# An Experiment with the Fridge

friends, last week we saw a VERITAS on the wave function collapse. We saw that an observation of a superposition :

a|+1/2> + b | -1/2> yields 1/2 or -1/2. And that the observation collapses the wavefunction into one of these two states.

One of my very close friends has raised an objection about this. We will call this friend of mine Saki for the rest of this VERITAS. Saki says: ” Thre is nothing very hi-fi about this … This in common man’s language is similar to the “light in the fridge” problem. How do you know if the light is switched off when the door of the fridge is closed? The way to find out is to open the fridge, in which case the fridge is not closed anymore.”

In today’s VERITAS we will examine Saki’s arguments in detail and we will see how our quantum mechanical example differs from this.

take a normal fridge. Open its door. You see a light inside it. Now open the door again, you will see light again. Do this experiment a 1000 times. Evertime you open the fridge you will see light. So you say that “when I open the fridge I see light”. And you are absolutely correct! Saki and I are in agreement here.

Now take a quantum fridge( dont bother where you will find it. This is a thought experiment.. the sort of stuff theoretical Physicists delight in). The quantum fridge has 2 doors. One door on the front and another at the roof. They are both connected to the same light. Now open the front door. You may see light or you may not see light. Open and close the same door 1000 times. And you will see exactly the same thing as you saw the first time. And you can say that there is no mystery here: either the light works or it does not work. But whenever I open the fridge I see what I EXPECT to see. If I saw light once then the future openings will always show me light. If I saw no light then the future observations will also show me no light. We have no right to think there is anything strange here. This is normal. Scientists dont make strange theories when simpler reasons are possible. Here too Saki and I are in agreement.

Now the mysterious : The quantum fridge has 2 doors. Open the front door. You may see light. Now close this and open the top door. You may or may not see light: lets say you do not see light. Now close this and open the front door again: there is NO gurantee that you will see light now! You may not see light. You expected to see light here because your earlier experiment with the front door showed light. But this is against your expectations. Now do this experiment a 1000 times : each time you open the front door, record the obsarvation and close it. Then you open the top door. record, close. After a 1000 observations you will see this : About 500 openings of the front door showed light. And about 500 openings of the top door showed light. THERE IS NO PATTERN HERE! Plot it and you will see NO corelation between the results of the top door and the results of the front door. There is NOTHING in our everyday lives that behaves like this. It is something like this: An observation of the top door destroys the results of the front door. If you open the top door then the results of opening the front door are RANDOM! There is a 50% probability of getting light and 50 % of not getting light.

And the opening of the front door make the results of the top door random. Here Saki’s line of reasoning breaks down.

The fridge is not a concorcted example. This is similar to the electron spin. If you measuse spin in the x direction you may get 1/2 or -1/2. Now if you measure spin along z direction you may get 1/2 or -1/2. Now if you measure spin along x you have a 50% probability of getthing 1/2 and 50% of getting -1/2.

But if you had measured spin along one direction always then you will always have got the SAME result. An observation along one direction COLLAPSES the wave function into a state. But an observation along a orthogonal direction will uncollapse it again into a superposition after which the results of its observation would be a probability.

The probability in Quantum Mechanics is real! And you will never see something like this in your everyday life!!

Friends, Nature is infinitely mysterious. The Universe is a grand game in which even the rules are more mysterious than anything you have seen. Why do you play with little games created by little people with trivial rules???!! Only the mysterious game of nature created by  the Infinite Intellect deserves your time and effort. We have a tool called Science to understand this game.

Byron said :

“THERE is a pleasure in the pathless woods,

There is a rapture on the lonely shore,

There is society, where none intrudes,

By the deep sea, and music in its roar:

I love not man the less, but Nature more,

From these our interviews, in which I steal

From all I may be, or have been before,

To mingle with the Universe, and feel

What I can ne’er express, yet cannot all conceal”

Kanwar

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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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# 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

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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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