The EPR Paradox and Quantum Nonlocality (Part 1)

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 (atom) which could be ruptured such that two electrons were dispatched to two differing measurement devices. Each electron would carry a property called 'spin'. Since the atom had zero spin, this meant one would have spin (+ 1/2), the other (-1/2). The diagram below illustrates this, the atom being disrupted inside the box, with its opposing spin electrons sent to the left and right.
 
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.

 Then, we need only know one spin to obtain the other. Say we know or can measure one spin to be (+1/2).[2] Since the total atomic spin is zero, the other electron must have spin (-1/2) since:   (-1/2) + (+1/2) = 0

 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, Einstein went one better at the 6th Solvay Conference held in 1930, actually designing a device (see image on next page) that he was convinced would have Bohr in tears trying to find a solution. (According to reports, it very nearly did, and a number of participants insisted Neils was in a state of "shock" believing there was no real solution.)

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/ c². Thus, the difference is taken as follows:

Weight(before door opens) - weight (after - with 1 photon of mass m = E/ c²   gone)

     Thus, 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 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)/ c²

where G is the Newtonian gravitational constant, M is the Earth's mass, and g is the acceleration of gravity (g = 980 cm/ sec² in cgs) and c = 3 x 10¹⁰ cm/sec.

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

dt/t ~ (980 cm/s²)(10^-4 cm)/ (3 x 10¹⁰ cm/sec )²

dt/t »  10^-22

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

 

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!

 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.

 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.

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", Bell then proceeded to place the E-P-R experiment in a rigorous and quantifiable context, which could be checked by actual measurements.

 In a landmark theoretical achievement in 1964, Bell formulated a thought experiment 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 the Bell Inequality.

 To test quantum conformity to Bell's Theorem, Alain Aspect and his colleagues at the University of Paris, set up an arrangement as sketched below.[3]  In these experiments, the detection of 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)

                                              

Here, the laser device is D, and the analyzers (polarization detectors) are A1 and A2 along with two representative polarizations 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 and we obtain, 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 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'.[5] 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:[6]   S = 2.70 ±  0.05 and in so doing experimentally validated Bell’s Inequality.

 The crucial significance of the Aspect experiment (1982) and earlier the Clauser experiment in 1969, had not been lost on physicist David Bohm.  Both experiments reinforced for him that a novel concept had to be introduced to account for these nonlocal results. The old answer of the Copenhagen theorists: '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.

---

    [1] Einstein, Podolsky, and Rosen.: 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] Aspect, Grangier, and Roger: Physical Review Letters, 91.

    [4] Polarization is the orientation in space of the electric field E, associated with light. This can be altered, subject  to the imposition of different filters and devices.

    [5] 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).

    [6] Aspect, A. et al, op. cit.

Why the Concept of "Natural Afterlife" Is Nonsense (2)

If you ask a serious, decently informed person if s/he believes a perpetual motion machine is feasible, the person will likely respond: "Of course not! It's nonsense!" This shows the person may at least have had some basic exposure (maybe in high school physics) to the 2nd law of thermodynamics.  In a more advanced course, i.e. Calculus Physics taken in first year university, two statements express the 2nd law. They are:

(I) The Kelvin -Planck statement:

It is impossible to construct a heat engine, operating in a cycle, which produces no other effect than absorption of thermal energy from a hot reservoir and the performance of an equal amount of work.


II): The Clausius statement:

It is impossible to construct a cyclical machine that produces no other effect than to transfer heat continuously from one body to another at higher temperature.

These are often generalized in another form to read:

“The entropy (degree of disorder of a system) increases in all natural processes”


Thus, for example, gasoline once burnt in your car engine cannot be captured from the exhaust gases and used over again.. Also, any energy process will also have a large part of any energy produced coming off as unusable waste energy. There is no way, or any process that can deliver 100% usable energy.

In terms of biological -organic systems it means that death is the highest entropy state. This means that once one is dead he remains dead.  There are no "Lazarus-type" resurrections.  Once one's life is extinguished it remains so. In other words, if one adheres to the laws of the natural world there can be no personal afterlives, i.e. peculiar to the individual which are contingent on a lower entropic state (e.g. dream ideation or experience) that pre-existed the person's demise.

However, the supernaturalist doesn't adhere to physical- natural laws, so of course, he is at liberty to invent "afterlives" - even eternal, or "timeless ones".  No biggie. He can even invent "heaven" and "hell" plus "purgatory" - if he happens to be Catholic.

The point is, that unless one is a supernaturalist, he cannot invoke a timeless state contingent on a "dream state" condition that had to involve a particular energy regime associated with synapses in the brain. In other words, a "natural afterlife" which demands indefinite preservation of a synaptic state pre-brain death,  must be as much nonsense as perpetual motion machines.

Let's delve into this further.

According to Bryon Ehlmann,  a proponent of this "theory":

The natural afterlife is timeless. Again, it is the final moment of your NDE. It is like a paused movie scene and the feelings and memories you have at the exact point at which the movie was unknowingly paused. Since it is timeless, no further events happen within the dream. You, however, are never aware of this and that your dream was not just “paused,” but actually stopped since you too were “stopped.”


Now consider: He at once invokes the presumption this "natural afterlife" is timeless. But what must happen in terms of the 2nd law, i.e. to be "timeless"? The answer is that the entropy of the dream- sustained system - whatever it is-  must be zero. However, the natural afterlife proponents decline and indeed reject nonlocal consciousness (e.g. of the Stuart Hameroff or Bohmian type), which means they are hoist on their own petards.  This means they are left with explaining a "dream state" system they invented that has arrived from a higher entropy state to a lower one, something completely disallowed for closed systems. (Wherein the entropy must always increase, unless it can avail itself of external energy, i.e.  green plants in terms of sunlight).

Consider that in the instants preceding actual death, and possibly with an NDE in train, successive brain states evolve leading to one final state:

{s₁, s₂, s₃, s₄……………s_n}   ®  Ã

Entanglement and increased entropy of neuronal states is dictated by:

 

ENT (Ã) = -Tr à ln Ã

Where Tr denotes the trace  (of diagonal elements)  of the  corresponding density matrix.

This means, using our model from the previous blog post, that synaptic function must begin to slow, i.e. as neural transmission and efficiency begins to recede. The person is headed toward a maximum entropic state as are the specific portions of the brain which create the ideations, dreams, thoughts a person has.

The entropy then will be the total aggregate of accessible states:

ENT(Ã) = ln Ã

Conservation of probability requires:

¶P/ ¶t = ¶ / ¶t (Tr(Ã)) = 0

In other words, the process must be one for which any change in the defined state  Ã   tends to zero , given there can be NO further entropy change. However, the natural afterlife bunch are asserting there is a change from what would be maximum entropy (at death) to a defined zero entropy ("timeless") state, post death, i.e. in their NED (never ending dream scenario). Hence, they are postulating a major contradiction of the 2nd law of thermodynamics.

If one agrees that the synaptic cleft dimension (see last post) is scaled to allow application of the Heisenberg Uncertainty Principle (as Physicist Henry Stapp has shown, i.e. in his 'Mind, Matter and Quantum Mechanics') then it is feasible to obtain a rough estimate of the final energy state potential just before death. I.e. let us imagine the last workable synapse firing to generate an ideation. For this estimate we will allow a   2τ time indeterminacy or:

2 τ = 2 x (10^-34) s

Then using:

ΔE Δ t ³  h/2π

the calculated energy change (‘indeterminacy in energy’) is:

ΔE » (h/2π)/  Δ t

Or:

ΔE »  1.05 x 10^-34 J-s/ (2 x (10^-34) s) » 0.5 J

So one half joule is available - which means for the end state to be sustained this energy must also be sustained, e.g. in the alleged "timeless" state. This is roughly equal to the energy given off by a half-watt bulb (say in a small flashlight) for one second..

 

It is also useful to estimate how much information - as bits-  this amount of energy corresponds to. We already know that one bit has 0.693 kT of energy (in joules) where k is the Boltzmann constant and T is the ambient temperature. Then the number of bits would be:

N(bits) = (0.5 J) / (0.693kT)

 

Taking k = 1.38 x 10^-23 J/K and T = 300 K (about typical room temperature), one obtains:

N(bits) = (0.5J) /  [(0.693 x 1.38 x 10^-23 J/K) ( 300 K)]

N(bits) = 1.74 x 10²⁰

This would be the total number of bits in the final ideation (dream state)  that would need to be sustained in the timeless state. (The only assumption made is that any given 'frozen'  dream image contains information, it cannot be content or information free, or it doesn't exist - especially to the person allegedly experiencing it.) Thus persistence of the dream image/content  cannot be done without energy, any more than a paused TV image can be sustained without electrical energy. But where is it coming from? The natural afterlifers reject non-local consciousness as even remotely possible, indeed they dismiss consciousness entirely! This leads one to believe they are making the error first identified by Prof. Daniel N. Robinson (op. cit., p. 6):

 

"The claim 'I am conscious of the rabbit in the garden' is different from the claim 'I know there is a rabbit in the garden'.  There is a difference between being conscious of and being conscious. The former is always subject to error. Being conscious or aware is to be the possible subject of an experience, the self."

He also expands on the  notion of self-reference, and takes to task those who believe it to be merely an epiphenomenon of the brain, by way of the 'Mary' problem. 

A bit of digression here: Central to discriminating opposing Materialist models of mind are qualia. The term refers to subjective properties perceived in the material world, including colors, shapes and sounds (music). Arguably, none of these have objective existence but are tied to our neural processing and mode of consciousness. The qualia problem is often also called the Mary problem since it presents a hypothetical character (“Mary”) who inhabits a black and white world, but knows everything about colors in physics terms. Still, though she knows what color signifies – a particular wavelength in the electromagnetic spectrum – she has never experienced it.  The qualia problem helps to distinguish between what many call monistic physicalism and what I refer to as quantum physicalism. Monistic physicalism in its most rudimentary form can be summarized by Victor Stenger’s comment[1]:

 

It does not matter whether you are trying to measure a particle property or a wave property. You always measure particles. Here is the point that most people fail to understand: Quantum mechanics is just a statistical theory like statistical mechanics, fundamentally reducible to particle behavior

 

And the biggest contradiction to Stenger’s interpretation is[2]:
 

Although Y is a real field it does not show up immediately in the results of a ‘single measurement’, but only in the statistics of many such results. It is the de Broglie –Bohm variable X that shows up immediately each time.
 

In Stenger’s monistic physicalism, reality is structured around locality (predicated on particles), and quantum wave mechanics and its inherent potentiality never enters the field Y  to the extent of overturning particle dominance. In this way, emergence and holism are kept at bay. Conversely, J.S. Bell’s awareness of the hidden variable X enables quantum waves to supersede particles and in turn, demands the brain is treated as a quantum mechanical device.

 

 

On account of the latter position, physicist Henry Stapp has correctly noted[3]:
 

Brain processes involve chemical processes which must, in principle, be treated quantum mechanically. In particular, the transmission process occurring at a synaptic junction is apparently triggered by the capture of a small number of calcium ions at an appropriate release site. In a quantum mechanical treatment, the locations of these calcium ions must be treated quantum mechanically
 

 All of this means, again, that the only "natural afterlife" plausibly (albeit improbably) on offer or even remotely feasible based on physical laws, is the one described in the previous post to do with de Broglie waves.

 

Bryon Ehlmann writes:

 

  The natural afterlife is relative. Others know that you are dead and that your brain is no longer functioning and that your last dream—what would have been an NDE had you recovered—has ended, but you do not. For you, the NDE becomes an NED.

 

But this really says nothing, not anything a physicist can hang his hat on, i.e. in terms of energies available, entropy, neural thresholds etc. So whether the 'natural afterlife is relative" is roughly like whether one million angels can dance on the end of a pin, or one thousand.  Others "know you are dead" - ok, fine, but if they have sense they will have an EEG attached at the last instant to see if any mercurial action potential causes wave spikes that might indicate a final dream state. (Better yet, keep the EEG attached over time to see if any tiny wave forms re-appear  - after all a 0.5 J end state in stasis ought to be detectable electrically!)

 

Bottom line: a dream state or dream, final or not, must have energy to support it as I showed. It can't persist indefinitely in a metaphysical vacuum, following death,  no matter how many words (or clever analogies)  the natural afterlife crew churns out.  (See A.J. Ayers'  Language, Truth and Logic).  Those interested in seeing Ehlmann's detailed responses to an earlier blog post of mine on the after life can go to this link.

 

http://possibilities-and-phenomena.quora.com/The-Natural-Afterlife-vs-a-Quantum-based-de-Broglie-Wave-Afterlife

 

 

Then make your own decision!

--------------------------------------
Addendum:
 

 Ehlmann's comment in his link response,  that:

"The deBroglie wave afterlife is described using phrases such as “de Broglie waves,” “essential energy associated with the microtubules disperses out from the brain and becomes ‘entangled’ in a larger, undifferentiated whole,” “quantum coherence,” and “quantum wave states are stored in a multitude of microtubules” as well as by numerous mathematical equations. The complexity is enough to make one’s head spin!"


Is really irrelevant. He mixes up the use of precise language (which any serious person ought to strive to employ to avoid ambiguity), with constructs that others have invoked. Thus, the terms "de Broglie waves", "quantum coherence" and "entanglement" are all well known within the context (QM) in which they apply. Their use doesn't make for 'complexity' but rather exactitude in referencing and distinguishing elements of a hypothesis related to the underpinning physical theory - something Elhmann would do well to attend to more.

"Undifferentiated whole",  likewise, is merely another term (synonym) for quantum nonlocality - which again is basic to discussing anything to do with quantum mechanics. Since de Broglie waves encompass quantum mechanics, it is natural for this term to appear. That doesn't mean the basis is "complex", only that the person approaching it from a more generic (anecdotal) perspective hasn't adequately done his homework.

Where the complexity actually arises is in the use of "micro-tubules" (an added structure of the brain inside neurons) but which is really due to Hameroff and Penrose, not me. Technically, the de Broglie wave hypothesis requires no special additional structures since these decay anyway at the time of death - the only thing really left are wave forms, i.e. the  de Broglie  waves themselves.  NO unheard of violations of natural law are required here, unlike the violations of the entropy law by the NED team.

Ehlmann maintains he is a "skeptic" and he:  "will wait until (my)  theory of de Broglie waves is published in a peer-reviewed scientific journal".  Of course,  this is ridiculous. I make no claim to having a "theory" that is in any way significant enough to qualify to be published in a journal. I only offer the de Broglie wave hypothesis as a scientifically plausible, albeit improbable, explanation for a possible afterlife scenario.  I offered it as part of two blog posts-   because I maintain the 'natural afterlife' proposition of Ehlmann et al isn't plausible at all.

Let me also again clarify that my own POV is that death means the end of whatever had previously existed, including ALL formerly conscious states, ideations and any residual derivatives of them.  That means I implicitly accept the scientific world view of entropy as defining the "arrow of time" (at least in the classical realm) and that death means one has reached a maximum entropy condition. This maximum entropy automatically rules out any "timeless state" embodying any kind of ideation, or "dream" - since such state would have entropy zero.  Others can go along with the natural afterlife if it makes them feel better, but I believe they will only be fooling themselves.
 

---

[1] Stenger, God and the Folly of Faith, 155

[2] Bell,: Foundations of Physics, (12,) .989

[3] Stapp, H. op. cit., p. 152