Hardy's approach to quantum gravity and QM interpretation

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@bhobba I agree that the modern desire for mathematical rigor is not necessarily warranted or even actually all that useful in theoretical physics as it can be in mathematics; I could go on at great lengths about this, but this isn't neither the time nor place for that discussion.

btw seeing the zeta function, did you already hear of Atiyah's purported proof? This is the most excited I have been about pure mathematics (compared to physics) since at least a decade.

 

[bhobba]

btw seeing the zeta function, did you already hear of Atiyah's purported proof? This is the most excited I have been about pure mathematics (compared to physics) since at least a decade.

Saw that one and am exited as well. We will need to wait and see if its verified. This is where 'pure math' comes into its own. Terry Tao will likely write about it in his blog at some point - that's when I will look more carefully at it.

What I gave was simply an example of the kind of math physicists use and what's required to make it rigorous, and in doing that one increases their understanding what's going on in the first place. In physics a hand-wavy demonstration like I posted is fine, but a few words that can only be justified by being rigorous is often of value - but unless you are interested no need for the detail. What interests me pure math wise waxes and wanes as I think is true for many guys, like me, trained in math but were seduced by physics.

Thanks
Bill

 

[Fra]

I agree with the essence of the below and its right in line my approach as well.

Einstein, unlike how most theoretical physicists do today, did this by way of philosophically reasoning about the conceptually conflicting principles underlying the old theories, identifying which are necessary and then through reformulation try to bring them in harmony under one unified conceptual framework consisting of only necessary ingredients. It is only when this step is finished that the mathematics of the theory is modified specifically by replacing the older mathematical formalism with more appropriate mathematics.
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This constructive framework is as Hardy says completely general, i.e. it is a theory independent constructive methodology, or more explicitly it doesn't limit itself to any particular theory or formulation of that theory. Instead the framework can, in principle, be used to solve any fundamental problem in physics through the process of analogy. Hardy illustrates this by way of example, i.e. by using the framework to tackle the problem of quantum gravity:
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In my opinion, such conceptual frameworks or methodologies, if even partially successful should even be taken a step further, namely not just a framework for one problem, but an entire research programme approaching all fundamental problems.

This is how is see this briefly:

The specific "conflicting principles" and the "philosophical reasoning" we need to do here are not random philosophy but that relevant to the logic of science, and the logic of inference. Scientific knowledge as compared to other random beliefs is about backing up your beliefs by documented evidence, next step is to quantify this, and here we are immediately getting into foundations of probability theory. Ie. we rationally hold a belief because it is more likely when "counting evidence" of the various options.

All of this is no news, but what i mean by taking this to the next level, is to face both the physical contraints matter systems have on this inferences. And what influence the inferences we made have on stabilising matter - Note the striking similarity here to the feedback we have between matter and geometry. Note also how such abstractions exist also on finance market. Market expectations, no matter how "wrong" as per a certain perspcetive, can actually stabilize things, and thus explain things.

This logic is ruling not only expectations on the future based on dynamical laws. It also applies to our knowledge of dynamical law itself. Failing to see this leads eventually to the cosmological fallacy as smolin coined it. This is what i label logic of inference. It is the common roots of both logic of science and the mathematics of probability theory. Thinking about this, brings us back also to the roots of mathematics because we have concepts like "counting evidence". We need a model for this, that respects the physical constraints. Ie. the counting is executed withing the complexions of an observer, so we can not make headless use of fictive infinite and uncountable systems here, unless we really tame them - this is so paramount that handwaving here is not an option imo.

As we now all predictions of QM and QFT take the form of "expectations". But we rarely think of the dynamical laws as expectations, at least not to the extent we should. This is just one of the pathological symptom i see.

From skimming Hardys paper i am not sure how far he has come, but his description of physical law was suspicuous to me.

/Fredrik