Momentum of light sans Maxwell

• Will Koeppen
In summary, light clocks work the same whether or not the mirrors are moving, because Maxwell's equations transform the E and B fields properly to take into account the motion. Aberration is when the path of the light beam in a moving frame becomes angled forward.
Will Koeppen
I have an easy question but nonetheless I have not been able to find the answer: within the context of special relativity, in particular with light clocks, where the two opposite mirrors of a hypothetical light clock are traveling along very fast, they nonetheless do not leave the emitted photon behind, where it would miss the opposite mirror completely because the mirror has sped away, but the light instead, due to it's momentum, "vectors" forward to just the right position to reflect off the opposite mirror and then in turn angle back to the first mirror. How is this momentum of light demonstrated experimentally?

Will Koeppen said:
I have an easy question but nonetheless I have not been able to find the answer: within the context of special relativity, in particular with light clocks, where the two opposite mirrors of a hypothetical light clock are traveling along very fast, they nonetheless do not leave the emitted photon behind, where it would miss the opposite mirror completely because the mirror has sped away, but the light instead, due to it's momentum, "vectors" forward to just the right position to reflect off the opposite mirror and then in turn angle back to the first mirror. How is this momentum of light demonstrated experimentally?

Well, there's the way that light pressure makes the tail of a comet point away from the Sun (although solar wind also contributes to that effect). There's the photoelectric effect, in which light striking a metal surface will impart momentum to electrons in the metal, knocking them free. You'll find plenty of other experiments if you google around.

However, you don't need this momentum to explain the behavior of the light in the light clock. If you start with Maxwell's equations and solve for the behavior of the light waves, you'll get the same path between the mirrors whether they're moving or not; this works because Maxwell's equations transform the E and B fields properly to allow for the motion.

Will Koeppen said:
I have an easy question but nonetheless I have not been able to find the answer: within the context of special relativity, in particular with light clocks, where the two opposite mirrors of a hypothetical light clock are traveling along very fast, they nonetheless do not leave the emitted photon behind, where it would miss the opposite mirror completely because the mirror has sped away, but the light instead, due to it's momentum, "vectors" forward to just the right position to reflect off the opposite mirror and then in turn angle back to the first mirror. How is this momentum of light demonstrated experimentally?
In the rest frame of the mirrors, you aim the photon to hit the second mirror, and it does. Intuitively then, it must hit the mirror in all frames. The fact that it hits the mirror cannot possibly depend on which frame you use to describe it!

Mathematically, it's called aberration, aka the headlight effect. The path of a photon in a moving frame becomes angled forward.

Let's say in the mirror's rest frame, the photon is moving at an angle θ wrt the x axis. The wave vector of the photon is then

k = (kx, ky, kz, kt) = (ω cos θ, ω sin θ, 0, ω).

The Lorentz transformation is

kx' = γ(kx + (v/c) kt) = γω(cos θ + (v/c))
ky' = ky = ω sin θ
kz' = kz = 0
kt' = γ(kt + (v/c) kx) = γω(1 + (v/c) cos θ)

from which we can read off the relationship between ω and ω' (the Doppler effect), and the relationship between θ and θ' (the aberration)

kx' = ω' cos θ' = γω(cos θ + (v/c))
ky' = ω' sin θ' = ω sin θ
kt' = ω' = γω(1 + (v/c) cos θ)

In our particular case, in the original frame the light beam is perpendicular to the relative motion, so cos θ is zero, but cos θ' is not.

Thanks Nugatory and Bill_K, it's back to the books for me. I guess I have been too pre-occupied looking for an experiment that basically duplicated a light clock. I see now there are other angles from which I might consider the answer to my question.

The momentum of light is a fundamental property of electromagnetic waves and is described by Maxwell's equations. These equations were developed by James Clerk Maxwell in the 19th century and provide a comprehensive understanding of the behavior of electromagnetic radiation, including light.

In the context of special relativity, the momentum of light can be seen in the phenomenon of time dilation, where the speed of light remains constant regardless of the observer's reference frame. This has been experimentally demonstrated through various experiments, such as the Michelson-Morley experiment and the Kennedy-Thorndike experiment.

Additionally, the momentum of light can also be demonstrated through the photoelectric effect, where light particles (photons) transfer their momentum to electrons, causing them to be ejected from a metal surface. This phenomenon was first observed by Albert Einstein in 1905 and has since been confirmed through numerous experiments.

In the case of the hypothetical light clock described in the question, the momentum of light can be seen in the fact that the photon is able to reach the opposite mirror despite the high speed of the mirrors. This is due to the fact that the photon carries momentum and can change its direction of travel to compensate for the movement of the mirrors.

Overall, the momentum of light has been extensively studied and demonstrated experimentally through various experiments and phenomena. It is a crucial concept in understanding the behavior of light and electromagnetic radiation.

What is momentum of light sans Maxwell?

Momentum of light sans Maxwell refers to the concept of light having momentum without taking into account the contributions of James Clerk Maxwell's theory of electromagnetism. This theory suggests that light is made up of electromagnetic waves that carry energy and momentum.

What is the significance of momentum of light sans Maxwell?

The significance of momentum of light sans Maxwell is that it challenges our understanding of light as being purely a wave phenomenon. It suggests that light also has a particle-like nature and can exert a force on objects, which was not fully understood until the development of quantum mechanics.

How is momentum of light sans Maxwell measured?

Momentum of light sans Maxwell can be measured experimentally using various methods. One common method is through the use of a light mill, which consists of a set of vanes that are suspended in a vacuum. When light shines on the vanes, they begin to rotate, demonstrating the transfer of momentum from the light to the vanes.

What are the implications of momentum of light sans Maxwell?

The implications of momentum of light sans Maxwell are still being studied and debated. Some theories suggest that this momentum could have significant effects on objects at the microscopic level, while others argue that the effects are negligible. Further research is needed to fully understand the implications of this concept.

How does momentum of light sans Maxwell relate to other fundamental concepts?

Momentum of light sans Maxwell is closely related to other fundamental concepts such as energy, mass, and velocity. It also has implications for the nature of light and its interactions with matter, as well as the development of theories like quantum mechanics and relativity that seek to explain the behavior of particles at the atomic and subatomic levels.

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