales? In this case we have the Compton length and this seems to fix the scale. In other words, establishing rigorously the RG is necessary.

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  • Post #69

Your question is a pretty good one. To be honest I will have to read exactly what I wrote. The upshot is this. Renormalization group flow, in particular conformal flow, works when mass is zero or sufficiently small. The HIggs mechanism then comes in and things get muddied up and RG flow becomes broken up so to speak. So there is an apparent end to RG flows. However, if the zitterbewgung, the mass of basic elementary particles (quarks, leptons etc), the Higgs field and so forth are involved with noncommutative geometry then there might be some way in which RG flow can be continued to zero energy. I think it should be possible in principle to continue to ever lower energy where the zitter motion of particles enter into a type of condensate.

The Higgs field enters into the vacuum at 10^{-16}E_{planck} and the physical vacuum appears to have no RG flow. Yet at much smaller energy it appears that if zitter is due to non-commutative geometry and a gauge-like field that RG flows can be continued from the MeV scale down. There appears to be a grey zone here from the TeV to MeV range that I don't understand, and I am not clear on whether RG flow holds there. So there are some open questions here.

LC

Lawrence,

If non-commutativity of the space-time is ultimately responsible for electron's mass, it should also be responsible from muon's mass as well, and the two whould not be different. The three generations of particles show that the story is more complicated.

Errata:

After submitting the paper, the author discovered the typos below. Because FQXi does not allow correction after submission, these errata will list the corrections.

Page 5, second paragraph, line 4:

Change "background invariance" to "background independent"

Page 5, second paragraph, line 10:

Change "approached" to "approach"

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  • Post #72

Of course the situation is more complex. The three doublets of leptons and similar doubles of quarks have different masses. In the SM approach this mass is determined by a Yukawa lagrangian of the form q-bar Hq or l-bar Hl (q, l = quark or lepton), which are different. If the Higgs field is dynamical it might be due to some gauge-like force or in a technicolor sense due to top quark condensates. So clearly if there is anything to this idea of mine there are additional complexities of coupling strengths for different quark and lepton generations and their components.

LC

6 days later
5 days later

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  • Post #74

I intend to do much the same. I have written the mathy-technical paper for this and am now converting a copy of it for a more general audience.

Cheers, LC

Lawrence,

I started with a bigger paper and half way through I discovered the FQXi limit and I had to greatly compress it. I added the last sections in hope to post it on the achive, but I did it only for logical cohesion purposes.

If any qualified endorser for hep-th is reading this, likes my entry, and is willing to endorse my essay, please contact me at fmoldove@gmail.com

It is very unfortunate FQXi does not allow corrections, and one particular typo I was mortified when I discovered it: instead of writing background independent" I said "background invariance". I was thinking diffeomorphism invariance and after I discovered the typo I was only thinking how bad this would look to all those LQG experts that will judge the papers. I guess typos are unavoidable because you become blind at them as you re-read the paper and know what you mean already.

Anyway, good luck writing a paper for this contest, as of right now there are very few entries compared with last time and the rate of new entries is very slow as well.

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  • Post #76

How many loop variable (LQG) people are there vs string people? I have an idea that string theory and LQG should work together or unify. But I might want to tailor some things with that in mind if necessary.

I am composing a general perspective on what I am presenting. I will attach a more detailed version for those who want to look.

Cheers, LC

I think in general the ratio of LQG to string research is 1:9, but on FQXI, the ratio is reversed, something like 7:3. I do not quite see how string and LQG research can merge. From the pure general relativity point of view, LQG is better than string theory, but it is very unfortunate that the ¼ factor for the entropy of the black hole cannot be directly obtained in LQG.

It does not seem possible to unify LQG with strings because of the background independence issue, and string theory is rather rigid in this aspect: either you tie down the curled dimensions and prevent them from changing, or you can allow the dimensions to change at the expense of instability.

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  • Post #78

The connection between LQG and string theory is with the electric-like field component in LQG constraints and the quantum critical point which ties AdS in string theory according to AdS_4xV^7 for V^7 a world volume for a 6-brane in 11-dimensions. The 4-field form indcident on D7 is set by a quantum critical point, the same which set the constraint on the LQG charge

Q_a = nabla_iE^i_a

I am not sure about the 1/4 or the Barbero-Immirzi ambiguity. But this appears to be some sort of connection between the two.

The natural background here is a de Sitter cosmology, or the anti-de Sitter cosmology. On the dS the gravitational perturbation (gravitons on the background) might have some sort of connection to LQG by the above argument.

Cheers LC

I submitted my article this morning. I can't imagine why it would be rejected, so we can compare notes on LQG and strings

Chhers LC

Good luck with the paper. If it is under the character limit, it will get posted.

Yes, the Barbero-Immirzi parameter is liked with the ¼ and there were quite a few papers about it. I am not a string expert, and I cannot comment on your proposed link, but it still looks improbable.

By the way, I just discovered some very interesting works of Irving Segal. He did fundamental work in algebraic quantum mechanics, and he unified classical and quantum mechanics in the same mathematical structure. But I did not know that he was interested in axiomatizing relativity and that he invented a different kind of cosmology called the chronometric cosmology. Very interesting, but not quite believable. Anyway, he also studied SO(2,4), SO(3,3), and SO(1,5) in the context of relativistic quantum mechanics.

(By the way, he was also the advisor of John Baez.)