I find plane waves are uncompatible with light cone.

Perhaps plane waves are "virtual" and can never be measured in that case, shouldn't we call plane waves as "virtual plane waves"? (other option could be that plane waves allows waves travel faster than c)

I would like to clarify this point through this question.

If plane waves would exist(as measurable), then higher than c speed could be reached like this:

A wave going from X to Y at a speed c, it will reach Z at higher than c speed, because it will reach at same time, traveling more distance.

(X).
|   
v   
________________________________________________
plane waves ________________________________________________
going X to Y ________________________________________________
(Y). (Z).

In a real situation the wave will be a circle (or a sphere in 3d) so it will get Z later then that's not a plane wave.

The other three forces' mediating particles (photons etc.) are absorbed by their appropriate charge-carrying particles, but I can't seem to find a clear answer that applies to the gravitational force in a quantified scenario.

The different answers to this most basis question seem to elude me in frameworks of String theory and LQG, though it becomes more intuitive in the latter

A water pipe having a 2.55 cm inside diameter carries water into the basement of a house at a speed of 0.760 m/s and a pressure of 237 kPa. If the pipe tapers to 1.56 cm and rises to the second floor 6.04 m above the input point, what are the (a) speed and (b) water pressure at the second floor?

Please Explain. Thanks!

Two very large parallel sheets are 5.00 cm apart. Sheet A carries a uniform surface charge density of -8.30?C/m2 , and sheet B, which is to the right of A, carries a uniform charge of 12.2?C/m2 . Assume the sheets are large enough to be treated as infinite.

Find the magnitude of the net electric field these sheets produce at a point 4.00 cm to the right of sheet A.

Find the magnitude of the net electric field these sheets produce at a point 4.00 cm to the left of sheet A.

Find the magnitude of the net electric field these sheets produce at a point 4.00 cm to the right of sheet B.

Three children, each of weight 361 N, make a log raft by lashing together logs of diameter 0.21 m and length 1.60 m. How many logs will be needed to keep them afloat in fresh water? Take the density of the logs to be 800 kg/m³.

Laser beams are said to have high "spatial coherence". This means that the beam is highly concentrated even at long distances (low spread).

Can this be achieved with radio waves (much longer waves) or is it due to laser's stimulated emission?

Is is possible to set a swing into oscillations without touching the ground? This occurred to me while watching the second pirates movie. There is a scene where the ship's crew is suspended in a cage from a bridge in between two cliffs. They escape by swinging the cage towards one of the cliff. Is that even possible?

Update: From the answers, it is clear that it is possible to make the swing oscillate. Assuming the model Mark has proposed would there be limits to much you can swing? Is it possible to quantify it?

When you stick ice in a drink, AFAICT (the last physics I took was in high school) two things cool the drink:

• The ice, being cooler than the drink, gets heat transferred to it from the drink (Newton's law of cooling). (This continues after it melts, too.)
• The ice melts, and the cool liquid mixes with the drink, which makes the mixture feel cooler.

My first question is, to what extent does each of these cool the drink: which has a greater effect, and how much greater?

Secondly, how much of the cooling by the first method (heat transfer) is without melting the ice? That is, is there any significant amount of heat transfer to each speck of ice before it's melted, and how much does that cumulatively affect the drink's temperature?

I suppose all this will depend on a bunch of variables, like the shape and number of ice cubes and various temperatures and volumes. But any light that can be shed, let's say for "typical" situations, would be appreciated.

I'm trying to get motivated in learning the Atiyah-Singer index theorem. In most places I read about it, e.g. wikipedia, it is mentioned that the theorem is important in theoretical physics. So my question is, what are some examples of these applications?

I am studying social networks in terms of graph theory and linear algebra. I know that physicists have published and worked a lot in this field. This causes me to assume that there are sub-fields in physics which overlap in the essence of their problems with those of small world networks. Which natural phenomena exhibit these kind of features similar to small world networks?

I would like to know that, so maybe I can look at those problems to get inspiration that can be taken to social network theory.

To suck water through a straw, you create a partial vacuum in your lungs. Water rises through the straw until the pressure in the straw at the water level equals atmospheric pressure. This corresponds to drinking water through a straw about ten meters long at maximum.

By taping several straws together, a friend and I drank through a 3.07m straw. I think we may have had some leaking preventing us going higher. Also, we were about to empty the red cup into the straw completely.

My question is about what would happen if Superman were to drink through a straw by creating a complete vacuum in the straw. The water would rise to ten meters in the steady state, but if he created the vacuum suddenly, would the water's inertia carry it higher? What would the motion of water up the straw be? What is the highest height he could drink from?

Ignore thermodynamic effects like evaporation and assume the straw is stationary relative to the water and that there is no friction.

I want to compare the much-talked about Cheeta running prosthesis to a the normal running process in terms of force and energy, but I don't know where to start. How would you start the comparison? A mathematical model would be much appreciated.

A 0.66 kg copper rod rests on two horizontal rails 0.66 m apart and carries a current of 65 A from one rail to the other. The coefficient of static friction between rod and rails is 0.54. What is the smallest magnetic field (not necessarily vertical ) that would cause the rod to slide?

a)What is the angle of B from the vertical? (deg)

b) What is the magnitude of B?

What does an atom radiate: a wave packet or a single photon?

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?