# Quantum Fizz is so counterintuitive!

## Main Question or Discussion Point

I know photons have what is termed as 'moving mass', but what exactly does this mean? And what implications does it have?

I recently did a question where i had to work out the force green light exerted on a mirror. I did this by finding the momentum of the photons, calculating their change in momentum as they hit the mirror, and the using newton's second law (F=dp/dt) to find the force on the mirror -- and the answer was to the order of magnitude 10^-3 N! Hey! That's quite a lot, don't you think?

I find it incomprehensible that light exerts a force on a mirror of order of magnitude 10^-3. If it was of order of magnitude 10^-30 or 10^-20 (ie miniscule), then i'd be able to reconcile it with my intuition, but this i just can't.

Perhaps this is just something that cannot be considered intuitively?

Anyways, here's my hypothetical question:
If I was stationary in space (perfect vacuum, g=0 N/kg -- not that it matters) relative to, say, the Earth, and i shone a REALLY powerful (ie intense -- lots of photons emitted) torch, would i accelerate as a result of shining the torch?

Trying to get my head around it, hehe...

Cheers

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jtbell
Mentor
Note that light (and all other electromagnetic radiation) carries momentum according to classical physics. Most all electromagnetism textbooks discuss this, and derive it from Maxwell's Equations and the electromagnetic force laws. It's not just a quantum physics thing.

Also, people are actually planning seriously to use this as a means of spacecraft propulsion. Do a Google search on "solar sail".

catalyst55 said:
I know photons have what is termed as 'moving mass', but what exactly does this mean? And what implications does it have?

I recently did a question where i had to work out the force green light exerted on a mirror. I did this by finding the momentum of the photons, calculating their change in momentum as they hit the mirror, and the using newton's second law (F=dp/dt) to find the force on the mirror -- and the answer was to the order of magnitude 10^-3 N! Hey! That's quite a lot, don't you think?

I find it incomprehensible that light exerts a force on a mirror of order of magnitude 10^-3. If it was of order of magnitude 10^-30 or 10^-20 (ie miniscule), then i'd be able to reconcile it with my intuition, but this i just can't.

Perhaps this is just something that cannot be considered intuitively?

Anyways, here's my hypothetical question:
If I was stationary in space (perfect vacuum, g=0 N/kg -- not that it matters) relative to, say, the Earth, and i shone a REALLY powerful (ie intense -- lots of photons emitted) torch, would i accelerate as a result of shining the torch?

Trying to get my head around it, hehe...

Cheers
I believe there is also an assumption in your argument that the mirror is perfectly reflective and there is no energy lost in the reflection. That will make the amount of force slightly less.

Just a thought.

catalyst55 said:
I know photons have what is termed as 'moving mass', but what exactly does this mean? And what implications does it have?

I recently did a question where i had to work out the force green light exerted on a mirror. I did this by finding the momentum of the photons, calculating their change in momentum as they hit the mirror, and the using newton's second law (F=dp/dt) to find the force on the mirror -- and the answer was to the order of magnitude 10^-3 N! Hey! That's quite a lot, don't you think?

I find it incomprehensible that light exerts a force on a mirror of order of magnitude 10^-3. If it was of order of magnitude 10^-30 or 10^-20 (ie miniscule), then i'd be able to reconcile it with my intuition, but this i just can't.

Perhaps this is just something that cannot be considered intuitively?

Anyways, here's my hypothetical question:
If I was stationary in space (perfect vacuum, g=0 N/kg -- not that it matters) relative to, say, the Earth, and i shone a REALLY powerful (ie intense -- lots of photons emitted) torch, would i accelerate as a result of shining the torch?

Trying to get my head around it, hehe...

Cheers

Yes, light has energy and therefore a mass equivalent by $$E=mc^2$$.

And yes, you would feel reaction forces and be accelerated by shining a
flashlight.

But a milliNewton is way too big unless the intensity was immense.
Something is probably wrong with the arithmetic.

Antiphon said:
Yes, light has energy and therefore a mass equivalent by $$E=mc^2$$.
I think this is not correct. Photons have zero rest mass:

http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/relmom.html#c2

From

$E^2 = (pc)^2 + (m_0 c^2)^2$

it follows with $m_0 = 0$ for a photon:

$E = pc$

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A mass equivalent is not a rest mass.

But the photon would gravitate as if it had a mass of $$m_0$$.

Hey catalyst55,

there are attempts to develop a laser propulsion:
http://science.howstuffworks.com/light-propulsion.htm
(There's also a video of it there)

And here's another video:
http://www.cnn.com/SPECIALS/cold.war/experience/the.bomb/route/04.white.sands/ [Broken]

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Thanks, Edgardo. It's quite intriguing.

Let's say that there's a perfectly reflecting mirror in space and it is hit by incident sunlight. The sunlight experiences a change in momentum and consequently accelerates the mirror. The energy of the light is the same before and after the reflection (i.e. light does not change frequency when it reflects - e=hf). So, isnt the mirror, in effect, getting KE from nowhere?

This kind of scenario seems to satisfy the law of conservation of momentum but apparently not the law of conservation of energy....

What am i missing? Thanks.

jtbell
Mentor
catalyst55 said:
The energy of the light is the same before and after the reflection (i.e. light does not change frequency when it reflects - e=hf).
No, the frequency (and wavelength) of light does change when reflected from a moving object. That's how police radar and laser guns work. You mean the Doppler effect?

But.. if the mirror was stationary (say, on earth), the light incident on it would exert a force on the mirror pushing it towards the wall. How would the doppler effect explain this? The mirror is not moving....

i always perceived the dopper effect sensually, in the sense that i can hear the sound of a car change as it passes me..

Here's a better example:

If the police officer shone his laser on a stationary car, the photons from the laser would exert an infinitesimal force on the car, right? The police officer's laser gun, realising that no change in frequency has occured, would register a velocity of zero, would it not?

If the laser gun is registering the velocity of a stationary car as 0 (via detecting no change in frequency), how can the photons be exerting a force on the car?

Cheers

catalyst55 said:
Thanks, Edgardo. It's quite intriguing.

Let's say that there's a perfectly reflecting mirror in space and it is hit by incident sunlight. The sunlight experiences a change in momentum and consequently accelerates the mirror. The energy of the light is the same before and after the reflection (i.e. light does not change frequency when it reflects - e=hf). So, isnt the mirror, in effect, getting KE from nowhere?

This kind of scenario seems to satisfy the law of conservation of momentum but apparently not the law of conservation of energy....

What am i missing? Thanks.
I think the the energy of the light is NOT the same after the reflection, it must be slightly smaller. But since you have a heavy object, the change in the wavelength is very small.

It's like in Compton scattering, where the wavelength changes:
http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/comptint.html

In my view, you could plug in the mass of the mirror into the formula instead of the electron mass. From this you should see that $$\Delta \lambda$$ is very small.

jtbell
Mentor
Correct, the Compton-scattering formula applies here, with a scattering angle of 180 degrees. I checked it by working out energy and momentum conservation from scratch, and got

$$\frac{1}{E'} - \frac{1}{E} = \frac{2}{mc^2}$$

where E and E' are the initial and final energies of the photon, and m is the mass of the mirror. In terms of wavelength this becomes

$$\lambda' - \lambda = \frac{2h}{mc}$$

For m = 10 grams = 0.01 kg, the change in wavelength is on the order of $10^{-40}$ meters. Now, that's small!

Hurkyl
Staff Emeritus
Gold Member
I think that if a photon struck a stationary mirror in space, then the photon's wavelength would change!

Here's a quick, elementary explanation:

(1) Photon strikes stationary mirror.
(2) Mirror absorbs photon, and begins moving.
(3) Moving mirror emits photon.

Thus, we can see that the doppler effect does occur here!

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Hurkyl
Staff Emeritus