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Quantum Physics - Bell's inequality experiment
This experiment was performed to test the validity of entanglement or more appropriately ‘non locality’ in quantum systems, by using a bell inequality.
Now first I will explain what entanglement is as this is the mind boggling but interesting bit
Some of the brightest physics minds of history didn’t like this theory, including Einstein; he referred to it as ‘spooky action at distance’. He believed that future mathematicians and physicists would find it to be an error in their calculations…how wrong he was. Einstein’s major hang-up with this theory was its apparent incompatibility with a section of relativity, the fact that information cannot be transferred faster than the speed of light.
Entanglement is the process, when pairs of particles are created together by a process such as radioactive decay or through induced collisions. Now these pairs are called entangled because they have linked but opposite equalities; for example the spin of an entangled pair will be 1 will have a spin-up and the other spin-down.
Now if we think in terms of the Copenhagen interpretation (see this hub for info on Copenhagen interpretation) it is the “measurement” which creates this state, the spin of the electron.
The analysis of entangled particles by means of Bell's theorem, can lead to an impression of non-locality (that is, that there exists a connection between the members of such a pair that defies both classical and relativistic concepts of space and time).
Great Books on Entanglement
Watch the viseo on the right than let me use an example to try to explain what this means:
Quantum mechanics states that states such as spin are indeterminate until the spin of the object in question is measured (see this hub for more on wavefunction). In the non entangled state of two spins it is equally likely that any given particle will be observed to be spin-up as that it will be spin-down. Measuring any number of particles will result in an unpredictable series of measures that will average out to about 50/50. However, if this experiment is done with entangled particles the results are quite different. When two particles of an entangled pair are measured, one will ALWAYS be spin-up and the other will ALWAYS be spin-down. The distance between the two particles is irrelevant.
What this means is that even though these particles are in superposition, have both spin-up and spin-down. When you measure one of the particles it collapses the wavefunction of both particles instantaneously no matter what the distance and the other particle is seen to be in the opposite state to the one observed.
What about Einstein’s theory of relativity it says that information cannot be carried faster than the speed of light, however it is widely believed that no ‘useful’ information could be transmitted this way, thus preventing causality from being violated.
So now we know what Bells Inequality experiments were trying to prove we can take a look at the actual experiment.
The experiment visually
- Further Reading on Bells Inequality Therom
A detailed paper on Bells Inequality Experiment. A very interesting read, with a good amount of mathermatical proof, not for the faint hearted.
The first series of tests, used photon pairs produced in atomic radiative cascades, it was performed in the early 1970s. Most results agreed with quantum mechanics, but the method was far from ideal; in particular, the use of single-channel polarizer’s only gave access to the + outcome see image. Progress in laser physics and modern optics led to the next series of experiments carried in the early 1980s. They were based on a highly efficient source of pairs of entangled photons, produced by non-linear laser excitations of an atomic radiative cascade. An experiment involving two-channel polarizer’s, as in the ideal EPR experiment, gave an incontrovertible violation of Bell’s inequalities by an impressive agreement with quantum mechanics.
A next series of tests, begun in the late 1980s, they used nonlinear splitting of ultraviolet photons to produce pairs of entangled EPR photons. With such pairs, measurements can bear either on discrete variables such as polarization or spin components, as considered by Bell, or on continuous variables such as amplitudes and wavelengths.
A useful feature of this photon source is the production of two narrow beams of entangled photons that can be fed into separate optical fibers, allowing for tests with great distances between the source and the detector, this was done in Geneva over 10km! The experimenters used this method to address a important point raised by Bell.
Bell's Experimental set-up
Great books available
In the experiment shown in the image on the right, where the polarizer’s orientations are kept fixed during a run, it is possible to bring together the quantum mechanical predictions and Einstein’s conceptions by invoking a possible interchange of information between the polarizer’s. To avoid this loophole, Bell stressed the importance of experiments “in which the settings are changed during the flight of the particles”.
So that any direct signal exchange between polarizer’s would be impossible, provided that the choice of orientations is made randomly in a time shorter than the flight time of the particle or photon, to ensure that relativistic separation is enforced.
The results of these experiments even though they are still not yet perfect, are within 30 standard deviations of the results predicted by quantum mechanics, thus indicating even when a ‘perfect’ bell equality experiment is performed Bell’s inequalities will still be violated! Now this proof of the entanglement concept has lead to a new branch of physics called quantum information theory, which specifically focuses on quantum cryptography and secure transfer of information. I will be doing another hub on this so stay tuned. If you fond this interesting some fantastic books can be found on this subject.