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Quantum Mechanics: The Theoretical Minimum…

Quantum Mechanics: The Theoretical Minimum (2014)

by Leonard Susskind, Art Friedman (Author)

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275665,175 (4.31)4
Explains the theory and associated mathematics of quantum mechanics, discussing topics ranging from uncertainty and time dependence to particle and wave states.




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This book is a continuation of The Theoretical Minimum which covered Classical Mechanics in physics. Using simple language and explaining the terminology, Susskind and Friedman go through the basics of Quantum Mechanics. They talk about eigenvectors and eigenvalues, bra-ket notation, wave forms, uncertainty and linear operators. Even more is covered, but you get the basic idea I hope.

This book leaves some things to the reader, for instance, you might have to prove some sort of mathematical theorem or something, but all in all this book is more of a guide you by the hand sort of book. Don't get me wrong. The book is challenging, and it does expect you to build on your imparted knowledge, but it goes step by step logically in a manner that I understood.

As was explained in the book, Quantum Mechanics deals with very small things, things that we as a species are not equipped to understand. This book teaches abstract mathematical theorems and techniques that work in describing quantum behavior. This makes it difficult, because there is no intuition for it. A baseball player may not know the kinematic equations that describe a baseball flying through the air, but the human brain can make predictions and move the arm accordingly. This is not the same for quantum mechanics.

I enjoyed it, but it isn't a book that you read through. It requires you to study it and understand it first. So hopefully one of these days I will have the time and inclination to do both. Five out of five nonetheless. ( )
  Floyd3345 | Jun 15, 2019 |
I was on a train the other week and I was sitting opposite Einstein who asked me if I would mind changing seats because he liked to see where he was going for a half a journey and then he liked to see where he had been for the other half of the journey and I told him I didn't mind changing seats and I asked him if he minded me asking him if he was dead and he said, "When?"

Why was the universe in such a low entropy initial condition? As many have pointed out, that might be even more unlikely than random macroscopic decreases in entropy. Also, if the universe had a low entropy initial condition, might it have a similar boundary condition at the other end? If so, then someday, entropy will start to decrease!

The public is always excited about quantum mechanics, and consequently there is a potential for careless journalists to exploit that, by mentioning all the exciting parts (e.g., quantum teleportation - people often think this 'spooky' phenomenon violates special relativity), but omitting all of the constraints (e.g., the fact that non-random information in quantum teleportation is actually transmitted at the speed of light or even less). The old Carl Sagan quote is very relevant on all things quantum (and throughout the totality of human thought, in fact):

“Where we have strong emotions, we're liable to fool ourselves.”

I show that, within a quantum mechanical framework, all phenomena which leave a trail of information behind (and hence can be studied by physics) are those where entropy necessarily increases or remains constant. All phenomena where the entropy decreases must not leave any information of their having happened. This situation is completely indistinguishable from their not having happened at all. In the light of this observation, the second law of thermodynamics is reduced to a mere tautology: physics cannot study those processes where entropy has decreased, even if they were commonplace. Meaning: "The past exists only insofar as it is recorded in the present."

Problem: what about phenomena which "leave a trail of info" (say 100 bits) behind, but (going in the reverse time direction) leave a trail of info (say only 50 bits) behind? Plainly it can be "studied by physics" in either direction, and also the "past exists" in either direction. So, no, it wasn't a tautology. But anyway, plausibly there is something wise here (and for that matter, plausibly there was something wise in H. Everett's many worlds interpretation from the 1950s); I just think all this stuff is basically speculation and not rigorous. Maccone uses words like "I will make these ideas rigorous" but that is bunk. There is not a single theorem and proof in the paper, it is all "proof by example" and by assertion (e.g. "the eventual correlations in all macroscopic systems are practically impossible to control and exploit" he asserts, with zero justification). Non-rigorous arguments are ok, but falsely saying they are rigorous, is not.

What really puzzles me in the realm of probabilities is that events with an infinitesimal chance of happening do occur: The ball hitting the gate post instead of going goal, the coin falling on edge and into a crack instead onto the infinite floor space around, or bird`s poo on my car and not on the other hundreds of cars around mine. The interesting point is that although the probability of entropy decreasing events, and other physical events, is infinitesimally small, it is NOT zero and therefore just might occur. Interestingly is that one cannot measure x and p simultaneously for a quantum particle. So we cannot know if a particle doesn't have x and p values at the same time. In the Bohm (ontological) interpretation, particles have defined paths which cannot be known accurately.

The vacuum and ΔE Δt ≥ ℏ/2 (c.f. Δx Δp ≥ ℏ/2); why not have definite energies, but which cannot be measured, in the same sense? It seems there is ambiguity in the meaning of what's going on in the vacuum and perhaps looking at all interpretations of QM would help (or not!).

I find the meaning of what's going on here very difficult because one is importing classical physics ideas, time, energy, position, momentum into quantum phenomena. You can calculate with it all and build computer chips etc. but the meaning??? I still believe a version of one of the "hidden variables" interpretations like Bohm's will prove to be a better understanding of what’s going on at the Quantum level. There is no real evidence that there are discrete packets that form particles in EM - rather the discrete packets are the atoms in our measuring instruments.

The "hidden variable" idea (e.g., "the photon DOES have a well-defined position and momentum, we just can't measure it") was around from the beginning of quantum theory, but it was discounted in the 60s and by many experiments since (c.f. Bell's Theorem in Becker’s book). It's a complicated one to explain, but the gist of it is that you can send a photon through three polarized screens, one of which (at least) should stop it if it has a well-defined polarization. It doesn't however, the photon seems to be able to flick back and forth between DIFFERENT polarisations in between each screen. It's complicated to get your head around, but the evidence seems to show there are no hidden variables, it's not an artefact of our measuring systems; it’s just the way the universe is. If you don't mind spending a little time scratching your head, it is well worth watching the first QED lecture that Feynman did in New Zealand. It's advanced stuff, but Feynman does have a way of explaining things that I find extremely helpful. He also helpfully advises viewers at the very start of the lecture that they will probably not "get" most of it, but “not to worry about it.”

Teachers don't spend enough time on the particulars of the slit experiment. What EXACTLY is used to measure the photons on the back screen? What EXACTLY causes the slight randomness of the photons going thru ONE slit? Is it the frequency shift of photons coming out of the "laser", is it the human error in designing a perfect laser shooter? Is it the photons nicking the inner sides of the slit? And then in the advanced notion of the slit experiment which talks about measuring WHICH slit the photon goes thru, which alters the results (from quantum mechanical, back to mechanical expected results), how is the slit-choice ACTUALLY measured, perhaps the device is affecting the result? Also, I think the fluid physics dudes should always chime in on slit experiment presentations with talk about carrier-waves, which after many, many decades STILL hasn't been proven wrong.

Physics teaching is so bad nowadays, and so one-sided, new students get bad education, thinking they know something, when in fact due to being presented the questions and solutions wrongly, the education system has actually created a barrier for those trying to ADVANCE human knowledge. If teaching something, like the way Susskind does in this book, do it right, do it completely, and spend some actually time on it, rather than trying to get to a pre-determined endpoint.﻿ Could Susskind have given us a more objective visualization of quantum mechanics if we had an interactive emergent process unfolding photon by photon? This idea is based on: (E=ˠM˳C²) ∞ with energy ∆E equals mass ∆M linked to the Lorentz contraction ˠ of space and time. The Lorentz contraction ˠ represents the time dilation of Einstein’s Theory of Relativity. We have energy ∆E slowing the rate that time ∆t flows as a universal process of energy exchange or continuous creation. Mass will increase relative to this process with gravity being a secondary force to the electromagnetic force. The c² represents the speed of light c radiating out in a sphere 4π of EMR from its radius forming a square c² of probability. We have to square the probability of the wave-function Ψ because the area of the sphere is equal to the square of the radius of the sphere multiplied by 4π. This simple geometrical process forms the probability and uncertainty of everyday life and at the smallest scale of the process is represented mathematically by Heisenberg’s Uncertainty Principle ∆×∆pᵪ≥h/4π. In such a theory we have an emergent future unfolding photon by photon with the movement of charge and flow of EM fields. This gives us a geometrical reason for positive and negative charge with a concaved inner surface for negative charge and a convexed outer surface for positive charge. The brackets in the equation (E=ˠM˳C²)∞ represent a dynamic boundary condition of an individual reference frame with an Arrow of Time or time line for each frame of reference. The infinity ∞ symbol represents an infinite number of dynamic interactive reference frames that are continuously coming in and out of existence (this is just wishful thinking on my part…lol). ( )
  antao | Nov 25, 2018 |
Just skimmed this
  Baku-X | Jan 10, 2017 |
As the previous volume on classic mechanics, this is an excellent introduction with no fake examples and bullshit. Just the right amount of mathematical detail to understand what quantum mechanics is all about. The explanations of how Pauli's bra-ket annotation work and what it means is particularly useful. ( )
  amarcobio | Jun 28, 2015 |
The second volume of the _Theoretical Minimum_ series, presenting real physics to non-expert but mathematically college-level readers. Covers the QM fundamentals, including the Schrödinger equation, uncertainty, entanglement, and relation to classical mechanics. It seemed to me that the difficulty of the many equations (often with bra-ket or wavefunction expressions and distant back-referencing) and abstract concepts peaked just after the midpoint but eased off again thereafter. Admirable.
  fpagan | Jul 22, 2014 |
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For our parents,
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Irene and Benjamin Susskind

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Albert Einstein, who was in many ways the father of quantum mechanics, had a notorius love-hate relation with the subject.
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