EPR, Aspect, Bell, and Understanding Quantum Weirdness

[my_wan]

Due to the exorbitant length of the post and the twisted nature of the way the concepts are presented some responses are left out. If anyone wants anything missed here please ask.

Well, to some extent, that is so; but I'll wait to see what precisely you have in mind before I state a definite position.

Have in mind? I stated what I had in mind in that post. I thought this was history by now. That statement is actually a bit weird. I thought I was asked an opinion on Afshar and gave it. Was it really just a tutorial?

Well, according to four sources I produced, photons are quanta, and photons are particles, and according to three of them, they are elementary particles as well. I think you have a definition problem here; I expect that you will make clear what you mean, but since you seem to feel that technical accuracy is important, I will take you at your own evaluation and state that this is technically inaccurate. Quanta are the fundamental entities of which our universe is composed. Quantization does not always mean the rendering of a parameter into elementary particles; for example, the quantum of action, hbar, does not (as far as we can tell) have direct physical existence as an elementary particle. Nevertheless, some quanta have real physical existence, so much so that we can see individual spots on a phosphor screen, or a CCD chip, that mark their positions of impact.

It was a pain but it seems these are the four sources you mentioned; "quanta of the electromagnetic field". This is funny. In the llu.edu link it gives common definition of a photon as;

Photon: A quantum (energy packet) of electromagnetic radiation; the elementary particle of photon radiation therapy. X rays and gamma rays are photon radiation.

Now look at the definition of quantum in wiki.

In physics, a quantum (plural: quanta)

Now if a fundamental particle (photon) consist of a plural of fundamental particles (quanta) how can a photon be a fundamental particle? It is not me with "a definition problem here".

As far as whether quantization is limited to energy, the existence of a quantum of action shows that this cannot be so. Further, spin is also quantized. Not only that, but so is charge.

Yes I conceded this to pragmatist and give the reason.

While this is true of continuous parameters, my intent was to use spin, since that is the parameter used in Aspect and the DCQE. And because spin is discrete, it is in fact correct to state that in the case of spin, if you know the spin on one axis, you can't know it to some arbitrary precision; you know it to absolute precision, or you do not know it at all. And and spin on two axes is conjugate under uncertainty, so if you know the spin on one axis, you know it absolutely, and therefore cannot know anything of it on any other axis.

Ok so we'll take "certain parameters of quanta" to mean spin. For simplicity I will not even go into the concepts of spin. The Uncertainty Principle applies to conjugate (seperate) variables on a single particle. EPR uses measures of the same variable on seperate entangled particles. The statement "is conjugate under uncertainty" is an oxymoron. It is the uncertainty as defined by CI (an interpretation) that EPR was designed for.

I couldn't really seperate the mixture of concepts used after this and following this is my/your opinion. No real point going there unless someone has a more specific question.

You have my permission to ignore me or ask questions. There is no need to respond to this before continuing.

 

[rtalman]

Now look at the definition of quantum in wiki.

In physics, a quantum (plural: quanta)

Now if a fundamental particle (photon) consist of a plural of fundamental particles (quanta) how can a photon be a fundamental particle? It is not me with "a definition problem here".

The definition read a little further says:

In physics, a quantum (plural: quanta) is an indivisible entity of energy. For instance, a photon, being a unit of light, is a "light quantum."

I know zero about quantum mechanics, but the definition is clear. One photon, one quantum. Many photons, many quanta.

 

[my_wan]

The definition read a little further says:

I know zero about quantum mechanics, but the definition is clear. One photon, one quantum. Many photons, many quanta.

Since quantum is plural og quanta saying "one photon, one quantum" is like saying "one flock, one birds". It should read like this;
One photon, a quantum. One photon, many quanta.

 

[rtalman]

Since quantum is plural og quanta saying "one photon, one quantum" is like saying "one flock, one birds". It should read like this;
One photon, a quantum. One photon, many quanta.

Are we reading the same definition? It says a photon is a light quantum, singular. Nowhere in the Wiki definition does it say a photon is made up of (plural) quanta.

If the definition in Wiki is incorrect (a strong possibility) then please say so.

If you replace the word quantum with the word chunk:
In physics, a chunk (plural: chunks) is an indivisible entity of energy. For instance, a photon, being a unit of light, is a "light chunk."

 

[my_wan]

Are we reading the same definition? It says a photon is a light quantum, singular. Nowhere in the Wiki definition does it say a photon is made up of (plural) quanta.

If the definition in Wiki is incorrect (a strong possibility) then please say so.

If you replace the word quantum with the word chunk:
In physics, a chunk (plural: chunks) is an indivisible entity of energy. For instance, a photon, being a unit of light, is a "light chunk."

It is easy enough to speak of a a group of birds as singular such as one flock of birds. Yes wiki is not terribly unreliable so let's try one from cern.

quantum: The smallest discrete amount of any quantity (plural: quanta).

The energy of a photon is defined by e=hf.
e = Energy
f = freaquency
h = Planks constant
Planks constant here is a quanta of energy, not a quantum of energy. The photon therefore is a quantum of quanta.

 

[Schneibster]

It was a pain

Why?

but it seems these are the four sources you mentioned; "quanta of the electromagnetic field". This is funny. In the llu.edu link it gives common definition of a photon as;

Now look at the definition of quantum in wiki.

Now if a fundamental particle (photon) consist of a plural of fundamental particles (quanta) how can a photon be a fundamental particle? It is not me with "a definition problem here".

I couldn't follow this at all, and neither apparently could anyone else. Each definition says a photon is a quantum. Each definition says a photon is a particle. Three of the four say it is an elementary particle. I don't see how anything you said either opposes that, or modifies it. Did you have some point here? I don't see one. Did you just want to bicker?

Ok so we'll take "certain parameters of quanta" to mean spin. For simplicity I will not even go into the concepts of spin.

Without going into it, how can you argue for or against it? The essence of the matter is that quantum mechanical spin is quantized, coming only in whole units, and for elementary particles, small integer whole units. You can't change a half-integer spin into a whole-integer spin, or vice versa. Any given elementary particle, such as an electron, or a photon, will have a particular value of spin; that is part of the definition of that particle. Electrons have a spin of 1/2. Photons have a spin of 1. You can't have a photon with a spin of 2, or 0; only 1. But that spin can have two senses; it can be +1, or it can be -1. Any time you measure the photon's spin, you must pick an axis to measure it about. The spin about any other axis is conjugate to the spin about the axis it was measured about. So if you actually complete the measurement, then you know everything about the spin around one axis, and therefore can know nothing of the spin about any other axis. That's what "spin is a discrete variable" means.

The Uncertainty Principle applies to conjugate (seperate) variables on a single particle. EPR uses measures of the same variable on seperate entangled particles.

Sigh. "Entangled" means "if I know the spin about an axis on one particle, it unambiguously tells me the spin of the other about that same axis, unless conservation of angular momentum is violated." So if I know the spin about the x axis for photon 1, and photon 1 and photon 2 are entangled, then I know the spin about the x axis for photon 2, too. So what EPR says is, what if I measure the spin about the x axis for photon 1, and the spin about the y axis for photon 2? Doesn't that mean I know the spin about both the x and y axes for photon 1, which is a violation of the uncertainty principle for conjugate spins about multiple axes?

You've just completely failed to understand the meaning of EPR, CHSH, Bell, Aspect, the DCQE, and Afshar.

The statement "is conjugate under uncertainty" is an oxymoron. It is the uncertainty as defined by CI (an interpretation) that EPR was designed for.

Uncertainty is not subject to or affected by which interpretation of QM you consider it under. Uncertainty is a basic characteristic of quanta. This is how they behave. An interpretation is a statement of what that means; but uncertainty is in the math, not the interpretations.

I couldn't really seperate the mixture of concepts used after this and following this is my/your opinion. No real point going there unless someone has a more specific question.

You have my permission to ignore me or ask questions. There is no need to respond to this before continuing.

I'm kind of curious why you even posted this. It seems incoherent.

 

[my_wan]

Are we reading the same definition? It says a photon is a light quantum, singular. Nowhere in the Wiki definition does it say a photon is made up of (plural) quanta.

This is getting... You say "a light quantum, singular". I could just as easily say; 'a pigeon flock, singular'. Does that mean that a pigeon flock is only one pigeon?

Look again;
a light quantum
a pigeon flock

No wiki was not wrong though questioning wikis' validity is so I included a link to cern to verify.
http://pdg.web.cern.ch/pdg/cpep/glossary.html

 

[my_wan]

Why?

Because the references you referred to were buried several very long post back and hidden within the text of the message.

I couldn't follow this at all, and neither apparently could anyone else. Each definition says a photon is a quantum. Each definition says a photon is a particle. Three of the four say it is an elementary particle. I don't see how anything you said either opposes that, or modifies it. Did you have some point here? I don't see one. Did you just want to bicker?

A photon is a fundamental particle.
A photon is a quantum. (consisting of many quanta)
A quanta is not a particle.

New analogy;
A dog is fundamentally an animal.
A dog is a group molecules.
A molecule is not an animal.

I'm not impressed with confusion by proxy.

Without going into it, how can you argue for or against it?

Let's see, this was specifically in reference to spin. Spin, classical spin, quantum spin, angular momentum, etc, etc. Not going there. Having enough trouble with what plural means. Don't even try.

The essence of the matter is that quantum mechanical spin is quantized, coming only in whole units, and for elementary particles, small integer whole units.

There you said it; "and for elementary particles, small integer whole units". Plural of unit. So we now agree that elementary particle quantum is plural of quanta. Do you feel better now?

The spin about any other axis is conjugate to the spin about the axis it was measured about.

There's the oxymoron again. Conjugates consist of Fourier transform duals of each other such as time and frequency or position and momentum. Never ever different measurements of the same variable like spin and spin. Your still confusing the mathematics of QM with how the Copenhagen Interpretation characterizes the the reality of QM.

Sigh. "Entangled" means "if I know the spin about an axis on one particle, it unambiguously tells me the spin of the other about that same axis, unless conservation of angular momentum is violated." So if I know the spin about the x axis for photon 1, and photon 1 and photon 2 are entangled, then I know the spin about the x axis for photon 2, too. So what EPR says is, what if I measure the spin about the x axis for photon 1, and the spin about the y axis for photon 2? Doesn't that mean I know the spin about both the x and y axes for photon 1, which is a violation of the uncertainty principle for conjugate spins about multiple axes?

Which is why the original idea of EPR was to say that the uncertainty was an artifact of the statistical nature of the mathematical description. Not uncertainty in the actual system itself. It remains a valid though empirically irreducible argument. It was CI not QM that EPR was after. This is why CI now assumes that these variables (that you are trying to call conjugates of themselves) don't even exist before being measured.

Uncertainty is not subject to or affected by which interpretation of QM you consider it under. Uncertainty is a basic characteristic of quanta. This is how they behave. An interpretation is a statement of what that means; but uncertainty is in the math, not the interpretations.

The Uncertainty Principle applies to conjugates in classical thermodynamics to. It is exactly analogous to trying to define the frequency of sound at a single moment in time. Without a period of time there is no frequency. Does that mean that classical mechanics is inherently uncertain? So it is subject to interpretation but so far empirically identical to the statistical interpretation. This is what makes EPR and Afshar important. Otherwise nobody would care.

I'm kind of curious why you even posted this. It seems incoherent.

So when I skip on rebutting some content because you were incoherent you say my response is incoherent? Or was it that I give you permission to not respond? Maybe it was the fact that I noted this so an interested party could object?

 

[Ziggurat]

There's the oxymoron again. Conjugates consist of Fourier transform duals of each other such as time and frequency or position and momentum. Never ever different measurements of the same variable like spin and spin. Your still confusing the mathematics of QM with how the Copenhagen Interpretation characterizes the the reality of QM.

I think his confusion is actually not about interpretation but just about semantics. I think what he's doing is using the term "conjugates" to mean observables whose operators do not commute, for which there is always a form of the Heisenberg uncertainty principle. Though conjugate observables will have non-commuting operators, the latter is indeed more general than the former, and spin along different directions (while non-commuting and hence subject to an uncertainty relation) are not, as you say, conjugates of each other.

 

[rtalman]

Are we reading the same definition? It says a photon is a light quantum, singular. Nowhere in the Wiki definition does it say a photon is made up of (plural) quanta.

This is getting... You say "a light quantum, singular". I could just as easily say; 'a pigeon flock, singular'. Does that mean that a pigeon flock is only one pigeon?

Look again;
a light quantum
a pigeon flock

No wiki was not wrong though questioning wikis' validity is so I included a link to cern to verify.
http://pdg.web.cern.ch/pdg/cpep/glossary.html

I do not mean to be deliberately obtuse about this, but by the Wiki definition a quantum is indivisible. A flock of geese, a gang of gorillas, a pack of wolves, these are all divisible.

Certainly you could grammatically say "a quantum of quanta" using different senses of "quantum", just as you grammatically say "That that, that that boy wrote, is not that that, that that boy wrote." using different senses of "that".

 

[Jekyll]

My_wan, aren't you just getting the singular and collective confused.
If I take one quantum and another, I have two quanta.

These two quanta are not a quantum of quanta or whatever you wanted to call it.

And last time I looked both electrons and photons are indivisible, single particles, that can not be reduced into smaller packets.

 

[Beth]

The Uncertainty Principle applies to conjugates in classical thermodynamics to. It is exactly analogous to trying to define the frequency of sound at a single moment in time. Without a period of time there is no frequency. Does that mean that classical mechanics is inherently uncertain?

You may have meant this as a rhetorical question, but I'd appreciate it someone could expound on the answer. Are classical mechanics inherently uncertain too?

So it is subject to interpretation but so far empirically identical to the statistical interpretation. This is what makes EPR and Afshar important. Otherwise nobody would care.

Thanks

 

[Jekyll]

You may have meant this as a rhetorical question, but I'd appreciate it someone could expound on the answer. Are classical mechanics inherently uncertain too?

No. There are some events which are undefined in classical mechanics such as; what would happen if three balls simultaneously collide. But this is very different to what's going on in quantum physics, and normally there is no uncertainty.

The way I like to think about what is happening with uncertainty in quantum physics is that it's like a blind man playing snooker.

If he wants to know where a ball is, he has to hit it with another ball and the harder he hits it, the louder the click, and the more accurate his guess of where the ball is is. However, the harder he hits the less chance he has of knowing where the ball will go.

In classical mechanics, you can get round this by hitting the ball you want to find with smaller and smaller objects, so it doesn't get moved very much by the collision. Planck's constant describes a bound on how small the smallest ball can be, and so on how much information or certainty you can get out the system.

I'm sure someone more physics minded than me will be along to point out the flaws in my analogy, but I hope it points you in the right direction.

 

[rtalman]

These two quanta are not a quantum of quanta or whatever you wanted to call it.

http://dictionary.reference.com/browse/quantum

1.quantity or amount: the least quantum of evidence.
2.a particular amount.
3.a share or portion.
4.a large quantity; bulk.
5.Physics.
a.the smallest quantity of radiant energy, equal to Planck's constant times the frequency of the associated radiation.
b.the fundamental unit of a quantized physical magnitude, as angular momentum.

A quantum (def. 2) of quanta (def. 5a)

 

[my_wan]

I think his confusion is actually not about interpretation but just about semantics. I think what he's doing is using the term "conjugates" to mean observables whose operators do not commute, for which there is always a form of the Heisenberg uncertainty principle. Though conjugate observables will have non-commuting operators, the latter is indeed more general than the former, and spin along different directions (while non-commuting and hence subject to an uncertainty relation) are not, as you say, conjugates of each other.

Even in the less general case non-commuting variables are not simply different values for the same variable but different variables altogether. Take the simplest mathematical case of subtraction which is non-commuting. a-b does not equal b-a in general. a-b and b-a are different variables altogether and not different measurements of the same variable. Also non-commuting does not by itself indicate that the Uncertainty Relation applies. For instance a-b or b-a. Knowing the values for one does not decrease the accuracy you can know the values of the other.

The interpretation I speak of of neither mine nor his but the Copenhagen Interpretation CI. QM does not need CI for empirical validity. It was added after the fact. It order to be logically consistent with empirical data using the statistical interpretation of CI CI had to presume that quantum values did not exist before being measured. Not unknown not uncertain as in the Uncertainty Relation but simply nonexistent. This is not defined by QM like the Uncertainty Relation but an assumption of the statistical interpretation for consistency. It was originally posited to get around the objections of the EPR paper.

 

[my_wan]

I do not mean to be deliberately obtuse about this, but by the Wiki definition a quantum is indivisible. A flock of geese, a gang of gorillas, a pack of wolves, these are all divisible.

Certainly you could grammatically say "a quantum of quanta" using different senses of "quantum", just as you grammatically say "That that, that that boy wrote, is not that that, that that boy wrote." using different senses of "that".

Yes good question. I started to answer this before but the post get oversized easily. In Quantum Field Theory QFT the quantization is described as properties of a Field. Somewhat like an ether without parts just properties. In this case talking about a quanta being a part of a particle is like talking about the speed of a car being part of the car. The thing is we only know about quantum particles by their properties. We call quantum particles fundamental particles because they bump into our detectors, quanta do not. The properties of quantum particles remain whole unit sets of quanta. Without quantization an ether would be the de facto explanation. Nobody knows how to reconcile Quantum Mechanics with mechanics.

 

[my_wan]

My_wan, aren't you just getting the singular and collective confused.
If I take one quantum and another, I have two quanta.

These two quanta are not a quantum of quanta or whatever you wanted to call it.

And last time I looked both electrons and photons are indivisible, single particles, that can not be reduced into smaller packets.

Using the previous anology if you take one speed and double it you don't get two speeds. The previous response to rtalman has more detail on this.

 

[rtalman]

Yes good question. I started to answer this before but the post get oversized easily. In Quantum Field Theory QFT the quantization is described as properties of a Field. Somewhat like an ether without parts just properties. In this case talking about a quanta being a part of a particle is like talking about the speed of a car being part of the car. The thing is we only know about quantum particles by their properties. We call quantum particles fundamental particles because they bump into our detectors, quanta do not. The properties of quantum particles remain whole unit sets of quanta. Without quantization an ether would be the de facto explanation. Nobody knows how to reconcile Quantum Mechanics with mechanics.

 

[my_wan]

You may have meant this as a rhetorical question, but I'd appreciate it someone could expound on the answer. Are classical mechanics inherently uncertain too?

Thanks

Yes it was in fact a rhetorical question. Except for quantization itself Quantum Mechanics and Classical Thermodynamics shares the same mathematical foundation. We describe groups of particles in classical thermodynamics but in QM these same statistics apply instead to quantized properties of single particles. There is a little confusion about the difference between a statistical interpretation (classical uncertainty) and the Uncertainty Principle. The Uncertainty Principle by itself is not dependent on statistical uncertainty. The Uncertainty Principle has an exact analogy in classical physics. It is classically related to the idea that if you stopped time how could you know how fast that bird is flying overhead. If you will notice the conjugates even in QM are time vs time Dependant properties such as position and momentum or time and energy.

It is unfortunate that uncertainty can refer to both the Uncertainty Principle and statistical uncertainty. Statistical thermodynamics was developed well before the Kinetic Theory of Gases but they turned out to be equivalent. Classically the uncertainty resulted from ignoring the speeds and interactions of individual particles and only describing the odds of interactions or average speed. We actually measure these averages with a thermometer. Do to the same statistics describing the properties of individual quantum particles CI interpreted this to mean the statistics was the reality and not just an approximation like it is in classical thermodynamics.

It might eventually turn out to be possible to interpret quantum randomness the same way it is in classical physics. There are a number of questions it must address to do so. Put in simplest terms it must address why and how quantization takes place as well as the wave-particle duality. Finally it must also provide a framework for Relativity which to date doesn't even share a similar mathematical foundation. I have chosen my bets and said a little about it in my "opinion".

 

[Ziggurat]

Even in the less general case non-commuting variables are not simply different values for the same variable but different variables altogether.

I guess you could argue about whether or not the z-component spin was a different variable than the x-component spin. It's a semantic issue which I have no interest in. But either way, the operators for z-component spin, x-component spin, and y-component spin do not commute.

Also non-commuting does not by itself indicate that the Uncertainty Relation applies. For instance a-b or b-a. Knowing the values for one does not decrease the accuracy you can know the values of the other.

Sure, but that doesn't contradict what I said. Subtraction is not a quantum mechanical operator with a corresponding observable. An uncertainty relationship applies in any case in which two quantum mechanical operators for observables do not commute, but for operators without obervables no such relationship exists (not surprising, since the relationship revolves around said obervables).