Can intuitionist math bridge the QM/GR divide?

[TheVat]

https://www.quantamagazine.org/does-time-really-flow-new-clues-come-from-a-century-old-approach-to-math-20200407/

(This is a pull-quote, but I have to warn that reading the full article may be necessary to follow what Gisin is up to.  I can't cut/paste everything on this device, sorry.)

Over the past year, the Swiss physicist Nicolas Gisin has published four papers that attempt to dispel the fog surrounding time in physics. As Gisin sees it, the problem all along has been mathematical. Gisin argues that time in general and the time we call the present are easily expressed in a century-old mathematical language called “intuitionist mathematics,” which rejects the existence of numbers with infinitely many digits. When intuitionist math is used to describe the evolution of physical systems, it makes clear, according to Gisin, that “time really passes and new information is created.” Moreover, with this formalism, the strict determinism implied by Einstein’s equations gives way to a quantum-like unpredictability. If numbers are finite and limited in their precision, then nature itself is inherently imprecise, and thus unpredictable.

[Markus Hanke]

It’s a very interesting approach, thanks for sharing +1

I’m definitely looking forward to seeing how this develops further, and personally I’m quite open to an approach such as this - on the other hand, extraordinary claims require extraordinary evidence, and just doing away with unitarity as a fundamental symmetry is most certainly extraordinary. So I’m open to this, but not in any way convinced.

[studiot]

10 hours ago, TheVat said:

https://www.quantamagazine.org/does-time-really-flow-new-clues-come-from-a-century-old-approach-to-math-20200407/

(This is a pull-quote, but I have to warn that reading the full article may be necessary to follow what Gisin is up to.  I can't cut/paste everything on this device, sorry.)

Over the past year, the Swiss physicist Nicolas Gisin has published four papers that attempt to dispel the fog surrounding time in physics. As Gisin sees it, the problem all along has been mathematical. Gisin argues that time in general and the time we call the present are easily expressed in a century-old mathematical language called “intuitionist mathematics,” which rejects the existence of numbers with infinitely many digits. When intuitionist math is used to describe the evolution of physical systems, it makes clear, according to Gisin, that “time really passes and new information is created.” Moreover, with this formalism, the strict determinism implied by Einstein’s equations gives way to a quantum-like unpredictability. If numbers are finite and limited in their precision, then nature itself is inherently imprecise, and thus unpredictable.

Thank you for posting this +1.

I would warn that intuitionism is in area of (mathematical) philosophy the Stanford Encyclopedia (Plato) is highy questionable about.

[joigus]

Interesting, but I'm skeptic. Revolutions in physics normally stem from a well-balanced mixture of conservatism (a lot of it) and at most one very bold new statement. Sounds too revolutionary for the likes of me.

If professor Gisin gave me a good account of something playing the role of,

 

QP−PQ=iℏ

with something other than continuous mathematics, I would pay a lot of attention, if not be immediately won over.

It's not that some aspect is better addressed with the new idea. It's the not-so-easy order that everything else stays more or less where it was.

[TheVat]

27 minutes ago, joigus said:

It's not that some aspect is better addressed with the new idea. It's the not-so-easy order that everything else stays more or less where it was.

 

Hard for me to judge, though the rebuff to David Hilbert has an aesthetic appeal to my sense of the fuzziness of things.  I am always finding the concept of information as a physical thing quite slippery, as in the part where the article addresses the problems Gisin has with the universe's initial conditions leading to a block universe...

 

Now expand this idea to the entire universe. In a predetermined world in which time only seems to unfold, exactly what will happen for all time actually had to be set from the start, with the initial state of every single particle encoded with infinitely many digits of precision. Otherwise there would be a time in the far future when the clockwork universe itself would break down.

But information is physical. Modern research shows it requires energy and occupies space. Any volume of space is known to have a finite information capacity (with the densest possible information storage happening inside black holes). The universe’s initial conditions would, Gisin realized, require far too much information crammed into too little space. “A real number with infinite digits can’t be physically relevant,” he said. The block universe, which implicitly assumes the existence of infinite information, must fall apart.

 

2 hours ago, studiot said:

I would warn that intuitionism is in area of (mathematical) philosophy the Stanford Encyclopedia (Plato) is highly questionable about.

Yes, thanks, the dependence of intuitionism on time - that statements could evolve towards validity over time - is rather mind bending and I have to acknowledge it could be nonsense.  I'm only scratching the surface on this, and want to read Brouwer further to get some historical background.   

Like @Markus Hanke I am open to all this but need to see what kind of evidence there could be.  

[joigus]

22 minutes ago, TheVat said:

Hard for me to judge, though the rebuff to David Hilbert has an aesthetic appeal to my sense of the fuzziness of things.  I am always finding the concept of information as a physical thing quite slippery, as in the part where the article addresses the problems Gisin has with the universe's initial conditions leading to a block universe...

 

Hey, for me as well. We should keep an open mind... and filter out ideas too out there.

Another very interesting revolutionary more in a direction that resonates with me is Julian Barbour. I don't know if you've heard of him. His core idea is that the relevant quantities to describe the Cosmos should be interrelationships expressed in the form of ratios, rather than coordinates. I gather that he and his collaborators are having a hard time relating this --at first glance-- very interesting idea to the nuts and bolts of the physics we already know and love.

Maybe I will start a thread about Barbour, if I can.

Edited November 27, 2022 by joigus
minor correction

[studiot]

13 minutes ago, TheVat said:

Yes, thanks, the dependence of intuitionism on time - that statements could evolve towards validity over time - is rather mind bending and I have to acknowledge it could be nonsense.  I'm only scratching the surface on this, and want to read Brouwer further to get some historical background.   

Like @Markus Hanke I am open to all this but need to see what kind of evidence there could be.  

I will have to look closely at your references, but sorry I thought you would have no probs finding the plato article.

https://plato.stanford.edu/entries/intuitionism/

 

As for 'information'.  The mathematical theory of information is seriously limited to its domain of definition, which most of mathematics is of course.
And people so often forget this limitation. Maths inormation is about subjects which are carefully specified. So there is no mathematical definition or description of indirect forms of information.

As an example, I don't know if you have seen the pigeon advert for the Vauxhall Mokka  -  (I don't know what it is called in the US)  -  I don't know of any way of translating the advertising information into maths or logic, but they certainly get their message across to any human.

4 minutes ago, joigus said:

Maybe I will start a thread about Barbour, if I can.

Look forward to it !

[TheVat]

7 minutes ago, joigus said:

Another very interesting revolutionary more in a direction that resonates with me is Julian Barbour....

Maybe I will start a thread about Barbour, if I can.

I am familiar with his end of time theory, and would be glad to follow any thread you start on him.  And I recognize that formula you posted earlier as Heisenberg's quantum conditions formula.... though time will be needed for me to understand the implications of a revision with a non-continuous sort of math.

5 minutes ago, studiot said:

will have to look closely at your references, but sorry I thought you would have no probs finding the plato article.

I didn't have probs, thanks.  Still catching up. The Stanford entry is a good starting point, and I will get back to it.  If only to get some grasp on what someone means when they say real numbers can't exist inside black holes...as this fellow at Princeton did:

 

Several experts agreed that real numbers don’t seem to be physically real, and that physicists need a new formalism that doesn’t rely on them. Ahmed Almheiri, a theoretical physicist at the Institute for Advanced Study who studies black holes and quantum gravity, said quantum mechanics “precludes the existence of the continuum.” Quantum math bundles energy and other quantities into packets, which are more like whole numbers rather than a continuum. And infinite numbers get truncated inside black holes. “A black hole may seem to have a continuously infinite number of internal states, but [these get] cut off,” he said, due to quantum gravitational effects. “Real numbers can’t exist, because you can’t hide them inside black holes. Otherwise they’d be able to hide an infinite amount of information.”

[iNow]

23 minutes ago, joigus said:

Another very interesting revolutionary more in a direction that resonates with me is Julian Barbour. I don't know if you've heard of him.

I read a book of his almost 20 years ago called The End of Time about time slices and their similarity to stacked photographs. IIRC the premise was we experience them similar to watching a film where individual photo frames play back to back such that we merely perceive movement… and how our experience of time is similar. Interesting ideas, but hard to judge the veracity. 

Edited November 27, 2022 by iNow

[joigus]

3 minutes ago, TheVat said:

And I recognize that formula you posted earlier as Heisenberg's quantum conditions formula.... though time will be needed for me to understand the implications of a revision with a non-continuous sort of math.

You're right, though it's hard for me to concede that time were to be discrete without space --and momentum-- getting affected in a similar way.

3 minutes ago, iNow said:

I read a book of his almost 20 years ago called The End of Time about time slices and their similarity to stacked photos. IIRC the premise was we experience then similar to watching a film with individual frames playing such that we merely perceive movement and how our experience of time is similar. Interesting ideas, but hard to judge the veracity. 

Yes. Predictions? Another thing I'm missing in most of these revolutionary ideas is the conservative aspect. Namely: How you keep in its place everything else we know to work. If you want to improve a building, you normally don't go about it changing the foundations.

Another interesting aspect of these revolutionary ideas is that their authors are no spring chickens. New physics used to be the preserve of people in their twenties. Now it's coming from people who've been there for quite a while. I think that says something about the "crisis of theoretical physics" we're going through.

[studiot]

44 minutes ago, TheVat said:

Several experts agreed that real numbers don’t seem to be physically real, and that physicists need a new formalism that doesn’t rely on them. Ahmed Almheiri, a theoretical physicist at the Institute for Advanced Study who studies black holes and quantum gravity, said quantum mechanics “precludes the existence of the continuum.” Quantum math bundles energy and other quantities into packets, which are more like whole numbers rather than a continuum. And infinite numbers get truncated inside black holes. “A black hole may seem to have a continuously infinite number of internal states, but [these get] cut off,” he said, due to quantum gravitational effects. “Real numbers can’t exist, because you can’t hide them inside black holes. Otherwise they’d be able to hide an infinite amount of information.”

 

45 minutes ago, TheVat said:

I am familiar with his end of time theory, and would be glad to follow any thread you start on him.  And I recognize that formula you posted earlier as Heisenberg's quantum conditions formula.... though time will be needed for me to understand the implications of a revision with a non-continuous sort of math.

I see QM uncertainty as being a manifestation of the fact that ours maths tries to place properties as concentrate at a point (in the coordinate space concerned) when they are not so concentrated in fact. Alternatively what does it mean to say both  "The electron wavefunction has a presence throughout all space" and to say "the electron is also at point x in space "? 

[TheVat]

@joigus  I recognize that Gisin's math would really be replacing a foundation under the building, in order to resolve things like the black hole information paradox.  (that does have to happen with actual buildings, like those seaside condos in Florida which are threatened with collapse due to salt intrusion).  I admit I don't understand a lot of this...

In quantum mechanics, information can be shuffled or scrambled, but never created or destroyed. Yet if the digits of numbers defining the state of the universe grow over time as Gisin proposes, then new information is coming into being. Gisin said he “absolutely” rejects the notion that information is preserved in nature, largely because “there is clearly new information that is created during a measurement process.”

 It feels like playing fast and loose with the concept of information.  As @studiot mentioned earlier,  "Maths information is about subjects which are carefully specified. So there is no mathematical definition or description of indirect forms of information...."

4 minutes ago, studiot said:

I see QM uncertainty as being a manifestation of the fact that ours maths tries to place properties as concentrate at a point (in the coordinate space concerned) when they are not so concentrated in fact. Alternatively what does it mean to say both  "The electron wavefunction has a presence throughout all space" and to say "the electron is also at point x in space "? 

Yes.  The reality of these entities and their correspondence to mathematical models is always questionable.  One may well ask after the ontology of real numbers.  In what sense does Ahmeiri say that they cannot exist?  Like Gisin, he says that you can take the digits only to a finite number in the physical world, like the .49999 that may or may not ever become one half.  We don't know if a 7 may appear in the string.  

[joigus]

On 11/27/2022 at 5:32 PM, studiot said:

I see QM uncertainty as being a manifestation of the fact that ours maths tries to place properties as concentrate at a point (in the coordinate space concerned) when they are not so concentrated in fact.

+1. I love the depth of this comment. At a distance, dynamics works well enough assuming field sources to be point-like, or smooth distributions of point-like things. These densities would have to end abruptly on the boundary. When you get closer, you must change the map, because more details are available to you --if for no other reason. Complex numbers and wave variables seem to be Nature's way of telling us that we must blur things out when we get closer.

When you try to get even closer, and gravity becomes relevant, entropy seems to be summoned up from out of the blue... The suggestion seems to be that the mapping must be re-thought, and the conceptual scaffolding reconsidered.

On 11/27/2022 at 5:47 PM, TheVat said:

I recognize that Gisin's math would really be replacing a foundation under the building, in order to resolve things like the black hole information paradox.  (that does have to happen with actual buildings, like those seaside condos in Florida which are threatened with collapse due to salt intrusion).  I admit I don't understand a lot of this...

 

I should learn more about Gisin's proposal before dismissing it. So I'm not actually dismissing it. My idea of it so far is more of a "too good to be true" kind of objection. I think I'm also spotting a subtle element of anthropomorphism about it that makes me uneasy. If Gisin and/or others managed to demonstrate GR and QM as appropriate limits of the idea, I would have to admit it's really cutting some ice. I do have to say, though, that skepticism towards any new idea is a very comfortable position. When you reach a certain age, you no longer want for anybody to come around and shatter the earth under your feet.  

[studiot]

51 minutes ago, joigus said:

+1. I love the depth of this comment. At a distance, dynamics works well enough assuming field sources to be point-like, or smooth distributions of point-like things. These densities would have to end abruptly on the boundary. When you get closer, you must change the map, because more details are available to you --if for no other reason. Complex numbers and wave variables seem to be Nature's way of telling us that we must blur things out when we get closer.

When you try to get even closer, and gravity becomes relevant, entropy seems to be summoned up from out of the blue... The suggestion seems to be that the mapping must be re-thought, and the conceptual scaffolding reconsidered.

Thanks, but it's more than just 'at distance'  v small scale. There is also 'close up and personal'.

Clasically we don't bat an eyelid with the concept that a system passes from one state to another, but we can only know the difference between before and after, not the values of the 'state variables' during transition.
QM is also state bound or state based and has the same restrictions. Transitions beween states are defined by 'before and after' and are not instaneous. The closer we know the energy difference, the less certain we are about exactly when such a transition will happen.
When two particles collide, where exactly is that collision ?
At the point of 'first contact' ?
Partway between their centres ?
When they coalesce ?
Again there is some position uncertainty.
Matched by the small but finite distribution of the particles' masses which makes ther momntum slightly uncertain.

[joigus]

8 hours ago, studiot said:

Clasically we don't bat an eyelid with the concept that a system passes from one state to another, but we can only know the difference between before and after, not the values of the 'state variables' during transition.

What do you mean?

[studiot]

4 hours ago, joigus said:

What do you mean?

Sorry if the post was a bit rambling.

What part was not clear?

[joigus]

29 minutes ago, studiot said:

Sorry if the post was a bit rambling.

What part was not clear?

"Clasically we don't bat an eyelid with the concept that a system passes from one state to another,"

Isn't solving the law of motion what classical mechanics is all about?

 

[hoola]

the original thread seems to indicate that the concepts of math divisions and time intervals are closely linked. Why can't math be "infinitely divided" and time composed of blocks of those infinite bits, therefore time being intuitionist and the bulk infinite? When I say the bulk is infinite, I mean it is heading to infinite, and will do so forever, perpetually subdividing down, so the bulk is at once intuitionist, but trending infinite and time is independent of those underlying actions, and functions in intuitionist status.

Edited December 5, 2022 by hoola