# Negative and Complex Probability?

• WhiteRae
In summary, in quantum mechanics, probabilities can be represented by complex numbers known as probability amplitudes. These amplitudes are like arrows in the plane, and the probability of a system going into a particular state is the length squared of the corresponding arrow. This concept can be difficult to understand without a background in calculus, but it is explained in Richard Feynman's book "QED" in a more accessible way.

#### WhiteRae

I'm currently reading "The Black Hole War" by Leonard Susskind. I'm the book the author says that when predicting probability in quantum you can have positive, negative, or complex numbers. How is this possible? The book literally says, "Do not try to understand this. Just accept it." I asked the AP Physics teacher at my school but she never even heard of this before. Is it possible to explain this to someone with no calculus background? Thanks.

Probabilities are never negative or complex. Probabilities are always numbers satisfying 0 ≤ x ≤ 1.

In quantum mechanics, there are complex probability amplitudes, which are not the same as probabilities.

Now that I reread it I see it said probability amplitudes can be positive, negative, or complex numbers. What exactly is that? Every explanation I find involves complex math (since I'm not taking Calc 1 until next year almost all math is complex to me).

You can think of probability amplitudes as arrows in the plane. If a quantum system can go into either of two states upon measurement, then there are two of these arrows, one for each process. The probability that it goes into the first state is the length squared of the first arrow. The probability that it goes into the second state is the length squared of the second arrow.

It's actually not a very difficult concept. I highly recommend Richard Feynman's popular book "QED: The Strange Theory of Light and Matter" where he explains what probability amplitudes are and how you can use them to understand various phenomena, all without the use of any advanced mathematics.

Thanks.