# If light has no weight, how can it push objects?

1. ### Jarfi

327
Your probably familiar with the solarsail tech when people use light to push space ships with sails.

This is light that is pushing matter with mass, I learned in school that in order to have momentum you have to have mass and light has no mass and therefor no momentum.

And if you get hit with no momentum you wont get pushed.

So how can solarsails be ''pushed'' by light?

And also when I shine a light on paper and it heats the paper(gives it momentum?) does it loose energy and change wavelength?

2. ### I like Serena

6,183
The proper statement would be that photons do not have "rest" mass.
But since they represent energy they have an associated mass given by E=mc2.

From wikipedia:

"Einstein proposed – and experiments confirm – that photons have a momentum p=E/c,[2][3] hence each light photon absorbed by or reflecting from a surface exerts a small amount of radiation pressure. This results in forces of about 4.57x10−6 N/m2 for absorbing surfaces perpendicular to the radiation in earth orbit, and twice as much, if the radiation is reflected.[4]"

[EDIT]Note that wikipedia has articles about "Solar sail", "Electric sail" and "Magnetic sail" that make use of respectively radiation pressure, electric charge of protons in the solar wind, and speed of protons in the solar wind.[/EDIT]

3. ### G01

2,698
Light carries momentum even though it possesses no rest mass. The momentum carried by a photon is given by the relativistic formula:

$$p=E/c$$

where E is the energy of the photon and c is the speed of light.

4. ### Jarfi

327
So it carries momentum, Isn't it the smallest momentum a body can have than?

5. ### Dickfore

Actually, it is the largest momentum a body with energy $E$ can have.

6. ### I like Serena

6,183
You can put as much energy (and by proxy, mass) into a photon as you want.
If you put enough energy into it we call it "cosmic radiation".

7. ### I like Serena

6,183
Here's the light mill that turns by reflecting photons.

8. ### ideasrule

2,315
The Crookes radiometer rotates in the wrong direction to be explained by light pressure. Take a look at the "Explanations for the force on the vanes" section of the wiki article.

9. ### HallsofIvy

41,264
Staff Emeritus
Your picture doesn't come through but I suspect it is of th.e same kind of gadget I saw when I was in highschool many, many, years ago. (I went to high school in the years "B.C."- before computers.) One side of each vane is white or silver, reflecting light, while the other side is black.

My physics teacher showed one to the class and pointed out that this is NOT true. The momentum exchange on the black side, where the photon is absorbed is E/c. The one I saw turned so that the light side was leading. The momentum exchange on the light side, where the photon is reflected and goes from "c" to "-c" is 2E/c so if it were momentum from photons that caused the turning, it would be goint the other way. What is really happening is simply that the black side is warmer, because it absorbs the light, than the light side and that is causing air currents in the globe.

Last edited: Mar 29, 2011
10. ### I like Serena

6,183
Interesting!
I keep learning new things! Even about stuff I already thought I new!

[EDIT]It does seem strange though, that even though the photons do not give enough push to turn the mill in vacuum, that absorbing photons generates enough heat to move gas molecules that do turn the mill![/EDIT]

11. ### ideasrule

2,315
I don't think it's that strange. If a photon transfers its momentum of E/c, it increases kinetic energy by p2/2M=E * E/2Mc2. The ratio of a photon's energy to the rest energy of the blades is very small, so only a tiny portion of the photon's energy get transferred. On the other hand, a heat engine could transfer a substantial portion of E to the blades, because its theoretical efficiency is 1 - Tcold/Thot.

12. ### JK423

389
You ask, how light can 'push' since it has no mass. Ask yourself, how can an electric field 'push' a charge since the former has no mass...? Well, mass has nothing to do with pushing. The electric field exert force (gives momentum) on things that carry the property of 'charge'. Light, photons, is an electromagnetic field which exerts force on charges --> Push objects.

13. ### lightarrow

Probably the OP asked that question because he/she assumes that momentum is m*v even for photons. Of course it's not.

The formula p = m*v is valid:

1. only for massive objects
2. only at low speeds.

The formula which is *always* valid, for massive or massless objects and at low as well as at high speeds, in special relativity is:

E2 = (mc2)2 + (cp)2

E is the total energy.

For m = 0: p = E/c

So a massless object have momentum, if it has energy.

Last edited: Mar 30, 2011
14. ### jnorman

308
i thought a radiometer had a vacuum inside the globe. if so, how could there be "air currents", and even if there are air currents in a (partial) vacuum, why would they be distributed such that the vane would turn ina specific direction?

15. ### vivimartinez

2
Could anyone please tell me what's the update on Einstein's equation E=mc2? I did some research on that formula but get no anwers? How does it work? DOES ANYONE KNOW????? PLEASE REPLY. Thanks.

16. ### I like Serena

6,183
Nope. It turns out that in vacuum the radiometer does not turn (see wikipedia).

17. ### I like Serena

6,183
Which update do you mean?
The equation E=mc2 simply means that energy equals mass.
To an observer there is no real difference.

18. ### lightarrow

It's not an "update" but something not often remarked: the formula E=mc2 is valid *only* if momentum p = 0.
The formula which is always valid (in the special relativity context) is the one I wrote in my previous post.

19. ### vivimartinez

2

Then why is it so famous? What is it used for?

20. ### I like Serena

6,183
It's part of "relativity" theory.

If you're in a falling elevator with no view to the outside, you wouldn't be able to tell whether you're falling or whether you're weightless.
According to Einstein, there IS no difference. It's just a matter of perspective.

It's the same with E=mc2.
If you have a moving electron, we might say it's a particle with a specific mass that is moving at a specific speed, or we might say it's an packet of electromagnetic energy.
This has been a controversy for the longest time, because moving electrons exhibit both particle properties, and wave properties.
Again, according to Einstein, there IS no difference. The mass of the electron can be seen as the same as an electromagnetic wave with an energy that corresponds to the mass of the electron as given in the formula E=mc2.

As you know Einstein's vision had a revolutionary impact on physics.