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There is an advantage to the original formulations of QM and they are precisely these. It's true that in Quantum Field Theory you don't see these Bell Inequalit
by drostie 14y ago
There is an advantage to the original formulations of QM and they are precisely these. It's true that in Quantum Field Theory you don't see these Bell Inequality ideas and I've seen people working in Quantum Information theory who struggle to prove that you can multiply a wavefunction by an arbitrary phase factor and it is an unobservable change. QFT has real current statistics and Lagrangian densities and Feynman diagrams, which give you a much more tangible feel of what physics you're describing.
In my experience it is just another math course and there is no Physics anywhere.
Heisenberg equations of motion are a good place to start. The original way we stumbled upon quantum mechanics was due to Heisenberg, who noticed that a lot of the wavy stuff people wanted to explain could be explained if Hamilton's equations of motion df/dt = {f, H} + ∂f/∂t were generalized by treating x(t) and p(t) as matrices and insisting that they do not commute, leaving instead [x, p] = i ħ as a matrix version of an "uncertainty principle."
The corresponding quantum equation for an observable  is that dÂ/dt = i [Ĥ/ħ, Â], which allows you to start (most famously) with a harmonic oscilator Ĥ and derive the Hamilton equations dx/dt = p/m, dp/dt = - k x, precisely due to the failure of x and p to commute.
So you get this direct connection between known physics equations and the quantum theory, and often the same thing which is responsible for driving the uncertainty relation also drives all of classical physics.
What does a particle with some particular wave function look like?
|Psi|^2 in the appropriate basis, I should say.
As it evolves in time it "smears" out according to the time evolution equations, but how fast is the process? Does it occur on scale of nanoseconds? Seconds? Hours?
In quantum mechanics there is a discrete energy level spacing ΔE, and the answer is that no observable can change much faster than ħ / ΔE. For the harmonic oscillator for example, nothing can change much faster than 1/Ω by this criterion.
What exactly is an example of a measurement?
This can get a little touchy but a good example is a photon hitting a photomultiplier tube and generating a click -- especially if you start to play with the polarization of the photon to generate entanglement and so forth.
Edit: With all that said, I highly recommend watching Feynman's New Zealand lectures which explain, among other things, why CDs show rainbow patterns (in a time, sadly, before people had CDs and so Feynman kind of just says "I wish I could have brought you an example.") http://vega.org.uk/video/subseries/8 http://vega.org.uk/video/subseries/8
- Dn_Ab 14y agoYou're right. And it's well explained despite the subtle jabs at Quantum Informations theory =P. There are definite advantages to the physics focused approach. As a physicist (which I am not), in your practice of QM you get familiarish concepts like spin, momentum , oscillators and Lagrangians. But despite the wild successes of QFT, when it comes to explaining things it is extremely hard to do without either using broken analogies or talking about Feynman diagrams, Lagrangians and Hamiltonians. To realistically depict what is going on you are replacing one branch of math with another more complex branch with the main advantage being that someone who has learned the math of classical mechanics can have a slightly stronger physical intuition. The advantage of QIT is that because it is relatively simple already, a slightly simplified form is still easier to understand and more representative of the real thing than a highly simplified explanation of QFT. The other advantage of this is that the simplicity allows the raw structure to be exposed and tackled much more readily. If I would bet I would say answers to questions like what is the wave function exactly , how does the macroscopic universe arise from the cloudy quantum picture, what is really going on in measurement etc will come from QIT. I get the impression that many physicist don't have much respect for foundations but these questions are still worth answering and would have a practical effect on our world right away. QIT is young yet, there are advantages to being able to take multiple viewpoints of the same thing. The correct viewpoint can vastly simplify a problem. To quote Egan: " Everything becomes clearer, once you express it in the proper language."
- drostie 14y agoOh, I don't mean to demean the field of Quantum Information. Especially, I find it really useful to run through the double-slit experiment by labelling one slit as |0> and one slit as |1>, and then going through both slits comes out as sqrt(1/2)[ |0> + |1> ] = |+>, which has certain "off-diagonal terms" in its "density matrix." If all that formalism is built up, you can have fun working through when these off-diagonal terms exist and when they do not, especially in cases where you take a new qubit as |0> and then entangle it into the system with a CNOT gate, where you get |00> + |11>. If folks are confused by the above, I have begun trying to explain it here: https://github.com/drostie/essay-seeds/blob/master/physics/doubleslit.md https://github.com/drostie/essay-seeds/blob/master/physics/d... It's really kind of rough (in particular I'd like to use proper HTML subscripts rather than Unicode subscripts eventually) but it should be intelligible to a bright student who wants to know the basic ideas of QM.