# Photon Powered Windmill

#### MarsGhost

Okay, I got one for you all.

Years ago, in school, I saw a propellor shaped thing, mirror side up, black side down. It was resting on a pin in, what I assume was, a vacuumed bell jar. It spins in sunlight as per what you'd expect... But what is the physics behind this? As light never slows due to energy loss, and light is massless, it can't be through that mechanism. The light never changes wavelength is no energy is lost that way. Maybe the force which drives it is proportional to the light absorbed by the mirror and blown out by the black surface? I'd like to know for sure thanks.

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#### JohnnyTheFox

Light moves in little particles called photons which have no mass but momentum < (the part I dont get!) so they basicly hit the blades and give them momentum to move... maybe someone else can give more detail.

#### MarsGhost

But if the momentum is transferred, we have loss of energy in the wave. Something that can never happen unless you have a change in frequency. It'd be like saying you bounce a ball that bounces back with the exact energy it hit an object with, and still move the object. Hmm, creation of energy is where I have a problem.

#### pervect

Staff Emeritus
MarsGhost said:
Okay, I got one for you all.

Years ago, in school, I saw a propellor shaped thing, mirror side up, black side down. It was resting on a pin in, what I assume was, a vacuumed bell jar. It spins in sunlight as per what you'd expect... But what is the physics behind this? As light never slows due to energy loss, and light is massless, it can't be through that mechanism. The light never changes wavelength is no energy is lost that way. Maybe the force which drives it is proportional to the light absorbed by the mirror and blown out by the black surface? I'd like to know for sure thanks.

sci.physics.faq
http://math.ucr.edu/home/baez/physics/General/LightMill/light-mill.html

howstuff works
http://science.howstuffworks.com/question239.htm

the answer turns out to be an effect known as thermal transpiration as mentioned in the FAQ. It takes a more sophisticated instrument to directly measure the pressure of light (but such an instrument is possible - it mostly involved a better suspension and a better vacuum than is found in the typical radiometer).

As far as accounting for energy goes, note that light is reflected by a mirror, and absorbed by a black surface.

Reflection light from a non-moving mirror does not change the frequency (or energy) of the light, it just transfers momentum. However, reflection from a moving mirror does change the frequency (and hence the energy) of the light via the relativsitic doppler shift.

When light is absorbed by a black surface, all of the energy and momentum in the light is absorbed by the surface.

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#### rbj

JohnnyTheFox said:
Light moves in little particles called photons which have no mass but momentum < (the part I dont get!) .
perhaps the reason you don't get it is because it isn't true. i have read this same non-fact (that photons have no mass, but they have momentum) before on this forum and i wonder how this is taught nowadays.

since momentum is

$$p = m v$$

if either mass $m$ or velocity $v$ were zero, so would momentum $p$ be zero. what light doesn't have is rest mass and that's because its velocity is $c$.

since $$E = m c^2$$

and $$E = \hbar \omega$$

then the mass of the photon is $$m = \frac{\hbar \omega}{c^2}$$.

but since relativistic mass is also

$$m = \frac{m_0}{\sqrt{1 - \frac{v^2}{c^2}}}$$

where $m_0$ is the particle's rest mass, and $v$ is the particle's velocity, then

$$m_0 = m \sqrt{1 - \frac{v^2}{c^2}}$$

and because $v = c$, then $m_0 = 0$.

photons have mass. that's the only way they can have momentum with a finite velocity.

r b-j

#### pervect

Staff Emeritus
rbj said:
perhaps the reason you don't get it is because it isn't true. i have read this same non-fact (that photons have no mass, but they have momentum) before on this forum and i wonder how this is taught nowadays.
This is not correct - photons do not have mass. They do however, have energy.

See the sci.physics.faq

http://math.ucr.edu/home/baez/physics/Relativity/SR/light_mass.html [Broken]

for a fuller discussion.

I'll take the liberty of posting a brief quote:

Does light have mass?

The short answer is "no", but it is a qualified "no" because there are odd ways of interpreting the question which could justify the answer "yes".

Light is composed of photons so we could ask if the photon has mass. The answer is then definitely "no": The photon is a massless particle. According to theory it has energy and momentum but no mass and this is confirmed by experiment to within strict limits. Even before it was known that light is composed of photons it was known that light carries momentum and will exert a pressure on a surface. This is not evidence that it has mass since momentum can exist without mass. [ For details see the Physics FAQ article What is the mass of the photon?].

Sometimes people like to say that the photon does have mass because a photon has energy E = hf where h is Planck's constant and f is the frequency of the photon. Energy, they say, is equivalent to mass according to Einstein's famous formula E = mc2. They also say that a photon has momentum and momentum is related to mass p = mv. What they are talking about is "relativistic mass", an outdated concept which is best avoided [ See Relativity FAQ article Does mass change with velocity? ] Relativistic mass is a measure of the energy E of a particle which changes with velocity. By convention relativistic mass is not usually called the mass of a particle in contemporary physics so it is wrong to say the photon has mass in this way. But you can say that the photon has relativistic mass if you really want to. In modern terminology the mass of an object is its invariant mass which is zero for a photon.

If we now return to the question "Does light have mass?" this can be taken to mean different things if the light is moving freely or trapped in a container.
and encourage the interested reader to read the entire FAQ article (and some of the articles referred to by this article, which can be found at the sci.physics.faq homepage:

http://math.ucr.edu/home/baez/physics

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#### Doc Al

Mentor
rbj said:
perhaps the reason you don't get it is because it isn't true. i have read this same non-fact (that photons have no mass, but they have momentum) before on this forum and i wonder how this is taught nowadays.

since momentum is

$$p = m v$$
In line with pervect's comments, I think it's become standard to use the term mass (m) to refer to what used to be call "rest mass". (So if you mean relativistic mass, you have to say relativistic mass.)

Momentum is defined as:

$$p = \frac{m v}{\sqrt{1 - \frac{v^2}{c^2}}}$$

only equalling the Newtonian form for small speeds.

#### Antiphon

Edit: as noted by Pervect,

The device is called a radiometer.

It doesn't work by momentum transfer of photons, that wouldn't
be strong enough with room lighting.

There is neearly but not completely a vacuum in the device. The
dark sides of the vanes get warmer and there is an increased
pressure on that side by the gas.

The device spins away from the black side toward the white. If it
worked by photon pressure it would spin away from white toward black.

Hope that helps...

#### Astronuc

Staff Emeritus
In a radiometer, the dark side absorbs photons (in the optical range) which produce thermal energy (atomic vibration) in the dark surface material. The light side is cooler because photons are reflected.

The air molecules strike both surfaces, but on the dark side the vibrating atoms in the dark material transfer some energy/momentum to the air molecules and this causes the radiometer to spin.

So it is simply a transfer of energy/momentum involving the air molecules.

Photons have momentum, p = E/c = h/$\lambda$, but not rest mass. Refer to the work by Arthur Compton, and the effect known as Compton scattering. This is however a small quantity compared to the momentum of a molecule, even at room temperature.

#### Ouabache

Homework Helper
This thread seems like déjà vu ? :uhh: 1, 2, 3

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