EPR
Paradox-II |
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23^{rd} July 2016 |
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"We
should not forget that only a small portion of the world is
known with accuracy."
- Charles Darwin, On the Origin of Species by Means of Natural Selection. "The requirements was, and is,
to obtain the most profitable result from imperfectly
postulated data; and the data may possibly be subjected to
conditions, which likewise are imperfectly postulated."
- A. R. Forsyth, Calculus of Variations. "Tell me the environment, and I'll tell you the probability after a next moment of time that this point is at state s. And that's the way it's going to work, okay?" - Feynman discussing Quantum Computers. "Indeed, we find ourselves here on the very path taken by Einstein of adapting our modes of perception borrowed from the sensations to the gradually deepening knowledge of the laws of Nature. The hindrances met with on this path originate above all in the fact that, so to say, every word in the language refers to our ordinary perception. In the quantum theory we meet this difficulty at once in the question of the inevitability of the feature of irrationality characterising the quantum postulate. I hope, however, that the idea of complementarity is suited to characterise the situation, which bears a deep-going analogy to the general difficulty in the formation of human ideas, inherent in the distinction between subject and object." - Neils Bohr, Como Lecture, 1928. |
For
the structures A and B as shown in the diagram, the quantum entanglement condition can be
defined by the following wave-function
^{1}:
Above
relationship represents two structures
A and B which are not independent of each other. If the structure A is measured as in state
|0〉 then the structure B is simultaneously
measured as in state |0〉. Similar
argument holds for the state |1〉. The important
point is to note that Locality
condition holds for the structures A, B and the
entangled state, i.e. the communication between the
structures A and B is restricted to the speed of light.
Which in turn means that the structures A and B and the
entangled state, belong to the same measurement space.
Please note that the Locality condition is implicit in VT-symmetry
which defines the origin in measurement space. The maximum measurement capacity possible is v/c ~1.
The
measurement themselves are being performed by the
macroscopic observer Obs
The measurements corresponding to the state |0〉 as performed by
Obs
We are trying to determine whether in j-space the behaviour of two structures is influenced by each other, if they had interacted with each other at an earlier instant. The situation is described in the following diagram: Each
observer
is allowed to measure
with arbitrary precision within his measurement
metric. Important to
note is that the arbitrary precision does not imply
infinite precision.
Arbitrary precision is equivalent to the maximum
capacity of the
observer making the measurement. Consider the
situation shown above for
t = 0
For Obs
The
j-space is the discrete measurement space
corresponding to the
observer's capacity. In j-space we can not have
absolute stillness or
structures moving with infinite velocity
Furthermore the Λ
So what happens if the one of the structures, let us
say A, is
dropped in to a black-hole? Is an interaction still
possible between
the structures A and B? The definition of the
black-hole is dependent on the observer's capacity. If a black-hole exists per
measurements
of Obs
In our discussion so far, we have used neither the wave-function nor the
stochastic
nature of Quantum Mechanics while discussing
the "entanglement". We have
used measurements made by the observer Obs
We
will later argue that the stochastic
nature of QM, is due
to the fact that we are trying to estimate the mean
of a real-valued
variable based on a sample size (n), which is much
smaller than the actual spectrum (N → ∞)
of the variable. We will try to understand it geometrically. It is also
important to resolve this perceived conflict between Special Theory of
Relativity and Quantum Mechanics. Both of them are powerful
methodologies who at best approximate the physical reality for the
macroscopic observer in Λ Non-locality vs. Local Hidden Variables? Non-locality! ^{1}Note
that
we have used the inner-product symbol ⨂
instead of the scalar product. The reason being that
we wanted to highlight the fact that we can perform
addition and hence multiplication only for stable distributions in j-space.
Therefore |0〉 and |1〉
states must be represented by one of the stable distributions. The
addition of probability distributions is not a standard arithmetic
operation. The conventional arithmetic operations are legitimate only in the measurement metric for the observer Obs_{M} (v/c << 1).^{2 }Being
completely still or moving with infinite velocity are
equivalent to
stating that the observer has an infinite capacity to
measure the source.
But then we will not be in j-space to begin with.^{3} If that was the
case then the macroscopic observer
Obs_{M} will not be able to measure
the structures A and B simultaneously. |
Previous
Blogs:
Nutshell-2015 Chiral Symmetry Sigma-z and I Spin Matrices Rationale behind Irrational Numbers The Ubiquitous z-Axis Majorana ZFC Axioms Set Theory Nutshell-2014 Knots in j-Space Supercolliders Force Riemann Hypothesis Andromeda Nebula Infinite Fulcrum Cauchy and Gaussian Distributions Discrete Space, b-Field & Lower Mass Bound Incompleteness II The Supersymmetry The Cat in Box The Initial State and Symmetries Incompleteness I Discrete Measurement Space The Frog in Well Visual Complex Analysis The Einstein Theory of Relativity |

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