# How does light slow in the presence of gravity?

DrGreg
Gold Member
Yes, that is what Bergmann says in my posted quote....it makes sense, actually, because attached to a photon, you'd be freely falling (no acceleration) and all would be "normal" from your frame of reference...
Sorry, but you can't attach yourself to a photon, not if you have non-zero mass. By a "free-falling observer" I mean a free-falling massive observer, not quite the same thing as (free-falling) photon. A photon does not define a local inertial reference frame.

Potential energy IS independent of frame of reference,
In my rocket example, the apple has zero kinetic energy and zero potential energy in the apple's own inertial frame. In the rocket's accelerating frame, the apple initially has increasing kinetic energy, offset by decreasing potential energy. So, potential energy is dependent on reference frame.

so if we say light slows down near massive object then would that mean the value of \epsilon_0 \ and \mu_0 \ changes ?

If George were talking about the standard Einstein-synchronised Minkowski coordinates of an inertial observer, he would be wrong. But I reckon he was talking about:

- either accelerated coordinates in SR (see my previous post in this thread)

- or non-standard coordinates of an inertial observer, such as those at the bottom of this post

And in either of those cases, the coordinate speed of light need not be c.
So the moral of the story is, don't use stock quotes for coordinates or don't confuse temperature with time. Which begs the question, what constitutes 'good' coordinates.

DrGreg
Gold Member
So the moral of the story is, don't use stock quotes for coordinates or don't confuse temperature with time. Which begs the question, what constitutes 'good' coordinates.
If an observer A wants to set up a "physical" coordinate system at event E.

1. Find an inertial observer B who is momentarily stationary, relative to A, at event E. An observer is inertial if they are free-falling i.e. they carry an accelerometer that measures a constant proper acceleration of zero. B is the "co-moving inertial observer" at E.

2. Observer B sets up a (local) coordinate system using his proper-time clock and a lattice of relatively-stationary clocks all synchronised to his using Einstein's synchronisation convention; and measuring distance by radar.*

3. Observer A makes local measurements near event E by asking B to make the measurement on her behalf. "Near" means over ranges where spacetime curvature can be ignored and any relative acceleration between A and B can be ignored. This rough statement can be made mathematically precise through calculus.

Under these conditions, A will measure the speed of light at E to be c. However, if she extrapolates her coordinate system to "non-local" events, she may calculate that the speed of light somewhere other than E takes a different value. The extrapolated coordinate system is no longer a "physical" coordinate system (except at E).

It's possible to set up coordinate systems (using time, distance or related quantities such as angle, but not unrelated quantities such as temperature) that don't coincide with "physical" coordinates anywhere.

When studying black holes, it's traditional to use a spherical polar coordinate system extrapolated from a "stationary" observer notionally "at infinity". Such a coordinate system never exactly coincides with a "physical" coordinate system as defined above, but at very large distances the difference is negligible.

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*It has just occurred to me that by specifying in step 2 that distance is measured by radar, the "physical" speed of light is c by definition. This corresponds to the modern-day definition of the metre. However we could instead say that B uses stationary rulers to measure local distance. It's an experimentally verified hypothesis that ruler distance and radar distance are locally the same for inertial observers.

DrGreg...

I posted
Yes, that is what Bergmann says in my posted quote....it makes sense, actually, because attached to a photon, you'd be freely falling (no acceleration) and all would be "normal" from your frame of reference...
You posted

Sorry, but you can't attach yourself to a photon, not if you have non-zero mass. By a "free-falling observer" I mean a free-falling massive observer, not quite the same thing as (free-falling) photon. A photon does not define a local inertial reference frame.
I agree, my wording "attached to a photon" was extremely sloppy, unnecessary....

but what distinction do you make between a free falling mass and a photon...if mass energy equivalence holds, do they move along different curves in free fall??

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DrGreg
Gold Member
but what distinction do you make between a free falling mass and a photon...if mass energy equivalence holds, do they move along different curves in free fall??
The big difference is that non-zero masses always travel slower than light, whereas the photons travel at, ..er.., the speed of light (as measured by any local inertial observer's local coordinate system). So they're not identical in every respect. In 4D spacetime they follow different curves. In 3D space it depends which direction they travel. Anything can travel in a spatially-straight line radially, massive particle or massless photon. But these would be different 4D curves (actually, from the point of view of a local inertial observer, they would be different locally-straight 4D lines).

Here, by "mass" I mean "rest mass" a.k.a. "invariant mass" (not "relativistic mass" which includes kinetic energy). In this terminology, inertial particles have mass ("are massive"), photons are massless.

"Mass energy equivalence" means that mass can be considered as one form of energy (just like kinetic energy, potential energy, heat energy etc are different forms). It doesn't mean all energy "is" mass. It does mean that when you add up all forms of energy to see what has been conserved, you have to include mc2 to get the equations to balance.

why was my post with the link to a pdf of 'the relativity deflection of light' deleted?
its a pdf of an article in the journal of the royal astronomical society of canada by the professional astronomer Charles Lane Poor.