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mox

Can someone help me understand entanglement pls?

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Hi, new here! 😀

I'm not "getting" the idea of entanglement? I read an analogy online - you buy a pair of shoes, take the box home & open it, only to find just one shoe in the box. By implication, the other shoe is still back at the store, and will be the other "foot" to what you have at home. Although just an analogy, I don't see how that's any different to two entangled photons, which by their very "entanglement" have oppositive polarities. No "locality" or "realism" is being violated, surely? The photons could be at opposite ends of the universe, but when we check one's polarity, we KNOW the other one will be the opposite! Where is the problem? Where's the "quantum weirdness"?

Edited by mox
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12 minutes ago, mox said:

Although just an analogy, I don't see how that's any different to two entangled photons, which by their very "entanglement" have oppositive polarities.

The difference is that the shoe in the box was always a left foot. Opening the box doesn't define whether it is left or right; it is inherent to the nature of the shoe. In that sense the "handedness" (footedness? chirality) of the shoe is technically "real". Opening the box just reveals what it is.

Whereas the spin (for example) of a photon is not only unknown before it is is measured, but it doesn't even have a defined value until it is measured. In that sense it is not "real". So by measuring the spin, you don't just find out what the value is, you cause it to have a value. And, instantly, cause the entangled partner to have the opposite value.

Another important difference is that the shoe can only be left or right. Whereas you can measure the spin at any angle and get a + or - value for the spin at that angle. And if you measure the spin of the entangled partner at the same angle, you will find it has the opposite value.

How do we know that the values of the spin are not "real" (defined, like shoes, when the entangled pair were created)?

Now, this is where it gets subtle and tricky (and therefore where I might well get the details wrong!). If you were to measure the spin of the entangled partner at 90º to the angle you measure the first photon, you would find there was no correlation. If you measure the spin at some angle between 0º and 90º, you will find there is statistical correlation. The probability of this correlation can be calculated assuming the particles had "real" (defined) values for the spin or they can be calculated using the rules of quantum theory. These two calculations give different results (known as Bell's Inequality). So by measuring this, we can test whether quantum theory gives the right answer or not. (Spoiler alert: it does!)

Hopefully someone who knows what they are talking about will correct any errors in that! But I hope it helps a bit.

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5 minutes ago, Strange said:

If you were to measure the spin of the entangled partner at 90º to the angle you measure the first photon, you would find there was no correlation. If you measure the spin at some angle between 0º and 90º, you will find there is statistical correlation. The probability of this correlation can be calculated assuming the particles had "real" (defined) values for the spin or they can be calculated using the rules of quantum theory. These two calculations give different results (known as Bell's Inequality). So by measuring this, we can test whether quantum theory gives the right answer or not. (Spoiler alert: it does!)

Thanks Strange, this paragraph helps a lot, I've had trouble following along with the Bell stuff, I can follow it up with this in mind.

Can I ask, how do we actually "know" that the properties of the photon are not "actual" or "real" until we measure/detect? I understand that the very act of "measurement" is intrusive and can perturb the particle we are looking at, thus throwing up uncertainties in the results. I can understand that, say, narrowing your resolution to precisely locate a particle, you thereby lose information about how fast it is going (for velocity or momentum, you need to see the particle travelling, therefore lose the precision of location/position)... Or, I may have got this all wrong eh!?

Isn't this all about how we "interpret" quantum mechanics? Don't some interpretations actually say the particle properties do actually exist, regardless of whether we measure them or not?

If a photon, say, exists in some superposed ambiguity of states that includes all polarities etc... doesn't that mean that "realism" is out the window, and that observation (whether measuring apparatus, or our minds) basically "create" the world around us? Also, if it is "realism" we are binning, how does that solve the locality problem of two entangled particles separated at vast distances?

(Sorry for noob/lay questions, just trying to learn! 🤨 Certainly not trying to espouse any of my own ideas or anything! 🙂 I hope it's ok asking this sort of stuff here. Please let me know if I'm infringing any guidelines, thank you! 🙂)

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26 minutes ago, Strange said:

The difference is that the shoe in the box was always a left foot. Opening the box doesn't define whether it is left or right; it is inherent to the nature of the shoe. In that sense the "handedness" (footedness? chirality) of the shoe is technically "real". Opening the box just reveals what it is.

Whereas the spin (for example) of a photon is not only unknown before it is is measured, but it doesn't even have a defined value until it is measured. In that sense it is not "real". So by measuring the spin, you don't just find out what the value is, you cause it to have a value. And, instantly, cause the entangled partner to have the opposite value.

Another important difference is that the shoe can only be left or right. Whereas you can measure the spin at any angle and get a + or - value for the spin at that angle. And if you measure the spin of the entangled partner at the same angle, you will find it has the opposite value.

How do we know that the values of the spin are not "real" (defined, like shoes, when the entangled pair were created)?

Now, this is where it gets subtle and tricky (and therefore where I might well get the details wrong!). If you were to measure the spin of the entangled partner at 90º to the angle you measure the first photon, you would find there was no correlation. If you measure the spin at some angle between 0º and 90º, you will find there is statistical correlation. The probability of this correlation can be calculated assuming the particles had "real" (defined) values for the spin or they can be calculated using the rules of quantum theory. These two calculations give different results (known as Bell's Inequality). So by measuring this, we can test whether quantum theory gives the right answer or not. (Spoiler alert: it does!)

Hopefully someone who knows what they are talking about will correct any errors in that! But I hope it helps a bit.

Hope it’s not too wrong - I found it a really helpful and simple explanation.

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1 minute ago, mox said:

Can I ask, how do we actually "know" that the properties of the photon are not "actual" or "real" until we measure/detect? I

From testing Bell's Inequality. If the values were real (as in classical physics) we would get a different result from that predicted by quantum theiry. When we do the experiment, we get the value predicted by quantum theory.

3 minutes ago, mox said:

I understand that the very act of "measurement" is intrusive and can perturb the particle we are looking at, thus throwing up uncertainties in the results. I can understand that, say, narrowing your resolution to precisely locate a particle, you thereby lose information about how fast it is going (for velocity or momentum, you need to see the particle travelling, therefore lose the precision of location/position)... Or, I may have got this all wrong eh!?

This is correct. But there are two different things here.

There is the "observer effect" which is where attempting to measure something will have an effect on it and change the thing you are measuring. For example, putting a voltmeter across a circuit can draw some current and change the voltage. You can correct for the effect. And you can design the voltmeter to minimise it.

Then there is uncertainty. There is a limit to how accurately you can measure some values even if you had perfect equipment, that had no effect on the system you were measuring. Again, one can say that the values are not even "defined" (or don't "exist") any more accurately than that.

7 minutes ago, mox said:

Isn't this all about how we "interpret" quantum mechanics? Don't some interpretations actually say the particle properties do actually exist, regardless of whether we measure them or not?

I'm not sure. I suppose, for example, the Many Worlds interpretation says that the properties exist, but there are infinite different worlds each with different values (or something - I'm not that familiar with it).

8 minutes ago, mox said:

If a photon, say, exists in some superposed ambiguity of states that includes all polarities etc... doesn't that mean that "realism" is out the window, and that observation (whether measuring apparatus, or our minds) basically "create" the world around us? Also, if it is "realism" we are binning, how does that solve the locality problem of two entangled particles separated at vast distances?

Yes, realism is out of the window (or, at least "local realism"; I think you can have realism if you also allow faster than light communication; but we know that isn't possible). 

I don't think it solves the locality problem; they are just two (related) non-intuitive aspects of quantum theory.

Whether that means that "observation creates the world around us" is more of a philosophical question. 

11 minutes ago, mox said:

I hope it's ok asking this sort of stuff here.

Absolutely. People here love to discuss and answer questions about things like this!

13 minutes ago, mox said:

Thanks Strange, this paragraph helps a lot, I've had trouble following along with the Bell stuff, I can follow it up with this in mind.

One of the best descriptions I have found is from "Dr Chinese" (no idea why he uses that name).

This is an overview: https://www.drchinese.com/Bells_Theorem.htm

And a fairly simple worked example: https://drchinese.com/David/Bell_Theorem_Easy_Math.htm (you may have to go through it several times to get the hang of it)

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Thank you, Strange! You've given me a lot to go on, much appreciated! 🙂

It is also nice & refreshing to be able to ask such questions in a friendly and helpful forum environment (not mentioning any names out there ha ha).

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Perhaps a simpler version might help.

We start with a single wavefunction describing a system of two particles isolated from the rest of the universe.

We then allow the system to interact in some way with the rest of the universe.

We call this interaction taking a measurement.

So why are we suprised when the wave function changes following that interaction.
We call this collapse of the wavefunction.

I am sorry the florid language (measurement and collapse) obscures the Physics

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Reading the original EPR article - and without fully grasping the algebra, mind you - I get the impression that when they're talking about "entanglement", they're describing when two particles come together, interact, and then go on their merry separate ways? Somehow that interaction (collison, bounce, forcefield interaction, whatever) makes them forever "connected" in some really weird unexplained way forevermore, no matter how far they travel. Is this correct? That sounds like "particle memory" to me lol!?

Lol I'm jusy not "getting" it!? I've looked at lots of Youtube videos, science articles etc. They ALL seem to be glossing over the details, the "logic" simply isn't there for me? That's not good enough for me! I want to understand the logical basis of the whole thing! The EPR article just seemed full of assumptions to me - eg what constitutes a "complete" and "correct" theory of physical reality, for one thing - it's philosphical twist & turns. And are experiments proving this spooky entanglement thing, it (i'm most probably wrong here, mind you) seems to be the experiments are designed to agree with the equations. I dunno, something just seems off with the whole thing ha ha...

Is there any actual DETAILED explanation out there, from the ground up, that doesn't gloss over the logic? I am learning linear algebra & stuff,  but to be honest I want it logically explained without equations. If this CAN'T be done - isn't there a big problem there?

Is there a book I can get stuck in to? Or something online that starts from "first principles" kinda stuff? Like I said, I don't need the mathematical proofs, just the chain of logic spelt out for me, no skipping steps, no presumptions we are told to take onboard with faith!

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47 minutes ago, mox said:

Reading the original EPR article - and without fully grasping the algebra, mind you - I get the impression that when they're talking about "entanglement", they're describing when two particles come together, interact, and then go on their merry separate ways? Somehow that interaction (collison, bounce, forcefield interaction, whatever) makes them forever "connected" in some really weird unexplained way forevermore, no matter how far they travel. Is this correct? That sounds like "particle memory" to me lol!?

One element of this is that you don't know (and can't know) the states of the particles after the interaction, but because of the interaction and the nature of the states (and conservation laws) the state of one particle dictates the state of the other, whenever they are determined.

Another element is the weirdness of QM. Superposition, and indeterminate states. There's no "memory" of the states, because they aren't in a particular state. 

 

 

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8 hours ago, swansont said:

One element of this is that you don't know (and can't know) the states of the particles after the interaction, but because of the interaction and the nature of the states (and conservation laws) the state of one particle dictates the state of the other, whenever they are determined.

 

What you don't know and more importantly can't know is one of the keys to understanding entanglement without advanced maths.

 

On 1/24/2020 at 8:46 PM, mox said:

I read an analogy online - you buy a pair of shoes, take the box home & open it, only to find just one shoe in the box. By implication, the other shoe is still back at the store, and will be the other "foot" to what you have at home. Although just an analogy, I don't see how that's any different to two entangled photons, which by their very "entanglement" have oppositive polarities. No "locality" or "realism" is being violated, surely? The photons could be at opposite ends of the universe, but when we check one's polarity, we KNOW the other one will be the opposite!

 

There is also 'classical entanglement' which you are describing.
This is entirely deterministic (and therefore unsuprising) as you point out.
The point about quantum entanglement is has a probabilistic aspect which makes it different.

Note photons do not have a polarity.

 

On 1/24/2020 at 8:46 PM, mox said:

Where's the "quantum weirdness"?

 

The weirdness is in the part we can't know.

 

On 1/24/2020 at 8:46 PM, mox said:

I'm not "getting" the idea of entanglement?

 

Another one is to understand the requirements for particles to become entangled  in the first place.
This is part due to the inherent properties of the particles and part due to the environment/circumstances.

Both are required.


For example two electrons in the same atomic orbital are entangled. Their environment (the Pauli exclusion principle) requires them to have opposites spin quantum numbers .
Two electrons in different orbitals may have the same spin, but are not entangled.   
But if one of the entangled electrons is removed or promoted to another orbital it can end up with either spin.

A practical result of this occurs in spectroscopy with so called singlet and triplet states.       

 

I am trying to work through this without advanced mathematics, in deference to your other thread on linear algebra.
However please ask for expansion of any of these points.
Entanglement is a difficult and complicated subject.

On this how did you get on with my first post in this thread ?

I am also working up to recommending Susskind's 'Theoretical Minimum' three books.
These would take you well into modern physics - he explains the (sometimes advanced) maths he introduces, but does not overuse.
The middle book

Quantum mechanics The theoretical Minimum

is really very chatty about entanglement as well as the maths.
It is perfectly possible to understand the words only on first reading and cut and come again to the maths later.
Unfortunately there are two chapters worth of discussion, far too much for my usual posting an extract.

 

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Would socks make a better analogy?

You have one pair of white socks and one pair of black socks.

if you lose one white sock you instantaneously lose one black sock.

Edited by between3and26characterslon

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6 hours ago, studiot said:

 

Note photons do not have a polarity.

Incorrect photons has two measurable polarities in its transverse wavefunction. 

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7 hours ago, between3and26characterslon said:

Would socks make a better analogy?

You have one pair of white socks and one pair of black socks.

if you lose one white sock you instantaneously lose one black sock.

Not really. The equivalent would be a pair of socks of unknown and undefined colour. When you look at one of the socks, it becomes either black or white (as does the other one of the pair, even if it is some distance away).

But, actually, analogies like this can never really work. But different versions of the analogy might help visualise different aspects of the behaviour.

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7 hours ago, Mordred said:
14 hours ago, studiot said:

 

Note photons do not have a polarity.

Incorrect photons has two measurable polarities in its transverse wavefunction. 

Thank you for you comment Modred. +1

Since photons do not carry charge;

I assume you are referring to what I call polarisation so thank you for calling attention to what may be a difference of usage of terminology.
This will benefit all readers.

 

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The sock analogy is limited because the black sock is always black. A quantum sock does not have a color until it's measured. So if you grab one sock in the dark and put it in your gym bag, it doesn't have a color until you pull it out in a lit room. Then you instantly know the other sock has the (un)matched color. There are experiments you can do to tell whether or not the sock had a color while it was in the bag.

Another limitation of the analogy is that the color of the sock does not depend on how it is measured. But a quantum particle does — if the photon has a vertical polarization and you put your detector at 30º, you will get a transmitted photon 75% of the time and an absorbed photon 25%. But if the polarization is undetermined you get 50/50. These kinds of measurements are how you can show entanglement.

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8 hours ago, studiot said:

Thank you for you comment Modred. +1

Since photons do not carry charge;

I assume you are referring to what I call polarisation so thank you for calling attention to what may be a difference of usage of terminology.
This will benefit all readers.

 

Ah charge polarity got it.

The experiment is also done with photons using a beam splitter to entangle photons. 

Edit just noticed Swansont described that above.

Edited by Mordred

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