B Entanglement: How Does it Work and Its Implications in Everyday Life?

[zonde]

Assume Alice detector could detect vertical up or down, or horizontal left or right… an entangled pair was sent to both Alice and Bob, if Alice detected it as vertical down.. would Bob detect it as horizontal left or right? Or is it always vertical?

Polarization entangled photons are analyzed using polarizers. You place a polarizer at certain angle and photon either passes through it or it doesn't.

 

[Ken G]

Quantum cryptography is important application of QM. Never heard that quantum teleportation is an important application.

Quantum cryptography is an application of quantum teleportation, you simply teleport the quantum key so it can't be intercepted. The teleportation is the important step.

Simply take your approach and explain possible model for quantum entanglement. That's the topic of this thread.

The topic is not a "model" for quantum entanglement, quantum entanglement is already a model. The effort is in understanding the larger implications of the model. To that end, quantum teleportation is significant. The idea is, you entangle two particles, transport one a great distance, and use the entanglement as a kind of channel through which to teleport a quantum state. The reason this is relevant to secure communication is the no-cloning theorem, which says a quantum teleported signal cannot be intercepted without detection, because the signal can only go to one destination, to intercept it without detection would require cloning of the signal (which is trivial for classical signals).

So the relevance to understanding quantum entanglement is that we are getting a window into a very different world, one where states are never created nor destroyed, they are merely teleported from place to place. One can even regard the simple translation of a system from point A to point B as a teleportation involving entangled virtual particles, giving insight as to why systems tend to retain their integrity as they move across space. From this perspective, it is the classical world, where we seem to create and destroy states willy nilly, that is "weird," and it emerges from the complexity of combining ghastly numbers of logically simple quantum systems. The logical simplicity of the quantum systems is reflected in the no-cloning, no-deleting theorems, is manifested by entanglement, and seems very close indeed to what Parmenides intuited some 2500 years ago.

 

[star apple]

Polarization entangled photons are analyzed using polarizers. You place a polarizer at certain angle and photon either passes through it or it doesn't.

If you use a Stern-Gerlach devices on the ends instead of Polarizers.. there would be no correlations? And it's due to... ?

 

[zonde]

Quantum cryptography is an application of quantum teleportation, you simply teleport the quantum key so it can't be intercepted. The teleportation is the important step.

In quantum cryptography the information sent is classical. The aim is for both parties to share the same secret (classical) code. There is no such thing as "quantum key". The "quantum" in quantum key distribution does not describe the key but the method by which the key is sent.

The topic is not a "model" for quantum entanglement, quantum entanglement is already a model. The effort is in understanding the larger implications of the model.

Where did you get this? Let me quote OP:

Basically I want to know how does entanglement actually work? Is information being transferred faster than we can detect it or is there some invisible link between particles that causes the phenomenon we call entanglement?

OP asks about mechanism (model) behind particular phenomena (that goes by the name "entanglement").

 

[Ken G]

You can't explain a mathematical model without math - can't you see that? You can try and succeed some of the time - but with superposition the jig is up.

That may be pessimistic-- I agree that any plain English description is only going to recast what can be said much more succinctly mathematically, but any computer program can be said more succinctly in machine language-- we still use programming languages! So I think it's worth a try to capture the flavor of the mathematics of superposition in plain English.

Superposition essentially takes a situation we are all well acquainted with, which is having limited information about some situation such that we have to "entertain," if you will, multiple possibilities in our minds. I like the analogy of playing a card game, and assessing the probabilities that the opponents have various hands. But we are very clear this mixture is only in our minds-- the actual reality is one way or another. Superposition elevates that state of affairs into something much closer to the actual reality. Interestingly, there is no demonstrable difference in the classical realm, it's just that elevating our uncertainty into a kind of personal reality never seemed to have much point. But it has a point in quantum mechanics, because the multiple possibilities can interfere with each other and affect what you regard as the probable outcomes. We are used to having a separate probability for each of the potential states of the system, but in superposition, the potential different states combine into a whole new state that alters those probabilities.

When we include superposition of states of two particles, it ushers in entanglement. Entanglement allows the knowledge you have about the system (and the lack thereof, called the "indeterminacy") to be expressed in ways that refer to both particles. For example, if you have two coins that can be either heads (H) or tails (T), we could express what we know and don't know classically like "we don't know what either coin says but they are the same". If we elevate that state of affairs to the actual state of the system, and not just what we know and don't know, then not knowing what either coin is becomes indeterminacy in the H or T, but knowing they are the same means we have a superposition of HH and TT, a state that embodies the aspects of both HH and TT (i.e., that they are the same), without specifying H or T. That's a form of entanglement, because not only can we only state what we know by referring to both coins, but the two possibilities alter the probabilities beyond just what HH or TT alone would do (and that's called "interference").

Quantum teleportation means that if you have a superposition of HH and TT, you can still widely separate the two "quantum coins," and use the superposition as a kind of conduit for passing a quantum state from the vicinity of one coin to the other. That's a particular version of the interference between the HH and TT, and it allows secure communication of a bit via the teleportation of the state of a third "quantum coin."

 

[Ken G]

In quantum cryptography the information sent is classical.

Of course, all information is classical or we couldn't use it. The method of transport of the classical information is where the teleportation comes in. There's always teleportation there.

OP asks about mechanism (model) behind particular phenomena (that goes by the name "entanglement").

I didn't see the word "mechanism," did you? I saw "how does it work." That's not asking for a model, it's asking for an explanation of a model.

 

[zonde]

If you use a Stern-Gerlach devices on the ends instead of Polarizers.. there would be no correlations?

I would suggest you to try to look at some layman level descriptions of quantum entanglement if you are interested in this topic.You can try these links:
http://www.drchinese.com/Bells_Theorem.htm
http://quantumtantra.com/bell2.html
http://www.theory.caltech.edu/classes/ph125a/istmt.pdf
So if you will refer in your questions to things found in these links you will get better responses.
If you are particularly concerned about faster than light communication using entanglement you can try forum search with keyword FTL and entanglement.

 

[_PJ_]

Assume Alice detector could detect vertical up or down, or horizontal left or right… an entangled pair was sent to both Alice and Bob, if Alice detected it as vertical down.. would Bob detect it as horizontal left or right? Or is it always vertical?

If vertical is dot and horizontal is dash.. can’t they send morse code.. Alice can use vertical and horizontal to form messages and Bob can receive it horizontal or vertical and decode the sentences.

All right. Where has I got it wrong?

Alice is measuring VERTICAL Axis
Bob is measuring HORIZONTAL.

For the sake of argument/completeness let's assume that there are only two dimensions and that whatever entangled "things" are being measured in a way that what Alice considers VERTICAL and HORIZONTAL are exactly identical to that which Bob does too. Bob and Alice or their detectors are exactly aligned relative to each other - obviously "Horizontal" and "Vertical" are orthogonal.

Alice would have an equal probability, measuring ONLY the vertical - of detecting UP or DOWN. However her result would ALWAYS show either UP/DOWN
Bob, measuring ONLY the horizontal would have equal probability of detecting LEFT or RIGHT. However his result would ALWAYS show either LEFT/RIGHT
This would be true regardless of entanglement.

Assume for a moment that there is no Bob. He nor any entanglement exists. There is only Alice and her detector and the thing she is measuring.
Alice has a CHOICE in measuring HORIZONTAL or VERTICAL The choice represents a fork in a probability tree. We assume there is equal probability in her making either choice and that she will with absolute certainty choose to measure H or to measure V there is no other option. She cannot fall asleep, forget or go do something else. She MUST make a choice, must choose either H or V.
Depending on what she cxhooses, she will then measure:

If H
U or D

If V
L or R

There are no other possibilities. No other results nor outcomes exist.

This can all be represented with the following (Although the symbols represent operators and are in reality conjugated)

Alice chooses Horizontal or Vertical. There are no other options

IF Alice chooses H, the result can only be L or R
<V|U>=0
<V|D>=0
<H|L> + <H|R> = 1

OR
Alice chooses V and result must be either U or D
<H|U>=0
<H|R>=0
<V|U> + <V|D> = 1

Since the choice between V or H represents operation on states still part of the system, these can be combined, however, now the initial choice is only 50% of the entire probability contributions, but represents exactly 50%

<V|U> + <V|D> = 0.5 = <H|L> + <H|R><V|U> + <V|D> + <H|L> + <H|R> = 1
This encapsulates that there are only those possibilities. There is no possibility for, say choosing Horizontal and measuring UP.

Since we have established (for example simplicity) that Alice's chioce in measuring H or V is utterly equal, and that whether U/D or L/R within each choice are also completely equal :

<V|U> = <V|D> = <H|L> = <H|R>

and
<V| = <H|

|U> = |D> = |L> |R>

Experimentally, the results would agree here, that were the scene repeated, each particular result would occur on average 25 times in every 100 repeats.

__

Now, let's imagine that Alice "prepares" the entity before measurement. For the sake of simplicity the "preparation" only applies to the VERTICAL axis and it is prepared so that the state for this vertical axis is UP
After such "preparation", Alice again chooses what axis to measure and makes the measurement.
If Alice chooses VERTICAL, the result will ALWAYS be U
If Alice chooses HORIZONTAL, the result is ALWAYS L or R

There is STILL perfectly equal probability of L/R if she chooses H and Alice's decision to choose H or V is unaffected.

<V|D> = 0

The statement made earlier
<V|U> + <V|D> + <H|L> + <H|R> = 1
still holds. Although <V|D> can safely be omitted as it is now zero probability. (Just as we are not including operators for the probabity amplitudes that Alice might spontaneously turn into a banana - it's not going to happen, so there's no need to include it)

<V|U> + <H|L> + <H|R> = 1
And
<H|L> = <H|R> still, so this holds as before. Given that Alice still chooses perfectly equally between H and V, though,
<V|U> + <V|D> = 0.5 = <H|L> + <H|R>
also still holds.
we can omit <V|D> as mentioned, and see that
<V|U> = 0.5 = <H|L> + <H|R>

So the effect of the preparation does not affect the HORIZONTAL measurement (should Alice choose to make it) in any way whatsoever. Instead, it is only the VERTICAL that is affected.

Now forget the preparation and instead bring in Bob. Also we will eradicate any choice for Alice. She will ONLY measure VERTICAL. Bob will only measure Horizontal.
There is no <A(l)| or <A(r)| nor is there a <B(u)| or |B(d)> they simply do not exist at all.

However Bob WILL make A MEASUREMENT (either B(l) or B(r) only- no other possibility) and Alice will make A MEASUREMENT(either A(u) or A(d) only- no other possibility)

<A(u)|A(d)> + <B(l)|B(r)> = 1
<A(u)|B(l)> + <A(u)|B(r)> + <A(d)|B(l)> + <A(d)|B(r)> = 1

The effect of entanglement will cause whatever Alice measures (A(u) or A(d) that Bob's paired entity would, if measured in that axis, result in the opposite to that which Alice measured. That is, if Bob were ALSO to measure in the vertical, and Alice measured U then Bob would measure D. If Alice measured D then Bob would measure U
If Alice broke with tradition and measured Horizontally, then if her result was L and Bob also measured horizontally, Bob would obtain a result of R. HOwever if Alice measured her entangled particle Vertically and Bob measured his entangled particle Horizontally, there would be no measurable detectable change whatsoever.
50% of the time Alice would detect U and 50% she would detect down. 50% of the time Bob would detect L and 50% of the time he would detect R just as if the experimentors, the particles, the detectors etc. were utterly isolated.

In the entangled scenario, if either could choose to measure either

<A(u)|B(d)> + <A(u)|B(l)> + <A(u)|B(r)> + <A(d)|B(u)> + <A(d)|B(l)> + <A(d)|B(r)> + <A(l)|B(u)> + <A(l)|B(d)> + <A(l)|B(r)> + <A(r)|B(u)> + <A(r)|B(d)> + <A(r)|B(l)> = 1

The probabilities are affected thus:

<A(u)|B(d)> = <A(d)|B(u)> = <A(l)|B(r)> = <A(r)|B(l)>
And
<A(d)|B(l)> = <A(d)|B(r)> = <A(l)|B(u)> = <A(l)|B(d)> = <A(r)|B(u)> = <A(r)|B(d)>

But because of the omission of
<A(u)|B(u)> + <A(d)|B(d)> + <A(l)|B(r)>
which would be included and contribute to the overall unity were there no entanglement, the individual probabilities as experienced by the individual experimenters are not noticeable unless the experimenters specifically compare notes.
Note that Alice is not changing the particle or encoding it in any way. It is either UP or it is DOWN (or more accurately, superposited UPDOWN, and measuring it will reveal which - measuring is in fact the activity of resolving this superposition into a real distinct state) - she cannot know beforehand which it will be, unless she PREPARES it as described above. However, preparation would "destroy the entanglement", Alice's particle would definitely be in whatever state she prepares it, but Bob would measure a now disentangled particle where the state would be again, determined through his measurement.

This is why it's not possible (regardless of how you encode the information) to transmit information using entanglement.

 

[nnope]

I would suggest you to try to look at some layman level descriptions of quantum entanglement if you are interested in this topic.You can try these links:
http://www.drchinese.com/Bells_Theorem.htm
http://quantumtantra.com/bell2.html
http://www.theory.caltech.edu/classes/ph125a/istmt.pdf
So if you will refer in your questions to things found in these links you will get better responses.
If you are particularly concerned about faster than light communication using entanglement you can try forum search with keyword FTL and entanglement.

Whats up with that quantum tantra link, by far the wierdest stuff I've read on the net since alien invasion conspiracies.
http://quantumtantra.com/interview.html
Is this a reliable link? The name itself (referncing hindu magical texts) is as much a joke as the contents on telepathy.

 

[Ken G]

You should probably delete it, it's inappropriate and not particularly useful.

 

[zonde]

Whats up with that quantum tantra link, by far the wierdest stuff I've read on the net since alien invasion conspiracies.
http://quantumtantra.com/interview.html
Is this a reliable link? The name itself (referncing hindu magical texts) is as much a joke as the contents on telepathy.

The page is http://quantumtantra.com/bell2.html. I probably should have added some disclaimer that only this page is about physics but the site itself is not recomended.

 

[anothergol]

Then you said:
I wasn't talking about superposition of what's being observed, because I don't even know what it means.

The first is about observing position - you virtually stated it outright. Then say you weren't talking about observation in what being observed - not even understanding what that means.

See the contradiction?

I obviously can't tell if I'm talking about something I don't understand, but the way I understood things, superposition is when a particle isn't being observed. Thus superposition of what is being observed (as you first wrote it), I don't understand what it means, but it cannot be what I was talking of.

I mean come on, I've seen a lot of movies about the double slit experiment, Schrodinger's cat, and entanglement. I thought I at least got these basic things right. But none of them used equations to explain these.
A particle's position & its spin are different things, but aren't both in superpositions until observed?

The only thing here that really seems to require maths btw, is Bell's theorem. Which is key, because when you don't understand it (& I don't), you have to take it for granted (which I don't like), while it's that important thing that proves that entanglement is real.
As it's often explained, that it's not like a pair of gloves in 2 boxes, whether it's a left or right hand in each box isn't decided at the beginning, it's both left & right until observed, & when observed & collapsed to a left or right hand at pure random, then the entangled glove will be the other hand. But yes, that one thing that proves it wasn't left or right from the beginning, I can imagine it can't be explained in simple ways.
..or is it another thing I misunderstood?
And back to teleportation (of information, faster than light), what makes it impossible is the fact that the collapse of the LR hand into a L or R, is purely random, right? Thus the correlation can only be done afterwards, by normal communication.

 

[star apple]

Alice is measuring VERTICAL Axis
Bob is measuring HORIZONTAL.

For the sake of argument/completeness let's assume that there are only two dimensions and that whatever entangled "things" are being measured in a way that what Alice considers VERTICAL and HORIZONTAL are exactly identical to that which Bob does too. Bob and Alice or their detectors are exactly aligned relative to each other - obviously "Horizontal" and "Vertical" are orthogonal.

Alice would have an equal probability, measuring ONLY the vertical - of detecting UP or DOWN. However her result would ALWAYS show either UP/DOWN
Bob, measuring ONLY the horizontal would have equal probability of detecting LEFT or RIGHT. However his result would ALWAYS show either LEFT/RIGHT
This would be true regardless of entanglement.

Assume for a moment that there is no Bob. He nor any entanglement exists. There is only Alice and her detector and the thing she is measuring.
Alice has a CHOICE in measuring HORIZONTAL or VERTICAL The choice represents a fork in a probability tree. We assume there is equal probability in her making either choice and that she will with absolute certainty choose to measure H or to measure V there is no other option. She cannot fall asleep, forget or go do something else. She MUST make a choice, must choose either H or V.
Depending on what she cxhooses, she will then measure:

If H
U or D

If V
L or R

There are no other possibilities. No other results nor outcomes exist.

This can all be represented with the following (Although the symbols represent operators and are in reality conjugated)

Alice chooses Horizontal or Vertical. There are no other options

IF Alice chooses H, the result can only be L or R
<V|U>=0
<V|D>=0
<H|L> + <H|R> = 1

OR
Alice chooses V and result must be either U or D
<H|U>=0
<H|R>=0
<V|U> + <V|D> = 1

Since the choice between V or H represents operation on states still part of the system, these can be combined, however, now the initial choice is only 50% of the entire probability contributions, but represents exactly 50%

<V|U> + <V|D> = 0.5 = <H|L> + <H|R><V|U> + <V|D> + <H|L> + <H|R> = 1
This encapsulates that there are only those possibilities. There is no possibility for, say choosing Horizontal and measuring UP.

Since we have established (for example simplicity) that Alice's chioce in measuring H or V is utterly equal, and that whether U/D or L/R within each choice are also completely equal :

<V|U> = <V|D> = <H|L> = <H|R>

and
<V| = <H|

|U> = |D> = |L> |R>

Experimentally, the results would agree here, that were the scene repeated, each particular result would occur on average 25 times in every 100 repeats.

__

Now, let's imagine that Alice "prepares" the entity before measurement. For the sake of simplicity the "preparation" only applies to the VERTICAL axis and it is prepared so that the state for this vertical axis is UP
After such "preparation", Alice again chooses what axis to measure and makes the measurement.
If Alice chooses VERTICAL, the result will ALWAYS be U
If Alice chooses HORIZONTAL, the result is ALWAYS L or R

There is STILL perfectly equal probability of L/R if she chooses H and Alice's decision to choose H or V is unaffected.

<V|D> = 0

The statement made earlier
<V|U> + <V|D> + <H|L> + <H|R> = 1
still holds. Although <V|D> can safely be omitted as it is now zero probability. (Just as we are not including operators for the probabity amplitudes that Alice might spontaneously turn into a banana - it's not going to happen, so there's no need to include it)

<V|U> + <H|L> + <H|R> = 1
And
<H|L> = <H|R> still, so this holds as before. Given that Alice still chooses perfectly equally between H and V, though,
<V|U> + <V|D> = 0.5 = <H|L> + <H|R>
also still holds.
we can omit <V|D> as mentioned, and see that
<V|U> = 0.5 = <H|L> + <H|R>

So the effect of the preparation does not affect the HORIZONTAL measurement (should Alice choose to make it) in any way whatsoever. Instead, it is only the VERTICAL that is affected.

Now forget the preparation and instead bring in Bob. Also we will eradicate any choice for Alice. She will ONLY measure VERTICAL. Bob will only measure Horizontal.
There is no <A(l)| or <A(r)| nor is there a <B(u)| or |B(d)> they simply do not exist at all.

However Bob WILL make A MEASUREMENT (either B(l) or B(r) only- no other possibility) and Alice will make A MEASUREMENT(either A(u) or A(d) only- no other possibility)

<A(u)|A(d)> + <B(l)|B(r)> = 1
<A(u)|B(l)> + <A(u)|B(r)> + <A(d)|B(l)> + <A(d)|B(r)> = 1

The effect of entanglement will cause whatever Alice measures (A(u) or A(d) that Bob's paired entity would, if measured in that axis, result in the opposite to that which Alice measured. That is, if Bob were ALSO to measure in the vertical, and Alice measured U then Bob would measure D. If Alice measured D then Bob would measure U
If Alice broke with tradition and measured Horizontally, then if her result was L and Bob also measured horizontally, Bob would obtain a result of R. HOwever if Alice measured her entangled particle Vertically and Bob measured his entangled particle Horizontally, there would be no measurable detectable change whatsoever.
50% of the time Alice would detect U and 50% she would detect down. 50% of the time Bob would detect L and 50% of the time he would detect R just as if the experimentors, the particles, the detectors etc. were utterly isolated.

In the entangled scenario, if either could choose to measure either

<A(u)|B(d)> + <A(u)|B(l)> + <A(u)|B(r)> + <A(d)|B(u)> + <A(d)|B(l)> + <A(d)|B(r)> + <A(l)|B(u)> + <A(l)|B(d)> + <A(l)|B(r)> + <A(r)|B(u)> + <A(r)|B(d)> + <A(r)|B(l)> = 1

The probabilities are affected thus:

<A(u)|B(d)> = <A(d)|B(u)> = <A(l)|B(r)> = <A(r)|B(l)>
And
<A(d)|B(l)> = <A(d)|B(r)> = <A(l)|B(u)> = <A(l)|B(d)> = <A(r)|B(u)> = <A(r)|B(d)>

But because of the omission of
<A(u)|B(u)> + <A(d)|B(d)> + <A(l)|B(r)>
which would be included and contribute to the overall unity were there no entanglement, the individual probabilities as experienced by the individual experimenters are not noticeable unless the experimenters specifically compare notes.
Note that Alice is not changing the particle or encoding it in any way. It is either UP or it is DOWN (or more accurately, superposited UPDOWN, and measuring it will reveal which - measuring is in fact the activity of resolving this superposition into a real distinct state) - she cannot know beforehand which it will be, unless she PREPARES it as described above. However, preparation would "destroy the entanglement", Alice's particle would definitely be in whatever state she prepares it, but Bob would measure a now disentangled particle where the state would be again, determined through his measurement.

This is why it's not possible (regardless of how you encode the information) to transmit information using entanglement.

Such masterpiece explanation! Thanks!

 

[Ken G]

I obviously can't tell if I'm talking about something I don't understand, but the way I understood things, superposition is when a particle isn't being observed

That's not necessarily true, because if you have a superposition in regard to some observable, you can do an observation of a complementary variable without breaking the superposition in the original observable. So that might not be the best way to think about superposition. I think the best way to think about it is via the concept of "indeteminate" values of some observable-- whenever an observable has an "indeterminate" value in some state, then that state is a superposition with respect to that observable. But it does not need to be a superposition in regard to some other observable, it can have a definite value of something else. So there is no distinction between a "superposition state" and an "observed state"-- any time you observe anything and thereby give that observable a definite value, there will be other complementary observables that will be indeterminate and hence you have put the system into a superposition state with respect to those other observables.

In this light, we should say that entanglement is an example of a superposition with regard to the kinds of variables or attributes of systems that we normally regard as definite. It doesn't mean the entangled state doesn't have definite values for other observables! For example, the ground state of hydrogen is one in which the spin direction of the proton and electron are completely unknown, but it is known that they are opposite each other, whatever they are. So that's a prime example of the kind of information that is determined in entangled states-- mutual properties are determined, individual properties are indeterminate. So we have an observed state in regard to mutual properties (that kind of state can be observed by a "Bell measurement"), but a superposition state in regard to individual properties.

A particle's position & its spin are different things, but aren't both in superpositions until observed?

I'm pointing out they can be in superpositions after being observed as well. For example, after you observe a position, the momentum is in a superposition, and after you observe the spin in the up/down direction, the spin in the left/right direction is in a superposition.

The only thing here that really seems to require maths btw, is Bell's theorem.

And frankly, I think quantum teleportation is a better way to understand what is weird about entanglement than Bell's theorem. Bell's theorem is important for proving the untenability of local realism, but it generally doesn't come with a large "aha" feeling!

As it's often explained, that it's not like a pair of gloves in 2 boxes, whether it's a left or right hand in each box isn't decided at the beginning, it's both left & right until observed, & when observed & collapsed to a left or right hand at pure random, then the entangled glove will be the other hand. But yes, that one thing that proves it wasn't left or right from the beginning, I can imagine it can't be explained in simple ways.

We can try. The reason the gloves don't work is there is no "second aspect" to test (like the momentum in my position example, or the spin in a different direction than up/down), gloves have only individual properties not mutual ones. What is weird about entanglement is you can prepare two particles such that their spin components in all directions is indeterminate, but it is determined that they have the mutual property of being opposite each other. So there the only determined properties are mutual ones! Try that with gloves.

And back to teleportation (of information, faster than light), what makes it impossible is the fact that the collapse of the LR hand into a L or R, is purely random, right? Thus the correlation can only be done afterwards, by normal communication.

Right.

 

[anothergol]

mmmh.. maybe I'm misunderstanding what you wrote, but when you say "undeterminate", it sounds like the state/spin/whatever is only one value, but it's not known (yet).
Isn't it BOTH?

I mean, in the double slit experiment, surely the single particle that's interacting with itself, passed through both slits, isn't that what superposition is, all the possibilities being real, not that there is one and it's unknown?

You said: "The reason the gloves don't work is there is no "second aspect" to test (like the momentum in my position example)"
Which reminds me that I still don't fully understand what the uncertainity principle is really about.
I mean, from these 2 videos, for ex


I come from the audio world, and the analogy I'd make, is that the lower the frequency of a sinewave, the less precisely its "position" can be determined, because a low frequency needs enough time to even "exist". Like, a fourrier transform in a short window wouldn't detect a frequency for which the phase is larger than half of that window. (which isn't weird in any way)
But.. if that analogy is true, where is "randomness" involved here?
& that probability wave function for the position of the particle, does it mean
a) the particle is everywhere it is probable to be, until an interaction that forces it to pick?
b) the particle is somewhere it is probable to be, and interaction will only tell one position at a given time? (then I don't understand how the particle interacts with itself in the double slit experiment)
c) something else?You wrote "For example, the ground state of hydrogen is one in which the spin direction of the proton and electron are completely unknown, but it is known that they are opposite each other, whatever they are."
..so the spin direction is unknown, but it is definite? It's not both at once?
The way I understood it, the spin was both, and the observation forced it to be one, from that you can conclude that the spin of its entangled particle is the opposite. But "both" and "unknown" seems pretty different.
Or if you're saying that from the moment one thing (position) becomes known, its linked property (speed) then becomes blurry, ok, byt even this doesn't claim that whichever is blurry is "all possibilities at once", only that it's rough (but not random, and not "every possibility at once"). Well I'm more confused now than when I asked my questions.

Edit: there's this video that confused me the same way, and that was over 6 months ago, that says for how long I've been trying to understand this:
The audio-analogy I made is pretty much 1., and it says it's wrong... ok.
But 3. seems to be a combination of 1, with the probability wave adding the random factor to that position/speed link, resulting in "clear or blurry, but always random".
But I thought that the superposition was "the particle has lots of positions" ALONE.
And if it's not that, I'm even more confused about what makes the behavior of the particle -change- after interaction, in the double slit experiment.

 

[star apple]

Alice is measuring VERTICAL Axis
Bob is measuring HORIZONTAL.

For the sake of argument/completeness let's assume that there are only two dimensions and that whatever entangled "things" are being measured in a way that what Alice considers VERTICAL and HORIZONTAL are exactly identical to that which Bob does too. Bob and Alice or their detectors are exactly aligned relative to each other - obviously "Horizontal" and "Vertical" are orthogonal.

Alice would have an equal probability, measuring ONLY the vertical - of detecting UP or DOWN. However her result would ALWAYS show either UP/DOWN
Bob, measuring ONLY the horizontal would have equal probability of detecting LEFT or RIGHT. However his result would ALWAYS show either LEFT/RIGHT
This would be true regardless of entanglement.

Assume for a moment that there is no Bob. He nor any entanglement exists. There is only Alice and her detector and the thing she is measuring.
Alice has a CHOICE in measuring HORIZONTAL or VERTICAL The choice represents a fork in a probability tree. We assume there is equal probability in her making either choice and that she will with absolute certainty choose to measure H or to measure V there is no other option. She cannot fall asleep, forget or go do something else. She MUST make a choice, must choose either H or V.
Depending on what she cxhooses, she will then measure:

If H
U or D

If V
L or R

There are no other possibilities. No other results nor outcomes exist.

This can all be represented with the following (Although the symbols represent operators and are in reality conjugated)

Alice chooses Horizontal or Vertical. There are no other options

IF Alice chooses H, the result can only be L or R
<V|U>=0
<V|D>=0
<H|L> + <H|R> = 1

OR
Alice chooses V and result must be either U or D
<H|U>=0
<H|R>=0
<V|U> + <V|D> = 1

Since the choice between V or H represents operation on states still part of the system, these can be combined, however, now the initial choice is only 50% of the entire probability contributions, but represents exactly 50%

<V|U> + <V|D> = 0.5 = <H|L> + <H|R><V|U> + <V|D> + <H|L> + <H|R> = 1
This encapsulates that there are only those possibilities. There is no possibility for, say choosing Horizontal and measuring UP.

Since we have established (for example simplicity) that Alice's chioce in measuring H or V is utterly equal, and that whether U/D or L/R within each choice are also completely equal :

<V|U> = <V|D> = <H|L> = <H|R>

and
<V| = <H|

|U> = |D> = |L> |R>

Experimentally, the results would agree here, that were the scene repeated, each particular result would occur on average 25 times in every 100 repeats.

__

Now, let's imagine that Alice "prepares" the entity before measurement. For the sake of simplicity the "preparation" only applies to the VERTICAL axis and it is prepared so that the state for this vertical axis is UP
After such "preparation", Alice again chooses what axis to measure and makes the measurement.
If Alice chooses VERTICAL, the result will ALWAYS be U
If Alice chooses HORIZONTAL, the result is ALWAYS L or R

There is STILL perfectly equal probability of L/R if she chooses H and Alice's decision to choose H or V is unaffected.

<V|D> = 0

The statement made earlier
<V|U> + <V|D> + <H|L> + <H|R> = 1
still holds. Although <V|D> can safely be omitted as it is now zero probability. (Just as we are not including operators for the probabity amplitudes that Alice might spontaneously turn into a banana - it's not going to happen, so there's no need to include it)

<V|U> + <H|L> + <H|R> = 1
And
<H|L> = <H|R> still, so this holds as before. Given that Alice still chooses perfectly equally between H and V, though,
<V|U> + <V|D> = 0.5 = <H|L> + <H|R>
also still holds.
we can omit <V|D> as mentioned, and see that
<V|U> = 0.5 = <H|L> + <H|R>

So the effect of the preparation does not affect the HORIZONTAL measurement (should Alice choose to make it) in any way whatsoever. Instead, it is only the VERTICAL that is affected.

Now forget the preparation and instead bring in Bob. Also we will eradicate any choice for Alice. She will ONLY measure VERTICAL. Bob will only measure Horizontal.
There is no <A(l)| or <A(r)| nor is there a <B(u)| or |B(d)> they simply do not exist at all.

However Bob WILL make A MEASUREMENT (either B(l) or B(r) only- no other possibility) and Alice will make A MEASUREMENT(either A(u) or A(d) only- no other possibility)

<A(u)|A(d)> + <B(l)|B(r)> = 1
<A(u)|B(l)> + <A(u)|B(r)> + <A(d)|B(l)> + <A(d)|B(r)> = 1

The effect of entanglement will cause whatever Alice measures (A(u) or A(d) that Bob's paired entity would, if measured in that axis, result in the opposite to that which Alice measured. That is, if Bob were ALSO to measure in the vertical, and Alice measured U then Bob would measure D. If Alice measured D then Bob would measure U
If Alice broke with tradition and measured Horizontally, then if her result was L and Bob also measured horizontally, Bob would obtain a result of R. HOwever if Alice measured her entangled particle Vertically and Bob measured his entangled particle Horizontally, there would be no measurable detectable change whatsoever.
50% of the time Alice would detect U and 50% she would detect down. 50% of the time Bob would detect L and 50% of the time he would detect R just as if the experimentors, the particles, the detectors etc. were utterly isolated.

About these statements: “HOwever if Alice measured her entangled particle Vertically and Bob measured his entangled particle Horizontally, there would be no measurable detectable change whatsoever. 50% of the time Alice would detect U and 50% she would detect down. 50% of the time Bob would detect L and 50% of the time he would detect R just as if the experimentors, the particles, the detectors etc. were utterly isolated.”

Can you cite experiments that prove this? What if after Alice measured her entangled particle vertical and Bob tried to measure his particles horizontal, Bob won’t get any results (null results meaning neither left or right). Only if he measured vertical would he get result? Or maybe you were saying when Bob tried to measure vertical. It broke the entanglement?

Thanks again.

In the entangled scenario, if either could choose to measure either

<A(u)|B(d)> + <A(u)|B(l)> + <A(u)|B(r)> + <A(d)|B(u)> + <A(d)|B(l)> + <A(d)|B(r)> + <A(l)|B(u)> + <A(l)|B(d)> + <A(l)|B(r)> + <A(r)|B(u)> + <A(r)|B(d)> + <A(r)|B(l)> = 1

The probabilities are affected thus:

<A(u)|B(d)> = <A(d)|B(u)> = <A(l)|B(r)> = <A(r)|B(l)>
And
<A(d)|B(l)> = <A(d)|B(r)> = <A(l)|B(u)> = <A(l)|B(d)> = <A(r)|B(u)> = <A(r)|B(d)>

But because of the omission of
<A(u)|B(u)> + <A(d)|B(d)> + <A(l)|B(r)>
which would be included and contribute to the overall unity were there no entanglement, the individual probabilities as experienced by the individual experimenters are not noticeable unless the experimenters specifically compare notes.
Note that Alice is not changing the particle or encoding it in any way. It is either UP or it is DOWN (or more accurately, superposited UPDOWN, and measuring it will reveal which - measuring is in fact the activity of resolving this superposition into a real distinct state) - she cannot know beforehand which it will be, unless she PREPARES it as described above. However, preparation would "destroy the entanglement", Alice's particle would definitely be in whatever state she prepares it, but Bob would measure a now disentangled particle where the state would be again, determined through his measurement.

This is why it's not possible (regardless of how you encode the information) to transmit information using entanglement.

 

[bhobba]

I mean come on, I've seen a lot of movies about the double slit experiment, Schrodinger's cat, and entanglement. I thought I at least got these basic things right. But none of them used equations to explain these.

That's the problem.

They do not tell the truth. I will repeat it - they do not tell the truth.

There are very few books at the beginner level that do - I gave links to Susskinds books that do - I will do it again:
https://www.amazon.com/dp/0465075681/?tag=pfamazon01-20
https://www.amazon.com/dp/0465062903/?tag=pfamazon01-20

If you read them and have your thinking cap on, plus take your time (it's not a race) you will understand exactly what's going on including a much expanded version of what I wrote about entanglement before - plus the very important concept of how QM all by itself explains 'collapse' for all practical purposes, and exactly what the issue is with the explanation. Some say it explains it, and others saying - no - and other views as well - its actually a bit subtle - but after reading those books it will be a lot clearer.

So the first thing is forget whatever you have read - forget it - I will now tell you the truth - but it involves math - sorry - its just the way it is. I will make the math as easy as I can but there is no way out here - its the only way.

Ok to start with let's suppose a quantum system is described by a real number I will call its state - it never is but this is just for the purposes of explanation. Suppose its described by the number 6. 6 = 3+3. In quantum parlance 6 is said to be a superposition of 3 and 3. But 6 = 4+2 so 6 is also a superposition of 4 and 2. In fact if 6 = a+b then 6 is a superposition of a and b. That's all it is - its simple really. But note given any state a it can be broken down in innumerable ways so if a state, a = b+c, then a is said to be in a superposition of b and c but it is also a superposition of many many other states. This is what I mean when I say saying a quantum system is in superposition is pretty meaningless because any state is a superposition of many other states in many many different ways.

Now you have the general idea you ready for one of the fundamental concepts of QM, in fact its the foundational concept Dirac built his version of QM on, called the principle of superposition. Instead of real numbers we will now write states using a new notation |a>. |a> is called a ket and its simply fancy notation for the system is in state a. What a is don't worry about - its simply an abstract symbol for the state of the system - I haven't even told you what a state is - and neither did Dirac - its simply symbolic. Now for the statement of the principle of superposition - if a system can be in state |a> and state |b> then it can be in state |c> = d*|a> +e*|b> where d and e are any two complex numbers. If you don't know what a complex number is don't worry about it - I won't be using the concept - but if you want to understand QM at a reasonable level you should learn what they are. Now we have extended a bit what states are - we know you can multiply them by complex numbers and you can add them together. Its not a great deal to know - but basically it's what they are - strange hey - its just a simple mathematical concept - technically its called a vector space - but that's just a technical mathematical name for the principle of superposition.

OK - how does this fit in with wave-functions? Suppose I have states |xi> and these states have the property that if you observe the position of a system in |xi> then it always always will be in position xi. Ok let's apply the principle of superposition to these states of definite position so |a> = c1*|x1> + c2*|x2> ++++ cn*|xn> or using the summation notation |a> = ∑ ci*|xi>. Here is where we now apply another principle of QM called the Born Rule. This only applies if the ci are what's called normalized without going into what that is, but again its something you should eventually come to grips with. What the Born Rule says is if you observe state |a> for position then the probability of getting xi as the answer is |ci|^2. Now suppose the xi is so fine it can be considered as not discreet, but as a continuous real number x - the actual position - physicists say - suppose it goes to a continuum. Then the ci also are continuous and we have a function dependent on x, c(x). c(x) is called the wave-function. It has the following simple property - if Δx is small when you observe a system for position the probability for result to lye between x and x + Δx is Δx*|c(x)|^2.

Ok you now know what a superposition is and a wave-function is. Technically a wave-function is the coefficients of expanding a state in states of definite position. Now for some technobabble - states of definite position are called eigenfunctions of position. States of definite momentum are called eigenfunctions of momentum. States of definite spin are called eigenfunctions of spin. In fact states of a definite anything are called eigenfunctions of what that thing is.

So when speaking of superposition its rather vacuous unless you also say another thing - what is it a superposition of ie what the eigenfunctions it is a superposition of. For a wave-function it is superposition's of eigenfunctions of position - but there are many other things it can be a superposition of eg momentum or spin.

This is a lot to take in. Once you have understood it read the reply I previously gave on what entanglement is and see if things are now clearer.

If it isn't then I don't know any other way of explaining it. Remember physics is a mathematical model - its not a visual model, its not a philosophical dielectric - it's a mathematical model. Mathematics is unavoidable. Those that try to avoid it actually end up instead confusing people and to be blunt telling downright lies, like for example a particle is in many positions at once or takes all paths simultaneously. It doesn't - they are simply trying to get across in pictorial terms what's going on - but what they really end up doing is telling if not downright lies, at best half truths. Now I don't want to be too hard on those that write such populations - if they didn't do it then they would have to say something like what I said - in fact its what Susskind does. This turns most people off, so they resort to what they do and we have many misconceptions amongst beginners.

Also once you grasp it I can very elegantly explain the double slit:
https://arxiv.org/abs/quant-ph/0703126

You probably won't understand the above off the cuff, but give it a look and I will 'decode' it for you - but only if you get what I have said before.

Thanks
Bill

 

[anothergol]

I've already tried to make sense of complex numbers to be honest, because I needed them for my work (FFT's outputting complex numbers), but never really manage to. All I understood is that it was a purely mathematical trick to achieve things.

And I course don't understand (yet) what you just explained, but so you're saying that what's explained in all those videos, isn't a valid interpretation of what you just wrote?
Are you saying that in the double slit experiment, saying "the particle takes all paths simultaneously" is wrong, or rather "that's not precisely what the maths say, it's one possible interpretation, but not necessarily the truth"?

 

[_PJ_]

What if after Alice measured her entangled particle vertical and Bob tried to measure his particles horizontal, Bob won’t get any results (null results meaning neither left or right). Only if he measured vertical would he get result? Or maybe you were saying when Bob tried to measure vertical. It broke the entanglement? Thanks again.

Alice measuring spin on axis V will always get a result of either U or D
Bob measuring spin on axis H will always get a result of either L or R

_
Do not confuse A & B's measurements or effects of entanglement with with the idea that if you prepare an object at, say 45 degrees (partway between, say U and R) and then measure V, the result will be U with greater probability than D
If measured H, the result will have greater probability of R than L

I've already tried to make sense of complex numbers to be honest, because I needed them for my work (FFT's outputting complex numbers), but never really manage to. All I understood is that it was a purely mathematical trick to achieve things.

And I course don't understand (yet) what you just explained, but so you're saying that what's explained in all those videos, isn't a valid interpretation of what you just wrote?
Are you saying that in the double slit experiment, saying "the particle takes all paths simultaneously" is wrong, or rather "that's not precisely what the maths say, it's one possible interpretation, but not necessarily the truth"?

QM operations are complex. That's the nature of the beast.
The simplification that a 'aparticle takes all paths simultaneously' is possibly best understood (at least for me) in the underlying mathematics from the roots in Fourier Transformations as with signal processing.

If you hear a piano note, it can be represented as a soundwave of a specific frequency - this would be considered a pure wave.
However, Fourier analysis exemplifies (and actually, is how MP3 and other audio techologies allow for sounds to be encoded digitally) that even an apparent pure wave which has an amplitude at a given point and cycles according to the particular phase - could be represented by the combination of other frequencies of waves (which through interference can cancel and reinforce ) at particular amplitudes and phases - the contributions made to the outcome varies for each of these waves and is called a Fourier coefficient. Whilst some coefficients may be tiny and others less trivial, that non-zero contributions are made means that increasing the range of the frequencies and phases that contribute always increases the accuracy to which the ensemble wave matches the pure tone. This reaches a limit at infinity - that is, after the infinite range of waves are summed over (by amounts governed by their respective Fourier coefficients) the result exactly matches the pure tone.

It's a lot more simple in concept than trying to describe it in words - so here's a more abstract generalisation - Imagine a piano with an infinite number of keys and the infinite number of Beethoven's playing that piano press each key with varying strengths so some are louder, some are softer and with ever so slightly different timing - although you may expect the result to be a cacophonic noise, the interference of the soundwaves results in a perfect middle C

This is absolutely true of SP and the mathematics employed is well understood, and it is this same mathematics that underpins much of quantum process - which is why so many consider that it is a strange and counter-intuitive worlds - the mathematics of infinite and periodic phenomena describe the actions of real, assumed "non-periodic" physics. The uncertainty principle is also encapsulated within the same mathematics when considering the description of a particle at a given position, there is an equal and non-zero probability for every possible momentum state.
So the notion of a "particle" choosing every single trajectory" is not strictly accurate, but the mathematics that describe and predict a resulting trajectory from the given inputs are the same as the mathematics that describe phenomena where wave interference cancels out to reveal a single result - The PROBLEM, really, is with our intuition and assumptions as to what is meant by "a particle" or that such an entity moves from A to B.

 

[star apple]

Alice measuring spin on axis V will always get a result of either U or D
Bob measuring spin on axis H will always get a result of either L or R

_
Do not confuse A & B's measurements or effects of entanglement with with the idea that if you prepare an object at, say 45 degrees (partway between, say U and R) and then measure V, the result will be U with greater probability than D
If measured H, the result will have greater probability of R than L

So what’s where they got the words Alice and Bob.. from the letter A and B. Didn’t know that before.

Even if Alice measured in the vertical, the reason Bob could still measure the horizontal was due to Bob collapsing the wave function or breaking the entanglement?

 

[bhobba]

I've already tried to make sense of complex numbers to be honest, because I needed them for my work (FFT's outputting complex numbers), but never really manage to.

Of let's start with complex numbers. You know what 1, 2, 3, 4 etc is? You can have that many sheep etc - its a tool for modelling the number of things. But let's suppose you do something tricky - you loan some sheep, say 3, to a friend - how many sheep does he own? Well none of course - but he owes you 3. How can we model that - we say he has -3 sheep. You can't point to -3 sheep but its useful to model the situation. Its exactly the same with complex numbers. What's √-1. obviously no number exists like that. But what if you want to solve x^2 = -1? You can't do it. But sometimes you want to. So you do the minus -1 trick again - you try and figure out how to use it to model something. Consider the real number line. Now if you multiply 1 by -1 you rotate 1 through 180%. What if you rotate it through 90% then 90% again - well that 180%. So what you can think of √-1 as is a rotation through 90% so if you square it its rotated through 180%. You then put an axis at 90% to the real line and call it the imaginary axis. √-1 is called i and by having two axis you now have a plane instead of a line - its called the complex number plane. You can express any point on that plane as a + b*i. Ok that's how you model complex numbers and what it means. Its just like negative numbers - you can't point to a negative number of anything - but it is useful to model certain things. The same with complex numbers - you can't point to √-1 of anything but mathematicians have investigated complex numbers and have found some really interesting things about them. One is the fundamental theorem of algebra that says any polynomial can be solved if you use complex numbers. This leads to all sorts of interesting modelling consequences - for example you need it in biology to model populations by means of what's called Markov chains - you sometimes get complex numbers cropping up because polynomials often occcur. They have special meaning for populations such as they will oscillate. It really is a fundamental mathematical concept.

Why do complex numbers occur in QM? That is a very very deep question on which the following only touches:
https://www.scottaaronson.com/democritus/lec9.html

Are you saying that in the double slit experiment, saying "the particle takes all paths simultaneously" is wrong, or rather "that's not precisely what the maths say, it's one possible interpretation, but not necessarily the truth"?

Its a pictorial half truth good as a heuristic suggested by the math (the path integral formalism discovered by Feynman that is equivalent to normal QM) but not actually true. Popularizations say that sort of thing because being limited to no math its all they can do.

Thanks
Bill

 

[Ken G]

mmmh.. maybe I'm misunderstanding what you wrote, but when you say "undeterminate", it sounds like the state/spin/whatever is only one value, but it's not known (yet).

Just the latter-- it's not known. There's no need to say it is only one value if it's not known, but when and if it does become known, then it will be only one value. Why say more?

Isn't it BOTH?

No, there's no need to say it's both, because sometimes the situation never establishes the indeterminate parameter at all, so it just stays unknown and that's all. The double slit is a good example-- there's no need to say the particle goes through both slits if it is not established which slit it goes through, it suffices to say that nature does not establish which slit so you have to include both possibilities in all your calculations. Including both possibilities is not the same as going through both slits, but it gets into interpretation now. What I like to imagine is that there is a particle, and a wave the scientist uses to anticipate where the particle will go. The wave the scientist uses goes through both slits, but the particle simply has an indeterminate relationship with the "which slit" question-- the question simply goes unanswered because there is nothing in the apparatus that poses the question in the first place.

This is I think one of the key insights of quantum mechanics-- nature isn't some kind of "answer man" that specifies an answer to every question we can think of, even if we cannot know that answer. Instead, an answer that is impossible to know is one that is not answered at all, the question simply has not been given meaning by the apparatus. It may help you to realize that the question never posed in the reality is never answered in the reality. So if you got a question on an exam that said "which slit does a particle go through on the way to making a two-slit interference pattern", in my mind the correct thing to do is not say "both," but rather, leave the question blank-- it is not answered by nature so it should not be answered by you either.

I come from the audio world, and the analogy I'd make, is that the lower the frequency of a sinewave, the less precisely its "position" can be determined, because a low frequency needs enough time to even "exist". Like, a fourrier transform in a short window wouldn't detect a frequency for which the phase is larger than half of that window. (which isn't weird in any way)

Seems like a reasonable way to think about it, though I would instead say that it is really the length of the "wave train" that establishes the uncertainty in position, and that length is a combination of the wavelength and the number of cycles in the wave. The wavelength is related to your "low frequency" idea, but there's also the fidelity of the wave, which is the number of cycles. That all goes into the Fourier analysis of it as well.

But.. if that analogy is true, where is "randomness" involved here?

If you redo the experiment, but this time determine which slit, it's a different experiment but it will yield seemingly random answers to the question "which slit" that is now being posed, but wasn't before.

& that probability wave function for the position of the particle, does it mean
a) the particle is everywhere it is probable to be, until an interaction that forces it to pick?
b) the particle is somewhere it is probable to be, and interaction will only tell one position at a given time? (then I don't understand how the particle interacts with itself in the double slit experiment)
c) something else?

Those are all consistent with what we see, so choosing between them is choosing an interpretation. That is a famously subjective process!

You wrote "For example, the ground state of hydrogen is one in which the spin direction of the proton and electron are completely unknown, but it is known that they are opposite each other, whatever they are."
..so the spin direction is unknown, but it is definite? It's not both at once?

It is a combination of definite and indefinite. What is completely definite is that the spins are anti-aligned. What is completely indefinite is which direction either of them points individually. That sounds like an impossible combination, doesn't it? But that's the guts of entanglement, and this situation only seems impossible to us (and to Einstein) because classical systems never show that combination, the entanglements get so convoluted they simply cease to have any impact, like there are so many particles of water in a glass you don't notice any particles at all when you drink it. Is that such an unusual state of affairs?

The way I understood it, the spin was both, and the observation forced it to be one, from that you can conclude that the spin of its entangled particle is the opposite. But "both" and "unknown" seems pretty different.

Yes, if something is unknown, which it clearly is, there is no need to say it is "both", as that would suggest knowing something you don't in fact know. But more to the point, nature herself does not appear to know it either, the question simply hasn't been posed at all, until it is posed by the appropriate measurement. I think that's a big insight from QM: measurements don't just answer questions, they pose them in the first place.

Or if you're saying that from the moment one thing (position) becomes known, its linked property (speed) then becomes blurry, ok, byt even this doesn't claim that whichever is blurry is "all possibilities at once", only that it's rough (but not random, and not "every possibility at once"). Well I'm more confused now than when I asked my questions.

You don't sound more confused to me, you sound like you are starting to get it.

But I thought that the superposition was "the particle has lots of positions" ALONE.

I would prefer to say the superposition is a result of the fact that the question "where is the particle" has only been partially posed (or essentially not at all, in some cases) by the environment that particle has been subjected to. So it's not just that the answer hasn't been determined, it's that the question hasn't even been asked. We don't interrogate nature by thinking up questions for her, we do it by setting up experiments that actually pose the question in the reality. We can think hypothetically about experiments that pose questions, but then the questions are only answered in the hypothetical context of that experiment, not in the reality.

And if it's not that, I'm even more confused about what makes the behavior of the particle -change- after interaction, in the double slit experiment.

What makes it change is that a question needs answering, because it is being posed, that did not need answering before, because it wasn't being posed.

 

[anothergol]

Yeah I had seen that negative numbers analogy in this video already, but still couldn't really get it

I mean I don't agree that negative numbers are weird, because that minus sign is an operation sign in the first place. I mean I can picture minus 3 sheep, yeah.

 

[bhobba]

I mean I can picture minus 3 sheep, yeah.

But not a rotation through 90%?

Thanks
Bill

 

[_PJ_]

The description of complex numbers given earlier is great, but lengthy. When simple ideas take a lot of words to describe accurately, it can become easy to get "lost in the prose". The slightest misinterpretation or ambiguity of the target of pronouns etc. can also result in misunderstanding or uncertainty (no pun).

There is an imaginary number i for which i * i = -1
There exists a set of imaginary numbers are multiples of i

Complex numbers are vectors of imaginary and real axes of the form ai + b

All real numbers are complex numbers with ai + b where a=0

For every complex number ai + b there is a conjugate ai - b

The result of any complex number multiplied by its conjugate is real.

Don't overthink it, complex numbers are not inherently difficult. Some of the calculations involving them can be, but that's usually due to the operations rather than the nature of complex numbers.

 

[Ken G]

Here is I think a useful way to think about imaginary numbers. Imagine a Ferris wheel going around and around, and notice the shadow on the ground of one of the cars on the Ferris wheel. The shadow executes simple harmonic motion, it looks just like a block on a spring in one dimension rather than a car on a wheel in two dimensions. Now imagine ants on the ground that can notice the shadow doing its harmonic motion but are completely oblivious to the Ferris wheel in the other dimension. Let us now compare how we, in both dimensions, would model the situation, in contrast to how the ants, in their dimension, would.

The way to take the 1D model of the ants and turn it into our full 2D model is to combine 1D harmonic motion in the atom's dimension with 1D harmonic motion in the vertical direction, and just considering them both together at once. This could be done by calling the vertical direction a kind of 90 degree rotated version of the ant's dimension, just one the ants are unaware of. Mathematically, that same thing could be accomplished in the "complex plane" by attributing real numbers to the location of the shadow in the ant dimension, and imaginary numbers to the height of the car above the ground. We don't usually do that, we usually give real numbers to both an "x" and "y" direction, but that's just what you're used to-- it works just as well to give a single complex number to the whole business, by adding the real and imaginary parts I just mentioned!

Now, the complex-number version is actually more insightful, both because it's easier to manipulate mathematically (and we often do treat 2D harmonic motion that way), and also because it's very true that to the ants, the vertical dimension is "imaginary." Now if there was a very clever ant who realized that the shadow they see is easier to think about as something going in a circle through a second "imaginary" dimension, the ant could also use the same mathematics as we do, and it is actually quite insightful to do that-- the concept of "phase angle" has a much clearer interpretation, for example. But then would appear the various interpretations-- one ant might say the imaginary direction that makes the math work out is just in the ant's minds, a convenience if you will, while another ant interprets it, with a sense of irony, as completely real, as though they were only looking at the shadow of a car on Ferris wheel. There is even a third possibility, which is that the motion of the shadow comes from a superposition of a car on a Ferris wheel going around one way, together with a car on another Ferris wheel going around the opposite way, and you add together the two locations of the result to get what the shadow does-- which gives it a kind of doubly abstract character because not only do you have two imaginary dimensions (corresponding to opposite signs of i, either of which give -1 when squared), but you also have the concept of a true superposition. In that last interpretation, the ants only perceive things happening in the plane of the ground by a kind of accident of the two opposite signs of i acting concurrently.

Thus, the fact that we find ourselves forced to interpret complex amplitudes in quantum mechanics is perhaps not so surprising, given that we already had that same situation when interpreting various types of simple harmonic motion, and various types of oscillating fields, even in classical mechanics! It's customary to choose one of the above interpretations of complex numbers in classical mechanics, and another in quantum mechanics, but there's no necessary reason for this-- any are allowed in either context.

 

[anothergol]

The double slit is a good example-- there's no need to say the particle goes through both slits if it is not established which slit it goes through, it suffices to say that nature does not establish which slit so you have to include both possibilities in all your calculations. Including both possibilities is not the same as going through both slits, but it gets into interpretation now.

Ok now we're getting somewhere. So as I wrote, your problem is that the maths/experiments only tell something precise, and what's being said out there is an extrapolation of that. But it's still what I find the most interesting, any possible explanation of all this. Aren't you puzzled by it, or do you think that there's no need to bother trying to comprehend, because it will always remain out of our reach?
"Nature does not establish which slit", that does sound like the particle did go through both slits, to me. Or at least, it doesn't exclude it, whether it's in one or multiple universes, or whatever. Or yeah, perhaps the particle itself isn't everywhere, but follows a "guide" that's the result of all possibilities - but that wouldn't be much different, and equally weird & interesting.

You say it's not answered by nature, but isn't that itself an interpretation? What if it really is reality that the particle passed through both slits? Would experiments spit out different results if that was the case?

Those are all consistent with what we see, so choosing between them is choosing an interpretation. That is a famously subjective process!

Ok, but that's what I'm interested in, every interpretation that still sticks with the maths & experiments, considering I will never get deep into the maths or experiments.
Plus, isn't what physics is all about, trying to find models that explain experimental results?

It is a combination of definite and indefinite. What is completely definite is that the spins are anti-aligned. What is completely indefinite is which direction either of them points individually.

Is it certain that the spins of entangled particles are constantly anti-aligned, or only at the time of measurement?

But more to the point, nature herself does not appear to know it either, the question simply hasn't been posed at all, until it is posed by the appropriate measurement.

Ok, the question hasn't been posed at all, yet the result of what we observe is the result of all of the possibilities (the particle/wave interacting with itself), not just one. Doesn't that sound like it is all possibilities, until observed, if the result is the combination of them all?
I mean: whether it's really the particle that was everywhere, or some weird guide in space itself & not the particle, the fact that 1 single particle at a time will produce an interference pattern, should mean that something, whether it's the guide or the particle, was the product of all possible states, thus "all at once", no?

 

[anothergol]

There is an imaginary number i for which i * i = -1
There exists a set of imaginary numbers are multiples of i

Ok now that seems clearer to me.
Perhaps it's the utility of it that I'm missing. I suppose it makes sense in maths that I've never used.

 

[zonde]

You say it's not answered by nature, but isn't that itself an interpretation? What if it really is reality that the particle passed through both slits? Would experiments spit out different results if that was the case?

Interpretation of particle passing trough both slits is not enough to explain all interference experiments. There is an experiment as far back as 1967 that observed interference between two independent photon beams from separate lasers: http://dx.doi.org/10.1103/PhysRev.159.1084

 

[anothergol]

Mmhh, interesting. Then does that restrict interpretations as
-some kind of invisible guide in space time?
-some "trail" that a particle leaves in space time?

Has there been experiments 1 photon at a time from the same source, but with rather long periods between each? (that is, does the period change anything?)

Here is I think a useful way to think about imaginary numbers. Imagine a Ferris wheel going around and around, and notice the shadow on the ground of one of the cars on the Ferris wheel. The shadow executes simple harmonic motion, it looks just like a block on a spring in one dimension rather than a car on a wheel in two dimensions. Now imagine ants on the ground that can notice the shadow doing its harmonic motion but are completely oblivious to the Ferris wheel in the other dimension. Let us now compare how we, in both dimensions, would model the situation, in contrast to how the ants, in their dimension, would.

Funny because that looks like an analogy often made in video's about QM. That or the tesseract. So it's pretty much about guessing what happens in a dimension that we can't see, from what we see in 1 less dimension?