[Advaita-l] The mystery element in the Quantum Theory

[Shrinivas Gadkari]

Namaste,
Few weeks ago there was a thread on quantum theory and consciousness.Here is a write up that tries to capture the mystery element in theQuantum theory - as I understand it.
Regards,Shrinivas Gadkari
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The mystery element in the Quantum Theory 
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To clearly bring out the mystery element in the quantum theory that
has puzzled the foremost of the physicists, consider the following
thought experiment. The experiment here is a hybrid of Feynman's
double-slit experiment with electrons (Feynman Lectures on Physics,
Volume 3, Chapter 1), and the Schrodinger's Cat experiment.


   
                  |Barrier           ||
                  |                  ||
                  |                  ||
                D1|                  ||
                   S1                ||
Source            |                  ||
=====             |                  || Screen - S
                  |                  ||
                   S2                ||
                D2|                  ||
                  |                  ||
                  |                  ||

Description of the overall setup:

The Source is an electron gun. Electrons emitted from the Source
encounter a barrier before they hit the Screen.
The barrier has two open slits S1 and S2 that allow
electrons to pass through. Screen-S is a surface that can detect/ record
the location of electrons when they hits the screen.

D1 and D2 are two detectors that can detect if an electron passed
through slit S1 and S2 respectively, and yet allow the electrons
to pass.

Electrons are emitted from Source at a very slow rate, say one
electron every second. An electron emitted from the Source passes 
through the barrier B2 with slits S1 and S2, and then hits the screen-S.
The position of where the electron hit the screen is recorded on S
can be "read" off after the experiment.

Experiment Variation A:
-----------------------
Setup A: Detectors D1 and D2 are switched off. We conduct the
experiment for a long time, firing one electron per second. After the
experiment, we "read" the Screen-S to analyze the locations where the
electrons hit the screen.

Result A: We see an interference pattern on the screen. There are 
some areas where electrons arrive more frequently (bright strips), 
while there are some areas which are avoided by electrons (dark strips).

Explanation: For every electron that reached screen (not all electrons
fired by the Source reach the Screen due to presence of the barrier),
there were two possible paths that the electron could have taken:
Path-1: Source - S1 - S.
Path-2: Source - S2 - S.
In absence of any information about which path the electron took, we have
to consider the possibilities that the electron may have traveled both 
the paths, and add the complex valued exponentials that represent
the evolution of phase of the electron in each of the of paths. When we 
add complex valued exponentials in this way for the two paths, there are
locations on the screen where the complex exponentials cancel each other,
and there are locations where the complex exponentials boost each other.
The magnitude of the final complex valued sum of the two exponentials
represents the probability that the electron may be detected at that
position. The locations where the two exponentials cancel each other
have a negligible probability for electrons to hit the screen - these are
the dark strips in the interference pattern, while locations where the 
exponentials boost each other have a larger probability of electrons 
hitting the screen - these are the bright strips in the interference 
pattern. 

Experiment Variation B:
-----------------------
Setup: Detectors D1 and D2 are switched on and record the path each
electron took (Path1: S0-S1-S, or Path 2: S0-S2-S), and these 
results are available to be analyzed by the experimenter . We conduct 
the experiment for a long time, firing one electron per second. After 
the experiment, we "read" the Screen to analyze at what locations the
electrons hit the screen.

Result: We see NO interference pattern on the screen. The bright and
dark strip pattern us not observed.

Explanation: Now again there are same two possible paths that an electron
can take (Path1: S0-S1-S, or Path 2: S0-S2-S).
However, now that we have information about which path an electron takes,
we have to account for the two paths differently. The electron may have
taken path Source-S1-S OR Source-S2-S, but not BOTH the paths together.
So we again compute the complex valued exponentials that represent the 
evolution of the phase of the electron on each path. However, we now
compute the magnitude of each complex exponential SEPERATELY, and 
THEN ADD the magnitudes. That is we use a completely different mathematical 
procedure to compute the probability of detecting an electron at a specific 
location on the Screen. Now the possibility of complex exponentials 
canceling each other does not exit. We now have a more uniformly spread 
distribution of electrons - no very dark strips or much brighter strips 
- that is, no interference pattern. So our conclusion is: By observing 
which slit the electron passed through we have destroyed the interference 
pattern.

Experiment Variation C:
-----------------------
Setup C: Detectors D1 and D2 are switched on, they detect if an electron
passed through slit S1 or S2, BUT DO NOT KEEP A RECORD of this detection.
So physically they behave exactly as in set up B, but there is no way for
ANYONE to retrieve the record of detection.

Result C: We see again an interference pattern on the screen. There are 
some areas which electrons arrive more frequently (bright strips), 
while there are some areas which are avoided by electrons (dark strips).

Explanation: 
We are in principle back to variation A of the experiment. In absence 
of any record from the detectors D1 and D2, we have to again admit the
possibility that the electron may have traveled both the paths. So 
following the explanation A, we FIRST ADD the complex valued exponentials 
and THEN compute the magnitude of the complex valued sum. This results in
the dark and bright strips - interference pattern.

Our Conclusion: It not the physical procedure of the operation of detectors 
D1, and D2, that destroys/ disturbs the interference pattern. It is the 
AVAILABILITY of the results of detection that destroy/ disturb the 
interference pattern.


Experiment Variation D:
-----------------------
Setup D: Detectors D1 and D2 are switched on, they detect if an electron
passed through slit S1 or S2. However, this time, the data from detectors 
is "carefully" recorded on a memory device M. By "carefully", we mean:
"outside the device M, there is absolutely no trace of the outcome of the 
detection process". We conduct the experiment for a long time. After the
experiment we do not immediately "read" the pattern recorded on the screen. 
We detach both the memory device M, and screen S from the setup. Now 
consider the following two options:

Option D1: After the experiment, we DESTROY the memory device M, and THEN 
read the screen S.

Option D2: We keep the memory device M INTACT, and then read
the screen S.

Result: For Case D1, a interference pattern is observed on the screen,
while for Case D2, there is no interference pattern.

Explanation: The electron pattern on the screen is not completely
determined at the time of this experiment. The pattern on the
screen is a superposition of two possible states: "State with interference
pattern" and "State without interference pattern". For case D2, when memory 
device M is kept intact, the dual state pattern collapses to single
state pattern with no interference, when the screen is read.
For the case D1, when memory device M is destroyed, at this instant the
dual state pattern collapses to a single state pattern with interference.
This is what we observe when the screen is read.

Conclusion: Outcome of any physical event is (in general) not deterministic.
It is a superposition of possible outcomes. The exact outcome that is
finally presented to an observer (by nature) depends on how much information 
pertaining to details of the physical event is known to the observer or is 
in principle accessible to the observer.