The Formalism and the Interpretive Chasm

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The Formalism and the Interpretive Chasm

Postby hyksos on October 13th, 2018, 6:55 pm 

The Formalism is the mathematical underpinnings of the quantitative theory of modern physics, comprised of Quantum Mechanics and Quantum Field Theory.

Formalism__Monolith__UL.png


The Monolithic Formalism
  • Schrodinger wave equation
  • Matrix Mechanics. Given as the Heisenberg representation.
  • Phase Space formulation. Given as the Wigner Distribution Function WDF.
  • Dirac Equation. The relativistic version of the Schrodinger equation.
  • Path Integral formulation. A procedure developed by Feynman.
  • Field Theory Lagrangian. Also called the Lagrangian of the Standard Model.

Formalism__annotated_UL.png



What The Formalism lacks

The Formalism . . .
  • . . . does not contain classical particle trajectories. Instead it only contains a so-called position operator.
  • . . . does not contain wave function collapse. It is not merely the case that it does not depict a mechanism for collapse. The Formalism contains no wave function collapse -- at all.
  • . . . does not contain observers.
  • . . . does not contain or depict any random component. In fact the equations are linear, admit unique solutions, and so they may even be deterministic.
  • . . . does not single out a present moment.
  • . . . contains no special direction of time. In other words, the equations work in reverse just as well as in "forwards" time.

The Interpretive Chasm
A large gulf exists between the Formalism of Quantum Mechanics, and what human researchers actually measure in lab settings. This gulf is so wide, it has elicited a giant body of written work loosely referred to as the "interpretations of Quantum Mechanics". Human experience of the world is so alien to the Formalism, that it is as if we live in a different world set apart from the quantum world by a large, unbridgeable chasm. This incongruity between the two worlds, I hereby refer to it as the Interpretive Chasm.

Human experience with reality contains . . .
  • . . . particle trajectories. We see them regularly in bubble chambers. They are on-demand repeatable. The electron exhibits classical trajectories in magnetic fields, which can be predicted with simple application of Maxwell's equations.
  • . . . wave function collapse. Humans can invoke collapse on-demand in many lab settings, and even outside the lab in several common phenomena.
  • . . . observers who make measurements. Measurements which effect the outcome of experiment.
  • . . . inexplicable un-caused randomness. It has been measured as vacuum fluctuations in van Der Waals' forces and in the Casimir effect. Quantum fluctuations have been observed in ultra-cold cuprates. Whether or not a single radioactive atom will decay is random. Nuclear decay produces random numbers with exquisite randomness. So random that the data produced by them is suitable for cryptography.
  • . . . a special present moment that seems more real than the past and future. The Formalism borrows the lack of any "present moment" from Special Relativity, which was folded into the Formalism with the discovery of the Dirac Equation.
  • . . . a reliable and constant forward flow of time, with a past that leaves a memory, and a future that is unpredictable. The equations of QFT allow for particles moving "backwards in time" from the future. In some cases, these particles are included in the Path Integral.

The interpretive chasm plays the role as a justification for the interpretations of quantum mechanics. Those interpretations serve as an intellectual bridge between the human world and the quantum world.

The raw, quantitative approach to modern physics is sometimes called Shut-up-and-calculate. Many working physicists eschew a discussion of what The Formalism is depicting about the nature of reality. They see it as idle philosophy, tilting at windmills, or chasing rainbows. However, the actual predictions of the Formalism contrasted with human experience with the world is stark enough to elicit pause. Discussing the ontology of Quantum Mechanics through various interpretations is justified as more than "idle philosophy" or mere rainbow chasing.
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Re: The Formalism and the Interpretive Chasm

Postby hyksos on October 13th, 2018, 7:56 pm 

The right resolution of this non-unitarity problem is that there's nothing such as the collapse of a wave function. The wave function is not a real wave: it's a set of complex amplitudes whose squared absolute values don't describe "the reality" but rather just the probabilities of "different realities". The probability distributions mean that you always get just one outcome and the values of the probability distribution just tell you what the probabilities of different outcomes are. Nothing has to "collapse" because the wave wasn't a "real observable wave" to start with.

The idea that the wave function has to "collapse" and one has to look for a "mechanism" how it collapses is an artifact of a misinterpretation of the wave function.



-- Luboš Motl
October 16, 2011
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Re: The Formalism and the Interpretive Chasm

Postby hyksos on October 13th, 2018, 8:04 pm 

Most importantly, is wavefunction collapse even a real thing?

Or is it just an ad hoc explanation for a phenomenon that can perhaps be better explained by some better-understood mechanism, such as quantum decoherence ( a view that has become mainstream in recent decades. ) All of these questions, and many others, are part of the infamous measurement problem of quantum mechanics.



-- Barak Shoshany
Perimeter Institute for Theoretical Physics
18 May 2014
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Re: The Formalism and the Interpretive Chasm

Postby hyksos on October 13th, 2018, 9:33 pm 

We can illustrate the basic idea by including the coefficients in the Schrödinger’s catwave function , so that it reads

a1 {det. reads more than 99 counts} {cat dead} {observer sees cat dead}

and

a2 {det. reads less than 100 counts} {cat alive} {observer sees cat alive}

|a1|2+|a2|2 = 1

Now ‘collapse’ says that, for whatever reason, either a1 -> 1, a2 ->0, so that the live cat version of reality has simply gone away — collapsed — and a dead cat is perceived; or a1 ->0 , a2 -> 1 and a live cat is perceived. It is to be emphasized that the conventional equations of quantum mechanics do not imply this collapse; those equations imply that a1 and a2 stay the same size forever (see the appendix). So if collapse occurs, its cause must be outside conventional quantum mechanics.


--- Casey Blood
Rutgers Prof. Emeritus
27 August 2008
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Re: The Formalism and the Interpretive Chasm

Postby hyksos on October 15th, 2018, 3:45 pm 

Earlier I had described the above material as being an outline of a much larger PDF I was stitching together. Notice the six bullet points underneath "What the Formalism Lacks". Each bullet point there could be extended into an entire chapter of a book. In this sense there are too many explosive bombs placed in proximity to each other other without elaboration of the claim.

Some readers may have noticed that the three professor quotes all address wave function collapse in particular. The reason for that is the following -- if you google "wave function collapse" and spend several hours reading, you will be met with an armada of websites claiming that wave function collapse is part of canonical physics. The most blatant offender is this website that looks entirely academic in presentation and tone, from the university of Texas at Austin. It even appears to be the handiwork of a professor.

http://farside.ph.utexas.edu/teaching/qmech/Quantum/node29.html

Fitzpatrick wrote:immediately after the first measurement, a measurement of the particle's position is certain to give the value x0 , and has no chance of giving any other value. This implies that the wavefunction must have collapsed to some sort of "spike" function located at x=x0

You will notice how drastic the difference is between the above verbiage, versus what Lubos Motl said about this phenomenon.

Interestingly enough, outside this poorly-written utexas.edu page, I was unable to find anything else that corroborates it. Flanking websites instead contain verbiage such as :
Two thought experiments are analyzed, revealing that the quantum state of the universe does not contain definitive evidence of the wavefunction collapse.


Then we have Thomas MacFarlane's physics blog, containing the following paragraph of high sparkling lucidity..

Not only is collapse of the wave function totally unverifiable and nonphysical, but another big problem with collapse is that it is in blatant violation of the Schrödinger equation! Any other scientific hypothesis that both violates known laws of physics and is not verifiable would normally be immediately rejected as pseudo-science. Why, then, has the notion of collapse stuck? Perhaps because one consequence of rejecting collapse would seem to be that it would lead us inevitably to the many worlds interpretation. Strange as the many worlds interpretation may be, however, it does have the virtue of being consistent with the laws of physics, at least as we know them so far.


You can enjoy more of MacFarlane's lucidity here -- https://integralscience.wordpress.com/2009/03/22/the-imaginary-collapse-of-the-wavefunction/

In any case, that was my motivation for hammering away at the issue of wave function collapse. There was a lingering problem that a person passing through this forum would google the topic, and find dozens (or more) websites contradicting my original claim. At this point I would go as far as to actually say that there is a lot of disinformation and confusion out there in the world wide web.
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Re: The Formalism and the Interpretive Chasm

Postby davidm on October 16th, 2018, 10:08 am 

While I’m enjoying your posts on this subjects, I’m still not seeing very much new. Your Casey Blood cite is exactly what Tegmark has been saying since at least 1997, and of course the basic idea goes back to Everett in 1957. Unfortunately Einstein died in 1955, and once can’t help but wonder what he would have made of Everett’s relative state formulation.

I did like this interpretive thrust from Thomas McFarlane:

The many worlds interpretation is often rejected as outrageous because it seems to imply that all the separate “worlds” have some actual existence, just like ours. But, it’s more like none of the “worlds” have actual existence, including ours. To make an analogy with the theory of relativity, it’s not like there are many actual velocities of the earth in space, each existing as its own separate actualized “world.” Rather, it’s that the earth has no actual objectively existing velocity at all. Velocity only has meaning relative to a reference frame, and reality does not have any privileged reference frame. We happen to observe things in the reference frame of the Earth where that velocity is zero. If we were on the Moon, things would be different. Is there really some mystery here? How is this so different from quantum theory? The original “relative state” formulation of quantum theory seems to be in line with this view, and calling it a “many worlds” theory is just as misleading as calling relativity theory a “many worlds” theory. It’s just “many reference frames” and one world. One might complain that the “one world” is a strange one, but that’s no less true in relativity theory where nothing has any objective mass, length, time, etc. The only objective realities are the four-dimensional invariants. These are almost as weird as coherent superpositions.


This interestingly dovetails with Vesselin Petkov’s defense of the block universe: Minkowski spacetime means that there are many spacetimes, not just one spacetime, but this in turn can be reformulated as above, to say that there are no “actual” spacetimes, just many reference frames. So it’s not too much of a stretch to suggest that actuality itself is an indexical. This is what David K. Lewis did in his book “On the Plurality of Worlds,” in which he argued that all counterfactual worlds actually “exist” but only in the sense that they are actual to their inhabitants. Unlike the quantum many worlds thesis, Lewis maintained that all logically possible worlds existed in this indexical fashion, including worlds in which the Greek gods were literally real and other worlds at which donkeys talked and pigs flew.
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Re: The Formalism and the Interpretive Chasm

Postby Braininvat on October 16th, 2018, 11:53 am 

Some members are better versed in science than philosophy, so I'm putting this up here -

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

And I want to go back and read more of this entry. Where I am not quite clear is on how all counterfactual worlds "exist" but only in the sense that they are actual to their inhabitants. The scare quotes on "exist" are a little confusing.

Good thread - I enjoy seeing any protest/critique at how loosely "Many Worlds" is tossed around.
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Re: The Formalism and the Interpretive Chasm

Postby davidm on October 16th, 2018, 12:11 pm 

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Re: The Formalism and the Interpretive Chasm

Postby hyksos on October 16th, 2018, 6:07 pm 

davidm » October 16th, 2018, 6:08 pm wrote:While I’m enjoying your posts on this subjects, I’m still not seeing very much new. Your Casey Blood cite is exactly what Tegmark has been saying since at least 1997, and of course the basic idea goes back to Everett in 1957.


There is some cross-talk with a post I made in January.

GHirardi.png


(Not to split hairs, but) Casey Blood does not claim that collapse does not happen. Rather she wrote that if it does happen, then its causal chain would be a theory outside of the QM formalism.
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Re: The Formalism and the Interpretive Chasm

Postby dandelion on November 4th, 2018, 3:49 am 

This thread might suit this topic- viewtopic.php?f=72&t=29358
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