Interpretations of QM

[Genady]

47 minutes ago, joigus said:

Maybe observation carries with it this illusion of entities.

I think even beyond the observation. I suspect that it is a way our perception organizes whatever comes from our senses.

[joigus]

2 hours ago, Genady said:

I think even beyond the observation. I suspect that it is a way our perception organizes whatever comes from our senses.

This seems to suggest that the very process of observation involves some kind of "translation"... But the original "language" is not available to us. Pardon my quotation marks.

[Genady]

4 minutes ago, joigus said:

This seems to suggest that the very process of observation involves some kind of "translation"... But the original "language" is not available to us. Pardon my quotation marks.

Yes, translation into whatever our brain has evolved to process. Which is limited to the environment it evolved in.

[joigus]

On 1/1/2023 at 7:58 PM, Mordred said:

I've always been curious as to why so many have issues with probability.

 If you have a system or state where you have more than one possible outcome it's only natural to model all possible outcomes and give the probability of those possible outcomes.

This is true in classical as well as quantum mechanics.

So why is probability in quantum mechanics an issue?

To me it's not. I also think for @TheVat it isn't either --from a previous post. But QM goes further than probability. It speaks of amplitudes, which seem to be on a sub-level with respect to probabilities.

What is this sub-level about? Why do we need a choice of global and local phase, but the gauge principle makes it completely irrelevant? Those are questions that keep me awake.

5 minutes ago, Genady said:

Yes, translation into whatever our brain has evolved to process. Which is limited to the environment it evolved in.

I'm wary of interpretations that summon the brain into the big picture. I don't think it's a matter of brains. I also abhor of interpretations based on gravity, but I find a bit more difficult to explain why. I think it's more a question of classical mechanics appearing as a fully-fledged assymptotic approximation from within quantum mechanics, rather than by analogy or correspondence, plus a series of artificial assumptions. 

[Genady]

10 minutes ago, joigus said:

I'm wary of interpretations that summon the brain into the big picture. I don't think it's a matter of brains.

Yes, this is the difference. I think that our picture of the world is human picture of the world, and that it is inescapable.

[joigus]

2 hours ago, Genady said:

Yes, this is the difference. I think that our picture of the world is human picture of the world, and that it is inescapable.

Something we should never overlook as a possibility. We might have blind spots that are impossible to overcome. Why should the rules of the universe be written in a language that primates can understand?

[geordief]

52 minutes ago, joigus said:

Why should the rules of the universe be written in a language that primates can understand?

Because "they" may be turn out to be very simple .The approach** may be very confusing but there may be the possibility  that   the fog will clear ,the solutions will be relatively  simple and we will have to go back to wondering about questions that  affect us at the macro (and all other) levels -for the rest of our times.

 

**as in the roads leading up to them.

Edited January 4, 2023 by geordief

[swansont]

59 minutes ago, joigus said:

Why should the rules of the universe be written in a language that primates can understand?

Add to this that primates can only directly sense the tiniest sliver of the spectrum corresponding to each of our senses 

[joigus]

1 hour ago, geordief said:

Because "they" may be turn out to be very simple .The approach** may be very confusing but there may be the possibility  that   the fog will clear ,the solutions will be relatively  simple and we will have to go back to wondering about questions that  affect us at the macro (and all other) levels -for the rest of our times.

 

That's what I like to dream. But one look at the standard model is enough to realise that the dream seems to vanish in one fell swoop. It's like the basic idea is extremely simple, but Nature uses it to make crossroads and turnarounds in any possible way: Arbitrary mixings, symmetry "offsets," apparently idle copies of the same thing with arbitrary displacements. It's as if a master engineer had made a thing of beauty, and a naughty kid had been playing with it.

1 hour ago, swansont said:

Add to this that primates can only directly sense the tiniest sliver of the spectrum corresponding to each of our senses 

I agree, but I would like to add a note of optimism to it. Gravitational waves are something no ordinary primate would have dreamt of "seeing." We have this capacity to build an extraordinary prosthetics to extend the reach of our senses by cleverly arranging pieces of material.

[Genady]

37 minutes ago, joigus said:

We have this capacity to build an extraordinary prosthetics to extend the reach of our senses by cleverly arranging pieces of material.

Maybe if we understand better how it happened and how it works, we'll understand better our capabilities and limitations. 

[swansont]

34 minutes ago, joigus said:

I agree, but I would like to add a note of optimism to it. Gravitational waves are something no ordinary primate would have dreamt of "seeing." We have this capacity to build an extraordinary prosthetics to extend the reach of our senses by cleverly arranging pieces of material.

Our ability to sample data outside of our senses in a significant way, is less than 150 years old. (A little more for visual perception). We really haven’t been at this very long.

[Mordred]

On 1/3/2023 at 6:45 AM, joigus said:

This is not exactly what I meant, although it does partially overlap with what I meant. The adjective "topological" I didn't mean as applied to the background manifold, but to certain classes of solutions of differential equations on those manifolds. Thus, you can have many field theories defined on a topological manifold. Among all these theories, only a very restricted class of theories are topological, and most other theories are not. Topological theories have a Lagrangian not involving the metric. One interesting feature of these theories is that they are useful tools to study topological invariants of the manifold, like Wilson loops, probably Betti numbers too, and the like. They are invariant under diffeomorphisms, and once you incorporate the constraints --se below-- with the method of Lagrange multipliers, the constrained Hamiltonian becomes identically zero on the constraint surface. I say all this just to guarantee that we're talking about the same thing.

But from the strictly dynamical point of view, topological fields are very constrained in the way the can evolve. In fact, they are maximally constrained. They --the fields-- have no local degrees of freedom, which means they do not propagate. The number of constraints exactly equals the number of degrees of freedom.

Let me be as clear as humanly possible. As a warm-up, taking a 1st-order in time point-particle theory as a particularly simple example, what I mean by having #(DoF) = #(constraints) is the following:

 

q1(t),⋯,qn(t)

 

So a set of initial conditions q1(0),⋯,qn(0)=q10,⋯,qn0 completely determines the trajectory in the configuration space.

Equivalently, if we're extremely lucky --the system is integrable--, we may manage to find a set of n integrals of motion:

 

J1(q1(t),⋯qn(t))=0

 

 

⋮

 

 

Jn(q1(t),⋯qn(t))=0

 

This is (modulo condition of non-vanishing Jacobian) equivalent to fixing the previous n initial conditions. Integrals of motion for integrable systems depend on 1to1 on initial conditions.

Now, what are constraints? Constraints are both mathematically and physically very similar, but with a very important nuance. Assume n constraints:

 

F1(q1(t),⋯qn(t))=0

 

 

⋮

 

 

Fn(q1(t),⋯qn(t))=0

 

But these relations being in place for every set of initial conditions. What does this imply mathematically? It implies nothing other than that the system cannot move at all. Cannot evolve in any meaningful way at all. It's frozen dynamically. How much? It's just a point in configuration space.

Now, what happens to a field theory under analogous strictures? We must now promote the qi(t) to some φa(x,t) , where a goes from 1 to n. If we impose n initial conditions, that means specifying the value of the φ 's,

 

φ1(x,τ)|Σd−1=f1(x),⋯,φn(x,τ)|Σd−1=fn(x)

 

where τ is some curvilinear coordinate that specifies the sub-manifold Σd−1 the space-like foliations that define the Cauchy problem.

If, instead, we have a set of n constraints, and as any constraints worth their salt, they do not depend on initial conditions, but are the same for all posible initial conditions, we will have the system extremely limited in its evolution. But it is no longer true that the set of states compatible with this situation "shrinks" to a point in configuration space. It does freeze, but due to the presence of the space variables x it does so --it must-- to a fixed function sitting on the topological space. Or perhaps to a finite or countable set of such "frozen" functions. It is in that sense that I was talking about a quasi-rigidity. Known examples of constraints in field theory (valid for all sets of initial conditions) are transversalities and Gauss or Lorentz gauge-fixing constraints. Photons are known to "inhabit" a space of configurations with 4 degrees of freedom when you give them mass by assumption. If you impose masslessness, gauge fixing, they become more and more restricted in their evolution. If you imposed further constraints, there would be no dynamical situation that implies propagation. They would be "frozen." But not to a point. Instead they would be frozen to a pretty restrictive class of what I've tried to refer to by this term "quasi-rigidity."

The previous discussion generalises trivially to a 2nd-order-in-time system by substituting 1,...,n with 1,...,n,...2n, and the φ 's to those plus their canonical momenta.

Now, I know these musings not to be totally out of whack, because I've posed the question (the one about quasi-rigidity) elsewhere appropriate and I know for a fact that knowledgeable people consider it a totally-non-silly conjecture at least. Or, if you want, a question worth answering. But what would come next --the relation to the interpretation of QM-- does have speculative elements on my part, and would probably require a thread of its own.

Just so your aware I'm still looking into this as I get the time, part of the problem is the separating topological rigidity problem that is apparently more common than I initially realized lol. 

 

12 hours ago, joigus said:

 

What is this sub-level about? Why do we need a choice of global and local phase, but the gauge principle makes it completely irrelevant? Those are questions that keep me awake.

 

The local conditions often fit the  criteria to establish invariance. Or in the case common in particle physics the c.m. (center of mass frame) or lab frame. Gauge theory by criteria must be Lorentz invariant, however not all groups are Lorentz invariant particularly with the first order QM operators. The Schrodinger equation for example isn't Lorentz invariant which is one of the reasons QFT uses the second order Klein Gordon equation. Granted another reason directly applies to the conservation laws which are symmetric relations in closed systems.  You have via the continuum equation 

\[\frac{\partial\rho}{\partial t}+\nabla\cdot j=0\] for a conserved quantity. QM,QFT,QED, Navier Stokes and fluid dynamics have variations of this equation but in each instance can be shown the equivalent via the related mathematical proofs. Noether's theorem shows the symmetry relations to a conserved quantity being symmetric.

from wiki

"In physics, a gauge theory is a type of field theory in which the Lagrangian (and hence the dynamics of the system itself) does not change (is invariant) under local transformations according to certain smooth families of operations (Lie groups)."

does that help address the reason for local vs global. 

https://en.wikipedia.org/wiki/Gauge_theory

edit: @joigus Have you considered the above in terms if the rigidity like properties in regards to the topological spaces you have studied ? just food for thought but there is a good likelihood it will relate.

Edited January 5, 2023 by Mordred

[Markus Hanke]

22 hours ago, Lorentz Jr said:

Right, but that's not what I meant by "geometry". I was referring to gravity as curvature of space, which I don't think is present in GTG.

Ah I see, sorry, I misunderstood you then. You are right of course, in GTG gravity isn’t formulated by means of spacetime curvature.

22 hours ago, Lorentz Jr said:

"Deep models" is all I mean by "ontology".

Ok, that’s fair enough. And you are right - some models do go deeper than others, in that sense. So the question then becomes whether there is a “rock bottom”, ie a set of irreducible elements that make up reality on the most fundamental level; and what those elements are.

In contemporary physics the most fundamental “ontology” in this sense is spacetime, and the quantum fields that live on them. Personally I think neither of these are irreducible, and will turn out to be approximations to something more fundamental.

22 hours ago, Lorentz Jr said:

But it could be very useful to have a deeper model.

Yes, absolutely! It’s not just useful, but essential. This is why there is so much active research going on in the area of quantum gravity.

22 hours ago, Lorentz Jr said:

If there were an equivalent theory without Minkowski space, I would be interested in that.

There have been attempts to model (classical) gravity entirely without recourse to any notion of “spacetime”, flat or otherwise. One such example is Geroch’s “Einstein Algebras”:

https://projecteuclid.org/journals/communications-in-mathematical-physics/volume-26/issue-4/Einstein-algebras/cmp/1103858122.pdf

Then of course there are various candidate models for quantum gravity that do not take classical spacetime as primary and fundamental, such as Loop Quantum Gravity, or Causal Dynamical Triangulations, among others.

22 hours ago, Lorentz Jr said:

What I mean is that the principle of relativity bothers me more than modeling gravity as the curvature of (any) space.

I’m struggling to wrap my head around this - the principle of relativity in its most general form ultimately just boils down to the observation that all observers experience the same laws of physics. My laptop works in my living room in exactly the same way as it does on a spaceship travelling close to c, or someplace very near the event horizon of a BH, because all laws of electrodynamics, quantum physics etc are exactly the same in all frames. This is as much an empirical observation as it is a matter of logical consistency - to me it is completely natural to such a degree as to be almost trivial in its simplicity.

Why does this principle bother you? Again, I am genuinely curious to understand where you are coming from with this (we both already know the experimental evidence, so that’s not the point here).

22 hours ago, Lorentz Jr said:

Yep. And I'm interested in that.

And so am I  

15 hours ago, Genady said:

I think that our picture of the world is human picture of the world, and that it is inescapable.

Yes! I think this is a crucially important point, though I am unsure of the “inescapable” bit. It is inescapable in the sense that our direct experience - and thus the reality-model our brains construct - can never be anything else but human. However, it is possible to overcome these constraints by building mathematical models of the world that are not subject to the tacit assumptions our brains impose on us. For example, there are candidate models for quantum gravity that do not assume “space” and “time” to be primary and fundamental constituents of reality; just by being able to build and comprehend such models, we go beyond the constraints of human-centred reality.

[Lorentz Jr]

1 hour ago, Markus Hanke said:

So the question then becomes whether there is a “rock bottom”, ie a set of irreducible elements that make up reality on the most fundamental level

In other words, how deep is the Tower of Turtles? 😄

1 hour ago, Markus Hanke said:

In contemporary physics the most fundamental “ontology” in this sense is spacetime, and the quantum fields that live on them. Personally I think neither of these are irreducible

Certainly not fields. The most obvious explanation is that they're properties of the vacuum. I could have sworn I saw a youtube video where John Spence called them "liquids", but I can't find the quote. Maybe it was someone else. Maybe Sean Carroll, in a different video. 🤔

1 hour ago, Markus Hanke said:

the principle of relativity in its most general form ultimately just boils down to the observation that all observers experience the same laws of physics.

There are only two distance-preserving forms of velocity addition: Newtonian (3-translation) and Einsteinian (4-rotation). What's the reasoning behind that? I learned the rule a long time ago, but I've forgotten where it comes from, and I haven't been able to find any references to it. 😣

Anyway, my point is that relativity hasn't been absolutely proven. Lorentzian theory with Newtonian geometry (absolute space) is still scientifically viable.

1 hour ago, Markus Hanke said:

My laptop works in my living room in exactly the same way as it does on a spaceship travelling close to c, or someplace very near the event horizon of a BH, because all laws of electrodynamics, quantum physics etc are exactly the same in all frames. This is as much an empirical observation as it is a matter of logical consistency - to me it is completely natural to such a degree as to be almost trivial in its simplicity.

The apparent laws of acoustics depend on the observer's motion relative to the surrounding air, and there's nothing unnatural about that. And researchers at the Pierre Auger Observatory are looking for violations of Lorentz invariance in ultra-high-energy cosmic protons. (They haven't found anything yet, but there's no proof that they can't.) Have you ever tried running your computer at those speeds? Maybe there would be problems.

1 hour ago, Markus Hanke said:

Why does this principle bother you? Again, I am genuinely curious to understand where you are coming from with this (we both already know the experimental evidence, so that’s not the point here).

I don't buy the geometric argument for time dilation in the twin paradox ("The astronaut is younger because he took a shorter path through spacetime"). It seems like meaningless wordplay. Minkowski space is a very nice mathematical abstraction, very useful and convenient, but I don't see how it qualifies as "geometry" in the same physically intuitive way that 3D space (or any space with all positive terms in the metric tensor) does. As I said about GR, curvature is okay, because I can extrapolate from the shape of a balloon. But to my mind, adding negative terms to the metric invalidates the space as an intuitive explanation for physical phenomena, including time dilation (which is "real", i.e. frame-invariant, in the twin paradox).

Edited January 5, 2023 by Lorentz Jr

[Genady]

3 hours ago, Markus Hanke said:

the reality-model our brains construct - can never be anything else but human. However, it is possible to overcome these constraints by building mathematical models of the world that are not subject to the tacit assumptions our brains impose on us.

Yes, I think it is our only hope. The pictures which @Lorentz Jr refers to as ontological (deep, intuitive) are and will be human based, shaped by human experience. The rest of the picture can be painted mathematically. Moreover, the flexibility and adaptability of human mind will allow to bend our human intuition to accommodate the mathematical extensions to some degree.  

[Markus Hanke]

2 hours ago, Lorentz Jr said:

In other words, how deep is the Tower of Turtles? 😄

No one knows the answer to this. There is also the far less intuitive possibility of the “tower” being quite finite, while at the same time lacking any irreducible ontology. Rovelli’s relational interpretation of QM would be an example of this.

2 hours ago, Lorentz Jr said:

Certainly not fields.

I don’t think so either - though of course we can’t be sure. 

2 hours ago, Lorentz Jr said:

There are only two distance-preserving forms of velocity addition: Newtonian (3-translation) and Einsteinian (4-rotation). What's the reasoning behind that? I learned the rule a long time ago, but I've forgotten where it comes from, and I haven't been able to find any references to it. 😣

I don’t think the principle of relativity can be derived from any fundamental axioms - it’s an empirical observation about how the world works. We simply don’t see any variations in the laws of physics between observers, at least not within the constraints of our experimental abilities.

2 hours ago, Lorentz Jr said:

Anyway, my point is that relativity hasn't been absolutely proven.

You can never “absolutely” prove any model of physics. We can, however, but upper bounds on the magnitude of any possible Lorentz-violating effects, and these bounds are very stringent indeed.

2 hours ago, Lorentz Jr said:

The apparent laws of acoustics depend on the observer's motion relative to the surrounding air

The laws of acoustics are just a special application of the laws of fluid dynamics - and those can be written in fully covariant form using the energy-momentum tensor, so they don’t depend on the observer. Based on that you could, if you wanted to, write a model of relativistic acoustics that is observer-independent.

2 hours ago, Lorentz Jr said:

And researchers at the Pierre Auger Observatory are looking for violations of Lorentz invariance in ultra-high-energy cosmic protons.

Yes, there are very many tests of Lorentz violations, both historical and modern, and none of them has ever found any hint of such a thing in fact existing. Like I said, this places very stringent upper bounds on such violations.

2 hours ago, Lorentz Jr said:

Have you ever tried running your computer at those speeds?

Yes  In the rest frame of those very same ultra-high-energy cosmic protons you just mentioned, my computer does in fact operate at those very speeds.

2 hours ago, Lorentz Jr said:

I don't buy the geometric argument for time dilation in the twin paradox ("The astronaut is younger because he took a shorter path through spacetime"). It seems like meaningless wordplay.

What do you mean you “don’t buy it”? Do you doubt that the mathematics provide the correct answer when you run the numbers? It’s rather easy to show that they do in fact work out, in a fully self-consistent way.

Once again, Minkowski spacetime here is a descriptive model, the purpose of which is to provide a framework to make predictions for real-world scenarios. And it evidently does this really well. Of course, it has no explanatory power as to why this model - as opposed to some other description - works so well. Here’s where we come back to the question as to how fundamental (or not) spacetime is, and what, if anything, underlies it. These questions don’t as yet have an answer.

2 hours ago, Lorentz Jr said:

but I don't see how it qualifies as "geometry" in the same physically intuitive way that 3D space (or any space with all positive terms in the metric tensor) does.

You appear to be using a different definition for the term “geometry” than mathematics do.

Intuitiveness is not a required feature for any aspect of mathematics or physics, or any other science for that matter. It just needs to work, and be internally self-consistent. Euclidean geometry seems nice and intuitive to you only because as being human you happen to experience a domain of the universe that is roughly Euclidean in nature; this does not afford it any physically privileged status, however. Non-Euclidean geometries are equally well formulated and understood, and are equally self-consistent. Besides, intuitiveness is highly subjective - to me, for example, Minkowski space seems perfectly natural, and very well suited for the task at hand.

 

[Genady]

15 hours ago, joigus said:

It's like the basic idea is extremely simple, but Nature uses it to make crossroads and turnarounds in any possible way

Why do you expect it to be different? Everything else in Nature is like this, too. Look at biological evolution, for example. The principle is nice and simple, descend with modification and selection, but the result is messed and convoluted.

[joigus]

2 minutes ago, Genady said:

Why do you expect it to be different? Everything else in Nature is like this, too. Look at biological evolution, for example. The principle is nice and simple, descend with modification and selection, but the result is messed and convoluted.

I do not expect it to be different.

[Genady]

Just now, joigus said:

I do not expect it to be different.

Oh, sorry, I've misunderstood your reply then. We are on the same page 

[joigus]

4 minutes ago, Genady said:

Oh, sorry, I've misunderstood your reply then. We are on the same page 

Yes, I think we are, to the extent that I can follow all the arguments. It's a recurring theme in Nature, I think. Simple principles, very complicated consequences.

[Lorentz Jr]

3 hours ago, Markus Hanke said:

What do you mean you “don’t buy it”? ... Minkowski spacetime ... has no explanatory power as to why this model - as opposed to some other description - works so well.

But it's often presented as a "why" explanation. Sean Carroll and Lee Smolin have both said relativity can be "explained" by a "change of intuition", and I've encountered similar comments on internet forums. I always have to argue with people for at least a page of comments before they admit what you just said.

And the Lorentzian picture is consistent with a relatively simple "why" explanation. If the vacuum (a) has its own reference frame, (b) implements both center-of mass motion and internal time evolution of matter, and (c) has a fixed capacity to do so, then time dilation is a simple matter of "time sharing": the "processing power" required to implement CoM motion leaves less power remaining for internal motion, so that motion proceeds more slowly.

3 hours ago, Markus Hanke said:

You appear to be using a different definition for the term “geometry” than mathematics do.

Because I'm trying answer the "why" question, and mathematics doesn't do that. At least classical geometry feels like an answer.

Anyway, I'm tired of arguing about this subject. One of the key tricks that people use in "explaining" perpetual-motion machines is changing reference frames. Once all of the machine's behavior is analyzed in the same reference frame, it becomes clear that there's no perpetual motion. Relativity does the same thing. The only way you can "explain" anything in relativity is by changing reference frames. That's all I have to say, and I'll understand if you don't agree.

Edited January 5, 2023 by Lorentz Jr

[Genady]

32 minutes ago, Lorentz Jr said:

 the vacuum ... own reference frame

Is it a cosmological comoving frame, the one where CMB is isotropic?

[Lorentz Jr]

43 minutes ago, Genady said:

Is it a cosmological comoving frame, the one where CMB is isotropic?

Who knows? In principle, it's the frame of the vacuum, not matter, so for all we know, all the matter in the visible universe could be moving relative to it. I wouldn't want to guess about that.

Edited January 5, 2023 by Lorentz Jr

[Mordred]

2 hours ago, Genady said:

Is it a cosmological comoving frame, the one where CMB is isotropic?

The reference frame is the commoving frame however the FLRW metric uses this to apply commoving time. The commoving frame is set at mean average mass density of the the metric.

[joigus]

19 hours ago, Mordred said:

Just so your aware I'm still looking into this as I get the time, part of the problem is the separating topological rigidity problem that is apparently more common than I initially realized lol. 

 

Absolutely no rush. This thing about topological Lagrangians giving rise to systems (quantum or not) entailing some kind of rigidity has kept me wondering for years. For trajectories of point particles, it's clear that you get the system frozen to a point. But for field theories it's not so clear. If you allow for non-commutativity (quantum) the question is even more involved. To me, it both is interesting and makes sense. But for some reason people who study topological field theories haven't put it on the front burner, for years and years.

You only see it mentioned as some kind of quirk.

19 hours ago, Mordred said:

edit: @joigus Have you considered the above in terms if the rigidity like properties in regards to the topological spaces you have studied ? just food for thought but there is a good likelihood it will relate.

Yeah, OK. I must confess I have to think about this harder, and read more stuff with as much attention as possible. Some of these conditions coming from constraints do look a lot like continuity equations. It's peculiar to me that conditions like the Lorentz gauge-fixing condition are formally identical to local conservation laws for a Noether charge, although they're just constraints. And in the case of gauge fixing, they seem quite arbitrary. In the case of these topological theories, they seem to appear more "naturally." At least the way I saw Lee Smolin handle them in those lectures.

That's all I can say for now in the way of a reflection. It's just peculiar to me.