Want to take part in these discussions? Sign in if you have an account, or apply for one below
Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.
I added a blurb from and link to Connes most recent lecture (Temps et aléa du quantique (english)) on the time page. (Added both for its innate interest and to help understand the transit between mathematics and philosophical intuition).
When I was in preparatory school, my teacher asked me (…) “what is a variable?”. I reflected and reflected, and after a while, I said “time”. (…) The topic of my talk is that I believe we are all used, because of our constitution and so on, to attribute variability to the passing of time. The thesis which I will propose and try to back with mathematical results is the following: I believe that the true variability is quantum, and that the true variability is the fact that when you take a quantum observable it doesn’t have a single value, but it has many possible values which are given by the spectrum of the operator, plus the fact that discrete variables cannot coexist with continuous variables without the quantum formalism. I will explain how time emerges from these facts. I have never tried to explain this idea, I know it’s difficult, and its difficult because in my mind it is backed up by an intuition which comes from many years of work, and this is the most difficult thing to transmit. (…) How to explain this? (…) The answer I believe comes from Von Neumann (suitably implemented and very much ameliorated). (…) In the 40’s and 50’s Von Neumann was asking what does it mean to have a subsystem? What does it mean that somehow, the Hilbert space in which you work is a Hilbert space in which you have partial knowledge of things because the system is a composite system and there is a part of the system which you know and a part which you ignore? What Von Neumann was trying to understand was factorizations. (gives lecture on factorizations…) By the way, I should say that this is why I spent many years studying Noncommutative Geometry: the simplest geometric origin of Von Neumann factorization is foliations. If you take the simplest foliation (well, I don’t know if it’s the simplest), the [???] foliation of the sphere bundle of a Riemann surface, you get the most exotic factorization of Von Neumann? (type III1).
Thanks, Trent! I thought that lecture was in French, so I wasn’t going to watch it. But it looks pretty good from what I saw already. The comments about Newton-style infinitesimals are interesting…
What is the origin of the English text?
the text is composed of excerpts from 10:45 - 17something (w/ some paraphrasing) + the final comment starting at 57:52. despite the french title and youtube blurb, the lecture was delivered in english.
Since we had a talk on the philosophy of time here yesterday, I thought I’d add something brief on this at time.
Since Urs added
elsewhere. I’ve included it here too.
Our entry appears to be rather disorganised. For a while I’ve been meaning to start a conversation on time, which we could then use to improve the page.
A colleague of mine is a philosopher of time who starts out from the basic intuition that for us to make any sense of ourselves as moral agents, we must suppose time to be as it appears, in the sense that there is a present for us, an open future and a settled past. He adopts what is called the ’growing block’ view of the universe which takes the past and present to be real while the future to be unreal. He often comes up against opposition which remarks that general relativity rules out any such talk.
I’d like to get clearer in my mind what is best said to him from the perspective of physics. There used to be a topic called ’philosophy of matter’, which seems to have disappeared. Physics came to be able to say a great deal here, such as about the stability of matter. This explains a great deal about our everyday conception of matter. There seems then to be a difference between science explaining what gives rise to our ordinary experience, and occasions when it overturns it. For the latter, perhaps the discovery that the Earth is a spinning ball, rotating about the sun. Of course, even there, the discovery was compatible with what we experience. It’s just that we had taken the extra step to consider ourselves to be static.
So what of our ordinary experience of time is illuminated by physics, and where have we overreached? Perhaps a topic for the Christmas break.
Just to remark that it’s misleading (of whoever would do so, such the unnamed people you refer to) to appeal specifically to general relativity for determination (“reality” in the sense of your comment) of the future by the past. Instead this holds for every deterministic theory, and certainly for Newtonian theory. In fact it holds less so in general relativity, namely there it fails as soon as spacetime is not globally hyperbolic!
The new aspect brought about by general relativity is not determinism of the future, but observer-dependence of what counts as the future.
Now, regarding the issue: To have any chance of making any progress on questions of fundamental reality, one clearly must not disregard the best available knowledge about fundamental reality. Here: Since we know that fundamental reality is not controled by classical field theory (be it Newtonian or Einsteinian or otherwise), it is a non-starter to base any discussion of the possible fundamental nature of time on non-quantum concepts.
That’s where today’s article comes in
This develops an old observation, much highlighted by Alain Connes in the past, that Tomita-Takesaki modular theory implies canonical evolution outer automorphisms on von Neumann factors of algebras of quantum observables.
I think the main line of criticism was that the growing block view requires that there be a simultaneous ’now’ across space, i.e., a unique Cauchy surface, so that a non-globally hyperbolic universe rules it out. But I believe there are growing block views not requiring this.
Somewhat similarly, there’s the opposite response to the sentiment of Einstein that Carnap describes in his autobiography:
Once Einstein said that the problem of the Now worried him seriously. He explained that the experience of the Now means something special for man, something essentially different from the past and the future, but that this important difference does not and cannot occur within physics. That this experience cannot be grasped by science seemed to him a matter of painful but inevitable resignation. I remarked that all that occurs objectively can be described in science; on the one hand the temporal sequence of events is described in physics; and, on the other hand, the peculiarities of man’s experiences with respect to time, including his different attitude towards past, present, and future, can be described and (in principle) explained in psychology. But Einstein thought that these scientific descriptions cannot possibly satisfy our human needs; that there is something essential about the Now which is just outside the realm of science. We both agreed that this was not a question of a defect for which science could be blamed, as Bergson thought. I did not wish to press the point, because I wanted primarily to understand his personal attitude to the problem rather than to clarify the theoretical situation. But I definitely had the impression that Einstein’s thinking on this point involved a lack of distinction between experience and knowledge. Since science in principle can say all that can be said, there is no unanswerable question left. But though there is no theoretical question left, there is still the common human emotional experience, which is sometimes disturbing for special psychological reasons.
Some agree that the Now isn’t captured by physics and so conclude, against Einstein, that this is because there is no special Now.
But, as you say, the quantum nature of the universe must be addressed, hopefully without slipping into wordy interpretations. But why on the page is it all from the modular theory perspective? Doesn’t string theory have something to say? Does the 2-spectral triple approach consider outer automorphisms? I see Griess wonders about something like this for VOAs here, section 2. Won’t contact have to be made with your ’emergence from the superpoint’ story?
1 to 9 of 9