When a photon falls into a black hole, the black hole increases in mass by m = E/c^2, where E was the energy of the photon. This is required by the conservation of energy and momentum. Energy can be thought of as the zeroth component of the momentum 4-vector, and each component of the 4-vector...
Energy is fundamentally a mysterious concept. Energy is closely related to changes in time. E = hf is one example. How fast a quantum wave oscillates (frequency) is proportional to how much energy it has.
Another example is E = mc^2 from relativity. When a particle is stationary, it's still...
If they were identical quantum particles that were indistinguishable, then yes you wouldn't be able to tell Action A and B would be indistinguishable. With large objects like these balls, you could theoretically be able to tell based on studying the balls closely enough before hand, detecting...
Yo just plug that mofo numerator equation into WolframAlpha:
http://www.wolframalpha.com/input/?i=fourth+derivative+of+1-cos%281-cosx%29
I agree, it's a nasty numerator, but you can just plug in x = 0 now. Looking at it real quick, and it's looks like the numerator at 0 equals 3, so the limit...
Thank you for all your replies, especially you geoduck I liked your explanation of how at smallest enough time and length scales, the neutrino will spontaneously split apart into a W+ and e-, because the uncertainty in energy becomes very large at very small time and space scales.
From what I...
You've heard of fermionic fields though right? I just sort of made it up the terms "photon field" and "electron field" on the spot.
http://en.wikipedia.org/wiki/Fermionic_field
The electron field is just a type of fermionic field governed by the Dirac equation. That's my definition anyway...
This question is similar to asking what is a photon? Photons and electrons and other elementary particles are not actually little billiard balls that are flying around high speeds. They are both quantum excitations of their respective fields.
The entire universe is filled with a photon field...
I've read that the neutron has a magnetic moment because it is made of composite particles, namely 1 up and 2 down quarks.
But why does the neutrino, which is electrically neutral and a fundamental particle, have a nonzero (albeit very small) magnetic moment? How is that even possible? Does...
Maybe only closed timelike loops are allowed modes of time travel. What I mean to say is that perhaps time travel is only possible if A causes B, and B causes C, and then C causes A, thus closing a loop between those three events. For example, you could only send a message to your past self if...
It's there any shortcuts you use to writing \hbar? It's seems kinda cumbersome to have to keep having to copy and paste that over and over. Also, \hbar rocks, it's way better than h, wouldn't you agree?
Also, there's two reasons I'm worrying about this amplitude rotation business. Sure...
Also, I think made a huge mistake in my analysis, as you set L → ∞, V → 0. Which means it's totally possible to get E = 0 for a free particle as long has you extend a uniform negative potential energy across the entire x dimension. In fact there would even be negative energy states. Every...
Right, exactly, you can't have E = 0 when with V = 0. But what happens when we set V exactly to the negative of the first energy eigenstate when V = 0? Thus we set V = -h2(pi/L)2/2m, for a given L and m. What then, shouldn't the potential energy perfectly cancel out the kinetic energy from...
The particle can have a definite energy, it's position that's uncertain. When I think about a wavefunction on a one dimensional box, I imagine the x-axis as the position, which then leaves the y and z axises in my mind to represent the real and imaginary parts of the wavefunction. I like to...
What i meant is the intepretation of angular frequency w. the wave function is "spinning" in time through complex phase space. I am not referring to intrinsic spin. Anyway, the higher the energy, the faster the wave function rotates around in phase space. The magnitude squared stays the same at...
But what is the interpretation of E = 0? Does that mean the wavevector is standing still in Hilbert Space? Is this possible or impossible? Also, do negative energy states spin in the opposite direction such that ψ(x,t) = e+i|E|t/h*ψ(x)? This would affect the time evolution of normal states...