Encyclopedia of Mathematical Physics (2006) states in Introductory Article: Quantum Mechanics:
- QM in its present formulation is a refined and and successful instrument for the description of the non relativistic phenomena at the Planck scale, but its internal inconsistency is still standing on shaky ground.
- In this section we describe some of the conceptual problems which plague present day QM...
How is it possible that today 90 years after the formulation of Schrödinger's equation as the foundation of QM, this foundation is still inconsistent and shaky, plagued by conceptual problems. What have physicists been doing all these years?
 |
| Solway Conference 1927 |
Is it so strange that it's hard to formulate a physical theory that works at the planck scale given how many orders of magnitude we are from being able to do experiments on that scale? There is presumably new physics at higher energy, but as long as we can't test it our theories will be limited.
SvaraRaderaConceptual problems or not, QM is extremely succesful in predicting the results of experiments we can do.
The predictive success of QM is inflated, given that the Schrödinger equation is uncomputable for a many-electron configuration and thus cannot predict anything
SvaraRaderaab initio and can be twisted any way you may like to fit with observations. The proclaimed success of QM is thus invented fantasy which lacks real substance.
Do you think you could describe the internal inconsistency that is mentioned. I don't have direct access to that specific Elsevier publication.
SvaraRaderaWave-particle is an inconsistent concept in the same way that circular-square is inconsistent or contradictory. This is one of many contradictions of QM. In mathematics one contradiction leads to infinitely many contradictions.
SvaraRaderaIs that really the claimed internal inconsistency that your quote above refers to?
SvaraRaderaA wave-particle duality is a naive, and old, misconception that is trivially dissolved when using modern formulations of quantum mechanics without the teething problems associated with the time when a full quantum mechanic theory was not fully developed.
In the Copenhagen interpretation the wave-function isn't real. It is a mathematical guide for interpreting the outcome of an experimental setting. This has been evolved further in a modern interpretation where the wave-function is the subjective knowledge that an entity (scientist, particle, measuring device...) can use to set an a priori probability to the outcome of an experimental setting/event. After the experiment the entity updates this probability based on the outcome of the experiment. Hence there is no collapse of the wave-function.This interpretation also solves the locality issue in that such an interpretation necessarily means a local reality with realism. The difference from a classical description is that there are no classical hidden variables so there is a limitation of what is possible to know. This connects beautifully with your next blog post in where you describe Helmoltz words
Science, the goal of which is the comprehension of nature, must begin with the presupposition of its comprehensibility and proceed in accordance with this assumption until, perhaps, it is forced by irrefutable facts to recognise limits beyond it may not go.
The limit is here set by quantum mechanically limitations. How can renouncement of experimental facts in an attempt to straight-jacket the theory into a pre- 20th century physics setting coincide with Helmholtz reasonable words? That if nothing seems ass irrational.
Based on modern and current research the explanation of "quantum weirdness" is that there are no weirdness at all. There is merely an incapability of our minds to correctly understand certain fundamental physical processes other then by assigning probabilities to possible outcomes.
So to summarize. In quantum mechanics, there is no necessity for a wave-particle duality. With a decent interpretation of the theory there is no necessity for a collapse of the wave-function. There is no dice-game going on. Reality is both local and real. And the beauty of it all is that the formal part of the theory stands intact the same as it was formulated in the 1920s, so all the computational methods developed is still useful and true. The Born-rule is the workhorse that enables one to actually be able to formulate the necessary probabilities to assign a priori to an experimental outcome. The only possible unsatisfactory part of it may be that there is no way, and that means fundamentally no possibility at all, to get a complete understanding of what really is going on. We are limited to the information we can get from making experiments. But I think Helmholtz words are both true and comforting there so that should be ok.
Your long defense of "quantum weirdness" expresses the inconsistencies which you seem to claim to not contradict consistency. This is a contradiction if any.
SvaraRaderaYes or no.
SvaraRaderaIs spin important?
Not to Schrödinger, and me.
SvaraRaderaWhere did Schrödinger write this?
SvaraRaderaYes or no.
SvaraRaderaIs a theory that is not able to describe spin consistent with the reality?
What reality is described by spin according to standard QM?
SvaraRaderaThe wave equation Schrödinger presented does not include spin, and so Schrödinger probably did not consider spin to be important, assuming that he wanted his equation to describe important aspects of atomic physics.
SvaraRaderaNo, no...
SvaraRaderaSchrödinger derived his equation based on a comment made by Debye regarding de Broglie's hypothesis. He just search for a wave-equation that a particle should satisfy it is behaved as a wave. His first unsuccessful attempt gave the Klein-Gordon equation. He didn't manage to make any physically reasonable interpretation of this and so continued with the simpler case of a non-relativistic equation. He had to get help from Herman Weyl to manage this equation. He settled for the simplest possible case and from there managed to derive the hydrogen spectra. Probably not deeper than that. Schrodinger was actually beaten to it, both the equation and and hydrogen energy eigenvalues already in 1921 by Arthur C. Lunn, who unfortunately got his paper rejected. Dirac was close upon the equation but got beaten to it by Schrodinger.
I don't think you should put Schrodinger on a pedestal, he did write some stuff in his last years regarding physics and science that you probably would find utterly revolting based on your narrow mindset on physics...
The particles are simply dancing along in a wave-like fashion that are only statistically predictable. And whem you measure, you find where the particle is at a specific moment. This interpretation might violate relativity, but what so? You cannot expect the principles of relativity to be true at any physical Level. So there is not any real contradiction.
SvaraRadera