A Universe Programmed with Strings of Qubits by Philip Gibbs

quote:

What about space, time and matter, are they discrete or continuous? Again the answer is open to interpretation. Space and time could emerge from interactions between discrete entities, yet their symmetries are continuous and perfect.

end of quote

Please outline how you came to this conclusion.

What you put up is the heart of your essay and affects its adherance to the topic. thank you for your essay. I enjoyed it immensely

Andy

Andy, I agree that knowing where the strings and branes come from is crucial to making further progress in this theory.

I know that many people are not keen on string theory these days so I dont expect my essay to score high points, however I still see it as the correct appraoch to understanding the principles of nature. My reason is that there must be a description of nature when looked at perturbatively around nearly flat spacetime and weak fields. String theory is the only solution for that.

Continuous symmetries are very important in everything we know about physics. You cant approximate them well with discrete symmetries so I assume they are exact. The Fermi observations also seem to show that Lorentz invariance holds even beyond the Planck scale.

With qubits we can keep the exact symmetries even when the information content is discrete and finite, so there is no reason to abandon these symmetries.

I don't agree with people who say that symmetries are emergent from equations. I think they are fundamental. Without invariance principles such as the invaraince opf the laws of physics at different times and places we could not make sense of the universe.

Good luck with your essay too.

I second your assessment. Discrete structures play a role with quotient structures or Galois cohomologies and with conformal completion of hyperbolic symmetries. This plays a role with the conformal complete of the AdS. However, a pure discrete symmetry can only define a charge, but not a current. You can't have Noetherian conservation principles with only a discrete symmetry. The only exception is with E_8, where the root space structure (a discrete symmetry) is equivalent to the continuous group of E_8.

I have been a bit out of action this month, for I have been terribly ill. I think the light is at the end of the tunnel --- though it could be a freight train coming my way. So I have not been commenting much on FQXi.

Cheers LC

Dear Philip, Lawrence and Guest,

I also agree. In my essay, I concluded that nature is both continuous and discrete. That is the way that we observe nature because of wave-particle duality. The discrete properties are expressed by quantum charges, such as color, electric, and weak charges. But the continuous properties are expressed by fields (and waves or classical strings) such as electromagnetic and gravitational.

Qubits of Strings are the best of both worlds: "discrete" quantum charges and "continuous" strings.

I think that this contest had three legitimate answers, either:

1) Nature is fundamentally discrete, or

2) Nature is fundamentally continuous, or

3) Nature is fundamentally both discrete and continuous.

Perhaps Qubits of Strings and the third answer aren't popular because:

1) Strings aren't popular, and

2) "both" continuous and discrete sounds indecisive

But I honestly don't think that popular "democratic" science is the best science. I would prefer that we work out all of the details, and see which approach best fits all data and details.

Lawrence - I hope you get well quickly.

Have Fun!

Dr. Cosmic Ray

Hi Phil,

Just finished reading now. I like how you string all of the interesting concepts together (pun intended). It is remarkable the way some of the Math comes together so nicely. But that fact becomes a lot less remarkable if you take the quantum computing universe scenario seriously.

Since I'd read your paper on Elliptic curves and Hyperdeterminants, the portion which might have been too Math heavy was pretty easy to follow. And I agree; your event symmetric concept closes the loop nicely, to allow a complete symmetry to emerge.

I think perhaps nature exploits decoherence for natural computing, rather than using error correcting codes, but then again if my premise is right nature would use whichever route is more computationally efficient. I guess that's part of what makes dualities like the holographic principle significant too.

If the universe is a quantum computer, it makes sense part of its root function would be to determine the most efficient means to proceed with its task. This essay looks like a winner to me. I'll say more if there is time.

All the Best,

Jonathan

p.s. - I also wish Lawrence a speedy recovery. - jjd

I agree that democracy is not what determines science but for the record I make it 24 essays for Analog, 50 for Digital, 37 for both and the other 50 were not committed.

WOW! 50 uncommitted out of ~160? What was the primary purpose of the essay contest? Isn't it better to say both than to remain uncommitted?

Phil

On 2nd slower reading I followed your logic, but I couldn't help feeling I hadn't arrived anywhere solid, and couldn't derive the same conclusion as you from the Fermi results, in fact taking that along with other incoming anomalies I'd rather tended to conclude the opposite! Could you explain your logic there?

I do however fully agree that space and time themselves are quantified into discrete units, not just the macro discrete inertial field manifolds I refer to but Planck scale 'stem cell' type quanta, condensed only to implement change of motion (E). This gives a = g. (acceleration = gravity) but as quantised mass.

I'd greatly appreciate your criticism of the logic of my own essay, though again it cannot be scanned but the implications considered at each stage. I believe it proves our failure has been purely in power of logical thought. I've focussed on pure empirical logic but unfortunately few seem to have the power of logical thought to follow it and derive the implications! I hope you can, and can find any logical flaws. You never know, there may even be some stringy interlacing in the PMD and diffraction inside the stem cell (ion)!

I suppose I'm suggesting the reason Eddington let that duck fly past instead of shooting it was because he couldn't see it waddling or hear it quacking!

Best wishes

Peter

PS Was the 'nots' in the last para a typo? or if not do explain!

Dear Philip,

You write

-"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."-

If in a universe which creates itself, particles have to create themselves, each other, then (the properties of) particles must be as much the product as the source of their interactions. Though the same then holds for the force between particles, to be particles, requires a backbone to their properties so they can absorb and emit energy in a change of their kinetic energy instead of changing their properties continuously, in which case they couldn't have any property at all, have an identity, exist as particles. This 'backbone-requirement' in fact is the reason for the discreteness of particle properties.So within the conditions particles can exist, are stable in, they attract or repulse only as far as needed to conserve their rest energy. This means that though these properties appear to be autonomous, as if they don't depend on any interaction, they only are 'switched on', so to say, when preserving, protecting their rest energy, and, obviously, only for as long as they exist, that is, within the conditions they are stable in. This means that they have no infinite 'bare' mass or charge 'of their own', so forces never become infinite at infinitesimal distances. It is because we assume that particles have passively been created in some mysterious way that we regard their properties to be only the source of their interactions. As such infinity problems are of our own making, they cannot be solved by any theory. What's more, I'm afraid that any such theory only worsens the problem by making the misconceptions it is based upon more respectable. For details see my essay (forum/topic/838).

Regards, Anton

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