Massless mass

[Moonshane]

Hi all

I am slowly trying to educate myself and have read a number of books which both provide me with information and some knowledge (some of it sinks in) but also a lot of confusion.

Having no formal training in physics apart from my O level, I am a definite novice, hence my confusion!

I read recently that 'light is heavy' and hence its path gets bent by gravity. This made me think. I always though that light (photons) were without mass and hence their ability to travel at the speed of light with other electromagnetic particles. BUT I also thought that mass = stored energy.

So, my question is assuming light has energy, where does that energy come from if it has no mass? The answer is presumably related to the fact that something with mass gains more mass and not speed as it approaches the speed of light and therefore I have it wrong that mass = stored energy or that at least don't understand some of the methods by which the energy within mass is converted for 'use'?

Sorry for the long winded question but hopefully you follow it

Please provide a Layman's answer as I don't understand complex maths.

Cheers

Shane

[jinstan]

A very good question !

My thought is light/photon doesn't have rest mess, but it has mass when has momentum.

[brianb]

My thought is light/photon doesn't have rest mess, but it has mass when has momentum.

Well momentum is just mass time velocity...

You need special relativity to understand this. An object with rest mass gains in mass as its speed increases, the formula is

m(v) = m(0) / sqrt(1 - v^2 / c^2)

so when v is small compared with c (the velocity of light) m(v) is nearly equal to m(0), but tends to infinity as v approaches c (v^2/c^2 tends to 1).

A photon has zero rest mass but does have mass/energy because it travels at the speed of light - its mass would be zero if it was travelling at any other speed. The energy of a photon is dependent on its frequency (shorter wavelength = higher frequency = more energy) and the effective mass can be obtained from E=mc^2.

[themos]

I read recently that 'light is heavy' and hence its path gets bent by gravity.

That is just wrong. Gravity (as understood in the General Relativity theory of Einstein) bends spacetime and consequently bends the path of ANYthing (when no other forces are present). It has nothing to do with how heavy the particle is.

[toml42]

Well momentum is just mass time velocity...

You need special relativity to understand this. An object with rest mass gains in mass as its speed increases, the formula is

m(v) = m(0) / sqrt(1 - v^2 / c^2)

so when v is small compared with c (the velocity of light) m(v) is nearly equal to m(0), but tends to infinity as v approaches c (v^2/c^2 tends to 1).

A photon has zero rest mass but does have mass/energy because it travels at the speed of light - its mass would be zero if it was travelling at any other speed. The energy of a photon is dependent on its frequency (shorter wavelength = higher frequency = more energy) and the effective mass can be obtained from E=mc^2.

I would argue that it's more useful to say that a photon never has mass, and that mass is invariant, as in special relativity momentum is defined as , so introducing the non-relativistic momentum p= mv and the concept of 'effective mass' as well only confuses matters, Einstein himself said he didn't think the concept of effective mass was helpful.

[jinstan]

m(v) = m(0) / sqrt(1 - v^2 / c^2)

so when v is small compared with c (the velocity of light) m(v) is nearly equal to m(0), but tends to infinity as v approaches c (v^2/c^2 tends to 1).

A photon has zero rest mass but does have mass/energy because it travels at the speed of light - its mass would be zero if it was travelling at any other speed. The energy of a photon is dependent on its frequency (shorter wavelength = higher frequency = more energy) and the effective mass can be obtained from E=mc^2.

Zero rest mass means m(0) = 0. If so when photon travels at the speed of light, m© = 0 / 0, which can be anything from 0 to infinite.

Where am I wrong?

[Revs]

What gets me when we talk about speed is; speed is relative. When we say, for example, a car is travelling at 40mph, that's relative to the earths surface. So when we're talking about the speed of something in space, what is it in relation to? The observer?

[themos]

It is in relation to something else. For a star, it would be its galaxy. For a galaxy, it would be its cluster. For bigger stuff, there's always the cosmic background radiation.

[toml42]

Zero rest mass means m(0) = 0. If so when photon travels at the speed of light, m© = 0 / 0, which can be anything from 0 to infinite.

Where am I wrong?

You're not wrong, that equation is undefined for the case of a photon, one of the reasons i don't like concept effective mass.

[George Jones]

I read recently that 'light is heavy' and hence its path gets bent by gravity.

Gravity (as understood in the General Relativity theory of Einstein) bends spacetime and consequently bends the path of ANYthing (when no other forces are present). It has nothing to do with how heavy the particle is.

I like what themos wrote.

So, my question is assuming light has energy, where does that energy come from if it has no mass?

Electromagnetic fields can do work, and thus electromagnetic fields have energy. For example, the electromagnetic field inside a microwave does work on food, and the food heats up.

Sorry for the maths.

A nice, general equation is

E^2 - (cp)^2 = (mc^2)^2,

where E is total energy (includes energy of motion and energy of rest mass), c is the speed of light, p is momentum, and m is rest mass. This equation is valid for particles that have non-zero rest mass, and for particles that have zero rest mass.

If a particle is at rest, then momentum p = 0, and we have the special case

E^2 = (mc^2)^2

E = mc^2.

If rest mass m = 0, then we have the special case

E^2 = (cp)^2

E = cp.

This second case applies to electromagnetic radiation, both quantized (photons) and classical (fields).

A bit of playing with the general case at the top, with both p and m non-zero, results in the formula that brianb gave.

[Moonshane]

Hi all

Thanks so much for the brilliant explanations. I will probably read this several times before I understand it and will try and work through the equations a little too.

The irony is (like a lot of people I expect) I found physics really boring at school - it's only now that I appreciate how amazing it is. We should work as children and then go back to school to retire! We'd definitely enjoy it more