4: The Universe is Inherently Probabilistic
- Page ID
- 94035
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- 4.1: Basics of Probability Theory
- We start with a look at the fundamentals of probability theory, and how this can be used to help interpret double slit interference for both light and particles.
- 4.2: Continuous Probability Distributions and Probability Density
- Probabilities for discrete outcomes like coin flips and dice rolls are one thing, but what if there are an infinite number of random outcomes, such as the final position of a dart on a dartboard? We explore this aspect of probability theory.
- 4.3: The Uncertainty of Random Outcomes
- Given that measurements of values like the positions of particles that land on a screen after passing through a double slit are random, it is useful to know to what degree we can predict these measurements. If all we can hope for is a ballpark figure, then we should at least be able to determine the size of the "ballpark". We look at the mathematical treatment of uncertainty in this section.
- 4.4: Physical Measurements with Random Outcomes
- Here we will tie together and mathematically formalize the notion of probabilistic outcomes with physical measurements, and further develop the idea that all of the information of a quantum state is held in a single wave function.
- 4.5: Incompatible Measurements
- The are even stranger consequences of quantum theory than the fact that values we measure are inherently probabilistic. We will say that as we take steps to improve some physical measurements (i.e. reduce our uncertainty in their values), our steps simultaneously make other physical measurements more uncertain!