Do shadows weigh anything?

Dear Cecil,

I would like to pick a nit with you. Solar wind consists mostly of electrons and protons, which both have mass, which are responsible for any pressure that is applied to such things as comet tails or solar sails. Photons, having no mass, do not contribute to this. Since “light” - that part of the electromagnetic spectrum that our eyes can detect - is made up of photons, I don’t think that you can correctly say that light has weight, since it has no mass.

Bob Levittan
Huntington, NY

Well, I know this girl, she so fat. . .

Link to the column in question: Do shadows weigh anything? - The Straight Dope

With respect Bob, you may be confusing two different things. Solar wind exerts a pressure, true, when it’s not filtered out or blocked by something like Earth’s magnetic field. However the electromagnetic force of light is indeed measurable, as postulated by Maxwell, and later proven as far back as the turn of the last century by Nichols, Hull, and Lebedev. Look up online about the super-accurate torsion balance radiometer which Nichols and Hull used, or wait until later today when the sources/citations are posted in the column.

If your nitpick is with respect to calling the electromagnetic pressure of light “weight”, Cecil never called it such in the column. And for all practical purposes, the pressure from a directed force can be considered a weight - think of an experiment of pouring water on a kitchen scale. It’s not the same as “weight” but there is a little creative license at play in the way Cecil’s answering what is somewhat of an off-the-wall question.

Actually the point I noticed in that piece was the lowness of the figure Cecil cited, 300 pounds of force from the sunlight over the whole city of Chicago.

I am certain that I once read a description of this measurable phenomenon (within a discussion of Einstein) which said that the light on a field of wheat (or possibly another crop) weighed several tons. I’m pretty sure that the city of Chicago is way larger than whatever field the other writer had in mind.

Here’s the thing. I think the other writer may have said that the several-tons figure represented the light on the field over the course of a full day. Cecil mentions no time period relative to the 300-pounds figure.

Is it in fact meaningful–or essential–to describe the “weight” of light in terms of time?

They shouldn’t have asked Cecil this. They should have asked Lamont Cranston instead.

I wouldn’t think so. The light force is a pressure, I mean, it would be like saying how many tons of air press against the wall of your tires over a day. I can’t wrap my head around that frame of reference. I’m happy to entertain ideas…

What about this?

Not that this yields figures anywhere near those mentioned before, but it incorporates the time element.

If those calculations are reasonable I guess that might give you an effective mass per second hitting the entire Earth, but I also note it doesn’t take into account what hits the Earth’s surface versus what is absorbed or reflected/re-radiated into space. And while it is interesting on its own merits, I think it’s a related issue to the light pressure question which tied into the actual continuous force.

Believe it or not, but the photon pressure is actually significantly larger than the pressure from the protons and electrons of the solar wind. Yes, massless particles do have momentum, and thus contribute pressure: This is part of the wonders of relativity.

Well… we don’t know the exact value of g on Z’ha’dum, but it seems reasonably close to that of Earth…

I don’t mean…scratch that, I mean to nitpick :slight_smile:

  1. If the shadow is casted on a gas cloud (on a planet with tangible gravity and atmosphere), the drop of temperature due to the decrease of solar radiation would make the gas heavier. We can argue that the shadow is exerting a weight on the gas (come on, if we argue the momentum of photons count as weight, why can’t we do it the other way around?)
  2. Depending on the shape of the object covered by the shadow, a drop of surface temperature could lead to lesser air convection. If there is an opening underneath the object, then less hot hot air would push it up :slight_smile:
  3. Lower molecular temp -> less mass through e=mc^2 (if the shadow is large enough) -> less weight on, say, earth.

Why yes, my co-workers love me :slight_smile:

And if light had no mass, there would be no such thing as gravitational lensing. Photons have zero mass when they are at rest. But they never are at rest.


I’m not a physicist, but I don’t think that’s how it works. Having zero mass just means that they get their paths shifted the least, not that they don’t get shifted at all. They travel along a “geodesic”, the shortest path between two points; and where space is curved, that path is curved.

Nevertheless, when photons are moving, they have momentum.

Just one more reason to weigh yourself in the dark!

Even as I read the question before downloading the Podcast I grinned smugly thinking, “I know where he’ll go with this …”
And Cecil, you did not disappoint!
Perhaps the most significant demonstration we have of the pressure that light (an all encompassing term for a multitude of forms of radiation from the Sun in this context) can exert is the Sun itself. It is well established that one of the ways a star can “die” is when it runs out of nuclear fuel at the end of its main sequence it “puffs off” its outer layers and contracts down to form a white dwarf. This depends on the mass of the star falling within a certain range (measured in solar masses). The white dwarf will continue to glow from residual heat and will gradually become less luminous as the heat radiates away in the form of light.
But it is graitational collapse that shrinks the dying star down to a white dwarf. So, what keeps the star “puffed up” prior to this collapse? Radiation pressure! Indeed the “pressure” exerted by radiation is so great that it gives the star a much greater size than it would otherwise have by balancing the outer layers of the star against its own gravity. It should come as no surprise then that we can measure the effects of this in tangible ways and utilise the effects in so called “solar sails”.


The question was, “Do shadows weigh anything?”
If I recall my high school physics correctly, “weight” is a measure of the force that acts on our mass due to the gravitational attraction between our bodies and the earth.
“Weight” therefore is measured in Newtons, and not pounds or kilograms. Fortunately for us, the gravitational attraction is relatively constant near sea-level and so we have been allowed to become accustomed to assuming that our “weight” will remain closely aligned to our “mass”. It is in fact our mass that we are more interested in when we jump on the scales - I can’t remember the last time was told that my target weight was 569 Newtons! But we do often hear about our body mass index…

Back to the question, “Do shadows weigh anything?”. Whilst I would be foolish to argue that light does not exert a pressure, a shadow does not have mass and therefore cannot have weight. It would not matter if the shadow were being cast on a black hole (with gravity so strong that matter has infinite “weight”), a shadow is a lack of light. The “pressure” (not “weight”) being exerted by light falling around the shadow does not influence this.

On another note, I remember considering e=mC^2 and reading that if were able to accelerate an object to near the speed of light, relativity shows that that object would tend towards having infinite mass …

The math involves a division, so that the number involved goes toward x/0 as the speed approaches c. But a photon has zero mass when it is standing still (except that it never does stand still), and therefore the number is 0/0. As you may recall, 0/0 can be equal to anything.

I say “the number” because, although older reasoning said that the mass behaved this way, some now prefer to say that the momentum goes up while the mass stays the same. The math works either way, and so do the observed facts.

The pound is a perfectly cromulent unit of weight (disregarding the fact that there is more than one unit called a “pound”).
Powers &8^]

Seismic, meet the lbf, also known as “pound force” or sometimes, shorthand, “pound.” Pound force, meet Seismic.

In fact, the pound (when not specified as a “pound mass” or “pound force”) is generally assumed by default to mean the force unit. There are plenty of reasons not to use pounds, but “it’s not a force unit” isn’t one of them.