This Time - What a Strange Turn of Events by Philip Gibbs

Does anyone else have trouble loading my essay in Internet Explorer or is it just me? I find the browser hangs when I click on the essay link. The PDF was generated from Word using microsofts own PDF generator so I did not expect any incompatability. I have no such problems with anyone elses essay.

If anyone does have this problem there is an easy workaround. Right click on the link "Download Essay PDF File" above, and select "Save Target As..." from the popup menu. Once it is saved on your filesystem it can be opened with Acrobat (PDF viewer) as a local file.

If anyone still has trouble please let me know by posting here about it.

A central idea of the thesis in my essay is that symmetry is still important in going beyond our current understanding of physics. Actually it is a dual message. One half of it is that time reversal symmetry (or CPT at least) should not be ignored in deeper theories of quantum gravity or cosmology. In other words we should not be looking at models where temporal causality running in one direction is fundamental. The other half is that there is a huge gauge symmetry in string theory that includes all other known symmetries in physics including spacetime symmetries. I want to elaborate a little on this second half here.

Every physicist knows how important symmetries have been in physics. General relatvity is based on covariance of equations under diffeomorphism groups. The standard model of particle physics has an internal gauge group that is expected to be unified into a larger gauge group at higher energies. The great thing about these symmetries is that once you recgnise them you can easily construct the simplest models of dynamics that respect them. Although more complex dynamics are possible it has turned out that the simpler ones work. In short, symmetry has made predictions easy.

In string theory everyone agrees that there are lots of new symmetries and supersymmetries. The gauge groups for E8 x E8 and SO(32) are found to work well. The worlsheet action also has symemtries. Infinite dimensional symmetries such as E10 and E11 have been suggested as symmetries of M-Theory. Dualities also form discrete subgroups of E7. Target spacetime has suppersymmetry. The list goes on.

Yet there has been a failure to find a universal group that could encompass all these symmetries as subgroups. Witten's puzzle was cited (and refuted) in the essay as one argument that symmetry principles must fail. I think there is a general concensus amoungst string theorists that they must look to other unknown principles for guidance because symmetry is not sophisticated enough to explain string theory. I think they are wrong. If you need further examples of the arguments against symmetry in string theory then please do read the excellent article on the blog of Lubos Motl at

http://motls.blogspot.com/2006/07/evaluating-extreme-approaches-to.html

The relevant section is the one with header "The world is all about a gigantic gauge group" which he refutes. I think this reflects a view held by many of his colleages in string theory.

Part of the reason for string theorists giving up on symmetry is that they failed to develop a string field theory that embodies it. It turns out that for open string field theory you can define a very nice lie algebra out of open strings that cancel at the sections where they join, but for clsed strings this is not possible. This is sgnificant because even open string theories must include closed loops and these loops are the ones that include gravitons. If there is to be a universal group for string theory it must overcome this problem.

My starting point is that the diffeomorphism groups must be subsumed into the larger permutation group on all spacetime events. Since I proposed this idea it has been taken up independently by several other physicists in other contexts (cited in the essay) and has even been identified in string theory matrix models. Yet the full power of the concept has not been acknowledged.

What I found 13 years ago was that if you redo string field theory starting from a discrete set of events then you get a beautiful superlie algebra for discrete closed strings analogous to the lie algebra for open strings on continuous space. The symmetry of this lie algebra includes the permutation symmetry on events as well as the gauge symmetries of strings. It can be defined as a necklace algebra using partial commutation relations as given in my essay.

At the time I first proposed this the use of discrete arget spaces would have been a cause for concern but subsequently the discovery of matrix models and matrix string theory should have given the idea the credibility it needed. I hope this essay will bring the details of the mathematics behind event symmetric string theory under a wider scrutiny so that others can appreciate its beauty and promise.

I mentioned the holographic principle in my essay and mentioned it as another justifcation for the idea that string theory has a hige hidden symmetry. I want to say a bit more about what I meant by that.

First a gistorical note. The idea of a holographic universe was much vaunted by David Bohm in the 1970s as what he called the holomovement. There was also an idea about holography as an interpretation of conciousness due to Karl Pribram. These were sometimes brought together in what was (or is) known as the holographic paradism which formed part of "quantum mysticism". See the relevant wikipedia articles for more details

http://en.wikipedia.org/wiki/Holographic_paradigm

I mention this only beacause there are several essays in the contest that cover conciousness and maybe someone would be interested in that.

The holographic principle that was later brought into quantum gravity by 't Hooft and then Susskind is (a litle) less mystical and of course they made no reference to Bohm's theory. See this wikipedia article

http://en.wikipedia.org/wiki/Holographic_principle

It is this theory that I am concerned with.

The idea is that to explain the black hole information loss paradox we must accept that the amount of information in a volume of space is actually limited by the area of the surface that surrounds it. You can have at most one bit of information per planck area on the surface.

In string theory the holographic principle has been realised as a feature of AdS/CFT duality between theories in different dimensions differing by one. Nobody has proved that the duality is correct but it has passed many consistency checks and is generally accepted. Of course this means that nobody knows how it actually works.

If the principle holds in general then the apparent fact that we can fill volumes of space with densly packed information is an illusion which would be thwarted by a collapsing black hole, but how can that be the case? I propose that the actual mechansim at work is just a huge symmetry. When a symmetry is present in nature the fundamental variables that describe matter are partly redundant and can be removed in part. The real quantity of information in the system is given by the number of indepedend invariants of the system under the action of the symmetry. As an example consider a model represented by a single symmetric N x N matrix but with dynamics invariant under SO(N) orthoganal simialrity trnasformations on the matrix. The apparent degrees of freedom in the system iare the N-squared elements of the matrix. But we know that using the symmetry the matrix can be diagonalised and the remaining observable degrees of freedom are the N eigenvalues of the matrix. The number of degrees if freedom is reduced to the square root of what was originally given.

Suppose we could fill spacetime with random fields but with a minimum length and time scale, then the amount of information in a region of spacetime with a lengt scale L and time scale L/c would be L to the fourth power. But we know that wavefunctions evolve in time using a unitary matrix on the Hilbert space so the information in any single spacelike 3D hypersurface determines all the information in others at different times. So from quantum mehanics the amount of information is reduced to L to the third power. We understand how this works using the group of unitar matrices (at least in quantum field theory). Now the holographic principle tells us that in fact a configuration of fileds on any 2D surface in space is sufficient to determine everything so some unknown mechanism must reduce the information to L to the second power. It is reduced to the square root of what we started with, just like with the matrix, but lets consider that detail a coincidence even though it might not be.

The point is that a group or symmetry structure was used to reduce the information content in the first step so perhaps there is another symmetry that can be used to reduce the inforamtion in the second step in the same way. it would have to be a huge symmetry because ordinary gauge symmetry and diffeomorphism invariance is not normally enough to do that except in lower dimensional gravity and topological quantum field theories.

Talking of TQFT lets think about how they can be applied to this situation.

http://en.wikipedia.org/wiki/Topological_quantum_field_theory

In the language of category theory a TQFT is a functor from the category of cobordisms to the category of vector spaces (see the wikipedia article if this is not known). This means that you have a hilbert space on each spacelike hypersurface and unitary matrix transformation between them. To geeralise this to include a holographic principle you would presumeably need a 2-TQFT which is a 2-functor from the 2-category of 2-cobordisms to the 2-category of 2-vector spaces. This would mean that you would have two quantisations instead of one.

The concept of multiple quantisations can be exptended further and is seen in the structure of further natural extensions to my necklace algebras. It is a crazy and illdefined idea but also one that has been championed by some unexpected people so i hold out much hope for this idea

see e.g. http://motls.blogspot.com/2006/07/evaluating-extreme-approaches-to.html once more.

Dear Phil,

You posted three on 14 Nov. and all these are elaborations by you on your own essay. My post of Nov., 11 was left untouched in the process.

i note that you have indicated about the theories, including a quantum theory for ' consciousness '.i fail to understand how a non-physical parameter can be quantified using scientific methodology developed thus far. Awareness at lower level and other higher states of consciousness are estimated by human experience. One can parametrize the brain functions to the extent we have understood its biology. The human mind is talked about but it is something taht may well have its confines extended far outside the concerned body. It is here that one may consider the higher states of consciousness to be significant. Cosmic consciousness/mind is the total knowledge/intelligence that has generated our Universe and all objects therein. It is just not possible to scientifically parameterize consciousness, through the concept of Planck length or otherwise. These are based on space/time concepts and the constancy of the velocity of light.

Dear Narendra,

Thanks for your previous comments. I thought they were perfectly reasonable and rounded off the discussion nciely. I didn't appreciate that you expected further replies and I did not really have anything to add anyway.

As a general point of protocol I dont necessarily feel oblidged to respoind to all comments that appear here, although the ones I have had so far have been worth answering at east in part.

I only mentioned the subject of conciousness so that I could distinguish between the Bohm/Pibram holographic paradism and the 'tHooft/Susskind holographic principle. I am only really interested in the latter.

Actually I dont really have a theory of conciousness and would neither agree nor disagree with most people's opinions on it.

I think that our comment threads are a good place to make further points about our essays even if nobody asks about them so you may see a few more posts of this type from me if I find the time.

best wishes

Philip,

i am sorry that you felt compelled to respond.As i admired your essay, i felt like seeking your ideas on ' consciousness'. You say that you want to remain a bit confined on this aspect in view of your professional interests. Fine, all good luck in your activities. Personally, i feel the interaction of science with 'consciousness' may well provide expanding paradigms for the benefit of science itself. The same was emphasized by me in my essay in the competition! No need for you to comment anymore on this response.

I'd like yo asnswer dome more FAQs here and am wondering if the system will allow HTML equations so here's a test

S = 陆T∫d2ξ√(-h) hab ημν聽∂aXμ聽 ∂bXν

and another

Δ = ann-2

∏

(ri - rj)2

i < j

cheers Phil!

Appreciate your sense of humor, am already posting on another dozen essays. All good luck in your professional endevors. Nath

Thanks Nath, Good luck!

Dear Dr. Philip Gibbs,

I enjoyed reading your essay, and the way it presents the relational approach to recovering the spacetime as emerging from the event symmetric physics.

Best wishes,

Cristi Stoica

“Flowing with a Frozen River”,

http://fqxi.org/community/forum/topic/322

Phil,

In your Essay, you wrote: "However the arrow of time is a cosmological influence left over from the big bang, not a fundamental property of the laws of physics. We should not build temporal causality into our fundamental theory."

I think it depends on the interpretation of time. If we consider the hypothetical Heraclitean Time, as emerging along with the emergence of 3-D space, we are in the murky waters of quantum gravity: please check out the so-called biocausality here.

Sorry for giving links to my web site. I learned about this contest on December 2nd, and was too late to submit my proposal.

Dimi

Dimi, Quantum Gravity and the small scale structure of space-time is what interests me most, even if it is still a murky subject. The idea based on event-symmetry is that the big bang singularity has a huge unbroken symmetry which accounts for its low entropy.

For intermediate scales temporal causality is valid but on very large scales greater than the size of the observable universe causality could be more complicated. Perhaps something like your biocausality applies.

Phil, please notice that the so-called biocausality is supposed to cover everything that can be put into 'the whole physical universe', simply because 'potential reality' is a notion much wider than 'physical reality'. The idea goes back to Aristotle, as I'm sure you've noticed by following the link in my preceding posting. In other words, I can install "boundaries" on 'the whole physical universe'. Can you?

Symmetry has been fundamental to every unification step taken in the history of physics.

Symmetry removed us from the centre of the universe.

It underpinned the relativity of Galileo and Einstein.

It unified electricity and magnetism.

Quantum theory brought us permutation symmetry of particles and further unifications from gauge theory.

The quest to further unify through symmetry then brought us Grand Unified Theories and culminated with supergravity.

Then the rise of superstring theory dramatically changed the way physicists thought about symmetry.

Superstring theory is full of symmetry, but its different superselection sectors have very different gauge groups.

Topology change made it hard to see how different diffeomorphism groups could be combined into one form.

String theorists no longer believe that there can be a universal symmetry that unifies them all.

Other approaches influenced by complexity theory have suggested that symmetry in physics could be emergent rather than fundamental and that is now becoming the prevailing view.

Even the symmetry which combined time and space is being challenged by the idea that time by itself is fundamental and absolute after all.

My opinion is that symmetry principles are still the key to understanding how the laws of nature work.

My principle of event-symmetry which I proposed 15 years ago can be used to unify matter and spacetime by combining the permutation symmetry of particles with the diffeomorphism symmetry of general relativity.

I am gratified that this symmetry has since been utilised by physicists persuing a variety of approaches to quantum gravity.

I cited some of them in my essay but a more complete list can be found at http://www.weburbia.com/press/cite.htm

However, in each case the physicists have reinvented the idea without reference to my work or each others and they have missed the important insights that I have been trying to communicate.

My claim is that event-symmetry is just part of a much larger symmetry that can be extended to gauge symmetries using matrix models.

By applying the principle to string field theory I found that it can be further extended using a form of necklace lie algebra and multiple quantisation.

The result is a symmetry so huge that it has the potential to include all the symmetries of string theory in one all-encompassing universal symmetry.

It is my belief that this approach is the best way to find the missing principles that underlie string theory and all of fundamental physics.

Although I have a doctorate in theoretical physics I have not had any affiliation with a research institute for the last twenty years.

This makes me an outsider to the physics community and it is becoming harder to express my views.

These days the peer-reviewed journals are obsessed with their impact factors and there is no chance for an outsider such as myself to publish a paper on such foundational issues.

In the 90's I was able to submit articles to the arXiv but since then it has become very difficult for someone with no affiliation.

Like many others in the same position I have been blacklisted and can no longer contribute there.

My only other option has been to use my own websites and blogs to promote my theories but this medium is seen as the preserve of crackpots and is ignored by serious physicists.

As a researcher who is unfunded and lacking the collaborative discussions that are necessary to stimulate ideas, it is increasingly hard to continue working on physics.

As this essay competition draws to its conclusion I would like to thank the FQXi for providing a new avenue for promoting foundational research that is open to all contributors.

For independent physicists like myself it provides a fair opportunity to get recognition for our work.

Any prize in this contest that goes to an outsider could give them the status they need to make people take their work seriously.

From my own personal position I can also say that failure to gain any recognition here will tell me that there is no further way open to me.

Perhaps it is finally time to accept that I have lost touch with the modern approach and I should give up my own personal quest.

Whatever the outcome I will be indebted to the FQXi for determining the future course of my work.

I remember thinking about coincidences on the eve of the new millenium. Such a day comes round only once in every 365,242 days. As the hour before midnight approached the coincidence rose to a 1 in 8,765,820 chance. If only I could have such luck in the lottery, I thought. One minute before midnight I was experiencing a one in half a billion moment rising to one in 30 billion for a second before Big Ben struck. Then the power of the moment faded away as I watched the firework display over the Thames and turned to go home.

Nine years on the coincidence does not seem so great. In a liftime of 80 years I would have a one in twelve chance of experiencing a new millenium. But wait - what about the coincidence of being alive now in the long history of the universe? After 13 billion years during which the universe has existed I am now in the middle of just a short 80 year (ish) lifespan. That's already a one in a 160 million chance coincidence lasting my whole life. What if I count the future as well? the universe could be habitable for many more billions of years and we currently think it will exist for ever. What sort of coincidence is life then?

This paradox can be removed if we think about time in the same way as we think about space. We see no coincidence in the fact that we live on a friendly blue planet which occupies a tiny volume in the vastness of uninhabitable space. We are simply here because we could not exist anywhere else. In the block picture of spacetime our location in time is no more of a coincidence than our location in space. We do not exist beyond our lifespan and should not regard it as luck that we happen to be alive at this time. The apparent paradox comes about only when we think in terms of the flow of time as part of our experimence, but that flow must be an illusion, unless you belive in very large coincidences.

The results are finally out. Many of the winners were people whome I admire and amd happy to see them win. For the rest of us it has been something of an anticlimax because we got no feedback from the judges about our essay. We dont even know how many judges there were or where they came from, and we dont know if we made the shortlist of 50 essays or not. That makes it very difficult to know whether or not it is worth trying again.

I have been promoting my ideas about spacetime symmetry, and emergence of spacetime for 15 years now. When I started it was easy for anyone to publish in the arxiv and the physics journals but today that is not possible for an outsider like myself. The FQXi essay contest appeared to be a new way to be heard but in the end there was very little discussion of my essay despite my attempts to spark some interest in these comments. That contrasts with most of the essays contributed by well know physicists which many people wanted to discuss, but the authors were often unwilling (The excpetion was George Ellis who took part in a very enlightening discussion of his work).

During the past 15 years I have seen my ideas used by many physicists from within the community. That includes the permutation symmetry on spacetime events, matrix models for quantum gravity and the emergence of spacetime from a disordered phase. Some of the winning entrants even used these ideas in their essays without apparently knowing where they originated. Noone has ever cited my work or considered that someone from outside the physics community who thought of these things first might actaully have further insights worth discussing. Eventually someone will rediscover the importance of the necklace algebras I was led to, but they will not notice that they were published before by me. They will certainly not be familiar with the more advanced deformed versions of these algebras whose beautiful propoerties I have appreciated, or the relations to hyperdeterminants, error correcting codes and multiple quantization that I have begun to see. That is because I have no way to complete that work or publish it.

I find myself saddened that the quantum gravity community has been divided in two by the structure of funding. Physicists working on quantum gravity are now either string theorists or people looking at alternatives to string theory. There will be no progress until they realise that only a combination of these ideas will provide the solution. The program for moving forward seems so clear to me but it will require a paradism shift in the sociology of theoretical physics before it is seen by the community. As they lose site of their goals the best people will no longer want to enter the field and the public will not want to fund it. I susspect it will therefore be a very long time before new progress is made.

For me it is time to bow out of physics and concentrate on other endeavors. I have finally seen that there is no means for my ideas to be heard and the only recognition of my contributions will come in the form of plagiarism. It has nevertheless been an exciting journey and I wish good luck to those who continue to seek the ultimate truths about our existance.

This year I am walking towards my fiftieth anniversary of my time in the universe. At this age I find that the ability to take on new mathematics fades, but experience brings a wider perspective that allows deeper insights. I dont have students to pass on my knowledge to, so as I "retire" from physics I will use this space to drop a few pearls of wisdom that some younger researchers in quantum gravity may find.

Firstly, do not be a casualty of the string wars. As you start your postgraduate studies you will be assigned a supervisor. The current structure of funding means that he will either be a string theorist who considers all other appraoches to be worthless, or he will be someone with an alternative idea who thinks string theory has failed and must be abandonned. No matter how much authority your supervisor commands, do not accept either of these viewpoints. Learn the basics of all the approaches and make up your own mind.

Do not dismiss a good idea just because it is incomplete. At present all approaches to quantum grvaity are incomplete so that would not be a good strategy. Look at the parts of each approach that work mathematically and think about how they might be brought together in a more complete theory.

Do not get lost in a mathematically abstract sideline. Some physics students have become lost in the pursuits of n-category theory or the langlands program. These are fascinating areas but they are also wide and deep oceans. A theory of quantum gravity may ultimately be best understood in terms of such abstractions but the basic ideas will probably come from more concrete mathematics.

Do not get overly concerned with the measurement problem in quantum mechanics, the origin of times arrow or other aspects of macrophysics. These things are emergent and the fundamental laws are not concerned with them.

Do not stick to a philosophical idea such as everything is continuous or everthing must be discrete and finite, or the laws of physics must be simple, or they must emerge from the laws of complexity. Keep an open mind and follow where the interesting mathematics takes you.

Do not spend all your time on one toy approach. Of course you will have to develop some toy model to investigate some idea that you find compelling so that you can write meaningful papers about it. But move on and dont neglect the big picture. You will have to understand many such approaches and be able to bring them together to solve the final puzzle.

Do not sit waiting for the experimental result that will lead to the true theory of quantum gravity. We already have all the clues we need and it is unlikely that any experimental result can shead much more light on the problem.

Now for some more positive and specific advice.

Believe in the power of symmetry and its algebraic origins. Syemmetry has been at the heart of every great advance in our understanding of the universe, yet some people will now try to tell you that it is no longer important. They say that symmetry is not fundamental, it is just an emergent feature of differential equations. They are wrong. There is a huge symmetry that is hidden because it breaks in different ways in different superselection sectors. You may have to go beyond the algebras of lie groups and superlie groups to find its ultimate form, but symmetry is the key to the final breakthrough, just as it has been in every breakthrough that came before.

Think hard about the mystery of multiple quantisation. No one really understands why we talk about first, second and third quantizations. What is behind the quantization process? Rovelli has written here about how time might emerge from thermalisation. In fact thermalisation is a process analogous to quantisation and the more general principle is that each dimension of spacetime and the p-brane structures within is generated by processes of multiple quantization. This is linked to the algebraic structure of universal symmetry. Work out the details and you have the answer.

Finally, look at a wide range of interesting mathematical ideas. Think hardest about the ones that look relevant but that other physicists have neglected. An example is the theory of hyperdeterminants that was negelected for a century. Now it is appearing in the theory of quantum information and in string theory. Hyperdeterminants are linked to elliptic curves, and error codes that relate to excpetional structures in mathematics, and to monstrous moonshine that is still mysteriously linked to string theory. More generally there is a theory of hypergeometric functions related to hyperdeteriminants. there are connections with dualities and trialities in algebraic geometry. These are the areas of mathematics that need to be developped before we can construct the fundamental laws of physics. Study them hard while you are young and still have the capacity to learn them well. Follow this advice and the clues will eventually come together. The true form of quantum gravity lies in the deepest and most beautiful areas of *concrete* mathematics. Take heart, I feel it is accessible to someone smart enough to look for it in the right places without being led astray by others.

The aspect of this contest that gave me most disquiet is emphasised in the FAQ where is says

"each applicant must provide a brief biography with his or her entry. Judges are free to consider or ignore this information."

In other words judges are given full authority to judge entrants on the basis of who the applicant is rather than the content of their essay, if they wish.

For someone like myself who sits outside the institutional system it would not be worth entering unless there are explicit statements in the rules that the entrants are to be judged on essay content alone, and this must be made transparent by providing enough details of the judging process for us to see that fairness has been observed.

Congratulations! I just read about it. If I'm not mistaken viXra is a complete permutation. I'll be submitting any preprints there for sure and I know you'll allow them :)