How light is deflected by gravitational field

[vaishakh]

I have a general doubt. It is sai that light is deflected by gravitational field. That means photons are subjected to gravitational attractions.
Then how can they have mass 0? In fact if we put mass as zero and follow the Newton's law of gravitation, then there must be no attractive force for a photon.

 

[jtbell]

In general relativity, a particle does not have to have mass in order to be influenced by gravity. In GR, gravity is basically a manifestation of curved spacetime, which affects the motion of all objects whether they have mass or not.

 

[Doc Al]

The deflection of light by a gravitational field is a consequence of general relativity, which supersedes Newton's law of gravity.

 

[pervect]

I have a general doubt. It is sai that light is deflected by gravitational field. That means photons are subjected to gravitational attractions.
Then how can they have mass 0? In fact if we put mass as zero and follow the Newton's law of gravitation, then there must be no attractive force for a photon.

That's easy to answer. In GR, gravity is coupled to energy, not mass (specifically, the stress-energy tensor). And light has energy.

The source of gravity is mass in Newton's theory of gravity. It is not mass in Einsteins theory - in Einstein's theory the source of gravity is the stress-energy tensor.

You should also DEFINITELY read the usual FAQ on the topic:

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

which talks about "relativistic mass" vs "invariant mass". This removes some important semantic ambiguities from the discussion.

 

[robphy]

In the OP's question, "light" is not the "source" but the "target".
In other words, "light" is an example of "matter" in the often quoted "spacetime tells matter how to move" [as opposed to the rest of quote "matter tells spacetime how to curve"], due to John A. Wheeler.

 

[rbj]

You should also DEFINITELY read the usual FAQ on the topic:

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

which talks about "relativistic mass" vs "invariant mass". This removes some important semantic ambiguities from the discussion.

just to add to the fray, I'm one them old-schoolers that prefer to think of "mass", without further qualification as "relativistic mass" rather than "rest mass" which is the same as "invariant mass". photons actually do have relativistic mass. their (relativististic) mass is $m = E/c^2 = h\nu/c^2$. the relationshipship between relativistic mass and rest mass (or invariant mass) is

$$m = \frac{m_0}{\sqrt{1 - \frac{v^2}{c^2}}}$$

where $m_0$ is the rest mass or invariant mass. since, for photons, $v = c$, the rest mass must be zero and that is why it is commonly said (in recent times) that light has no mass.

 

[Doc Al]

But even using "relativistic mass", you can't just plug that into Newton's law of gravity and expect a correct answer.

 

[vaishakh]

What do we mean by relavistic mass and rest mass? - Like inertial mass means resistance against force.

 

[pervect]

What do we mean by relavistic mass and rest mass? - Like inertial mass means resistance against force.

Did you read the FAQ?

 

[vaishakh]

I am sorry if you feel disturbed. I had originally posted this in Gen Phys but it was moved here since relativitistic concepts give answer to this. However I am a big 0 in relativity and I know nothing about it? Anyway Whatare you talking abt FAQ? I couldn't see FAQ in relativity column. I am extremely sorry if I am frustrating you?

 

[Doc Al]

Anyway Whatare you talking abt FAQ? I couldn't see FAQ in relativity column.

Reread post #4.

 

[pervect]

One of these days, someone will actually READ the link when I post it! I'm sure of it!

So, vaishakh, did you find the link this time around (in my post #4), and read it?

 

[rbj]

But even using "relativistic mass", you can't just plug that into Newton's law of gravity and expect a correct answer.

i think i agree with you in general, but i don't see how the deflection of a photon in the presence of an acceleration of gravity $g_0$ would be different from what a physicist around Newton's time (who doesn't see the speed of light as being qualitatively different from any other fast speed) would expect for a particle of some non-zero mass traveling at speed c. would not the parabolic deflection be the same?

 

[Doc Al]

My point is that applying a Newtonian gravitational model to calculate the deflection of light implicitly assumes a flat spacetime. To find the full deflection of light as it passes a massive body one must also consider the curvature of spacetime as treated in general relativity.

 

[pervect]

i think i agree with you in general, but i don't see how the deflection of a photon in the presence of an acceleration of gravity $g_0$ would be different from what a physicist around Newton's time (who doesn't see the speed of light as being qualitatively different from any other fast speed) would expect for a particle of some non-zero mass traveling at speed c. would not the parabolic deflection be the same?

The deflection of light by masses in GR is twice that predicted by Newtonian theory - that is one of the classical tests of GR.

The deflection of light is controlled by a differential equation, called the geodesic equation, that's fairly similar in large to the Newtonian differential equation.

The difference is that there are additional terms, which can losely be ascribed to spatial "curvature", that become important at high velocities, and cause the beam of light to curve more under GR than it would under Newtonian theory.

There's a little bit about this in the wikipedia article, under "bending of light"

http://en.wikipedia.org/wiki/General_relativity