# Momentum of Light and Weirdness

Q:
If it's true that light has momentum, then could formula (3) in this paper be correct? http://arxiv.org/abs/physics/9904018 It is demonstrated in paper http://arxiv.org/abs/physics/0212033 ,where it appears as formula (55) , but this paper is very very weird, so I don't know what to think.
- luca cassioli (age 38)
Rome, Italy
A:
It's certainly true that light has momentum, but after a superficial glance at those papers I agree that they are too weird to worry about. Their basic ingredients are just the ones that people have been working on for about 100 years, so I strongly doubt that such basic points have somehow been missed. We'll look for a competent person to have a closer look.

OK, let's get back to the part I can answer, about light's momentum. This momentum has been known, quantitatively, since Maxwell. Think of an electromagnetic plane wave ExB hitting a thin sheet of weakly conducting material. (We keep it thin so the fields are almost the same on the way out as in.) Let's work in CGS units, to keep things simple.

The current density in the sheet is J=Eσ, where σ is the electrical conductivity. The power dissipation density is then E·J = E2σ. That's the rate at which the wave is dumping energy into the sheet, per unit volume. The rate at which it's dumping momentum into the sheet is just, by definition, the force. The force per unit volume in the direction of the wave (the only part that doesn't average to zero over an oscillation) comes from the magnetic force on the current, whose magnitude (per unit volume) is BJ/c= E2σ/c. (In CGS, the magnitudes E and B are equal for a wave in free space.) The reason this doesn't change sign as the fields oscillate is that it involves the product ExB, not just one of the oscillating fields.

So the momentum loss rate is just the energy loss rate/c. This can be applied over many layers until there's nothing left of the wave, so we have that the momentum magnitude p of the wave was just its energy/c.

I'm not sure exactly when Maxwell figured this out, but it may have been in the 1860's.

Mike W.

Whoa- I read more of that paper. Completely nuts.

(published on 06/16/2011)

## Follow-Up #1: gravitational mass

Q:
Thanks for your answer. Yes, last pages of the paper are completely nuts (integrand of God?!? LOL ) But I'm interested just on formula (3).
- luca cassioli (age 38)
rome, italy
A:
I'm embarrassingly ignorant of General Relativity, but this seems answerable on simple principles. For small masses, the gravitational effects are linearly additive. Consider two small masses traveling in opposite directions. If you treat them as one object, with momentum of zero, that formula gives one answer:  gravitational mass equal to inertial mass. If you treat them as two separate objects, it gives a different ratio. So it can't be right.

Mike W.

(published on 06/17/2011)

## Follow-Up #2: disagreement about relativity

Q:
The subject URL (http://van.physics.illinois.edu/qa/listing.php?id=1424) is flawed in many areas: 1. The author is anonymous and because the site is supported with public/taxpayer money, there is a self-serving and private interest at work in the subject and the running of the URL. 2. Discussion is not provisioned -- only replies or comments to existing comments 3. Comments are filtered and only the ones that agree with the postulate are displayed 4. Statements such as "It's [light's momentum] been measured in countless experiments." are offered but not one of the countless examples are cited. In fact, there is no experiment that *measured* light's pressure. 5. The author is hiding behind equations but cannot follow a simple logic of explaining the perpetual motion machine if light were to bounce between parallel mirrors. 6. The pretend objectivity demeans the UofI record and hints at fraud. 7. Cannot communicate with the (hidden) author directly via email, which would establish a minimum platform for fairness. 8. The page "Ask the Van: Report Baloney" insults people who use their own monies to express not only free speech but also ideas superior to those sanctioned by the public monies from the University of Illinois. Regards, Mike Ivsin
- Mike I
Boston, MA
A:
Wow, I've taken some controversial stands at times, but didn't think that a routine presentation of Maxwell's equations and Special Relativity would draw this kind of reaction.

Just for fun:
"1. The author is anonymous.." except for,  you know, my name, photo, and individual website url being on our volunteer list () posted on the site.
"...because the site is supported with public/taxpayer money, there is a self-serving and private interest at work in the subject and the running of the URL..." since nothing says "self-serving and private interest" more than volunteer labor.
"2. Discussion is not provisioned -- only replies or comments to existing comments" and those can never take the form of discussion, because...?
"3. Comments are filtered and only the ones that agree with the postulate are displayed" as is evident in this post itself.
"4. ...there is no experiment that *measured* light's pressure" other than the ones dating to 1900, the working solar sail experiments, the measured effects on satellites, etc. as partially described in obscure sources such as  .
"5. The author is hiding behind equations..." which certainly ought not to appear in any discussion of physics.
"6. The pretend objectivity demeans the UofI record and hints at fraud. " Furthermore the ability of the device on which you are reading this to process data and transmit it using Maxwell's equations shows the vast extent of the Conspiracy.
"7. Cannot communicate with the (hidden) author directly via email,.." without resorting to extreme measures such as using the Dept. web site or other dangerous Intertubes.

OK, maybe enough snark for  now.

Mike W.

posted without checks (Lee, lucky dog, is in Paris, but he'll get a kick out of this when he gets back.)

(published on 12/01/2011)

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