Entanglement is like splitting a coin in half, so you have a tails and a head half. Then you put one in your left pocket and give the other to a friend.
Then, just by looking in your left pocket, you can learn that your friend has the heads half—instantly!
In other words, it’s not as spooky as it is made out to be.
First, I assume I’m missing some critical detail and am wrong somewhere.
Both the ERP, and the explanation of the CHSH with the difference being cos^2(theta) an isn’t that just Malus’s law? So in the case of the ERP experiment, if you fired single polarized particles at a polarizing filter at one angle or the other you still get cos^s(theta) as the difference without requiring entanglement, no?
That implies, in the case of entangled particles there is more than one dimension of “whatever” that causes the polarizing filter to “choose” whether to extinguish the particle on non-equal angles - like azimuth/elevation instead of just theta? It just seems to me that rather than disproving a “hidden variable”, it requires one?
Like I said, I assume I’m missing something and am wrong.
Yes, it is just Malus's law. The key is what angle is relevant.
Suppose you did CHSH but instead of pairs of entangled photons with was pairs of non-entangled photons that were polarized in the same direction. They players do the same thing as with entangled photons: use the bit from the referee to pick their measurement angle. A measures at 0 or 45 degrees, where 0 is the axis the photons were polarized on. B measures at -22.5 or 22.5.
Let's say the 0 degrees the players are using is the direction of the original polarization axes.
When the referee gives a 0 to A then A is measuring on the same axis the photon was polarized on, so will get a 1. When the referee gives a 1 to A then A measures at 45 and Malus gives a 50/50 chance of 1.
Player B is always measuring 22.5 from 0, so Malus says B gets a 1 85% of the time.
In the last two rows the players win 50% of the time (due to A's 50/50). In the first two rows they win when they get the same bit, which happens 85% of the time. Since all 4 referee results are equally likely, the result is the players win 67.5% of the time.
If the player's setup isn't aligned with the initial axis the result will differ. For example let's say their set up is 10 degrees off from the setup described above. Then their angles are 10 and 55 for A and -12.5 and 32.5 for B. If I did the numbers right they will win around 62% of the time.
Without entanglement when each player measures a photon the θ for Malus's law is the angle between the axis they measure and the axis the photon was originally polarized with.
With entanglement the θ is the angle between the two axis that the players used.
You might find this interesting [1]. It's a report from a couple of probably 3rd or 4th year undergraduate physics students who did a CHSH experiment with entangled polarized photons for one of their physics lab classes. They measured the correlations with entangled pairs and with non-entangled pairs.
What if there are hidden properties that affect each particle of a pair after they are split, in predetermined ways? that would certainly create correlations that seem to be created on the fly, but they would simply be the result of the inner workings of particles that don't communicate.
For example, if we have two balls, each containing a spin mechanism inside them which makes them spin in relation, let's say, to the magnetic north, and we throw one of them to the other...and later we discover that their spin is somehow correlated.
That is not action at a distance, that is the result of the inner mechanism of each ball.
To recap, you want to design a pair of devices that each have 3 buttons labeled A, B, and C, a red LED, a green LED, and a counter. The counter starts at 1000. When you press any one of the buttons one of the LEDs flashes and the counter decrements. When the counter reaches 0 the device stops responding.
You should also specify a way that if the devices are brought together the pair of them can be reset.
You can specify any kind of non-quantum hardware you want in the devices. As much computing as you need, as much RAM and ROM and disk as you want, and physical sensors. Include clocks if you need to. You can include true random number generators. It doesn't have to be limited to current technology--it just has to be limited to known physics and not use quantum entanglement.
What are need to achieve with that hardware and whatever algorithms you specify is:
1. Suppose someone has used one of the devices, and recorded the results of a very large number of interactions.
Suppose that a statistician is given a list of 5-tuples (P, F, n, R, t) of those interactions with one of the devices, where P is which button was pressed, F is which LED flashed, n is the value on the counter when the button was pressed, and R is how many times the device has been reset (i.e., R = 0 the first 1000 times the device is used, then when it and the other device are reset R = 1 for the next 1000 uses and so on), and finally t is the time at which the button was pressed.
It should not be possible using any known statistical test on that list of 5-tuples for the statistician to distinguish the device from a device whose algorithm is simply:
if any_button_pressed():
r = uniform_true_random_from_0_to_1()
if r < 0.5:
flash(GREEN)
else:
flash(RED)
2. If the lists of 5-tuples from both devices matched up by n and R we should find that (1) if the same button was pressed on both, the same color LED flashed on both, (2) if B was pressed on one and A or C on the other, then 85.355% of the time the same color flashed on both, and (3) if A was pressed on one and C on the other than 50% of the time the same color flashed.
A couple things to note.
1. The above has to hold even if the users take the devices very far apart from each other before they start pressing buttons.
In particular the users might choose to take the devices so far apart before they start pressing buttons that each has finished their run of 1000 before any possible communications from their device could reach the other.
2. The users might wait a long time before starting a run of 1000, and they might wait a long time between presses within a run.
3. The users are determining when to press independently so you can't count on them alternating. You can't even count on them overlapping: one might do all 1000 presses before user the other starts.
4. The users might use a true random number generator to determine which buttons to press.
The splitting a coin analogy doesn't capture anything about entanglement though. It is just capturing a property of all distinguishable persistent objects: if you have two distinguishable persistent objects and you know one is at location A and one is at location B, then if you find out which one is at A you know what the one at B must be.
To be a reasonable analogy it has to capture something this is different between entangled and not entangled particles. That's the thing that is sometimes described as "spooky" and completely missing from the split coin analogy.
But correlations like that happen all the time. You put the tape that was supposed to "Back Door Sluts 9" into the VCR and see that it is "Lord of the Rings" then you immediately know that when you gave your kids "Lord of the Rings" to take to a friends house you got the tapes swapped and the kids are now walking around with the hottest porno ever made. You know this because the two tapes are correlated because you rented them together and have no other rental tapes. No information had to be transferred for you to know the kids have BDS9.
Or your daughter Lisa calls from school and tells you there is meat in her lunch. You immediately know that you must have mixed up the bag lunches that morning and Bart had the vegan meal. You make the lunches together, one vegan and one not, so they are correlated without information transfer.
What makes entangled particles different from other pairs of correlated things is that they correlate in ways the seem impossible without communication.
It's like if someone answered the question of why frogs sometimes rain from the sky by saying that because frogs cannot fly and are heavier than air, just like hail or rain or snowflakes, they feel a downward force from gravity which pulls them to the ground.
It's right...but no one has trouble understanding the gravitational aspect of frogs falling from the sky. The thing people want to understand is how a bunch of freaking frogs got into the sky in the first place.
Classical analogies only go so far. What's spooky about entanglement is that it works even if you change the measurement basis (as long as the two parts are using the same basis), which you cannot do with a coin.
In this case the coin is neither heads nor tails until you check it and then it becomes one or the other and it's counterpart becomes the opposite, no matter how far apart they are. So yeah it's kind of spooky.
My understanding is that entanglement has nothing to do with the particles and everything to do with what is known about the particles in advance by dint of the experimental setup.
For example, that two electrons are created in a closed system with a net spin of zero, so as long as you do not allow their waveforms to collapse (EG, so long as the system remains closed) then no matter where they go they must maintain that net spin of zero when perceived in relation to one another.
But if this is the case then the "entanglement" precedes the creation of the particles: it is nothing more than an accounting that they are required to obey in concert by the symmetries of physics.
It’s more like looking in your pocket and finding that sometimes it’s actually become a head due to beta decay, and spookily your friend now instantly has tails.
It's more like splitting the timeline in half: in one branch it's heads, in the other it's tails, and you don't know which timeline you're in until you look at the coin. The Bell's inequality says the coin has no state until it's been observed.
Then, just by looking in your left pocket, you can learn that your friend has the heads half—instantly!
In other words, it’s not as spooky as it is made out to be.