Light, Mass, and Black hole question

1. Oct 16, 2004

Demiwing

I heard from another thread that as u progress the speed of light, you'll eventually reach infinite mass. How come light itself dont reach infinite mass? And infinite mass means infinite gravitational force right? I heard there was a theory that the Black Hole has infinite mass, does that mean it is center of the universe? infinite gravational force means everytihng will eventually draw itself into it.

2. Oct 16, 2004

Omar

Seeing how it is assumed that almost 90 (not sure but it's something like that) percent of the mass of the universe is comprised of dark matter from which presumably black holes are made up of, I would think that black holes have that kind of gravitatinal force.

Off-topic: I heard something about time running 'slower' as you approach a black hole (maybe due to the high gravitational pulses it produces) which made me a little confused. Can someone elaborate?

3. Oct 16, 2004

pervect

Staff Emeritus
You have to be a bit careful about your wording here. The "relativistic mass" of a particle increases as it approaches the speed of light, but its "mass" or "invariant mass" stays constant.

So the situation is this: normal matter, with a non-zero rest mass, cannot achieve the speed of light. It's mass will remain constant with velocity, but its relativistic mass will increase as its velocity increases, approaching infinity at the speed of light.

Light, with a zero rest mass, cannot travel at any speed other than the speed of light. Light has no mass (no rest mass), but it does have a relativistic mass.

If you try to apply the mathematical formulas that apply to particles with a non-zero rest mass to light, you'd find that you multiply the inital zero rest mass of light by infinity to get light's "relativistic mass". This yields an undefined result. When you use the correct formulas, though, you find that light has a finite relativistic mass.

You might also find the sci.physics.faq "Does mass change with velocity" helpful in understanding this point.

http://math.ucr.edu/home/baez/physics/Relativity/SR/mass.html

4. Oct 16, 2004

Demiwing

Hmm... I see. But can someone elaborate on relativistic mass, invariant mass, and mass?

5. Oct 16, 2004

pervect

Staff Emeritus
Did you read the URL I posted? It goes into some detail.

6. Oct 19, 2004

ArmoSkater87

for particles with a non-zero rest mass...
$$m = \frac{m_0}{\sqrt{1 - \frac{v^2/c^2}}}$$
This equation gives you the mass of a particle relative to you, going at velocity v.

particles with a zero rest mass, for example, photons, naturaly travel at the speed of light, they cannot travel slower or faster that lightspeed relative to any frame. You are not allowed to use the equation i gave you to calculate relativistic mass of light, because special relativity equations dont work for anything that travels at lightspeed. It's clearly seen because the equation would yield 0/0, which is undefined. But like the others said light DOES have relativistic mass, which you can calculate using the mass-energy equivelance, E = mc^2.

The mass of light would be equal to E/c^2 or...
$$m = \frac{h\nu}{c^2}$$
where h is planks constant and nu is frequency of the light.

Last edited: Oct 19, 2004
7. Oct 19, 2004

Phobos

Staff Emeritus
Welcome to Physics Forums, Demiwing.

The mass-relativistic mass idea can be a complex one. Check out the link pervect mentioned. Plus, there are several past discussions on it in this forum.

No, black holes have a finite mass, which is based on how much stuff went into making it (e.g., the core of a dead star plus whatever falls into it). But that mass is compressed to zero volume (the singularity of the black hole), so it has infinite density. The finite gravity is still based on the finite mass.

8. Oct 19, 2004

pmb_phy

Yep. But that really depends on what people mean when they use the term "mass." Some people use it to refer to m = inertial mass (which is a function of speed) and some people use it to refer to m0 = proper mass (which is not a function of speed). They are related by $m = \gamma m_0$
You're trying to apply something to photons which applies to particles with non-zero rest mass. You get into trouble in this way. Mass is defined as the ratio m = p/v (mass = momentum/speed). Photons have a finite momentum and therefore have a finite mass. For particles which travel at speeds less than c the mass is a function of speed and as v-> c, m -> infinity.
Not neccesarily. Take a straight cosmic string as an example. The mass per unit length is enormous. Yet these objects don't exert any gravitational force on objects, even those which are right next to it.
You heard wrong. Its possible to have a black hole of any mass. Mini black holes have a mass of Mt. Everest, and that's certainly not infinite.

However if you have a simply object like the Earth and you move relative to it then the gravitational force on an object will be a function of the speed of the Earth.
pervect is refering to the speed of light as measured locally. The coordinate speed of light, i.e. v = dx/dt, depends on things like the strength of the gravitational field.
E.g. "relativistic mass" is defined as the m such that mv is a conserved quantity. p = mv is defined as the momentum. Anything with momentum will have a well defined mass.

Note: If an object is isolated and does not interact with anything else then the "inertial" energy E = Rest Energy + Kinetic Energy will be related to the mass m = p/v by E = mc2. However this relation does not hold in general. If there are external forces acting on the body, and thus giving it stress, then the mass will be a function of the stress in the body. In that situation p/v does not equal E/c2. This was shown by Einstein in a 1906 in fact, altough he addressed it in the form of the kinetic energy of the body.
See -
http://www.geocities.com/physics_world/sr/inertial_mass.htm
http://www.geocities.com/physics_world/sr/invariant_mass.htm
Actually its quite simple; (relativistic) mass = m = m(v) is defined as m = p/v. Proper mass (aka rest mass) is defined as m(0). It can't get simpler than that.

Pete

Last edited: Oct 19, 2004
9. Oct 19, 2004

franznietzsche

Black holes do not ahve infinite mass, they have finite mass. Infinite density.

Light has no mass. It has energy and momentum, but no mass. It has an equivalent mass, but that is not its mass.

10. Oct 21, 2004

pmb_phy

Such a statement is meaningless unless one first states the definition of mass. As many relativists define "mass" as m = p/v it follows that light has mass. You're speaking of proper mass which is something different.

Light has inertial mass mI (defined as that which gives matter a momentum) which, passive gravitational mass (that on which gravity acts) and active gravitational mass (that which generates a gravitational field). It has zero proper mass . What you've called "equivalent mass" is what many simply call "mass."

All this was all discussed above. Was there something in particular that you think was incorrect? If so then what is your basis for such a position beyond the semantics of arguing how a term is defined? Thanks.

Pete

11. Oct 22, 2004

Phobos

Staff Emeritus
Perhaps I should have qualified it as "a complex idea to someone new to Relativity".

12. Oct 25, 2004

pmb_phy

I see it not so much a complex idea as one that is surprising, i.e. surprising as in the surprise one gets with time dilation and length contraction.

Re - " I heard there was a theory that the Black Hole has infinite mass, .."

I see this alot. It appears that people think that a black hole must have a lot of mass. This probably comes from the notion that some stars will collapse into a black hole. But what the student is forgetting is that before the collapse the star is stable and not collapsing and yet, if nothing else, the star is actually loosing mass. So if one really paid attention to all this they'd realize that all objects which collapse to a black hole always had that amount of mass or greater and at those times the star was not a black hole.

Pete