The embarrassing lightness of photons

Here’s a conundrum for you. What is the momentum of light in a transparent dielectric medium?

If the answer doesn’t trip off your tongue, that might be because nobody else knows either. Amazingly, there are two lines of thought:
In 1908, the German mathematician Hermann Minkowski guessed that the momentum was equal to nE/c (where n is the refractive index, and E and c are the energy and speed of light in a vacuum).

A year later,  his contemporary Max Abraham suggested that the momentum is equal to E/nc.

A century since then and we’re none the wiser. An embarrassing state of affairs for theoretical physics, wouldn’t you agree?

Today Weilong She and pals from Sun Yat-Sen University in Guangzhou, China, announce that they have the answer. And they got it by measuring the recoil on the end face of a nanometre-sized fibre exerted by outgoing light. (This isn’t the well known pressure caused by specular reflection but something  a little more subtle.)

The experiment is impressive because it is designed in such a way that if Minkowski were correct the fibre should be pushed in one direction and in the other if Abraham were correct.

So the result is the first to unambiguously favour one theorist over the other.

And the winner is…drum roll…Abraham.

Ref:  arxiv.org/abs/0806.2442: Observation of a Push Force on the End Face of a nm Fiber Taper Exerted by Outgoing Light

7 Responses to “The embarrassing lightness of photons”

1. Kent says:

I wonder how Minkowski came up with the idea that the momentum increases when the speed of the photon decreases (with the mass of the proton staying the same, i.e zero). I’m sure he had his justifications though. He was a smart boy. 🙂

Great experiment by the way.

2. mofa says:

This is not so unusual: if jou set E~mv² and p~mv you have p~E/v (classical).
This is however surely not Minkowskis complete consideration.

3. Enginerd says:

“This is not so unusual: if jou set E~mv² and p~mv you have p~E/v (classical).
This is however surely not Minkowskis complete consideration.”

This would be the wrong thing to do for photons. For photons, we know that p= hbar * k, at least in a vacuum.

If we assume the conservation of photon energy in the medium (which I believe we must), then E_vac = E_med. E_vac = p_vac*c = hbar*k_vac*c. E_med = hbar*k_med*n*c. So if E_vac = E_med, and p_med = hbar*k_med, then E_med = p_med * n * c = E_vac, and p = E/(n*c).

I sort of had to reason backwards from the solution to get this, but the axioms are E_vac = E_med (conservation of energy) and p_med = hbar*k_med, momentum in the medium is determined by the wavenumber in the medium same as vacuum. Both quite reasonable things to assume, except how the photon loses momentum upon entering a medium and gains in back again I don’t know.

4. mofa says:

It was not my intention to give a derivation of any of above formulas but to show that p~E/v does not necessarily mean that the momentum p decreases with increasing velocity v.

5. Robert says:

Surely you mean E/(nc).

6. mofa says:

No with n being n=c/v I mean (En)/c which is the Minkovski-suggestion.
It was meant as a reply to “I wonder how Minkowski came up with the idea that the momentum increases when the speed of the photon decreases”.

7. ZEPHIR says:

2mofa: I haven’t studied these derivations, but maybe Minksowski has applied a dual view to the same phenomena. For example, by Aether Wave Theory the gravitational lensing can be explained by two dual perspectives: the relativistic and quantum mechanics one:

http://superstruny.aspweb.cz/images/fyzika/aether/light_gravity.gif

The first perspective considers, the light speed is constant and the space-time is deformed. The perspective of quantum mechanics considers, the light speed is changing in flat space-time. It’s apparent, the observer inside of gravitational lens would prefer the first perspective, while the outer observer will tend to describe the relativistic aberration from Hamilton mechanics perspective. With the same dual view we can met at the example of LQG and string theory duality and in many other places of contemporary physics (every truth has at least two sides).

So MAYBE it’s possible, Minkowski has considered, the light is moving along a longer path in the dense refractive environment, thus exhibiting a larger momentum related to the unit of volume, as perceived from outer perspective. This example illustrates clearly, a more general approach of Aether theory (Tertium comparationis) is required in physics to distinguish safely between two dual perspective.