# Heavy light?

## Main Question or Discussion Point

We know light made up of photons which is massless, but why it can absorbed by black hole? Is it becuz the Einstein's relativity about every object can curve time space

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phinds
Gold Member
2019 Award
We know light made up of photons which is massless, but why it can absorbed by black hole? Is it becuz the Einstein's relativity about every object can curve time space
LIght doesn't have mass but it has momentum and it moves along geodesics just like everything else that is not being acted on by outside forces.

LIght doesn't have mass but it has momentum and it moves along geodesics just like everything else that is not being acted on by outside forces.
But Accord to momentum itu also need mass "p =mv which is non

Nugatory
Mentor
$p=mv$ is a classical formula that is valid only when $m$ is not zero and $v$ is small compared with the speed of light. Neither of these are true of photons, so you have to use the more general formula $E^2=(mc^2)^2+(pc)^2$.

ZapperZ
Staff Emeritus
But Accord to momentum itu also need mass "p =mv which is non
I can also write the momentum of light as p = ħk. So where is the "mass" requirement there?

Please note that even before 1900, i.e. before Special Relativity and Quantum Mechanics, classical theory of electromagnetism and light already know about the momentum of light, all without even considering the picture that light consist of "photons" or the possibility that it has mass. So even back then, there was zero need to introduce mass to account for the momentum of light that they had observed. This means that just because something has a momentum, it doesn't automatically means that it must also have a mass.

BTW, in solid state physics, we also designate a crystal momentum as p=ħk without invoking any mass. So this isn't specific just to light. It means that there is a more universal definition of momentum than what you already know.

Zz.

Photons have a rest mass of zero, but they can never be at rest.

Consider that photons have a defined energy and then apply energy mass equivalence. This is a bit of hand waving, but should be adequate to answer your original question.

ZapperZ
Staff Emeritus
Photons have a rest mass of zero, but they can never be at rest.

Consider that photons have a defined energy and then apply energy mass equivalence. This is a bit of hand waving, but should be adequate to answer your original question.
You cannot simply "apply" the mass-energy equivalence, because the "mass" in that is the rest/invariant mass. It will also mess up the full relativistic energy equation, because now, the "m" in E2 = (pc)2 + (mc2)2 is no longer zero.

Zz.

RPinPA
Homework Helper
Is it becuz the Einstein's relativity about every object can curve time space
Yes. That was precisely the point that made Einstein famous to the general public. Newton's theory of gravitation predicted light, with no mass, will not be affected by gravity. Einstein predicted that light, because it follows geodesics in distorted space-time, will be affected. Well-respected astronomer Sir Arthur Eddington, through observations of a solar eclipse, verified that Einstein was right and Newton was wrong.

Not merely in the actual fact, but the amount to which it is bent by gravity is precisely predicted by general relativity. A lot of people seem to miss the fact that when physics makes predictions, they have actual numerical values.

Newton's theory of gravitation predicted light, with no mass, will not be affected by gravity.
Can you provide a corresponding calculation? In case of light deflection by a central mass I get half the effect compared to relativity.

phinds
Gold Member
2019 Award
... Newton's theory of gravitation predicted light, with no mass, will not be affected by gravity.
Can you provide a corresponding calculation? In case of light deflection by a central mass I get half the effect compared to relativity.
I'm puzzled. How could you do a calculation in Newtonian physics that says light, being massless, is affected by gravity at anything other than zero effect? How does Newtonian gravity affect something that has no mass?

How could you do a calculation in Newtonian physics that says light, being massless, is affected by gravity at anything other than zero effect?
The gravitational force is zero but not the effect. Keep in mind that the force required to accelerate a massless object is zero too in classical mechanics. Calculating the resulting effect is quite easy:

According to Newton's law of gravitaton, the force acting on an object with mass m in the gravitational field of a central mass M is

$F = - \frac{{M \cdot G \cdot r}}{{\left| r \right|^3 }} \cdot m$

According to the second law of motion the resulting acceleration is

$\ddot r = \frac{F}{m} = - \frac{{M \cdot G \cdot r}}{{\left| r \right|^3 }} \cdot \frac{m}{m}$

If light is assumed to be massless (that's not obvious in classical mechanics) L'Hôpital's rule results in

$\mathop {\lim }\limits_{m \to 0} \ddot r = - \frac{{M \cdot G \cdot r}}{{\left| r \right|^3 }}$