Sunday, September 30, 2012

Physics/Quantum physics


A summary of the basics of quantum physics derived from well known texts (e.g. Feynman's lectures) as well as popular books (e.g. books by Hawking and Greene), and primarily Susskind's lectures on quantum physics (part of his Theoretical Minimum series) at Stanford. The lecture series was divided into 7 topics:

  • System/state definition
  • Mathematical foundation
  • Basic principles of quantum mechanics
  • System evolution with time/change
  • Uncertainty
  • Entanglement

Topic 1. System/state definition

Approach which focuses around the definition of a system and its state. He describes a system whose state behaves according to certain rules (described below). The system behavior under these rules are studied using mathematics and the behavior is derived. The behavior that emerges is non intuitive with effects such as uncertainity and entanglement emerging from the math.

The basic rules have experimentally been shown to be the rules under which physical systems really behave at a quantum scale, so the emergent behavior described by the math must be true, no matter how non intuitive it is. Susskind doesn't discuss the reasons why the rules are true. It's a somewhat philosophical discussion, though he does say that you either
  • accept the rules as ground truth, and therefore accept the non intuitive consequences as the way our universe works, or,
  • believe that there exist hidden variables, behaving deterministically, responsible for the visible non deterministic behavior and you're free to continue to search for them, though almost a hundred years of experimental science has failed to find them
Here is the description of system/state and it's rules. Consider a system whose behavior is governed by two rules:
  • Measurement of state is probabilistic: Consider a system with two states (+1, -1) whose state can be measured by an apparatus. Any attempt to measure the state of the system using the apparatus gives a result of either +1 or -1. If the apparatus is used to try to measure the system by forcing the apparatus to measure possible intermediate states (between +1 or -1), the result of the measurement is still either +1 or -1, with the average of a large number of measurement samples converging to the value of an imaginary intermediate state E.g. Let say that +1 and -1 represented two orientations of the system at 180 degrees from each other. If the apparatus is aligned to the axis, the result is either +1 or -1 and will continue to be so, ad infinitum if nothing else changes. However if  the apparatus is not aligned to the axis, the result will still be either +1 or -1 and will change from measurement to measurement. However, the average of a large number of measurements taken using the apparatus not aligned to the axis will converge to the cosine of the angle between the apparatus and the axis. 
  • Measurement causes state change: Consider a system whose state (+1, -1) can be measured using an apparatus. Measure the state of the system, by aligning the apparatus and the system. The state is measured to be either +1 or -1 and will continue to be so ad infinitum, if nothing else is done to the state, except for the same measurements. However, if the apparatus is rotated through an angle less than 180 degrees, and a measurement is taken, then it may be either +1 or -1. If the apparatus is once again aligned to the system axis, and a measurement is taken, it will no longer necessarily be equal to the first set of measurements.
Its important to note that the first rule is not a limitation of the resolution of the apparatus, but a property of the system. The second rules implies that logical propositions (AND/OR) do not carry the same implications for this system as they do for classical physics. Temporal ordering of the operands will  influence the result of the operation. The uncertainty principle will follow from this rule.
This description of the system, which along with a mathematical foundation (Topic 2) will be used to derive the principles of  quantum physics (Topic 3).

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