Been studying hopping conduction and something that everyone is taking for granted is bothering me.

Let's say we have a bunch of sites that are either unoccupied, singly occupied, or doubly occupied. Due to on-site Coulomb repulsion the two electron levels are separated by U energy at a doubly occupied site. Now everyone is saying that the two electrons on the double site are in the spin singlet state due to, I assume, Pauli exclusion. However the two electrons are not in the same energy level - they are separated by U so why is there a restriction on their spins?

Sorry for the layman question, but it's not my field.

Suppose this thought experiment is performed. Light takes 8 minutes to go from the surface of the Sun to Earth. Imagine the Sun is suddenly removed. Clearly, for the remaining 8 minutes, we won't see any difference.

However, I am wondering about the gravitational effect of the Sun. If the propagation of the gravitational force travels with the speed of light, for 8 minutes the Earth will continue to follow an orbit around nothing. If however, gravity is due to a distortion of spacetime, this distortion will cease to exist as soon as the mass is removed, thus the Earth will leave through the orbit tangent.

What is the state of the art of research for this thought experiment? I am pretty sure this is knowledge that can be inferred from observation.

For each statement select P for Positive, N for Negative, or Z for Zero charge (Neutral). (If the first answer is positive, the second negative, and the third neutral (zero net charge), enter PNZ.

A) A negatively charged rod is brought close to a neutral isolated conductor, but it does not touch. The rod is then removed. What is the final charge of the conductor?
B) A negatively charged rod is brought close to a neutral isolated conductor, but it does not touch. The conductor is then grounded while the rod is kept close. If the rod is first taken away, and THEN the ground connection is removed, what is the final charge of the conductor?
C) A negatively charged rod is brought close to a neutral isolated conductor, but it does not touch. The conductor is then grounded while the rod is kept close. If the ground connection is first broken, and THEN the rod is removed, what is the final charge of the conductor?

If I poured water into my tea, would I see more or less of the bottom of the tea-cup?

Intuitively, there would be as many particles blocking as many photons, and so I'd see the bottom just as clearly as before

For S and S' in standard configuration, the Galilean transformations are:

x' = x - vt, y' = y, z' = z, t' = t

From the Lorentz transformations for v << c:

x' = x - vt, y' = y, z' = z, t' = t - vx/c^2

So it looks as if the Galilean transformations become increasingly accurate for:

vx -> 0, v << c

And exact for v = 0 for all x.

Yet, all text books I've come across state that the Galilean transformatons become more accurate for the condition v << c only.

So what are the conditions under which the Galilean transformations become more accurate and why?

Inspired by How do we know that dark matter is dark? and What is the temperature of the surface and core of a neutron star formed 12 billion years ago now equal to?

Where exactly does CMB come from. I've seen it in documentaries as a huge sphere with Earth in the middle. But if all this radiation was ejected from the start of the universe some time after the big bang; why can we see it? Surely the radiation should be travelling away from us? Just like every galaxy is?

In general relativity, light is subject to gravitational pull. Does light generate gravitational pull, and do two beams of light attract each other?

Many physics papers now have dozens of authors per paper. Experimental physics may have multi-organizational and multi-country contributing staffs, but I'd guess that most of the names don't contribute a word or equation to a paper, yet they get individual authorship credit. My question is who determines the author list, does everybody listed have editing privilages, and perhaps most importantly, who decides on their listed order?   

A particle moves in the x-y plane with constant acceleration. At time zero, the particle is at r = <5.0, 2.0> m and has velocity v = <-4.0, 9.0> m/s. The acceleration is constant and is given by a = <4.0, 6.0> m/s2 . (a) Find the velocity at t = 2.0 s. (b) Find the position at t = 4.0 s. Give the magnitude and direction of this position vector. (c) Sketch (approximately to scale) the vector diagrams for vi , vf , and ?v, and for ri , rf , and ?r

From the "no hair theorem" we know that black holes have only 3 characteristic external observables, mass, electric charge and angular momentum (except the possible exceptions in the higher dimensional theories). These make them very similar to elementary particles. One question naively comes to mind. Is it possible that elementary particles are ultimate nuggets of the final stages of black holes after emitting all the Hawking radiation it could?

What percentage of physics PhDs leave physics to become quantitative analysts, work in computer science/information technology or business? Is physics that bad that so many people leave? Was it worth it?

Will a CFL light bulb and an incandescent light bulb, in separate respective closed systems, produce exactly the same amount of overall temperature increase over time?

Assume you have two identical closed systems with gray walls, with a system input of 20 watts of power each.

EDIT added for clarity: (On the packaging of the CFL light bulb the large print equivalent wattage is irrelevant... the input current of both bulbs is a consistent 20 watts of power each. The comparison wattage vs. the actual wattage of the CFL is off subject.)

One has a CFL, one has an ordinary incandescent light bulb. Will both systems increase in heat the exact amount, every hour?

Due to conservation of energy it shouldn't matter if one light source is more efficient, right?... it's the same amount of energy input. One light makes more heat one makes more light, but the light when it hits the gray wall is converted to heat, right?

There is no such thing as loss of energy... it's just converted to another form of energy... and light is converted to heat, right?

The back story of this question is my wondering that if my wife leaves an incandescent light bulb on in the winter time it's not so bad because even though no one is in the room it's still heating up the room. On the other hand if she leaves on a CFL it's more efficient but it should still add heat to our "system," i.e., our home.

(a) Consider two identical metal plates of area A, separated by a non-conducting material which has a thickness d. They are connected in a circuit with a battery and a switch, as shown above. When the switch is open, there is no excess charge on either plate. The switch is then closed. What will happen to the amount of net excess charge on the metal plate that is attached to the negative terminal of the battery? What will happen to the amount of net excess charge on the plate that is connected to the positive terminal of the battery? Explain.

(b) Can excess charges on one plate of a charged parallel plate capacitor interact with excess charges on the other plate? If so how? Note: To say that two charges interact is to say that they exert forces on each other from a distance.

(c) Is there any limit to the amount of charge that can be put on a plate? Explain.

(d) Use qualitative reasoning to anticipate how the amount of charge a pair of parallel plate conductors can hold will change as the area of the plates increases. Explain your reasoning.

(e) Do you think that the amount of net excess charge a given battery can store on the plates will increase or decrease as the spacing, d, between the plates of the capacitor increases? Explain

An airplane flies 560 miles with a tailwind in 2 hours 20 minutes. It takes 3 hours to fly against the headwind. Find the speed of the airplane in still air and the speed of the wind.