There is, of course, the final, the ultimate ending of a discussion: "I can't prove your are wrong. I can't prove I am right. I don't want to discuss my axioms. But I disagree with you anyway become I don't want to agree with you."
It has a spout to drop balls through, a board with pegs, and channels to collect falling/rolling balls.
The picture created by Feynman was beautiful and clear. An electron can travel along all trajectories at the same time (how - who cares! why - who cares! it's an electron, not a ball, so - why not?). For each possible trajectory, Feynman could calculate the probability of an electron traveling along that trajectory.
Balls just do not have amplitudes, but electrons do.
Those mysterious “amplitudes” which have to be used for calculating final probabilities are closely related to wave-functions.
Richard Feynman was a genius also because he invented a method to visualize complicated calculations, and that significantly lowered the difficulty of mental operations required for carrying out such calculations (like an invention of an excavator for trench diggers). After mentioning that fact (sorry in advance for double negative) I just cannot not to pock - again - people in the field of artificial intelligence. I can bet a million dollars that within ten years from now there still will be no developed artificial intelligence system such that could match the creativity of Richard Feynman. For anyone who may be interested in - why, I would recommend to start from reading "Relax! The real AI is not coming any soon!".
Feynman was fine with his interpretation (naturally). And everyone who seeks a different interpretation needs to be strong enough to go against Feynman (or his spirit).
The majority of scientists is divided into two large groups. People in one group don't even know that quantum mechanics has some internal difficulties. Nothing is rotten in the state of Denmark. And BTW: if everything is fine, why spend money on research, offer promotions, tenure? People in another group prefer pretending that everything is fine; they know it is not, but they have no intention to do anything about it (this is not going to help getting money on the research, promotions, tenure).
“Breaking news” – I just (12/03/2018; 21:35 pm) learned about this paper “Quantum theory cannot consistently describe the use of itself”
There is another one in the same series:
"A tennis ball is released 5 m from above the ground. Solve the Schrödinger's equation for the ball and find its wave function for t > 0".
When presented with such problems a physicists would say that those problems do not make any sense. For example, a spin is a specifically quantum variable and only quantum objects can be described using that variable. In principle, the Schrödinger's equation should be ably to be applied to any objects, including all macroscopic, i.e. classical, objects, like a tennis ball, but no one would do that. In fact physicists do not even know for sure how to do that (that is what decoherence theory tries to understand).
In short, using quantum theory - in its current state - for describing the behavior of macroscopic objects is simply wrong because it means applying a theory beyond the limits of its applicability, exactly like using classical theory for describing
the behavior of microscopic objects- it is wrong!
Now I would like to make only one short comment:
As "an observer" a scientist who is a part of an experiment can do only one thing - register states of other classical systems. But he cannot think. Thinking is not a part of any physical law, not classical, not quantum. The only observer/thinker who can think is the who reads the paper (i.e. the one who makes an interpretation of all the data provided by the measuring devices - classical objects/systems).
The fact that logical paradoxes exist does not make formal logic wrong.
The fact that a paper uses scientific terminology does not make it yet scientific.
I would like to stress again that if a system includes "a reasoning device" (a.k.a. observer), this system does not belong to physics. If term "observer" ("agent", etc.) only represents "a registering device" (a.k.a. "measuring device"), there is no reason to keep that term at all.
Maybe this particular paper would have no logical inconsistencies left after all "observers"/"thinkers"/"reasoners" would have been replaced with just measuring devices which can have a specific set of states, or maybe not, it is the responsibility of the authors to make that check.
A scientific paper cannot have any ambiguity. Term “observer” brings that ambiguity.
Some time ago the editors of all scientific magazines stopped accepting papers on the development of a Perpetuum Mobile.
It is a time for editors to stop accepting papers on quantum mechanics which describe an observer as an intrinsic part of a quantum system. And for the scientific community - there is simply no reason for paying any attention to such papers.
And now, after all the logic about the role of an "observer" the final nail in the coffin.
When describing the though experiment authors write, quote: "Agent W could instead model agent F's lab as a big quantum system".
Right here we find the reason for this whole article being wrong.
There is no such thing as "a big quantum system".
A system is either quantum, hence microscopic and can be described by the quantum theory - in its current state.
the system is big, hence macroscopic, and CANNOT be described by the quantum theory - in its current state.
Remember two problems about a tennis ball?
Now you know the reason we talked about them in the beginning.P.S. What I am kind of also curios about is how would we explained the way magnetic field acts on an electron - but using QED? I mean, Stern-Gerlach experiment treats magnetic field classically. But we all know that in quantum reality we have to use photons. So, when an electron is traveling through a magnetic field it is being bombarded by photons. An electron has a spin, and photons are polarized, so it is not just the standard Compton effect. And one collisions should not be enough to make the beam of electrons split in "+" and "-" z-components.If we consider only an individual collision between one electron and one photon, how does an electron "know" in which direction is the magnetic field; how does an electron "know" that there is a magnetic field - for an electron there is only one photon which collides with it?
Saying that "a single photon is reflected by a mirror" is not much different from saying "Mars population of unicorns doubled".
A single photon simply cannot be reflected by a mirror; reflection is a macroscopic phenomenon describing the result of an interaction between a wave and a matter; or between a large number of photons and a matter. A single photon can only interact with matter, be absorbed, and then a new photon is released. The new photon does not have to "carry the torch" of the first photon; there is not reason to expect the photon leaving the device (mirror, splitter) must behave in exactly same way as a hypothetical reflected/transmitted photon would behave. The direction of the new photon does not have to obey the law of reflection; only on average, when many photons absorbed and released the wave traveling away from the material object called a "mirror" will be described by the law of reflection.
If an experiment assumes using laser beams, that automatically assumes the use of large number of photons, hence, light can and should be treated as a wave - automatically.
BTW: it means that experiments designed to study entanglement using photon are wrong. Not the idea of entanglement - that remains to be investigated. But the experiments based on photon interference, because the photons which interfere in the end are not the same photon which are prepared in the beginning, and there is no clear connection between those photons (at last, to my best knowledge).
The majority of my ideas come to me while I am in traffic or in a swimming pool. During a day there is not much time to formalize them in a fashionable way. This blog is the best I can do (so far, let's wait for retirement).
The idea for this Appendix came in traffic, and for the next one - in a swimming pool.
After a ninety-year long discussion, physics community still have no commonly accepted understanding of the origins of quantum mechanics and keep searching for those. Some experiments (at least thought experiments) which try to demonstrate inconsistency or internal contradictions in quantum mechanics are being discussed on a regular basis. This means that all the hype about quantum computing so far is, well, just hype. Kind of a scientific way of money laundering. Cool! Exciting! Yes - promising (no one knows yet exactly what?). But so far - a hype (exactly like AI).
I am not a physicists, so why am I so confident in my assertions?
Well, I have taken all the same course physics PhD candidates take in the U.S. (checked). But I also had to take additional philosophy courses, because every university student in Russia had to take (plus a philosophy course required for PhD students). Many students hated those course, but I liked. And after my graduation I kept reading a lot professional and popular literature on the origins of science in general and quantum mechanics in particular. On the top of that, I had be able to develop so deep understanding of the matter so I could explain it extremely clear to my student (which is reflected in my student evaluations).
In his 1948 paper “Space-time approach to non-relativistic quantum mechanics” Richard Feynman wrote two equations
represents the probability amplitude for the happening of event C if event A has happened before that, and the probability of that to happen is directly and simply related to its amplitude:
I’ve asked this question before, but I want to repeat it again, because from my point of view this is the most fascinating problem of quantum physic: why does the universe needs amplitudes? What do quantum particles have what classical don't? What do quantum particles lose when they become classical? Of course, the can't become classical by growing up. The become classical by joining together. When more and more quantum particle join together and form a large classical object, it seems they lose something. It kind of contradicts the laws of large systems called "synergy": properties of system are richer, broader than the sum of the properties of its parts. But quantum particles seem having no synergy. Or, we are missing something very important about them.
I believe that the answers to these questions will automatically remove all other remaining question about the origins of quantum mechanics.
How would we approach the answer to this fascinating question?
We know that there is (kind of) a way to “derive” Newton’s laws from quantum mechanics. That means, if we would use a similar approach, equation (5) should eventually transform in equation (4).
But what we are looking for is for clues, which could lead us from equation (4) to equating (5).
For example, we could imagine that probabilities P also depend on some “hidden” variables and equation (4) is the result of taking the sum over all those variables. The “actual” equation should be in some other form, like (5).
This idea my lead us to searching for some type of more general definition of “probability”, beyond the standard definition based on counting events.
It also may lead us to take a new look at the classical examples which are commonly used to understand how probability works, and trying to find new views on those examples.
One of such classical examples is running a die.
When it stops, it has only one of the six possible states.
Here I would like to pause for a moment to have a short discussion about the meaning of this term “state”, because lots of confusion comes from using this term and implying many different meanings.
There is a statement we can make about anything in the universe; we can make the statement about everything in the world; about any object, about any system.
This statement is very simple and clear:
everything in the universe exists and evolves.
This statement, however, represents an axiom, a basic fundamental principle; basically, it is a belief; we believe that everything in the world exists and evolves.
Of course, the statement is a result of a long practice, which includes many experiments, discussions, long and deliberate thought process, but in the end this statement cannot be logically derived from any other statements. If it could have been possible to derive this statement from other statements, than those other statements would have been axioms and basic fundamental principles.
The fact that something exists comes from the realization that that object or system is not alone; it is different from something else that surrounds us. To describe that difference, we start searching for various attributes of this object or system which would allow us to differentiate it from other objects or systems. A set of such attributes allows us to describe properties of an object which are usually described by a set of variables or parameters or quantities to which we may be able to assign some numerical values. The examples of those parameters are mass or charge.
Objects or systems evolve. Evolving means they change, the become different from themselves. To describe those changes, to describe that evolution were also search for some attributes, which can be described via a set of parameters. When we select that set of parameters we say – we can describe the state of an object or a system.
When we say “state”, we mean parameters which we use to describe how system changes, how it becomes different from itself. And usually, we do all we can to minimize the set of such parameters, and if we have other parameters we use to describe the existence or the evolution of a system, those parameters usually can be described in terms of the parameters we use to state the state of a system (pun intended).
For a classical point-like object the state is given by six variables.
For a quantum point-like object a common definition of a states is via a wave-function. However, from my point of view, the jump coordinates and components of velocity to a wave function is too large. That is why I define as a state of a quantum particle its three coordinates.
When a classical particle evolves, we study the evolution of six variables.
When a quantum particle evolves, we study the evolution of three variables.
There should be a way to reconcile those two evolutions (which is my belief).
But we need to study a such classical particle that exhibit behavior some kind of similar to a quantum particle.
That is why a die attracts my attention.
Before it reaches the final resting state, it evolves in a complicated unpredictable manner.
We could try to develop the exact description of that behavior (at least in principle) and see if it gives any hints on a similar unpredictable behavior of quantum particles.
First, we need to introduce a variable which describes the state of a die during the process leading to the final state, which is a die with a specific number on its top face.
We can imagine a vector inserted inside a die, which moves with it. In the final state this vector may point up, down, or be horizontal. When it is horizontal, we still cannot make a statement about the final state. To do that we have to add two more vectors; basically, we need to describe a die as a rigid body with a Cartesian reference frame inserted in it (no surprise here! A die is a rigid body).
We should write the Newton’s law for a die; solve it for the parameters describing its evolution/motion (transnational plus rotational), but in the end, we need to strip off all the information except z-components of each vector we stuck in a die (the one and only, the beloved "function collapse"). One of those components will not be equal to zero, and will be either positive or negative, and that will tell us what number will the die have on its top face.
The problem is that when a die rolls the forces acting on it are unpredictable, random.
That means, we have to apply a stochastic method for analyzing the evolution of a die.
A stochastic interpretation of quantum mechanics exists.
One of the proponents of the interpretation is Prof. Lee Smolin, whose book “Troubles With The Physics” I love.
My mathematical apparatus is not strong enough to assess if his approach answers my question “why does the universe need amplitude?”
However, I hope that the pressure on the existing approaches (hidden variables, decoherence) would bring more attention to his (and other proponents of stochastic) work.