Thread: Photons and Momentum

I understand how photons can have velocity and speed, one being a vector and the other a scaler. However how does it have momentum? It dosnt fit with the classical definition of momentum, as it dosnt have mass nor dose it have a momment of inertia?

From special relativity, E²=(pc)²+(mc²)²

Since m=0 (the photon is massless)

=> E=pc

=> p=E/c=hf/c

Since the energy of a photon is hf.

Here, E = energy,
p = momentum,
c = speed of light,
m = mass,
h = Planck's constant, and
f = the frequency of the photon.

Also...
photons can exert a pressure. Mathematically, it is the Poynting vector divided by c with a factor of 2 depending on whether the photon is absorbed or reflected (P=2S/c if reflected).

This 'radiation pressure' exists because the photon has momentum....

Cheers,
william

That looks familiar from my first-year quantum chemistry

Photons:
1.velocity=c=3*10^8 (m/s)
2.mass=m=0 (kg)

When we study objects which travel at lightspeed the Newtonian laws of pysics can't be applied.
If we use the classical momentum (Newton):
p=m*u
p=0*c=0 (wrong)
However,the relativistic momentum:
p=γ*m*u , where γ=1/sqrt[1-(u^2)/(c^2)]
p=0/0 which is not zero,but a real number.

So photons do have a finite momentum which is not zero...

So why does the photon not aquire mass to stop it travelling at the speed of light? If we assume the light is in vacuum?

Thanks for the replies.

Originally Posted by tasos

p=0/0 which is not zero,but a real number.

How do we know 0/0 is a real number and not zero? I believe it is undefined. In other words, you can't define 0/0 as anything....

Cheers,
william

Originally Posted by Petroleum

So why does the photon not aquire mass to stop it travelling at the speed of light? If we assume the light is in vacuum?

Thanks for the replies.

Hi Petrol,

Firstly, don't confuse 'mass' with 'matter.' This is usually a point of confusion with people new to relativity.

Secondly, mass is a fundamental property. Either a particle has it or not. If a particle doesn't have mass, then it doesn't have any mass to increase. A photon doesn't have mass. It's as simple as that.

Cheers

Originally Posted by william

Firstly, don't confuse 'mass' with 'matter.'

What do you mean by that?

Originally Posted by Petroleum

Originally Posted by william

Firstly, don't confuse 'mass' with 'matter.'

What do you mean by that?

This is a mistake I myself made when I first started learning about relativity. As an object travels near the speed of light, its mass increases. Mass (in physics) is defined as the resistance to a change in motion - in essence, its inertia.

If you imagine the particle moving near light speed as gaining matter instead of mass, it makes things incomprehensible - and it's wrong.

cheers

I don't understand, I thought mass is the quantitative measurement of matter, with mass defined as the resistance to acceleration? (inertia). Then, matter may have some mass locked away as binding energy - the mass deficit. With the relationship between the 2 being E=mc^2

On another point - if you start with something very light - say an electron, and accelerate, the mass would keep increasing as you approached the speed of light - linked by a function. I understand this in principle.

would the mass continually increase if you kept incrementally increasing the acceleraion force? Since you could, given enough force, accelerate exponentially up to but not including the speed of light, is there no limit on the mass?

Where does all this increased mass go? Or rather, what form would it take? I know doing calculations prove that you may get an appreciable mass increase, but what happens to it?

Thank you. = oh could we explain it without a large amount of maths please? My mathematical grounding isnt that solid.

Originally Posted by Petroleum

Where does all this increased mass go? Or rather, what form would it take?

This is a naive way to explain it... but here it goes;

Let's say you weigh 75 kg on Earth. If you went to the moon you would weigh less. And if you went to Jupiter, you'd weigh more. But on all three planets/moon, you'd appear the same. You can think of your weight as a property you have - and that property can change.

A similar thing happens to the electron you mentioned. It would appear the same, but it would 'feel heavier' (to use the analogy).

Again, you must force yourself to make the disconnect between the concepts of mass and matter. In my planet analogy, your weight changes, but your body doesn't gain or lose matter. In the case of the electron, it gains mass (not weight), but not matter.

Well, that's the best I can do for now.

Cheers

Petroleum, this explains it in terms you can grasp:

http://www.thescienceforum.com/MASS-EXPLAINED-5069t.php

Originally Posted by Petroleum

I understand how photons can have velocity and speed, one being a vector and the other a scaler. However how does it have momentum? It dosnt fit with the classical definition of momentum, as it dosnt have mass nor dose it have a momment of inertia?

Actually it does have mass according to E = mc^2. This mass is called its "inertial mass". The mass which = 0 is the so-called "rest mass".

Pete