The document provides an overview of the EPR paradox proposed by Einstein, Podolsky and Rosen in 1935. The key points are: 1) The EPR paradox uses a thought experiment involving two entangled particles to argue that quantum mechanics provides an incomplete description of physical reality. 2) By measuring properties of one particle, corresponding properties of the distant entangled particle can be known instantaneously, appearing to violate relativistic constraints on information transfer. 3) While Einstein believed there were "hidden variables" not accounted for in quantum mechanics, experiments have verified quantum mechanics and shown that measurements do not reveal pre-existing states.

1. EPR Paradox
Presented By;
D Surat
M.Sc. Physics
Dayalbagh Educational Institute

4. OUTLINE
Introduction
Copenhagen Interpretation
Quantum Entanglement
Schrodinger cat paradox
EPR Paradox
Albert Einstein (1879-1955)

5. Introduction
• By the 1920s, it had become clear to most
physicists that classical mechanics could not
fully describe the world of atoms, especially the
notion of “quanta” first proposed by Planck and
further developed by Albert Einstein to explain
the photoelectric effect. Physics had to be
rebuilt, leading to the emergence of quantum
theory.

6. Called Copenhagen interpretation of quantum mechanics
• Thus, Quantum Mechanics which was born in
the 1900s, marked a revolution in Physics.
• Werner Heisenberg, Niels Bohr and others
helped to create the theory, called Copenhagen
interpretation of quantum mechanics .
• This is the most genereal interpretation of
quantum mechanics.

7. The Copenhagen Interpretation
The Copenhagen
Interpretation is
an interpretation
of quantum
mechanics. It
arose out of
discussions between Bohr and Heisenberg in 1927 and
was strongly supported by Max Born and Wolfgang
Pauli.

8. The Copenhagen Interpretation
• A system is completely described by a wave
function Y, which represents an observer's knowledge
of the system. (Heisenberg).
• The description of nature is probabilistic. The
probability of an event is the mag squared of the wave
function related to it. (Max Born).
• Heisenberg's Uncertainty Principle says it’s
impossible to know the values of all of the properties of
the system at the same time; properties not known with
precision are described by probabilities.

9. • Complementarily Principle: matter exhibits a wave-
particle duality. An experiment can show the particle-like
properties of matter, or wave-like properties, but not both
at the same time. (Bohr).
• Measuring devices are essentially classical devices,
and they measure classical properties such as position
and momentum.
• The correspondence principle of Bohr and Heisenberg:
the quantum mechanical description of large systems
should closely approximate the classical description.

10. Objections :
• Werner Heisenberg, Niels Bohr and others who
helped create the theory insisted that there was no
meaningful way in which to discuss certain details
of an atom’s behavior: for example, one could never
predict the precise moment when an atom would
emit a quantum of light.
• Some who rejected this interpretation were Albert
Einstein, Max Planck, Louis de Broglie, and Erwin
Schrödinger.

11. • Einstein said to Born,
•He wasn’t alone in his discomfort: Erwin
Schrödinger, inventor of the wave function, once
declared of quantum mechanics,
“I, at any rate, am convinced that God does
not play dice (with the universe).”
“I don’t like it, and I’m sorry I ever had
anything to do with it.”

12. Challenging the completeness of Q.M., in
1935, Einstein together with Rosen and
Podolsky published their famous article
“Can Quantum Mechanical Description be
considered complete?”. Here, they
introduced the EPR experiment which
demonstrated the deficiencies of Q.M.

13. Schrödinger’s Cat
To reveal what he considered its absurdity,
Schrodinger proposed (but fortunately never
implemented!) putting a cat in a sound-proof box and
killing it with a ½ probability. Before we open the box, is
the cat alive or dead?
Even though the cat may feel otherwise, quantum
mechanics says the cat is both! It’s in a superposition of
“alive” and “dead.”

14. Making a measurement
on the system (peaking
into the box) collapses
the cat’s state to either
“alive” or “dead.”
1 1
2 2
alive dead  

15. Quantum Entanglement
Quantum entanglement is a physical phenomenon
that occurs when pairs or groups of particles are
generated or interact in ways such that the quantum
state of each particle cannot be described
independently of the others, even when the particles
are separated by a large distance – instead, a quantum
state must be described for the system as a whole.

16. • The basic idea of quantum entanglement is that two
particles can be intimately linked to each other even if
separated by billions of light-years of space; a change
induced in one will affect the other.
• Measurements of physical properties such
as position, momentum, spin, and polarization,
performed on entangled particles are found to be
appropriately correlated.

17. • For example, if a pair of particles are generated in
such a way that their total spin is known to be zero, and
one particle is found to have clockwise spin on a certain
axis, the spin of the other particle, measured on the
same axis, will be found to be counter clockwise, as to
be expected due to their entanglement.
• this behaviour gives rise to paradoxical effects: any
measurement of a property of a particle can be seen as
acting on that particle and will change the original
quantum property by some unknown amount; and in the
case of entangled particles, such a measurement will
be on the entangled system as a whole.

18. • thus appears that one particle of an entangled pair
"knows" what measurement has been performed on the
other, and with what outcome, even though there is no
known means for such information to be communicated
between the particles, which at the time of
measurement may be separated by arbitrarily large
distances.

19. Definition of Quantum Entanglement:
measurements on spatially separated
quantum systems can instantaneously
influence one another.

20. Planks time: It is the time required for light to travel, in a
vacuum, a distance of 1 Planck length, approximately
5.39 × 10-44 s.
There are two entangled state A with wave function Y1
and Y2 and sate B with wave function X1 and X2. then,
Superposed state: Y1X1+Y1X2+Y2X1+Y2X2
Entangled state: (Y1+Y2)(X1+X2)

21. The EPR Paradox

22. • The EPR Paradox (or the Einstein-Podolsky-Rosen
Paradox) is a thought experiment intended to
demonstrate an inherent paradox in the early
formulations of quantum theory.
• It is among the best-known examples of quantum
entanglement.
• The paradox involves two particles which are
entangled with each other according to quantum
mechanics.

23. • It seems that our consciousness plays a role in
quantum mechanics.
• Einstein became uneasy about such implications and,
in later years, organized a rearguard action against
quantum mechanics. His question, “Do you really think
the moon isn't there if you aren't looking at it?” highlights
the depths of his distaste for the role of the
consciousness.
• His strongest counter-argument was a paradoxical
implication of quantum mechanics now known as the
Einstein-Podolsky-Rosen (EPR) Paradox.

24. The Einstein-Podolsky-Rosen Paper
• Einstein believed that, while quantum mechanics
could be used to make highly accurate statistical
predictions about experiments, it’s an incomplete
theory of physical reality.
• In the May 15, 1935 , Einstein, working with physicists
Boris Podolsky and Nathan Rosen, published the
paper, “Can Quantum-Mechanical Description of
Physical Reality Be Considered Complete?”

25. • In this paper, they devised a clever thought
experiment that “beat” the Uncertainty Principle. So
they concluded that there must be more going on than
quantum mechanics knew about, concluding:
The quantum-mechanical description of reality given
by the wave function is not complete, that is, there
must be Hidden Variables that we don’t know about
and hence don’t measure that cause the uncertainty.

26. EPR: Entangled States
• Imagine a pair of particles
whose quantum spins are
known to be opposite. We
can actually know that the
total spin S of the two-
particle system is zero if it’s
in an S = 0 or “singlet” state.
So one is spin-up, and the
other is spin-down, but we
don’t know which is which.
Two particles
emerging from
initial system with
opposite spins
Initial two-
particle system
with zero spin

27. • Now separate them and measure the spin of one
particle. Because they were paired, they have a
combined entangled wave function:
1 1
2 2A B A B
      

28. • But we’re free to choose
which component of the
spin we’d like to measure.
Let’s now pick a
perpendicular direction.
We can write the same
statement about that
direction also:
1 1
2 2A B A B
      
Two particles
emerging from
initial system
Initial two-
particle
system

29. • Of course, Quantum Mechanics says we cannot make
precise measurements of both components; making
one measurement perturbs the other.
• In any case, making a measurement of either
component of one particle’s spin determines the other.
When the measurement is made, the wave function
collapses:
1
2 A B
   
1
2 A B
   or
1
2 A B
   
1
2 A B
  

30. The EPR Paradox
Now do something really interesting:
Measure the vertical spin component of particle A and
the horizontal spin component of particle B.
Because the particle A measurement determines both
particles’ vertical spin components, and the particle B
measurement determines both particles’ horizontal spin
components, haven’t we determined two components of
each particle’s spin? And beaten the Quantum
Mechanics?

31. This would be an argument for the
existence of Hidden Variables—
additional quantities that exist and
affect systems, but we just don’t
know about yet and so can’t
control them.
If this works, then Quantum Mechanics
is incomplete, that is, it’s actually
possible to make precise measurements
if we’re clever, and there’s more going on
than is in Quantum Mechanics.

32. Alas, Einstein’s trick doesn’t work!
Measuring the vertical-spin component of particle A collapses
both particles’ vertical-spin-component states, as predicted. But,
in the process, it randomizes both particles’ horizontal-spin
components! Measuring A’s vertical spin is just like measuring
B’s also!
Even though we never touched particle B!
Quantum Mechanics wins! Quantum Mechanics 1. Einstein 0.

33. But now you might wonder: Information can’t travel
faster than the speed of light. Suppose we let the
particles travel many meters (i.e., many nanoseconds
for light) apart, and we make the measurements only
picoseconds apart in time, so there isn’t time for the
information from the measurement on particle A to
reach particle B in time to mess up its measurement.
That should save Einstein’s idea.

34. But it doesn’t! This information appears to travel
infinitely fast. So this appears to invalidate Einstein’s
beloved Special Relativity!
Quantum Mechanics wins again! Quantum Mechanics
2. Einstein 0.

35. Implicit assumptions of EPR
The principle of reality: individual particles possess
definite properties even when they’re not being
observed.
The locality principle: information from a
measurement in one of two isolated systems cannot
produce real change in the other, especially
superluminally (faster than c).

36. Taken together, these two seemingly obvious principles
imply an upper limit to the degree of co-ordination
possible between isolated systems or particles.
Interestingly, they both turn out to be wrong.

37. John Bell showed in a 1964
paper entitled "On the
Einstein Podolsky Rosen
paradox,” that local realism
leads to a series of
requirements—known as
Bell’s inequalities.
John Bell (1928-1990)

38. Alain Aspect has
performed numerous
beautiful experiments,
proving conclusively that
our universe violates
Bell’s Inequalities big time.
And quantum mechanics
explains the effects quite
nicely.

39. Applications
Entanglement has many applications in quantum information
theory.
Among the best-known applications of entanglement are superdense
coding and quantum teleportation.
Most researchers believe that entanglement is necessary to realize
quantum computing.
Entanglement is used in some protocols of quantum cryptography.

40. THANK YOU …