Q & A: Acceleration of light and electron motion

What is the acceleration of light and how is it worked out? and also why do electrons move, where do they gain the energy for this movement, as they never stop moving within their energy levels does it mean their energy is infinite?
- James (age 17)

Ahh, your first question is the easy one! Light travels at the speed of light in vacuum, which is a constant. So there's no speeding up or slowing down.

Light "slows down" however when it travels through materials, like glass or water. In reality, photons are absorbed and re-emitted by the atoms of the material in which the light is traveling. You can work out the speed of light in a material by dividing the speed of light in vacuum (about 3 times 10^8 meters/second) by the refractive index of the material, which is around 1.4 for most kinds of glass, for example.

Light will react to a gravitational field and change its direction (again, not really "accelerating" -- Einstein tells us this effect comes from the fact that space and time are not "flat" and the light rays just follow the shortest distance between two points, which may be curved). When a photon travels into a gravitational potential, it picks up energy and changes color, becoming "blueshifted". On the way out, it becomes "redshifted" as it loses energy. An observer will always see the photon traveling at the speed of light as it reaches him, however.

Electrons move all the time. There are two kinds of "perpetual motion machines" -- machines in which the parts move all the time, and machines from which you can extract energy from it while leaving it in the original state. The first kind doesn't violate energy conservation or anything -- motion may continue indefinitely without adding or subtracting energy -- there's no "friction" for electrons in their lowest energy state orbits around atomic nuclei. There's also no average velocity of these electrons either, but if you were to make a measurement of the instantaneous speed of an electron in an atom at any instant of time, you will find it is moving.

What makes this all okay is that the electrons cannot lose energy if they are already in their lowest energy state. Quantum mechanics has the weird feature that there is such a thing as a lowest energy state, which is usually a tightly bound state where the electron is found close to the nucleus of an atom. Get it any closer on average, and you have to confine it to a smaller volume of space. Confining electrons to small volumes of space increases the expectation value of their speed (while reducing the electrostatic potential energy because opposite charges attract). At some happy equilibrium, the energy is minimized -- bring the electron in closer and it has to move more quickly, increasing energy, take it away, and the electrostatic potential energy is higher.

Tom

(published on 10/22/2007)

I understand that light continues at a constant speed going forward and backward, however I have heard rumors that it actually accelerates going 'sideways'. Is this true? please explain. Thank you.
- Ryan (age McCartney )
Fenton, MO, USA

Ryan- Those rumors are right. I changed some slightly misleading words in the previous answer.

If we try to picture the behavior of light in the sort of space we intuitively believe in (Euclid's), then we say light curves. You can measure that curvature as light from a distant star goes past the sun. Plot the apparent position of a star as the earth turns, and you get a circle in the sky. As the starlight goes near the sun the apparent position gets ahead of schedule or behind or a little off-track sideways, just as it would if the light ray bent toward the sun.

The effect agrees with the predictions of General Relativity. However, those predictions are not quite in agreement with that intuitive picture. If we thought of light as a particle whizzing along in Euclid's space, attracted to the Sun, we'd get some curvature- but only half of what's measured. The rest comes from the full structure of General Relativity, which says that the geometry of space is altered by gravity. You can say that light travels in the closest thing to a straight line that's available in that spacetime.

As Tom mentioned, the part of the gravitational effect that you might classically expect to speed the light up or slow it down instead ends up changing the clock rates in different parts of space. You see that as the light's frequency being shifted up or down.

Mike W.

(published on 03/31/11)

You explain that light does not accelerate when it moves at the speed of light. But when light is sent out, as a photon, it has to accelerate from speed 0 m/s to 3,0*10^8 m/s. How fast does this happen? Light can't just suddenly move at its maximum speed, it has to accelerate like every other object in motion has to.
- Oda (age 18)
Norway

You say "Light can't just suddenly move at its maximum speed, it has to accelerate like every other object in motion ..." Although that sounds reasonable, it just isn't true. Light is born moving at its full speed.

Mike W.

(published on 07/17/12)