How to explain in simple terms why Entanglement is more than just complicated hidden variables I haven't taken a graduate level physics course on quantum mechanics so I get lost in the strange looking equasions.
It's hard for me too see in any of the explanations of how quantum computers and entanglement work without thinking that it looks like a big parlor trick.  It's like a magician taking a black and white marble shuffling them in a cup then taking one in each hand without anyone seeing which is in which hand and then revealing a white marble in his left hand and declaring: 

  
*
  
*I can predict with absolute certainty that the marble in my right hand is black.
  
*Until I had actually observed the white marble in my left hand, neither marble actually had a definite color.  They were just a
  superposition of two possibilities.
  

A magic trick isn't very convincing unless the audience can understand it and not explain in simpler terms.  Are there experimental results that the average person can understand and not explain using classical intuition?
 A: Sorry to answer my own question...
I would like to thank the many answers and explanations from Luboš Motl as well as the Harvard lecture by S. R. Coleman, Quantum Mechanics in Your Face for helping me understand the experimental results the refute the above idea.  It took me a while to grasp the meaning of the GHZM experiment and the 'see' the contradiction between classical logic and experimental results but I believe I have it now.
Here is an explanation of the experiment that requires no math to understand.
Three lab assistants are each given a black box that every minute, on the minute lights up either one of two lights.  The one light is labeled 1 the other labeled 0.  The black box also has a switch on it that the lab assistant can toggle between two states, one labeled A, the other B.  Their instructions are this: toss a coin, if heads, toggle the switch, if tails leave it alone.  Record the 12:00 reading (true/false) and the state of the switch (A,B), toss the coin, toggle the A,B switch if heads and wait for the next minute and record the result.  Repeat 100,000,000 times.
After the Experiment, each lab assistant returns with a log that looks like this:
Time      State         Result
12:00     A             1
12:01     A             0
12:02     B             0
...

Now we observe the following correlation in the results.
When we just look at the times when the first and second assistant had the switch in the B position and the third assistant had the switch in the A position we only see the results in the following table:
State         Result    SUM
BBA           1 0 0     1
BBA           0 1 0     1
BBA           0 0 1     1
BBA           1 1 1     3
...

These were the only four results ever observed in the BBA state.  The sum of the results is always odd.
Upon further investigation, we notice that the order of the state doesn't matter.  State ABB and BAB also always have an odd result sum.
We deduce then that we can predict what a lab assistant would measure for A if we just had the other two lab assistants measure the value for B.  If the two B values agree, then A would be 1, if they disagree, then the A value must be 0.  We would be insane to believe, after running the experiment millions of times and getting the same result to expect to ever get a different result in the future.
Can we deduce what we would see if we look though the logs for where all three assistants chose to measure A at the same time?
Let's set up a truth table for all possible measurement of the three B values and derive a truth table for A with the following definitions:
A1 is 1 if and only if B2 == B3
A2 is 1 if and only if B1 == B3
A3 is 1 if and only if B1 == B2

B             A          SUM of A's
1  2  3       1  2  3   
0  0  0       1  1  1    3
0  0  1       0  0  1    1
0  1  0       0  1  0    1
0  1  1       1  0  0    1
1  0  0       1  0  0    1
1  0  1       0  1  0    1
1  1  0       0  0  1    1
1  1  1       1  1  1    3

So we see that logically, the only possible states for AAA is where the sum of the A results are odd.
However, looking through the logs, we see exactly the opposite!  The sum of the A results are always even!  This essentially means that lab assistant 3 changes what lab assistant 1 or 2 measures by doing nothing more than measuring.  There wasn't enough time for the black boxes to communicate with each other to synchronize results with each other and any logical signal sent to each of the devices would have had to take into account a perfect prediction of the state of the A/B switch when the signal was processed.  These results agree with the equations of quantum mechanics while disagreeing with conventional logic.
These are real experimental results that replicate even when the lab assistants are separated by too much space for the black boxes to communicate with each other and synchronize the results during measurements.  It is also possible in the experiment for different observers to observe any measurement ordering via the principles of relativity.
