Spooky Action At A Distance - Why The Universe May Not Be Real
Spooky Action At A Distance
Since it is Halloween today, I thought it would be appropriate to do a post on something spooky. In 1935 the Einstein-Podolsky-Rosen paradox was created. This paradox suggested that particles could influence each other across space instantaneously and Einstein called this spooky action at a distance.
Local Realism
2 basic assumption in science is that the universe is real and obeys the principle of locality. Quantum mechanics has shown however that both these are not possible. Either the universe is not real, or it does not obey the principle of locality.Realism
A particle has an objective pre-existing value for any possible measurement. This means before the measurement is made, there is a definite real value for the observable.This is the idea that nature exists independently of the human mind. Even if the result of an experiment does not exist before the act of measuring it, it does not mean that the result is the creation of the human mind. The result was there the whole time, we simply hadn't observed it.
Locality
An object is only directly influenced by its immediate surroundings.For an action at one point to have an influence at another point, something in the space between those points (such as a field) must mediate the action. To exert an influence, something, such as a wave or particle, must travel through the space between the two points, carrying the influence.
Which One Is Right?
An object on one side of the universe influencing another on the other side of the universe instantaneously seems absurd. Special relativity puts the maximum speed of any signal at the speed of light and so this must be impossible.
But the idea that the universe we see is only there because we look is also absurd? Is the sun not there when I am not looking at it? Are all the people I know not there while I am not looking at them? Is the universe even real?
Now we know what locality and realism are, we are ready to delve into quantum entanglement.
Spin
All fundamental particles have a property called spin. This does not mean they are literally spinning but it does mean that they have an angular momentum and an orientation.You can measure the orientation and this will result in one of two results. The particle will be aligned with the direction of measurement (spin up) or it will not be aligned (spin down).
If the particle's spin is vertical but we measure its spin horizontally, it has a 50% chance of being spin up and a 50% chance of being spin down. After it has been measured, the particle will maintain its spin and so measuring spin actually changes the spin of a particle.
If you take a particle with vertical spin and measure its spin at 60° to the vertical, it will be spin up 3/4 of the time and spin down 1/4 of the time. The probability of measuring spin up is given by cos2(x/2) (where x is the angle from the vertical).
EPR Paradox
Einstein proposed a thought experiment. If you take two particles formed spontaneously out of energy, the particles will have opposite spins because the total angular momentum in the universe must be constant (particles who's properties must be correlated are called entangled particles).
So if you measure one to be spin up, you know that the other particle (if measured in the same direction) will be spin down.
So if you take one particle to one side of the universe and measure its spin, then one second later someone on the other side of the universe measures the spin of the other particle, it's as if your measuring of spin affected the other experiment. You seemed to violate the principle of locality.
Well the obvious answer may be the particles already had a spin and we just did not know it. We simply observed the spins of the particles and noticed they were opposite. This is wrong however.
Take two particles with vertical and opposite spins and then measure them in the horizontal direction at the same time.
If they have pre-determined properties then the probability of being spin up is 50%. So there is a 50% chance of them both being spin up and this would violate the law of conservation of angular momentum.
According to quantum mechanics:
the particles do not have a defined spin (violating realism) but yet they will always be opposite if measured in the same direction
or they can send signals between each other faster than light (violating locality)
Einstein did not like this and so thought that the particles contained hidden info on which spin they would have if measured in any direction. The information was in the particles when they formed and so no signal ever had to travel between them. In the case of the example above, the particles would have a plan that if a detector was put perpendicular to their spin, then particle A would be spin up and particle B would be spin down.
This sort of hidden information seems impossible to test for however in 1964, John Bell managed to think of an experiment to test if the particles do have hidden info.
Violating Local Realism
There are two spin detectors that can measure spin in 3 directions separated by 120° as shown in the diagram below. |
| These are the 3 directions that spin can be measured in |
The direction the detectors measure spin in will be picked randomly.
Entangled particles will be sent to the detectors and we will measure if the spins measured are the same or different. We will then check the probability that particles have different spins. This probability will depend on whether the particles have hidden information.
So what if the particles do have hidden information?
The particles have a plan that they agree to and the only requirement for the plan is that if spin is measured in the same direction, they will give opposite spins.Mathematically there are two possible plans.
Particle A measures spin up in all directions meaning particle B measures spin down in all directions
Particle A measures spin up in 2 directions and down in 1 meaning particle B measures spin down in 2 directions and up in the other.
Any other plan will give a result identical to one of the plans above.
Using Plan 1
They will always measure different spins no matter what direction we measure the particles in.Using Plan 2
If you measure both the 1st direction then they will have be different.If you measure A in 1st direction (the plan means this gives spin up) and the other in 2nd direction (the plan means this also gives spin up) the result will be spin up for both.
You can continue this analysis and see what possible combinations of spin the particles can have
If we measure A in the 1st direction and then measure B in the different directions the possible combinations are.
Up Down
Up Up
Up Down
(Remember the plan at B is to be spin down for 2 directions and spin up for one).
Measuring in the 2nd direction at A gives spin down and then we measure in the different directions at B.
Down Down
Down Up
Down Down
Measuring in the 3rd direction gives spin up and then we measure in the different direction at B.
Up Down
Up Up
Up Down
These are all the possible results we can get and we can see that the spins are different 5/9 times.
So we can conclude that if the particles contain local hidden variables, we will see different results at least 5/9 times.
But in reality we see different results 50% of the time meaning there is no hidden information... How does quantum mechanics explain this?
If you measure particle A in direction 1 and get spin up, then measuring particle B in direction 1 wil give you spin down.
What about directions 2 and 3?
There is 120° between detectors. A vertically spinning particle therefore makes a 60° angle with directions 2 and 3.
Therefore there is a 3/4 chance of being spin up.
Directions 2 and 3 are selected 2/3 of the time therefore
Detector B gives spin up 2/3 x 3/4 of the time
Which is 1/2
Quantum mechanics aligns with reality.
What Does This Mean?
There is debate over how to interpret the results. Some believe that there is still hidden info but particles can signal faster than light to update the info to ensure angular momentum conserved (the universe is real but violates locality).
Some believe that there is no hidden information in particles and that you should only talk about spin after they've been measured (the universe is local but not real). This is the Copenhagen interpretation of quantum mechanics and poses some deep philosophical questions. It suggests that the things we see only have definite states because we are there observing them. If we were to disappear then would those things even be there? Would the universe even be there?
So Information Can Travel Faster Than Light?
What we do know is that we can't use entangled particles to communicate faster than light. This is because the results at either detector are random. They are opposite but random. There is always a 50% chance of measuring spin up and down.
Only after the experiment when the results are compared would you notice that the data showed opposite spins when measuring in same direction.
Spooky!
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