**The EPR Paradox**

In 1935, Einstein along with two colleagues, Boris Podolsky and Nathan Rosen, devised a thought experiment.[1] This has since been called the EPR experiment based on the first initials of their names. Einstein, Podolsky and Rosen (E-P-R) imagined a quantum system (helium atom A) which could be ruptured such that two electrons were dispatched to two differing measurement devices, X1 and X2.

X1 (+ ½ ) <-----(A)------>(- ½ ) X2

Each electron would carry a property called 'spin'. Since the helium atom itself had zero spin (the 2 electrons canceling each other out), this meant one would have spin (+ 1/2), the other (-1/2).

Thus, we manage to skirt the Indeterminacy Principle, and obtain both spins simultaneously without one measurement disturbing the other. We gain completeness, but at a staggering cost. Because this simultaneous knowledge of the spins implied that information would have had to propagate from one spin measuring device (on the left side) to the other (on the right side) instantaneously! This was interpreted to mean faster-than-light communication, which violates special relativity.

In effect, a 'paradox' ensues: quantum theory attains completeness only at the expense of another fundamental physical theory - relativity. By this point, Einstein believed he finally had Bohr by the throat. Figuring Bohr might come up with some trick or sly explanation up his sleeve, Einstein went one better at the 6th Solvay Conference held in 1930, actually designing a thought experiment device that he was convinced would have Bohr in tears trying to find a solution:

**Einstein’s Thought Experiment Device**

According to reports, it very nearly did, and a number of participants insisted "*Neils was in a state of shock". * Einstein wasn't a meanie, he merely 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 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

The "device" featured a spring-based 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)**

(E.g. with 1 photon of mass m = E/ c^{2 }gone)

Since the time for brief opening is known (** Δ t**) 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

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

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

*deterministic*basis! Bohr for his part 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 according to Einstein's general theory of relativity, 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,

dt = (10^{-22} )(0.01 sec) = 10^{-24} sec

In 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!

Decades later, to actually test the original E-P-R quantum system (used in the EPR thought experiment), Alain Aspect and his colleagues at the University of Paris, set up an arrangement as sketched below. (In the original EPR set up both spins could be identified - with the sole assumption that both were in definite states from the instant of their parent atom's disruption.)

In the Aspect experiments this was not the case, the spins - or rather polarizations- had to be detected and determined. The detection of *the
polarizations* 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 ****¯****|
<------------[]-------------> |******** P2**

** A1 D A2**

Here, the laser device is D, the analyzers (polarization detectors) are A1 and A2 and two representative polarizations are given at each, for two photons P1 and P2. The results of these remarkable experiments disclosed apparent and instantaneous connections between the photons at A1 and A2. In the case shown, a photon (P1) in the minimum (0) intensity polarization mode, is anti-correlated with one in the maximum intensity (1) mode.

Say, twenty successive detections are made then one obtains at the respective analyzers (where a ‘1’ denotes spin +1/2 detection and ‘0’ spin (-1/ 2):

**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

On inspection, there is found to be a 100% anti-correlation (i.e. 100% negative correlation) between the two and an apparent nonlocal connection. In practice, the experiment was set out so that four (not two - as shown) different orientation 'sets' were obtained for the analyzers. These might be denoted: (A1,A2)I, (A1,A2)II, (A1,A2,)III, and (A1,A2)IV. Each result is expressed as a mathematical (statistical) quantity known as a 'correlation coefficient'.[3] The results from each orientation were then added to yield a sum S:

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

In his (1982) experiments, Aspect determined the sum with its attendant indeterminacy to be: S = 2.70 ± 0.05 and in so doing experimentally validated Bell’s Inequality and in the process reduced the EPR Paradox to a simple misunderstanding of quantum mechanics in the authors' minds.

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. In the
orthodox Copenhagen (and most conservative) interpretation of quantum theory,
there can be no separation of observed (e.g. spin) state until an observation
or measurement is made. Until that instant (of detection) the states are in a
superposition, as described above.

More importantly, the fact of
superposition imposes on all quantum phenomena an inescapable ‘black box’. In
other words, no information other than statistical can be extracted before
observation.

[1]
Einstein, Podolsky, and Rosen.:1935, *Physical
Review*, 777.

[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.

3] For example, if a set of data: 1, 1, 1, 1 is correlated with another set: 0.5, 0.5, 0.5, 0.5, the correlation coefficient is 1.0. The range is between 0 (no correlation) and 1.0 (perfect correlation).

**SEE ALSO:**