From: jerry 2/03/99 11:40:09
Subject: Quantum entaglement post id: 2555
(Part 1)

Dear Jerry (please call me Karl),

Hi, and thanks for your excellent and well thought-out answer/comment! I
have been trying to understand this stuff for years! Quite frankly, I
still don't understand it, so I'm not yet qualified to answer it.

Would it be possible for you to post your answer in the appropriate
section, of the appropriate week, of the Signal to Noise Section, of our
homepage, so that everybody else (67,000 pages down-loaded per week) can
enjoy your answer as well?

Cheers, karlkkkkk



>Dear Dr Karl,
>I am trying to get my head around this quantum stuff - and my question
>therefore is simple, "Do you agree with my arguments below?"
>
>Many thanks.
>Jerry.
>
>Quantum superposition and entanglement.
> Feb 26 1999
>
>In quantum mechanics we may consider an electron with the property spin.
>Whichever "direction" you measure the spin, you will always find either spin
>`up' or spin `down'.
>
>However, if the spin of the electron has not been measured, then the
>electron is in a superposition of these two distinct states.
>
>It's a little similar to a penny, spinning on the table-top. If you slap
>your hand on it, then it will either show heads or tails after the
>measurement, never something in between or "both". However, before the
>measurement, all that we can calculate about the head/tail state of the
>penny is that it will be either heads OR tails after measurement, with
>corresponding probabilities of each state summing to 100%. With electrons
>and photons the situation is somewhat dissimilar in that a measurement does
>not physically prevent the particle from "spinning" since the term "spin"
>when applied to quantum particles does not actually mean "spin" in the sense
>that a penny spins on the table but the analogy does add some degree of
>understanding. (It is also not possible to catch and measure a given
>particle every time - so we are back into statistics again for determining
>the likelyhood that the two particles are actually 100% entangled as it were
>- a fine point in the context of this argument.)
>
>We represent this mathematically as two equal length (1/2) (50:50 chance of
>heads or tails) perpendicular vectors in an abstract space (a so-called
>Hilbert space). A superposition is defined as the vector sum of these two
>vectors. The vector we associate with a superposition therefore lies in the
>plane spanned by the vectors `up' and `down' or 'heads' and 'tails'.
>Different angles phi (the angle of the superpotition vector) correspond to
>different superpositions and different probabilities (represented and a s a
>result of the relative lengths of the vectors) so that one rather than the
>other will prevail after measurement. It is easily conceived that a system
>may consist of a superposition vector that traverses Hilbert space
>dynamically with respect to some independent variable such as time. In the
>case of the penny, while it is spinning fast, it's vector will have phi at
>about pi/4 radians implying a 50:50 chance of falling heads or tails after
>measurement. If we imagine what happens to the vector if we let the penny
>spin to a halt without hitting it, then the vector may be imagined to waver
>about pi/4 and then rapidly fall to zero or pi/2 when the penny finally
>starts to spin with one particular face up. The "heads" vector and "tails"
>vector either shrinks to zero or expands to one. If a penny was biased heads
>or tails, then the two vectors from which the superposition vector is
>created would be nominally unequal - but still sum to one.
>
>In the case of electrons and photons, there is a system involving a pair of
>particles that are produced in the same source that are entangled. This
>means that, independent of subsequent separation in distance, you may
>determine the spin of one such particle and then predict to 100% certainty
>that the other particle has opposite spin. At the risk of the effects of a
>very bad pun... the experiment performed in mid 1977 which actually observed
>quantum entanglement has spun-out many people. There has been talk of
>instantaneous information transfer, teleportation and paradoxical meanings
>with respect to special relativity and quantum mechanics. As it turns out,
>FLT signaling is NOT possible using this system simply because the
>measurement result of one particle must subsequently be transmitted to the
>owner of the other particle, and this is subject to the rules of special
>relativity. I have read texts that use words like "spooky action at a
>distance" (borrowed from Einstein) and "Somehow the other photon "feels" the
>result of the measurement of the measured one." I've even read text that
>blames the confusion on limitations in our language! All seem silly
>explanations and I would like to pose the following analogy using pennies as
>a slightly better popular account of quantum entanglement.
>
... continue
From: jerry 2/03/99 11:44:43
Subject: re: Quantum entaglement post id: 2557
(part 2)

>Mathematically, measurement of one of an entangled pair is said to "collapse
>the wave function" - a statement that does not help the layman understand.
>But the layman has a possibility of understanding the superposition vector
>explained earlier. What we are representing by this superposition vector in
>the case of the spinning penny, is the probability of heads vs. tails before
>the penny has stopped spinning. In this macro-scale case the state is
>determinable either because of a measurement or because of natural loss of
>momentum. The "wave function" spoken of just now is a "probability curve - a
>distribution of probabilities spread over an infinite range." and so
>"collapsing the wavefunction" is equivalent to drawing the mathematics from
>the sphere of statistics into the world of fact. Once a measurement has been
>made, the statistical distribution is no longer of any use because the state
>of the system becomes determinable. What we tend to do is confuse the
>mathematical concept of probability distribution with actual physical fact.
>Statistical representations of systems do not target one particular state -
>only the likelihood of finding a given state. Let me now explain a two-penny
>entanglement system.
>
>Imagine this: I take a seemingly normal penny and peel it apart so that I
>now have two disks and I set them spinning on different trays. Two people
>who were NOT ALLOWED [thinks: "the plank constant"] to witness the
>creation of the entangled pennies then walk away from each other each
>carrying a tray until they are far apart. One person looks at their penny
>once it has stopped (or stops it) and declares the state of the other penny.
>The other person takes a look at the stopped penny and finds that the other
>person's prediction is correct.
>
>How is this possible? Simple. The original penny that was peeled apart is
>actually two pennies. Still don't get it? What if I said that the original
>penny was made of one double-headed penny and one double-tailed penny? Now
>it all makes sense. The outcome of the experiment is actually determined at
>the source - long before the measurements were taken. They are guaranteed to
>be complementary since that is how we defined the system. Similarly, an
>entangled pair of photons can only coexist (entangled) upon creation in the
>source by having complementary characteristics and because of the exclusion
>rules of quantum mechanics - things like "two electrons only may occupy the
>same energy level". If they don't have complementary characteristics - then
>they are not entangled!. In both cases - with the entangled pennies and with
>entangled photons, before actual measurement, we can only mathematically
>describe the state using the Hilbert space (or similar tools). Once the
>measurement is made the Hilbert space is not required and facts can be
>stated about the system regardless of the subsequent separation of the
>individual pennies or photons. Before any measurement is made - even though
>the outcome is physically pre-determined, we have no idea what it is and
>therefore have to invoke the stochatic power of mathematical concepts in
>order to describe the system. It is the nature of these concepts as
>mathematical tools, not reality, which provoke the use of language that
>suggest that "Schrödinger's cat can be both dead and alive".
>
>The important point to note about all teleportation experiments and
>entanglement experiments is that the entangled particle must be created in
>the same source. It would be impressive indeed to be able to independently
>create and entangled pair at different spacetime coordinates but that has
>never been done.
>
>Could it be therefore that a "normal photon" for instance is a bit like the
>double-penny glued together head-head-tail-tail so that it looks like a
>familiar penny and the production of an entangled pair is like peeling the
>pennys apart? In principle I can't see why not.


[end]
From: Terry Frankcombe 2/03/99 14:14:27
Subject: re: Quantum entaglement post id: 2565
Hmm. While I don't pretend to understand entanglement, I don't like the fact that you are using a classical analogy to explain a very QM effect. Pennies are macroscopc and therefore deterministic. Photons are microscopic and probabilistic.
From: jerry 2/03/99 14:56:22
Subject: re: Quantum entaglement post id: 2582

While I agree that trying to explain a quantum idea using a macro analogy is questionable - What alternatives are there? What I am trying to do is invent a hypothetical macro system that we can all understand which, when modeled mathematically, uses similar concepts as the quantum description. People seem happy to explain the expanding universe in terms of rubber balloons and flies, or raisin bread in the oven.

In my attempt, I use spinning pennies, but point out clearly that the physical analogy is way off the mark as far as quantum particles are concerned.

The main point of the whole argument is to try and determine if the worldwide confusion about quantum entanglement is due to an over emphasis on what the stochatic mathematical model means as far as a physical system is concerned at a point just before the wave function is collapsed. The result is confusing or at best irrelevant. The physical implications of trying to imagine a real system state that would be described by a system actually IN superposition being bizarre but holding high media value. I mean - people say daft things like, "The electron is everywhere at once." No it's NOT! It's just that we are forced to work with probabilities of where it is - and the mathematics says it can be anywhere (to a more or lesser degree of certainty.)

In the example with the spinning entangled pennies, it does not irk us too much to think of them as being in both a "head" and a "tail" state until the point of measurement. And of course, the act of measuring one will indeed predict the outcome of the other and collapse the stochatic equations involved in the system as a whole. But for us - since we set up the trick in the first place and are privy to the initial conditions - we make no attempt to imagine the pennies as talking to one another at the point of measurement! We also have some kind of physical representation of a "head AND tail" state - i.e. a spinning disk. In contrast, we have no decent visual representation of a photon.

What I am looking for is someone who can say, "No - your analogy is wrong - and this is why:…"
Or someone who can enhance the analogy in some way.

Cheers.


From: Chris (Avatar) 2/03/99 15:03:09
Subject: re: Quantum entaglement post id: 2584

Well, I like the spinning penny as an analogy for unresolved probabilities co-existing.

However I think you're overextending it in quantum entanglement terms. I found from reading your account that the penny analogy didn't really add anything to the issue of separation, and it is potentially very confusing. For instance I thought you were going to get confused on the spin issue - and whilst you extricated yourself by saying the penny spin doesn't correlate with a particle's angular momentum, that section became sloppy. (The fact that the penny spins is entirely irrelevant - what is important is that we don't know whether it will be heads or tails till we stop it, ie until we actively observe).

What you seem to be basically asserting is that the twin photon system can be described by a single wave function, which is a standard interpretation anyhow. And I don't see how your split pennies help with that - in fact I'd have to say it would probably do more to confuse people.

I find that a similar problem occurs in GR, SR, etc where people take simplistic analogies (eg the inflating balloon model of the expanding universe) and then over-use them. The model is intended to help understanding about the physical reality, not to substitute for it. In that sense, as I say, I thought the spinning penny is a good analogy for unresolved probability or superposition of states, but not for entanglement.


Hope this helps!
Chris
From: Stephen Bosi 2/03/99 15:11:16
Subject: re: Quantum entaglement post id: 2585
I'll tell you exactly why your analogy is wrong. Because you said that the result was determined at the moment the pennies were peeled apart. This is completely contrary to the spirit of quantum mechanics as we presently understand it. Einstein wanted to believe that in these kind of experiments, the result was predetermined BEFORE observing the spin on one of the electrons (or the polarisation on one of the photons), whereas the more conventional quantum explanation is that the result is determined at the moment of measurement. The two pictures are NOT equivalent and yield different experimental results. The experiements have been done and the non-Einsteinian picture makes the correct prediction.
From: Chris (Avatar) 2/03/99 15:25:49
Subject: re: Quantum entaglement post id: 2588

The main point of the whole argument is to try and determine if the worldwide confusion about quantum entanglement is due to an over emphasis on what the stochatic mathematical model means as far as a physical system is concerned at a point just before the wave function is collapsed. The result is confusing or at best irrelevant. The physical implications of trying to imagine a real system state that would be described by a system actually IN superposition being bizarre but holding high media value. I mean - people say daft things like, "The electron is everywhere at once." No it's NOT! It's just that we are forced to work with probabilities of where it is - and the mathematics says it can be anywhere (to a more or lesser degree of certainty.)

This argument has been going on since the earliest Solvay Congresses in the '20s, and spawned what we call the Copenhagen Interpretation of QM. You're arguing the point of view of Einstein, et al, who insisted that the quantum theory can not be a statistical mathematical theory without an underlying description of the "physical reality" whatever that may be.

Bohr and his supporters (and students) countered that since the underlying reality is observation dependent it becomes less meaningful to try to describe the physical situation prior to observation, as in "yes, but what's actually going on before we look at Schroedinger's cat?"

Terry is exactly right in his assertion that you can't really attempt to model a QM system classically. It may help with visual cues, etc, but to base your math on such a model is a mistake, after all QED is the most mathematically accurate theory ever devised! Keep in mind, also, that other visualisations such as schroedinger's cat, etc, were coined in an attempt to point out how ridiculous the quantum theory is at a macroscopic level!

What I am looking for is someone who can say, "No - your analogy is wrong - and this is why:…"

Ok, your analogy is fine enough for a single spinning penny representing an unobserved superposition of two possible eigenstates.

Your analogy is confusing when you separate the penny into two and remove them. I understand that you are trying to show that the head and tail are interrelated before splitting, and remain that way. However because you introduced the idea of collapsing the wavefunction=stopping the penny spinning, you're in trouble. Stopping one penny spinning will not stop the other. The lay person will get confused. Since there is no physical connection between the two half pennies, how does this improve on the situation with two separated photons? This is why I think it helps with the single penny, but not with the two.

Consider how your pennies will help explain the EPR paradox to someone. The penny can only handle one variable with two possible eigenstates. The heart of EPR is the second variable which is mutually non-commuting with the first. I don't see how the pennies help here.


Hope this helps!
Chris
From: jerry 2/03/99 16:05:47
Subject: re: Quantum entaglement post id: 2592
Said Chris: "I thought the spinning penny is a good analogy for unresolved probability or superposition of states, but not for entanglement"

Thank you for your comments. I would like to reinforce the entanglement argument. ( We have got out of phase. I'll digest your latest post in a while and reply to it - but admit that my missive is confusing if it was interpreted as meaning:
[ "However because you introduced the idea of collapsing the wavefunction=stopping the penny spinning, you're in trouble" ]. I never intended to imply that as an equality. I'll have to re-read the original post to see how that popped out! I've been flipping between QM and classical terminology too much. Sorry.

If we can leave aside the *spinning* pennies and concentrate on the initial conditions, the two discs constructed from one doubled-headed and one double-tailed disc , H-H-T-T "look" at first glance like a single disc because of the way that they are put together - back to back. What I am saying is, "this is an entangled system in our hypothetical world." Then I say, that no observer is allowed to be privy to the construction - in the same way that we are barred from knowing what goes on at distances smaller than the plank length. However, because we can peel these discs apart and THEN look at them separately, we can infer that the system has certain rules. In our hypothetical system the rules being perhaps, "No construction H-H-H-H is allowed… only a maximum of two disks per object are allowed and they must have complementary H and T"… and anything else that we might theorise and test about the system.

"Entanglement - and the outcome of subsequent measurements" therefore is a property of the initial conditions. Maybe these discs can be created by a wacky energy change or something - but only in the form H-H-T-T. If we work out how to "create" two separate entities from the same source at the same instant, an H-H and a T-T, such that they can subsequently be *separated* in space, this is still an entangled system. Again, if we are not allowed to witness their creation and construction at that point in time, we either have to look at one of them or apply stochatic mathematics to determine probabilities about the state of the system.

I would be surprised if no one has a problem with the statement "Entanglement - and the outcome of subsequent measurements" therefore is a property of the initial conditions." - only for the fact that this is coming straight out of my analogy and I've never read it anywhere with respect to QM.

It would sort of beg the question, "Are all photons/electrons actually tightly coupled entangled pairs that appear to be a single unit to an observer? Entangled pairs still look normal but for the complementary characteristics." Could it be that we are fooled into thinking that each of an entangled particle is bog standard - just the same as a "normal" particle whereas the reality may be that what we see as non-entangled particles are actually elaborate systems of pairs that just look normal? Just like the head-head-tail-tail penny. After all, if we are only allowed to look at a head-head penny once it has been stopped, then we can't know what is on the other side, and may well assume that it is a "normal" Head-tail penny. From this aspect - I see comfortable analogies. Again, if we did many independent experiments with "normal" pennies, we would find that 50% are heads, 50% are tails. We may even come to the conclusion that each is constructed HT - even though they are actually of HHTT construction. We may then further experiment with peeled-apart pennies (the act of peeling we cannot see) and conclude that, since the experiments never show with acceptable certainty that entangled pairs both land heads or both tails, that they somehow communicated instantaneously across any distance. We will never conclusively be able to show that the actual construction of a separated entangled pair is HH ( or TT )! And if that idea never occurs to us and we live on in the belief that each separate entangled pair is HT - just like our idea of "normal" discs, then the "spooky action at a distance" seems plausible as a mathematical explanation but quite perplexing in reality. I can see why Einstein balked.

From: jerry 2/03/99 16:15:17
Subject: re: Quantum entaglement post id: 2594
Thanks Stephen,

I'm not trying to oust QM or take Einstein's side either - so I do appreciate your comments. I'm just trying desparately to get my head around this stuff.

Do you have any further details on the experiments of which you speak?

[ The experiements have been done and the non-Einsteinian picture makes the correct prediction. ]
This forum is un-moderated. The views and opinions expressed are those of the individual poster and not the ABC. The ABC reserves the right to remove offensive or inappropriate messages.
From: Chris (Avatar) 3/03/99 9:13:47
Subject: re: Quantum entaglement post id: 2652

Stephen is probably referring to the EPR paradox. In the late 60s John Bell wrote an inequality which could help determine what happens when non-commuting variables in entangled but separate particles are observed.

In the 80s Alain Aspect devised a physical experiment to test the inequality. The results came down in favour of Bohr - against Einstein (the two protagonists in the original paradox).

The details of the inequality, and aspect's experiments have been published, critiqued, etc. You will probably even find them online - although physics review is the best place.

The remaining controversy centres around the mathematical formulation of the inequality and its correctness - or completeness - and some limitations which may or may not have affected aspect's experiment. Dr Ed holds a slightly different view to mine on the validity of aspect and bell, and the arguments continue!! :o)


Hope this helps!
Chris
From: jerry 4/03/99 11:56:29
Subject: re: Quantum entaglement post id: 2751
Thanks Chris, I am aware of the EPR "paradox". I've been reading up on Bell's theory and at least one author actually states,

"The two photons are correlated when measured because their potentialities-their indeterminate, wavelike aspects-were never separate in the fist place." (pp65-67 "Who's afraid of Schrodinger's Cat? Ian Marshall, Danah Zohar")

This is precisely what I am saying with regard to the system of back to back double-head,double-tailed pennies - nice to read that but I beg the question, "Have I interpreted this correctly?".



Also, according to the author of the web page…

http://www.mtnmath.com/faq/meas-qm-faq-5.html

"…It might seem that the tables have been turned on Einstein. The very argument he used in EPR to show QM must be incomplete requires that hidden variables models have explicit nonlocal operations. However it is experiments and not theoretical arguments that now must decide the issue. Although all experiments to date have produced results consistent with the predictions of QM, there is general agreement that the existing experiments are inconclusive3. There is no conclusive experimental confirmation of the nonlocal predictions of QM. If these experiments eventually confirm locality and not QM Einstein will be largely vindicated for exactly the reasons he gave in EPR. Final vindication will depend on the development of a more complete theory…"

3 P. G. Kwiat, P. H. Eberhard, A. M. Steinberg, and R. Y. Chiao, Proposal for a loophole-free Bell inequality experiment, Physical Reviews A, 49, 3209 (1994).

------------------

This bit that I have picked up on is "There is no conclusive experimental confirmation of the nonlocal predictions of QM"

Can anyone add any degree of credulity to this?
Does anyone know the current status of the certainties of these QM experiments involving nonlocality?
From: jerry 5/03/99 14:33:51
Subject: re: Quantum entaglement post id: 2932
Hi,

A quote from


http://cosmopolis.com/topics/quantum-nonlocality.html

"...The Phenomenon of Quantum Nonlocality
Because the spin of a particle does not exist until a measurement is made, the act of making the measurement and determining the axis of spin of particle 1, will also determine the spin of particle 2, no matter how far apart it is from particle 1. Particle 2 will instantly respond to the state of particle 1, even if it is on the other side of the universe..."

Is this really really true ? Experimentally proven? I mean the bit about the "other" particle "responding" - I don't mean 'just that we instantly "know" it's state', I mean, is there an experiment that shows, say some interference effect that vanishes or wobbles or something before the eyes of the experimenters on the "other" particle at the instant that particle one's spin is measured? Even if the other spin is not known by those far away experimenters because they have to await the result of the spin measurement from the first using normal signaling.

I think not 'cause then you could transmit a code by setting up an array of entangled pairs, take them far apart and then "send" ones and zeros by measuring or not measuring in the array. "Does watching ANY property of the other particle or relationship between the two cause a collapse of the wave function"?

Therefore, - back to my original analogy and conclusions - that the spin states are predetermined. It's just the mathematics that "pops" into actuality from probability.

Still struggling with this one!

:0)

From: Chris (Avatar) 7/03/99 16:11:12
Subject: re: Quantum entaglement post id: 3023

Jerry

Your struggle is going to continue for quite some time because it is a struggle with conceptualisation, which QM tends to resist.

I refer you again to Bohr's interpretation. He pretty much comes straight out and says that QM doesn't deal with "what happens before a measurement is made". The theory is observation dependant, to the extent that traditional "reality" is only defined on the basis of measurement.

In this sense, I could describe the situation with entangled photons simply with a single SWE (schroedinger wave equation). This is a powerful conceptual tool for those who have looked at the mechanics of the quantum theory. Let us not forget that QED, the crown jewel in the quantum theory, is the most accurate mathematical theory ever devised.

Consider (for example) the decay of a neutral kaon, at rest in the laboratory frame, into two back to back photons which are then separated and individually examined. Now ask yourself whether it is possible to describe the two photon system by a single SWE (examine complimentary variables) and then ask what this tells you about the system.

Now compare to a penny spinning which is split into two. Which tells you more?

On your question about Bell's theory and Aspect's experiments, yes both the inequality and the experimental design and execution have been questioned. The experiment ruled out hidden variables, and may still do so. However there is still debate on the topic. I might add that if the aspect/bell result is shown to be wrong, and there are hidden variables which account for non-locality then I think your pennies are in even bigger trouble! :o)


Hope this helps!
Chris
This forum is un-moderated. The views and opinions expressed are those of the individual poster and not the ABC. The ABC reserves the right to remove offensive or inappropriate messages.