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

[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?

 

[Ken G]

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?

I'm very puzzled by it, and the resolution that satisfies me is that the same environment that answers a question is also what poses that question. The important ramification of this is that if the environment leaves an answer indeterminate, it simply means the question is never posed in the first place! It's a bit like when you take an exam in school and go over the answers afterwards, you look at questions that were asked that you either knew or didn't know the answers, and you might also wish certain questions were asked that you knew the answer to, but I'll bet you spend zero time thinking about questions that weren't asked that you wouldn't have known the answer to! Apparently nature is a bit like that too, in regard to the two-slit experiment.

"Nature does not establish which slit", that does sound like the particle did go through both slits, to me.

I can't agree, not saying which is not saying both. It's like if you have neither a like for beets nor a dislike for them, it doesn't mean you both like and dislike them, it means you have no opinion on them. The mistake is in thinking the particle has to either go through one slit or the other, or both-- that leaves out the possibility that the issue is simply indeterminate.

Or at least, it doesn't exclude it, whether it's in one or multiple universes, or whatever.

Oh sure, there are plenty of other interpretations, I'm just saying it already invokes an interpretation to say "both," and in my opinion, not a terribly useful interpretation.

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.

Yes, I think as long as you regard it as weird and interesting, there's not much better you can do.

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?

Yes, my approach is indeed an interpretation, but I like to think it is a kind of "minimal" interpretation that adds the least to what we are actually being given. It does not appear that experiments can distinguish these interpretations, as any experiments that agree with quantum mechanics predictions can be interpreted in multiple ways.

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.

Which leaves you to pick your own favorite interpretation, or even to accept a little dose of them all.

Plus, isn't what physics is all about, trying to find models that explain experimental results?

This is already an interesting question in the philosophy of science. Are we only trying to get power over our environment via successful predictions, or is there also an aesthetic goal to feel like we understand something, that we are learning some kind of lesson? I think almost all scientists have a significant portion of that latter perspective, it's usually what draws them to science in the first place. Even those who claim they only "shut up and calculate" rarely really do restrict themselves to that.

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

That's interpretation dependent. Personally, I don't even regard the spin as an attribute that the particle possesses at all, neither all the time nor during measurement. I see it more like information that we have about the particle, which reflects simultaneously (another type of superposition, perhaps) some truth about the reality and some truth that our thought processes interpret into the reality. In other words, all these "attributes" reflect a kind of dialog between us and nature (and that dichotomy is already an idealization), where both parties play a crucial role and could not be the same without either one.

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?

And that's why many people like to say it goes through "both." But I prefer to say it arrives at the detector, because that question was posed, and how it got there is simply a question that is not posed, so there is no truth to saying the particle actually went through both-- however, the mathematical waves we use to predict the answer to the question that was posed (where it arrived) does involve amplitudes that go through both slits. But remember that amplitudes aren't "things" so don't really "go through" anywhere, they are mathematical constructs.

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?

I don't mind saying the "guide" involves hypotheticals that, by themselves, would look like a particle going through one slit or the other, so the combination of them kind of looks like going through both slits, but there's still no need to say the particle itself goes through both, when the slit it goes through seems more like it is fundamentally indeterminate.

Consider this analogy: a photon that is polarized at a 45 degree angle has an indeterminate polarization in regard to being either vertical or horizontal. Should we then say that the photon is polarized both vertically and horizontally? That sounds a bit incoherent, so we instead say it is polarized at a 45 degree angle, which sounds like something quite different but which can be regarded as a superposition of vertical and horizontal, and hence is indeterminate in regard to those directions. A superposition of two slits is not as clearly a "thing" as the polarization at 45 degrees, but that's just because we haven't figured out a measurement that gives a definite result if it's a superposition of two slits, whereas we can tilt a polarizer 45 degrees. Does that represent a fundamental difference in those types of superpositions? I couldn't say, but I won't regard them as fundamentally different without a good reason to.

 

[bhobba]

Regarding the double slit which seems to be mentioned a fair bit for me its utterly boring - see the paper I posted.

Its a good illustration, for beginners, how to apply in practice, the Principe of Superposition and the uncertainty principle - the wave particle duality explanation is a crock. Feynman's path integral approach is good, but unfortunately some take it too literally - its not really going down both paths. The path integral approach is simply suggestive of that view. If you take it literally you end up with a hidden variable interpretation but of a very novel and unusual type - if it attracts you - that's OK - but I personally would rather face QM head on - I find that more instructive. What then is QM - formally its simply the most reasonable extension to probability theory to continuous changes in states, in the general sense of probability models. But maybe I am strange.

Thanks
Bill

 

[Ken G]

Regarding the double slit which seems to be mentioned a fair bit for me its utterly boring - see the paper I posted.

Yes, though entanglement gets interesting for just about anyone-- so that's just the extension of the superposition principle to multiple particle systems.

What then is QM - formally its simply the most reasonable extension to probability theory to continuous changes in states, in the general sense of probability models.

This is very insightful, I think. For those not following the crux of this remark, it encapsulates the concept of indeterminism when dealing with discrete states (which are all the states in any measurement system we could ever employ), because if there would be continuous changes in states, where the observables are discrete, then indeterminism in the observables is required. So then, one can regard the issue of superposition as a kind of tension between the need to have states change continuously, and the need for the observables of any obtainable experiment to be discrete.

The fact that this tension does not appear classically is often interpreted as saying that classical systems are "normal," whereas quantum systems are "weird." But what I was pointing out above, by quoting ancient philosophers using pure logic rather than classical instruments, is that it seems the only reason classical systems don't encounter this rather fundamental and logically required tension is that the extreme complexity of classical systems allows us to pretend that continuous outcomes of observations are actually possible, even though none of our instruments are actually capable of it. The simplicity of quantum systems often force us to abandon that pretense, and hence the tension appears.

Incidentally, if you'd like a quote attributed to ancient philosophers that points straight to the logical tension between continuously varying states and discretely accessible observables (which you can also interpret as a tension between how we can mathematically rationalize systems as continuous superpositions, yet how we can only measure systems in terms of definite discrete attributes we call "collapsed states"), consider Zeno's statement of his paradox of denseness:
"If there are many, they must be as many as they are and neither more nor less than that. But if they are as many as they are, they would be limited. If there are many, things that are are unlimited. For there are always others between the things that are, and again others between those, and so the things that are are unlimited."
Ponder those words from over 2000 years before quantum mechanics, and see if you don't hear in them the tension between the continuousness of the possible "superposition states," and the necessity of finiteness in what we can actually observe or know, the discrete "eigenstates" of a quantum system. Yet quantum mechanics is regarded as weird, even though Zeno was hinting at its logical requirements thousands of years before Newton's classical dynamics!

 

[bhobba]

This is very insightful, I think.

I have been saying it for a long time - but answering the above ie how insightful is it - the answer IMHO is yes and no.

From a mathematical modelling point of view it's very very insightful and easily explains the formalism of QM elegantly from very intuitive assumptions. Basically the why of the formalism is solved - and beautifully solved at that.

The no bit is - like all mathematical models - what does it mean. That is very hard and leads to all sorts of long debates with great subtlety on all sides.

My personal view, and its just my view, is the model is the physics - the rest is just endless debating - which is why I subscribe to the ignorance ensemble interpretation. But like with Bell it occasionally leads to profound and valuable insights - but unfortunately only occasionally. I do like understanding other interpretations though because they all shed light on the formalism.

So what is the central mystery of QM? Its simply we have so many different interpretations - pick something you do like - and you will find an interpretation that has it - but you can bet your bottom dollar it will have something others don't like. No other theory of physics is like that.

Thanks
Bill

 

[Lord Jestocost]

I don't have much of a background in quantum physics so be patient with my questions please. 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?
Also just an extra question how does all of quantum mechanics translate to every day life? Does my bed disappear when I am not looking at it?

Entanglement, what is it?

Quote from E. Schrödinger, "Discussion of probability relations between separate systems", Proceedings of the Cambridge Philosophical Society, 31, 1935.

“When two systems, of which we know the states by their respective representatives, enter into temporary physical interaction due to known forces between them, and when after a time of mutual influence the systems separate again, then they can no longer be described in the same way as before, viz. by endowing each of them with a representative of its own. I would not call that one but rather the characteristic trait of quantum mechanics, the one that enforces its entire departure from classical lines of thought. By the interaction the two representatives (or ψ-functions) have become entangled. To disentangle them we must gather further information by experiment, although we knew as much as anybody could possibly know about all that happened. Of either system, taken separately, all previous knowledge may be entirely lost, leaving us but one privilege: to restrict the experiments to one only of the two systems. After re-establishing one representative by observation, the other one can be inferred simultaneously. In what follows the whole of this procedure will be called the disentanglement. Its sinister importance is due to its being involved in every measuring process and therefore forming the basis of the quantum theory of measurement, threatening us thereby with at least a regressus in infinitum, since it will be noticed that the procedure itself involves measurement.

Another way of expressing the peculiar situation is: the best possible knowledge of a whole does not necessarily include the best possible knowledge of all its parts, even though they may be entirely separated and therefore virtually capable of being "best possibly known", i.e. of possessing, each of them, a representative of its own. The lack of knowledge is by no means due to the interaction being insufficiently known - at least not in the way that it could possibly be known more completely - it is due to the interaction itself.”

 

[anothergol]

To me, coming from programming, the "quantum" in QM is actually -more- intuitive. That is, things like a definite speed of causality, the Planck length/time, that's more logical to me.
In the musical/audio world, logarithmic scales are more often used than linear, and that seems to be the case in nature in general. But what's a log scale without a base? That's why I find it more intuitive that there would be a smallest length & time (with everything a multiple or exponent of that).

It's the superposition that I don't find intuitive at all. Which is why I don't understand why Everett's theory is one of the least liked, because to me, it's what makes the most "sense". Where the superposition wouldn't be just maths, the particle would really be everywhere, in an infinite branches of the universe, "close enough" so that there is an interaction between them, and once there is interaction with another particle, there is no "collapse" at all, because there doesn't need to be any. I mean, we asked the particle where it is, and we didn't get one result, we got all of the results. But our brains being made of particles, we can only feel being in one universe, even though we are in all of them, and we did observe the infinity of states the particle could have.
It makes the most sense with entanglement as well, here entanglement is elegant, entangled particles simply shared branchings of the universe, they wouldn't need any other link than that.
Is it this infinity of branching that's so much disliked?

But is it really just debating? Aren't some interpretations fragile enough that specific not possible yet experiments, or things not found yet, will discard them?

 

[Ken G]

Which is why I don't understand why Everett's theory is one of the least liked, because to me, it's what makes the most "sense".

A lot of people do like Everett's approach, which is essentially the bent of the "rationalist"-- someone who thinks the mathematics is the reality, and observations are only there to check which is the right mathematics. (As opposed to the empiricist, who thinks the observations are the reality, and the mathematics is just our best stab at making sense of it.) I'm not a fan of taking the mathematics as literally as a rationalist, because I regard it as a "maximal" interpretation (one that adds a great deal to what we can know and test), whereas I feel interpretations should be "minimal" (add as little as necessary).

In particular, it requires taking the theory quite literally, even though mathematical theories have a way of getting replaced later. We saw this with Newton's laws, which if you take literally seem to imply that the conditions in the past completely determine the conditions we will experience in the future. Then along comes quantum mechanics, which says that what we will actually experience in the future is very far from determined. So which was the mathematics we were supposed to take literally as how things actually work?

But our brains being made of particles, we can only feel being in one universe, even though we are in all of them, and we did observe the infinity of states the particle could have.

I think it's hard to argue that "we" are in all the universes, given how different the people could be from us in those other universes-- especially if the outcomes in question have a significant impact that could even kill us in some universes. Also, if you think that "you" in some sense are present in all the branches in which you survive, you can run into the "quantum suicide" perspective, which would doom all of us to horrendously extended and infirm old ages, and which has a logical basis that I regard as highly strained.

It makes the most sense with entanglement as well, here entanglement is elegant, entangled particles simply shared branchings of the universe, they wouldn't need any other link than that.

Yet treating entanglement as a type of information denies that some kind of physical link is maintained, we are only culling possibilities that are constrained in a way we are not used to. If one does not take the existence of particles too literally either (another example of minimal interpretation), then there is no particular difficulty, it's all about culling possibilities according to unfamiliar constraints as new information comes in.

Aren't some interpretations fragile enough that specific not possible yet experiments, or things not found yet, will discard them?

I think what will happen is eventually quantum mechanics will need to be replaced, and the new theory might ascribe more obviously to one of the current interpretations, even if it also introduces some new ones. If so, then it will be useful to be versed in all the interpretations, because we never know which one will be the most conducive to the development of the new theory. We saw this with classical mechanics, where the Hamiltonian formulation is more conducive to quantum mechanics and the Lagrangian formulation is more conducive to quantum field theory. Ironically, often overlooked is the fact that the interpretation of the existence of "forces" is not particularly conducive to either! Yet we prefer that interpretation so much that we still teach it in high schools, which goes to show you that perhaps we should not be interpreting our interpretations as "what is really happening" anyway!

 

[anothergol]

I think it's hard to argue that "we" are in all the universes

no, I meant "we are in every branching after our existence". I meant, after measuring the state of a particle, we are in every branch for every state of that particle, but obvisouly we can only see ourselves in one, even though in each branch we are there & concluded that we measured something different.
You say this is a maximal interpretation, but to me it looks like the opposite, the one that seems to add the least. The need for a collapse function, the fact that randomness is introduced, entanglement not being explained, yeah perhaps the Copenhagen version limits itself to what we can safely conclude from observations, but.. perhaps the observation of the ant seeing the shadow of things with an extra dimension, to get back to that analogy.

 

[Ken G]

You say this is a maximal interpretation, but to me it looks like the opposite, the one that seems to add the least.

You need to take the equations as the literal truth, rather than some kind of effective approximation. That's adding far more than is ever necessary for science.

 

[anothergol]

But the concept of collapse doesn't come from equations but experiments, if I'm right. And entanglement has to be explained as something else than what seriously conflicts with with established theories (FTL communication). I mean, stating things as they are observed is hardly "interpreting", so the Copenhagen interpretation is simply not interpreting entanglement (or is it?).

Interesting new video of PBS space time btw, on that subject of whether particles are everywhere or not, questionning if those virtual particles are purely mathematical or could be real .

Now I thought that it was already stated that particles pop in & out all the time in vacuum, but now I'm reading that we've ever only observed the results of those (like, Casimir effect), not the particles directly (I assume, because they have to pop in/out in times short enough that they cannot be observed?).

That's interesting because this doesn't really fit in Everett's theory.. unless those would be particles traversing parallel universes perpenticularly.. thus appearing in a vacuum because coming from some universe in which it wasn't a vacuum.

But how do "virtual particles out of nowhere" fit in the Copenhagen interpretation anyway? Say those virtual particles are mathematical helps to compute where a real particle can be, they are all related to one real particle. But then why do you find those in a vacuum?

 

[zonde]

And entanglement has to be explained as something else than what seriously conflicts with with established theories (FTL communication).

Where do you see serious conflict with with established theory? If entanglement is explained using FTL coordinated changes of quantum phase it does not lead to FTL communication. Absolute phase is unobservable but to observe relative phase you have to compare both ends. There is no way how you can use quantum phase to communicate FTL. And quantum phases are out of scope of relativity so it says nothing about them.

 

[anothergol]

Where do you see serious conflict with with established theory? If entanglement is explained using FTL coordinated changes of quantum phase it does not lead to FTL communication. Absolute phase is unobservable but to observe relative phase you have to compare both ends. There is no way how you can use quantum phase to communicate FTL. And quantum phases are out of scope of relativity so it says nothing about them.

No I'm not talking about "third party message communication" FTL, but about that "coordination" itself. Simply stating that the changes of phase are coordinated is stating the observation, it's not interpreting it. Such a coordination, if we accept that it exists (because it doesn't seem to have to in Everett's theory), requires FTL communication, or something else like a shared property in another dimention, but in any case it requires something. If entangled particles are -really- linked, and that link can't be made through space because it would imply it's FTL, then it's made from something/somewhere else. Well sure you can say "it's the way it is, just accept it" but that sounds a little religious to me.

 

[zonde]

No I'm not talking about "third party message communication" FTL, but about that "coordination" itself. Simply stating that the changes of phase are coordinated is stating the observation, it's not interpreting it. Such a coordination, if we accept that it exists (because it doesn't seem to have to in Everett's theory), requires FTL communication, or something else like a shared property in another dimention, but in any case it requires something. If entangled particles are -really- linked, and that link can't be made through space because it would imply it's FTL, then it's made from something/somewhere else.

Yes, this "coordination" requires FTL physical process. But where is this "serious conflict" with established theory (not interpretation or arbitrary extension of that theory)?

 

[anothergol]

Well define "process". Speed of light is supposed to be the speed of causality, and here you're describing a causality.. happening instantly.
Perhaps speed of causality is an interpretation, but it seems to be the way it is, what else violates it?
Seems simpler & safer to reword entanglement as not being a coordination, since it doesn't need to be. It has been established that it wasn't a local hidden variable, but that doesn't go against the idea of multiple universes.

 

[zonde]

Well define "process". Speed of light is supposed to be the speed of causality, and here you're describing a causality.. happening instantly.
Perhaps speed of causality is an interpretation, but it seems to be the way it is, what else violates it?

Yes, I agree that it is in conflict with our experience. But I do not agree that it is conflict with established theory.

Seems simpler & safer to reword entanglement as not being a coordination, since it doesn't need to be.

Go ahead, try to do that. This is the topic of this thread after all.

 

[Ken G]

Entanglement isn't any less mysterious is Everett's interpretation. Remember, the guts of entanglement is that two particles can share a property like "same polarization" even when the polarization of each particle is completely indeterminate. It doesn't matter if your interpretation includes collapse or not, the bizarreness of that fact is still there. Indeterminacy doesn't go away in many worlds-- you just have more versions of scientists who cannot predict what they will see. If you have many worlds, you escape the need for the particles to yield a single seemingly random result in just one world, but you still have to explain why in every world where one particle passed a polarizer at some arbitrary angle, the other one did too. Tack on as many worlds as you like, that still requires interpreting the outcome of the observations. (As for virtual particles, that's a whole other can of worms you don't want to get into, so let's stick to entanglement.)

 

[anothergol]

Entanglement isn't any less mysterious is Everett's interpretation. Remember, the guts of entanglement is that two particles can share a property like "same polarization" even when the polarization of each particle is completely indeterminate. It doesn't matter if your interpretation includes collapse or not, the bizarreness of that fact is still there. Indeterminacy doesn't go away in many worlds-- you just have more versions of scientists who cannot predict what they will see. If you have many worlds, you escape the need for the particles to yield a single seemingly random result in just one world, but you still have to explain why in every world where one particle passed a polarizer at some arbitrary angle, the other one did too. Tack on as many worlds as you like, that still requires interpreting the outcome of the observations. (As for virtual particles, that's a whole other can of worms you don't want to get into, so let's stick to entanglement.)

But isn't Everett's theory more deterministic?

but you still have to explain why in every world where one particle passed a polarizer at some arbitrary angle, the other one did too

ah, so that really implies that there is a link. A problem indeed

 

[zonde]

ah, so that really implies that there is a link. A problem indeed

Before attempting to solve the problem yourself you can try to look how others tried to do that. There are some references at the end of this article. In particular you can take a look at this reference (chapter 6.3).
It is attempting to make MWI local by introducing additional splits where future light cones meet. Well, because intersections of lightcones initially would be spacelike I would say you get ever increasing microsplits along this intersection and subsequent intersections. At the end you get very contrived mechanism that at single world level (if is conceivable at all in such a model) looks just like FTL coordination of outcomes.

 

[Ken G]

But isn't Everett's theory more deterministic?

Determinism isn't the issue with entanglement-- correlation is. All many worlds do is allow you to escape the question "which definite outcome occurs when you have an indeterminate state?", but the question with entanglement is "what maintains the tight correlation between polariation of two particles that can be widely separated even before the polarization angle is decided?" It's the nonlocality of the correlation that is the puzzle.

By the way, there are two very different flavors to "collapse" that often get confused. Let's take the case of two photons entangled to be in the same polarization state, but that state is indeterminate. You choose a random angle for your polarizer, and perceive both photons either going through, or not going through. The two different flavors of collapse happen in two steps-- first there is the "decoherence", which happens in any interpretation, it means that when you pass the photons through, the only realities that remain "coherent" are the ones where both photons pass through, and we perceive they both pass through, and where neither photon passes through, and we perceive neither photon passing through. What experiences destructive interference, so doesn't happen, is that the photons pass through, and we perceive them not passing through, and the inverse. The interpretations only kick in after that stage, when we wrestle with the issue of which of those allowed possibilities will happen, or will all of them happen. But the entanglement puzzle already appeared, which is how did the behaviors get bundled together in the first place.

ah, so that really implies that there is a link. A problem indeed

Exactly.

 

[bhobba]

Say those virtual particles are mathematical helps

That's exactly what they are. Specifically they are lines on a Feynman diagram which is just a pictorial representation of what's called a Dyson Series:
https://en.wikipedia.org/wiki/Dyson_series

They don't exist in the same sense as real particles.

Thanks
Bill