Dear Daniel,

The Schrödinger equation is not a scientific mistake. The mistake is that the community almost immediately forgot on what foundation it was introduced as soon as the Heisenberg statistical solution gained popularity, which was almost immediately.

If interested, this recently published paper retraces the historical reasons why it was introduced, and why it is in agreement with electromagnetism, despite Feynman's opinion to the contrary, titled "The Hydrogen Atom Fundamental Resonance States":

http://file.scirp.org/pdf/JMP_2018042716061246.pdf

Best Regards

André

Hello André

I much appreciate your comments and the link to your paper.

It is true that, in the sense that it is just a time dependent equation, the Schrödinger unitary evolution is not in itself a mistake. Any time dependent equation is just a mathematical entity that specifies how certain mathematical objects, in this case wave functions $\Psi$, behave as time progresses.

The scientific mistake arose when the mathematical objects governed by the equation were given a physical interpretation. For if the physical electron state at time $t$, say $e_t^-$, corresponds with the wave function $\Psi_t$, and if the mathematical object is ruled by the Schrödinger evolution then, when physical transitions between states at different energy levels occur, the physical energy of the electron energy changes while Schrödinger evolution is energy conservative. Mathematical evolution and physical evolution move along disparate ways.

This is a scientific mistake in the sense that the formal mathematical dynamics does not correspond with the physical dynamics revealed in the laboratory by the hydrogen emission/absorption lines.

The probabilistic interpretation was introduced as an ad hoc remedy, becoming an ideological monster much worse than the original malady.

The scientific mistake started around 1926 and persists to present times.

With most cordial regards,

Daniel Crespin

Dear Daniel,

The idea and notion of an "instant of time" should be revised or discarded, in particular in dynamical theories which try to describe phys. objects or processes at the atomic and subatomic scale, and which are involved with differential equations including time derivatives.

Whenever some "initial" value of something at an "instant of time" is necessary in order to solve a diff.eq., the question arises from where and how to get the correct "initial" value. If the "initial" value is just the result of a guess, then there is no ontological problem. However, if the "initial" value is the result of a measuring process which is performed not at an "instant", but in some FINITE period of time, say [t_1,t_2], then this "initial" value cannot be considered as value being valid for the phys. system at one "instant of time".

In order to eliminate this ontological problem, "smearing procedures" (similar to what is done in QFT) could be performed for (traditional) time-dependent phys. quantities, and thereby the notion of an additional variable "smeared time" could be introduced and used for setting up an eq. for time-evolution, i.e. "smeared time" is considered instead of "ideal time".

A second vague idea is to replace the idea and notion of "time" as being a real-valued quantity, by "time" as being a "fuzzy-number"-valued quantity. This would require that a type of "fuzzy-numbers" is introduced which results from much more elegant definitions than what is known today. Of course, ideas of "fuzzy time" are also involved with ideas of "fuzzy space-time" and attempts to setup QM as a "fuzzy" dynamical theory.

Best regards

Karl

Hello Karl

To smear time appears to be a very interesting idea, at least intuitively. However I am assuming a standard notion of time, collectively equal to an ordered continuum of individual instants which are faithfully representable by individual elements of the real number system. Recall that technically this system is, up to unique field isomorphism, the only Archimedean complete ordered field.

Thanks very much for your original comments.

With the best regards,

Daniel Crespin

Is is interesting to note that recently in math. rigorous QFT an attempt has been made to introduce an additional "time-like" parameter in order to eliminate the disaster of an interpretation of QFT of interacting fields due to unitary evolution in time and Haag's Theorem :

Article Avoiding Haag’s Theorem with Parameterized Quantum Field Theory

By the way:

If an electron is assumed to be a compound object of some constituents, the notion and feature of "correlation" of bound electrons "inside" an atom emerges in a very natural manner. For example, if an electron is assumed to consist of 6 constituents, then two bound electrons can be considered as a system of 12 constituents. Thus, the idea of assigning these constituents to an individual electron can be abandoned, because there is only one "cloud", so to speak, of constituents.

Dear Christian,

You wrote: "There seems nothing wrong with Schrödinger's equations. Only Bohr and Heisenberg did not like it. They preferred the mystery."

And so did most in the community almost from the start.

De Broglie and Schrödinger already considered transitions as "not instantaneous" even as Schrödinger introduced the wave equation, and this was practically 100 years ago, not a few decades ago, and this is what they were attempting to address, but could interest nobody else.

At the beginning of the 1950's, Schrödinger himself very publicly and futilely protested again about the very idea of instantaneous quantum jumps. Unfortunately, nobody paid attention.

If you had even glanced at the paper I referred Daniel to in the first answer in this thread, you would have found the direct quotes from him and the actual references where you can find them.

It is to this 100 years disconnect that I have been trying to draw attention.

At long last, some research seems to be resuming in the right direction.

Best Regards

André

If the atomic transitions were timeless, no interference would ever succeed, no anti-reflect coating would work, no duck, no pawn, no lapwing, no credit card could ever have interferential colors, no radiocrystallography would ever work, and no spectrography either. The official church in QM is as wrong as possible.

In the real world, Erwin Schrödinger made two scientific mistakes, which you did not notice: He forgot to come back into the relativistic frame, so the frequencies he considered in 1926 (Physical Review) are fictitious. And he forgot to set the emission and absorption mechanisms on an equal foot. Though it had been proved in 1868 by Gustav Kirchhoff.

The consequences are dramatic.

And whichever the deliria taught by the Göttingen-København sect, never the unitarity is violated.

Simply this sect teaches delirious boundary conditions, with sudden and mysterious apparitions of the absorption reaction on the absorbers, whose properties are systematically despised.

The unitary evolution, described by the Schrödinger equation (a) is mathematically consistent and (b) does produce transition probabilities that can and have been measured. It would be useful to actually learn quantum mechanics, from textbooks, not popular books and to avoid mixing up the history of the subject with the technical subject itself.

@Stam Nicolis. The history of the dominating mistakes is not unuseful.

"intrinsically probabilistic quantum jumps" surreptitiously pre-suppose that you know and monitor the initial conditions and the final conditions.

These presomptuous assumptions are impossible to justify by experiments.

You can isolate one blackboard from the other blackboards, but you cannot isolate any "quantum system" from the remaining of the world and the resulting broglian noise. You cannot isolate any emitter from the absorbers.

While at some point people were talking about ``quantum jumps'' it turns out that this notion isn't necessary. So it doesn't make sense trying to understand it, since it doesn't mean anything.

Dear Stam,

If quantum jump doesn't mean anything then please explain Fermi-Golden rule which have been used all over the place in transition matrix in quantum transport..

@Gokaran Shukla . What exist are transfers from one emitter to one absorber, and transitions from one stationary state to another stationary state. But all stationary states are held by quantic rules, as shown by de Broglie in 1924 and Schrödinger in 1926.

What escapes to the quantic rules are the Brehmstrahlung and the synchrotron radiations.

The Fermi golden rule doesn't have anything to do with any jumps.

The quantities that are computed in quantum mechanics are transition probabilities, from some initial state to some final state. Nothing more, nothing less.

Bremsstrahlung and synchrotron radiation can be described, when the number of photons can be resolved-that's nothing new, either. When the number of photons can't be resolved, the quantum effects are described by the classical limit, i.e. classical electrodynamics.

Dear Stam,

And how you get transition probability? Even wikipedia people knows this !!! Take a look here ... https://www.wikiwand.com/en/Fermi%27s_golden_rule ...

Dear Jacques Lavau ,

Much advancement has been done since 1926 in display technology... There is something called Frank Condon principle... If you really want to handle emitter and absorber problem quantum mechanically, then you must know the transition matrix which can only be calculated using Fermi-Golden rule...

@ Stam Nicolis. But what about the precise frequencies, in Bremsstrahlung and synchrotron radiation? There is no QM theory predicting them.

Transactional microphysics explains why the standard QM is impotent there. The standard QM is anti-transactional because it is primarily anti-relativist (anti-Einstein), anti-frequency and anti-undulatory (because it is anti-Fourier, anti-de-Broglie, and anti-Schrödinger), anti-optical (anti-Fraunhofer, anti-Fresnel, anti-Kirchhoff...)...

Please have a look on the following paper which says we have primarily missed one part of the story.

Preprint On the Magnetic Current Density in the Maxwell Equations Bas...