Faster than light signalling via an EPR type mechanism
- From: John Hudson <johnhudson20032003@xxxxxxxx>
- Date: Fri, 27 Mar 2009 21:19:59 EDT
I believe I have a way of sending faster than light messages via
an EPR / Bell Inequality type mechanism, and would appreciate some
feedback (and hoping this is a suitable venue).
I am aware that faster than light signaling is generally not
considered possible by this process. The reason being that the
inequality is determined by comparing the spins of the correlated
pairs of photons at the two stations ... and this can only be done
at the end of the run at subluminal speeds.
However my proposal -- although it employs a typical EPR type set
up -- is not used to demonstrate the Bell Inequality, and does not
require post-test communication between the two stations. All the
information required can be obtained from the 'receiving' station
alone.
The set-up and procedure are described in more detail below, but
briefly it involves measuring the difference in the number of
'spin-up', and 'spin-down' photons passing through a nominated
'receiving' filter for a large number of counts, over a series of
runs, and then calculating the standard deviation for the series.
The test is carried out at different angles between the two filters
and the standard deviations compared for the various angles.
I am predicting / expecting that the standard deviation will increase
as the angle between the filters is increased.
Based on the above an observer at the 'receiving' filter is able
to predict the relative angle between that filter and the 'sending'
filter - without subsequent reference to the 'sending' filter. So,
with pre-arranged signs for the different relative angles between
the filters, messages can be sent at the speed of the interaction
between the photons which is considered either instantaneous or at
least significantly faster than the speed of light.
The cause of the increased scatter / standard deviation is that the
photons at the 'receiving' filter receive an additional set of
'adjustments' when their original alignment is changed as a consequence
of their correlated photons passing through the other 'sending'
filter. And the extent of this 'adjustment' increases as the angle
between the filters increases - more spins get changed - (although
the average number of counts per unit time remains essentially
unchanged ... and very close to half the electrons observed to be
passing through the filter will be 'up' and the other half 'down').
John Hudson.
N.B. Contact details are as follows:
Email: johnhudson20032003@xxxxxxxx
Mobile phone: + 66 81 841 9712
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Proposed Procedure and Set Up allowing FTL communication
Set-up
The set up is essentially the standard EPR gedanken experiment with
photons (for example as described by Alain Aspect in his article
"Bell's inequality test: more ideal than ever", Nature -- Vol 398
-- 18 March 1999) with slight modifications and not requiring the
fast switching techniques generally employed.
It comprises a centrally located source of correlated photon pairs
and two twin-channel polarisers able to measure the spin of each
member of the pair, arranged on either side of the source.
One filter is designated the 'receiving' filter, R, and is placed
at a slightly greater distance from the source than the other filter
designated S, the 'sending' filter, so that for correlated pairs
of photons, the photon reaching the 'receiving' filter, R, arrives
somewhat later than its partner at the 'sending' filter.
Each filter is able to measure the spin of the arriving photons in
both the spin up or spin-down direction. The designation spin-up
or spin-down depends upon a pre-agreed orientation of the filters.
For ease of description the filter on the right is the 'receiving'
filter, R, and the filter on the left the 'sending' filter, S. The
spin-up electrons are described as 'up'; and spin-down electrons
as 'down'. Thus there are four possible descriptions of the filters:
S-up, R-up, S-down, R-down.
For the test, filter R is fixed in position.
Filter S can be rotated at different angles M-NM-8 with respect to
R.
[N.B. the set-up I am proposing is essentially the same as one which
has already been considered and rejected as not allowing faster
than light communication (for example in the on-line article 'Spooky
Action at a Distance - An Explanation of Bell's Theorem' by Gary
Felder). However as explained, the objection of needing to obtain
post-test correlations between the filters does not apply for my
proposal ... which is not a determination of the Bell inequality
and does not depend upon the correlations of individual photon
pairs.]
Correlation between the filters:
When an individual pair of photons is emitted in opposite directions
(due to the correlation) it is known that one will be an 'up' photon
and the other 'down', although as the process is purely random, it
cannot be predicted which photon, left or right, will be 'up', and
which 'down'.
However when the filters are set at the same angle, if filter 'S'
records an 'up' photon then its correlated pair will be a 'down'
photon.
If the angle between the filters differs from zero (or 90 degrees)
then the correlation can no longer be predicted and the proportion
varies according to sin2 M-NM-8. So for example with the filters
set at 45 degrees the correlation would be 0.5.
Rate and nature of photon emission:
The number of photons emitted from the source in each direction is
essentially constant per unit time and is determined for the apparatus
in question beforehand and the accuracy known.
We choose the number of photons N we wish to count for an individual
test. N is the total number of photons passing through filter R and
is thus the sum of R-ups and R-downs for each test. N is the same
for all the tests.
The number N chosen will depend upon the set up. A high number for
N is preferable but this will need to be balanced by the number of
counts required in order to obtain a reliable figure for the standard
deviation.
We call 'n' the number of R-ups recorded per test and 'm' the number
of R-downs.
Thus n + m = N
It is important to appreciate that for any particular count it is
unlikely that n and m will be equal, and whilst it is true that for
large counts the fraction of ups to downs approaches half, the
actual numerical difference between the two also tends to increase.
The situation is similar to the random walk or the tossing of a
coin and follows the binomial distribution. In the binomial
distribution the expected difference from the mean, or the standard
deviation, is given by M-bM-^HM-^ZN/2, where N is the sample
population.
So for the test under discussion, with the angle between R and S
set at zero, individual values of n will vary from N/2. And it would
be expected that the standard deviation of the counts of the number
of R-ups over a series of counts would be close to M-bM-^HM-^ZN/2.
And this of course can be checked.
However when the angle between the polarisers is increased I am
expecting that the standard deviation as measured will also increase
as discussed below. This gives a means of determining the angle
between the polarisers.
Testing Protocol and Discussion:
There are two stages to the test:
Firstly, with the filters in a single position: the number of R-up
photons, n, is determined during the period that the total number
of photons N pass through the R filter, i.e. for n + m = N. Sufficient
counts need to be made to enable a reliable indication of the
standard deviation.
Secondly the whole series is repeated with the filters set at
differing relative angles.
What I expect is that the standard deviation, i.e. the spread of
the value of n, will be seen to vary as the angle between the filters
is increased. As mentioned above when the filters are set at zero
I would expect that the calculated standard deviation will be close
to the standard deviation predicted by the binomial distribution,
i.e. by M-bM-^HM-^ZN/2. For other angles I would expect that the
standard deviation will increase from M-bM-^HM-^ZN/2 by a factor
of sin2 M-NM-8, where M-NM-8 is the angle between the two filters.
This is despite the fact that the number of R-ups recorded per test,
averaged over the individual series of tests, will still be close
to N / 2, regardless of the angle between the filters. So the
standard deviation will appear to have come from a larger population
than is actually the case. (This is perhaps counterintuitive but
then again so is the Bell Inequality).
My reasoning is as follows (Unfortunately I haven't found an easy
way to say this, though the idea is not complicated):
When the filters are not set at zero then the very fact of measuring
/ polarizing the photons at S (where they arrive first) means that
a proportion at R (those from particular correlated pairs) are
subjected to an additional change in their spin (due to entanglement,
or whatever) in order to realign them ... compared to when the
filters are at zero. (N.B. This is the change which is detected in
the determination of the Bell Inequality, where the correlation
between R-up and L-up is measured.) However the number of R-ups
that are recorded per test will still be close to N / 2, because
the additional number of R-ups (which would otherwise have been
R-downs), will be almost cancelled by the additional number of
R-downs (which would otherwise have been R-ups). Even so, due to
the randomness of the process, for the individual tests, the two
will not precisely balance, and there will be an additional number
of R-ups or R-downs than would otherwise have
occurred. And overall this will be reflected in an increased scatter
in the individual R-up counts and manifested overall as an increased
standard deviation (e.g. for a count that would have been already
quite distant from the mean with the polarisers set at zero, there
is an equal possibility that the realignment will result in a count
closer to the mean or to a result even further from the already
distant mean -- i.e. an increase in the spread).
Another way of saying this is that the spread observed at the various
angles will be that of a population of the number N plus the
proportion due to the additional changes in the spin caused by the
changes in the correlated electrons at the 'sending' station.
I predict the factor will be sin2 M-NM-8, where M-NM-8 = the angle
between the filters, as determined by Quantum Theory. And the
standard deviation of the series will be found to be
M-bM-^HM-^Z{N(1 + sin2 M-NM-8)} / 2.
So, as determined by the binomial distribution this standard deviation
relates to an apparent sample number of N(1 + sin2 M-NM-8) - although
the average number of R-ups will still be close to N / 2.
(N.B. Another consideration is to see how the standard deviation
determined at zero degrees compares with that predicted by the
binomial distribution of M-bM-^HM-^ZN/2. I have supposed that they
will be close to within experimental error. However, on reflection,
it seems to me there is a possibility that there is some pre
'adjustment' due to the initial act of polarization, i.e. simply
passing the photons through a filter in order to polarize a previously
unpolarised stream, may also entail some kind of adjustment ... in
order to bring them all into line with the polarizer angle. And
this may introduce an additional component to the spread. So I
suggest it would be worthwhile to compare the standard deviations
obtained from a count when simply passing the photons through the
polarizer (i.e. with the second filter removed ... or it can be
conducted on separate apparatus). Should the results differ from
M-bM-^HM-^ZN/2 it would certainly be very interesting, and whilst
not invalidating the argument above, it would introduce an added
complexity. (N.B. I don't know if the standard deviation has ever
been measured on a single polarized source, but hesitantly offer
that the increase would be the (integral) M-bM-^HM-+ sin2 M-NM-8
between zero and M-OM-^@ / 2 degrees (an alternative would be
M-B1/2 M-bM-^HM-+ sin2 M-NM-8) ... which would give a standard
deviation increase of 78.5% (or 39.3%), for straight polarized
photons compared to M-bM-^HM-^ZN/2).)
Examples:
If N = 1 million (I have no idea what an appropriate number should
be but Bell Inequality tests seem to like high numbers).
Filters set at zero: Predicted standard deviation = 500 (calculated
on M-bM-^HM-^ZN/2, where N = 1,000,000) So the calculated standard
deviation is expected to be close to 500.
Filters set at 22.5 degrees: Predicted standard deviation = 535
(calculated on M-bM-^HM-^Z{N(1 + sin2 22.5)} / 2, = M-bM-^HM-^Z{1,146,446}
/ 2) The standard deviation over the test series is expected to be
close to 535
Filters set at 45 degrees: Predicted standard deviation = 612
(calculated on M-bM-^HM-^Z{N(1 + sin2 45)} / 2, = M-bM-^HM-^Z{1,500,000}
/ 2) The standard deviation over the test series is expected to be
close to 612
N.B. The above calculation is only for demonstrating the correlation
and not of course the one that would be used for sending messages.
In order to send messages the calculation would be carried out in
reverse in order to give a predicted angle M-NM-8.
Testability
One thing regarding the proposal is that it should be easily testable
-- easily being in this case a relative term -- by which I mean
compared to some of the highly sophisticated switching techniques
used in attempts to overcome objections to the determination of the
Bell Inequality.
The data may perhaps already be available from earlier testing.
I think the only issue would be to clearly determine that the
receiving filter was more distant from the source than the sending
filter.
Conclusion
Hopefully I have shown that the usual objections to faster than
light signaling via an EPR / Bell Inequality type mechanism do not
apply to my proposal.
It rests on the idea that the standard deviation, or spread, in the
count of spin up versus spin-down photons will increase as the angle
between the filters is increased.
Should this be correct the relative angle between filters can be
determined from information obtained at the 'receiving' station
alone, and the only information needed to be passed between the
filter stations are the pre-established protocols re timing of the
tests and the coding for the relevant angles between the filters.
It seems clear to me that the degree of scatter in results will
increase as the angle between the filters is increased. Whether
this follows strictly the equation proposed is a matter for
determination.
An additional observation is that it may be that the simple act of
polarizing an unpolarised stream of electrons will change the
standard deviation from that predicted by the binomial distribution.
The data may already be available to enable the proposal to be
checked.
John Hudson 23 March 2009.
.
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