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**Current Law Students / Re: Legal Reasoning**

« **on:**May 30, 2008, 02:13:46 PM »

Bell's Inequality in Detail

To explain away this quirky paradox, some scientists said that there were "hidden variables" that exist in the photons that allow them to behave this way. Hidden variables are variables that we have yet to discover. They would be aspects of each of the photons that are the same, since they were entangled, but that did not depend on the other photon.

Bell proved mathematically that this was impossible with this inequality:

Number(A, not B) + Number(B, not C) >= Number(A, not C)

David M. Harrison, a physicist at the University of Toronto, explains it this way:

What does this have to do with quantum mechanics? Here goes: you can shoot photons at a detector that detects the arrival time of the photon, and the photon's energy. If energy and arrival time were absolute values, that is, if the energy and arrival time of the photon exists whether it is measured or not, then the values would have to satisfy Bell's inequality, regardless of hidden variables.

The Punch Line: Does Quantum Mechanics Violate the Inequality?

In experiment after experiment Bell's Inequality is not violated, but instantaneous communication, or "spooky at a distance", seems to occur. If you rule out instantaneous communication, Bell's Inequality is violated. The most interesting experiment was carried out by a physicist at the University of Geneva, Switzerland, Nicolas Gisin in 1997. He split a single photon into two "smaller" photons (which meant they were entangled) and sent them down fiber optic cable in opposite directions. When the photons where about 10 kilometers apart they ran into a detector. Gisin found that even though a large distance separate the photons, something done to one photon at one end very much affected the photon at the other end...instantaneously.

What does this mean?

Let's take a look at assumptions. Here we invent two assumptions:

We can conclude from these two assumptions that all birds fly. If we find a bird that has wings but doesn't fly, we know that at least one of our assumptions was wrong. In this case, it's obviously the last assumption (all the birds I know have wings).

It's interesting to know that Bell's Theorem has assumptions, too. They are:

The last assumption is called locality. Locality says that everything that is bound by relativity, everything that can't go faster than light, is local. If something is non-local it is thought to be part of a larger reality.

So which assumption is wrong in Bell's Theorem? Nobody knows.

Logic could be wrong. In 1930, Kurt Gödel proved that any theory proposed for the foundation of mathematics will be either insufficient for mathematics, incomplete, or inconsistent. This was a wild and crazy thing for a logician to do, as it essentially proved that logic was incomplete. There may be no reality separate from its observation. This is where physics melds with philosophy and religion. Could it be that the universe only exists because we are conscious of it? Perhaps we only exist because someone or something is conscious of us? The EPR paradox isn't the only paradox that raises this possibility. Erwin Schrödinger proposed a way to link the classical world that humanity knows to the quantum world of electrons and protons. He proposed that in a closed box one could put a live cat, a vial of poison gas, a geiger counter that smashes the vial if it detects radiation, and a radioactive atom. In an hour, the atom's likelihood of having decayed is 50%. In quantum mechanics, before you measure whether of not the atom decayed, it actually exists in a superstate of both decayed and not decayed. It's not that you just don't know, it's that it actually exists in both states at the same time. Thus, after an hour's time, before you peer into the box to see if the kitty is alive or dead, it must exist in a superstate of both dead and alive. If a tree falls in the forest and no one is around, did it actually exist at all? Information might be able to travel faster than light. Consider a one-dimensional creature, we shall call him a 1d, that exists on a line. Everything the 1d creature knows is in terms of length and nothing else. Then along comes a two dimensional creature, call him 2d. The 1d can measure the length of the 2d, but isn't aware of anything else. In fact, it's possible for the 1d to measure two lengths for a single 2d, making the 1d think that the 2d exists in two places at once, and in his universe he does! The same could be true for our universe.

The popular press likes to claim that quantum physics allows for faster than light communication of information. So far, physicists have not come to this conclusion. Dr. Ken Caviness, chair of the Physics Department at Southern Adventist University in Tennessee, says this:

To explain away this quirky paradox, some scientists said that there were "hidden variables" that exist in the photons that allow them to behave this way. Hidden variables are variables that we have yet to discover. They would be aspects of each of the photons that are the same, since they were entangled, but that did not depend on the other photon.

Bell proved mathematically that this was impossible with this inequality:

Number(A, not B) + Number(B, not C) >= Number(A, not C)

David M. Harrison, a physicist at the University of Toronto, explains it this way:

Quote

In class I often make the students the collection of objects and choose the parameters to be:

A: male

B: height over 5'8"

C: blue eyes

Then the inequality becomes that the number of men students who do not have a height over 5'8" plus the number of students, male and female, with height over 5'8" but who do not have blue eyes is greater than or equal to the number of men students who do not have blue eyes. I absolutely guarantee that for any collection of people this will turn out to be true.

What does this have to do with quantum mechanics? Here goes: you can shoot photons at a detector that detects the arrival time of the photon, and the photon's energy. If energy and arrival time were absolute values, that is, if the energy and arrival time of the photon exists whether it is measured or not, then the values would have to satisfy Bell's inequality, regardless of hidden variables.

The Punch Line: Does Quantum Mechanics Violate the Inequality?

In experiment after experiment Bell's Inequality is not violated, but instantaneous communication, or "spooky at a distance", seems to occur. If you rule out instantaneous communication, Bell's Inequality is violated. The most interesting experiment was carried out by a physicist at the University of Geneva, Switzerland, Nicolas Gisin in 1997. He split a single photon into two "smaller" photons (which meant they were entangled) and sent them down fiber optic cable in opposite directions. When the photons where about 10 kilometers apart they ran into a detector. Gisin found that even though a large distance separate the photons, something done to one photon at one end very much affected the photon at the other end...instantaneously.

What does this mean?

Let's take a look at assumptions. Here we invent two assumptions:

Quote

All birds have wings.

Everything that has wings flies.

We can conclude from these two assumptions that all birds fly. If we find a bird that has wings but doesn't fly, we know that at least one of our assumptions was wrong. In this case, it's obviously the last assumption (all the birds I know have wings).

It's interesting to know that Bell's Theorem has assumptions, too. They are:

Quote

Logic is valid.

There is a reality separate from its observation.

No information can travel faster than light.

The last assumption is called locality. Locality says that everything that is bound by relativity, everything that can't go faster than light, is local. If something is non-local it is thought to be part of a larger reality.

So which assumption is wrong in Bell's Theorem? Nobody knows.

Logic could be wrong. In 1930, Kurt Gödel proved that any theory proposed for the foundation of mathematics will be either insufficient for mathematics, incomplete, or inconsistent. This was a wild and crazy thing for a logician to do, as it essentially proved that logic was incomplete. There may be no reality separate from its observation. This is where physics melds with philosophy and religion. Could it be that the universe only exists because we are conscious of it? Perhaps we only exist because someone or something is conscious of us? The EPR paradox isn't the only paradox that raises this possibility. Erwin Schrödinger proposed a way to link the classical world that humanity knows to the quantum world of electrons and protons. He proposed that in a closed box one could put a live cat, a vial of poison gas, a geiger counter that smashes the vial if it detects radiation, and a radioactive atom. In an hour, the atom's likelihood of having decayed is 50%. In quantum mechanics, before you measure whether of not the atom decayed, it actually exists in a superstate of both decayed and not decayed. It's not that you just don't know, it's that it actually exists in both states at the same time. Thus, after an hour's time, before you peer into the box to see if the kitty is alive or dead, it must exist in a superstate of both dead and alive. If a tree falls in the forest and no one is around, did it actually exist at all? Information might be able to travel faster than light. Consider a one-dimensional creature, we shall call him a 1d, that exists on a line. Everything the 1d creature knows is in terms of length and nothing else. Then along comes a two dimensional creature, call him 2d. The 1d can measure the length of the 2d, but isn't aware of anything else. In fact, it's possible for the 1d to measure two lengths for a single 2d, making the 1d think that the 2d exists in two places at once, and in his universe he does! The same could be true for our universe.

The popular press likes to claim that quantum physics allows for faster than light communication of information. So far, physicists have not come to this conclusion. Dr. Ken Caviness, chair of the Physics Department at Southern Adventist University in Tennessee, says this:

Quote

I don't know of anyone in the field who seriously proposes instantaneous communication. On the contrary it seems that despite quantum entanglement information cannot be extracted from the system without some (at most) light-speed exchange of information.