Im just taking the easy course of QM by Suesskind. He had an example like you have two coins and give them randomy to your kids. The they move far away. Then one kid discovers what it got, it knows what the other has.
So what I dont get is why QM you could argue that there is some hidden shared state. Guess this is a typical question. But anyway I‘m somehow not convinced that it is really random.
That example cannot describe the 'spooky action at a distance'. Because it involves 'local variables' which have been dis-proven by the bell-inequality in actual experiments.
Taking the standard example of an entangled pair of photons. Those must have opposite spin. We then move the photons rather far apart measure the spin on one side. Then because of entanglement and conservation, the spin someone will measure on the other side is guaranteed to be the opposite.
A 'local variable theory' explains this by saying that the moment the entangled pair of photons is created it is already determined what the two spins are. This variable (the pre-determined spin) then travels with both photons (hence being 'local' to the photon). And the one measurement does not affect the other measurement.
The bell inequality shows this to be false. Crucial to the bell inequality is that, when measuring spin, You don't get back the 'angle'. Instead you choose a reference plane, and measurement will tell you whether the spin is pointing above or below that plane.
Now in the bell experiment. You measure in two different planes at the two different ends. If you pick two planes at a 180 degree angle. You will always find the same result on both sides (perfect correlation). If you pick two planes at a 0 degree angle, you will always get the opposite results (perfect anti-correlation). If you pick the planes at a 90 degree angle, the results will be totally independent, and this completely uncorrelated.
On these 3 angles (0, 90 and 180), quantum mechanics and a 'local variable theory' agree on the correlation coefficient between the measurements. (-1, 0 and 1 respectively). Bells inequality concerns the other angles. In those cases quantum mechanics predicts a stronger correlation (either more positive or more negative) than the local variable interpretation can predict. This discrepancy is strongest around angles of 45 degrees. Where a local variable theory means the correlation cannot be above 0.5, but quantum mechanics allows a correlation of up to ±1/√2 = ±0.7071.
These correlations were measured experimentally, and something close to the QM maximum of 0.7071 was measured. Hence disproving there are local variables.
I did, and they make perfect sense if you look at them through the lens of MWI, which however seems weirdly unpopular in QM circles. I was taught the Copenhagen interpretation, which is just... madness.
Which interpretation seems to make the most sense depends a lot on the framing of the explanation, and not very much on the experiments themselves. This comment [1] really drove home the Copenhagen interpretation for me, I quote:
>It's painfully easy to have a clear intuitive picture of quantum physics. You just have to ditch one concept.
Then I don't think I understood your question. I agree the Copenhagen interpretation doesn't make sense, mostly because I listen to Sean Carroll's podcast.
Others have provided good examples, but I'll put it in a way that might make more sense, albeit with a slightly less correct simplification.
>So what I dont get is why QM you could argue that there is some hidden shared state.
Because when you measure one of the coins in a particular way, there's an established probability that you'll change it some percentage of the time. (I.e. if you measure in this way 100 pre-prepared heads, you'll get some percentage of tails. [think of this as say measuring polarization of some photons after they've passed through a filter oriented to 0 degrees, by then placing a filter oriented at 45 degrees and seeing how many go through)
However, even after you do that measurement, you'll find that the other entangled photons are still correlated with the result of the ones you measured. So there's something "extra" going on, which is QM entanglement. I.e. that shared state.
You can actually see the effect of the "changing states" (not really what's going on, but if you were assuming the behavior was classical, it's what you'd start with. If you place two polarized filters at 90 degrees to each other and shine a light through it, you'll get basically zero photons out. Then, without changing anything else, you can put a third filter in-between the two but oriented 45 degrees from the others, and all of a sudden, about 25% of the light will pass all the way through the three filters! It's pretty cool. You could explain THAT part classically by saying that you are "changing the state of some of the photons by measuring them". But then... if you do that, you can't explain the correlation that happens when you do that with entangled photons, and classical explanations just don't really cut it unless you give up something like non-locality.
Suppose you were asked to build a device that works as follows.
1. It consists of a base unit and to hand-held units that can dock in the base unit.
2. Each hand-held unit has a counter, a button labeled "A", a red light, and a green light. The counter initially reads 0. The base has a button labeled "Reset".
3. If you put both hand-held units in the docks in the base and press "Reset", the counters in the hand-held units are set to 1000.
4. If you press the "A" button on a hand-held unit nothing visible happens if the counter is 0. If the counter is greater than 0, exactly one of the lights flashes briefly, and the counter goes down by 1.
5. If someone records the results of a large number of presses of the "A" button on one of the hand-held devices, every statistical test they can device will be consistent with the probability of getting the red light being 0.5. As far as they can tell it is completely random what color they get. This is true both within a run of 1000 presses after a reset, and across resets.
6. If two people compare their result from a run of 1000 "A" presses of two hand-held units that were last reset together, their results are identical. I.e., if person 1 got red on one of the units when the counter was 1000, blue for 999, red for 998, 997, and blue for 996, then so did person 2 on the other unit.
It would be pretty easy to build such a device. The hand-held units could simply have 1000 bits of storage. When the base unit resets them it merely has to generate 1000 random bits using a true random number generator and store that random bit sequence in both units. The units use that sequence to choose the light color when the "A" button is pressed.
Now suppose we want a more elaborate device. Same basic setup with the base and the two hand-held units, but now the units have three buttons, "A", "B", and "C". Still two lights, red and green. Pressing any button gives you a short light flash and decrements the counter.
Like with the single button device, if you play with one of the hand-held units alone every test you can think of is consistent with the light color being entirely random, with red and green equally likely.
If you record the results of your 1000 presses, and compare results with someone else doing the same with a unit that was reset when yours was, we want to see these results:
1. When you just look at your results, every statistical test you can device is consistent with it being completely random what color you get with the two colors being equally likely.
2. When you two pressed the same button with the same counter value, you find that you got the same color on your two units 100% of the time.
3. When one of you pressed "A" and one "C" with the same counter values, you find that you got the same color on your two units 50% of the time. It seems to be completely random whether or not you got the same color or different colors.
4. When one of you pressed B" and one of you pressed "A" or "C" with the same counter value, you get the same color 85% of the time. It seems to be completely random whether or not you got the same or different colors, but instead of being 50/50 like in #3, it is 85/15 for same color.
You might think this device could be built with just minor changes to the earlier "A" only device. Just expand the storage from 1000 bits to 3000 bits so it can have a table for each button saying what color to flash if that button is pressed for any particular counter value. That base can download values that give the desired distribution.
But when you try to actually figure out those tables you will run into a problem. You will find that you cannot devise values that will actually give the right distribution unless you know ahead of time which sequence the users are going to choose for their button pushes. If the users are free to decide which button to press for each of the 1000 rounds and they don't have to decide until after the tables have been initialized, there will always be sequences they can press that those tables won't give the right distribution for.
You will find that the only way, if you limit yourself to pre-quantum physics, to make the units actually work is to include some kind of communications channel between the units so that whichever unit gets a button pressed first for a given counter value can tell the other what it choose and the other can then adjust its response to make sure the right distribution happens.
That could work, but then you would have a limitation that your units only work according to spec if they are close enough together when the buttons are pressed for them to get a message from the first one pressed to the second one before it is pressed.
If two people took a pair of units, reset them together, separated them by say a light-hour, and then started pressing their buttons at the same time the devices would not be able to give the right correlations.
You can make the devices work, but instead of making your table use regular bits, you need to use a table of qubits. Use 1000 qubits in each device, with the qubit in each hand-held unit for counter value N entangled with the corresponding cubit in the other device. A button press measures the value of the qubit, with each button corresponding to a measurement in a different basis. With the right choice of basis for each button, you get the correlations given in the spec, and it works no matter how far apart the units are.
As far as I know nobody has built the specific devices described above, but there have been experiments done with entangled qubits or entangled particles that show that they do work that way yielding those correlations when measured in different bases, and that this works even if they are very far apart, so you could definitely build the devices described above.
You can think of scenarios in which any classical state (i.e. the shared state is completely specified by the local states of the two kids) does the task with some success probability that is upper bounded, say by 75%. And you can even include some unspecified hidden variable in your classical state and could even allow the two kids to share some classical randomness (think: each of them has a button that returns the same random number for both kids). This hidden variable could be anything (a single unknown property, a whole collection of unknown properties or whatever really) and represents possibly incomplete knowledge, for example due to imperfect microscopes or equipment. Since you don't specify what this hidden variable is, it encapsulates anything that is allowed by classical physics (remember we started out with a classical state).
Now lets allow entangled states between the kids (states that can only be specified if you have both subsystems, locally if you measured such a state your result will look at least a bit random or even completely random). Then you can prove that the two kids can do the task (that has classical success probability 75%) with success probability ~85% all of a sudden.
You can write down general inequalities that describe such behaviour and that's what Bell inequalities are. The fact that entangled states in quantum mechanics violate the classical bound (which you cannot break if you demand your two kids can only share states allowed by classical physics, even if you allow unspecified hidden variables), proves that nature is not classical. It doesn't prove that nature is quantum, it just proves that nature is not classical. Bell inequalities have also been unambiguously experimentally verified [1].
In conclusion, nature allows for two-party (or multi-party) states that cannot be described by just describing the local parts of it. There is no information in the local parts, but if you look at both parts together then there is information. Think "the whole is more than the sum of its parts". Classically, the whole is the sum of its parts. Classically, you read a book page by page. If your pages are entangled with each other, you could only read your book by looking at all pages together, because if you looked a single pages separately anything written there would look like random garbage to you.
The question that remains is: Where is the information then, physically? In some sense you could say it does not exist before measurement, because only when you look at the correlations between the local measurement results of the two kids will you find out that the underlying state must have been entangled (which you get to know if the state violates a Bell inequality). But that is just one possible interpretation, there still is a lot of scientific debate about what quantum mechanics really means.
These are exactly the scenarios that make quantum so weird but fascinating at the same time.
But as I understand if you break the non locality assumption for the state, then you could make it kind of work. So lets just say by introducing a global variable for the shared state you could explain it (hidden dimension or whatever). Ok maybe it breaks a classical assumptions. I have no doubt that QM works, just wondering if it is really the final resolution we can get.
Non-local hidden variable theories can work. The Wikipedia page on interpretations of quantum mechanics has a comparison table sortable by different properties[1]. de Broglie-Bohm and Time-symmetric theories are non-local with hidden variables.
So what I dont get is why QM you could argue that there is some hidden shared state. Guess this is a typical question. But anyway I‘m somehow not convinced that it is really random.