Negative and Complex Probability?

Click For Summary

Discussion Overview

The discussion centers around the concept of probability in quantum mechanics, specifically addressing the notion of negative and complex numbers in relation to probability amplitudes. Participants explore the implications of these ideas for understanding quantum phenomena, with a focus on accessibility for those without a calculus background.

Discussion Character

  • Exploratory
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant references Leonard Susskind's "The Black Hole War," noting that the book suggests probabilities can be negative or complex, but expresses confusion about this claim.
  • Another participant asserts that probabilities are always non-negative and confined to the range 0 ≤ x ≤ 1, distinguishing between probabilities and complex probability amplitudes.
  • A participant seeks clarification on the nature of probability amplitudes, acknowledging difficulty with complex mathematics due to a lack of calculus knowledge.
  • One participant explains probability amplitudes using a geometric analogy of arrows in a plane, suggesting that the squared lengths of these arrows correspond to probabilities of different outcomes.
  • A recommendation is made for Richard Feynman's "QED: The Strange Theory of Light and Matter" as a resource for understanding probability amplitudes without advanced mathematics.

Areas of Agreement / Disagreement

There is disagreement regarding the interpretation of negative and complex numbers in the context of probability. While some participants maintain that probabilities must be non-negative, others reference the concept of probability amplitudes, which can take on complex values.

Contextual Notes

Participants express varying levels of mathematical background, which affects their understanding of the concepts discussed. The discussion does not resolve the confusion surrounding the relationship between probabilities and probability amplitudes.

Who May Find This Useful

This discussion may be useful for individuals interested in quantum mechanics, particularly those seeking to understand the foundational concepts of probability and probability amplitudes without a strong mathematical background.

WhiteRae
Messages
13
Reaction score
0
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.
 
Physics news on Phys.org
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.
 

Similar threads

  • · Replies 8 ·
Replies
8
Views
2K
Replies
2
Views
2K
  • · Replies 11 ·
Replies
11
Views
4K
  • · Replies 1 ·
Replies
1
Views
1K
  • · Replies 4 ·
Replies
4
Views
2K
  • · Replies 6 ·
Replies
6
Views
2K
  • · Replies 2 ·
Replies
2
Views
3K
  • · Replies 28 ·
Replies
28
Views
4K
  • · Replies 2 ·
Replies
2
Views
2K
  • · Replies 6 ·
Replies
6
Views
3K