essay patrice.delon does quantum mechanics entail world is non local essay

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Does Quantum Mechanics entail that the world is non-local?
1 - Introduction
Quantum mechanics, according to the interpretation of the Copenhagen’s school, is a very special
theory among the corpus of physics theories. Quantum mechanics, based on quantification of all
quantities, is an indeterminist and non-realist theory and appears to be non-local. The quantification
of quantum mechanics has been accepted by all physicians, as Einstein, because this theory is only
relative to microscopic world which is constituted by particles and their interactions. The
indeterminism and the probabilistic interpretation of wave function, introduced in first by de Broglie,
has been rejected by some physician as Einstein; even Schrodinger doesn’t agree with the
indeterminist and probabilistic interpretation of his equation. Bohm has tried to solve this difficulty
introducing the determination of position and two new concepts: the quantum potential and the
pilot wave. Bell, studying mathematical consequences of Einstein’s paper and Bohr’s reply, has
established a theorem which authorizes to conclude at non-locality of quantum mechanics. Using the
up to date technology developed on optical system measurement and generation of entangled
particles, Aspect has realized crucial experimentations from 1980 until 1986 demonstrating that it is
possible to have system in which there is non-local interaction.
The main problem of non-local interaction is the contradiction with the limitation of the light speed
according to special relativity. Even there is no agreed understanding of non-local experimental
results, we will try, in this essay, to establish that the non-local aspect of quantum mechanics
observed in some experiments entails that world is non-local.
2 – The thesis and the argument
Most studies on locality concept use references based on entangled couple of particles as photons.
But non-locality is not only linked to entanglement. More generally, with a single particle
experiment, we can observe a non-local behavior, as for example in a Mach Zehnder interferometer
using single photon. According to the complementary principle, we know that every particle can have
a double aspect: wave or particle. Wave aspect can be described by Schrodinger’s equation. The
choice made by an object, in an experiment, between the two aspects, is only determined by the
experimental system. As long as we do not try to make measurement on one particle on its inside
path, particle will be described with a wave packet. Since about twenty years, a lot of experiments
have been realized using not only photons but also other particles and recently atoms and molecules
as fullerene C
60
. Therefore, every type of particle, photon, neutron or molecules, used in a non-local
experimental device, lead to a non-local behavior provided there is no inside procedure
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using an
external measurement system. Then the particles get a non-local behavior.
In this essay we argue that all particles entangled or not, and not observed by an external
measurement system in such way the wave function couldn’t show us the particle aspect, have a
non-local behavior. Then the universe, which can’t be under measurement operation by an external
measurement system, is globally non-local.

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Entanglement of particles requires that particles have strong interaction in a sufficient manner and
time to be not separable, so to be mathematically described with a unique wave function. Then it
becomes impossible to describe only one particle without the other one, the only way is to describe
the complete system of both particles, even particles that are separated by a very long range, beyond
the authorized value of light speed communication in case of interactions with both particles in a
very short interval of time. Entangled particles have been observed, up to now, only via spin or
polarization, but some experimental researches are being done to find out other way to
entanglement.
More often, for one single particle, we can observe non-local behavior, for example in a Mach-
Zehnder interferometer, except if we try to directly determine “where the particle is” with an
external measurement process. In that case the wave function collapse and particle is observed as a
small volume of matter, a classical particle described by classical mechanics.
Bohm has tried to explain the non-local behavior of a particle as a direct consequence from what he
called “the quantum potential”
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. For Bohm, this quantum potential is an overall property of the
universe. For him quantum potential is the “one wave function” of the complete universe. Then if a
particle “knows” the global description of the interferometer before go to in, it is because quantum
potential contents all information about it. That’s for Bohm the explanation of non-locality. More, he
explains that if one tries to realize interferences with a beam of single particle, one by one, he will
still observe it because the particle will be accompanied by a special stationary wave, “the pilot
wave”, discovered by de Broglie
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, able to guide each particle to the right position to produce
interference figures. Stationary matter wave discovered by de Broglie has a wave length given by
, where m is the mass of particle and  its speed measured in an inertial frame. It
is constituted by two waves, one delayed and one advanced, this one, quite strange, could be
explained in Bohm theory as coming from the global wave function of universe. We see that wave
length is proportional with the reverse of mass, then for macroscopic objects, the wave length will be
too small, so unmeasurable. Thus macroscopic world can be described using continuous classical
mechanics and relativity.
We have now to look at the origin of this global wave function. At the origin of universe a Big-Bang
was happening. According with the cosmological standard model, the universe at the beginning was
very small: physicists estimate his diameter was about 10
-51
meter. From time about 10
-34
seconds to
10
-32
seconds, there was an inflationist period meanwhile the universe was growing by a factor higher
than 10
60
. During the inflation period, all existing particles were generated from the vacuum, in a
very small volume, under the effect of a scalar file, the inflaton. Thus all particles of the universe, at
this time, had interactions strong enough to build up a global entanglement system and then a global
universe wave function. That one has been defined by Bohm as the quantum potential, the global
wave function of universe. Then, if all particles of universe can be described by a global wave
function, which is a superposition of all individual states of particles, world should be non-local few
times after universe’s birth. But an important question is pending: how come this global wave
function can still exist after a so long time?

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As far as we understand quantum mechanics, the non-local characteristic linking some particles can
be gotten by two main procedures: entanglement or physical objects interacting with system without
any in between external measurement procedure. In the entanglement effect, a source system
generates two identical particles at the same time and from the same generation procedure. For
example, a Rydberg atom coupled with microwave cavity is one possibility. Such entangled states
aren’t separable. Let’s take an example: two particles having only two states   and  ; a non-
entangled state of these two particles will be described by the global wave function:
,
And an entangled one by the global wave function:
.
This special state is a result of a so strong interaction between two or more particles leading to the
impossibility to describe separately each particle. This configuration is totally different from having
two linked particles described in a unique inertial framework. For entangled particles, any
measurement action on one component of entangled state determines immediately characteristics
measured for the other parts of the system, even components are at supraliminal distance, by the
collapse of entangled particles wave function. The nature of entangled state is still unexplained. Until
now we get entangled system with photons and some particle with mass
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.
But hopefully, entanglement is not the only way to get non-local behavior for particles. Some
experimental results cannot be explained without non-local argument. That is the case for Mach
Zehnder interferometer. Such experimental system uses semitransparent mirror to get two different
optical paths for photons. Mirrors are disposed in such way that the two different paths,
geometrically of the same length, have optical lengths which differ by a 180° difference of phase (see
figure). At the output of last semitransparent mirror, there are two detectors which count the
number of photons arriving. For a light beam, as a laser, all photons will be detected by the counter
in path with the 0° phase’s difference (TT or TR), and none in the other one (RT or TR). That the result
of classical optical laws according with Maxwell theory and coherence length of used light. Now, if
we use a very weak beam able to generate photon one by one, we will continue to receive all
photons on the same detector. But on the first semitransparent mirror, each photon makes a choice
corresponding to only one path. So we should detect the same number of photons in both counters,
because there is not anymore interference between different photons using different paths. But
anyway, we still detect all particles on the same detector. The only explanation on this result seems
to be instantaneous information of the global experimental system got by the photon arriving at the
first semitransparent mirror. So it is non-local behavior for photons. Of course this detection on only
one counter is conditioned to no one external measurement in any way and to any point on the
possible paths followed by photons. If we try to do any measurements on photon during the time

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transit from input to output, wave function will collapse and we will detect 50% photons, as pure
particles behavior, on each counter.
Now, getting explanation of this strange particle behavior, we do have a look on Bohm theory. The
de Broglie–Bohm theory is known as the pilot-wave and quantum potential theory. The pilot wave
has been established by de Broglie in his thesis. He also postulates in a realist position that an actual
configuration, a material device, exists even when unobserved. De Broglie was thinking that
evolution of his wave function over time was given by Schrödinger's equation. But it was confused
understanding: pilot wave is different from Schrodinger wave function which represents a function of
probability density. In addition, de Broglie pilot wave is a stationary one, constituted by two waves: a
delayed one and an advanced one. This advanced wave is a strange one: from where this advanced
wave is coming from? Bohm can answer to this question, adding four new assumptions to the
quantum mechanics:
- The wave function  is real and not only a mathematical object
- Particles exist and their positions are known any time in a deterministic way
- It exists a pilot wave accompanying particles with a frequency function of particle’s speed
- He adds also a new concept: the quantum potential   
! where !  "" ;
this quantum potential is the manifestation of universe wave function
Other rules are those of quantum mechanics as described by Copenhagen’s school. Bohm add also a
new equation to guide the particles with the pilot wave:
#$%
&
'
$' 
&
(#)*+)%
&
,'
The de Broglie–Bohm theory is explicitly nonlocal: the velocity of any particle depends on the value
of the guiding equation, which depends on the configuration of the entire universe “This undivided
whole is not static but rather in a constant state of flow and change, a kind of invisible ether from
which all things arise and into which all things eventually dissolve. Indeed, even mind and matter are
united: "In this flow, mind and matter are not separate substances. Rather they are different aspects
of one whole and unbroken movement" (Bohm, in Hayward 1987, 25). In de Broglie-Bohm theory,
the wave function travels through both slits, but each particle has a well-defined trajectory that
passes through only one slit. The final position of the particle on the detector screen and the slit
through which the particle passes is determined by the initial position of the particle. Such initial
position is not knowable or controllable by the experimenter, so there is still an appearance of
randomness in the pattern of detection. The wave function interferes with itself and guides the
particles in such a way that the particles avoid the regions in which the interference is destructive
and are attracted to the regions in which the interference is constructive, resulting in the
interference pattern on the detector screen. Bohm assumption is that the environment is registering
the detection effectively separates the two wave packets in space’s configuration. The wave
function, and not the particles, determines the dynamical evolution of the system. In Bohm theory,
quantum potential is a wave-like term that provides information to the particle, linking it to the rest
of the universe. The quantum potential is responsible for the well-known wave-particle duality and
all the other strange phenomena. This quantum potential action has been demonstrated by a very
famous experiment, the Aharonov - Bohm effect
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. Experimental system is an interferometer using
electron’s beam. Between slits there is a solenoid giving a magnetic field in a volume covered by a
magnetic shield isolating totally solenoid from the rest of the system. So no magnetic field is
detectable in the rest of the interferometer. Nevertheless, when the magnetic field, being off, is

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turning on, we observe a shift in the interference lines and when we reverse magnetic field direction,
we get the opposite shift direction for interference lines. Electrons don’t have any information on an
existing magnetic field. But the only fact that, somewhere, an event able to potentially modify the
path of electrons exists is sufficient to change the interferences figure. If we do the same experiment,
but with an electron’s beam going one by one, we get of course the same result.
So it appears that a global world wave function exists and not collapses under our measurements.
3 – Argument’s justification
Comparing Copenhagen school positions and Bohm one, we find they get similar results in term of
experimental explanation and theoretical forecast. In Bohm theory, the particle’s position is known
using a separate equation which completes the Schrodinger one. Bohm used for the wave function a
very classical relation:  -.
&
/
, where R is a real number and S a phase function. Using this relation
in the Schrodinger equation, we get two equations: a guiding equation for particles and a new
Schrodinger equation in which appears a new term representing quantum potential. The main
question is then to examine whether Bohm theory is describing correctly all quantum mechanics
results. Many philosophers have studied this problem, as Bricmont
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, and have concluded that Bohm
theory is compliant with mathematical corpus of quantum mechanics as described by Copenhagen’s
school provided we agree Bohm theory is a non-local one. But Bohm theory is really a non-local
theory, non-relativistic, and also a realist and determinist one.
In quantum mechanics, any particle is described by a wave function, until any physical characteristics
of the particle is measured by the means of an external system. That’s the complementary principle
postulated by Bohr and never been pushed in fault by any experiment. So using the superposition
principle, and Bohm world representation, we can assume that all particles in the world, provided
they are not under measurement procedure of physical characteristics are described by a unique
wave function. This global wave function is a non-local one as long as we don’t make measurement
by an external system.
The fundamental question is now how to prove that “unique wave function for the universe” exists.
The answer is on the quantum potential, whose realism Aharonov and Bohm have experimentally
proved. But we can object that, since a long time, we have often done some measurements on some
parts of the world system to understand physical laws. Then global wave function should have been
collapsed since a long time ago. In fact, all experiments trying to measure such physical parameter of
a system need two things: a physical system in which we do experiment and an external
measurement apparatus. When all these conditions are gathered, the wave function will collapse and
provide a result, a numerical value on the measurement apparatus screen. Bigger is the