Re: Is there any experimantal proof that electromagnetic wave has momentum?

There is strong evidence that photons have measurable momentum. The experiments of P. N. Lebedev, a professor at the University of Moscow, and published in 1910, showed strong evidence of light exerting a pressure on objects. A good description of this, including the experimental setup, can be found here. You can also look this up in the Encyclopedia Britannica under Lebedev, Pyotr Nikolayevich.

In summary, Lebedev was able to measure the torque on a very light rod due to light hitting, what you might consider to be, a "light lever". Light either hits a dark part of the lever, where the momentum imparted comes from absorption, or it hits a shiny part, where the momentum imparted comes from reflection - twice the momentum change that you get with absorption since the photon ends up with the opposite momentum (Newton's third law). Looking at the difference between these two cases gives the torque due to the momentum of the photons. I want to stress that this is a very very very small torque and this is what we commonly refer to as a "hero experiment". It is tricky.

Before I jump into a further discussion about light pressure (or photon momentum), I want to make it clear that we don't need quantum mechanics to understand that photons can exert a force. It is somewhat simpler to think about the momentum of a single photon, assuming you believe Einstein's explanation of the photoelectric effect in terms of "lumps" of light, but James Clark Maxwell had already predicted light pressure almost a century before in classical electrodynamics. It was this theory that had motivated Lebedev. Light was a wave in those days.

Now let us get into the interesting discussion:

First I want to start with something called a light mill. The rotation of a light mill was thought to be the first experimental observation of light pressure, but it was soon realised that the mill turned the wrong way. A light mill has vanes which are black on one side and shiny on the other. Recall that a shiny surface gets twice the force as a dark surface and then when you watch a light mill turn in the direction "towards the shiny side", you know you are in trouble. We used to have one in the classroom when I was at school and it really bothered me that it went the wrong way. Something like a pie in the face of Newton and Maxwell. Fortunately, the solution as to why it goes the wrong way, is now well known (if not quite complicated), so we can sleep easy once more. See the link to the light mill above.

Well, that was my cautionary note about light mills so let us now think about what light pressure is useful for: Firstly I want to let you know that light pressure is now a widely used tool in cooling atomic gases. Light pressure is used in making something called "optical molasses" where atoms in a light field find it very difficult to move. Generating optical molasses was the first step for Eric Cornell, Wolfgang Ketterle and Carl Wieman to put a bunch of atoms into a state called a Bose-Einstein condensate. These three won the Nobel Prize for their efforts in 2001. These guys were "standing on the shoulders of giants" since they were using techniques for laser cooling developed by Steven Chu, Claude Cohen-Tannoudji and Bill Phillips who won the prize in 1997. If two Nobel prizes in Physics are won within four years one cannot underestimate the importance of the photon momentum.

The second application of light pressure that I want to talk about is in thinking about making "solar sails". By using light pressure to power a space craft, just like a sailing boat uses the wind, it is predicted that a such a craft could propel itself in the vacuum of space without the need for rocket propulsion. This sounds like science fiction (and was for a long time), but a Russian project called Cosmos 1 will very likely be launched at the start of next year (2005) to test this method of propulsion. If it is found to be efficient and controllable, this will be a major step forward in space propulsion since a large fraction of the weight (and cost) of satellites and probes is in the fuel required to get them where they are going. There is also some suggestion that higher speeds will be reached due to the continuous acceleration of the light pressure.

It may be small, but the momentum of a photon is very important.