How do you combine quantum mechanics and relativity in simple terms?
Of course you can combine them, it's very simple, embarrassingly easy, and I've done it myself.The only reason you wouldn't be able to combine them was if one or both of them was not an accurate description of reality. (They're not however exactly an accurate description of reality, but simply by amending each of them by making small simple corrections they can be made accurate and can easily be combined, as well as combined with gravity).Basically, the only correction that you need to make is accepting that photons interact with electromagnetic fields, - that's it. The rest all follows from that and is almost self-explanatory. And in a nutshell that's the answer to the central mystery of Quantum Mechanics - that of Wave-Particle Duality.I've written more detailed papers about this, though I have not and cannot publish these anywhere official of course as I am not an established Physicist, and I haven't sought to distribute these widely as I'm still intending to add a bit of detail. But you can read and download them at this Dropbox link - GUTI presume there might be some appeal to being almost the only person ever to have correctly understood the fundamental nature of reality, so please enjoy. You might wish to start with the Relativity section as it's shorter.Established Physicists however unfortunately refuse to unlearn what they've learned including a few errant fundamental unproven assumptions our current theories were built upon, - including that photons don't interact with anything, (although there is of course plenty of evidence for that including evidence that you can observe yourself with a sensitive photon receptor such as your naked eye).Take lasers; we use lasers because they produce coherent light; and therefore a laser beam does not spread out. In contrast, the photons in a non-coherent beam of light will interact with each other and cause the light to spread out. So Physicists use lasers in labs every day strictly because the photons from it don't interact, but still will still argue to their deathbed that photons never ever interact. (Rephrased; if photons did not interact then there wouldn’t be any reason to ever have a laser). That takes a level of cognitive dissonance that I cannot begin to fathom, but would anyone wish to take a stab at explaining that??
What is the best book for relativistic quantum mechanics for a beginner?
I’m not exactly sure there is one. I was unsatisfied with all of my texts after Griffiths QM, resulting in my more or less learning relativistic QM from Wikipedia and by myself. I was particularly unsatisfied by Mann, Intro to Particle Physics, which didn’t really explain any of what it did to my satisfaction. Others I have looked at always relied heavily on a separation of space and time, even though the whole point of relativistic QM is to unify space and time. Wikipedia did that too actually. Maybe I’ll write one. I’ll keep you apprised.
Quantum Mechanics -- Questions?
there has never een any conflict between quantum mechanics and special relativity. all the formulas hold - and are more accurate - when you factor in the effects of special relativity. relativity makes the math harder, so it is rarely seen until advanced qm. general relativity deals with the effects of large objects changing spacetime - gravity, and quantum mechanics deals with incredibly tiny objects. it is really tough to measure the effects of gravity in an atom because quantum mechanical forces are so much stronger, so its like looking for a needle in a haystack. the opposite is true for measuring qm in large scales, its like looking for hay in a needlestack. they both involve making different assumptions about the universe. i know i haven't given a real answer, this is partly because i don't know exactly why they don;t fit, and also because nobody really does - if they did, they could fix it. feynman predicted quarks, among other things. check http://en.wikipedia.org/wiki/Feynman for more
Relativity vs Quantum Mechanics - How do they conflict?
To answer this question properly requires a significant amount of background information for which the space provided is insufficient. Thus, I believe I found a good link which talks about this issue: http://en.wikipedia.org/wiki/Quantum_gra... It is also necessary to understand the postulates of general relativity as well as quantum mechanics. http://en.wikipedia.org/wiki/General_rel... http://en.wikipedia.org/wiki/Quantum_mec... Basically the issue lies with a matter of philosophy: is the universe deterministic or indeterministic? Einstein believed that we could know where a particle is, and the fact that it ends up somewhere else is the fault of our theory. The Copenhagen interpretation states that there is no objective statement about where a particle is, it is the act of observing which causes the wavefunction to "take a stand". General Relativity is "deterministic" while QM is not. The solution probably will lie on the side of QM, in my opinion, because it can shown to be reduced to the macroscopic level for situations that do not involve strong gravitational forces. However, until the Standard Model is either shown to be true (ie finding Higgs Boson), or shown to be false (Supersymmetry or Grand Unification Theory etc. shown to be true) we will not know the answer.
Does Quantum Mechanics predict localized time dilation?
It looks like what we’re dealing with here is not an ‘objective’ passing of time (something that could be recorded and agreed upon by multiple observers in different lab settings, observers not necessarily being human, but just measuring devices that can ‘witness/measure’ an event), but rather the perception of the passing of time. While we’re able to describe how time actually dilates when an object approaches relativistic speeds (relativity theory), describing our experience of the passing of time is more of a phenomenological or philosophical question. While there may be a scientific answer for why this may be the case in a field such as cognitive science, there is not any formal physics for describing our perception of time. This is more within the realm of philosophy of mind or cognitive science. I would suggest funneling your questions towards those fields.One great place to start would be the Stanford Encyclopedia of Philosophy. I’ve found an article titled “The Experience and Perception of Time” here: The Experience and Perception of Time
Is General relativity as important as Quantum Mechanics?
Roughly speaking:About 40% of today's physics depends, directly or indirectly, on Quantum Mechanics.About 20% of today's physics depends, directly or indirectly, on Special Relativity.About 10% of today's physics depends, directly or indirectly, on General Relativity.Comparatively speaking:While on the Earth, Quantum Mechanics is more crucial than General Relativity.While in the Space, General Relativity is more crucial than Quantum Mechanics.
Are Entropy and Quantum Mechanics related? If so, how?
The relation is considered by many scientists as yet not satisfactory. Quantum physics describes two distinct processes: 1. Evolution 2. Measurement (or observation). The entropy does not change with evolution, because the distribution among states does not change. The only difference from classical physics here is that the states are quantum states, not classical states. The entropy can increase only at observation, when any quantum state may be projected to a few observation/measurement states. There are different approaches to understand the evolution and measurement in unified manner. For example: there is a 'standard orthodox' interpretation, there is Everett multi-universe, and there is Penrose hypothesis. The issue is being given more attention now also in relation to development of quantum computing.
Must one know Hamiltonian/Relativistic/Lagrangian mechanics to study quantum mechanics?
For Griffiths[1], I don’t think there are any prerequisites other than the usual Calc. I, II, III, Differential Equations, and Linear Algebra.For Shankar[2], it would help to know some Hamiltonian and Lagrangian Mechanics, because although he goes over it in Chapter 2, it is more of a review than a introduction to the topic. To go over this, I would suggest going over those sections in Marion and Thornton’s Classical Dynamics of Particles and Systems[3]. I would also suggest doing a quick review of electromagnetism through Introduction to Electrodynamics by Griffiths[4].If I may also provide a couple suggestions, you should also read The Feynman Lectures on Physics Vol. 3[5] and Dirac’s Principles of Quantum Mechanics[6]. After this you can start reading Feynman and Hibbs’ Path Integrals in Quantum Mechanics[7] and other higher level books with ease.Right now my internet is slow, so comment on this to tell me if the links are working.EDIT: Link 7 was not correct. Trying a new one in a few minutes.EDIT 2: Sorry, couldn’t find it for free online :(Footnotes[1] http://www.fisica.net/quantica/G...[2] http://home.basu.ac.ir/~psu/Book...[3] classical dynamics[4] http://www.ifm.umich.mx/~villase...[5] FLP Vol. III Table of Contents[6] http://digbib.ubka.uni-karlsruhe...[7] Quantum Mechanics and Path Integrals: Emended Edition (Dover Books on Physics): Richard P. Feynman, Albert R. Hibbs, Daniel F. Styer: 0800759477227: Amazon.com: Books
Explain quantum mechanics in one sentence?
One sentence? That's easy: "Give up!" I mean, it's a bit like asking for a one-sentence synopsis of Tolstoy's "War and Peace." StarrySky gave a taste of it in 5 or 6 sentences. If it has to be a single sentence, maybe (and this is strictly the non-relativistic form), Everything that can be known about a physical system is contained in its wave function, which is a complex-valued function of space and time, which obeys the superposition principle, and whose time-development is determined by the Schrödinger equation, such that its squared modulus is the probability density of finding a given particle at a given location in space and time. It would take more verbiage to explain a lot of those things, and many, many more sentences to describe some of their fundamental consequences. Or, you could always just give up.