B Quantum state of the Universe?

[laymanB]

I am trying to read through this paper discussing what quantum fluctuations mean in their various contexts, particularly in de Sitter space. I have come across this passage and am curious to what it actually means?

https://arxiv.org/pdf/1405.0298.pdf

pg. 10, second paragraph:
"If a quantum state describes the whole universe (as it does in cosmology)..."

What does it mean to describe the whole universe as a quantum state?

 

[jerromyjon]

What does it mean to describe the whole universe as a quantum state?

I'm not sure if it is unique to the many-worlds interpretation (I believe it is) but it means that there is a single "universal" wavefunction which instead of ever collapsing, just branches into different universes, only one of which we ever observe.

 

[hilbert2]

If some theory is supposed to apply to everything, then it can be used to describe a system of any scale, from a single proton to the universe.

It's not possible with the current theory to handle quantum gravity, and it isn't possible to do accurate QM calculations for anything near a macroscopic-scale system (except in the model of quantum ideal gas or similar non-interacting system), but there's no reason to suspect that for instance the superposition principle would not hold for every system, meaning that if $\left|\psi_1\right.\left.\right>$ and $\left|\psi_2\right.\left.\right>$ are normalized and physically possible quantum states then $\frac{1}{\sqrt{2}}(\left|\psi_1\right.\left.\right> + \left|\psi_2\right.\left.\right>)$ is too and so on. Therefore, you can play with the algebra of state vectors and operators even if they describe the whole universe.

 

[A. Neumaier]

it isn't possible to do accurate QM calculations for anything near a macroscopic-scale system

One can do quite sophisticated statistical mechanics calculations of macroscopic systems of real interest.

Therefore, you can play with the algebra of state vectors and operators even if they describe the whole universe.

The only problem is that this requires an observer that is part of the system. This is impossible in various interpretations (e.g. the Copenhagen interpretation).
Moreover, we can observe only one universe (even in a many-world setting), so the probabilities in this single realization of the universe needs to be justified. My thermal interpretation is supposed to do that.

 

[laymanB]

I'm not sure if it is unique to the many-worlds interpretation (I believe it is)

It turns out that the paper is written in the context of a many worlds interpretation of QM.

https://arxiv.org/pdf/1405.0298.pdf

pg. 29
"Throughout this paper we have worked in the context of the Everett/Many-Worlds formulation of quantum mechanics, in which a single wave function evolves unitarily in Hilbert space according to the Schr¨odinger equation. Our conclusions could be dramatically altered in other formulations."

"It seems we are dealing with one of the rare cases in which one’s favorite formulation of quantum mechanics can drastically affect one’s expectation for how observable quantities evolve."

 

[bhobba]

It turns out that the paper is written in the context of a many worlds interpretation of QM.

Only in some interpretations is it possible to speak of the wave-function of the entire universe and not have issues arise. Many Worlds is one of those - the Ensemble is one you really can't because a state and preparation procedure in such interpretations are synonymous. What prepared the universe? I suppose we have some theories about that - but to apply Ensemble you would really be discussing some scenario where the origin of the universe is a preparation procedure is some sense. Rather than get into that its best to use an interpretation where you don't have to worry about it - many worlds is the most common.

Thanks
Bill

 

[Fra]

Rather than get into that its best to use an interpretation where you don't have to worry about it

This is very common attitude, that i could never stretch myself to adopt.

I like to think that the "best" is rahter to hang onto the important problems any worry until they are solved, who is else is going to worry about these things?

I have a feeling that the reason for so modest progress on some foundational conceptual quesions - such as how make conceptual sense of of a measurement theory for cosmology, where the observer is physical part of the universe - is because a lot of professional physicists adopt this attitude to not worry. However to "worry" would mean to look for the right mathematical framework that implements the concepts in the "right way", that makes these questions go away.

Given the publish or persih pressure, its is forgivable, but its nontheless hard to defend from an intellectual perspective.

/Fredrik

 

[bhobba]

is because a lot of professional physicists adopt this attitude to not worry. However to "worry" would mean to look for the right mathematical framework that implements the concepts in the "right way", that makes these questions go away.

We know the right mathematical framework and we even know why it works and is necessary.

I have posted it so many times I will not post the detail again, but all QM, at the formal level, is, is generalized probability theory that allows continuous transformations between pure states.

I will even spell out what a generalized probability theory is. Its simply a system that can be in some kind of state without saying anything really what a state is. We impose a very simple condition on states. Any state can be expressed as the sum of states of the form ∑pi*ai where pi are positive numbers Σpi = 1 and is usually interpreted as the the probability of it, when you measure, observe it etc, its in state ai. Pure states are those states such that sums contain just one element - itself. ie can't be written as an actual sum of other states. It's a rather general sort of model covering all sorts of situations which is why its called generalized probability theory. Its like generalizing the axioms of euclidean geometry and you get something even more general like Riemannian geometry that covers all sorts of situations not covered by Euclidean geometry.

Which one is best - now that is where history comes in. Way back in the dim dark ages of the 18th century science and philosophy wasn't as compartmentalized as now. We have two giants of their discipline - Gauss in Math and Kant in Philosophy. Now Kant said Euclidean geometry was a-priori correct and had this dialectic supposedly proving it. But Gauss knew otherwise. He had proven that other geometries were equally logically correct - he showed they were all just as correct as Euclidean geometry so which one we lived in was an experimental matter. He even conducted experiments to see what was what - but the results were inconclusive. The disgusting thing is, despite Gauss's greatness he was scared of Kant so didn't publish. However what did history teach us - Gauss was right and Kant wrong. Since then philosophy has taken less and less of a place in science. And guess what - science progressed and philosophy still never actually decided on anything. This is why scientists generally don't worry about philosophy and why it's off topic here - its not science and by doing that science has advanced.

So if you model a physical system as a pure state, you aren't assuming much. Now, physically you would like to be able to continuously go from one pure state to another through other pure states. This simply means if say a system is in a state at t=0 and another state at t=1 it must be in some state at t=1/2. QM is the simplest model that allows that. Formally that's all it is. There is really nothing mysterious, weird, funny etc etc about the formalism of QM. Just like Riemannian geometry is the correct framework for GR (technically its a pseudo Riemannian geometry - but no need to go into that here) generalized probability theories are the correct framework for QM. And just as considerations like no-prior geometry and a few other things that look pretty obvious lead to GR, this idea of continuity leads to QM.

Now what it means - that is another matter. But its the exact same situation as probability theory. Formally we know exactly what ordinary probability is - it is not QM because of the issue with its pure states - there is no continuous transformations between such and that is something you want in modelling physical systems. But what does ordinary probability theory mean? It's exactly the same as QM - there are different views each with advantages and disadvantages in solving problems. Sure philosophers argue about it - that's what philosophers do - but those that actually use it don't worry - they just accept that's the way it is and go ahead, solve problems and make progress. The philosophers haven't made any progress - but those that don't worry about it have.

That all that going on in QM - yet we have some that post here that think its a big issue that needs resolution. To be blunt it isn't. Understanding different interpretations and when to apply which one is of value - most of the time it doesn't mater but occasionally in QM, like considering the wave-function of the entire universe it does. Just like with probability in practice its nothing to worry about - but for reasons I don't quite understand some really think its of critical importance in QM.

Thanks
Bill

 

[Fra]

Whoa, there was a lot of things in there i am not sure what to address, i pick the most important thing as you seem to deny the existence of a problem to be solved which i find remarkable:

1) The core of the discussion here, is the physical justification of the probability spaces and the probability measures. This point was also raised by Neumaier in post #4..

Please note that this is as much of a physical question as it gets! and not something else!

The physics part of all this is to map the elements in a mathematical theory to reality, in the sense that we must be able to explain the physical process that are producing numbers that we compare with those computed from theory. Then and only then with both these things we have a physical theory(or hypothesis).

This means that anything that fails to map its "observable parts" to reality by means of such a physical process(measurement), or any theory that fails to actually be able to produce computable numbers in a consistent way are not fulfilling the most basic requirement on a physical theory.

And the probability numbers here, are precisely one such thing.

I could write more but i will stop there.

/Fredrik

 

[bhobba]

The physics part of all this is to map the elements in a mathematical theory to reality, in the sense that we must be able to explain the physical process that are producing numbers that we compare with those computed from theory. Then and only then with both these things we have a physical theory(or hypothesis).

You missed the point of my post.

I tried to explain it as carefully as I can. But I see I failed.

I will rephrase it.

Just about everything you wrote above is loaded with philosophical hot potatoes so to speak eg what is reality, what is explain, what is a physical process etc etc. These alone has led to pages and pages of discussion that goes nowhere. I mentioned probability theory - the axioms talk about events. What are events - what elements of reality are they? What does this thing called probability mean? These are not easy to answer. Indeed take good old Euclidean geometry, it speaks of points as having position but no size - lines length but no width. They don't exist - yet we are able to use it. How is that? Are they elements of reality - they don't exist so how can they be elements of reality? Deep questions - deep indeed. But to use it - there is no issue. Everyone who learns it can and solve problems with it.

What some on this forum think is we need to answer these deep questions - it vital to make progress. However history says otherwise - progress is not made that way - except maybe occasionally like with Bell. The tale of Gauss and Kant is cautionary. By deliberately not worrying about the kind of issues you raise (ie what is reality etc that was central to Kant) we get to the bottom of what's really going on. He thought he knew the answer - but was wrong - Gauss took a different route (looking at the logical structure of geometry itself as I explained the logical structure of QM) and found the answer's

So worry about them if you want - but history simply does not support your claim - 'However to "worry" would mean to look for the right mathematical framework that implements the concepts in the "right way", that makes these questions go away.' We already know the right mathematical framework - its not an issue - just like we know the right mathematical framework of probability. What history tends to show is we do not know what is needed to make progress - in fact those like Kant that went down such a path and create a dialectic to supposedly do just that and answer these kind of questions end up with egg on their faces. As Feynman said a trick that worked before to make progress is not likely to work again because everyone knows it and will try it so progress is made and we are not stuck. The philosophical trick that was used at the turn of the 20th century to birth QM and Relativity is logical positivism that provides a certain answer to those very deep questions. But it soon stopped working. Einstein was asked about it - you once used logical positivism yet you don't seen to rely on it anymore - he said you can't do the same joke twice. Other tricks were needed - they were found and progress happened. The new trick is symmetry - its very beautiful and powerful. So far it has worked - but perhaps has now stalled.

We do not know what's needed now - maybe what you say - but the same tricks do not seem to work twice.

Thanks
Bill

 

[Fra]

You missed the point of my post.

Interestingly - but most probably not coincidentally - that impression is mutual.

You wrote alot, and i responded first only to what i considered to be the relevant part in context of this thread in order to not get a divergent discussion. Your tales from 200 years ago and logical positivism might be interesting on their own but of little relevance to my point, and also not overly relevant from the point fo view of physics. So i passed commenting on all in this thread. I think the situation is very different today. To discuss why is a separate discussion elsewhere so let's leave that here and focus on the open problems in the foundations physics.

So before i explain my argument again, let me try to express my impression of your point first:

It seems your point is that we have more or less an axiomatic formulation of physics (lets agree to call it the generalized probability theory of QM/QFT), where the connection to physical processes have been "good enough" to unquestionable has served us well for the last 100 years or so, given the success of the standardmodel or particle physics. And even in the light of the open questions in physics, such as how to unify forces in a coherent description you do not see any reason that we need to revise this mathematical framwork that is "proven" to work so well for the very special domain of high energy physics? The power of symmetry and mathematical constraints on physical theories is unquestionable?

Thus, any claims we need to do so are labeled as unconstructive philosophical hot potaties that is not science?

Is that a reasonable summary of your point?

(I know its hard to discuss some things briefly, i make that mistake as well, so i will try to not type too much at once)

/Fredrik

 

[bhobba]

Is that a reasonable summary of your point?

Its simpler than that.

You used terms that are very ill-defined like elements of reality, physical explanation etc in your view of what needs to be done. In order to do what you suggest you need to first pin those down. That has proven very difficult to the point of impossibility.

However what has in the past proven fruitful is understanding and elaborating the mathematical structure of a theory.

Thanks
Bill

 

[Fra]

You used terms that are very ill-defined like elements of reality, physical explanation etc in your view of what needs to be done. In order to do what you suggest you need to first pin those down. That has proven very difficult to the point of impossibility.

Two points:

You seem to be mixing up difficulty and relevance of a problem. You are correct that this is diffcult, this is not what we are discussing. You were rather claiming that the problem was not important, and not even existing. What i said is that i think the reason why not more progress has been made on this problem is not only because its difficult, but because a lot of people adpapt your attitude, and denies the problems because they are difficult. All your responses just confirm this.

Second major point is also, that you are trying to defend your reasoning by pretending the objections are just philosophy. IMO this is just wrong. Physics as a natural science is about understanding nature/reality (not here that i am using ordinary language, don't read in any ontological meanings of ancient philosophy in my words), and for this we create mathematical theories because in physics understanding nature means we need to be able to make quantiative predictions. This is where things like mathemtics, computations and algorithms come in. Just like mathematics is the language of any quantiative science, like economy etc. Now in order to distinguish physics from just the idealized world of mathematical physics where you indeed to not deal with these questions, you have to be able to cope with the fuzzy problem of mapping the mathematical or algorithmic elements of theory to processes and experiments in nature that we can use to make experimental contact with the theory.

I think you are just talking about a branch of applied mathematics that is mathematical physics, if so, it is pretty clear that all i am saying here is irrelevent, but i am presuming we are talking about trying to understand nature, not just investigate some of the theories that has been propose in the past.

With all due respect but to think that you already know what the mathematical framework is for unifying interactions - and specifically to be able to unify particle physics with cosmological theories in a coherent way to me appears very naive. Let's hold this claim until we have solved the problems.

Are you aware of for example what Lee Smolin calls the cosmological fallacy? Those reasonings specifally addresses the "unreasonable effectiveness of mathematics" (originatlly coined by Wigner) and explains that the reason for its effectiveness is because its limited - to subsystems of nature. And if you have given this any thought you probably realized that this is exactly the situation we have in HEP. And its is no conincidence why strategies so far has been successful to infer timeless matehmatical law for subsystems. But one should understand why it might well be a deep fallacy to think that this is the right framwork for a cosmological theory.

However what has in the past proven fruitful is understanding and elaborating the mathematical structure of a theory.

Again, if you have been thinking about this, one can correlate the reasonable effectiveness of mathematics to the fact that HEP is about subsystems, that into the category where we can prepare and repeat experiments, and it is expected that the idea of timeless mathematical laws operating in a timless state space will work fine.

Any ad hoc attempts like multiple universes as some basis for "statistics" is merely an excuse for trying to save an in appropriate framework when applied it to cosmology. This is not an explanation in terms of a physically realizable experiment. Its just a metaphysical construct - an poor excuse.

The phrase "quantum state of the universe" IMO, breathes conceptual confusion. While you can mathematically make sense of it, is not solving the problem from the point of view of physics.

/Fredrik

 

[bhobba]

You seem to be mixing up difficulty and relevance of a problem. You are correct that this is diffcult, this is not what we are discussing.

What I am suggesting is such questions are so difficult that perhaps they can't be resolved - you will continually get no-where or think you have solved it when you haven't. However by accepting that and looking at the actual mathematical structure of our theories then progress can be made. Its not the type of progress those that think these questions are vital, but it is progress none the less. Can I prove this - of course not - you may be right - solving these kinds of issues is vital - but history seems to suggest otherwise - that's the cautionary tale of Gauss and Kant.

Because of that I won't actually be drawn into discussing these issue ie many worlds is a better interpretation than say ensemble - I find such discussions useless.

i will, and am always happy to, explain interpretations I am familiar with, but engaging in discussions about which one, or maybe none, resolve things like requiring a physical explanation I will not be drawn into. Two reasons why. First - exactly - what is physical explanation, reality, elements of reality etc etc - exactly what does it mean. I believe it really can't be done. The closest I can come to say - what is reality - is its what our theories model - its a very unsatisfactory definition to some but I simply can't do any better. And even if you agree on what it means applying it to our theories is a whole minefield in itself. Thats why to me its useless. Others here say it leaves them cold - they know you will get nowhere.

Thanks
Bill

 

[bhobba]

Are you aware of for example what Lee Smolin calls the cosmological fallacy? Those reasonings specifally addresses the "unreasonable effectiveness of mathematics" (originatlly coined by Wigner) and explains that the reason for its effectiveness is because its limited - to subsystems of nature. And if you have given this any thought you probably realized that this is exactly the situation we have in HEP. And its is no conincidence why strategies so far has been successful to infer timeless matehmatical law for subsystems. But one should understand why it might well be a deep fallacy to think that this is the right framwork for a cosmological theory.

My view on that ie mathematical beauty in physics - see:


Thanks
Bill

 

[Fra]

I think we can conclude we have different routes to insight into this... Gell-Mann's talk was fun as a historical perspective, but it relates to particle physics, not cosmology or quantum theories of cosmology.

What I am suggesting is such questions are so difficult that perhaps they can't be resolved - you will continually get no-where or think you have solved it when you haven't. However by accepting that and looking at the actual mathematical structure of our theories then progress can be made.

I just want to say that what distinguishes physics from pure mathematics is that one has to strike a balance between the deductive power of mathematics and justification of the particular CHOICE of theory the defines the deductions. For me, that justificaiton is evolution. And nothing i said suggest we don't need to look at hte mathematical structure. That is in fact my point. And the specific mathematical framework that is "problematic" in the cosmological setting is what smolin called the Newtonian schema. It is the abstraction of a timless statespace, and timeless matehmatical constraints and defines histories of time in a timeless manner. This is not a problem at all for particle physics! This is important to stress (*)

But it looks like a big problem for 1) cosmology and generally 2) meaasurement theory for "inside observer", which relates to the concept of unification(*). So its exactly looking at the mathematical framworks that makes me think they need to revised to solve 1 and 2. This gets complicated because the deductive power is depending on things, that likely need to be deformed, and this means that the mathematical deductive systems is also deformed. Now all this needs to be "clarified mathematically". So it is indeed a mathematical challange, but unless you understand the motivation, you don't know where to start.

/Fredrik