Unitarity, Locality and Spacetime Geometry: Foundations That Are Not Foundations by Lawrence B Crowell

Lawrence Crowell

I will try to get to your paper in the near future.

Cheers LC

Lawrence Crowell

My quote from Wittgenstein is I think closer to the actual German.

The emergence of unitarity means that it is the simplest of modular functions which occurs when there is no nonlocal physics with the singularity. In some of my comments on this blog I discuss this in some greter detail.

Cheers LC

Lawrence Crowell

Whether one can argue from a 130 year old experiment for something other than relativity is irrelevant. If relativity were false then a proton injected into the LHC accelerator would pass light speed within the first few meters of its acceleration along the RF cavities.

I am not some how going have some intended epiphany here whereby I acknowledge what you are saying. You might as well be trying to argue that Newton was all wrong and that Descarte's vortex theory is really right. There was a paper last year or before by somebody advocating something like that. This is old stuff, and this dog has long been put to sleep.

Cheers LC

[deleted]

Planck scale Lp is wrong assumption according my essay

[deleted]

Lawrence

Arnold was great mathematician,not metaphysics

but is favor observation was trinity

http://www.neverendingbooks.org/index.php/arnolds-trinities-version-20.html

[deleted]

Lawrence Crowell: "Whether one can argue from a 130 year old experiment for something other than relativity is irrelevant."

You are right. Initially the Michelson-Morley experiment confirmed the variable speed of light predicted by Newton's emission theory but if that was true, Einsteinians would not have taught the opposite for more than a century wouldn't they? And after all, how do we know that initially the Michelson-Morley experiment confirmed the variable speed of light predicted by Newton's emission theory? If both the past and the external world exist only in the mind, and if the mind itself is controllable what then?

http://www.liferesearchuniversal.com/1984-7

George Orwell: "In the end the Party would announce that two and two made five, and you would have to believe it. It was inevitable that they should make that claim sooner or later: the logic of their position demanded it. Not merely the validity of experience, but the very existence of external reality, was tacitly denied by their philosophy. The heresy of heresies was common sense. And what was terrifying was not that they would kill you for thinking otherwise, but that they might be right. For, after all, how do we know that two and two make four? Or that the force of gravity works? Or that the past is unchangeable? If both the past and the external world exist only in the mind, and if the mind itself is controllable what then?"

Pentcho Valev

Lawrence Crowell

To be honest I am not terribly interested in matters that were decided a long time ago. I guess I am not one to "fight for a cause, long ago forgotten," to quote Simon and Garfunkel in "Scarborourgh Fair." I am primarily interested in far more recent developments. Issues concerning the MM experiment or the validity of special relativity are simply not on my radar screen.

Cheers LC

Benjamin Dribus

Dear Lawrence,

I found your essay very intriguing and absolutely packed with interesting information, which will require some more thought to digest. One question: near the end of the paper you are discussing path integration involving paths in "what becomes the emergent spacetime." Now, of course in some theories that make use of path sums, the paths are in a configuration space of "universes" (geometries, triangulations, or whatever), rather than in a single lower-level structure. I am wondering if there are two different quantum notions occurring here, one involving the "spacetime" itself, and one involving paths in the spacetime? Take care,

Ben Dribus

Lawrence Crowell

Ben,

I have not gotten yet to reading your essay. There are lots of these here and it is not possible to read more than one or two in a day. I have it in mind to read yours, as it has been lofted for the most part towards the top of the ratings.

What you are asking is related to a discussion I had with Torsten Asselmeyer-Maluga . He argues that spacetime is completely continuous. This could represent one complementary aspect to spacetime; the quantization of spacetime may include a classical continuum in one representation and a noncommutative non-classical representation. This may play some role in the two quantum concepts you are referring to. Sabine Hossenfelder makes an argument similar to this.

The BCFW recursion formula is a twistor theory, which has been used in the HopHat algorithm for computing gluon amplitudes at the LHC. Gravitation is in one sense the square of QCD gauge theory. After reading Giovanni Amelino-Camelia , which has regrettably and I think wrongly fallen down the community ranking, I suggested a connection between the boosts employed in κ-Minkowski and twistor theory. This might be a connection between string theory and the more loopy or striangulated theories like LQG. The Wheeler DeWitt equation has not time variables. Physically this means there is no Gaussian surface one may arrange in spacetime to localize energy. So HΨ[g] = i∂Ψ[g]/∂t = 0. The time variables is a coordinate time, used in QFT equations, which is not a proper variable in general relativity. Hence this equation is a constraint equation, classically NH = 0 and N^iH_i = 0. String theory on the other hand requires some external background field from which gravitons as closed strings are represented. This has been a problem the LQG folks like to point out --- never mind LQG has failed to produce even a first order renormalizable calculation. I speculate that somehow the two views of quantum gravity might connect, where LQG provides the background or constraint for string theory, and the field calculations of strings makes LQG more tractable.

Cheers LC

[deleted]

What is your opinion about Gerard 't Hooft

Discreteness and Determinism in Superstrings ?

arXiv:1207.3612 (replaced) [pdf, ps, other]

Lawrence Crowell

It looks interesting. It might take me a day or two to read it.

Cheers LC

Lawrence Crowell

Hi,

I am a bit uncertain about what you are saying here. Mass and weight are different things. Weight is just mass under the acceleration of gravity F = ma, where the acceleration a is just the local gravity on a planet, such as on earth a = g = 9.8m/s^2.

The Higgs field is a pair of doublets, with four components in total, where three of them couple to the Z^0 and W^{+/-} particles and the remainder is the Higgs particle recently detected. At very high energy these four components are free, where the three absorbed into the Z^0 and W^{+/-} particles are also free particles. At lower energy these are absorbed. This is the Goldstone mechanism.

Good luck in the essay contest,

Patrick Hutchinson

Hello Lawrence

Thank you for your essay. It gives the clearest presentation I have yet come across of what seems to be a fundamental muddle pervading the subject. It appears in the notion which you describe very clearly on your page 3:

"The light cone at any point is subject to quantum fluctuations. Consequently the point where all null rays pass through is indeterminate; null rays in the region are not connected to a unique point."

To start with, the term "light cone" is an unfortunate misnomer. Light consists of waves. It does not travel along lines in cones.

The quoted passage does not say what the Heisenberg uncertainty principle asserts. Heisenberg's idea implies that any attempt to observe the region where null rays converge will produce fluctuating answers. This is not the same as asserting that there is no point where these rays converge. The uncertainty principle just says that we can't see it clearly; in fact, any physical phenomenon can't be relied on to behave as if there were such a point because of the modern equivalent of Newton't third law. If an event occurred at that point and had an effect on some physical phenomenon then the phenomenon whould have an equal and opposite effect on whatever caused that event, and knock it off that point.

It would be foolish to speculate how theoretical physicists think. However, maybe one can outline a sequence of mental conceptions which lead in the direction of this muddle.

Conception 1: an event occurs when two or more particles bounce off each other.

Conception 2: we see a thing by detecting particles which have been bounced off that thing.

Conception 3: particles are wave-like, and fuzzy, in accordance with QT.

Conception 4: our faculties and intellects are not fuzzy. If it is impossible for us to see something then it isn't there.

The problem lies in Conception 4. We are fuzzy, and we can't escape this fact precisely because we are huge lumps of interacting wave-like particles. The muddle occurs because we are reluctant to admit our own limitations.

I think this is the root cause of the notion that space-time is granular, not a smooth continuum, and all the consequent hassle.

Best wishes

Alan H.

Lawrence Crowell

A light cone is a spacetime representation of the path a spherically expanding light pulse takes in spacetime. If spacetime is noncommutative on a small scale this light cone point is not a point but a region where a set of null rays pass. Here the term ray used here is mathematical more than an geometric optical concept of a ray.

Cheers LC

Patrick Hutchinson

If one is discussing physics then a "a spherically expanding light pulse" cannot start from a point but from a region. If one is discussing maths then what a light cone is depends on one's assumtions. I know nothing worth mentioning of noncommutative geometry, and take your word for it that a light cone in noncommutative geometry has some sort of a vertex which is, as you say, a region, but one can make other assumptions.

The first two pages of your essay are very nicely written. On page 3, you lose me. Do you regard "quantization of spacetime" as an assumption or a theorem or what? The essay seems to be based on some sort of premiss that spacetime must be quantized in any mathematical model of observed physics. Is that what you assume? If so, as seems on your page 4:

"Our world is on the boundary of an anti-de Sitter (AdS) spacetime, where the interior is quantum gravity ..."

there has to be justification. I think it is conceivable that physics has other models in which spacetime is not "quantized", whatever that means, but is just a straightforward manifold with a metric and connection. The metric and connection may not be as Einstein suggested, but not very different. It seems quite possible that all the noncommutative aspects of observed physics can be modelled by solutions of assumptions expressed using much more conventional functional methods.

This is not to say that noncommutative geometry and quantization of spacetime and e.g. Asselmeyer's ideas about exotic smooth structures are "wrong". It is also conceivable that all these different approaches yield equivalent models which all reflect observed physics, much as the Schrodinger and Heisenberg approaches to QT match each other. (If they are, that would suggest some fascinating theorems.) As yet, I think it is just too soon to commit to one set of assumptions and reject all others. At the very least, assumptions should be stated.

bw. Alan H.

Lawrence Crowell

I attach a picture of a light cone in spacetime. There is a hypersurface of space that is a frame of simultaneity, and the future and past cones meet at the origin of this coordinate system.

The work of Asselmeyer is complementary to the noncommutative description. There are probably deeper principles at play here. The FERMI spacecraft measured the time of arrival of photons from distant gamma ray burstars. Photons of different wavelengths arrived at the same time. If there were Planck scale grainy properties or so called spacetime foam then shorter wavelengths would couple to these more strongly. The result is there would be a dispersion of light. None was observed. This measurement is different from what an extremely high energy experiment might observe where the probe scale is near the Planck scale. In the case of the FERMI experiment the probe scale was cosmological, billions of light years to a burstar, so this reflects a different type of experiment. This may suggest a type of quantum complementarity at work here. Asselmeyer works with exotic spaces which are absolutely smooth, but this exotic structure may have some duality or categorical equivalency with noncommutative geometry.

The AdS spacetime comes in with the AdS~CFT correspondence of Maldacena. You can look this up on Wikipedia. It is a rather deep and involved topic in connection to string theory and D-branes.

Cheers LCAttachment #1: light_cone.JPG

Patrick Hutchinson

Thanks for the portrait of a light cone. I first saw pictures like that in the 1960s. It is pretty.

This still doesn't clarify what it means. Is it meant to depict a singular 3-surface in 4-space? It looks like the boundary of the set of points influenced by its vertex under some linear hyperbolic PDE (see e.g. Peter Lax: Hyperbolic PDEs, AMS Courant lecture notes 14, 2006, chapters 1,2). It appears so, but if it is then it does not correspond to any post-1864 theory of a "light pulse" because light pulses are diffuse.

Thanks for your account of the FERMI experiment. It is news to me, and sounds significant. Are you assuming AdS spacetime, and string theory, D-branes etc? Are they compatible with the results of the FERMI experiment?

Alan H.

Patrick Hutchinson

Hello again Lawrence

Please forgive me. I have been nit picking. I hope it has helped to clarify things somewhat. It is such fussiness which distinguishes maths from theoretical physics, and ultimately maths is the more reliable subject.

Best wishes

Alan H.

[deleted]

Dear Lawrence,

I noted the sketch you made concerning shape/causal duality on my thread, and made some remarks in response. In the future, please feel free to post at the bottom of my thread... that way I will see your comments immediately. Take care,

Ben

Lawrence Crowell

It is often the case that mass and weight are used interchangeably in ordinary language.

Cheers LC

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