An analogy for superposition

[geordief]

Is this a good analogy?

 

Take a word,any word.

"Phantasy" will do.

Suppose I use it.

 

it has a meaning in my mind  when I say it and another(indistinguishibly different)  meaning  if I say it  the next day 

 

To the person I address it has another meaning  and to a third person  another meaning too (never exactly the same)

If  the intrinsic meanings of the words we use to represent ideas are built of of layers of context  does that make them  analagous to how superposition works on objects in the quantum world?

[joigus]

I like this analogy better:

A coin tumbling and wobbling with no significant amount of dissipation of energy would be the equivalent to a quantum state being in a superposition and "rotating" according to the Schrödinger equation. Not heads, nor tails. Not yet.

At some point, the dissipation comes into play --equivalent to the projection postulate = measurement = formal violation of unitarity-- and the coin has to "decide" whether it's heads or tails.

The problem I see with your analogy, which is otherwise as valid as any other --with the natural limitations that no classical logic can totally reproduce the quantum-- is that it assumes the "observer effect." The result is brought about by the act of measurement (different people seeing different things, as they measure.)

There are many things I like about this example of the wobbling coin.

[geordief]

9 minutes ago, joigus said:

I like this analogy better:

A coin tumbling and wobbling with no significant amount of dissipation of energy would be the equivalent to a quantum state being in a superposition and "rotating" according to the Schrödinger equation. Not heads, nor tails. Not yet.

At some point, the dissipation comes into play --equivalent to the projection postulate = measurement = formal violation of unitarity-- and the coin has to "decide" whether it's heads or tails.

The problem I see with your analogy, which is otherwise as valid as any other --with the natural limitations that no classical logic can totally reproduce the quantum-- is that it assumes the "observer effect." The result is brought about by the act of measurement (different people seeing different things, as they measure.)

There are many things I like about this example of the wobbling coin.

I am a bit hamstrung  in that I feel that I am not in command of the experimental results  (in order to judge how close any particular  analogy  approaches*) but can I ask you this?

 

Einstein famously struggled against his notion of spooky action   and looked for hidden variables but in my ,admittedly badly informed mind it seems very intuitive  to me that two halves of an identical  production will maintain the mutual relationship until such time as they have revealed their characteristics by interaction with another system

 

What do you think I might be missing?It seems so simple to me**?

 

 

(I can't see how ftl signals could be imagined to be  a part of this -even though the practical uses of this phenomenon ho totally over my head)

* but yes ,the coin analogy seems good.(but does it illustrate superposition?)

**am I just whistling in the dark  and believing whatever makes thinking easy for me?

[joigus]

23 minutes ago, geordief said:

Einstein famously struggled against his notion of spooky action   and looked for hidden variables but in my ,admittedly badly informed mind it seems very intuitive  to me that two halves of an identical  production will maintain the mutual relationship until such time as they have revealed their characteristics by interaction with another system

The EPR argument is really a bit complicated historically. Einstein did not think of entanglement right away when he co-authored that paper. He was more concerned about completeness at that point in history. Schematically, he said:

If I can predict with 100% accuracy the result of an experiment without actually measuring it, there is a something, there is a presence, there is a variable, real as can be, (a value of momentum in his case; he very shrewdly used a conserved quantity of which no exception is known) which must somehow be there. Therefore, your theory (quantum mechanics) must be incomplete. If your quantum mechanics purports to insist on incompatibility of certain variables, your quantum state must be updated by means of an outrageous violation of relativistic causality. There's no other way.

In other words: He was pushing QM's completeness claims against relativistic causality --a principle that he knew better than any other was "sacred"--. Both of them, completenes of QM, and relativistic causality, cannot hold at the same time. It's one or the other. 

But he (and Rosen, and Podolski) missed a couple of tricks.

1) You cannot prepare a bipartite quantum state in which the momentum is zero in the CoM system with total accuracy. So momentum is actually always indefinite.

2) The state is actually entangled: (momentum p)_{particle 1}(position x)_{particle 2}-(momentum -p)_{particle 1}(position -x)_{particle 2}.

Here, David Bohm enters the story. He took the whole discussion to the case of spin. Why? Because angular momentum is exactly conserved, but for angular momentum (spin is a particular case) you can actually prepare states that are totally indefinite in each variable, while completely definite for the sum of both. Then you can do the correlation analysis very cleanly, and reasonably clearly.

Then comes John Bell, and for some unfathomable reason --IMO-- rescues a word from Einstein's old toolbox that had better been left out, because --again, IMO-- plays no actual role in the argument, except indirectly. Namely: "locality."

In fact, if you go over Bell's papers on the subject, and its antecessors: V. Neumann, Gleason, Jauch and Piron, etc., and its sequel: Clauser, Greenberger, Horne, Zeilinger; the position of the particle plays no role in the theorems. It's not even mentioned in the axioms. It's only there because these great physicists mention it over and over. Why? Because Einstein mentioned it in his original argument. And they have deep respect for Einstein. And they don't want to be wrong.

They all knew in their heart of hearts they were doing a theorem about realism, but didn't want to drop this word "locality," --IMO-- only just in case they missed something essential. But all those theorems about "local realism" were actually theorems about "realism." If I disprove local realism, it's just as good to disprove realism. If there isn't any realism, there certainly won't be any local realism.

59 minutes ago, geordief said:

What do you think I might be missing?It seems so simple to me**?

Imagine a modification of reality as we know it by means of some kind of "ghostly presence" of every which property of a composite system. A glove can be black and not black at the same time, a glove can be left-handed and right-handed at the same time. Etc. But in such a way that the "potential right-handedness" is equally likely than the "potential left-handedness," and so on. But the total handedness is zero exactly, the total color is grey = black + white exactly, etc. Holding these two experimental truths in your mind is what's very, very hard.

When you measure, the system filters, selects, shows, highlights... whatever you have decided to see, and it shows the correlations that were there all along. You select a "component of reality" and bring it onto reality. Something like that, for lack of better words.

Does that help at all?

[Bufofrog]

2 hours ago, joigus said:

A coin tumbling and wobbling with no significant amount of dissipation of energy would be the equivalent to a quantum state being in a superposition and "rotating" according to the Schrödinger equation. Not heads, nor tails. Not yet.

I really like this analogy.

[Ghideon]

3 hours ago, joigus said:

A coin tumbling and wobbling with no significant amount of dissipation of energy would be the equivalent to a quantum state being in a superposition and "rotating" according to the Schrödinger equation. Not heads, nor tails. Not yet.

(+1)

Side note: I have in my head an image of the coin far from any source of gravity. It tumbles and wobbles and can't land anywhere. Predictions about heads or tails are not possible; there is not even a definition of where the coin will land. The gravity is introduced and the coin falls down (=measurement) and we have heads or tails.

[joigus]

39 minutes ago, Bufofrog said:

I really like this analogy.

It's taken from Swansont's toolkit. I liked it too. I've just added a couple of pictorial features. 

1 minute ago, Ghideon said:

(+1)

Side note: I have in my head an image of the coin far from any source of gravity. It tumbles and wobbles and can't land anywhere. Predictions about heads or tails are not possible; there is not even a definition of where the coin will land. The gravity is introduced and the coin falls down (=measurement) and we have heads or tails.

I'd rather you included dissipative forces coming into play, and that's because they replicate this "effective loss of unitarity." But what happens when the environment selects a particular projection, how the environment selects that particular projection? In still other words: What physical variable tells Nature "this is what happens," and "not the other," and effectively interrupts the causal and reversible course of Schrödinger's equation, that's up for grabs:

Many universes... meh!

Empty waves... mmm --this is the one I like more.

TIQM... eew!

Superdeterminism... eeeeew!!!

...

You can say --semantically totally equivalent to the former-- the measured component becomes "green," and we can only see "green" things.

The non-measured components become schmancy, and we can only see non-schmancy things.

An angel told me this is the one and only

etc.

 

[swansont]

2 hours ago, Ghideon said:

Side note: I have in my head an image of the coin far from any source of gravity. It tumbles and wobbles and can't land anywhere. Predictions about heads or tails are not possible; there is not even a definition of where the coin will land. The gravity is introduced and the coin falls down (=measurement) and we have heads or tails.

It can be a regular toss but with no information about the mechanics of the flip itself. You don’t know how high or anything about the rotation. 

[Ghideon]

33 minutes ago, swansont said:

It can be a regular toss but with no information about the mechanics of the flip itself. You don’t know how high or anything about the rotation. 

You are correct. It is clear once I think it through*.

2 hours ago, joigus said:

I'd rather you included dissipative forces coming into play

Tossing a coin into a wishing well? The coin's rotation is slowed down by the water would be the dissipative force (air resistance is neglected).

 

*) I (incorrectly) thought of a regular toss as a measurement starting when the coin leaves the hand. 

[joigus]

58 minutes ago, Ghideon said:

Tossing a coin into a wishing well? The coin's rotation is slowed down by the water would be the dissipative force (air resistance is neglected).

 

*) I (incorrectly) thought of a regular toss as a measurement starting when the coin leaves the hand. 

I would try not to overthink it, as it's an analogy after all. As Swansont said, in the end there's no information that can tell you how it's going to end up, really, only the odds.

[geordief]

8 hours ago, joigus said:

Imagine a modification of reality as we know it by means of some kind of "ghostly presence" of every which property of a composite system

What are you talking about when you say "composite system"?

Is it a  potentially  macro system like a molecule of water?

If so,how many properties  could  that water molecule have (if it is a good example)?

 

 

And do all those properties  have an "anti property" with which it is  superpositioned on top of all the other property/antiproperty pairs  so that ,when an interaction occurs only one of each property/antiproperty choices  comes to the fore?

 

Is it something  like that you are suggesting?

 

 

Edit: unless you are only talking about entangled systems.....

Edited October 15, 2022 by geordief

[joigus]

6 hours ago, geordief said:

What are you talking about when you say "composite system"?

Sorry, the words "composite system" were not essential. This "ghostly presence" happens in a simple system too.

What I meant by "composite" is 2-particle, 3-particle systems, etc.

Anti-properties is not the key. That's just for spin because for every possible value of it you have the corresponding negative value. It's just two or more values of the same property. Take the example of benzene. The molecular orbitals of the double bonds are not in a definite position. That's what I meant.

[geordief]

5 hours ago, joigus said:

Sorry, the words "composite system" were not essential. This "ghostly presence" happens in a simple system too.

What I meant by "composite" is 2-particle, 3-particle systems, etc.

Anti-properties is not the key. That's just for spin because for every possible value of it you have the corresponding negative value. It's just two or more values of the same property. Take the example of benzene. The molecular orbitals of the double bonds are not in a definite position. That's what I meant.

I think  I understand. The term "ghostly presence"  can ,I think  be understood  as a purely mathematical concept.(probabilities)

Are you  treating it to represent a physical  reality ,or maybe just as a way to picture the model (a close analogy)** as something like a  moving object surrounded by wraithy versions of itself that may or may not assume the position of king pin when an interaction  is encountered?

My initial  feeling is that the passage btw interactions in completely empty  and that the interval btw interactions may constitute something  like a "unit of existence" for these simple systems but  I don't understand  the basics of the theory so that is just hot (or v cold) air.

 

**after all ,an analogy is what I asked about in the OP.

[joigus]

1 hour ago, geordief said:

I think  I understand. The term "ghostly presence"  can ,I think  be understood  as a purely mathematical concept.(probabilities)

Exactly. |state of the cat> = (1/sqrt(2))|cat dead>+(1/sqrt(2))|cat alive>

These numbers 1/sqrt(2) are called probability amplitudes, and their squares 1/2, 1/2 are the probabilities.

I don't want anybody to run away with any hurried conclusions, but the truth is the best analogy for these quantum superpositions is perhaps the human mind itself: When you're not sure about something, it's neither here nor there. It's only when you learn what happened that your mind gets either here or there.

In the meantime, there's this Schrödinger equation, which is like the indefinite mind rotating between one and the other. When you measure, the state vector stops on one of the axis. Now, this stopping on one of the axis is called the projection postulate, and is known to be incompatible with the Schrödinger equation.

[geordief]

1 hour ago, joigus said:

Exactly. |state of the cat> = (1/sqrt(2))|cat dead>+(1/sqrt(2))|cat alive>

These numbers 1/sqrt(2) are called probability amplitudes, and their squares 1/2, 1/2 are the probabilities.

I don't want anybody to run away with any hurried conclusions, but the truth is the best analogy for these quantum superpositions is perhaps the human mind itself: When you're not sure about something, it's neither here nor there. It's only when you learn what happened that your mind gets either here or there.

In the meantime, there's this Schrödinger equation, which is like the indefinite mind rotating between one and the other. When you measure, the state vector stops on one of the axis. Now, this stopping on one of the axis is called the projection postulate, and is known to be incompatible with the Schrödinger equation.

 Thanks.I think I am done with analogies  but I have another question  or 2  and I suppose  I should  start a new thread on those musings..