Einstein's famous 1905 paper on Relativity applied this principle to Translational Frames, showing it requires the Universal constant c (speed of light) to be the same in all such frames. Were it not, the frame in which c was highest would be the only frame at rest.
But the same principle must require there to be no Preferred Orientation. This leads to the requirement that Planck's constant h be the same in all frames. If the Stern-Gerlach experiment could give results between +h and -h, then the orientation producing the maximum value would be a preferred frame.
And because of that, when Alice and Bob measure entangled quantum particles, their combined results must violate Bell's inequality.
But to my mind, the biggest take-away is that Einstein's Principle of Relativity absolutely requires that conservation can only be on average.
All right, that's a ridiculously condensed summary. Enough to make your head spin :-)
The title paper is for general audiences, and references the original paper at https://www.nature.com/articles/s41598-020-72817-7.pdf
OK, I think I understand that.
> And because of that, when Alice and Bob measure entangled quantum particles, their combined results must violate Bell's inequality.
Could you be slightly less ridiculously condensed here? Give a one-or-two-paragraph, accessible-to-the-semi-layman explanation of why this means the result must violate Bell's Inequality?
> But to my mind, the biggest take-away is that Einstein's Principle of Relativity absolutely requires that conservation can only be on average.
And the same request here. Why does the principle of relativity require that?
> > But to my mind, the biggest take-away is that Einstein's Principle of Relativity absolutely requires that conservation can only be on average. > > And the same request here. Why does the principle of relativity require that?
The way I read this comment was that "the principle of relativity cannot conserve angular momentum on a per-trial basis".
In a Mermin Device a pair of entangled spin particles is set to two Stern-Gerlach experiments. The two particles has net (spin) angular momentum of 0 because that's was the net angular momentum of starting material. But if you measure the angular momentum of the two particles in two non-parallel directions, and if we also require that the only answers you are allowed to get are +hbar/2 or -hbar/2, then the sum of the angular momentum you get by adding +/-hbar/2 times one direction plus +/-hbar/2 times a different direction can never be 0.
If angular momentum cannot be preserved on a per-trial basis, then I suppose it must be preserved on average, because, I suppose if it isn't preserved on average, then I don't think you can say that angular momentum is preserved at all.
> And because of that, when Alice and Bob measure entangled quantum particles, their combined results must violate Bell's inequality.
> > And because of that, when Alice and Bob measure entangled quantum particles, their combined results must violate Bell's inequality. > > Could you be slightly less ridiculously condensed here? Give a one-or-two-paragraph, accessible-to-the-semi-layman explanation of why this means the result must violate Bell's Inequality?
The really short answer is that if we preserve the angular momentum on average then it entails that the correlations we observe from Mermin Device must match the correlations predicted by quantum mechanics, and therefore violate Bell's inequality for the same reason that predictions of quantum mechanics do.
In more detail, if we take the results of a measurement where Alice measures angular momentum in the vertical direction and Bob measures the angular momentum off vertical by theta degrees where Alice gets a result of +hbar/2, then in order for angular momentum to be preserved, Bob's measurement would have to be -cos(theta)hbar/2.
Of course Bob is only allowed to get hbar/2 or -hbar/2, so if we want angular momentum to be preserved on average then when we take an ensemble of trials, and filter out only those trials were Alice measures hbar/2, then the average of all of Bob's measurements for those trials should be -cos(theta)hbar/2. That requires that the probability Bob geting hbar/2 when Alice does is (1-cos(theta))/2 (= sin^2(theta/2)), which I believe is the value predicted by quantum mechanics. Once you have the predictions made by quantum mechanics, a violation of Bell's inequality follows by the usual arguments.
But I have absolutely no idea how to visualise entanglement. Any tips? Or do we just have to shut up and calculate?
Edwin James had some interesting commentary on things like this:
"From his reply to EPR, we find that Bohr's position was like this: 'You may decide of you own free will, which experiment to do. If you do experiment E1 you will get Result R1. If you do E2 you will get R2. Since it is fundamentally impossible to do both on the same system, and the present theory correctly predicts the results of either, how can you say that the theory is incomplete? What more can one ask of a theory?'
While it is easy to understand and agree with this on the epistemological level, the answer that I and many others would give is that we expect a physical theory to do more than merely predict experimental results in the manner of an empirical equation; we want to come down to Einstein's ontological level and understand what is happening when an atom emits light, when a spin enters a Stern-Gerlach magnet, etc. The Copenhagen theory, having no answer to any question of the form: 'What is really happening when - - -?', forbids us to ask such questions and tries to persuade us that it is philosophically naive to want to know what is happening. But I do want to know, and I do not think this is naive; and so for me QM is not a physical theory at all, only and empty mathematical shell in which a future theory may, perhaps, be built."
https://bayes.wustl.edu/etj/articles/cmystery.pdf
...and which he goes on to makes some interesting observations about the Bell Inequalities.
"Just as Bell revealed hidden assumptions in vonNeumann's argument,so we need to reveal the hidden assumptions in Bell's argument. There are at least two of them, both of which require the Jeffreys view point about probability to recognize..."
Looking at a single object with a fixed angle camera produces similar observations to an entagled pair when the pair is in a similar configuration and where each object in the pair is observed by their own camera except one of the cameras sees a negated result.
In the entanglement experiment described the particles have angular momentum every which way until the angular momentum of one is pinned down by measurement whereupon the other one is also pinned down to the opposite by conservation of momentum. There is still a sort of spooky action at a distance when that happens or perhaps a splitting of the multiverse 'at a distance' into many worlds where the spins point different ways.
Rotational invariance would rotate both the source and the detector, and there would be no surprise that the possible results and statistics over them are unchanged.
The quantum surprise is that rotating the source relative to the detector leaves the possible results unchanged (though the statistics do change).
What's the difference between this and quantum entanglement?
Personally, I'd prefer third party summaries of the thesis when it has been established as an interesting contribution, and the original article to stick to what is actually accepted by the mainstream; or at the very least to be more up-front that this is actually based on a new paper by the author.
That's not to say this paper is wrong - I'm not remotely qualified to judge (and it happens regularly in articles plugged on HN); I just find the way these things are presented as a bit iffy.
If me observing the particle in Australia alters the probability distribution of your particle in USA, can't I only observe the particle when I want to communicate 1 and never observe it when I want to communicate 0?
Edit: thanks a lot for the answers! I guess it boils down to the fact that the Australian guy cannot condition his decision on the (unknown) spin of his particle -- if he could (eg: had access to the local hidden information) then he would be able to update the USA's probability distribution instantaneously and use it to communicate
For both theories the physics surrounding them just happens to make their presence undetectable. In the case of the ether, the ether wind just happens to shrink the arms of the Michelson-Morley interferometer by exactly the amount needed to prevent the interference pattern from detecting the ether wind. In the case of hidden variable theories, the predicted joint probability distributions just happen to make the hidden variable values themselves uninferable.
First, if confused more than clarified things. And second, I suspect the principle does apply to all forms of entanglement.
Now if I could only prove that, I'd be on my way to Stockholm. :-)
There are enormous engineering challenges with quantum computing, but no fundamental challenges.
https://spectrum.ieee.org/computing/hardware/the-case-agains...
(I've also just submitted that link to HN separately fwiw)
There is a famous test, Bell's inequality [2], that specifically rules out local hidden variable interpretations of QM.
Nonlocal hidden variable interpretations, such as De Broglie - Bohm theory [3], are potentially still on the table, however.
It is somewhat ironic that Bell's theorem is sometimes presented in popular media as a general disproof of all hidden variable theories, in a context where locality is taken for granted -- because Bell himself seems to have been partial to nonlocal hidden variable theories. An article by the same Mermin mentioned in the OP is worth a read, on this subject [4].
[1] https://en.wikipedia.org/wiki/Hidden_variable_theory
[2] https://en.wikipedia.org/wiki/Bell%27s_theorem
[3] https://en.wikipedia.org/wiki/De_Broglie%E2%80%93Bohm_theory
"The Chaotic Ball: An Intuitive Analogy for EPR Experiments"
Say SOMEONE ELSE puts the marbles in two envelopes and sends them to you and your friend in Australia. (it's someone else because we don't actually create the entangled particles, we just "get" them)
The marbles being red and blue (or both red or both blue, depending on what you're measuring) from the beginning would be a LOCAL hidden variable. It's local because it's been predetermined at the moment of creation and the marbles carry the property on themselves and it's hidden because you don't know how/why the person putting the marbles in those envelopes decided those colors and you can't see them until you open the envelope (measure the particle).
This way if you don't open your envelope, your friend's envelope contains a marble that's 50/50 red or blue and the color will be the predetermined one no matter what you do with your marble at home. So whatever decides the marble's color has nothing to do with your marble, it's local to the friend's one.
The actual measurements work differently. It's been experimentally proven many times that at the moment you look at your marble, the other marble's 50/50 probability of being red and blue shifts substantially to, for example 75/25. And that's without it having any way of knowing that you've seen your marble. So there are hidden variables that we don't understand, but they're not local. They somehow affect both marbles.
In real life there aren't only two colors and the probabilities aren't those nice numbers, but you get the principle.
This is completely incorrect, to the point where what you were trying to correct was actually more accurate, though incomplete.
The usual setup is that for any given axis, each person always measures 50:50. Measuring your own doesn't change the odds of the other.
Knowing the _results_ of your own does. For the same axis, the correlation is exact. For axes with an angle theta between them, we get a correlation of R ~ cos(theta/2).
The upshot is that there is no underlying (classical) probability distribution that can give rise to this that can explain things for all measurement axes. This is sometimes glossed as "correlation without correlata".
The rest of your explanation was super easy to grok (thank you!) but this part I can't wrap my head around. If the balls can be red or blue, and it's 50/50 before, how would the probability go to 75/25? I would expect it to either stay at 50/50 (no change) or to 100% (because the other ball is known).
Can you elaborate on this part? This is really fascinating.
I always imagined the two "marbles" as possibly being two similar but differing clocks instead. The clocks will align more or less often depending on how similarly they're set and how fast each run. With this analogy you can come up with any distribution that fits your fancy.
Its probably a silly analogy but it lets me cling my notions of no spooky action.
Same if my friend is opening the envelops.
Now for all the opened envelops if I have got 10 red balls. Now if my friend open the paired envelops, he will probably get 7 blue and 3 red.
My observation of the balls had an effect on his side and shifted probabilities on his side.
If that's what you mean, what does observation or measuring even mean? How do the balls know the envelop has been opened.
In quantum entanglement they are both truly and really random until you measure one. And it's not random in a sense that you closed your eyes when putting them into envelope. They actually both don't have a "selected" color. They "snap into one of two colors" when you measure (look at) one. And the "unbelievable" thing is that when you measure one, the other one immediately snaps into opposite color, no matter how far it is.
If you look at the marble you got and it's red (or blue) the size becomes indeterminate. Focusing now on the size you will find it's large or small, but the color becomes indeterminate. It could be red the next time you look at it.
When you take your entangled marble, look at the color and see it's red you know the other marble is in the "blue" state (and the entanglement is broken). If someone looks at the color of that marble you know they will find it's blue. But if they look at the size before looking at the color it could be large or small (and looking now at the size of your marble will tell you nothing about it) and if they look at the color later it could be red or blue.
In the classical case, if there is a large red marble in one envelope and a small blue marble in the other it doesn't matter in what order you look at the color and the size. You will always know what the other person found.
In the quantum case, if both look at color first they will find complementary colors. If they both look at size first they will find complementary sizes. But the second measurement will be uncorrelated. And if they make the measurements in a different order, everything will be uncorrelated.
Most advocates of the hidden-variables idea believe that experiments have ruled out local hidden variables
Source: https://en.wikipedia.org/wiki/Bell%27s_theorem#Bell_inequali...
A shared RNG seed is essentially entanglement.
This delves more into complex hidden variables, that normal analyses ignore: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC137470/
In order to help you out, after you two have made your guess we are going to give you two a chance to back out and lose nothing. After your prediction we are going to reveal one coin to you and another coin to your partner. Together you and your partner will have an opportunity to back out, but the catch is that you two are not allowed to communicate!
Instead of communicating, you can raise either a red flag or a green flag after seeing your coin. Similarly, your partner can raise either their red flag or their green flag after seeing their coin. If you both raise the same colour flag, the game keeps going and we see if you win or lose. If you both raise different colour flags, the game stops and you lose nothing.
To ensure you don't cheat, we've separated you and your partner by 200 million kilometers and you have one minute to raise one of your flags after seeing your coin, otherwise you lose the game. (Alternatively you are your partner are separated by 400 meters and you have 100 nanoseconds to raise one of your flags.)
Good luck.
---
The above casino game cannot be beaten using envelopes of marbles, but it can be beaten (i.e. positive expected value) using envelopes of entangled particles. See quantum pseudo-telepathy.
https://en.wikipedia.org/wiki/Reinhold_Bertlmann#Bertlmann%E...
The other replies explain why it's wrong, but here's a link to Bell's refutation for good measure
Why is the difference in orientation of the detector necessarily linear? What is the control aspect of this experiment where classical-system shows this linear pattern? Or can the argument be made more fundamentally?
What separates a coherent "quantum" superposition, say, |0> + |1>, from a probabilistic "non-quantum" 50:50 mixture is that I can choose a measurement basis in which the coherent state always yields a definite result, say "1", whereas measuring the mixed state always yields a 50:50 mixture of "0"s and "1"s.
A continuous sweep of the angle of the measurement basis generally results in an interference pattern, the amplitude of which can be used to assess the fidelity of the quantum state.
(I get paid to work on quantum communication and related experiments.)
https://www.youtube.com/watch?v=j6Mw3_tOcNI&ab_channel=Sabin...
What makes people say information travels faster than light with quantum entanglement?
Maybe this will help https://html.duckduckgo.com/html?q=bell%27s%20inequality%20s... I imagine the youtube links might be more comprehensible.
The crux with quantum mechanics is that you can show (very easily, understandable by the layman, look up the Bell inequality) that in the quantum case the ball only takes on a color the moment you look at it, and so instantaneously is setting the color in the USA as well.
However, the basic setup still applies. You cannot send information by merely observing something.
We don't actually know that this is an accurate description of what is happening, although it is consistent with what is happening.
Very likely, the underlying physical process still operates below the speed of light. "Instantaneous" isn't something that makes physical sense in this context.
https://www.youtube.com/watch?v=dEaecUuEqfc
It is based on this (unpublished) paper:
http://www.flownet.com/ron/QM.pdf
The key insight is that measurement and entanglement are actually the same physical phenomenon. A measurement is nothing more than a very large network of mutual entanglements.
Because physicists can not tell the difference between a particle whose "wave function collapsed" and one that didn't.
The faster than light communication would be equivalent to modulating the collapsedness of a stream of particles by measuring-or-not their entangled counterparts. Since the is no discernable difference between particles pre and post collapse, no information can be transmitted.
The simplest one is that you need to be able to tell the partner when you've made your changes and that you're ready for them to measure
Well that's easy enough to understand, even though I have absolutely no idea if it's true or not.
Basically, either quantum computing works or we'll learn a lot more about quantum mechanics we didn't already know.
https://arstechnica.com/science/2017/07/a-brief-history-of-q...
More seriously, I interpreted "darker corners of the internet" in the parent to be a bit tongue in cheek, but to generally be indicating fora where there's a higher ratio of layman to expert, and crackpot to serious practitioner. There was no claim that it isn't discussed outside of that setting, just that it occurs more frequently there (as a proportion of QM discussions in general). This squares with my (poorly informed) general impression.
Imagine we both open our boxes at around the same time, and communicate each other results at the speed of light.
- From my point of view, I opened the box first, got red and caused you to get blue. Your message confirms my hypothesis.
- From your point of view, you opened the box first, got blue and caused me to get red. My message confirms your hypothesis.
We can repeat this experiment thousands of times, every time, we both get a 50/50 chance of red vs blue, and every time, the hypothesis is confirmed.
In order to know who really was first, the only way is to wait for the other person result. For example: when you open the box, start a timer, stop it when you receive my message. It the time is less than the times it takes for light to travel between us, I was first. But in order to have this information, you have to wait, so it is not faster-than-light anymore.
The only way I can foresee this being used to transmit data faster than light is that if you both agree to perform an action depending on what color ball they see. If you both view the ball at some agreed point in the distant future, you will instantly know what action the other person will do.
it is very easy to measure something entangled at the same time (or at least within a margin that is faster than light travel) and confirm you always get the correct results. If the wave function didn't collapse together, you would get results that break quantum laws, such as measuring two entangled particles with both up-spin.
The two top explanations are either some info can travel faster than light (from our perspective), or the universe forks into copies when needed.
> Knowing the color of one marble is enough to know the color of the other marble
I guess so.
> without information travelling between the marbles?
The marble colours are in sync on measurement. Somehow that info has travelled instantaneously. You just can't use it to send information, at all..
above is just my understanding. I have no background in this. Just a programmer.
If you told me causally this detector which measures electrons/photons/whatever and varies by the cosine of the orientation, I don't think any (non-physics person) would bat an eye; it seems like a pretty normal thing a sensor might do.
I think one of the appeals to actual physicists who do experiments is that is how things are usually set up - there's some equipment that makes a measurement and the Schrödinger equation stuff till collapse thing gives the correct result for what is observed. Obviously the universe got on ok for billions of years before physicists evolved so it's a simplification of reality.
But that is not the same, right? I mean, if it interacted with a force and no observation was made, the wave function doesn’t collapse, does it? Honest question (to avoid any defensiveness, I should disclose that I don’t subscribe to panpsychism).
> or anything along those lines
Any suggestions?
Simple interaction between two systems doesn't cause "collapse" it makes the two systems become entangled. Classical systems are a bit contagious in this sense, anything that gets entangled with them becomes classical.
To be a bit more precise, this distinction between classical and quantum is a bit our fault. Everything is quantum at a fundamental level, classical system is one for which we do have not have a precise knowledge of the state of the system, instead we have a coarse representation. This should make more obvious in which way "classicalness" is contagious. Since the knowledge of a part was coarse, the knowledge of the newly entangled system is also necessarily coarse.
Consider the classic two-slit interference experiment. Whether the electron goes through the left or right slit can be treated a single qubit. Use a controlled-NOT gate to copy that qubit onto a second storage location, without observing either. Optionally drop the second qubit into a black hole to head off any claims about supposed future observations. Allow the electron to continue. Do you still observe interference pattens as in the non-copying version of the experiment? Why or why not?
Any two systems interacting will cause the collapse. It doesn't matter if the system is attached to a scientist or not.
> Any suggestions?
No, I'm a software developer, not a quantum physicist. :)
https://www.amazon.com/Probability-Theory-Science-T-Jaynes/d...
And there is a website with more information and a collection of his papers:
https://arxiv.org/abs/1005.2357
http://dl.icdst.org/pdfs/files1/77964f05542451c01e8e420e975d...
Classical entanglement, which is not good enough to explain quantum entanglement.
In QM, experiments show us that entangled particle spin probabilities vary non-linearly with the angle between detectors (even if those detectors are far apart).
This means that either: 1) locality is broken.. state is somehow transmitted faster than the speed of light between particles. 2) realism is broken.. god plays dice with the universe
But there's also a 3rd, which is: the choice of detector angle is not an independent variable (a necessary assumption for Bell's inequalities to hold).. instead the state of the universe is pre-determined and the experimenter's choice of detector angle is known beforehand so there is no need for spooky action at a distance. This isn't a very popular explanation since it provides no reason as to why we don't see this weird lack of independence elsewhere.
I don't think so. You can have a wave function in physical 3-D space as a (very common) special case and you still have the wave-particle dichotomy.
Why do you think configuration space explains WPD?
The really odd part to me is that at macro scales the probability waves collapse neatly into classic physics in 3D space, but still react in quantum fashion at small local atomic scales. As in the configuration spaces generally can only be determined for small subsystems but not a whole macro system without the “conversion” step.
I suppose that means if a photon, say, is reflected by a mirror, that should collapse its wave function and any measurements after that should not have any effect on it?
Maybe it should be qualified what kind of interaction collapses wave function?
> I'm a software developer, not a quantum physicist.
Great, I’m not a quantum physicist either—yet here we are, talking about quantum physics!
I'm not sure if that example is the right one to use, but yes, that's roughly my understanding.
I suppose if we can calculate exactly how a given force would influence a photon, that would be essentially the same as “measuring” it.
The thing about the change of "colour" in this analogy is you don't know in which direction it changes. So let's say you observe you "marble" through a "purple filter", which gives has:
- a 50% chance of being transparent to your marble (corresponding to a red-blue superposition marble collapsing to a purple marble)
- a 50% chance of being opaque to your marble (corresponding to red-blue superposition marble collapsing to a green marble).
The issue is that when you learn your marble is purple, while you know with 100% certainty the marble in australia is green, there is no way you can send information to Australia using that. This is because the other 50% of the time, your marble will be green, and the marble in Australia is purple.
So if I'm sitting in Australia, when I measure the marbles in my envelopes with purple filters, all I see is purple marbles 50% of the time and green marbles 50% of the time no matter what measurements you are performing at your end. So you can't send me messages by performing measurements at your end because you can't change the statistics of those measurements.
But you'll know the answer to every measurement I performed, if you've measured the other marble with a purple filter too.
The problem comes in when the angle between your two measurements is anything else. The chance that the measurements match is based on the cosine of that angle. There's no way for this to happen if the measurements are independent.
If you try to write two equations, where the first equation takes the secret particle state and first angle and gives you 1 or 0, and the second equation takes the secret particle state and second angle and gives you 1 or 0, you won't be able to reproduce the odds you get in the real world. Only equations that know both angles will work.
Using the word copy in conjunction with C-NOT is slightly misleading as the copies do not behave independently.
Tongue-in-cheek explanation: Maybe whoever wrote our simulation used shallow copy when they should have done a deep copy.
That's what the word "copy" means. If you flip a coin and copy that bit, you will observe that those copies do not behave independently either. If you want independent bits, flip two coins.
Similarly, "erasing" a (qu)bit technically consists of performing a exchange operation between it and a known-zero bit. In typical electronic computers, this would generally involve diffusion-like exchanges between the voltage level in a memory capacitor (such as a FET gate) and that on the GND rail, which has a much greater effective number of bits and therefore will stay mostly zero, but eventually requires a thermodynamic expenditure of known-valued bits (aka negentropy) from some external source to maintain its voltage level / bit zeroness. (This is rather simplified; there's lots of other sources of known-zero and known-one bits getting depleted and replenished, and the exact accounting depends on how you interpret various physical states information-theoretically.)
That should have had a "for example" in front.
Now, that is obviously not true for macroscopic objects like balls. Those are not in a superposition of colors until they are observed, but it is true for quantum objects like electrons.
But then what is it that can I do with two entangled electrons that I can't do with two literal billiard balls known to be different colors than one another?
You can also prepare two photons in the same state, so the have the same polarization for some direction chosen at that time. But the measurements along other axis won't be perfectly correlated (if they are correlated at all).
The red/blue color example is too simple to be interesting.
The way to think about it is a box with 3 buttons. There is no such thing as 'observation', the only way you can interact is to push one of the 3 buttons and as a result the box will output either a red or green light.
You must push a button to get the light, but the button may mutate the internal state of the box. Using this model, there's nothing special about human or conscious observation. Every interaction via a particle or otherwise is simply pushing a button.
The crazy thing is.. no matter how clever an algorithm you write to drive the lights from the buttons, you cannot match the observed probabilities. (100% if the same button is pushed, 25% if different buttons are pushed).
But there is something kind-of-special about the box with the buttons and the lights.
Not every interaction is simply pushing a button that lights one lamp or another. Keeping the analogy, the result of an interaction between two particles may be a combination of the "red on", "green on" states. You need to keep adding particles to have a box with buttons and lamps that works as expected.
My intuition is you have two particles, and you don’t know what concrete states they are in, but you know all possible states (that may be represented as some sort of system of equations).
By observing a single particle you unlock a variable in that system of equations and can therefore solve the whole thing. To me it would be more straightforward to say the concrete state of the particle is simply unknown until it is observed. The concept of superposition seems like an overly complex description for this phenomenon.
I understand my view is wrong, but I don’t understand how I’m wrong
https://www.wired.com/2014/01/bells-theorem/
In other words, modeling particle pairs as having matching static hidden "meta data" in them doesn't work. They do act as if there is instantaneous communication between the particles, but in a limited way that prevents us from using them for instant communication. Quantum mechanics is a weird tease, having magical properties that always serve up loopholes when we try to leverage the magic for real-world benefits. The quantum universe seems built by insurance lawyers who are masters at screwing consumers with fine-print when they go to make a claim.
The state of the entangled particle over there, a light year away (for example) is also decided. Instantly. Faster than the speed of light. Nothing travelled from here to there. No particle, no photon, nothing. How does over there "know" that I did something over here?
Sure feels kind of spooky.
To me it would be more straightforward to say the concrete state of the particle is simply unknown until it is observed.
It's not just unknown. It's undecided. It has no concrete state. It's not that it IS a one or a zero and you just don't know it. It's not yet been decided whether it's a one or a zero, but as soon as the decision is made for one of the entangled particles, the decision is also made for the other one, a light year away. Instantly. Spooky.
John Bell demonstrated that in order for a hidden variable theory to make predictions in agreement with quantum mechanics, it must have nonlocal interactions, which means any workable hidden variable theory must also be pretty spooky.
Consider an electron fired at a dual slit with a phosphor screen. While traveling from the electron gun, thru the slits, to the screen, the electron is described by a Wave Function. It has no fixed position or momentum. The Schrodinger wave passes through both slits and interferes with itself on the other side. The wave function evolves into a series of lines.
But when the electron interacts with the screen it always appears as a single point. It must do so by the laws of conservation. At the interaction it must have a specific location and momentum in order for there to be conservation of charge, momentum, energy, etc.
This interaction is enough to 'collapse the wave function'. No 'observation' is required.
How does this happen? There is no localized mechanism that can possibly make this work. The conservation laws are not local restrictions. They are universal.
Please note that this is my own explanation of now QM works, and does not necessarily reflect the official position of any school of thought. It does, however, reflect the actual use of Quantum Mechanics, in that systems evolve via the Schrodinger Equation and interactions must obey conservation laws. And No, it cannot explain how entanglement works.
That would make some sense if by interaction you mean "interaction with the macroscopic environment". When small-enough quantum systems (like two particles) interact there is no collapse and the evolution is unitary.
> This interaction is enough to 'collapse the wave function'. No 'observation' is required.
How do you distinguish the interactions that 'collapse the wave function' from those who do not?
Aside: (Personally, I see this more as Bohr's way of dodging questions he had no answer to, and not a viable way to think about Quantum Mechanics. A better answer would have been "I don't know. Let's figure it out." But that was impossible for political reasons. Bohr was being attacked by Einstein for 's sake. He can be forgiven for adopting Ali's "rope-a-dope" tactics if he felt that Einstein was trying to destroy his entire field in its infancy. But I find "there is no quantum world" simply unacceptable.)
Now to answer your question as best I can, an interaction must collapse the wave function when it is required to fulfill a conservation rule. For example, if an electron is captured by a nucleus it becomes bound and emits a photon. This is an interaction that must conserve momentum, angular momentum, energy, and charge. Because of that, the electron can no longer be represented by a non-localized wave function. The universe must concentrate those properties down to a point in order to "do the accounting" necessary for the conservation rules.
No, I don't know how it does that. But then, NONE of the available interpretations answer that question. This indicates to me we are thinking about it wrong.
What I like about Stuckey's paper is that it adds another factor: besides conservation rules the universe seems to require that "measurements" obey the Relativity Principle (No Preferred Frame of Reference). I have yet to figure out how to incorporate that.
It's a mystery how the particle "knows" (In other words, nobody knows when the wave function collapses) but one popular interpretation is that the particle exists in all states, i.e. in a pure description of reality. When any quantum system interacts with it, then it becomes entangled with the result of that measurement, branching it into a new universe (edit for clarification: a new world where it was as if it was never a wave, and it was always a particle). That's my understanding of the many-worlds theory.
That entanglement propagates across nearby particles, so it doesn't have anything to do with eyes or consciousness. If the air molecules around your body interact with the particle then that entanglement propagates through your body and places you in the new world.
You can't observe something without sending information. In order to make an observation, you must interact with whatever is being observed, so that information about the interaction can come back to you.
In the bag example above, we can observe the Australian ball and know the color of the American ball, and we cannot use this interaction in Australia to send information to America. But we cannot avoid sending information to the Australian ball when we observe it.
>> You cannot send information by merely observing something.
This is, at the least, very poorly phrased. As explained above, not only can you send information by observing something, it's impossible not to do so. The question here is where the information goes.
https://phys.org/news/2020-10-quantum-mechanics-reality-pers...
It's as if God's code looks something like:
if (event.thisParticle.isBeingObserved()) {
thisParticle.assignAttributes();
}This is a case of a simple theory that indeed models the mystery well. However, it seems "wasteful" in that it would branch into gazillion trees of reality. In Occam's Razor, does "simplicity" include quantity of "stuff" needed? Because sometimes the brute force algorithm/model is the "simplest" if we ignore quantity of stuff and time, such as bubble-sort. Bubble-sort is one of the simplest sorting algorithms known, but is inefficient from a time and resource standpoint.
If there are "free" dimensions to spare out there, then the "wasteful" multi-verse model may not really be wasteful. We humans are used to thinking in terms of economic trade-offs, and a model that uses up large quantities of space/time rubs our instincts wrong.
If true, the theory means that in some universe somewhere I'm a billionaire who married a supermodel.
However, I agree with you that it seems implausible because it implies absurd situations like, there is a world in which someone lives a life of celebrity because every time they roll some dice it always lands on 6, and every time they flip a coin it lands on heads, etc.
In a way, it could be interpreted as very efficient. Only the branches where some "measurement" is done are "calculated". I suppose the others are garbage collected at the end of time, or something like that.
And maybe it's not a tree, but a graph of universes. In the same way that a universe split in two, two universe could also fuse into one when they share the previous state. Somehow it feels like this have to be connected to reversible vs. non-reversible computation.
Ah.. it's a good feeling being a fearless dilettante.
The two-slit experiment contradicts this. You get different results depending on when you perform the observation(s).
So the new world is a world where the particle was originally a wave, and became a particle when it was observed. Not a world where the particle was always a particle.
But that's adding complexity back into it. You are increasing complexity of the theory/model by adding a complex cleaner/trimmer in order to reduce the quantity of resources consumed.
And your answer is simply wrong. An excited atom can emit a photon, for example, and the system will still be described by a “non-localized wave function”. It won’t even be well defined if the spontaneous emission has happened or not yet.
The evolution of a quantum system according to Schrödinger’s equation doesn’t violate conservation rules. And, in case it’s not clear, the quantum system described by the wave function in the example above is the atom-photon(-or-not) pair.
You’re definitely thinking about it wrong.
I remember reading an article here a while back that involved a macroscopic re-creation of the double slit experiment results, but where mere observation remained possible, because light did not sufficiently influence the substrate. In that experiment the particles were droplets traveling on top of a set of waves, working in the pilot wave fashion.
Any attempt to use anything of similar scale to the particles to observe which slit the drop went through would break the interference pattern, but mere light did not, allowing one to visually see how a pilot wave style interpretation could work, if it were not for that whole (photons travel at the speed of light, so these would need to be faster than light propagating pilot waves) thing.
Indeed it looks like flubert linked a video from an earlier study of the same basic mechanics, prior to the more recent one that included the double slit experiment replication.
http://math.mit.edu/~bush/wordpress/wp-content/uploads/2017/...
Math is a modeling technique, not a "thing". To me it doesn't make sense to say the universe "is" math. Maybe it's a machine "running" math notation (programming code), but that's not the same as it "being" math.
(Is "God" the server admin?)
not proven of course.
Why can you see the solution of the equation for the entire surface of the pond at once, but only for a single instant of time at any given moment?
Conversely, the Schrodinger equation gives an amplitude to the same particle/wave at many locations at time T. However, when you look for it at time T at all of those locations at once, you only find it in one of them. If you perform the experiment many times, you will find it at all of those locations some amount of the time. But then, if you try to use the Schrodinger equation to model movement before AND after interaction with the detector, you will not be able to find the particle at any position that doesn't match what the detector initially saw.
That is, say the Schrodinger equation predicts the particle has the same amplitude at locations X and Y. Then, after interacting with something at locations X and Y at time T1, it will have some amplitude at locations X1, X2, Y1, Y2 at time T2.
Now, if we try an experiment where the interaction at time T1 happens with a particle, and you have detectors at positions X1, X2, Y1, Y2, you will find it with equal probabilities at any of the 4 locations. However, if at X and Y there is a detector, and you detect the particle at X, it will never be found at positions Y1 or Y2. You have to update the Schrodinger equation after you find out that the particle is found at X, which is never how classical mechanics work.
I mean, I get that time is a little different in that you will eventually experience and remember all possible solutions as you stand there watching the system, because classical time is a linear chain of events. In the multi-world case, it's a branching chain, and your experience and memories of the different solutions are stuck in their own branches.
That does make worlds weird and different from the other dimensions, but we accepted time as being weird and different from space for a very long time.
> Now, if we try an experiment where the interaction at time T1 happens with a particle, and you have detectors at positions X1, X2, Y1, Y2, you will find it with equal probabilities at any of the 4 locations. However, if at X and Y there is a detector, and you detect the particle at X, it will never be found at positions Y1 or Y2. You have to update the Schrodinger equation after you find out that the particle is found at X, which is never how classical mechanics work.
This makes total sense if it's actually a wave and the particle is merely a solution for a particular world W. The detector didn't change anything about the wave. It just coupled you to the wave system earlier, so now your branch of the many-world tree can only see the subset of solutions that correspond with whatever you detected. The only thing that has changed, though, is your ability to see the other solutions. You branched earlier, so now each branch you exist in only sees a subset of the full solution.
That said, I am not a physicist. The many worlds explanation was just the first thing that actually made sense to me about quantum mechanics. It's so conceptually simple.
Now, the question is: what causes this discontinuity in the equations of motion? Why is interaction with a detector different than interaction with another particle? Many Worlds simply reframes this problem, but doesn't get rid of it. In MWI, you would say 'the particle moves in all universes according to the wave function, until it interacts with a detector, possibly interfering with versions of itself in other universes. Then, when it encounters the detector, the world line of the detector splits - in some universes it passes the detector, in others it doesn't. However, it no longer interacts with other versions of itself,so we must update the wave function inside the universe where it passed the detector'.
> Many Worlds simply reframes this problem, but doesn't get rid of it.
Maybe I'm misunderstanding. It's like asking "why is there a difference between me jumping in a swimming pool and someone else jumping in it? I don't get wet when someone else is swimming." The difference is... one of you is in the pool. It's not going to spontaneously make the other person wet.
In MWI the difference is that if it interacts with a particle, you're not entangled, the particle is. If it interacts with a detector then you're entangled. So, there is no difference except for what gets entangled.
What that means is the wave function can only appear to collapse when you entangle. If some particle entangles, it will collapse for that particle and branch into a new world, but you're not in that world; for you it's still a waveform.
Edited for clarity.
If the alternative universes are in different dimensional planes, it's pretty obvious why we couldn't observe them.
This explanation only works if either the detector is not itself made of particles, or if there is a detector wave that you could become entangled with by observing.
But the first one can essentially be discarded, and the second one is not experimentally confirmed. The equations happen the way I described whether you observe the detector or not. The detector could be hundreds of light years away from you, but you would still be able to predict what happened after the particle hit it with classical mechanics. So one particle's interaction with a detector instantly branches at least its entire future light-cone, but two particles interacting doesn't have the same effect. So at what scale does this happen? Or in what conditions?
I don't think that is the whole story. If you want to predict the motion of a particle correctly, you still need to update the Schrodinger equation after interaction with the detector, but not after interaction with another particle. And this is independent of whether you personally look at the detector or not, even if the detection occurs outside your light-cone. This is evident from the fact that MWI still needs both the Schrodinger equation and the Born rule to accurately predict experimental results.
> What that means is the wave function can only appear to collapse when you entangle. If some particle entangles, it will collapse for that particle and branch into a new world, but you're not in that world; for you it's still a waveform.
But this is not true for macroscopic objects. The motion of a detector, and indeed even the motion of a particle after it interacts with a detector, does not behave like a wave, regardless of whether I have ever interacted it. Even if the interactions are space-like separated from myself, I can still predict them with classical mechanics, and confirm when the data finally reaches me. For example, I can predict the location of a particle in a double slit experiment if I know that there is a detector at one of the slits, regardless of where in the universe that experiment happens. How can I be entangled to a detector that exists outside my past light-cone? But then, I can't predict the outcome of a double slit experiment without a detector near the slits, regardless of how close I am to the experiment.
This still shows to me that there is an observer-independent collapse happening when a particle interacts with a detector, where we don't have a physical description of what a detector actually is.