Wave Function Collapse

 

        In the last few weeks I and a friend have had a number of discussions on this subject. I thought I should share some of these mysteries with the whole VERITAS gang.

        In quantum mechanics a particle( say an electron) is represented by a wavefunction or a state. Lets take some examples:

1)   An electron have a spin of +1/2. So we represent this electron as:

     |electron>  = |+1/2>

2) An electron may be found with a spin of -1/2. We say:

     |electron>  = |-1/2> 

3) Now there is another possibility. And this is at the core of the

   mystery of quantum mechanics. An electron may be found in the following

   state:

    |electron> =  a |+1/2>  + b |-1/2>

    This state is said to be a superposition of the +1/2 state and the

    -1/2 state. So it is neither in the +1/2 state and nor is it in the

    -1/2 state. So what happens when we measure the spin of such an

    electron? The  measurment of this electron might yield a value of +1/2

    or a value of -1/2!!! A measurment of this electron will yield +1/2

   with a probability of a^2 and will yield -1/2 with a probability of

   b^2. Of course a^2 + b^2 = 1.

      These probabilities are very different from the ones that we encounter when we toss a coin. When we toss a coin then the coin is either in a heads state or in a tails state. Our observing it reveals the state that it actually is in. So our observation just increases our knowledge about the state of the coin.

      But before we observe a quantum superposition state then the electon is NOT in a +1/2 state or in a -1/2 state. It is in a a|+1/2> + b|-1/2> state. Our observation will CREATE the |+1/2> state or the |-1/2> state.

In the language of quantum mechanics the observation COLLAPSES the wave function into the |+1/2> state or into the |-1/2> state. The observation creates the reality!

      How do we know that the electron was not in a |+1/2> or |-1/2> state before we observed it? We will not discuss that question in detail here. But this much I can tell you: There are ways to observe the electron without collapsing the wave function and such observations tell us that the electron was NOT in a |+1/2> or |-1/2> state. So the wave function collapse is for real.

      But what decides the probability of collapse into the |+1/2> or |-1/2> state. No body knows the answer to that! But we know that after an electron has collapsed into a |+1/2> state or a |-1/2> state it will stay in that state and a future observation will show you the same state with 100% probability.

      So in a sense an observation creates the reality. And nature adopts a probability in deciding what reality to create! All this seems very strange to us who are used to the deterministic world around us.

      Some people do not believe in the current theory of quantum mechanics. But in Science there is no room for belief or disbelief. These things belong to religion. In Science the validity of a theory is decided by experiments alone. And EVERY experiment ever performed to check the validity of quantum mechanics has found it to be correct. Einstein was a real scientist and instead of saying things like “I dont believe in QM”, he invented some very innovative thought experiments to show that Quantum Mechanics was conceptually wrong. But every experiment showed instead that quantum mechanics is a solid theory.

 

       But lots of mysteries remain to be answered. Quantum Mechanics is the theory of the universe. It is valid for everything: electrons to billiard balls, to humans to planets to galaxies. But then why dont we see superpositions around us. Why dont I see my Tv in a superposition of several states ??? How does an deterministic world around us arise from the basic principles of probability? We will study these questions in a future VERITAS. But let me tell you that there is a Decoherence theory that answers these questions. And you can derive the Newton’s laws of motion from the laws of Quantum Mechanics.

      I leave you with a few quotes on Quantum Mechanics by some eminent scientists:

“If quantum mechanics hasn’t profoundly shocked you, you haven’t understood it yet.”

                                                                Niels Bohr

 

“Here lies the revolution. Quantum theory says that what happens to any individual photon is genuinely and inescapably unpredictable. It has a 95 per cent chance of being reflected, and a 5 per cent chance of being transmitted or absorbed, and that’s all there is to it. There’s nothing about any photon, no secret property or hidden clue, that can tell you any more precisely than that what it will do. The unpredictability is innate.”

 

                                                                Max Plank

 

“God does not play dice with the world.”

-Albert Einstein

 

“Einstein, don’t tell God what to do.”

-Niels Bohr in response to Einstein

 

“I think it is safe to say that no one understands quantum mechanics.”

                                                -Richard Feynman

 

“I believe that the existence of the classical ‘path’ can be pregnantly formulated as follows: The ‘path’ comes into existence only when we observe it.”

                                                Heisenberg

 

Kanwar

 

 

|======================================================|

  Go, wondrous creature! mount where Science guides:                 

  Go, measure earth, weigh air, and state the tides:                 

  Instruct the planets in what orbs to run,                          

  Correct old time and regulate the Sun;                             

|======================================================|

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