In the world of our scale - planets,
humans, ants - could follow Newton's laws:
if we know the position of something,
direction, and speed, we can determine
its past and future position
(ignoring the variables, of course).
The billiard balls follow a predictable
behavior and everything else also
seems to respect the laws of motion
and Einstein's Theory of Relativity.
Quantum mechanics can determine
with complete accuracy the
microcosms behavior, but no one
can explain this behavior.
We can say that we enjoyed the success
that the theory had (all our digital
technology is based on quantum mechanics,
like many other relevant techniques),
but the microcosms behave
in such a strange way
that our shared sense
not able to understand.
Well, what about the microscopic world?
How to behave atoms and
subatomic particles?
The behavior of the most basic units of
nature can be considered schizophrenic:
subatomic particles can be in two
places at the same time, behave both as
waves and as particulate matter and
can go from point A to get to B...
before leaving it can also
go from point A to the
point B, C, D, E (etc.,
etc.) at the same time!
Never able to determine
with complete accuracy
where you are and where you're
going a subatomic particle;
if we know the position of
an electron, for example, we
lose the information of its
direction, and vice versa.
There is always an
uncertainty (Heisenberg
Uncertainty Principle) in
the microscopic world.
To help the party, subatomic particles
are in perpetual motion and may
disappear from your room and appear
in China or Jupiter ... instantly!
Our universe seems to have two
behaviors: our range is predictable
and boring, at the level of atoms
is unpredictable and crazy.
Scientists try to "unify" what
we know about the macro- and
microcosms in a single theory: the
so-called "Theory of Everything."
Some historical aspects
The fable above describes in a reasonable
manner, albeit with some reservations,
the status of physical after
the emergence of quantum
mechanics in its present
form in the mid-twenties.
Perhaps the major difference is
that, in the case of physics, there
was no group of wise travelers
giving us with the new weapon.
A more accurate analogy would
be to say that our friends just
stumbled on rifles and found how
to shoot by trial and error,
while some of them, more astute than the
others, prepared the attempted explanation.
At this point in history enters
the scene our friend questioner,
who in real life did not correspond
to one, but various physical,
which drew attention to
conceptual inconsistencies and
diverged from the prevailing
view in different ways.
Among them, the most notorious were
undoubtedly Einstein, who never
accepted the orthodox interpretation
of the formalism of quantum mechanics,
known as "the school of Copenhagen D".
There are no words to describe the
resounding success experienced
by quantum mechanics in the
twentieth-century physics.
It is surely the most successful
theory in the history of science.
Their results explain the nature
of the behavior in dozens of
different areas, their Mo forecasts
verified by perfect experience
(coming sometimes to reproduce
the experimental data
to the eighth decimal
place), its applied use
is the basis of
microelectronics, a science of
materials, laser technology,
modern chemistry.
The behavior of light,
metals, superconductors,
organic molecules, atoms,
nuclei, elementary
particles obey him blindly,
and to this day do
not know any limits of
validity of the theory.
In other words, the material world
is, without a doubt, quantum.
This state of affairs explains
the indifference that the bulk
of the scientific community
nurtures the foundation issues.
But at the same time, it
emphasizes the importance of these
because the fact is that the
sixty years of its discovery,
the most basic and comprehensive
theory of modern physics
have not had their nature
embraced by us entirely.
Show that these difficulties are
indeed severe and disturbing, and
what the range of alternatives that
we are the goals of this work.
In the remainder of this opening chapter,
we discuss briefly the conceptual
assumptions that always adopted
the elaborate a physical theory.
Then quantum mechanics is presented
succinctly in its current formulation.
Finally, to illuminate and highlight
the oddities of the theory, we
present and discuss three specific
situations (thoughts and experiments)
where forecasts of the
same actively violate
our intuition, and they
even seem paradoxical.
In the next chapter, when
we discuss the different
interpretation of the
formalism of alternatives,
we will use these situations to test
them and shed some light on them.
Like the last comment, I
would point out to the
uninitiated that the
adjective 'quantum c',
used to describe the theory,
does not bring itself worthy any
particular meaning of note and should
be its use to historical reasons.
Throughout this work we will use
the terms 'quantum mechanics'
interchangeably 'N quantum theory',
'quantum physics' and 'quantum theory.'
A Little bit of Philosophy
Almost all of us who are dedicated
to the physics, mathematics or
philosophy already had fun, at least
once, with the solipsistic argument.
It is that line of reasoning
that says that the
only reality of the world
is your consciousness,
and all sensory by you experienced,
whether visual, auditory or
tactile, a mere hallucination - dream
even - generated by your mind.
There is, therefore, no
reality outside the material
and independent of you, there
are only your feelings,
and your conscience is all illusory
rest: the chair where you sit,
the floor, your body, and all
others - including I tell you that.
The solipsistic argument is fun for two
reasons: to be unanswerable, fascinates.
Also, since it adopts, it
will not go any further.
We stayed for a few
minutes to laugh at
imagining a discussion
between two solipsistic,
each firm and/what
the other is only a
hallucination of his mind,
and then forgotten.
There is not much to do
when it is solipsistic.
But at least in one aspect
solipsism is quite useful:
it underscores the fact that the
only unquestionable realities are
my conscience and my feelings, all
the rest being subject to doubt.
Lest we fall in deadlock already
mentioned, we need to go further
and adopt the hypothesis that
other people as much as I,
are also endowed with the
conscience (feelings and thoughts).
It is where the game
starts and once you choose
this line, the following
steps are necessary.
How to explain the fact
that two different people
perceive the same things,
at least apparently?
That is, both claim to see
and hear the same stuff,
the book on the table, the
barking of the dog, etc...
The solution is to postulate the existence
of something external to our consciousness,
which is the source of those feelings which
we both give the name of, say, "book".
Here it is appropriate
to call the reader's
attention to a question
that often goes unnoticed.
This entity whose existence just
postulating is that it generates, somehow,
the sensations experienced by us,
but not to be confused with them.
These two beings, although
somewhat related, have different
natures, because this is a
fact and that a hypothesis.
Consider, for example, the fundamental note
there, which is the sound wave of 440 Hz.
That there is absolutely
no connection between the
musical note and vibration
in the air is easy to see.
If we can disconnect the acoustic
nerve auditory region of the brain
and reattach -10 in the area that
processes visual information,
every time someone play
violin near us catch
sight a flash or any
other visual sensation.
The analogous reasoning can
be carried out with the
electromagnetic wave of 5,500
A and the feeling “green H”.
We can, of course, argue that the links
between sensation and matter are
given at the level of nerve activity
in the brain, and not on the above.
We end, therefore, by bumping the problem
of mind-body relationship, which
is a matter still open, not only
scientific but also philosophically.
What we can do concerning this is to assume
that, despite having different natures,
there is at some level a direct
correspondence between sensations and a
particular group of physical phenomena
(e.g., nerve activity in the brain).
According to this hypothesis,
implicitly science always
assumed, consciousness is no
more than a shadow of matter,
an 'epiphenomenon' as the
philosophers say, allowing us
to limit ourselves to describe
the activity of matter,
whose internal dynamics only
depend on itself, as we shall see.
Starting from our consciousness, a
level unquestioned - fact, we decided
to accept another's knowledge to
escape the solipsistic doldrums.
From this point we
are led, almost
inevitably, to adopt a
series of hypotheses.
The first is that there is
something that produces various
sensations correlated minds
(matter, the concept substance).
The belief is blind that the existence
of something is independent of mind.
"The moon is there when
no one is looking" or
"Neptune existed before
being discovered".
Moreover, we usually go further
and make the hypothesis, indeed
quite high that mind does not
affect in any way the matter,
even though it affects
the mind by definition.
In other words, fully assume,
as we have said, the idea
that consciousness is just
an epiphenomenon of matter.
In term of this conceptual
framework, the science project
becomes evident: it is
simply to discover the laws,
expressed mathematically, describing
the internal dynamics of matter,
and in possession of, predict and
explain phenomena all of the nature.
Since the test for our knowledge are
the observations and experiments,
completed the total objective of science
with the following assumptions:
that the disturbance introduced
by the measuring device in
the observed system can always
be made arbitrarily small,
or at least inferred and calculated,
and that the interaction
of said apparatus to the
observer's mind is safe
(this is a particular case this hypothesis
exposed in the previous paragraph).
It is the picture that always ruled
classical physics, and for three whole
centuries (the seventeenth to the
nineteenth) was an absolute success.
But it is far from obvious
or compulsory conceptual
framework, as it might
seem at first glance.
On the contrary, a large number of
assumptions that have to be made, and
all the guarantees their validity
is their suitability to the facts.
The science and physicists of the
past were aware of this situation
shows us the Helmholtz article, where
part of this issue is discussed.
But, after all, how what was discussed
here affects quantum mechanics?
In fact, it is the opposite: how quantum
mechanics affects what was discussed here.
The issue in question in Quantum Mechanics
is above all conceptual in nature
(which does not mean that your solution
brings verifiable news experimentally).
Some proposed solutions,
as you shall see in the
next chapter, involve the
abandonment of one or more
cases among those cited above.
It is the case of contributions of von
Neumann, Wigner or Bohr, among others.
With these considerations in
mind, let us now turn to the
presentation of quantum theory
in its aspects capital.
THE THEORY
The undoubtedly fascinating
oddities of quantum
mechanics stimulated
countless disclosure
attempts at a level accessible to laypeople,
the main features of the new theory.
Such texts are quite
common in newspapers,
journals in science, or
basic physics books.
The goal of all is always
the same: to note the
essential differences from
the classical physics.
0s points, in general, are focused or
wave-particle duality, or the uncertainty
principle or quantum indeterminacy, or the
apparent active role of the observer.
However, it seems that none
of these features is the
most appropriate way to reach
the heart of the matter.
Another factor here plays the central role.
Any physical theory consists
of a set of statements
which we call laws or
N c <postulates B.
Thus we have Newton's laws
of mechanics, the laws of
electromagnetism, the postulates
of quantum mechanics.
These laws define and relate
the concepts involved in a
quantitative manner so that we
can verify them experimentally.
All this is commonplace for anyone
connected to the technical area.
The difference between quantum
theory and other theories,
which is nothing visible,
lies in another point.
It is the fact that these are all without
exception ontological principles
- i.e., its statements describe how the
material world is, how it behaves.
Behind these declarations,
it is always an implicit
model, picture, a hypothesis
about how things are.
On the other hand, is never
said not a word about how to
verify the laws on how to measure
the relevant parameters.
It is because in the classical
theories to medicate
the processes are always
considered distinct,
and in principle can always be done
carefully so as not to interfere
significantly with the experiment,
consisting of the art experimenter.
Take, for example, Newtonian mechanics.
Here the world is of
material bodies moving in
deterministic mode space
(predicted) over time,
and interacting by mutual forces
that can be described mathematically
forces such that alter the motion
of bodies equally known manner.
In the case of electromagnetism there is
also no doubt about who the characters are,
what there are material bodies
endowed with electro cargo loads
that generate these space around
well-defined electric fields,
which in turn act on the
charges alternating - their
state of motion, and can,
in certain circumstances,
be self-sustained without the
presence of loads, constituting
the so-called electromagnetic
waves, which light is an example.
In this respect, even the theory of
relativity is no longer a classical theory.
There is no doubt about how to
observe the world, what are the
observed objects, how to relate the
data obtained by two observers.
The only relevant question
in this conceptual theory
concerns the new status of the
concept of time caused it.
About what concerns us, it
is as classic as the others.
Let us return now to quantum mechanics.
Early in the century a series of
phenomena, all connected in one
way or another to the microscopic
world (on the scale of atoms),
challenged the scientific community to
explain it using the known laws of physics.
Initially, the situation
appeared to be simply a case
of inadequacy of the latter
to the microscopic world,
then simply find out which
rules correctly describe the
atomic level without contradicting
the existing physical.
But the reality was different
(in more ways than one).
The physics community then was forced to
admit that, contrary to what was assumed,
the measurement process is
not evident and suffers
essential and perhaps
irremovable restrictions,
and therefore it was imperative, first of
all, know the nature of these limitations.
And so we come to the postulates of
von Newmann of quantum mechanics.
Unlike all other statements of physics,
it is not a statement ontological but
epistemological, i.e. refers not to how
things are, but what we can know about them.
It certainly is the essential read
best to understand what are the
difficulties in the exegesis of quantum
theory and is what we will use.
Just one last clarification
before we move on: although
historically have been developed
to explain the atomic behavior,
quantum mechanics has, as far as
we can see, universal application.
Another way of saying this is to
affirm, in the light of the above, the
limits to what we can know about a
physical system are always the same,
always obey the same rules (quantum
mechanics), independent of
the physical system concerned,
of their nature, their anthology
(by physical system we understand any
object or material entity, or a combination
of these: an atom, a stone into the
water, a bacterium, a ray of light, etc.)
This universality of quantum
mechanics is not a priori in
contradiction with the fact that we
do not realize, in everyday life,
no limitation in our ability
to observe and describe
whatever it is, the only limits
are those of practicability
(the accuracy of the rule
the definition of the
photographic plate, the
microphone sensitivity, etc.).
We do not realize because,
although there are, these limits
are usually so subtle, so tiny
that unless the atomic scale,
the above mentioned practical
limits are always more relevant,
so that we can treat as the
classic - day objects a day.
Later we will see better how this happens.
Anyway, should accentuate that the
universality of the theory into question
by itself at least one of the events
that make up the standard framework
(the lack of restrictions
on the act of observing).
We spent the actual content of the theory.
We can say that it claims,
first of all, the following:
you fined a measurement process
is not unique any a priori have
can two or more (or even infinite)
different possible outcomes.
That is, even depart the same
initial conditions, it is not
possible to predict in advance
the outcome of an experiment.
Similarly, even if a certain
number of measures are taken
in two physical systems
producing identical results,
we can not conclude based on
this fact that the two systems
were in the same situation
before you make the move.
It is precisely this feature theory,
above, we call quantum indeterminacy.
The family of classical physics
predictability disappears here, giving rise
to a situation that differs significantly
from what we are accustomed.
Despite the temptation, leave to discuss the
possible reasons for this state of affairs
when we analyze the various interpretations
of the theory, in the next chapter.
However, one aspect of
what has been said above,
may have surprised the
most attentive layman.
If quantum mechanics destroys
any predictability of nature,
how we want laws if they
can not predict anything?
Quantum theory introduces the
concept of the state of a system.
If a physical state of an object
(a system) understand its
ontological status, i.e.,
what it is, how it is, etc.,
as "quantum state" we are referring to its
epistemological situation, i.e., to what
we know about it, what we can measure,
regardless of the nature of the system.
The theory teaches
us to characterize
mathematically, the quantum
state of a system.
With this, the theory says that 44 the
likely results of any measures can
be determinated primary from knowledge
of the quantum state of the scheme.
Moreover, we can not determine
in advance, as we have
said, what will be among
these the result obtained;
but we know how to predict
exactly what is the probability
assigned to each result, i.e.,
with relative frequency,
that they will be obtained if we repeat the
experiment an infinite number of times.
Similarly, just for that, we know
the quantum state of the system.
It is, undoubtedly, a
forecast, and possession
of it we can now get
back to doing science
(consistency with classical physics
is assured when we note that
to apply the theory to measurement
processes in classic cases,
the possible outcomes with
non-negligible probability
are concentrated around the
expected value classically,
with a much smaller
dispersion than the usual
inaccuracies of
measuring instruments).
But the theory says more.
It states that the quantum
state of the system changes
over time, and teaches us
to predict this change.
It is necessary, however, that we can
first find out how a given mathematical
entity, called 'evolution operator'
to carry out the prediction.
It is precisely here that one finds perhaps
the most important subtlety theory.
Let's see.
Up to this point the presentation
of the theory content,
the epistemological status
(quantum) and the ontological
status (physical) walked
parallel but disjunct, i.e.,
we are, of course, all the time
assuming the existence of the
physical system on which we may
or may not know this or that,
but we have not made any demands or
assert anything about his physical
description, the quantum description
being made independently.
We could certainly ask
ourselves about the meaning of
theory, i.e., in what ways the
world must be what ontology,
which picture of the mind and matter
can adopt so that there is no
contradiction with the restrictions and
epistemological rules just discussed.
The evolution operator varies from
one physical system to another.
Nothing surprising in this, because the
changes that he operated in the quantum
state of the system reflect the changes
undergone by the physical system,
i.e., the action of the evolution operator
is linked to physical processes themselves.
In fact, that quantum
theory does not conflict
with classical physics
it is necessary that,
by applying that to the processes
of day-to-day action of the
evolution operator play the
traditional laws of physics.
And indeed so it is given in general.
As in classical physics
epistemology superimposed
on ontology, the
verification of this limit -
known as correspondence principle - is
sufficient to ensure compatibility.
But again, back to the evolution operator.
It is an entity of the quantum formalism
and, in principle, and nothing
prevents us from just guessing its
form, its structure in each case.
However, there is a certain
method to build the corresponding
evolution operator of a
particular physical system,
consisting of transposing,
in the quantum formalism
language, a particular
physical system image.
It works well, sometimes
with subtle changes.
It is the most explicit linkage of quantum
formalism with the physical nature of the
system, and must be
taken into account when
we carry out the discussion
mentioned above.
Concluding this section, we would like
to insist that quantum mechanics, being
an epistemological statement in no way
responds to the ontological question.
On the contrary, it
practically cries out for
an anthology of the
world to it coherent.
It is precisely this that is the
problem basics of quantum mechanics.
Sixty years after Von Neumann
formulation of the postulates of
quantum theory, his enigmatic
partner has not yet appeared.
Since then we got was overwhelmingly
confirm the quantum formalism, a brilliant
career whose latest bid is subject to
the third chapter of this dissertation.
We also have in the meantime show that the
world, although not yet know exactly how
it is, surely is not as we imagine it to
be, as we shall see in the next chapter.
The concept of state in quantum mechanics
In physics, it is called
"system" a concrete
reality fragment was
separated for study.
Depending on the case, the word
system refers to an electron
or a proton, a small hydrogen
atom or a large uranium atom,
an isolated molecule or
a set of interacting
molecules forming
a solid or vapor.
In all cases, the system
is a fragment of concrete
reality to which you
want to draw attention.
Depending on the particle can be inverted
polarizations following neutral point.
The specification of a physical
system not only determines
the values that experiments
provide for their properties
(or likely to measure these values, in
the case of probabilistic theories).
Also, physical systems are
not static but change with
time, so that the same
system, prepared similarly,
can give rise to different
experimental results
depending on the time in which
performs the measurement
(or different histograms in the
case of probabilistic theories).
This idea leads to another fundamental
concept: the concept of "state".
A state is a mathematical quantity
(which varies according to the theory)
which completely determines the
values of the physical properties
of the system associated with
it a particular moment in time
(or the probability of each
of its possible values
are measured when it is
and probability theory).
In other words, all the
information possible to
know in a given system
constitute their state.
Each system occupies a
country in a moment in time,
and the laws of physics should
be able to describe how a
particular system part of a
state and comes to another.
In other words, the laws
of physics should tell
how the system evolves
(from state to state).
Many variables that are clearly
defined in classical mechanics
are replaced by probability
distributions in quantum mechanics,
which is an intrinsically probabilistic
theory (i.e., have only probabilities do
not for a simplification or ignorance, but
because that's all theory can provide).
The state representation in formalism
of quantum mechanics, the state of
a system in a moment of time data can
be represented in two main ways:
1. The state is described
by a complex function of
position or momenta of each
particle renders the system.
This representation is
called wave function.
2. You can also represent the state by
a vector in a vector space complex.
This representation of quantum
state is called state vector.
Due to the notation
introduced by Paul
Dirac, such vectors are
usually called kets.
In short, both the "wave functions"
and the "state vectors" (or kets)
represent the states of a given physical
system complete and equivalent form and the
laws of quantum mechanics describe how state
vectors and wave functions evolve in time.
These abstract mathematical objects (kets
and wave functions) allow the calculation
of the probability of obtaining precise
results in a particular experiment.
For example, the quantum mechanics
formalism allows calculating the
probability of finding an electron in a
particular region around the nucleus.
To seriously understand
the calculation of
probabilities from the
information represented by
the state vectors and
wave functions you need
to master some linear
algebra fundamentals.
First mathematical foundations
It is impossible to talk
seriously about quantum
mechanics without making
some accurate notes.
That's because many quantum phenomena
difficult to imagine concretely can be
represented without further complications
with some mathematical abstraction.
There are three basic concepts
of mathematics - specifically
linear algebra - which are consistently
used by quantum mechanics.
These are:
(1) the idea of an operator;
(2) eigenvector;
and
(3) self-worth.
Vectors and vector spaces
In linear algebra, a vector space (or linear
space) is a collection of abstract objects
(called vectors) that have some properties
that are not thoroughly detailed here.
For now, it is known that
such objects (vectors) can
be added together and
multiplied by a scalar number.
The result of these operations is always
a vector belonging to the same space.
The vector spaces are the primary
objects of study in linear algebra and
have various applications in
mathematics, science, and engineering.
The most simple and familiar vector
space is Euclidean space bidimensional.
The vectors in this space
are ordered pairs and are
graphed as "arrows" endowed
module and direction.
In the case of two-dimensional
Euclidean space, the sum of any
two vectors can be accomplished
using the parallelogram rule.
All vectors can also be
multiplied by a scale -
that in Euclidean space
is always a real number.
This scalar multiplication
can change the vector
module and its meaning but
preserve their direction.
The behavior of geometric
vectors under these operations
provides a good intuitive model
for the behavior of the vectors
in more abstract spaces which need not
have the same geometric interpretation.
As an example, you can
mention the Hilbert space
(where "live" vectors
of quantum mechanics).
Operators in Quantum Mechanics
An operator is a mathematical
entity establishing a
functional relationship
between two vector spaces.
The functional relationship
which an operator
sets can be called
linear transformation.
The more formal details will
not be singled out here.
Consider the Euclidean space.
For each vector in this space
to perform a rotation (at
an angle) and find another
vector in the same space.
As this rotation is a functional
relationship between the vectors of
space, we can define an operator
to carry out this transformation.
Thus, two very concrete examples of
operators are the rotation and translation.
From a theoretical point of view,
the seed of division between
the quantum and classical physics
is the use of operators.
In classical mechanics, it
is usual to describe the
motion of a particle with a
scalar function of time.
For example, imagine that we see a
flower vase falling from a window.
At each time point, we can
calculate how high is the vessel.
In other words, we describe
the position quantity
with a number that varies
as a function of time.
A distinctive feature of
quantum mechanics is the
use of operators to represent
physical quantities.
That is, not only are
the rotations and
translations can be
represented by operators.
In quantum, mechanical quantities
such as position, momentum,
angular momentum, and energy are
also represented by operators.
Up to this point, it is possible
to realize that quantum
mechanics describes the
nature of quite abstract.
In short, states that a physical system can
occupy are represented by state vectors
(kets) or wave functions (which are also
vectors, only the space of functions).
The physical quantities are
not directly represented by
scalars (such as 10 m, for
example), but for operators.
To understand how this
abstract way of representing
nature provides information
on real experiments
is necessary to discuss
a last topic of linear
algebra: the problem of
eigenvalue and eigenvector.
Principles
• First principle: superposition principle
In quantum mechanics, the state of a
physical system is defined by the set of
all information that can be extracted
from this system by making some extent.
In quantum mechanics, all
states are represented
by vectors in a
vector space complex.
Hilbert H. space, thus,
each vector in space H
is a state that could be
occupied by the system.
Therefore, given two
states any, the algebraic
sum (superposition) of
them is also a state.
As the norm (mathematics) of
the state vector does not have
physical meaning, all state vectors
are preferably normalized.
Usually, mathematics, are called
functional all linear functions
associated vectors of a
vector space any to a scalar.
It is known that the
role of the vector space
also forms an area, which
is called double space.
• Second principle: measurement
of physical quantities
For all physical quantity, A is associated
with a linear self-adjoint operator Â
belonging to A: Â is observable (eigenvalue
driver) representing the magnitude A.
• Third principle: System Evolution
If the system is not subjected
to any observation, its
evolution over time is governed
by the Schrödinger equation
The most important conclusions
of this theory are:
• Inbound states, as the electron
spinning around the nucleus
of an atom, the energy does
not change continuously,
but discretely (discrete)
transitions whose
energy may or may not
be equal to each other.
The idea that states have linked levels of
discrete energies is due to Max Planck.
• The fact that it is impossible to assign
both a position and exact momentum of a
particle, resigning is thus the concept
of course, vital in classical mechanics.
Instead, path, the movement of particles
in quantum mechanics is described
by a wavefunction, which is a function
of particle position and time.
The wave function is played by Max
Born as a measure of the probability
of finding the particle at a
given position and at one time.
This interpretation is the most
accepted by physicists today, the set
of Quantum Mechanic's assignments
regulated by the Copenhagen School.
To describe the dynamics of a quantum
system must, therefore, find its
wave function and for this purpose
to use the equations of motion,
proposed by Heisenberg and Erwin
Schrödinger independently.
Despite its formal structure ready
since the 1930s, the interpretation
of quantum mechanics has been the
subject of study for several decades.
The main thing is the measurement
problem in quantum mechanics
and its relation to the
non-locality and causality.
Already in 1935, Einstein,
Podolski, and Rosen
published their
Gedankenexperiment, showing
an apparent contradiction
between town and the
measurement process
in quantum mechanics.
In the 60 J. S. Bell published a series of
relationships that would be respected if
the city - or at least as we understand
classically - persist in quantum systems.
Such conditions are called Bell
inequalities and were tested experimentally
by A. Aspect, P. Grangier, J.
Dalibard for quantum mechanics.
As you would expect,
such an interpretation
still causes unease among
various physical, but
much of the community accepts that correlated
states can violate causality in this way.
Such a radical revision
of our concept of reality
was based on brilliant
theoretical explanations
for experimental results that could not be
described by classical theory, and include:
• Radiation Spectrum
Blackbody, solved by Max
Planck with the proposition
of energy quantization.
• Experimental explanation of the
double slit, in which electrons
produce a pattern of consistent
interference with the wave behavior.
• Comment of Albert
Einstein's photoelectric
effect discovered
by Heinrich Hertz,
which suggests that the
light also propagates in
quanta (defined energy
packets), so-called photons.
• The Compton Effect, which
proposes that photons can
behave like particles when
their power is large enough.
• The question of the specific heat
of solids at low temperatures,
which discrepancy was explained by
the theories of Einstein and Debye,
based on energy equipartition according
to a quantized interpretation of Planck.
• The resonant and discrete
energy absorption by
gasses, proven in the
Franck-Hertz experiment
when subjected to certain electric
potential difference values.
• The explanation of atomic stability and
the distinct nature of the spectral lines,
thanks to the Bohr model of
the atom, which postulated
the quantization of the
atom's energy levels.
The formal development of
the theory was the work of
real sets of many efforts and
mathematicians of the time
as Erwin Schrödinger, Werner
Heisenberg, Einstein, P.A.M.
Dirac, Niels Bohr and John
von Neumann, among others.
