A Universe Programmed with Strings of Qubits by Philip Gibbs

Many of the "uncommitted" authors discussed the question and concluded that it is too soon to tell, or that the question does not have meaning, or that it is neither. These seemed like reasonable and interesting arguments. There are really just a very small number that did not seem to address the questions at all.

The question is not likely ever answerable. The reason is the question involves an existential problem. Normally in physics we do not ask analytical questions about the ontology of things. We do not really have a mathematical prescription for such concepts. What is interesting to note in reading some of these papers is how people can argue in an adroit manner both sides of the dichotomy: nature is digital or nature is analogue. The relationship between the two borders on the metaphysical, for we have little physical idea of what we mean by ontology and epistemology. Quantum mechanics by Bell's theorem on inequality violations tells us that the universe fundamentally is not realistic in a classical sense. So wave functions are considered to be epistemic, and they do not have exactly the same ontology of a particle --- in fact no ontology. The measurement produces a particle which we register as a discrete "click." We can point to that and say "it exists." However, to interpret all that discrete stuff we need to think according to all that continuous stuff. Noether currents are not conserved in discrete structure, only in continuous ones. So we are left with a question on existentialism, where we ponder whether something which is purely epistemic can have the same existential categorical status of something ontological.

So the question is to my mind more properly about the relationship between continuous and discrete structures. That relationship is presented within the formulation of a theory, or hypothesis, or as some has written within a philosophical setting. I am less interested in philosophy, and I must confess I have certain jaded opinions of philosophy. I find myself largely in disagreement with virtually all papers I have read here which propose to prove the matter one way or the other. In fact one paper which argues for a discrete world, "Could Infinity Solve the Analog-Digital Dilemma?" by Antonio Leon attempts to illustrate how the whole foundations of mathematics are wrong. An argument on page 5 sets up a flawed argument and then claims a contradiction. Conversely the paper, "There Are No Pea Shooters for Photons" by Marty Green argues for a continuous world based on electrical engineering arguments ---- there are no photon particles. Never mind that Feynman admonished us to think more of the particle than the wave in the quantum picture. David Tong's paper is curious as well. There are about 6 papers ahead of mine which I find "funny," where one of them is near to top. I also think some reasonable papers beneath mine have fallen a bit below where they may deserve. I think it most likely that modern physics is not a subject which concerns itself in some "hard" or proven exclusive way with matters which are ontologically external to us. There is this epistemic aspect to modern physics, which involves things like waves, fields and other quantities that are usually modeled as continuous structures. In the case of quantum mechanics the wave is something which can't have "reality" in a standard sense. The discrete aspects of nature pertain to particles and events, where n-tuples of numbers can be put on a list.

Cheers LC

Phil

Thanks for the Fermi link. It did what you said in the packet, but only on the basis of as assumption which is not the only one possible. Conceptually, if an inertial frame is represented by a London bus, we could find that both postulates are complied with inside it, and similarly for all buses, but also for the backgrounds they're moving in. The real difference then is, if we have a bus within a bus, the same is true within the smaller bus. The background itself is then local, overcoming the problem of a single 'absolute' field. The windows of the bus do the same transformation (n=1.5) whether glass or plasma. (Thus my earlier reference to Eddington and Ducks). This avoids inequalities by the same token to allow Local Reality.

I agree when you say; "It is a widely held view that spacetime is not fundamental, but instead emerges from a description of interactions between particles that remains somehow free from the constraints of placement in a background spacetime."

Also; "It is possible to imagine a model of reality in which the vacuum emerges from a sea of interacting spacetime atoms, just as a continuous fluid or solid is made of molecules, but in such a picture the discrete atoms would affect the passage of light waves in a way we could detect. Just as we can probe the structure of a crystal using diffraction, we should be able to probe the structure of spacetime using the passage of light or other waves."

The Fermi results wouldn't falsify the London bus approach. No-one has (yet!) falsified the logic, but I'm struggling to get many to take it seriously enough to try. It seems only to resolve empirical issues (identified in the previous papers you know). It only needs Doppler equations, but it still also needs some kind of maths basis developed, which is not my personal bag so needs help.

I do hope you'll be able to perceive the quite testing initial dynamic relationships conceptually, and let me know if there are any problems you can find. I'm kind of getting desperate for someone to find something not based purely on prior beliefs.

In terms of the essay subject, it says the continuum )(or dis-continuum!) is continuous up to the point where change is needed and matter condenses to implement the change, i.e. initially a plasmasphere or fine structure cloud/halo.

Very many thanks. Well done with your own essay, not as obscure as I'd feared.

Peter

"String Theory and its offshoots such as M-Theory are the most advanced theories we have for unification of all the physical forces and matter including gravity. But string theory is not without its problems."

Sophisticated argument.

Requiring many dimensions and utilized for Multiverses and recycled galaxies and universes, string theory and its adaptations make it seem analogue to me. The vast possibilities you speak of grow more vast.

Jim

Most people have a conception of string theory that emphasis's its continuous side, but there is an underlying discretness too.

I remember being at the string conference in 1997 and after the main scientific sessions on the last day there was an evening of public lectures. These can be interesting because they are less mathematical and physicists reveal more about how they see things philosophically and what motivates them.

Two of the lectures were by Ed Witten and Brian Greene who talked of strings and spacetime entirely in continuous terms. The two other talks were by Gerard 't Hooft and Leonard Susskind whose gave a contrasting picture based on discrete string partons and holographic bits of information.

The public audience may have wondered how these speakers could have been talking about the same subject, but of course there is no conflict between these continuous and discrete viewpoints. The mathematics behind them are the compatible.

While the discrete and continuum are both present we should continually ask ourselves if one is more fundamental than the other. In my view the discrete bits are fundamental but they must be seen as quantized qubits. The quantization dresses them with real number amplitudes for states in Hilbert space. This is where the continuous side comes from. Continuous space, time symmetries and world-sheets must all emerge from the algebra of these qubits, turning them into a perfect embodiment of continuous geometry, not merely a discrete approximation to it.

I like to think of strings as discrete according to the vibration modes they support, where the tension in the string is given by the Heisenberg uncertainty principle. The continuous aspect of the string, say that it is a cord or a loop is such that as it evolves in time it sweeps out an area, which is the string world sheet. This sheet is a continuous space, actually 2-dimensional spacetime. What this continuous aspect of string theory gives us is that when two string interact they define connecting world sheets. The scattering of two closed strings (loops) is a plumbing job of connecting four pipes together at a junction. Now that junction is not a point, which it would be if we had point particles. This vertex for a point particle interaction is not covariant in a spacetime setting, it is an "absolute point" and not a transformable, but the sphere at the junction of 4 string world sheets is. This gives a vertex function, or Veneziano amplitude, that is well behaved.

This permits us to compute the spectrum of the string, and we get this plot between mass and J = spin, sometimes called the Regge trajectory. So this means those vibrational modes correspond to particle states, and these interact nicely by these vertex functions. So string theory is this interplay between continuous and discrete structures.

Cheers LC

Peter, thanks for your nice comments. I agree that the conclusion from the Fermi results makes some assumptions. This is always the case for any experimental observation. All you can really do is falsify any model that would predict variations in light speed that are not observed and thus strengthen belief in the models that are left standing.

It is good to see that your essay is doing very well in the ratings. Good luck for the final round.

Lawrence. What you describe is consistent with my old necklace algebra formulation for string theory. The string can be divided into partons each of which has Fermi like statistics and half spin. The graviton is therefore made of four partons to give it spin two. This is consistent with the four qubit picture of the one loop bosonic string.

However, you can also q-deform the necklace algebra to change the statistics and spin of the partons to be fractional. A continuum limit can be reached by taking the fractions towards zero while keeping the overall spin and statistics for a string finite. In the target space you do not see the fractional statistics because these can't work in more than two dimensions. But on the string worldsheet they make perfect sense.

I hope to revivie that work at some point now that it looks promising again.

Read a reply I gave to Tejinder Singh March 7 on my area:

http://www.fqxi.org/community/forum/topic/810

where Tejinder's paper is interesting. I talk about what I think is the substructure to string theory. It is similar in a sense to what you mention.

Curiously a long time ago I suggested the idea that strings were "loaded chains." The example in classical mechanics is a discrete version of the classical string. My idea was that each node had a Lie algebraic action and there were connection terms between the nodes which reflected the phase across this system. I was told the idea was crazy.

Cheers LC

The idea is not crazy. You should try to formulate what it means and we can compare notes.

This idea could come in a number of forms. We might think of the string has having a discrete number of elements, so it is similar to a loaded chain. It might also be that at the Hagedorn temperature that open string link up in a fashion which is similar to a set of interacting nodes or masses. These nodes are similar to particles, so that at the Hagedorn temperature field theory is described by a long chain of strings, where the D_0 branes or endpoints (Chan-Paton factors etc) are "partons" that have flux tubes of fields that connects them together.

Assign φ_i as the field that connects SU(n) and SU(m) (or SO(n) and SO(m)) at the i^{th} side, and ψ_{i,i+1} as the field that attaches SU(m) at the i^{th} node to the SU(n) at the i+1^{th} node. The S matrix is then defined as

S_{i,i+1} = g_s< |φ_iψ_{i,i+1}| >.

A local gauge transition on this matrix is then determined by the SU(m) groups at the vertices of the edge link by g_i^{-1}S_{i,i+1}g_{i+1} and S_{i,i+1} is an mxm matrix of bosons. These bosons are then "link variables" for the chain. When the gauge coupling g_s becomes large there is a confinement process that defines a mass, and by necessity breaks any chiral symmetry. We set the renormalization cut offs for confinement by the two groups defined as Λ_n and Λ_m, where free fermions and their gauge bosons (e.g. quarks and gluons) are free from confinement for E >> Λ_n, Λ_m. Under this situation where the strength of the SU(n) is small the differential of the scattering matrix in a nonlinear σ-model is,

D_μS_{i,i+1} = ∂_μS_{i,i+1} - ig_sA_{μi}S_{i,i+1} + igS_{i,i+1}A_{μi+1},

and the effective Lagrangian for the field theory is then of the form

L_{eff} = -(1/2g^2)sum_i F^a_{μνi}{F^{aμν}}_i + g_s^2 sum_i Tr|D_μS_{i,i+1}|^2.

This is the Lagrangian for a five dimensional SU(m) theory, where the additional dimension has been placed on the N-polygon. The last term in the Lagrangian determines a mass Lagrangian of the form

L_{mass} ~ g_s^2 sum_i(A_i - A_{i+1})^2

This mass matrix then connects this with the loaded string or loaded chain.

The theory is simplified of course when the n = m and the interlinking group is the same as the group at the nodes. This might then prove to be interesting in the context of the BFSS theory where there are D_0 brane interacting by SO(9) in the infinite momentum gauge. The SO(9) is an interesting group, for it shares with the SO(8) subgroup status in the F_4 heterotic group. The SO(8), which is the 3 and 4-qubit group (or the split SO(4,4)) for the SLOCC. The exact nature of this relationship I as yet do not understand well enough to construct qubits from.

Cheers LC

Haha Phil. What, wait?? This is MY essay! ... well not really. ;)

I'm sure that you-know-who will verify that I asked him every possible stupid question about these very same fundamental topics covered in your essay, and that I got nowhere fast. Where you took the topics is just awesome. I'm so glad I didn't even bother. :)

- Shawn Halayka

That's nice. When I do it I start one level up the quantization ladder, so instead of having amplitudes on sites and links round the string I have amplitudes for the whole configuration of the string. So the field variables look like

$\phi_{ijkl...n}$

and you can have any number of indices. The amplitutdes are commuting if the number of indices is even and anti-commuting if they are odd. There are cyclic/anticyclic rules

$\phi_{ijk} = \phi{jki}$ etc.

With these amplitutudes you try to build a super lie algebra and surprisingly it turns out to exist in an elegant form.

I would like to have seen your essay. You should try it next time.

In effect the S matrix produces essentially this state as

|k_1,k_2,...,k_n> = S(φ_1ψ_{1,2}φ_2ψ_{2,3}, ..., φ_{n-1}ψ_{n-1,n}|p_1,p_2,...,p_n>

The state vector |k_1,k_2,...,k_n> is the set of entries determined by the application of a field φ(k_1,k_2,...k_n) on a Fock basis element. The fields φ_a, where I drop the two indicial notation define a boson vertex operator ∂X^μφ^a exp(ikx), where the string term ∂X^μ ~ ψk^μ. The field has a superconformal weight (0, 1/2) and defines the current G_{-1/2}φ_a = j^a. This field and the current obey the standard operator product expansions. The ordering of these elements which make up the S matrix, or equivalently define the state φ_{ij...k} is then dictated by the superconformal algebra and the graded Lie algebra.

I think in a way this discrete approach leads to much the same construction you indicate. The difference might be a difference in perspective with "quantization," but I think it leads potentially to the same or a similar result.

Cheers LC

There is a podcast available of the 11th Asimov Memorial Debate at http://www.amnh.org/news/tag/isaac-asimov-memorial-debate/ The debate returned to the topic of the first meeting ten years ago to discuss whether string theory is still a viable "Theory of Everything" (This controversial phrase should be read as a "Theory that encompasses everything in physics", not a "Theory that solves everything" which is of course impossible)

The debate was lively and well balanced and worth listening to. Of particular interest here were the comments of Jim Gates who mentioned the idea that information theory is at the heart of string theory. Those who have read my essay will see the connection with Gate's mention of the appearance of error correcting codes in M-theory. One technical article is at http://arxiv.org/abs/0806.0051

I was not aware of Gate's part in the research before. It would have made a good reference to add to the essay if I'd known sooner.

In my opinion these ideas build on the observations of Mike Duff and his coworkers about connections between string theory and qubits. This is gaining wider recognition and could be the first hints of a new string theory revolution, but we are still waiting for the main breakthrough that will explain what is behind it.

I wonder if the 21st Asimov debate in ten years time will look back at string theory again with positive answers to some of the questions.

Phil

Thanks. I hope you make it to the last 35 too, very interesting microstructure approach, an area I feel bound to get more in vogue soon.

I think mine's doing well as, despite my non classical (meant non non classically) approach, an increasing proportion are now able to upgrade their conceptual dynamic visualisation skills to see how it produces some pretty exciting results.

I look forward to your own views, if you get to read it. But I warn you it's demanding in very different ways. Do look at the logical analysis, thought Gedankens and comments in the strings too.

It it proves correct, it was on viXra first, and may just prove how bad the mainstream publication system is!

Best of luck.

Peter

Hi Phil,

Saving the best for last, I suspected in advance that you would turn out a superior essay, and I was not disappointed. There are too many good technical points to review in this brief format, so just a couple in particular:

Your explanation of "complete symmetry" is right on. A similar line of reasoning led me to the conclusion, accompanied by a precise numerical model, that the 4 dimension horizon is identical to the 10 dimension limit. (My essay entry doesn't get into the technical; I chose to survey the broad subject of discrete vs. continuous instead.)

I noticed Ervin Goldfain's objection that quantum gravity assumes classical gravity can be quantized. On the contrary, your approach, mine and several others assume that quantum gravity can be classicalized.

I hope you get a chance to read my essay, too.

Excellent work, thanks.

Best,

Tom

Point of clarification -- the link is a 2008 preprint, not my essay.