I was told that the Galilean relative velocity rule does not apply to the speed of light. No matter how fast two objects are moving, the speed of light will remain same for both of them.

How and why is this possible?

Also, why can't anything travel faster than light?

A wheel of radius b is rolling along a muddy road with a speed v. Particles of mud attached to the wheel are being continuously thrown off from all points of the wheel. If v2 > 2bg, where g is the acceleration of gravity, find the maximum height above the road attained by the mud, H = H(b,v,g).

I heard somewhere that quarks have a property called 'colour' - what does this mean?

I am trying to get a common understanding from these two previous questions:

Why does the mass of an object increase when its speed approaches that of light?
What happens if light/particles exceeded the speed of light for a particular medium (sic)

Does the increase of mass occur only if the particle approaches c (speed of light in a vacuum) or if it simply approaches the speed of light in its current medium? For example, does the mass of charged particles increase during Cherenkov radiation?

The nose of an ultralight plane is pointed south, and its airspeed indicator shows 39m/s . The plane is in a 12m/s wind blowing toward the southwest relative to the earth.

Question A:

Letting x be east and y be north, find the components of v? P/E (the velocity of the plane relative to the earth).

Question B:

Find the magnitude of v? P/E.

Question C:

Find the direction of v? P/E.

Any help is appreciated!

Three identical point charges of charge q = 5 uC are placed at the vertices (corners) of an equilateral triangle. If the side of triangle is a = 3.3m, what is the magnitude, in N/C, of the electric field at the point P in one of the sides of the triangle midway between two of the charges?

Yesterday I looked underwater with my eyes open (and no goggles) and I realized I can't see anything clearly. Everything looks very, very blurry. My guess is that the eye needs direct contact with air in order to work properly. With water, the refraction index is different, and the eye lens are not able to compensate for correct focalization on the retina.

Am I right ? If so, what lenses should one wear in order to see clearly while under water ?

Two equally charged particles, held 4.2 x 10^-3 m apart, are released from rest. The initial acceleration of the first particle is observed to be 7.4 m/s² and that of the second to be 11 m/s². If the mass of the first particle is 5.9 x 10^-7 kg, what are (a) the mass of the second particle and (b) the magnitude of the charge (in C) of each particle?

Decoherence times can be estimated and are inverse functions of mass. Since there are no upper bounds on mass, can decoherence time be shorter than Planck time?

Initially Wheeler and Feynman postulated that, the electromagnetic field is just a set of bookkeeping variables required in a Hamiltonian description. This is very neat because makes the point of divergent vacuum energy a moot point (i.e: an example of asking the wrong question)

However, a few years later (1951), Feynman wrote to Wheeler that this approach would not be able to explain vacuum polarization.

Anyone knows what was the argument for saying so? I don't see how allowing both processes with entry and exit particles and processes that begin in pair-creation and end in pair-annihilation makes the existence of a field a requirement.

You've probably ridden on the fairground ride called the "Tilt-A-Whirl", or--as Disneyland calls it--the "Spinning Teacups", as well as other fairground rides that employ epicycles. You can really feel the centrifugal force strongly when your car spins complementary to the spin of the main rotor.

Now, can that extra force be measured on Earth as our orbit around the Sun complements the Sun's orbit around the galactic hub? Has anyone done it?

What are the main practical applications that a Bose-Einstein condensate can have?

Two tiny objects with equal charges of 83.0

Suppose you have to specify the moment in time when a given event occurred, a "zero time". The record must be accurate to the minute, and be obtainable even after thousands of years. All the measures of time we currently have are relative to a well defined zero, but the zero is not easy to backtrack exactly.

One possibility would be to take a sample of Carbon with a well defined, very accurate amount of 14C, and say: the event occurred when the 14C was x%. At any time, measuring the rate of decay, you would know when the event occurred. This however, requires a physical entity to measure, which may be lost.

Another way would be to give the time lapsed after a well defined series of solar eclipses. In order to define precisely the context, you would say a list of (say) five consecutive eclipses and the places on Earth where they were total, and then a time gap from the last of the set. At any time in the future, you can backtrack the specified conditions into a celestial mechanics program and find when the event occurred.

Is there a standardized or well recognized method to do so?

I've seen foliation used in the context of "foliation of spacetime" here and elsewhere in papers and such. Generally defined in reference to a "sequence of spatial hypersurfaces." But I don't know what that means either.

Again, I can imagine what these terms mean because of the English language meaning of the words. But what do these mean specifically in reference to the physics of spacetime?