It is said that,

 

Speed of light is c, locally.

 

What does locally mean here?

Loosley without mathematics, this means that in small enough regions of space-time all physics reduces to that of special relativity. That is we always have in small enough regions inertial reference frames and the speed of light will be measured as c in these frames.

Edited May 30, 201411 yr by ajb

As ajb said, locally is a small enough region of space-time. This is a region which is so small that the effects of gravity are negligible. So you can use special relativity here.

 

Local space-time: Put simply, imagine you are inside a small enough elevator which is in free-fall above the Earth. You feel weightless. Any objects in the elevator fall at the same rate of acceleration as you do (ignoring air effects). So these object appear to be floating alongside you. It feels the same as if the elevator is in outer space with no gravity. This is a local region of space-time.

 

Global space-time: Now imagine a second elevator at the same height above Earth but far away. The two elevators fall towards the center of the Earth. Thus they get closer together as they fall. Here the effects of gravity are observable. If you look from your elevator to the other, you see it getting closer to you over time. So you can tell that you are in a gravitational field and not floating in space. This is a global region of space-time. Over this region, general relativity is required.

 

As I say in Einstein Relatively Simple, "gravity does not show its effects locally -- over a small enough space and time. The effects of gravity are only seen on a global scale."

As ajb said, locally is a small enough region of space-time. This is a region which is so small that the effects of gravity are negligible. So you can use special relativity here.

 

Local space-time: Put simply, imagine you are inside a small enough elevator which is in free-fall above the Earth. You feel weightless. Any objects in the elevator fall at the same rate of acceleration as you do (ignoring air effects). So these object appear to be floating alongside you. It feels the same as if the elevator is in outer space with no gravity. This is a local region of space-time.

 

Global space-time: Now imagine a second elevator at the same height above Earth but far away. The two elevators fall towards the center of the Earth. Thus they get closer together as they fall. Here the effects of gravity are observable. If you look from your elevator to the other, you see it getting closer to you over time. So you can tell that you are in a gravitational field and not floating in space. This is a global region of space-time. Over this region, general relativity is required.

 

As I say in Einstein Relatively Simple, "gravity does not show its effects locally -- over a small enough space and time. The effects of gravity are only seen on a global scale."

 

Isn't local speed of light affected by the spontaneous creation of particles in empty space?

If as speed of a neutrino increases to near Cee, & time slows down relative to a fixed observer, does the photon, traveling at Cee experience time? Or has time stopped for the photon, that is, does the photon experience time? That is, if one were to ride on a photon, does all time stop? Or does almost all time stop for a neutrino at 99.9999% Cee?

 

That is, is there instantaneity for the photon?

Edited June 3, 201411 yr by herb w.

here is another example, if you have two ships at relativistic uniform motion

 

ships A's time would appear normal from his frame of reference clock, ie clock on his ship, however if he could see a clock on ship b it would appear to be running slowly and vice versa.

Isn't local speed of light affected by the spontaneous creation of particles in empty space?

I think virtual particles are not constrained by the speed of light (or they can be interpreted as being able to exceed c) but they don't define the speed of light.

If as speed of a neutrino increases to near Cee, & time slows down relative to a fixed observer, does the photon, traveling at Cee experience time? Or has time stopped for the photon, that is, does the photon experience time? That is, if one were to ride on a photon, does all time stop? Or does almost all time stop for a neutrino at 99.9999% Cee?

 

That is, is there instantaneity for the photon?

No a photon doesn't experience time. It doesn't have a valid frame of reference and you can't ride on a photon. You can't describe sensible observations at that speed, it is an analogy at best. By analogy, distance in the direction of travel is contracted to 0 and can be traversed in an instant.

 

A neutrino experiences time at the usual rate (1 second per second). Ie. it ages normally, or "its clock" ticks normally. Generally other clocks would be slowed to a near stop.