Classical and Quantum determinism

[hyksos]

Pierre Simon Laplace is attributed with framing mechanical determinism in 1814. Given all the position velocities, and energies of all particles in the universe, all of the future events could be determined.

However, our modern understanding of linear and non-linear systems do not permit this under many situations. Any theory which is non-linear will admit multiple solutions. Which solution actually happens in the future cannot be calculated from the equations of that theory. Two examples are the non-linearity in the Navier-Stokes equations. (whether Navier-Stokes has unique solutions is an unresolved problem in mathematics). Electromagnetism is non-linear. More shocking : Newton's mechanics are non-linear , and so situations can be constructed where many possible outcomes could happen, all consistent with the equations.

One proponent of this problem is an american professor, John D Norton who chairs the Philosophy of Science department at Pittsburgh. More detail can be found here : http://philsci-archive.pitt.edu/2943/1/Norton.pdf

In summary, not even classical physics is deterministic.

Things are about to get doubly ironic.

Word on the street is that Quantum Mechanics is a linear theory. This means QM is the only known physical theory that both admits unique solutions and allows for actual determinism --- Laplacian style determinism.

A caveat disclaimer should be inserted here. This is Quantum Mechanics in its unitary evolution, without observer events and other wave-function-collapsing oddities. This the "raw form" of the Schroedinger Equation. Many-a-reader have likely heard about quantum vacuum fluctuations, and other random aspects of quantum mechanics , such as the "measurement problem". A regular on this forum even went as far as to conclude :

Nature has at its disposal, in every fermion, a perfect random value generator - far better than any possessed by a digital computer. Our brains may well make use of this, perhaps relating to free will and the unpredictability of individual behaviors.

This so-called "perfect random value generator" is not part of any known equation or theory in physics. If for example, you consider Many-worlds or even quantum Bayesianism, those are from a cluster of interpretations that demand that the wave function never actually collapses. In other threads, I described these as No-Collapse Interpretations. These sit opposite from a cluster of interpretations called Collapse Theories.

Proponents of MWI, such as Max Tegmark, have often advertised Laplacian determinism as being a selling-point for MWI. I will try to link some lectures where Tegmark makes these kinds of claims... time permitting.

[hyksos]

(my apologies. I meant to post this in Personal Theories section)

[Faradave]

interpretations that demand that the wave function never actually collapses. In other threads, I described these as No-Collapse Interpretations. These sit opposite from a cluster of interpretations called Collapse Theories.

The arrow of a common game spinner can illustrate compatibility of collapse and no-collapse models. Given a spin, one provides a reasonable approximation of random selection by the direction in which stops. While spinning it might be considered in its wave state. When it lands, the wave has collapsed. So, how can it illustrate both at once?

1. Attach a motor so the spinner doesn't stop. Now you have a no-collapse state from the spinner's perspective.

2. Pump a drop of water through the axil so that it forms quickly just to the pointy side of center on the arrow. Of course, the drop flies off, but in only a single direction. That's collapse, from the perspective of the drop and the person who gets wet.

With sufficient angular velocity, the arrow will effectively be in superposition, pointing in all directions at once in the plane of rotation.

An energized electron acts as if it has an arrow intrinsically pointing in every spatial direction (a 3-plane) at once, including through both slits of any nearby interferometer. The light quantum of course, is received at only one location.

[hyksos]

Faradave,

What you have described with the spinner is a hidden variable theory. In that context, the instantaneous direction of the arrow would be an objective state of the electron that is inaccessible to experiment. Many interpretations of quantum mechanics exist precisely because HVTs are not viable.

The only one-the-books interpretation of QM that looks something like HVT is DeBroglie-Bohm Guiding Wave. In my experience , however, proponents of DBGW make statements that are unfalsifiable. They often claim HVTs have "not yet been ruled out" and then cannot produce any situation that would rule them out. So they haven't been ruled out because nothing could ever rule them out. (It's a logical fallacy is what I am getting at)

When a particular radioactive atom will decay is considered to be a perfect random number generator. So the raw physical lab data is suggestive of an RNG in nature, but the formalism of QM does not contain this breakpoint at a "Wave function collapse". (and yet the formalism does not contain "observers" either, as Wilczek points out).

I'm going to try to be more concise here about this point. The formalism of QM does not contain the following.

• Perfect Random Number generators in every fermion
• Observers
• Wave function collapse.

We certainly live our lives in a world that contains all three of these. I mean, the radioactive RNGs can be demonstrated in a lab in front of a live audience. In many cases we have to refer to these things as physical events, even when the formal Schroedinger Equation on the chalkboard does not contain them. (because we are humans who have to talk to each other)



This thread is not an adjudication of the Measurement Problem. We have 100 threads on this forum that beat that issue to death. In this thread I'm actually talking about the formalisms on paper, outside of any of those other problems associated with humans measuring things. MWI and Quantum Bayesianism are both no-collapse interpretations, and both are compatible with the formalism of QM. I do not personally agree with them, because I support G-O-C. Nevertheless Tegmark et al are aware that QM is the only physical theory whose equations would produce exact solutions in principle.

This thread is about the linearity of QM. I really do not want to re-adjudicate the Measurement Problem all over again from the ground up. I am really not here to do that. I assume the moderators have not removed your ability to start new threads. You could always start a new thread and promote an HVT there.

I really wanted this thread to be posted in Personal Theories section, because this topic of determinism in classical mechanics and "linearity" in QM is not even really physics. It is barely metaphysics. I would say there is an interesting and fascinating topic here. (at least in my humble opinion). I made two wild statements (1) Classical physics is not even deterministic. (2) Formal QM could actually be deterministic. This is some saucy stuff and runs contrary to anything you would read in a magazine or a popular science website.

[davidm]

I see what you're saying, but I think the only wild thing would be the claim that classical physics may actually be nondeterministic. But the no-collapse interpretation goes back to Everett and has always been fully deterministic as well as local and realistic. In fact, if no-collapse is true, there is no classical physics, because everything is quantum. Then when we are calculating the probability of something happening, it seems we are calculating the probability of ourselves quantum entangled with a particular outcome, even though all outcomes are real.

[dandelion]

Yes, I think in a no-collapse view indeterminate experience might supervene on determinism. Incidentally, I noticed Penrose’s suggestions which were compared in a recent arxiv paper I’ve only glanced at regarding proposals about measuring effects of gravitationally induced entanglement between massive particles.

[hyksos]

I see what you're saying, but I think the only wild thing would be the claim that classical physics may actually be nondeterministic.

Non-linear equations often do not admit unique solutions. It turns out that the formalism of Quantum Mechanics is linear, and so it is the only known physical theory that admits unique solutions. This is a big dirty secret that popular science magazines and pop science website will never tell you. Not only is there no randomness in the equations of QM, those equations are the strongest candidate for determinism.

But the no-collapse interpretation goes back to Everett and has always been fully deterministic as well as local and realistic.

Yes this is actually true. This whole thread was started by me too early. I'm sort in the middle of writing a PDF that covers all of these topics and wraps them all in a clean and clear perspective. I may share a portion of it, but beware that this is a very early manuscript that will be edited heavily, and covered in citations. I'm going to use columnar format seen in many british physics journals' formats.

In fact, if no-collapse is true, there is no classical physics, because everything is quantum. Then when we are calculating the probability of something happening, it seems we are calculating the probability of ourselves quantum entangled with a particular outcome, even though all outcomes are real.

That sounds like some form of Quantum Bayesianism.

Ironically, I would almost prefer that you not respond to what I have written here. Things are getting very clear now to me and I'm compiling a very long article that will take me weeks to put together.

I have to make some big decisions now in my life in this regard. One of these may be that I need to create a new thread about this topic : The topic is not determinism as much as it is about why we, as humans, even need interpretations of QM to begin with. For years I had a wrongheaded misapprehension about this whole topic.


The second decision is whether I will continue to use this forum. I am now at a place in my personal development where I am ready to talk to professional physicists in those places on the internet where they hang out. That might be researchgate, or it might be somewhere else. In fact, I might start interacting directly with blogs like Lubos Motl's blog. I do know that Gerard t'Hooft blogs and has open discussions in the comment sections there. And he is a full-blown Nobel Prize laureate. I have quoted him in a few places on this forum.

[dandelion]

Not adding anything new, just more detail to my last post- the recent paper mentions the suggestion that linearity may be broken by a gravitationally induced physical collapse with proposals like this- https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.119.240402

[hyksos]

dandelion : I'm getting a soft paywall with that link. Did you get a copy of the whole paper?

[dandelion]

Here,
https://arxiv.org/abs/1707.06050
https://arxiv.org/abs/1707.06036
"Roger Penrose has suggested that the Planck mass is related to the scale at which the linearity of quantum theory is broken by a physical collapse induced by gravity [15]. While logically possible, this is not a straightforward consequence of quantum mechanics and general relativity alone, and it can be viewed as an intriguing but speculative suggestion, not necessarily a clearly plausible consequence of what we know about nature. Interestingly, if Penrose’s suggestion is correct, the BMV effect should presumably not happen, because quantum superposition of macroscopically different spacetimes should be suppressed, and the Penrose collapse time should be of the same order as the BMV time".
https://arxiv.org/abs/1808.05842

[hyksos]

Thanks. I will get around to all three when I have time.

[dandelion]

It seemed relevant. Thanks for raising all these thoughtful angles, I've enjoyed learning from them and hope to continue to.

[Faradave]

I assume the moderators have not removed your ability to start new threads. You could always start a new thread…

When I'm quoted in the OP, I'm part of the thread by the author's choice not mine. As the prevalent discussion is winding down, I reply.

What you have described with the spinner is a hidden variable theory. … HVTs are not viable.

Not really.

"In physics, hidden-variable theories are held by some physicists who argue that the state of a physical system, as formulated by quantum mechanics, does not give a complete description for the system; i.e., that quantum mechanics is ultimately incomplete, and that a complete theory would provide descriptive categories to account for all observable behavior and thus avoid any indeterminism."

QM is indeed incomplete but rather than avoiding indeterminism (as a hidden variable theory would), Phyxed helps complete QM by modeling an exact mechanism for indeterminism. Phyxed embraces Bell's theorem.

…the instantaneous direction of the [spinning] arrow would be an objective state…

If the spinner could spin infinitely fast, it would cease to be a spinner and instead become a field, a spinner in superposition, with the state of its direction (Ψ) given by:
√(1/3)<Red> + √(1/3)<Blue> + √(1/3)<Yellow>.

Of course, no material spinner can do that, but a spinor can. Electrons have fields and "intrinsic spin". Is it so surprising to think one might arise from the other?

When a particular radioactive atom will decay is considered to be a perfect random number generator. So the raw physical lab data is suggestive of an RNG in nature, but the formalism of QM does not contain this…

As I said, QM is incomplete. Atomic decay is a fine random value generator. So is light emission. In fact, the similarity of the two (when an emitted light quantum is seen as an orbital "decay" product) can be the basis of electroweak unification in that both shed mass-energy.

I really do not want to re-adjudicate the Measurement Problem…

I don't recall asking for that. When a drop of water flies off the spinner above, the spinning never stops (collapses). The spin field persists as an object in its own right, along with its wave function.

I am now at a place in my personal development where I am ready to talk to professional physicists in those places on the internet where they hang out.

I appreciate that you're busy on behalf of QM and I wish you well with that. No reply required.

[hyksos]

I have read the three papers. This is my response to the three papers.

A portion of the Rovelli paper (3rd link)

Some researchers have suggested that the Planck mass could signal the scale at which quantum theory may break down. After all, the mass of most systems we treat quantum mechanically is smaller than m_Planck and that of most systems we treat classically is larger than m_Planck. Roger Penrose has suggested that the Planck mass is related to the scale at which the linearity of quantum theory is broken by a physical collapse induced by gravity [15]. While logically possible, this is not a straightforward consequence of quantum mechanics and general relativity alone, and it can be vie . . .

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