Laser traveling near of a supermassive body

[Macedo Junior]

I would like to understand , how a beam laser changes its trajectory near of a supermassive body? Is there any relation with Einstein's equivalence equation between mass and energy?

 

[Jonathan Scott]

Light follows the curvature of space-time, in the same way as a material object in free fall. To a static observer, this shape of space-time is what gives rise to the gravitational field. The effective acceleration in a gravitational field of something traveling at a high speed is $(1+v^2/c^2)$ times that of an object at rest, where the velocity-dependent term is caused by the curvature of space. This means that light is deflected with twice the acceleration of an object at rest (and a material object traveling at near the speed of light is also deflected by a similar amount).

 

[Naty1]

Another way to think about the curving of the laser light is to note that because it's already moving at "c" in a local frame, it can't accelerate in the direction of velocity:it can't go faster than c. But a gravitational field CAN accelerate the light (change direction but not speed) at right angles to the direction of velocity; hence it can be curved by a force perpendicular to the direction of motion.

 

[cos]

Another way to think about the curving of the laser light is to note that because it's already moving at "c" in a local frame, it can't accelerate in the direction of velocity:it can't go faster than c. But a gravitational field CAN accelerate the light (change direction but not speed) at right angles to the direction of velocity; hence it can be curved by a force perpendicular to the direction of motion.

In his book 'Einstein's Universe' (62 BBC 1979) Nigel Calder wrote:- "Light travels faster towards the center of gravity than away from it."

So I assume that when a laser beam is aimed toward the center of gravity ILO horizontally across that field it accelerates 'in the direction of velocity'.

 

[Jonathan Scott]

In his book 'Einstein's Universe' (62 BBC 1979) Nigel Calder wrote:- "Light travels faster towards the center of gravity than away from it."

So I assume that when a laser beam is aimed toward the center of gravity ILO horizontally across that field it accelerates 'in the direction of velocity'.

Sounds like rubbish to me; light curves towards the direction in which it travels SLOWER, in the same way as we use Snell's law to describe refraction, and light beams in opposite directions at any location in a static metric travel at the same speed relative to the coordinate system (although that may not necessarily be the same speed as light beams in another direction, except in an isotropic metric).

In an isotropic metric, the momentum Ev/c^2 of a test particle relative to the coordinate system (using the coordinate system values of v and c) behaves in a more Newtonian way than its velocity. The rate of change of the momentum (that is, the effective force) is like the conventional Newtonian gravitational force, in that it is a vector directed toward the center and has the same magnitude regardless of the direction in which the test particle is travelling, although for relativistic speeds the magnitude is multiplied by (1+v^2/c^2) as previously mentioned. This rule applies even when v=c, for light, so even if light slows down closer to the center, its momentum increases in the same way as for a material object.

As the total energy E of the test particle is constant in this case (as in the Newtonian case where potential plus kinetic energy is constant), the same applies to the rate of change of v/c^2, provided that c is treated as a variable relative to the coordinate system.

 

[Naty1]

In his book 'Einstein's Universe' (62 BBC 1979) Nigel Calder wrote:- "Light travels faster towards the center of gravity than away from it."

Sounds like rubbish to me; light curves towards the direction in which it travels SLOWER

...yes...it slows...

But it also accelerates(!) meaning the direction of motion changes. The observed speed depends on the reference frame of the observer.

Such comments as Calder's must also provide the reference frame utilized.

But statement is backwards: Viewed from a great distance, light traveling towards a gravitational mass (say a black hole) appears to slow and to never reach the event horizon. Viewed from afar, everything slows in an increasingly strong gravitational field.

In such gravity, viewed locally in a free falling frame, light appears to remain at speed c ...

When viewed from a great distance strange things happen as space may be curved due to gravity ...and hence light curves..., time changes in different gravitational potentials, and large "distance" becomes ambiguous. Viewed locally for brief time periods, none of this is observed.

For a long discussion THREAD...see HOW DOES LIGHT SLOW IN THE PRESENCE OF GRAVITY.. today on pg 2 under Relativity...