What is the most confusing concept in quantum physics?

[sumansuhag]

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I'd propose the superposition principle:

If a quantum system can exist in one of two configurations, it can also exist in an arbitrary superposition of those configurations.

To visualize this, we can consider a single coin to be a quantum system. Say we flip the coin, then, without looking at it, we try to guess what face it landed on.

If we're operating under classical mechanics, the answer is obvious: the coin either landed on heads or it landed on tails. Let's call the probability that it lands on heads
A
and the probability that it landed on tails
B
.

We can safely say (disregarding the edge case, which we'll pretend doesn't exist for simplicity) that
A
+
B

1
. Clearly it has to land on one of the two sides, so this is just a fancy way of saying the probability that it lands on heads plus the probability that it lands on tails is 100%.

However, in quantum mechanics, probabilities aren't so easily defined — instead of definite states, we tend to describe them with wavefunctions. The probability of finding an object in a certain state is equal to the square of the wavefunctions describing its position. So, for example, the probability of it landing on heads would be (
A
(
x
)
)
2
, and the probability of landing on tails would be
(

B
(
x
)
)
2
(where
A
(
x
)
and
B
(
x
)
are the wavefunctions corresponding to the heads and tails state, respectively.)

So, if the coin could exist in either the tails or heads state, then its total probability would be the square of the sum of the wavefunctions. That doesn't seem too bad. Writing it out, we see that
(
A
(
x
)
+
B
(
x
)
)
2

1
. Seems fine, right?

Not so fast. If you've taken algebra at any level, you're probably familiar with the fact that exponentation is not distributive. In other words,
(
A
(
x
)
+
B
(
x
)
)
2
doesn't mean
(
A
(
x
)
)
2
+
(
B
(
x
)
)
2
— it means
(
A
(
x
)
+
B
(
x
)
)
∗
(
A
(
x
)
+
B
(
x
)
)
. So, multiplying out, we find that the equation comes out to (
A
(
x
)
)
2
+
A
(
x
)
B
(
x
)
+
B
(
x
)
A
(
x
)
+
(
B
(
x
)
)
2

1
.

Wait a second. We've already defined
(
A
(
x
)
)
2
as the probability of the coin landing heads up, and
(
B
(
x
)
)
2
as the probability of it landing tails up. But the equation we just derived seems to be suggesting that the probability of heads and the probability of tails don't add to one. That is, it is possible for the coin to land in a state that is neither heads nor tails. This is represented by the middle terms in the equation.

So, if the coin isn't heads, and it isn't tails, then what is it?

Exactly - it must be in a superposition of heads and tails. This superposition is a result of the interference between the two wavefunctions, and thus the two middle terms in the above equation are referred to as interference terms.

But wait. If the coin can exist in an arbitrary superposition of heads and tails, then why is it always in either heads or tails when we measure it? What determines which exact superposition it ends up in? And why the hell are we talking about a coin like it's some sort of wave?

To answer those questions, quantum mechanics (and later quantum field theory) was derived. All of the complex science that you're probably expecting in these answers the Casmir effect, the uncertainty principle, tunneling, entanglement — all of them arise directly as a result of the superposition principle.

(For anyone with experience in quantum mechanics, realize that I intentionally simplified the concept of wavefunctions here. Hence why there's no mention of normalization, weighted probability, complex conjugates, and the like.)

[Pranav4628]

🔑 Key Clarifications
Classical vs Quantum Probability

In classical mechanics, probabilities are real numbers that add up to 1 (e.g.,
𝑃
(
heads
)
+
𝑃
(
tails
)

1
).

In quantum mechanics, we don’t assign probabilities directly to states. Instead, we assign amplitudes (wavefunctions), which can interfere. Probabilities are obtained by squaring the modulus of these amplitudes.

Wavefunctions and Superposition

If a system can be in state
∣
𝐻
⟩
(heads) or
∣
𝑇
⟩
(tails), then quantum mechanics allows it to be in a linear combination:

∣
𝜓
⟩

𝛼
∣
𝐻
⟩
+
𝛽
∣
𝑇
⟩
where
𝛼
and
𝛽
are complex numbers (amplitudes).

The probabilities are given by
∣
𝛼
∣
2
and
∣
𝛽
∣
2
, with the normalization condition:

∣
𝛼
∣
2
+
∣
𝛽
∣
2

1
Interference Terms

In your algebra expansion, the cross terms
𝐴
(
𝑥
)
𝐵
(
𝑥
)
and
𝐵
(
𝑥
)
𝐴
(
𝑥
)
represent interference. This is the heart of quantum mechanics: unlike classical probabilities, amplitudes can add and cancel.

However, when we compute probabilities correctly (using modulus squared of amplitudes), the interference shows up in phenomena like the double-slit experiment, not in the trivial two-outcome coin flip. That’s why in actual quantum mechanics, we don’t say “the coin is in a third state”—instead, we say it’s in a superposition that collapses to one of the classical outcomes upon measurement.

Measurement Problem

You asked: “If the coin can exist in a superposition, why do we always see heads or tails when we measure?”

This is the measurement problem: quantum mechanics predicts superpositions, but measurement outcomes are definite.

The standard answer is the Born rule: measurement projects the wavefunction onto one of the basis states with probability given by the squared amplitude.

Why this happens is still debated—interpretations like Copenhagen, Many-Worlds, and decoherence all try to explain it.