10 Aug 2023 7:11:35 UTC

Topic 229942

(moderation:

I've just read Peter Woit's take on the latest String Theory conference. Mr Woit wrote one of my favorite books on non-physics : Not Even Wrong. It seems that even ardent string theorists are doing something else now. Thus I think ends an almost 50 year hiatus in theoretical physics, plus to me it seems possible that physical observations and measurements may come back into vogue to guide these theorists !! They seem to have gotten over the whole 'truth must be beautiful mathematics' thing. If you are young it might even be a good time to get into theoretical physics.

__For example__ One problem that certainly needs attacking is in quantum mechanics, and is generically called the 'collapse of the wave function' or 'the measurement problem'. This aspect of quantum theory is assumed to occur but there is no known ** agreed** mechanism as to how. If one has a general state |psi>, written in the energy representation thus :

|psi> = Sum_over_n_of{ a_{n} * e^{( - iEnt/h)} * |E_{n}> }

where the a_{n} are complex numbers, E_{n} is the energy value of the eigenstate |E_{n}>, ~~h~~ is the reduced Planck's constant and n is however many constants you need to completely describe the system that |psi> represents. The entire complex exponential acts like an endless clock, spinning around at an angular frequency^{*} of E_{n}/~~h~~. This equation describes the state |psi> as being a linear weighted product of terms, where for each a_{n} when the modulus is taken and squared is proportional to the probability of being in the given energy eigenstate |E_{n}> upon measurement. So it's a mixture of ( typically very many ) 'pure'/exact energy states and when a system evolves ( via Schrodinger's time dependent equation ) the a_{n}'s will change and so will those probabilities. OK. So now you perform an energy measurement to yield for one value of n, call it k:

|psi> = e^{( - iEkt/h)} * |E_{k}>

In other words, out of all the possible energy values that one could have measured E_{k} was the one that actually happened ( so a_{k} is now equal to one^{**} and all other a_{n}'s are zero ). The state is now one of the 100% pure eigenstates. Now the conundrum : how did the system transition from the multifactorial one ( 1st equation ) to the singular one ( 2nd equation ) ? That this transition exists at all is a non-negotiable part of quantum mechanics. A probabilistic aspect is also required. Complex numbers are mandatory. Some think that the lack of knowledge about the state of the measuring device prior to the act of measurement is what generates the uncertainty in the outcome of the measurement. But the question still stands.

BTW if the system was absolutely & positively left alone in that state of exact energy, it would be eternally so. In reality these exact energy states are never seen. After or during a measurement to yield a given energy value, there will be a disturbance from something to kick it into a new mixture of states. Here you need to blur the lines between the part of the world that is 'the system' and the part that is the 'measuring device', that is arbitrary ( a matter of descriptive choice ) and not intrinsic. Also bear in mind that quantum mechanics is absolutely stunning in it's predictive value, despite the probabilistic aspect, as ever so many phenomena attest.

Now over the years there have been a number of proposed ways to address the question, some quite challenging, and many attacking underlying assumptions eg. is the wave function a 'real' thing. I mention this measurement issue because if one is going for a unified field theory ( 'of everything' ) then you need gravity and quantum mechanics to have some common ground, and sitting in that common ground, like a landmine, is this problem. Or put another way : how can spacetime curvature be made probabilistic ? Should it be made so ? Etc ... etc .....

Cheers, Mike.

* Here the value of ~~h~~ is the key to understanding how quantum theory approximates classical physics for high values of n. Take a Mars bar for instance and call it a 100g lump/mass, with energy mc^{2}, and let it sit there on a table just existing. If it was in a state of definite energy, E_{n}, equal to it's mass/energy equivalent then it's angular frequency E_{n}/~~h~~ is of the order of 10^{50}. That's a 1 followed by fifty zeroes and that's in Hertz or cycles per second : it's an insane number to oscillate at and guarantees that you won't be seeing interference effects between Mars bars any time soon. :-)

** When 'proper normalisation' has been done all probabilities must add to one. This is just mathematical housekeeping done in order that quantum theory respects our intuition(s) about probability.

I have made this letter longer than usual because I lack the time to make it shorter ...

... and my other CPU is a Ryzen 5950X :-) Blaise Pascal

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## Ooopsie = "a linear weighted

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Ooopsie #1 = "a linear weighted product of terms"

Try "a linear weighted

terms" ... :-)sum of productOoopsie #2 = "that's in Hertz or cycles per second"

Well to be exact it is radians per second, with 2* PI radians a full circle/cycle, but you get the idea.

Cheers, Mike.

I have made this letter longer than usual because I lack the time to make it shorter ...

... and my other CPU is a Ryzen 5950X :-) Blaise Pascal

## I read Lee Smolin's book, The

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I read Lee Smolin's book,

The Trouble with Physics, years ago. I think it came out at the same time asNot Even Wrongand it made a similar argument. Sabine Hossenfelder has a more recent book along the same lines, and Sean Carroll has a fairly recent book,Something Deeply Hidden, that argues that multiple worlds is not getting enough study.I'm not qualified to engage with the math, but at a more philosophical level, I wonder if the problem isn't so much that people are enamored with String Theory and ignoring more promising paths, as that the quantum mechanics measurement problem and theories of everything are actually extremely well studied and String Theory is a symptom of theoretical physicists needing something to do when being stumped for decades. We need more than another Einstein; Einstein himself was stumped by these problems, and not much progress has been made since -- right?

Neal

## Well, there are two

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Well, there are two problems.

The first I'll politely call the sociology of physics, or of science generally, where suppression of dissent from the majority group leads to bad outcomes in terms of progress. I reckon you can pick any field of endeavour and there will be groupthink & punishments, it's a human

thing. Each generation has its own myths etc .... Thomas Kuhn's work^{*}The Structure Of Scientific Revolutionsis a good read, judge the accuracy of it for yourself.Second are the actual technical problems, and here there is more hope as we have already a tried-and-true methodology to guide us : experiment feeding back upon theory. What is needed is more Perimeter Institutes actually. Or just expand the Swiss Patent Office even. Now Einstein was stumped on his 'Unified Field Theory' because he wouldn't slide quantum mechanics into it. He remained classical up until his death. Some have said that he may as well have gone sailing for the last 30 years of his life. A bit harsh perhaps, but he liked sailing. You're right in that some core problems are still with us. The work of John Bell and Alain Aspect ( plus others ) on entanglement is an exception though. The careful logic needed to parse particle counts to give experimental validation is indeed Nobel worthy ( and so physics is really non-local ). For me, I think we are abutting up to the limits of what can be deduced about the Universe as studied from within. Hence maybe the joke is on us with QM being the perfect foil that prevents us seeing the real deal. At that point one wanders off into metaphysics and philosophy.

But physics especially has been here before : in the late 19th century the consensus was that what remained to do was more decimal points of accuracy. How wrong that was. But the future belongs to our youths !

Cheers, Mike.

* And it is hard to re-task any given brain that is used to thinking along certain lines. Max Planck said "A new scientific truth does not triumph by convincing its opponents and making them see the light, but rather because its opponents eventually die, and a new generation grows up that is familiar with it." This has been paraphrased as 'science progresses one funeral at a time'.

I have made this letter longer than usual because I lack the time to make it shorter ...

... and my other CPU is a Ryzen 5950X :-) Blaise Pascal

## Mike Hewson

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Mike Hewson wrote:Einstein was looking for a tidy theory like General Relativity, a theory that didn't exist, but it seems to me you can't fault him for looking.

John Bell's achievement, if I understand correctly, wasn't really to make sense of QM; it was to prove that some of the worst paradoxes were real and kind of crush hopes that it might be simpler*. Does that sound about right?

* I'm saying that the paradoxes actually exist in nature

I'm glad to read this, because I had that exact same thought. If humanity is incapable of understanding the whole thing, which seems likely, then physics could end one of two ways. We either run out of ideas for how to make higher-precision measuring devices; or else we hit some theoretical puzzle that defies all logic. The wave collapse problem in QM seems like a candidate for the perfect puzzle.

Anyway, my overriding point is to wonder if String Theory is the disease or if it's more of a symptom of quantum gravity being legitimately intractable, at least with the information we have now.

## John Bell in 1964, looking at

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John Bell in 1964, looking at the Einstein/Podolsky/Rosen paper of 1935 (quantum mechanics was incomplete) came up with a theorem that deterministic local hidden variables cannot reproduce the predictions of QM. That was subsequently shown in experiments. So the hopes that there was some 'sensible' classical layer underneath QM was dashed.

As for quantum gravity, it remains outstanding, and one observation that I would make is that gravitational energy is non local because of general relativity (the equivalence principle).

Cheers, Mike.

I have made this letter longer than usual because I lack the time to make it shorter ...

... and my other CPU is a Ryzen 5950X :-) Blaise Pascal