Some of you guys know that I was in IISSQI08 for the last two weeks. For me, this summer school was a great achievement in two ways: first, taking part in some fantastic lectures on quantum computing given by eminent international professors and secondly, having brilliant conversations with these lecturers and some new friends. One of these conversations was with David Gross who is a positivist physicist.
The conversation started just after his talk. He finished the talk by explaining the GHZ experiment and the Bell’s inequality to conclude that nature cannot have a deterministic AND local description.
Sina: It can only show that nonlocality cannot have a classical description. What if someday we had a local and deterministic physical theory which is not classical?
David: Like what? Look… This would be a classical theory and since you think classically you are not able to realize it! I can accept if somebody brings a physical theory that is deterministic (X)OR local. But it can’t be both deterministic AND local!
(At that time I couldn’t remember the Multiverse theory to bring an example. Actually, I by myself am not yet convinced by this theory. However it could be a good example of non-classical local and deterministic theory)
Sina: Assuming you are right, so the theory of everything won’t give us any better result than unification of the four forces! It is still indeterministic and is not able to describe the reality of nature!
David: This is the same mistake that Einstein did! You think that e physical theory must satisfy these conditions to be a complete description of reality. However, I believe that the nature is essentially not deterministic and a theory which claims to describe everything must be indeterministic too. Although classical mechanics is working well in classical sizes, but it is an approximation of the reality and it is not true to be considered as theory that is capable of making precise predictions.
Sina: Do you also believe that classical propositional logic is also imprecise?
David: You are entering a dangerous field, ha-ha… No! Why should I say such a thing?
Sina: Because of the intuition one can get from observing the relationship between physics and mathematics. Everything in physics has a counterpart in mathematics and vice versa! It can be seen in the relationship between physics and mathematics. Just like non-Euclidean geometry and relativity!
David: It was a great example. Here is where no one has an answer! No one knows why! But it doesn’t mean that we are allowed to build such a relationship. A counter example is that you deal with finite numbers in physics but you have infinity in mathematics.
Sina: There are some physicists who believe the universe in infinite. On the other hand there are mathematicians (intuitionistic logicians) who do not believe in infinity!
David: But you can image the largest length in a finite world while the largest number does not make sense in mathematics!
Sina: OK! Then if our universe is governed by the laws of quantum mechanics and in this theory there shouldn’t be any assignment to any object that is not yet measured, how do you answer this paradox: A star is born out of reach of any conscious observer. Two thousand years later, when we see the light we analyze it and find out that the star was born 2000 years ago, when nobody saw it!
David: This is the state of the star at time t=0
So the state of the system at this time is
Then at t=1 is
Finally at t=2000 you get
There is a superposition of you when you saw the star and the other you. One who is able to measure you from beyond your system will see you in one of these states with a certain probability and the other state in another probability!
The observer must stand out of the system.
Sina: But when I saw the light I realized that the star was born when I couldn’t see!
David: Physical theory doesn’t answer the questions like “when things happened”. It just gives predictions about the nature. You want to know: what really happened?! However, I want to know: what will I observe? I would be very happy if someone could answer the first question, but I believe that no one will do that! So I prefer to choose the second question.
There are people on your side. If you want to choose the first question I suggest you read David Deutsch’s book: The Fabric of Reality.
(I took his advice and just ordered the book from Amazon)
