Quantum Physics - Is the Schrödinger Equation True? of January 2014

This document contains comments about the article Is the Schrödinger Equation True? by John Morgan In Scientific American of 7 January 2021.
To read this article select: https://www.scientificamerican.com/article/is-the-schroedinger-equation-true1/



Some of the math she’s learning in school, Gracie Cunningham suggests, has little to do with the world in which she lives.
That is partly correct. More detail is required.
But how would you come up with the concept of algebra?
Gracie’s complaints struck a chord in me.
Since last May, as part of my ongoing effort to learn quantum mechanics, I’ve been struggling to grasp eigenvectors, complex conjugates and other esoterica.
Quantum mechanics is part of physics and requires 'complex' algebra to describe what it is.
I keep wondering, as Cunningham put it, “Who came up with this concept?”
Take Hilbert space, a realm of infinite dimensions swarming with arrow-shaped abstractions called vectors. Pondering Hilbert space makes me feel like a lump of dumb, decrepit flesh trapped in a squalid, 3-D prison.
The problem is, which physical process do you try to understand.
Reality, great sages have assured us, is essentially mathematical.
The reality is essentially physical. To understand the reality you don't need mathematics. To predict the future you need mathematics.
Galileo declared that “the great book of nature is written in mathematics.”
Only a small part of all physical processes can be desribed by mathematics.
We’re part of nature, aren’t we? So why does mathematics, once we get past natural numbers and basic arithmetic, feel so alien to most of us?
The problem is most physical processes are chemical reactions. These chemical reactions evolve in time, are difficult to measure and subject of change.
More to Gracie’s point, how real are the equations with which we represent nature?
These equations are theoretical real. They are valid under certain conditions. The reality can be more complex than these equations assume.
Physicists’ theories work.
That is not true.
A theory, in principle, is a prediction of how an actual process evolves in time. Often the prediction can be in the form of equations. Real experiments have to be performed to calculate the parameters of these equations. Sometimes the equations have to be modified to better match the observations. A typical case are Newton's Law and Einsteins equations.
But scientists, and especially physicists, aren’t just seeking practical advances.
Scientists, physicists and chemists want to understand how the processes, they study, operate in as much detail as possible.
When they do that they try to create new application, which are based on this improved knowledge.
They’re after Truth.
Not so much. They after the details
They want to believe that their theories are correct—exclusively correct—representations of nature. Physicists share this craving with religious folk, who need to believe that their path to salvation is the One True Path.
This has nothing to do with religion.
But can you call a theory true if no one understands it?
A theory is a prediction of how something operate.
The first time it is proposed, there is always a chance that the reaction is: disbelief.
A century after inventing quantum mechanics, physicists still squabble over what, exactly, it tells us about reality.
More information is required, what is process studied, in question.
For example, in the case of "Schrodinger's cat experiment" a the cat is placed in a the box,
It should be mentioned in the original experiment, inside the box, a very specific dangerous reaction takes place. In this case studied we don't know what is happening inside the box.
After the cat is placed inside the box, the cat is not vissible for the audience and is supposed to be in a state of both alive and dead.
The problem with this experiment, is that there is no difference if the cat is continuos observed or not.
As such the statement that the cat is both alive and dead does not make sense. In reality there should be no difference if a box is from wood or from glass. The size is important. If there is disc with milk inside the box is important. If the milk contains a poison, is important. If there is a container with gas, which can be released as a result of a radio active reaction, is important. But observers, inside the box, or outside the box are not important.
Consider the Schrödinger equation, which allows you to compute the “wave function” of an electron. The wave function, in turn, yields a “probability amplitude,” which, when squared, yields the likelihood that you’ll find the electron in a certain spot.
Take a glaspipe, with a rather large diameter and place a small marble inside the glaspipe. Next move the glaspipe, such that the marble starts turing inside the glaspipe against the wall. The position of the marble can be described by a sinus function in the z direction and a cosinus function in the y direction, both as a function of t. The position of the marble in the x direction is considered 0.
When the marble also moves in the x direction both the sinus function becomes a wave function in the x,z plane and the cosine function becomes a a wave function in x,y plane.
The wave function has embedded within it an imaginary number.
It should be mentioned that the wave function is used to describe the position of the marble in mathematical notation. In reality there is no wave function.
As such you can also use imaginary numbers, but from a physical point of view there are no imaginary numbers involved.
In mathematical notation the wave function is described as r*e^i.phi = r * cos(phi) + i * r sin (phi) = x + i * y
That’s an appropriate label, because an imaginary number consists of the square root of a negative number, which by definition does not exist.
Imaginary numbers are used to describe the evolution in mathematical notation.
Although it gives you the answer you want, the wave function doesn’t correspond to anything in the real world.
That is correct. But indirectly the wave function describes the movement and position of the electron or marble.
It works, but no one knows why. The same can be said of the Schrödinger equation.
It should be mentioned that the parameters of the Schrödinger equation should be calculated based on real experiments.
Moreover, the Schrödinger equation is far from all-powerful.
Although it does a great job modeling a hydrogen atom, the Schrödinger equation can’t yield an exact description of a helium atom!
Helium, which consists of a positively charged nucleus and two electrons, is an example of a three-body problem, which can be solved, if at all, only through extra mathematical sleights of hand.
All three-body problems are physical unpredictable. The major problem is to measure the exact positions.
And three-body problems are just a subset of the vastly larger set of N-body problems, which riddle classical as well as quantum physics.
But the formulas match experimental data only with the help of hideously complex patches and approximations.
When I contemplate quantum mechanics, with all its hedges and qualifications, I keep thinking of poor old Ptolemy.
Elementary particle mechanics and planetery mechanics are two distinct applications.
But Ptolemy’s geocentric model worked. It accurately predicted the motions of planets and solar and lunar eclipses.
What is the time span of this earth based model?>
Quantum mechanics also works, better, arguably, than any other scientific theory. But perhaps its relationship to reality—to what’s really out there—is as tenuous as Ptolemy’s geocentric model.
It is very difficult to compare Quantum mechanics, in general, with Ptolemy’s geocentric model.
The implication is that one day we will find the correct mathematical theory of reality, one that actually makes sense, like the heliocentric model of the solar system.
You cannot describe 'the reality' by mathematics. It is already difficult to describe the reality using text.
The heliocentric model is better than the geocentric model. A better approach is to take center of our Galaxy into account.
Wigner, a prominent quantum theorist, notes that the equations embedded in Newton’s laws of motion, quantum mechanics and general relativity are extraordinarily, even unreasonably effective.
For any specific problem only one of the three can be used. In my opinion to use GR with all its in and outs, trying to simulate the stars in our Galaxy is impossible.
But just because these models work, he emphasizes, does not mean they are “uniquely” true.
As I already mentioned, for each application, at the most one is true.
The “laws” of physics, Wigner adds, have little or nothing to say about biology, and especially about consciousness, the most baffling of all biological phenomena.
The only law that maybe can be used to understand consciousness is quantum mechanics.

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Created: 23 November 2022

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