Carroll's lecture on quantum mechanics

Oliver Knill, Harvard University, October 23, 2019

1. Sean Carroll lecture

Sean Carroll The lecture ``Something Deeply Hidden: Quantum Worlds and the Emergence of Spacetime" organized by the Harvard book store, the division of science and the science library was a packed lecture in Hall C. Even the stairs and side walls were filled with people. Carroll is an excellent speaker. Unlike others before, he was funny (one running gag was ``I have a book about that" had some new things (the Schroedinger cat is ``asleep or alive" rather than ``dead or alive" or when in the Q and A answer time, an audience member started with ``I understood everything you said in your lecture", Carroll interrupted ``Good start, don't ruin it with a second part", to which end the audience member ruined it with a second part. The last question was whether he ``would bet the life of his cat on the picture he described", Carroll answered ``I would not bet on the life of my cat, but on the life of your cat". The lecture was also clearly delivered, the slides were good and the talk was adapted well to a general audience (this is an art not many research scientists can do). One thing which kind of struck me was that Carolll switched from the ``many world paper" of Everett (written as a graduate student in the 50ies) to the de Whitt and Wheeler wave function idea which was influenced by Everett (de Whitt and Wheeler invited Everett once to give talks source) (which is very reasonable and probably the picture most mathematicians take towards the quantum theory: when considering the entire system, laboratory and observer together as a quantum system, the wave function collapse picture disappears.

M4V, Ogg Webm.

2. Interpretation of quantum mechanics

Sean Carroll I was lucky to learn QM as an undergraduate from Klaus Hepp, who would cover quite well the topic of the Kopenhagen interpretation, Einstein-Podolski and even discussed articles like ``is the moon there if we do not look at it?" etc, He gave good advise about the particle-wave interpretation of QM (you have to understand this on your own) and also made clear that QM is a model and not an ultimate theory. It obviously does not include special relativity (leading to quantum fields) nor gravity (needing to include a geometric frame work). So, philosophical questions about QM have since then been a bit tiresome for me. Later as a grad student, there had been seminars about Bohmian mechanics at the Zürich university to which I went as I had been working on random particle pictures (Isospectral deformations of random operators leading to Vlasov type integrable systems). But also there, for Bohmian mechanics, it was not so much the philosophy (it turns out that it produces the classical QM picture with more intuitive notions like particles) which is interesting as it does not lead to new insight. But it leads for example to an interesting existence problem: does the coupled De Broglie-Bohm system have global solutions? [It involves taking the log of the wave function which can be zero at some points which interested me as a mathematician. I had been working on existence theorems for infinite integrable Vlasov particle systems at that time]. And then there is the ``Shut up and calculate!" paradigm which I always admired: if you have a new theory, it has to be able to get something new, or substantially faster than an other theory, otherwise it is not much worth. Physics is always tied to experiments and a theory which can not relate to experiments eventually ends up in the garbage bin or lives on as interesting mathematics (which is valuable but not necessarily physics).

3. A martingale picture

Sean Carroll We use relatively crude models of equilibrium statistical mechanics to describe say a 1025 particle system using macrosopic mean field theories or partial differential equations, this is a way to DO stuff. The Kopenhagen interpretation also is a genius short cut to separate the observer from the experiment. The wave collapse picture is a point of view, a laboratory person takes. Of course, one should include the observer into the quantum picture as everything is entangled, but we do not do that because it usually does not matter. QM is an extremely successful theory. Why ruin it with philosophy? One reason of course is that we want to understand the merger QM+GR where it might be good to question old paradigms. But we do not write philosophical essays about ``the interpretation of Newtonian mechanics". It would be tiresome because it is obviously also just a model, an approximation. Early in the lecture Carroll warned about trying to get into the field of ``understanding QM". This is good advise. Any model in physics has a range of experiments, it can explain (which makes it valuable) and then boundary areas where it starts to fail. Trouble comes with physical theories which can not be confirmed by experiments. The Everett theory was for me one of these ``worthless theories". The lecture of Carroll a bit changed my point of view. He painted it not as a multiple universe theory as popular articles like this pointed out, but as a picture in which a fixed universe is described by in time finer and finer partitioned space. It is somehow a Martingale picture of the universe. The sigma algebra gets finer and finer. So, for me, it was the Martingale picture which was new in that talk and not the many world interpretation which was Everett's original paper.
Oliver Knill, Posted October 24, 2019