How does light slow in the presence of gravity?

[DrGreg]

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.

 

[spidey]

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

 

[Phrak]

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[/color]

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]

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.*[/color]

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.

___
*[/color]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.

 

[Naty1]

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??

 

[DrGreg]

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.

 

[granpa]

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.

wikipedia says this about him:

Charles Lane Poor (1866-01-18 – 1951-09-27)[1][2] was born in Hackensack, New Jersey, the son of Edward Erie Poor. He graduated from the City College of New York and received a Ph.D. in 1892 from Johns Hopkins University. Poor became an American astronomer and professor of celestial mechanics at Columbia University from 1903 to 1944, when he was named Professor Emeritus. He published a monograph disputing the evidence for Einstein's theory of relativity in the pre-war years before the theory became firmly established.[3][4] CL Poor published a series of papers (see bibliography) that reflect his lack of understanding for the theory of relativity.

For 25 years, Poor was chairman of the admissions committee of the New York Yacht Club. In addition, he was a fellow of the Royal Astronomical Society and an associate fellow of the American Academy of Arts and Sciences. He served several terms as mayor of Dering Harbor on Long Island, New York, and invented a "line of position computers" for yachting navigation. At Columbia University, Poor was a teacher of the astronomer Samuel A. Mitchell, who went on to become director of the Leander McCormick Observatory at the University of Virginia.[5]

its one thing to call me a crackpot and delete my ideas but it another thing entirely to delete a reference to an article by a professional astronomer in a professional journal. if there is anything wrong in his calculations then I would be the first to want to know about it. the math in it is simple and straighforward and it should be quiet easy for you to point out where the error lies.

except for the 'historical' section at the bottom of the frontpage most of the other papers in the website where the pdf was located are garbage. I stated so myself. yet you then give me an infraction for posting that link (to a professional paper in a professional journal) as though my only purpose in doing so was to somehow promote all the other crackpot ideas (that I myself called garbage) on that site which I did not link to (and never would)