
#1
Dec3106, 02:29 AM

P: 28

Yep I have seen that movie! :)
Ok I am crazy enough to explain, “how Q.M. actually works”. Lets start with simple explanation of waveparticle duality, which actually states that the light has a dual nature: It exhibits both wave and particle characteristics (& that is a FACT). In early 20th century Albert Einstein has won a Nobel prise for his famous experiment, which we know as photoelectric effect. This experiment states that the incident photon possesses nature of particles or quanta which has energy given by E = hf where h is Planck’s constant and f is the frequency of radiation. And from Optics or E.M. theory we know that light is variation of electric and magnetic fields, which poses the nature of waves. So here arises question which model is correct? Is light a wave or a particle? The answer depends on the phenomenon being observed (note the word observed). Some experiments solely can be explained with photon model and others with a wave model. In 1923, here comes the Louis de Broglie and postulates that: because photons have both wave and particle characteristics, perhaps all forms of matter have both properties. Guess what? He was right! From classical theory we know what we need to describe a particle, we need to know its energy and momentum which are given buy E = mc2 = sqrt[p2*c2+m2*c*4] (relativistic energy) => p = E/c so using these equations and E = hf we can find that p = h/l where l is the wavelength of particle oscillating. Therefore l = h/p = h/(mv) (nonrelativistic) this basic formula suggests that you me and all matter in the universe are also waves. By using this formula you can calculate your wavelength, which will be very small, much, much smaller than the atom its self. So the question is how can you observe that you are wave if the oscillation is infinitely small. So we all define our selves as I (particle, whatever) and yet we all posses the wave nature. Ok here comes my favourite topic (welcome to my world) Quantum Mechanics. Now before I go into this I want to assure you of that if you don’t understand anything you are on the right track. It is impossible for human who is attuned to everyday experience to understand quantum world. In my 3rd year one of the students in my class said that the QM is easy and he understands it, my lecturer took it very personally and was upset with that person. If you meet some one who said that they understand QM, it is most definitely that they saying that out of they ignorance and that they don’t understand it. Anyways the way I and most physicist “understand” QM is through mathematics, this is as good as it gets but don’t worry I will not go into proofs and theorems. The understanding of photon being a particle and the wave at the same time we can bring an example of free particle in QM theory. When we solve Schrodinger wave equation for a free particle (very complicated stuff if no advanced mathematical background) we find the Fourier transform which describes free particle being a wave and particle at the same time. A person must be crazy to even try to visualise how quantum world works (it’s madness) so here a mathematical or graphical description of a particle. Form engineering the amplitude modulation or (AM your radio) defines two sets of waves both at different frequencies one know as “envelop” and “ripples” (ref. type in google: Amplitude Modulation and then click on images). So here it works in the same way; a wavepacket is the superposition of sinusoidal functions whose amplitude is modulated by some function it consists of “ripples” contained by the “envelop”. So what correspond to the particle velocity or (a particle) is the speed of the envelop (or envelop) also known as group velocity and what correspond to the wave is the speed of the individual ripples or (the so called phase velocity). So a wave & packet is something that has envelope and ripples, which both travel at group and phase velocities respectively and fully dependent of one another and hence produce a wavepacket. Now lets get back to your question about the double slit experiment, this is very deep question in physics, which has yet to be answered. Lets consider the EPR paradox, which was designed to prove on purely theoretical grounds that the realist position is the sustainable one. Consider pi meson particle which decays into p > (e) + (e+) electron and its antiparticle positron. Now pion has a spin zero so that the conservation of angular momentum requires for the electron and positron to be of different spins. QM can’t tell us which combination you’ll get in particular pion decay, but it does say that measurements will be correlated and you will get each combination half the time on average. Lets say you measure the spin of electron 20 light years away you get spin up, then you will immediately know that some one who is 40 ly away will measure the positron with the spin down. But the interesting thing that happens is that you don’t know wether the electron is spin up or down until you measure it or observe it, before that you have 50/50 chance to get it right and once you measured or observed the wave function is collapsed and you instantly know that positron is indeed up or down, it is also known as quantum entanglement. Or you could think that some one else on the other side of the galaxy measures the positron to be spin up you will get for a fact electron with spin down (isn’t that cool). Einstein, Podolsky and Rosen considered this preposterous because in orthodox terms nothing can travel faster then speed of light and yet we observe such phenomenon as a collapse of wave function is instantaneous. This brings even more deeper questions regardless the reality and the nonlocality. It is evident that information can travel faster then speed of light (speed of a thought perhaps). Einstein always questioned quantum theory and even proposed the theory of hidden variables but QM have never failed an experiment and considered the most profound theory. It is still a great mystery how the collapse of a wave function mechanism really works but at least we know that one of the causes in nature is the observation. There are still great mysteries that exist in physics that we are not sure about and just except them as they are for example no one knows how the law of cause and effect really works. My conclusion is that there is so much we don’t know about the reality that it is always good to keep an open mind. I suggest further readings on EPR experiment and Quantum Eraser Experiment also Bell’s theorem, Quantum Zeno Paradox, Causality (physics) and least but not last (Correct view of Emptiness Buddhism). 



#2
Dec3106, 10:46 AM

P: 27

drphysica:
http://www.physicsforums.com/showthread.php?t=149243 DTF 


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