Studying General Relativity, Special relativity and Quantum Physics?
I don't know how far your high school Physics takes you, but let's see... your basic undergraduate coursework would be similar to this: Classical & Elementary Mechanics (kinematics, motion, forces, fluids, Newton, momentum, energy, angular momentum, rigid body motion, etc.) EM and Electrostatics (Coulomb's law, electric structure of matter; conductors and dielectrics, electrostatic field and electrostatic energy, currents, magnetic feilds, Maxwell's equations, etc.) Mech Vibrations and waves (harmonic motion, superposition, forced vibrations and resonance, coupled oscillations, reflection and refraction; phase and group velocity, optics, polarization) Then you get into Relativity: (simultaneity, time dilation, length contraction, and clock synchronization; Lorentz transformation; relativistic effects and paradoxes; Minkowski diagrams, invariants and four-vectors, momentum, energy, and mass, particle collisions, the Schwarzchild metric; gravitational red shift) Quantum Physics (photoelectric effect, Compton scattering, photons, Franck-Hertz experiment, the Bohr atom, electron diffraction, deBroglie waves, and wave-particle duality of matter and light, wave mechanics) Statistical Physics (probability, statistical mechanics, thermodynamics) Then you'll take your advanced courses in Quantum Physics, Mechanics, Electrodynamics, etc.
Is Quantum Mechanics hard to understand/learn? and if so... why?
Quantum Mechanics is hard in two ways: (1) mathematical formalism - it requires a deeper level of mastery of mathematics, and also QM is a theory of probabilities. (2) interpretation of physical reality - so what does the result of probability function tell us? this is not easy to figure out. So when the previous answerer say that even Richard Feyman tells us that no one understand quantum physics, this is what he means - that no one can understand the physical reality that QM presents to us, not that he can't understand the math. Richard Feyman actually invented a whole mathematical approach to solving QM problems, so that definitely was not his problem.
Do people actually understand the theory of relativity?
Generally, no. After watching some relativity youtube videos, remembering the stories my teachers told me, and reading many of the answers on Quora, my conclusion is : no. People here and on youtube do not understand relativity at all. Even those who teach the stories of the paradoxes to students largely don’t know what they are talking about.If you work with accelerators, you need relativity to explain how things work.If you work in astronomy, you use relativity to interpret things, but you don’t really have a controlled experiment where you can manipulate variables easily.Based on what I know about how relativity works with particle beams, all of the youtube videos involving trains, tunnels, flashlights and whatnot look WRONG in some significant way.Moving trains do not “look” contracted to a stationary observer. Depending on the method used to “see” them, either their particles look contracted and the train is a normal length OR their particles look normal but the train looks streaked out and long.When a bunch of particles is accelerated, the fields of the particles contract like pancakes in the direction of travel, but the space between the particles doesn’t contract. Since most of an object is made up of space, it won’t look contracted after it has been accelerated.I spent most of my phd/postdoc career measuring the length of relativistic particle bunches in various ways and they are the same length in the lab frame before and after they are accelerated, but after they are accelerated, their particles are short in the lab frame. In the rest frame of the particle bunch relative to our rest frame, the particle bunch is longer compared to when it was moving more slowly. For more details, see: Is length contraction only a result related to observation, or a real contraction?This interpretation is consistent with Feynmann’s How did Feynman explain that magnetic fields are created by moving charges due to length contraction? and Kyle Foot’s answer to Why does a moving charge produce a magnetic field around it? but not necessarily with all of Einstein’s writings involving short measuring sticks and contracted distances between objects.I tried to give answers to other questions on relativity, but because I didn’t answer in terms of nonsensical imaginary trains, people thought I was wrong and downvoted my answers.C’mon Quora - you are believing in fairytales.
Which do you think is harder for a layperson to understand, relativity or quantum physics? Why?
I’d say quantum physics, without a doubt.Relativity theory is not exactly easy to understand either, but there are visualizations. It can be grasped, so long as you are willing to let go of some preconceptions about the nature of space and time. And if you have the attention span to make sense of a coordinate chart, visualizations of the hyperbolic rotations that correspond to velocity transformations can even be considered intuitive.Quantum physics is something else altogether. When you follow the mathematical logic of quantum physics, you realize that the crucial departure from classical physics is when it offers solutions describing Nature that make no sense whatsoever classically. How can an electron not have a well-defined position? Any attempt at intuition fails: The moment you visualize that electron as some miniature cannonball, you are already going down the wrong path. For the physicist, letting go of naive intuition leaves the math; and after a while, that math may bring about its own intuitive understanding, which is much more abstract, not related to everyday, tangible (classical) experiences, but makes sense anyway. For the layperson lacking the math background, this option unfortunately is unavailable. So you are left with accepting bizarre statements from physicists on faith. Worse yet, you cannot tell the difference between real physics and hype: never mind the electron’s position, you may be reading pieces about Schrödinger’s cat being dead and alive (it isn’t), about “entanglement” (implying, wrongly, that it can be used for instantaneous communication), about “teleportation” (without the accompanying explanation that it is simply the quantum state of an elementary particle that is being communicated to a receiving station), or even speculative “interpretations” involving multiple universes and such nonsense (stuff you almost never see in the actual physics literature).Incidentally, quantum physics, especially quantum field theory, is also harder for professional physicists to master. In addition to the conceptual difficulties, the math is also much more cumbersome, much more involved, especially when you get down to the nitty-gritty details, e.g., something mundane such as calculating a cross-section in a particle physics experiment.
Is it true that the mathematics for general relativity are harder than the mathematics for quantum mechanics?
Holy cow, yes. Basic non-relativistic quantum mechanics requires just the mathematics of Hilbert space, which are fairly straightforward vector spaces. Solutions to simple problems can be found at the undergraduate level (and have to be, several times a week in problem sets).General Relativity involves tensor fields on various manifolds, and are horrible to work with. Solutions to simple problems are named in honour of their discoverers, because it is so rare to find them.That said, quantum mechanics gets much harder once you demand that it is relativistic (Dirac equation) and then extend it to quantum fields (QFT). There, the techniques required start to become comparable to GR, and in both cases, it is a matter of working with approximation and perturbation schemes, which are messy and difficult. And then when you head off into quantum chromodynamics and string theory, the mathematics gets properly hard.
Is Quantum Mechanics harder or Calculus?
Quantum Mechanics is harder, it uses calculus, but it also uses unfamiliar concepts such as tunelling and the wave nature of matter.
Deep questions on General Relativity?
You've asked a question no one has an answer for...what is gravity...really? There is a chicken and egg issue with Al's bent space model. The claim is that mass bends space-time around it (like that bowling ball on a rubber tarpaulin we've all come to know and love) So the bent space creates a gravitational force field with the lines of force pointing toward the source mass. What is glossed over is, if mass bends space-time and that causes the effects we attribute to gravity, then what bends the space-time? I understand bent space-time results from the fact that light speed is constant no matter what. So to explain that, space time has to bend to keep c constant no matter where or when the source and observer frames of reference are. But, and this is a big BUT, that's just mathematics...it doesn't tell us how space-time is bent, just that it has to be. On the other hand, the graviton model, which is far from confirmed, says there are tiny massless, lightspeed particles that fly out of all mass (continually without end) and give the come hither message to all other mass they encounter. The major thing this model has going for it is that we've found the messenger particles for the other three fundamental forces: strong and weak atomic, and EM. So why not for the fourth one...why not for gravity? So in the case of gravitons, we actually have a how...the graviton...to explain a gravity field. But we are clueless about what that particle is. Think about it, as long as there is a mass, it will spew forth gravitons at the same field intensity. Endless force and consequent energy...as long as the source mass is constant. And spewing out gravitons does not seem to erode the mass from which they spring...unlike photons. Photons are the messenger particles for EM force. But in creating them, stuff is used up. Stars, for example, fuse themselves to death while creating light and heat. The filament in your desk lamp eventually burns out. Energy and mass are used up in creating photons, but what energy or mass is used up in creating gravitons? What are these things that, like the TimeEx, keep on ticking? If the cosmos is really made up of strings, then the fabric they create is real. So, just perhaps, bent space time can be attributed to gravitons that give the come hither look to the mass bearing strings. That is, real space is just like a rubber tarpaulin after all...hey, could be.