Sir Michael Atiyah is here in the United States this month. Evidently he was at the Institute in Princeton last week during the Deligne conference, talking to Witten. Last Friday he gave a public talk at an AMS conference at the University of Nebraska on The Nature of Space, and will be giving another one tomorrow in Santa Barbara on the same topic.
Yesterday at the KITP he gave a talk on his own very speculative ideas about physics entitled Does the Universe Have a Memory?. He began by subtitling his talk “Crazy thoughts of an old man”, and noting that when he was at the Institute Witten had listened to him politely and then after a micro-second given him four reasons why his ideas wouldn’t work. One motivation he gave was that the current situation of string theory was somehow like Ptolemaic epicycles, with a fundamental idea that would drastically simplify everything still missing.
The speculative idea he was promoting was that perhaps quantum mechanics should be changed so that the future depends not just on the present, but on the history of the system during some short period before the present. So dynamics would be somewhat non-local in time. He hopes for some connection to the Connes version of the standard model, but this was all very vague. All in all, I fear that I wish Atiyah would go back to working on the relation between K-theory and physics….
Update: In a comment Doug provides a link to Atiyah’s public lecture.
That Atiyah would even give such a talk strikes me as a significant indicator of the level of disquiet that exists among leading figures in the string theory community and their allies in mathematics about the current state of work in the field, that is, about its presuppositions and goals.
He adopted a clear position on the debate between those who would abandon continuity in favor of discrete models, and those who see too much power in the mathematics of continuous structures to accept taking such a step. I think this dichotomy is suspect; I’ll say more about it later.
If the theory of gravity induced by string theory has arbitrarily high degree of derivatives, then what’s the problem?
[Oops! Sorry, I forgot to escape a < with a character entity…]
More on the above-mentioned dichotomy: Please read this discussion by Cosma Shalizi, and note the following:
Also, from Hendryk Pfeiffer (gr-qc/0404088):
..and this from the body of the paper:
I must quote a bit more from Pfeiffer:
Please remember this is NOT a forum for discussion of people’s favorite ideas about quantum gravity. This is not what the topic of the posting was about.
Chris W
Atiyah did not deny this dichotomy between continuous and discrete. On the contrary, he endorses it (a) by indicating a preference for Connes’ picture and (b) by saying explicitly that this Hale formalism for past dependent equations incorporates aspects of both.
I enjoyed the talk! Forget the physics – it’s full of subtle jibes and the sort of jokes that only very respectable old men can make.
Hi Peter
Sorry to go out of subject here. I am wondering about something. I see a rather surprising number of physicists and mathematicians having weblogs these days. Even more surprising to me is that these people get the time to write about things they have heard, talked or thought about. Now, some of these postings are rather long (I cannot recall any unreasonably long posting of yours so far. I see a lot of this on Lubos’ blog). Tell me… hasn’t blogging affected your productivity at work? Clifford at Cosmic Variance writes frequently, you too… It seems to me that a lot of interesting things are being said most of the time, but aren’t you better sometimes being busy at work or spending some time with friends away from the pc, or doing something different..?
I would like to hear from you on this matter.
Thanks
Nitin, Down Under
By the way.. I like the links you provide to interesting papers, notes, articles.
Hi Nitin: I think the problem is that guys like Peter have wireless connectivity to the internet all the time from their laptop or brain implant. It never gets turned off. Fortunately, they are able to do more than one thing at the same time…
Let’s face it, if a theoretical physicist does 2 hours of good work in a day, that’s a good day and the rest is his to do what he wants, like blog.
Following up on Ben’s response: for a high energy theoretician, ~4h of good work in a day is a GREAT day.
But, regardless, the sheer exercise of writing up, commenting, providing links, etc, etc, etc, is really good; it’s a win-win situation: it’s good for the audience (because they hopefully learn something new, leave interesting comments, etc) and it’s good for the writer, beucase he gets a chance to clear his mind, making sure that his thoughts are cohesive and so on.
So, say you teach, get 3h of good work and then you blog for ~1h, you may just have hit a pretty well rounded day: You can go home with a much better view of physics than when you came in.
But, maybe it’s just me… 😉
Hi Nitin,
You’re right that the weblog takes up a fair amount of time, and sometimes I do worry that it is taking away time I could be spending doing something more worthwhile, especially research. For now I think the time spent on this is worth it, but at some future point I may very well change my mind.
I don’t tend to write very long postings (I don’t know how Lubos does it….), so the actual writing isn’t that time consuming. Often I’m writing about things found by spending time looking around on the web, so in some sense the fact that I do a lot of that is the big time-waster, and there I’m probably not alone.
I keep intending to try and write some postings that are more explicitly about the research work I’m doing. Then time spent on those would be in some sense time spent on research. One thing I need to do first is to try out various methods for putting equations on WordPress, I may get to this pretty soon.
Peter
A fun talk but – from a systems science point of view – it makes the familiar mistake of focusing on a “single-scale” discrete~continuous dichotomy and not the more fundamental “scalefree” dichotomy of local~global.
Atiyah suggests incorporating the uncertainty of QM by making just a single Planck-sized step into the past. A scale-free approach to memory would want to model a powerlaw distribution of “pasts”. In this view the Planck scale defines not the fundamentally small (and discrete) but instead the fundamentally cogent (a web of interactions/gone to equilibrium).
Start by asking what is memory in a system. It is the general context within which a succession of particular states form. It is an ambience – a prevailing equilibrium in a system of interactions. So it is the “frozen” global view. And in hierarchical fashion, it exerts a downward constraint on any localised particulars. But of course, global constraint cannot “see” everything and so the local events (particle interactions, etc) are left with degrees of freedom. What we call their inertias.
So the memory of a system is its global coherent state which reflects some average of its past and – because the coherence is self-stable – also serves to predict the future for some reasonable distance. A universe that has developed certain constants, like the speed of light, is likely to continue to roll with those constants (barring a slow underlying evolution that eventually allows some further phase change to a new global vacua).
The point is that this globalised system memory is spread over all spatiotemporal scales. It is “scalefree” because the issue of scale has been thermalised.
So rather like a hologram, a very small “bite” into the past – like Atiyah’s suggested Planck-scale step – would give some kind of snapshot of the whole, but it would be very fuzzy. By definition, it would seem to give the most uncertain view!
By being the closest to the localised freedoms of the system, it would see the least of the global constraints, the global memory. It would be like trying to observe the convergence nature of the system, its tendency towards a global remembered balance, from exactly the most open and divergent viewing position. To offer another analogy, it would be like trying to gauge the temperature of a gas by measuring some particular passing molecule.
Prigogine has some arguments along these lines in his modelling of QM in “The End of Certainty”.
In the .mov version of Atiyah’s 24 Oct 2005 KITP talk at http://online.kitp.ucsb.edu/download/strings05/atiyah/snd/Atiyah_KITP.mov
Atiyah says (at about 1:12:24) that his class of models is based on “… the past history of a particle moving as a real particle …”, which seems to me to be the past world-line of the particle.
An audience member describes to Atiyah (at about 1:05:02) “… a common thread between the class of models you are suggesting, Connes class of models, and some unsolved problems in string theory.
So,
one simple way to think about the class of models you are talking about is just to do a power series expansion of x(t-r) in t and … the higher derivatives of t so then you have an infinite order differential equation.
Similarly,
quantum field theory on a noncommutative spacetime can be expressed in terms of a star product which is an exponential of derivatives and therefore is also in some sense a differential equation with an infinite number of derivatives
and
the best nonperturbative formulation of string theory we have is string field theory which is expressed in terms of Witten’s star product on strings which is also expressed in terms of some exponential of derivatives, but which we don’t understand how to grapple with as well …”.
It seems to me that a natural physical interpretation of that “common thread” is that strings should be interpreted as world-lines, NOT as individual particles or precursors of individual particles.
Tony Smith
http://www.valdostamuseum.org/hamsmith/
Tony Smith says:”Atiyah says (at about 1:12:24) that his class of models is based on “… the past history of a particle moving as a real particle …â€?, which seems to me to be the past world-line of the particle”.
An audience member describes to Atiyah (at about 1:05:02) “… a common thread between the class of models you are suggesting, Connes class of models, and some unsolved problems in string theory.
re:”So,
one simple way to think about the class of models you are talking about is just to do a power series expansion of x(t-r) in t and … the higher derivatives of t so then you have an infinite order differential equation”.
The problem with this is that for evolving systems, specifically, from Quantum to Macro and equally, from Present to Future, the systems would have to be equivilent?
From Atyiah’s talk of a “planck-memory” as representing some “past-initial-evolving-state”, a little “it” from bigger “bit” if ever I heard one!, but there has to be a same/equivilent comparable ‘worldline’ from Present-time to Future-time?..this very notion would condem stringworld lines to the “Non-Renormable-Un-re-cyclable-Bin” correct me if I am wrong, but Aytiah notion of Relative/Quantum domains seems to be teetering on insane?..this I take to be the deliberate interuptions(spoiler in audience?) in the said lecture.
Aytiah’s idea that a planck length is a Maximum Minimum “past-memory”, of a “present-time”, is no defferent from stating that the Present-time, is but a past memory of the ‘yet-to-exist’ future!
Just as a memory for any relative observer cannot contain 100% information (Reality is preserved in the Present-time), any worldline evolving from a planck domain, will contain very relevant Uncertainties?..you just cannot predict or construct, any present-time event from its past history!..if the speed of information recieved in any present-time event frame, exceeds the natural frequency of entropy, then theoretically, the Future, events that have not yet occured, could be manipulated directly from the Quantum past?
Slowing down an ordinary Photon would invoke a transformation in its “present-time”, it would no longer have any Uncertainty association, you could design the Future with complete absolute accuracy?
The Quantum Mechanical domain would collapse, by the fact H.U.P would be nullified?
If one combines Atyiah’s two-particle systems of [Past-Planck+Present-Time] with [Present-Time + Future Events], their equivilence would mean there is actually NO evolution whatso-ever.
Quantum Ranger said, about the “common thread” comment by an audience member at about 1:05:02 in Atiyah’s KITP talk online at http://online.kitp.ucsb.edu/download/strings05/atiyah/snd/Atiyah_KITP.mov
“… ..this I take to be the deliberate interuptions(spoiler in audience?) in the said lecture. …”.
That comment was made in the question and answer period following the lecture, so it was not a “deliberate interruption”.
Based on the context (Atiyah’s reply was “I agree with what you say” followed by extensive further discussion), it did not appear to me that the commenter was considered by those at the KITP talk to be a “spoiler”.
If you watch the .mov of Atiyah’s talk, you can see who made that comment. The camera shows him at about 1:07:58. I did not recognize him (but then I don’t know a lot of KITP people by sight).
Perhaps someone reading this can identify the one who made the comment.
Tony Smith
http://www.valdostamuseum.org/hamsmith/
Tony, my appologies, I had watched the lecture, but found the constant interuptions by the “same” audience member quite annoying, I do so admire Atyiah, but actually felt a little sorry for him being so obviously “heckled”.
I am going to re-watch the ‘whole’ talk, and hopefully the Q/A I missed would enlighten me, a question I had been contemplating form Atyiahs idea, is what happens to the missing “planck-memory”, it seems to be forever evolving “backwards”, as for sure, even the Planck-memory has to been formated from a previous “past”?
much of the interruption came from David Gross
during the QandA someone pointed out that there had really been two lectures going on, one by sir Michael and one by David, and reasonably enough that person asked David Gross a question related to HIS part of the lecture
the interruption was almost frantic and I think not malicious so much as instinctively defensive. If Atiyah ideas had been simply crazy it would not have been necessary to resist so hard. but the ideas, for good or ill, were somehow perceived (consciously or not) as plausible enough to be disturbing.
Quantum Ranger asked “… what happens to the missing “planck-memoryâ€?, it seems to be forever evolving “backwardsâ€?, as for sure, even the Planck-memory has to been formated from a previous “pastâ€?? …”.
I agree that is a good question, and it is also something that nagged in the back of my mind (in the form of why should the memory / past world-line be cut off at the Planck scale).
If there were no past time cutoff, then the basic entity would be the entire (back to the big bang?) past history world-line of each particle. Maybe such a model would be like that of Andrew Gray, who said in http://xxx.lanl.gov/abs/quant-ph/9712037 (in the abstract) “… probabilities are … assigned to entire fine-grained histories. The formulation is fully relativistic and applicable to multi-particle systems. It shall be shown that this new formulation makes the same experimental predictions as quantum field theory …”.
The same Andrew Gray proposed a “Quantum Time Machine” in version 1 of http://xxx.lanl.gov/abs/quant-ph/9804008v1, but he withdrew that proposal on 8 Aug 2004, the same day that he posted version 2 of http://xxx.lanl.gov/abs/quant-ph/9712037. Therefore, it seems to me that although Andrew Gray felt his “Quantum Time Machine” was flawed, he still feels that his formulation of quantum theory in terms of “entire fine-grained histories”, which sounds to me a lot like Atiyah’s model without the Planck-scale cutoff, is valid.
I wonder whether Atiyah knows of Gray’s model, and, if so, how he (Atiyah) thinks it compares with his (Atiyah’s) model.
Tony Smith
http://www.valdostamuseum.org/hamsmith/
For those who have been as frustrated as I have in trying to find Atiyah’s Nature of Space talk, here’s a link that actually works:
The Nature of Space
I have an innocuous question to ask: where would theoretical physicists generally tend to place Aityah, and his contributions, in their list of world-class mathematicians important to theoretical physics? And, BTW, what is the correct pronunciation of his name?
“where would theoretical physicists generally tend to place Aityah, and his contributions, in their list of world-class mathematicians important to theoretical physics?”
Very high.
Hi Doug,
I agree with Kea. I’d put Atiyah among the top three mathematicians of the last half of the 20th century (with Serre and Grothendieck), and more important for theoretical physics than any great mathematician since Hermann Weyl. His work on instantons and anomalies during the late seventies and early eighties was wonderful, and his conjectures made in 1987 about the existence of various TQFTs were influential in Witten’s amazing work in this area. Atiyah became less active in research mathematics after around 1990 when he became president of the Royal Society and master of Trinity College.
The pronunciation is Ah-Tee-Yaah.
Oh, and thanks for the link to Atiyah’s lecture!
Peter, I agree with you that Atiyah is “… among the top three mathematicians of the last half of the 20th century (with Serre and Grothendieck), and more important for theoretical physics than any great mathematician since Hermann Weyl. …”.
How does that square with the treatment of Atiyah by David Gross and Edward Witten?
As to David Gross, “who” said in a comment here: “… much of the interruption came from David Gross … the interruption was almost frantic and I think not malicious so much as instinctively defensive. If Atiyah ideas had been simply crazy it would not have been necessary to resist so hard. but the ideas, for good or ill, were somehow perceived (consciously or not) as plausible enough to be disturbing. …”.
As to Edward Witten you (and Atiyah) said: “… Witten had listened to him politely and then after a micro-second given him four reasons why his ideas wouldn’t work. …”.
If I am correct in my opinion that any evaluation given after only a micro-second is NOT a considered evaluation (nobody, not even Witten is that smart), then it seems to me that
1 – Gross and Witten are very insecure about the superstring theory in which
they have invested their lifework
and
2 – Gross and Witten are incapable of fair evaluation of any alternative ideas.
Tony Smith
http://www.valdostamuseum.org/hamsmith/
Hi Tony,
My take on Gross and Witten’s reaction to Atiyah was rather different. Atiyah has taken pains to not be especially critical of string theory (I’ve corresponded with him about this, and, much as I would love to count him as a string theory critic, he makes clear that’s not at all how he sees himself), so I don’t think they were worrying about defending string theory from Atiyah. Gross did interrupt and make extensive comments at Atiyah’s talk, but I took this as evidence that he was taking Atiyah seriously and trying to engage with him on his idea, even though it was pretty off-the-wall. I suspect Atiyah was exaggerating about the “microsecond”, and in any case Witten probably had plenty of time to think about Atiyah’s proposal while Atiyah was explaining it to him, enough time to come up with several pretty obvious problems.
Both Atiyah and Witten are extremely quick on their feet. I remember one time at MSRI talking to Raoul Bott, who had just walked away from Atiyah and Witten, shaking his head. He told me he found listening to the two of them “scary” since they were so much quicker than he was. Bott is a great mathematician also, but one who has to think everything through slowly and carefully to understand it, quite different than Atiyah or Witten.
What about Wheeler-Feynman & Aharonov 2-State QM in which present is a self-consistent global double loop 1/2(Advanced + Retarded)?
Thanks to Doug, I have just sat through the whole talk:The Nature Of Space.
My initial annoyance of the talk with D Gross was based on the lack of acoustics, not being able to hear what Gross was asking produced my unfounded accusation of “spoiler”, this self-evaluation is made from after the above linked talk.
What becomes clear from the Atyiah talk, is that there are numerous area’s of interpretations in nailing down what constitutes ‘Memory’?..for instance a mathematician who calculates a simple formula, is performing a repetative function based on “memory”, its an act of reproducing a “Time” and “information” event. In its simple way it is an act of “time-travel”, via a thought function contained in the bio-mass of braincells.
Relativity, in its conception gives presedence to the Observer in Time, we are the only forms that can perform “time-travels” mentally?..this is what a memory is.
Now interestingly Atyiah is stating that a planck-memory, is a decomposition of a real-time event,(a past-moment) located at some instant in the present. Matter has a specific evolutional path, it tends to move from one location to the next in constant fashion. If one take’s the electron and follows its trajectory, one finds that there is no continuation of its path, it can transfer itself from one location to another, without trancending the intervening space, from A to B, it can appear at B from the Future, without trancending the Present.
Feynman I believe made the “electron” statement:It is never located in the present-time, it always jumps from Past/Future or Future/Past?
The QM roots of H.U.P, contends that an Atyiah “planck-memory” must, at some moment along its timline evolution, make a transition from the Present-Time, to a Past-Time, it makes a ‘Jump’ into the Past?..the “moment” this occurs, it loses its memory of where it jumped from, it is re-configured, without any memory at all!
The Virtual Quantity ascociated with any energy of Quantum status, means that any finite Planck-Memory (any componant with all its paramiters), after it reaches the transitional ‘gap’, it has no choice but to reconfigure, as if it is appearing from the Future, and it has a new set of Quantum Numbers!!
Calibrating a decomposed planck-memory from a ‘present’ Spacetime, with that of a ‘future’ Space,(there has to be particles contained within present-time space, that are scaled from the future) means that at in a finite limit, energy and its memory of its evolution, exchange with that of particles emminating from the Future, there would therefore be Particles comparable to that of Planck Scale, appearing with a lot more Energy, future re-tarded Quantums?
Where is Planck-Memory stored?..is it within the present or future, ordinary memory by a conscious observer is stored within the mind, somewhere in the Observers present-time, scaled down and stored, never to be recalled as 100%, it always has some missing information, else it would reproduce reality events 100%, is this information lost to the Future or Present?..it has to go into the construction of the future, the future always needs more information than the Present, just as the Present always needs more informaiton than the Past!
Almost all said by Atiyah is pure nonsense in the best string tradition.
A basic discussion of why most of Atiyah’s remarks are completely outdated and some of them completely wrong is available at
http://www.physicsforums.com/showpost.php?p=806910&postcount=10
Jack Sarfatti said
What about Wheeler-Feynman & Aharonov 2-State QM in which present is a self-consistent global double loop 1/2(Advanced + Retarded)?
We are still waiting the promised Wheeler’s conference 🙂
Juan R.
Center for CANONICAL |SCIENCE)
juan r, the context of Atyiah’s “planck-memory” is surely an inquisitive inquiry into cause and effect, does a past memory effect present events?..can the present,’whole’, be created out of a finite memoric value, a minimum (planck) value?
At some moment the Present-time becomes the Past, and at the same instant the Future also becomes the Present?
If there is a “planck-memory”, a Quantum value of energy at miniscule scales, then there is also a comprable Macro value at the intesection moments of Present to Future. The scale difference increase’s at Present/Future boundaries, this is because the Future needs more energy/information, due to fact of increase in size, by volume?
If the future surely contains the same amount of energy(in discrete bundles of planck memory bits) as the Present, and consequently the Past energy, then symmetry could not be broken in a previous era?
At least 50% of ‘present-time’, is distributed into a past and future tense virtual domains. If planck scale “memory” is continueous in its attachment to a present spacetime location,then there is no cut-off point. If it is discrete at finite volume’s, then it is “seperate” and isolated from the present-time, therefore it no longer has a memory of its origin, it could take,choice? of a “memory” of infinite proportional value.
Virtual particles have virtual histories?.. accountable in terms of no memory of a previous existence, which I believe Feynman asscerted to certain particles mentioned by Jack Sarfatti above.
Again Atyiah seems to be poking little ‘peek-holes’ into certain “canned” models and interpretations.
Some canned models, contain worm-holes.
I think there is a whole new can of Wormholes being inderectly opened/presented by Atyiah, some of the nagging ‘worms’ are going to be hard to swallow, especially for certain string models.
If you do not want to shoot yourself in the foot, then controlled experimental particle physics is the sure way to avoid using “elephant-guns” to exterminate “M”, Theoretical mice!
I rate Atyiah as joint “number-2” in the context of greatness in contributing to scientific knowledge. There is no number one, this is yet to be filled, and he share’s this position with a vast number of other greats, I have a personal distrust of league tables, as the importance of stature can be over-rated by association and personal tastes.
Peter, as you say, “… Both Atiyah and Witten are extremely quick on their feet. … Raoul Bott, who had just walked away from Atiyah and Witten, shaking his head … told me he found listening to the two of them “scaryâ€? since they were so much quicker than he was. Bott is a great mathematician also, but one who has to think everything through slowly and carefully
to understand it, quite different than Atiyah or Witten. …”.
It is interesting that your characterization might be that Atiyah is a Hare and Bott is a Tortoise, yet working together they produced wonderful results. In an interview at http://www.ams.org/notices/200104/fea-bott.pdf Bott described his work with Atiyah, saying: “… In most of my papers with Atiyah he would write the final drafts and his tendency was to make them more abstract. …”.
Bott went on to say: “… I like the old way of presenting things with an example that gives away the secret of the proof rather than dazzling the audience. … on the whole I like the problems to be concrete. I’m a bit of an engineer. For instance, in topology early on the questions were very concrete – we wanted to find a number! …”.
Bott’s “we wanted to find a number” remark sounds to me a Feynman-like attitude toward physics.
As to physics and physicists, Bott made an observation about the Princeton IAS under Oppenheimer: “… Oppenheimer had taken over, and he was very dominant in the physics community. He had a seminar that every physicist went to. We mathematicians always thought they ran off like sheep, for we would pick and choose our seminars! …”.
Maybe superstring theory under Witten and Gross is a the contemporary manifestation of physicists’ sheep-like behaviour.
Tony Smith
http://www.valdostamuseum.org/hamsmith/
Hi Tony,
Your characterization of Atiyah and Bott as the Hare and the Tortoise is apt, as is the Bott quote. Together they did some truly wonderful things.
It’s always been true that physics is much more faddish than math, with particle theorists generally desperate to somehow contribute something to whatever the latest, hottest thing is, mathematicians more interested in digging deeply into one particular thing that they can become one of the few experts in and make their own. In the past, when experimentalists were regularly providing theorists new and surprising results that pointed out the right direction to go, a somewhat faddish concentration on figuring out the significance of these new results made sense as a way to make progress. The problem is that particle theory still has that sociology in place, but the experimental impetus that made it work is gone.
Regardless of the merits of Atiyah’s ideas on how to approach the QM challenge, the merits of his assessment of the current situation in theoretical physics are priceless, in my opinion. As an icon in the coummunity (gathered from the respect expressed here), his emphasis of the role of simplicity and elegance in nature’s secrets is crucial. From this perspective, he indicts string theory with one devastating observation:
“If a final theory emerges soon from string theory, we will discover a universe built on fantastically intricate mathematics.”
His point is made in the “conudrum” of imaginary numbers that he describes. The conundrum is perplexing because, if, fundamentally, the origins of mathematics are found in nature, then the “fantastically intricate mathematicsâ€? of string theory reflects something ugly and unsatisfying in nature, which would be so surprising, given humanity’s historical experience with her.
On the other hand, if mathematics is just a mundane tool for studying the physical structure of the world, and is no more than an invention of the human mind, how is it that its “biggest, single, invention,” imaginary numbers, show up in observed physical phenomena?!
He says that while his position is more moderate than Kronecker’s, he still believes that the origins of math are to be found in nature’s fundamentals, which then man develops and elaborates upon. Clearly, he’s implying that we have strayed too far from the origins of mathematics; that the vastness of string theory’s mathematical complexity has now taken on a life of its own, which abandons the vital reciprocal relation of math and physics.
It reminds me of Hestenes’ observation that
There is a tendency among physicists to take mathematics for granted, to regard the development of mathematics as the business of mathematicians. However, history shows that most mathematics of use in physics has origins in successful attacks on physical problems. The advance of physics has gone hand in hand with the development of a mathematical language to express and exploit the theory…The task of improving the language of physics…is one of the fundamental tasks of theoretical physics.
Coming from such eminent mathematicians, these are sage words indeed. Is Atiyah on a mission?
“From this perspective, he indicts string theory with one devastating observation: “If a final theory emerges soon from string theory, we will discover a universe built on fantastically intricate mathematics.â€?
String theory seems pretty natural if you have an organic metaphysics in mind – where something emerges as the constraint of a vaguer everythingness, rather than a creatio ex nihilio ontology.
So at the fundamental level, there is a chaos of potential with no mathematical structure. Then structure self-organises as resonances that lock into place. As this SO reduces dimensionality, the structure becomes more robust. Far out, you have only sporadic flashes of order – like the Monster lie group. Then as you get down to just 10 or 11 dimensions, the structures become increasingly robust.
Everything finally locks up pretty solid at three dimensions (with their emergent “fourth dimension” of a flow of time).
This is why we should expect a swamp as the fundamental ground for physical theory – it describes the vagueness, the potential, that would be a realm of “everythingness”.
The issue is then to understand whether the reduction of this raw potential to crisp (mathematically resonant and self-organising) structure has just one outcome, or a variety of possible outcomes. We could be the only possible kind of universe.
These points may seem off-thread but the metaphysics is important once you start asking whether maths is mechanically constructed or Platonically given. There is a third road which may be unfamiliar but was in fact widely prefered even in the time of Plato and Democritus.
Peter, you said “… All in all, I fear that I wish Atiyah would go back to working on the relation between K-theory and physics …”. Here are some related quotes and comments:
Bott, in his interview at http://www.ams.org/notices/200104/fea-bott.pdf , said “… the start of my long and wonderful collaboration with Michael Atiyah. We first of all gave a new proof of the periodicity theorem which fitted into the K-theory framework … Then Grothendieck, in the purely algebraic context, gave a … proof …[of]… the index theorem … using his K-theory in the formal, algebraic way. … Before, we had taken complex analysis or algebraic geometry as a given, so that the differential operator was hidden … here, suddenly the topological twisting of the differential operator came into the equation. Of course, Atiyah and Singer immediately realized that this twisting is measured with the homotopy groups of the classical groups, by the so-called symbol. Eventually the whole development of index theory fitted the periodicity theorem into the subject as an integral part. Atiyah very rightly chose Singer to collaborate on this project. …”.
In their book Spin Geometry (Princeton 1989 at page 277), Lawson and Michelsohn said: “… In 1982, E. Witten found a different approach … through consideration of symplectic geometry and supersymmetry. … he outlined a proof of the index theorem for the Atiyah-Singer operator … however … none of these methods [including Witten’s] applies to prove the index theorem for families or the Cl_k – index Theorem (in their strong forms). These theorems in general involve torsion elements in K-theory which are not detectable by cohomological means. …”.
In his book Introduction to Superstrings and M-theory (Second Edition, Springer 1999, 1988 at page 338), Michio Kaku said: “… new developments in supersymmetry have now made it possible to prove the Atiyah-Singer index theorem from a simple Lagrangian. Traditionally, the proof of the Atiyah-Singer theorem has been inaccessible to most physicists because of the intricacies of the mathematical formulation. …”.
Reading those excerpts in sequence leads me to think that a reason that superstring physicists are so attached to supersymmetry is that it is only through Witten’s supersymmetric approach that they can understand the Atiyah-Singer index theorem.
However, by restricting themselves to the Witten supersymmetric construction, the supersymmetry physics people are cutting themselves off from possibly very fruitful avenues of constructing new and possibly realistic physics models.
For instance, Lawson and Michelsohn, at page 270 of their book cited above, said [I have omitted some tildes etc from notation due to ASCII limitations]:
“… Given a real operator … in the basic case, no information is lost under complexification. This is not true, however, if one passes to the index theorem for families. The index of a family of real operators takes its value in the group KO(A), and .. for example … KO(Sn) = Z2 for n = 1 (mod 8) but K(Sn) = {0} in these dimensions.
For this reason Atiyah and Singer established a separate index theorem for families of real operators. It is a more subtle and profound result … the appropriate theory is not KO-theory … It is the more general KR-theory …”.
If Kaku’s assessment of physicists’ inability to understand a KR-theoretical index theorem is correct, then I share Peter’s sense of loss if Atiyah is not now “working on the relation between K-theory and physics”.
However,
I respect Atiyah’s right to follow his own intuition and to pursue his physics model based on Hale’s book Functional Differential Equations. It may even turn out that there is some connection between the two areas, and that Atiyah is smart enough to sense such a connection.
Tony Smith
http://www.valdostamuseum.org/hamsmith/
My immediately previous post seems to suffer from an inadvertent smiley.
The smiley should be the number 8 and the equation should read
KO(Sn) = Z2 for n = 1 ( mod 8 ) but K(Sn) = {0} in these dimensions.
As I indicated in the immediately previous post, the equation also suffers from suppression of such things as tildes etc due to ASCII limitations.
Tony Smith
http://www.valdostamuseum.org/hamsmith/
quantum ranger, As already said Atiyah’s talk is outdated.
Curiously the current tendency in the topic -Atiyah is of course NOT an expert- is the contrary of Atiyah’s proposal.
Retarded diferential equations have proved to be computationally intractable during more than 40 years (moreover do NOT solve the famous problem of the arrow of time). Today, there is emphasis on the abandonment of this way by either Marklovian equations in a generalized space functional -e.g. 90s Prigogine proposal in a RHS- or the use of sophisticated memory kernel techniques eliminating the convolution (the ‘memory’) from the evolutor, transforming the retarded equation into a local time equations that can be computationally solved.
Literature in this topic is very extensive and complex.
Atiyah’s talk is both outdated and wrong in several fundamental aspects. See above link for a dissection.
That universe has a memory is already very well-known, for example the standard Zubarev equation with an infinitesimal memory -Abel kernel-. Equations with memory are standard in many condensed matter disciplines. This is not new.
The discussion of Atiyah on causality structure of the universe is completely wrong and very outdated. It is unnecesary the appeal to Planck scale physics -see Prigogine theory for example, or CSM approach, or etc, etc, etc.-.
You would read The End of certainty by Prigogine
http://www.amazon.com/exec/obidos/tg/detail/-/0684837056/103-6383925-0546230?v=glance
for some recent views on the topic. Atiyah proposal would be good in the 50s and 60s. In fact, the first basic equation -generalizing mechanics- proposed by Prigogine was a retarded equation with a memory term and a complex diagranmatic technique acounting for all that cannot be explained via mechanics (see above book) or field theory. All of that is well-known in speciliazed literature. But further work did Prigogine and other abandoned that way. We are in the 2005!
Juan R.
Center for CANONICAL |SCIENCE)
I’ve read through the discussion above I can’t resist expressing a point of disagreement.
I found Atiyah remarkably charming and urbane—but I was kind of expecting that—but I thought the continual interruptions from Gross rude to the point of obnoxiousness. Atiyah couldn’t get two sentences out without being pulled up and forced to engage in a dialogue. This is not how one should behave in a talk, whether threatened, not threatened, malicious, not malicious. There is just no excuse for this boorishness. And it was very easy to sense Atiyah’s frustration.
Sorry, but I thought this was pretty much a disgrace. I can’t believe that the person chairing the talk didn’t exert some control over his audience.
I felt the same way, but the person causing the disruption is the head of the Institute, so the chair of the talk wasn’t about to try to exert any control. Which, of course, makes it all the more boorish.
Thanks Doug, that info does go some way to explaining it! I now see what others have been saying regarding his sensing Atiyah’s talk as a threat. Any suggestion of even the possibility of a new idea, or the need for one, seems to have been taken as a five alarm fire—to be extinguished immediately.
Poor Atiyah had the hose directed at him the entire time!
I have a more substantial thought on Atiyah’s talk which I think is on his side.
Modern explanations of EPR-like entanglement suggest that the composite system is in a pure state, whereas the component systems are in mixed states. The mixed states of the components do not uniquely determine the composite pure state—so some information resides in the state of the pair of particles (there from their anti-correlation origins) which does not reside in the component states. This is the so-called quantum holism, and it gives rise to the entanglement because of the non-commutativity of the operators that apply to the individual systems.
But then there is at least room for saying that the pure state contains information about the past of the system, which must be factored in when looking at the correlations at the time of measurement. I know it’s sketchy but it does suggest that Atiyah’s idea may have some kind of role to play.
Pardon the pun, but if string theory could go some way to explaining entanglement it would have done something interesting. But it doesn’t even appear to be in the right ball-park. Or am I wrong here?