Introduction to quantum physics


This page is old. The contents was moved in 2 parts : quantum states and measurements and quantum physics as related to classical mechanics.

Below are clues that I first wrote in a forum:

On the wave-particle duality : how quantum physics is articulated with classical mechanics

The descriptions of light in terms of waves on the one hand, in terms of particles (photons) on the other hand, are but two approximations of one the quantum law, that are each describable in the language of classical mechanics.
The description in terms of classical waves applies when the photons number is large and its value is undetermined (its undetermination is >> 1)
The description in terms of classical particles applies when the scale of the considered phenomena is much larger than the wavelength of the light involved.

These two domains of approximation have an intersection, a class of phenomena where they both apply, where both explanations in terms of particles or of waves are valid.
In fact this class of double approximation is very familiar to us as it is the way light most often appears to us in everyday life: it is the field of geometrical optics.

So, both "explanations" of the momentum of light, either in terms of the momentum of photons, or in terms of the force that the magnetic field applies to the electric current in a material absorbing the light, are equally valid, as two classical approximations of the same thing.

The same laws of geometrical optics can be "explained" in two ways: either in terms of classical particles or of classical waves. Moreover, the description in terms of particles can itself be reduced to a sort of third possible "explanation" by a pure space description getting rid of the time dimension, as photons have zero mass and go at the speed of light (too fast for us to track it): that is the laws of geometrical optics. A light ray (say, a laser one, with fixed frequency), can be compared to an elastic at equilibrium. An elastic that can be stretched without modifying its tension, whose value (equal to its linear density of energy, just like surface tension but with 1 dimension instead of 2) only depends on its environment (refractive index). The surface (say, an horizontal one) separating two materials with different refractive indices, exerts a vertical force on the ray; the point of intersection remains at equilibrium with respect to its horizontal movements slipping on the surface, so that the horizontal components of the tension on each side must stay the same. In other words, the amount of potential energy that each side would provide to this point for any given small movement on the surface, must cancel.
Now when the same question of geometrical optics is analyzed in terms of waves, the role of the potential energy is played by the oscillations number : for every small segment on the surface, the number of oscillations of the wave along that segment must stay the same whether it is measured on either side of the surface.
This is how we can see that different "explanations" in the language of classical physics, correspond to the same mathematical theory.

How can frequency be equated with energy or mass ?

This equality may seem difficult to understand as long energy is assumed to be a sort of primary physical substance before quantum mechanics is introduced and gives it further properties.

Instead, the real situation is that energy is a mathematical quantity that emerges from the laws of quantum physics, and that the frequency of quantum processes stands as the very definition of this quantity.
To understand how it happens that this quantity appears to us in the form of "energy", we need to remember the classical characterization of energy, that is a quantity which is conserved. So, to make a short story of that, the point is to explain the "law of conservation of frequency" in the same way as how it happens in quantum physics to give the conservation of energy.

Again this "law of conservation of frequency" can be directly experienced and understood as a daily life phenomenon, so to speak. All our radio communication systems are directly based on it. It simply says this: any radio wave emitted at a given frequency, is received anywhere at the same frequency. At least as long as all obstacles that the wave can bounce on, stand still. But if some object moves, then the frequency is modified by the Doppler effect. This corresponds to the case where a photon bounces on the object, and exchanges energy with it. The change of frequency has a precise value depending on the directions of the wave before and after, and on the movement of the object; it does not depend on how much of the wave bounces on it. Only two wave frequencies can be detected: the initial one and the reflected one (and possibly more obtained after bouncing on the object several times or through different trajectories), but none in between. So is the case for the photon: either it bounces on the object and exchanges energy with it, or it does not, but as long as we separately measure the different frequencies, there is no option in between.

How does a photon move and is it real while it goes until is it observed ?

A single photon cannot be detected at different places because the only way to detect it is by absorbing it. As the absorption of a radio wave cannot modify its frequency, its detection at different places requires this same frequency to be detected at different places. But if we start with only one unit of a given amount of energy, then we cannot get several copies of the same amount of energy at the end.

Arguments for the reality of randomness against the many-world hypothesis

Someone wrote the following supporting the many-world interpretation:

"I prefer to believe that the cat is neither alive nor dead, but that all possible versions of it continue to "really" exist, some of them alive and some dead, distributed in accordance with the probabilities derived from quantum theory, each in its own separate 3-D universe but all still part of a larger four-dimensional reality."

My reply:

Imagine an experiment producing a linearly polarized photon, and its polarization is measured by some detector in another direction forming an arbitrary chosen angle with the direction of the arriving photon.
In other words, it is an experiment with exactly 2 possible results with the "same quality" (one bit of stored information in the detector) but theoretical probabilities have an arbitrary value other than 1/2 each.

Now can you make sense of the claim:


I think such a claim is logically inconsistent. In other words, the idea of "real existence" of all possible results, is logically incompatible with the conformity of the effective (observed) probabilities to those predicted by quantum theory.
Thus, that the experimental verification of this conformity, refutes the idea of the "real existence" of all possibilities. Unless of course you find a way to make sense of the claim that a given precise scenario has x times more reality than an other if x is an irrational number, but I fail to figure out one now.

Let's further push the examination of the thought experiment:

Note that anyway, any possible "difference of quality" of the final state of the detector between both possible results, remains independent of the angle between the directions of arrived and measured polarization; and even if you consider the whole system "emitter + detector", I fail to see how to consider any "difference of quality" between its 2 possible final states (making the one "more frequent" than the other), in such a way that this "difference of quality" depends on the configuration of whatever optical device that could have been on the way of the photon and that could have modified the direction of polarization, without itself keeping any trace of its interaction with the photon.

If a possibility is said to "more probably exist" than another as defined by the ratio of the numbers of possible "final states", then it all depends on the time at which you choose to stop the experiment and make the count of the number of possible "final states". You may as well decide to cheat by waiting longer (make more experiments...) in one case than in the other before doing the counting, so as to change the ratio of these numbers. Finally, I think such a metaphysical definition of "probability" turns out to be empty and incompatible with the effective (experimentally verifiable) meaning of "probability".

Finally : if conciousness is divided (or multiplied) across all possibilities, then how can there still be anything "random", what is a probability, and how can it make any sense to claim that calculated probabilities are "correct" and can be or have been experimentally verified ?

Comments on the implausibility of an underlying classical mechanical determination, such the random appearance of a deterministic chaos

Nobody failed to think about the idea whether there could also be such an underlying reason for the appearance of randomness in quantum physics. Indeed, the idea of a fundamental randomness disturbed many physicists, and many tries at viewing this randomness as not fundamental but due to small causes, have been undertaken. If this may not seem visible from the outside, it is because for who clearly understands quantum theory, the hopelessness of such a quest may appear so quickly obvious that it is unworth publishing any article about the a priori feeling of philosophically uncomfortable character of the idea of fundamental randomness, before acknowledging the mathematical evidence for this hopelessness.

The fact that such tries of explanations have been abandoned and the fundamental randomness ideas have been kept, was not the result of prejudice or lack of imagination, but the result of a thorough examination of the theory and its experimental confirmations, that showed a heavy absence of any "reasonable" possible place for such hidden deterministic causalities.

It is easy to find great scientists from before that time [such as Henri Poincaré, and until Einstein], when these good reasons in favor of fundamental randomness were not yet known, who had such an opinion (a deterministic view). The fact is that such positions are now rather outdated.

But ironically, it also happens that even a hypothetical universe totally described by some "deterministic" classical physics, would produce absolutely random phenomena too.
And here is how:

Consider a physical system whose initial state is described by some quantity x=5.7843.....
After some chaotic processes, it arrives to a final state described by another quantity y that we can measure up to 5 decimals. The problem is that the determination of these 5 first decimals of y out of the exact value of x, must take account of, say, the first 1,000,010 decimals of x, as even a change of a decimal of x before the millionth may modify the value of y by several units.

In this situation, how can you meaningfully claim that "the first 5 measured decimals of y are not fundamentally random" ?

In my opinion, we can really consider them as fundamentally random, in the sense that, well, anyway, if the first thousand decimals of x are [whatever], then it will remain an excellent physical approximation to qualify its next thousands of decimals as "absolutely random".
Thus the excellent physical approximation of qualifying the first decimals of the final y as "absolutely random" too.

Finally, a classical mechanistic chaotic system is quickly full of randomness because the parameters of the initial state contain an infinity of digits of precision that, after the first few ones, necessarily turn out to be "absolutely random" for all practical purposes; and that intervene in macroscopic behavior very quickly.
[There are cases when this expression "for all practical purposes" can be used for subjective human dederminations that change over time. But this is not the case here. The global mathematical structure of the argument here needs to be closely examined, to see what non-trivial hints it can provide.
Some people react is based on the assumption that there is a fundamental difference between the "practical" and the "fundamental" aspects. Indeed of course there are some cases where the difference is clear, however there are other cases such as this, where, if you properly understand it, you will notice that the distinction between the "essential" and the "emergent" or "pratical" properties is effectively blurred - not just hidden but really broken.
That is the fallacy of essentialism that can "logically" lead to false conclusions such as those expressed by some Zeno's paradoxes.
See also the problem of renormalization in quantum field theory.]


This might even be worsened by the possibility of a chaotic process where the first decimal of a quantity depends on the 2nd decimal of its value 1 second before, which depends on the 3rd decimal 0.5 second before itself, which depends on the 4th decimal of its value 0.3 second before that, and so on, so that finally the number of decimals that it depends on, reaches infinity before a finite time interval.
And if I don't mistake, this may be the way things actually happen in fluids mechanics.

But this is all irrelevant because even if you choose to focus on the chaotic behavior of classical (macroscopic) systems, their very property of sensitivity to very small differences of initial conditions, drives the consequences of quantum fluctuations (random behavior) from their very small natural scales, to produce macroscopic effects.

As for some people's metaphysical argument for determinism: "any being that is at all a being must be a definite being, for otherwise it should fail to be a being at all", "randomness requires a being to not have a nature".

This argument can roughly be summed up as "Nothing can be half-real, half-unreal. Everything must either be totally real, or totally unreal".

In one sense we can see physical systems as real, so that physics is deterministic:
In the Schrödinger's cat experiment, the system deterministically evolves into a specific final state, which turns out to be more precisely some quantum superposition [dead cat]+[living cat].
But if you want to argue for a physical determination choosing between the dead and the living cat, then, well, there is a big problem.

In another sense we can see them as totally unreal:  since physical systems behave in a random way, thus we can say that they do not have a nature. So what ? Indeed, if you read my metaphysical view, you could see that I do consider physical systems as having no nature, but as being the mere expression of an articulation between both more fundamental natures : the concious and the mathematical ones.
Here randomness comes from the non-mathematical nature of conciousness, that produces a non-algorithmic behavior of its visit in the mathematical universe, visit which defines the physical processes. Now, if we focus on physical objects, which have a mathematical form, their non-algorithmic behavior has all the appearance of random processes.

But finally, if we want to understand how they work, then we have to articulate the different aspects.

The problem with the idea of an electron being a thing, is that when there are several electrons, they are the same thing.
Namely, if we initally have a system of two electrons, one in position A, the other in position B, then the system moves and finally observed as a system of two electrons in positions C and D, then quantum physics proves that it is exactly the same physical system (the same thing, as testified by interference between both scenarios) whether it comes from a movement of one electron from A to C and the other from B to D, or from the one from A to D and the other from B to C.

Similarly, quantum theory expresses the deep identity of nature of any two radioactive atoms of the same kind: they are indistinguishable, they have no clock inside them which determines when they will break. This is the reason why radioactivity is exponentially decreasing in time: no matter when they were created, radioactive atoms still have no age and thus each one that did not explode yet keeps the same probability of exploding in any time interval of a given length.
Einstein wrote:
God does not play dice with the universe.
Bohr wrote:
Einstein, stop telling God what to do!

Richard Feynman wrote:
When I sat with the philosophers I listened to them discuss very seriously a book called Process and Reality by Whitehead. They were using words in a funny way, and I couldn’t quite understand what they were saying. (...)
What happened [at the seminar] was typical—so typical that it was unbelievable, but true. (...). A student gave a report on the chapter to be studied that week. In it Whitehead kept using the words “essential object” in a particular technical way that presumably he had defined, but that I didn’t understand.
After some discussion as to what “essential object” meant, the professor leading the seminar said something meant to clarify things and drew something that looked like lightning bolts on the blackboard. “Mr. Feynman,” he said, “would you say an electron is an ‘essential object’?”
Well, now I was in trouble. I admitted that I hadn’t read the book, so I had no idea of what Whitehead meant by the phrase; I had only come to watch. “But,” I said, “I’ll try to answer the professor’s question if you will first answer a question from me, so I can have a better idea of what ‘essential object’ means. Is a brick an essential object?”
What I had intended to do was to find out whether they thought theoretical constructs were essential objects. The electron is a theory that we use; it is so useful in understanding the way nature works that we can almost call it real. I wanted to make the idea of a theory clear by analogy. In the case of the brick, my next question was going to be, “What about the inside of the brick?”—and I would then point out that no one has ever seen the inside of a brick. Every time you break the brick, you only see the surface. That the brick has an inside is a simple theory which helps us understand things better. The theory of electrons is analogous. So I began by asking, “Is a brick an essential object?”
Then the answers came out. One man stood up and said, “A brick as an individual, specific brick. That is what Whitehead means by an essential object.”
Another man said, “No, it isn’t the individual brick that is an essential object; it’s the general character that all bricks have in common—their ‘brickiness’—that is the essential object.”
Another guy got up and said, “No, it’s not in the bricks themselves. ‘Essential object’ means the idea in the mind that you get when you think of bricks.”
Another guy got up, and another, and I tell you I have never heard such ingenious different ways of looking at a brick before. And, just like it should in all stories about philosophers, it ended up in complete chaos. In all their previous discussions they hadn’t even asked themselves whether such a simple object as a brick, much less an electron, is an “essential object.”

Richard Feynman, in The Pleasure of Finding Things Out, wrote:
People say to me, “Are you looking for the ultimate laws of physics?” No, I’m not… If it turns out there is a simple ultimate law which explains everything, so be it — that would be very nice to discover. If it turns out it’s like an onion with millions of layers… then that’s the way it is. But either way there’s Nature and she’s going to come out the way She is. So therefore when we go to investigate we shouldn’t predecide what it is we’re looking for only to find out more about it. Now you ask: “Why do you try to find out more about it?” If you began your investigation to get an answer to some deep philosophical question, you may be wrong. It may be that you can’t get an answer to that particular question just by finding out more about the character of Nature. But that’s not my interest in science; my interest in science is to simply find out about the world and the more I find out the better it is, I like to find out…

Richard Feynman, in Lectures on Physics, volume I, wrote:
We cannot, however, predict when [an atom] is going to emit the light or, with several atoms, which one is going to. You may say that this is because there are some internal “wheels” which we have not looked at closely enough. No, there are no internal wheels; nature, as we understand it today, behaves in such a way that it is fundamentally impossible to make a precise prediction of exactly what will happen in a given experiment. This is a horrible thing; in fact, philosophers have said before that one of the fundamental requisites of science is that whenever you set up the same conditions, the same thing must happen. This is simply not true, it is not a fundamental condition of science. The fact is that the same thing does not happen, that we can find only an average, statistically, as to what happens. Nevertheless, science has not completely collapsed. Philosophers, incidentally, say a great deal about what is absolutely necessary for science, and it is always, so far as one can see, rather naive, and probably wrong.

By the way, do you know any example of a kind of "random" process that once seemed random in such a way that a precise probability law has once been formulated and appeared rather well confirmed by observations, until such causes were finally found that made the exact behavior predictable (or at least predictable with much better chances of correctness than by the former probability law) ? I cannot think of any.
Well, of course there are some obvious not-really-examples such as:
The ability to test and predict for a pregnant woman whether the baby will be male or female (not predictable before fertilization with unselected sperm)
The weather for tomorrow has never been given a seriously precise probability; the improvements to weather forecasts were painful but straightforward and remain impossible for the long term.
No probability laws were ever formulated for the movements of planets in the sky before understanding their precise orbits
Some refinements of formulas used by insurance companies and traders
The practice of insider trading
Improvements in the prediction of earthquakes remain slow and gradual.
The spreading of illnesses had not been given probability laws in the past, and is still not much predictable now.

Anything more striking than this ?

Reference to another author

Some years ago I read a book in French by Valerio Scarani, introducing quantum physics for a large public and focusing on its paradoxical aspects about randomness. Thus somehow the "metaphysics" of quantum theory except that the author seems to not have any precise metaphysical orientation, or more precisely, he describes all as if it was not metaphysics. He just focuses on accurately reporting the current state of science on quantum theory and its logical implications.
Now I see there is also an English version (however it is a book for sale, not free access) ; but you can also visit the author's blog. In that article he explains that we have a theorem stating some alternative we must make between different metaphysical hypothesis for compatibility with the experimental verifications of quantum physics, and his personal choice is that we have pure randomness because the available alternatives seem less plausible to him. If you want to reject randomness then you must choose an alternative, and be warned that it may make things worse than you are currently expecting.


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