Acceleration of Light ensity of Space

[Rezai]

Acceleration of Light:Density of Space

Here's the idea: If acceleration is defined as a change in velocity and velocity has two components of course, speed and direction then a change in direction can be said to be a form of acceleration even if the speed is constant. Therefore could one say that light accelerates when passing the event horizon of a black hole? If so would this suggest that the velocity of light may be directed by the density of space? And if this is true, how do we know that a change in the density of space such as within or around a black hole wouldn't affect the speed of light? To give an analogy, just as the speed of sound is set by the density of matter through which it travels, could the speed of light be set by the density of the fabric of space through which it travels?

Thanks.
Rezai

 

[Bill_K]

Rezai,

In general relativity, light follows a geodesic path in a curved spacetime, and therefore does not accelerate. One can try to model this behavior by pretending that space is flat, with some index of refraction chosen to give the correct deflection angle. However such models give only partially correct results. For example see http://www.mathpages.com/rr/s8-04/8-04.htm

 

[bcrowell]

Here's the idea: If acceleration is defined as a change in velocity and velocity has two components of course, speed and direction then a change in direction can be said to be a form of acceleration even if the speed is constant. Therefore could one say that light accelerates when passing the event horizon of a black hole?

It depends on what you mean by acceleration. These things aren't simple to define unambiguously in curved spacetime.

If so would this suggest that the velocity of light may be directed by the density of space?

It would be more accurate to refer to the curvature of spacetime, not the density of space.

And if this is true, how do we know that a change in the density of space such as within or around a black hole wouldn't affect the speed of light?

Because experiments show that the speed of light is independent of gravity. If such an effect existed, it would show up (more weakly) in the Earth's field. It doesn't. What we actually observe in experiments like the Pound-Rebka experiment is gravitational Doppler shifts that change the frequency and wavelength while keeping the speed the same.

 

[strongheart]

There is no test for the instantaneous speed of light - only the average round trip speed can be measured.
Therefore any claim that the speed of light is constant is possibly flawed - we don't actually know if light is faster in one direction and slower in another.

 

[harrylin]

Here's the idea: If acceleration is defined as a change in velocity and velocity has two components of course, speed and direction then a change in direction can be said to be a form of acceleration even if the speed is constant. Therefore could one say that light accelerates when passing the event horizon of a black hole? If so would this suggest that the velocity of light may be directed by the density of space? And if this is true, how do we know that a change in the density of space such as within or around a black hole wouldn't affect the speed of light? To give an analogy, just as the speed of sound is set by the density of matter through which it travels, could the speed of light be set by the density of the fabric of space through which it travels?

Thanks.
Rezai

Quite so. According to Einstein's GR it's not really the "density" of space (at least, no such model exists as far as I know), but the properties of space.
Nowadays it has become unpopular to formulate it like you do, but originally Einstein formulated and calculated the bending of light in a similar way as you do here. Even stronger: the bending of light is according to him a consequence of the gradient in speed ("in the sense of the Euclidean Geometry", or as determined from a distant reference system). If you know the Huygen's construction, then you will understand this; for that is what he used for his prediction of bending of light.

- http://www.bartleby.com/173/22.html (note: "velocity of propagation" is a translation of "Ausbreitungsgeschwindigkeit" which means speed of propagation)
- http://en.wikisource.org/wiki/The_F...Perihelion-motion_of_the_paths_of_the_Planets.

Regards,
Harald

 

[Passionflower]

What we actually observe in experiments like the Pound-Rebka experiment is gravitational Doppler shifts that change the frequency and wavelength while keeping the speed the same.

If the instrumentation would be accurate enough we would definitely measure a different speed of light between two points at different heights.

This is very easy to demonstrate using the Schwarzschild solution.

Only the speed of light at the point of measurement is guaranteed to be constant, the speed of light in a gravitational field between two points is not constant for different positions in a gravitational field.

 

[Drakkith]

There is no test for the instantaneous speed of light - only the average round trip speed can be measured.
Therefore any claim that the speed of light is constant is possibly flawed - we don't actually know if light is faster in one direction and slower in another.

What? If the speed of light, measured by how long it takes to get from its emission source to its absorption source, IE the observer, is always the same, then that is exactly what we mean by the speed of light.

 

[jtbell]

There is no test for the instantaneous speed of light - only the average round trip speed can be measured.

Repeat the round-trip measurement using shorter and shorter distances, and take the limit as the distance goes to zero.

 

[DrGreg]

There is no test for the instantaneous speed of light - only the average round trip speed can be measured.
Therefore any claim that the speed of light is constant is possibly flawed - we don't actually know if light is faster in one direction and slower in another.

What? If the speed of light, measured by how long it takes to get from its emission source to its absorption source, IE the observer, is always the same, then that is exactly what we mean by the speed of light.

There is no test for the instantaneous speed of light - only the average round trip speed can be measured.

Repeat the round-trip measurement using shorter and shorter distances, and take the limit as the distance goes to zero.

I think strongheart may be referring to the one-way speed of light.

The two-way speed of light is constant for all observers in the limit as the distance traveled tends to zero (that's the definition of a derivative), provided they use proper distance and proper time.

The one-way speed of light is a matter of convention, i.e. how you choose to define simultaneity, i.e. what coordinate system you choose to use. It's not that we "don't know" if 1-way light speed is isotropic (the same in all directions); we can choose to make it isotropic or not by our choice of coordinates.

 

[pervect]

I think strongheart may be referring to the one-way speed of light.

The two-way speed of light is constant for all observers in the limit as the distance traveled tends to zero (that's the definition of a derivative), provided they use proper distance and proper time.

The one-way speed of light is a matter of convention, i.e. how you choose to define simultaneity, i.e. what coordinate system you choose to use. It's not that we "don't know" if 1-way light speed is isotropic (the same in all directions); we can choose to make it isotropic or not by our choice of coordinates.

A good summary. I'd just add that one can't really avoid the consequences of relativity by one's choice of coordinate system (isotropic, or non-isotropic). This should be obvious, as a choice of coordinates doesn't have any actual physical significance, though it frequently leads to long and murky arguments :-(.

It's a bit easier to teach physics and to understand the physical significance of the results using isotropic coordinate, though. Explicitly coordinate independent methods, such as Lagrangians, aren't taught in high school. The high-school methods of doing physics DOES require that one make a specific choice of coordinate systems (and that choice is the isotropic choice!), in order that the physical laws (such as the expression for momentum) have their familar form.

 

[strongheart]

What? If the speed of light, measured by how long it takes to get from its emission source to its absorption source, IE the observer, is always the same, then that is exactly what we mean by the speed of light.

There is no way to measure the speed of light in a single direction.
If we could beam light from a source to a detector at some distance and then instantaneously receive the result that the beam reached it's target, then we could calculate the speed in a single direction and therefore the velocity of light.
Similarly if one could beam a photon at us from some distance and instantaneously communicate the exact moment that they initiated the beam, we could start our timer and come up with the velocity of light.

Unfortunately, there is no such method as instantaneous communication.
So, how would one propose to measure the speed of light in a single direction?
Another light beam (or the same beam)? Electricity? Tachyons? Carrier pigeons?
By reflecting the light back toward the source, the distance between the emitter and detector is minimized and the communication between start action and finish action is nearly instantaneous.
So, we may presume to know the round trip average speed of light and never it's velocity.

 

[DrGreg]

So, we may presume to know the round trip average speed of light and never it's velocity.

We can't discover the 1-way velocity by experiment. We can define it, though.

 

[GrayGhost]

We can't discover the 1-way velocity by experiment. We can define it, though.

Let's say we launch a probe with onboard atomic clock, transceiver, and processing system that eventually orbits (say) Neptune. It's synchronised with an Earth clock before launch, and it's trek to Neptune is basically a slow clock transport. Relativistic effects should be negligible. The probe emits digitized EM with clock reading upon transmission. An Earth transmitter could emit EM with earth-clock-time-readout embedded, and the Neptune probe could immediately transpond the signal with it's own clock readout embedded. Knowing the range to Neptune, why would the 1-way speed of light not be ascertainable?

GrayGhost

 

[pervect]

Neptune is probably a bad example, considering that there are significant relative velocities and effects due to the Sun's gravity.

But if you define clock synchronization by slow transport, that's equivalent to defining it by Einstein's method. So if you carry out the above thought experiment in intergalactic space well away from any gravity wells, you should be able to measure what you've defined, as long as "Neptune" and your starting point are at rest relative to each other.

 

[DrGreg]

Let's say we launch a probe with onboard atomic clock, transceiver, and processing system that eventually orbits (say) Neptune. It's synchronised with an Earth clock before launch, and it's trek to Neptune is basically a slow clock transport. Relativistic effects should be negligible. The probe emits digitized EM with clock reading upon transmission. An Earth transmitter could emit EM with earth-clock-time-readout embedded, and the Neptune probe could immediately transpond the signal with it's own clock readout embedded. Knowing the range to Neptune, why would the 1-way speed of light not be ascertainable?

Neptune is probably a bad example, considering that there are significant relative velocities and effects due to the Sun's gravity.

But if you define clock synchronization by slow transport, that's equivalent to defining it by Einstein's method. So if you carry out the above thought experiment in intergalactic space well away from any gravity wells, you should be able to measure what you've defined, as long as "Neptune" and your starting point are at rest relative to each other.

As pervect says, in flat spacetime it can be proved by logic that slow-transport synchronisation and Einstein synchronisation are the same thing. You could do the experiment, but we already know the answer is bound to give the 1-way speed of light equal to the 2-way speed (provided the slow transport is slow enough). You wouldn't be determining some previously unknown speed by experiment, you would simply be verifying that the theory is correct. The point is that you have chosen to use slow-transport synchronisation, and the answer you get depends on this choice; other synchronisations are available.

It would get a bit more complicated in the presence of gravity, as there may be some GR effects to consider. The argument above would still be true over short distances.