|Chapter 1. ||What can we expect from quantum me mechanics?|
| ||1.1. ||Who was the first physicist to blame quantum mechanics for a sin of nonlocality?|
| ||1.2. ||Any physical theory must be a local theory! Or, maybe, not?|
| ||1.3. ||What kind of non-local interaction is allowed in quantum mechanics and what kind is forbidden?|
| ||1.4. ||A quantum state cannot be observed directly|
| ||1.5. ||Spin as angular momentum|
| ||1.6. ||What is the spin projection?|
| ||1.7. ||Quantum nonlocality in pure form|
| ||1.8. ||Is it possible to outflank nonlocality?|
|Chapter 2. ||Discrete motion as a key to undestanding of quantum processes|
| ||2.1. ||Is there any alternative to continuous motion?|
| ||2.2. ||May a single particle be in two remote places simultaneously?|
| ||2.3. ||Three rules for discrete motion|
|Chapter 3. ||Quantum mechanics made simple|
| ||3.1. ||Pictorial presentation of quantum motion|
| ||3.2. ||Probability density|
| ||3.3. ||How probabilities can be summed up?|
| ||3.4. ||The law of addition for probabilities or why physicists use complex numbers in quantum mechanics|
| ||3.5. ||Wave ?function is a mathematic image of quantum state|
| ||3.6. ||Object's quantum state as a history|
| ||3.7. ||How we find a quantum state and build wave psi-function|
|Chapter 4. ||Why Einstein refuted quantum physics?|
| ||4.1. ||Einstein puts a pointblank question|
| ||4.2. ||Probability function for a white ball in a black box|
| ||4.3. ||Probability function for a quantum object|
| ||4.4. ||Einstein's position|
| ||4.5. ||Experiment with clock-work and further events|
| ||4.6. ||Why the exact coordinate is a concept without any sense|
| ||4.7. ||Nonlocality as a key moment of dispute|
|Chapter 5. ||Quantum logic|
| ||5.1. ||Wave-particle dualism|
| ||5.2. ||Can the quantum state be changed without impact to the object?|
| ||5.3. ||Wheeler's experiment with deferred choice|
| ||5.4. ||The Mach-Zehnder interferometer|
|Chapter 6. ||Einstein ? Podolsky ? Rosen experiment|
| ||6.1. ||Experiment formulation|
| ||6.2. ||Bohm's experiment|
| ||6.3. ||Photon polarization|
| ||6.4. ||A conclusive experiment|
| ||6.5. ||A trap of reductionism: only atoms and only void|
|Chapter 7. ||Quantum exotica|
| ||7.1. ||What can we expect from a good interpretation?|
| ||7.2. ||Why does interference disappear?|
| ||7.3. ||A quantum eraser|
| ||7.4. ||Quantum cyborgs|
Chapter 1. WHAT CAN WE EXPECT FROM QUANTUM MECHANICS?
When a person starts contemplating deeply on the subject of
quantum mechanics, he/she often becomes frustrated and fails to
understand ins and outs of this theory. Therefore we are
obligated to warn a reader what exactly he (she) will
encounter in this book.
1.1. Who was the first physicist to blame quantum mechanics for a sin of nonlocality?
Although I got my education at the Physics department in
Novosibirsk State University and we attended lectures on quantum
mechanics delivered by a famous Russian physicist Joseph B.Khriplovich, I did not hear a word about "quantum
nonlocality". I even cannot remember that our teachers
pronounced this word during my education course in university.
I remember how I heard about this concept at first time -- it
was merely by a chance. Once we returned home after a soccer
game and had a discussion on science on a way back to home. My
friend George told us bravely:
-- I cannot accept completely quantum mechanics because this is
a nonlocal theory.
George reallocated to Novosibirsk's University from another
site. I don't know who his previous lecturer on quantum
mechanics was. And sometimes my friend uttered the phrases
difficult to grasp immediately. I tried to grasp the meaning of
this phrase and asked:
-- George, what do you mean by "nonlocal theory"?
-- A nonlocal theory is a theory that admits a possibility of
instant action over a big distance. For example, the Newtonian
theory of gravitation supposes that gravitational impact is
transmitted instantly from one body to another.
-- What the stuff are you talking about? The age for nonlocal
theories had ended in the eighteen century. I suppose, even at
that time nobody believed that instant spreading of action is
real. After Faraday introduced the concept of a field into
physics, it became clear that any interaction occurs due to
a specific field and being spread with a final velocity. I don't
buy it! -- quantum mechanics was formulated after Relativity, so
it cannot be nonlocal theory! Most probably, you are talking
about non-relativistic quantum mechanics, which describes motion
of bodies with velocities much slower than the speed of light.
In this case we can disregard the time delay in interaction. But
if you want, you can take into account this delay.
But George insisted: nonlocality is the essential part of
quantum mechanics! You cannot remove nonlocality without
destroying the edifice of this theory.
These words were absolutely against my current vision of
scientific world, so I did not take his words seriously. If
quantum mechanics were a nonlocal theory, our professors in
university would have told us about this bizarre aspect and we
would discuss this at our seminars. But as I wrote already, we
had not discussed the concept of nonlocality in quantum
mechanics in classes; even more, this word was not uttered at
My scientific interests were not directly related to quantum
mechanics; however, they overlapped often with this theory. When
this happened, I have to go deeper and deeper into mysterious
and wonderful world of quantum mechanics. "Wow! -- I told
myself after the next occasion. -- Now I start to understand the
meaning of Niels Bohr's famous saying :
Anyone who is not shocked by the quantum theory does not
In some moments I had a feeling that I have just grasped the
deepest paradoxes of quantum realm. It seemed to me that the
quantum realm cannot present a more inconceivable and bizarre
idea that has settled down in my mind recently. But after a next
occasion I again was perplexed and confused: the "previous"
paradoxes had dimmed on the background of a "new" keen paradox.
As for the subject of nonlocality, I remember a story told us by
a professor from my university: he shared his reminiscence about
working together with a great Soviet physicist, Lev Landau.
Usually Landau's discussions with colleagues about paradoxes of
quantum mechanics were wrapped up with the phrase: "In general,
this is clear now, although some tricky questions remain, but
only Bohr might have ready answers for those" . These words
get stuck in my mind. Even great L.Landau did not know all
answers to some questions, and he was bold enough to admit this
fact in public. I think that some of these tricky questions were
generated by problem of quantum nonlocality.
Gradually, fancy melody of quantum realm became more clear,
closer, and habitual for me. Ultimately I had an insight. I
comprehended the elegance of "quantum jumps" and the beauty of
Now I know enough about nonlocality to write this book. I hope I
can explain this quantum phenomenon in clear and simple language
in a manner accessible both for experts in quantum mechanics and
Even more, I believe that teaching of quantum mechanics should
be started from the story about nonlocality. In a similar way,
before a teacher explains the Newtonian law of gravity, he/she
usually stars talking from an example of orbital motion of
Earth. It would be silly to give this message later. In the same
way, we should inform our listeners about effect of nonlocality
before we start writing the formulae of quantum mechanics.
Actually, this phenomenon is rather simple. It is comprehensible
not only for colleague students, but even for high school
students, as well for anyone who wants to know better the
edifice of this Universe.
Nonlocality is simple!
The only barrier on this way is prejudice against this
phenomenon. Today most of physicists are somehow convinced (and
I was among these ranks too) "that's impossible because this is
incredible". Here we should remind the golden rule of physics:
only properly arranged experimentation can decide what does
exist or not in nature.
"Gradually, the fancy melody of quantum realm became more clear, closer, and habitual
for me. Ultimately I had an insight. I comprehended the elegance of "quantum jumps"
and the beauty of nonlocality concept. Previously mysterious and bizarre things
became simple and clear. I even felt a slight nostalgia for the period when I wandered
by the surrealistic realm of quantum world and was bumping weird things here and there.
Now it is time to use all this -- wave-particle dualism, nonlocal connections, and
quantum jumps, -- in hi-tech industry. If we want to put technical devices onto a higher
level, we should work with quantum theory approach."
"The book introduces the reader to the world of quantum mechanics. Original author's style,
deep insight into the fundament of the subject thrill the reader immediately. I recommend
this book to those, who want to understand the beauty of Nature without equations."
D. A. Chestakov, PhD in Chemical Physics (Holland)
"Recently, I came across a book of Vasily Yanchilin entitled "Quantum nonlocality".
For more than twenty years I have been interested in "Einstein-Podolsky-Rosen" paradox and
successful experimental testing of nonlocality of quantum mechanics. I find the book
of Yanchilin very interesting from both historical point of view as, for example,
a detailed analysis of debates between Niels Bohr and Albert Einstein on quantum nonlocality
and Yanchilin╥s own new interesting concept of "discrete motion". The latter concept
was ingeniously used to explain many phenomena in the quantum world, which are "bizarre
and peculiar both for a young researcher and for a recognized scientist" as has been
admitted by Richard Feynman. I highly recommend this interesting book for both students
O. N. Antzutkin, Professor, Lulea University of Technology (Sweden)
and Professorial Fellow, The University of Warwick (United Kingdom)