A1 (+ ½ ) <----------->(- ½ )A2

Orthodox quantum mechanics forbade the simultaneous measurement of a property (say different spin states) for the same system. If you got one, you could not obtain the other. This was a direct outcome of the Heisenberg Indeterminacy Principle which stated that simultaneous quantum measurements could not be made to the same precision.

E-P-R
argued that this showed the incompleteness of quantum mechanics. It was not the
'paragon' of physical theories its apologists claimed, if such indeterminacy
was fundamentally embedded within it. At the same time they conceived an
'experiment' in which both spins could be identified - with the sole assumption
that both were in definite states from the instant of their parent atom's
disruption.

Using his hypothetical (purely on paper) thought device, Einstein wanted to put to rest once and for all the notion that quantum mechanics was complete, or was in any way a proper science. The mechanical device contrived by Einstein was designed as a counter-example to the Heisenberg Uncertainty principle for energy and time which states:

*ΔE Δ t*

*³*

*h/2π***Fig. 1: Einstein’s Thought Experiment Device**

In the device, a weight scale is located and one can see it when a door (front of box) opens, with the door controlled by a clock timer. Whenever the door flaps open, even for a split second, one photon escapes and the weight difference (between original box and after) can be computed using Einstein's mass-energy equation, e.g.: m = E/ c

^{2}. Thus, the difference is taken as follows:

Weight(

**before door opens**) - weight (

**after**- with 1 photon of mass m = E/ c

^{2 }gone)

Thus, since the time for brief opening is known (

**) and the photon's mass can be deduced from the above weight difference, Einstein argued that one can in principle find both the photon's energy and time of passage to any level of accuracy**

*Δ t**without any need for the energy-time uncertainty principle.*

In other words, the result could be found on a totally deterministic basis!

Bohr nearly went crazy when he studied the device, and for hours worried there was no solution and maybe the wily determinist was correct after all. When Bohr did finally come upon the solution, he realized he'd hoisted the master on his own petard.

The thing Einstein overlooked was that his very act of weighing the box translated to observing its displacement (say, dr = r2 - r1)

*within the Earth's gravitational field*. But in Einstein's general theory of relativity, he'd found that clocks actually

*do run slower in gravitational fields*(a phenomenon called 'gravitational time dilation') In this case, for the Earth, one would have the fractional difference in proper time, as a fraction of time passage t:

dt/ t » GM(1/r1 - 1/r2) » g(dr)/ c

^{2}

where G is the Newtonian gravitational constant, M is the Earth's mass, and g is the acceleration of gravity (g = 980 cm/ sec

^{2}in cgs) and c = 3 x 10

^{10}cm/sec.

Let us say the box deflection (r2 - r1)was 0.001 mm = 0.0001cm, then:

dt/t ~ (980 cm/s

^{2})(10

^{-4}cm)/ (3 x 10

^{10}cm/sec )

^{2}

dt/t » 10

^{-22}

and for an interval say t = 0.01 sec, and:

dt = (10

In other words, the observation would actually generate a time uncertainty of 10

Quantum theory prevails again!

Einstein's challenges to Bohr in the aftermath were all kind of half-hearted and had nowhere near the intensity of his clock-door device work of art. Rather than join happily with other QM theorists at the last Solvay Conference in 1933 Einstein - the perpetual determinist- remained on the sidelines "feeling the same uneasiness as he had before".

He went to work separately, on a "unified field theory" while the quantum theory edifice was formulated to its present maturity without him.

^{-22})(0.01 sec) = 10^{-24}secIn other words, the observation would actually generate a time uncertainty of 10

^{-24}sec- and hence an uncertainty dE in the energy of the photon. In other words, after the displacement (r2 - r1) arising from the measurement, the clock is in a gravitational field*different*from the original one. (The*Energy uncertainty*can meanwhile be computed from the Heisenberg energy -time relation to be dE » 10^{-10}J)Quantum theory prevails again!

Einstein's challenges to Bohr in the aftermath were all kind of half-hearted and had nowhere near the intensity of his clock-door device work of art. Rather than join happily with other QM theorists at the last Solvay Conference in 1933 Einstein - the perpetual determinist- remained on the sidelines "feeling the same uneasiness as he had before".

He went to work separately, on a "unified field theory" while the quantum theory edifice was formulated to its present maturity without him.

**Aside**: Most people outside physics are unaware there were seven Solvay Conferences in all, in the course of which the essential underpinnings and core interpretation of quantum mechanics was thrashed out – leading to the

*Copenhagen Interpretation*.

*2.*Bell 's
Theorem and the Aspect Experiment**Years later, mathematician John S. Bell asked the question: 'What if the E-P-R experiment could actually be carried out? What sort of mathematical results would be achieved?' In a work referred to as "**

*the most profound discovery in the history of science*",

**based on a design similar to that shown at the opening of the chapter. He made the basic assumption of locality (i.e. that no communication could occur between A1 and A2 at any rate faster than light speed). In what is now widely recognized as a seminal work of mathematical physics, he set out to show that a theory which upheld locality could reproduce the predictions of quantum mechanics. His result predicted that the above sum, S, had to be less than or equal to 2 (S £ 2). This is known as**

*thought experiment**the*Bell Inequality.

*the polarizations*[4] of photons was the key. These were observed with the photons emanating from a Krypton-Dye laser and arriving at two different analyzers, e.g.

(P1) A1
¯|
<------------> | A2 (P2)

**A1:**1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0

**A2:**0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1

S
= (A1,A2)I + (A1,A2)II + (A1,A2,)III + (A1,A2)IV

*'Leave it alone*!', wouldn't do any more. In essence, Bohm had become convinced that the entrenched vagueness and philosophical abdication of the standard Copenhagen Interpretation could no longer be supported.

[2] More
technically, this is what is referred to as ‘the z-component of electron spin’,
since the electron is visualized as a spinning top, with z-axis (i.e.
component) in the axial or z-direction.

## 2 comments:

Without special relativity, the "simultanious" reactions of the two fotons looked simply very fast no more.

But the envious adoration of the Einstein genious turned the realists to nonlocal world fantasy. This is not the physics,this is the psychology.

I don't think so You make the same error of Victor Stenger when he claimed nonlocality "violated causality" and special relativity. In fact, it does nothing of the sort.

What nonlocality shows is not superluminal transfer of information, but rather pre-existing connections in a higher dimensionality! This is totally different, since it doesn’t require separate localizations from which FTL signals emanate.

The point is that the two photons detected by A1, A2 in the Aspect experiment are already connected in a higher dimensionality, not readily accessible to us. The experimental results unequivocally show this, but we insist on using fragmentary language to refer to two photons - one at each analyzer, as if they are distinct entities separated by distance.

See also the papers:

1) Cufaro-Petroni and Vigier Physics Letters, (93A), 383.

2) Aspect, Grangier, and Roger: Physical Review Letters, 91.

3) Bell, J.S.: Foundations of Physics, (12,) .989

4) Stapp, H.: Foundations of Physics, (15), 35.

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