# The Naked Scientists Forum

### Author Topic: Does gravity alter the speed of light?  (Read 2204 times)

#### Kr.I.S

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##### Does gravity alter the speed of light?
« on: 08/10/2013 23:15:37 »
Light is affected by gravity, its path is bent by gravity, demonstrated by gravitational lensing.

This got me thinking: speed of light is a constant, as we all know, however if its path and therefore direction is changing, is its velocity too? is light under acceleration when passing through a gravitational field?
« Last Edit: 09/10/2013 09:27:42 by chris »

#### Pmb

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##### Re: Gravity and Light
« Reply #1 on: 08/10/2013 23:40:29 »
Light is affected by gravity, its path is bent by gravity, demonstrated by gravitational lensing.

This got me thinking: speed of light is a constant, as we all know, however if its path and therefore direction is changing, is its velocity too? is light under acceleration when passing through a gravitational field?
The speed of light is only constant in an inertial frame in flat spacetime. That is no longer true when there is a gravitational field present because such a field is equivalent to a non-inertial frame.

#### evan_au

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##### Re: Does gravity alter the speed of light?
« Reply #2 on: 09/10/2013 10:01:41 »
Velocity is composed of speed & direction. If the direction changes, the velocity has changed, even if the speed remained the same.

#### Phractality

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##### Re: Does gravity alter the speed of light?
« Reply #3 on: 09/10/2013 17:19:36 »
When we illustrate the path of light in warped space-time by drawing it on a flat 2D surface, the result is a curved path. If we draw the space-time grid on that same 2D surface, it should appear warped, and the light's path should be parallel to the warped coordinates. In Minkowski 4D coordinates, the path of light is a straight line. In fact, the 4D space-time grid is defined by the straight paths of imaginary photons. So, in Minkowski space-time, light does not accelerate in either speed or direction.

This doesn't mean that Euclidean space is invalid. It just isn't as useful as Minkowski space-time for calculating trajectories in gravitational fields. In Euclidean space, a photon does accelerate. It's momentum changes when passing near a star, which means the star is pulling the photon with a gravitational force. Conservation of momentum dictates the photon must exert an equal and opposite gravitational force on star. Thus, in Euclidean space, a photon has a gravitational field of its own.

Unfortunately, the use of Euclidean space necessitates a whole different set of definitions for units of space, time, etc. The math is unwieldy, even more so than the math of general relativity.

If I had any aptitude for math, I think I would use numerical analysis to predict paths in Euclidean space, and I'd expect to get results equivalent to those derived by Einstein's general relativity. The results should be equivalent in predicting whether two objects will collide or orbit. The two methods should agree on what a space traveler would observe on his clock and what he should see out his window.

#### Kr.I.S

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##### Re: Does gravity alter the speed of light?
« Reply #4 on: 09/10/2013 20:51:18 »
When we illustrate the path of light in warped space-time by drawing it on a flat 2D surface, the result is a curved path. If we draw the space-time grid on that same 2D surface, it should appear warped, and the light's path should be parallel to the warped coordinates. In Minkowski 4D coordinates, the path of light is a straight line. In fact, the 4D space-time grid is defined by the straight paths of imaginary photons. So, in Minkowski space-time, light does not accelerate in either speed or direction.

This doesn't mean that Euclidean space is invalid. It just isn't as useful as Minkowski space-time for calculating trajectories in gravitational fields. In Euclidean space, a photon does accelerate. It's momentum changes when passing near a star, which means the star is pulling the photon with a gravitational force. Conservation of momentum dictates the photon must exert an equal and opposite gravitational force on star. Thus, in Euclidean space, a photon has a gravitational field of its own.

Unfortunately, the use of Euclidean space necessitates a whole different set of definitions for units of space, time, etc. The math is unwieldy, even more so than the math of general relativity.

If I had any aptitude for math, I think I would use numerical analysis to predict paths in Euclidean space, and I'd expect to get results equivalent to those derived by Einstein's general relativity. The results should be equivalent in predicting whether two objects will collide or orbit. The two methods should agree on what a space traveler would observe on his clock and what he should see out his window.

very informative post thank you, euclidean spacetime is very wacky and intriguing.
So now im wondering in euclidean spacetime photons have mass correct? so can you accelerate any other massive particle to the speed of light?

#### Phractality

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##### Re: Does gravity alter the speed of light?
« Reply #5 on: 10/10/2013 02:53:12 »
Quote from: Kr.I.S
So now im wondering in euclidean spacetime photons have mass correct?
Euclidean space is what you learned in high school geometry. It includes such weird properties as the sum of interior angles of a triangle must total 180°, and parallel straight lines can only cross once. How weird can you get!?
Quote from: Kr.I.S
...so can you accelerate any other massive particle to the speed of light?
That would depend on how you define the speed of light in your Euclidean space. I doubt if it would make any sense for a particle with proper mass to exceed the speed of light, no matter how you define it.
« Last Edit: 10/10/2013 04:04:03 by Phractality »

#### Pmb

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##### Re: Does gravity alter the speed of light?
« Reply #6 on: 10/10/2013 05:00:05 »
Quote from: Kr.I.S
very informative post thank you, euclidean spacetime is very wacky and intriguing.
So now im wondering in euclidean spacetime photons have mass correct? so can you accelerate any other massive particle to the speed of light?
The term euclidiean refers to the way distances are measured in a particular space. To determine if a space is Euclidean it must first have a metric defined on it. When the metric is given one can determine if its Euclidean by observation.

Suppose we label spacetime coordinates using what is known as Minkowski coordinates, i.e. (t, x, y, z). If the metric in these coordinates is

ds2 = d(ct)2 - dx2 - dy2 - dz2

Then the space is called Minskowskian. If the metric is

ds2 = d(ct)2 + dx2 + dy2 + dz2

Then the space is Euclidean. If a space is non-Euclidean it does't mean that straight lines only cross once. That refers to curved spaces, not non-Euclidean spaces

Flat Minkowski spacetime is non-Euclidean.

#### The Naked Scientists Forum

##### Re: Does gravity alter the speed of light?
« Reply #6 on: 10/10/2013 05:00:05 »