Quantum Mechanics - 100 Years of Quantum Mysteries in Scientific American of January 2001

This document contains comments about the article 100 Years of Quantum Mysteries by Max Tegmark and John Archibald Wheeler In Scientific American of January 2001.
As quantum theory celebrates its 100th birthday, spectacular successes are mixed with persistent puzzles
A longer version of this article is available at this link:
https://arxiv.org/abs/quant-ph/0101077 100 years of the Quantum by Max Tegmark and John Archibald Wheeler.



Quantum Cards

A Simple falling card in principle leads to a Quantum Mystery

According to quantum physics, an ideal card perfectly balanced on its edge will fall down in both directions, in what is known as a superposition.
So does a coin with the same thickness as the card. See Reflection 1 - Is there a difference between a card and coin?. The problem is a card nor a coin can fall down in both directions.
In practice, this experiment is impossible with a real card, but the analogous situation has been demonstrated innumerable times with electrons, atoms and larger objects.
If this experiment can not be performed in practice, why mentioned it?
Why not mention an experiment which can be performed in practice in which an object is in two places at once.

The Hydrogen Disaster

page 56

Schrödinger went on to produce his equation, the master key for so much of modern physics.
To introduce the (intermediate) concept of a wave equation inorder to calculate the measured results of certain processes is a hugh performance, but does not validate the idea that the objects involved are waves.
Within a few years,physicists had explained a host of measurements, including spectra of more complicated atoms and properties of chemical reactions.

page 57

But what does that mean? What was this quantity, the "wave function" that the Schrödinger's equation described.
Again that is the question. Anyway it is not something physical except if it something to describe the interference between water waves.
Born had the insight that the wave function should be interpreted in terms of probabilities.
When experimenters measure the location of an electron, the probability of finding it in each region depends on the magnitude of its wave function there.
That is the wrong sequence of reasoning.
This interpretation suggested that a fundamental randomness was built into the laws of nature.
The subject is here the wave equation and not the laws of physics in general.
And the wave equation tells you that you can find an electron only at certain locations (which depents on many parameters).
This is more or less the same as what happens when you play roulette. The ball can only fall in one out of 33 holes. However this is a discrete situation and you can speak here about randomness.
Considering an electron, this is slightly different. An electron can only be measured at a certain distance from the nucleus of an atom, but with any angle. That means there are an infinite number of locations. Randomness is not an issue.
Einstein was deeply unhappy with this conclusion and expressed his preference for a deterministic universe etc.
The movement (behaviour) of the electrons can be described as deterministic and follow certain specific laws. The problem comes when you want to measure the locations of the electrons. This involves probabilities.

Curious Cats and Quantum Cards

page 57

Wavefunctions could describe combinations of different states, so-called superpositions.
Here it is very important to describe specific the experiment and the measurements involved to explain superpositions.
In the case of electrons, what the experiment tells you, is that the interference pattern changes when there are one or two holes involved.
For example, an electron could be in a superposition of several different locations.
Specific here: more information is required.
As a baroque example, he described the now well-know thought experiment in which a nasty contraption kills a cat if a radioactive atom decays.
Even in such a 'simple' case it is very important to describe the experiment in great detail.
Because the radioactive atom enters a superposition of decayed and not decayed etc.
Specific here the time involved for material to decay follows a probability function. At any moment there is either no decay or a decay. Or a second decay, or a third decay etc.
Never at any moment an atom is both not decayed and decayed.
Never as such the cat is both alive and dead.
You take a card with a perfectly sharped edge and balance it on its edge on a table.
Accordingly to classical physics, it will in principle stay balanced forever.
In principle: Yes. In reality: No.
Accordingly to the Schrödinger equation, the card will fall down in a few seconds even if you do the best possible job of balancing it, and it will fall down in both directions- to the left and the right- in superposition
This text is very unclear. How do you know that the card will fall down in a few seconds in superposition. The Schrödinger equation can only describe what is actual observed but not something that is in superposition and not observed.
If you could perform this idealized thought experiment with an actual card, you would undoubtly find that classical physics is wrong and that the card falls down.
When you actual try to balance a card, you will not succeed. This tells you nothing about classical physical versus quantum mechanics.
But you would always see it fall down to the left or to the right, seemingly at random, never to the left and to the right simulataneously, as the Schrödinger equation might have you believe.
The world does not operate accordingly to any equation or law.
Observations come first. Descriptions (in any form) come second.
Using these descriptions you can predict the future.
The Copenhagen interpretation of quantum mechanics, addresses the mystery by asserting that observations, or measurements, are special.
There is nothing special involved.
So long as the balanced card is unobserved, its wave function evolves by obeying the Schrödinger equation - a continuous and smooth evolution that is called "unitary" in mathematics and has several very attractive properties.
When nothing is observed, you do not know what has happening. Specific you do not if something obeys the Schrödinger equation. This equation is also not known because what it is supposed to describe is unobserved.
very shaky science
Unitary evolution produces the superposition in which the card has fallen down both to the left and to the right.
That is easy to write but difficult to explain. How does this work?
The act of observing the card, however triggers an abrupt change in its wave function, commonly called a collapse: the observer sees the card in one definite classical state (face up or face down) and from then onward only that part of the wave function survives.
Observing by a human of (almost) anything in the physical world does not change anything.
very shaky science
Nature supposedly selects one state at random, with the probabilities determined by the wave function.
Which is not known?
The Copenhagen interpretation provided a strikingly succesful recipe for doing calculations that accurately described the outcomes of experiments,
You can only accurately predict the outcome of any experiment in the future, based on accurate observations in the past.
This sentence continues:
but the suspicion lingered that some equation ought to describe when and how this collapse occured.
Again to devellop such an equation you need accurate observations.
This paragraph end with the following sentence:
Many successes of quantum mechanics involve its extension, quantum field theory, which forms the foundations of elementary particle physics all the way to the present-day experimental frontiers etc.
That is undoubtly true, but this leaves the issues related to superpositions and collapse of the wave function unanswered.

Copenhagen Interpretation

When a quantum superposition is observed or measured, we see one or the other of the alternatives at random, with probabilities controlled by the wave function.
The wave function has nothing to do with this card experiment.
For example, the Schrödinger's cat experiment is controlled by the half life time of the radioactive element and by the amount used.

Many Worlds

page 58

Everett pushed the quantum idea to its extreme by asking the following question: What if the time evolution of the entire universe is always unitary.
To understand that sentence you must first clearly define the meaning of the words: time evolution, entire universe, always and unitary
Next you must define what means: The answer is "Yes" and what means the answer is "No"
After all, if quantum mechanics suffices to describe the universe, then the present state is described by a wave function (an extraordinarily complicated one).
Which no one knows.
In Everett's scenario, that wave function would always evolve in a deterministic way, leaving no room for mysterious collapse or God playing dice.
Everett IMO follows the strategy to explain something that is mysterious by something else that is also mysterious.
Everett's brilliant insight was that the observers in such a deterministic but schizophrenic quantum world could perceive the plain old reality that we are familiar with.
IMO Everett makes everything overly complex.
This viewpoint (the many-worlds interpretation of quantum mechanics) simplies the underlying theory by removing the collapse postulate.
When you read this you should ask yourself the following question: What is the original problem (experiment) that you try to understand.

Many Worlds Interpretation

If a wave function never collapse, the Schrödinger equation predicts that a person looking at the cards superposition will herself enter a superposition of two possible outcomes: happily winning the bet or sadly losing.
Stacked cards (right) show 16 worlds that result when a card is dropped four times.
The figure does not show 16 worlds. The figure shows the average outcome when you toss 4 coins 1600 times. Each combination of 4 coins will than appear on average 100 times. Using coins is much better than balancing a card, because such an experiment can be highly biased.

Quantum Censorship - Decoherence

page 60

They found that coherent superpositions persist only as long as they remain secret from the rest of the world.
How can you establish anything based on the rest of the world? There exist not something as the rest of the world.
Specific how do you define the slippery concept: secret.
Our fallen quantum card is constantly bumped by snooping air molecules and photons, which thereby find out whether it has fallen to the left or to the right, destroying ("decohering") the superposition and making it unobservable.
The only thing that you can claim is that it almost impossible to balance a card. First because this is very difficult for the experimenter. Secondly because, if the experimenter succeeds, air molecules will take care that the card falls either to the left or right side.
It is almost as if the evironment acts as an observer, collapsing the wave function.

Decoherence: How the quantum gets Classical

The uncertainty of the quantum superposition (picture left) is different from the uncertainty of classical probability, as occurs after a coin toss (picture right).
Such a difference does not exist. See Reflection 1 - Is there a difference between a card and coin?
A mathematical object called a density matrix illustrates this distinction.
The wave function of the quantum card corresponds to a density matrix with four peaks.
This is fact #1
The density matrix of the coin toss has only the first two peaks etc.
This is fact #2.
The true question to ask what is the physical cause of this difference.

Decoherence and the Brain

Spliting Reality

The Schrödinger equation that governs the universe as a whole can be divided into terms that the describe the internal dynamics of each of these three subsystems and terms that describe interactions among them
When you study any process (i.e. a reaction) than in principle it is possible to specify a set of equations which describe this process. Given certain tools than in principle an operator can control such a tool to reach a certain objective.
Helas, for the universe such a set of equations does not exist neither is the universe governed or controlled in any way. The universe evolves by itself completely independent by any human influence, full of mysteries.
For our quantum card, its dynamics predict that it will fall both left and right in superposition.
The only thing we know that a card will fall either left or right. The chance which direction it falls depents on the experimenter.
At least one neuron in her optical nerves would enter a superposition of firing and not firing when she looked at the card, and this superposition would decohere in about 10^-20 second, according to recent calculations.
No .
There is no superposition involved.

Looking Ahead

Reflection 1 - Is there a difference between a card and coin?

Is there a difference between how a card falls or how a coin is tossed?
From a physical point of view the answer is "Yes" because a card is much larger than a coin and a coin is much thicker than a card.
From a physical point of view a coin can stay balanced on its rim. A card will always fall on one of its sides.
The physical distinction changes and disappears when you make the coin as thin as the card and that, is important, when you perform the same experiment on both. The two become the same. That means the uncertainty involved in any experiment, with both, is the same.

In fact there exist no difference between the two of what is called in the article: Quantum uncertainty versus classical uncertainty.

For the density matrix this distiction also disappears.

Reflection 2 - Thought experiment

To perform thought experiments and specific to demonstrate quantum mechanics is very tricky. Specific you can not perform any thought experiment which involves superposition. You enter a world of may believe.
Specific you can not perform any thought experiment where water waves are in volved.
Specific to demonstrate what happens when the water waves go through one hole, or two holes to demonstrate interference patterns.
The same when electrons are involved.
In all these cases you should perform real experiments in order to see the complications and limitations.

The quantum card experiment is impossible with a real card. So why bother. What can you learn from it?

Reflection 3 - Schrödinger equation

The Schrödinger equation is the name of an equation which describes certain processes, involving elementary particles, in the form of a wave.
The problem is not so much what is the Schrödinger equation, but how are the parameters which are part of the equation, tailored or calculated, for a specific application. In order to do that you have to perform an experiment and make observations
And that is the problem.
What this means that infact you can never describe how any reaction or experiment performs using mathematics.
IMO this is a very unsatisfactory situation.

What this means is that the concept of collapse is not a very pratical way to perform science.

IMO the only way to perform science is to perform experiments and to perform measurements in order to quantify the processes involved. Measurements in principle always will influence the experiment (i.e. the reaction). Its the task of the experimenters to limit such influence as much as possible.
Using this philosophy does not legalize the idea that part of the process is in some superposition state nor requires the idea of wave function collapse.

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Created: 17 January 2019

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