Q.Explain the idea of the lack of determinism in quantum theory and the many-worlds picture as Rajendra Deshpande presents them, and show how together they account for Professor Gaitonde's two-day experience of a different India. (Answer in 120–150 words.)

Quantum Superposition: From Intuition to Precision

Imagine you're standing in a dark room, and you flip a coin. While it's spinning in the air, is it heads or tails? The honest answer is: neither, and both at once. It's a blur of possibilities — a superposition of heads and tails. Only when it lands and you catch it does it become one definite outcome.

That spinning coin is a rough intuition for quantum superposition. A quantum particle, like an electron, doesn't have a fixed position, energy, or spin until you measure it. Instead, it exists in a blend of all the possibilities it could have. This isn't ignorance — it's not that we don't know which state it's in. The particle genuinely has no single value until an observation forces it to choose.

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The Precise Statement

In quantum mechanics, the state of a system is described by a wavefunction, often written as $|\psi\rangle$ (pronounced "psi"). The wavefunction lives in a mathematical space called a Hilbert space. A key rule: if $|\psi_1\rangle$ and $|\psi_2\rangle$ are both possible states of a system, then any linear combination of them is also a possible state:

Here $c_1$ and $c_2$ are complex numbers called probability amplitudes. The squared magnitude $|c_1|^2$ gives the probability that a measurement will find the system in state $|\psi_1\rangle$, and similarly $|c_2|^2$ for $|\psi_2\rangle$. Since probabilities must sum to 1, we require $|c_1|^2 + |c_2|^2 = 1$.

This is the superposition principle. It says the quantum world is fundamentally additive: a particle can be in a superposition of being here and there, spinning up and down, or having two different energies — all at once.

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What It Does Not Mean

A common trap: superposition is not a mixture. A mixture is like a bag containing one red marble and one blue marble — you just don't know which you'll pull out. That's classical probability. Superposition is different: the particle is simultaneously in both states, and the two possibilities can interfere with each other, like waves on a pond. This interference is what produces the famous double-slit pattern — each electron passes through both slits at once and interferes with itself.

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A Concrete Example: Spin …