[JohnDuffield]

You seem to think that you can stick to one aspect of one physical scenario and use it to defeat many unrelated aspects of physics. If you accept Newton's Third Law, then you accept that a photon falling into a black hole also attracts the black hole. So the energy increase in the photon is exactly matched by a loss in the black hole

No it isn't. This is clearer if you use a falling brick. Momentum p=mv is shared equally, but kinetic energy KE=½mv² isn't.

One cannot simply measure the total energy of the system, that does not change, and then say that none of the energy for any part of the system never changes; that's simply the fallacy of division.

The brick's energy doesn't change. Gravity merely converts potential energy into kinetic energy. Read this:

"As an illustration, consider two objects attracting each other in space through their gravitational field. The attraction force accelerates the objects and they gain some speed toward each other converting the potential (gravity) energy into kinetic (movement) energy..."   

John, you can measure a expansionary redshift, and their photons too, and also find them having lost 'energy' due to it.

True enough. But where did this energy go?

In fact any redshift of a photon means a loss of energy, and it's just as strange due to me moving away from its source than with a expansion.

Like Bill was saying, your motion doesn't actually change the photon. It hasn't actually lost any energy.

I don't see how I can argue the same with a expansion though? That supports what you see looking at a light source redshifting, moving away from you, relativistically speaking, and also supports your definition of a photon staying intrinsically the same.

Interesting, isn't it?

The point is that no matter ones direction, from, or towards the photon source, those photons will have a exact same speed.

That's another can of worms. If you head towards a star that's two light years away at 0.99999c, and if that star goes nova just as you set off, you will see the flash when you're halfway there. Your local measurement of that light coming towards you is c, but you and the light covered the two light years in one year of my time. Your closing speed was 1.99999c.

The only difference is one of energy lost, or gained. and that is one he* of a mystical thing to me. So we can use classical physics to describe it through the idea of momentum, but we can't use light slowing down or speeding up, relative ourselves...

What you measure is not always the way it is.

[PhysBang]

You seem to think that you can stick to one aspect of one physical scenario and use it to defeat many unrelated aspects of physics. If you accept Newton's Third Law, then you accept that a photon falling into a black hole also attracts the black hole. So the energy increase in the photon is exactly matched by a loss in the black hole

No it isn't. This is clearer if you use a falling brick. Momentum p=mv is shared equally, but kinetic energy KE=½mv² isn't.

Sure, but the momentum of the brick changes if we examinie it alone. The momentum of the photon changes as well. And where is the momentum of a photon?

The brick's energy doesn't change. Gravity merely converts potential energy into kinetic energy. Read this:

"As an illustration, consider two objects attracting each other in space through their gravitational field. The attraction force accelerates the objects and they gain some speed toward each other converting the potential (gravity) energy into kinetic (movement) energy..."   

OK, so you found a single sentence that supports what you are saying. But that sentence does not say that the momentum doesn't change. Nor is attempting textual analysis of individual quoatations a replacement for physics.

The point is that no matter ones direction, from, or towards the photon source, those photons will have a exact same speed.

That's another can of worms. If you head towards a star that's two light years away at 0.99999c, and if that star goes nova just as you set off, you will see the flash when you're halfway there. Your local measurement of that light coming towards you is c, but you and the light covered the two light years in one year of my time. Your closing speed was 1.99999c.

Some people make a very basic mistake in relativity theory, thinking that the speed of light is always relative to some object. The speed of light is, in special relativity, constant relative to nice systems of coordinates where Newtonian mechanics works. In general relativity, the speed of light is constant in every infinitesimal region of every system of coordinates.

[JohnDuffield]

Only it isn't constant in the room you're in:

[PhysBang]

Again, cherry-picking quotations from Einstein does not help us understand physics.

[Bill S]

Again, cherry-picking quotations from Einstein does not help us understand physics.

That's true, but for non-experts like me some explanation of what Einstein meant by (for example) the last sentence of John's quote would be of great value.

[PmbPhy]

Again, cherry-picking quotations from Einstein does not help us understand physics.

He was explaining that the coordinate speed of light only has the value c in an inertial frame, in a vacuum in the absence of a gravitational field. If there is a gravitational field present then the coordinate speed of light varies with the gravitational potential. This is a fact of general relativity and well tested.

I derived this here - http://home.comcast.net/~peter.m.brown/gr/c_in_gfield.htm

The derivation for a uniform gravitational field/uniformly accelerating frame of reference is the same as the one Einstein did in his 1911 paper on the subject.

And there's absolutely nothing wrong with quoting a physics source. It is doing physics in the sense that you're referring to the calculations of results obtained by others. Doing it correctly is the challenge.

[PhysBang]

It is one thing to recognize that the coordinate speed of light changes over finite distances. It is another thing to deny that the speed of light is constant over infinitesimal regions.

[PmbPhy]

It is one thing to recognize that the coordinate speed of light changes over finite distances. It is another thing to deny that the speed of light is constant over infinitesimal regions.

I see. Is that what he was claiming? In which post did he make such a remark?

By the way. If you're interested a derivation from a text there here's one from Gravitation and Spacetime - 3rd Ed. by Ohanian and Ruffini

http://home.comcast.net/~peter.m.brown/gr/Ohanian_sol.pdf

[PmbPhy]

But the fact remains that when you send a 511keV photon into a black hole, its mass increases by 511keV/c², not a zillion tonnes.

Do you know how to calculate the mass of a particle when it's in a gravitational field?

We know of no situation where it isn't.

There's no reason to assume that the energy of any particle, including photons, is conserved when its moving through a gravitational field. The law of conservation of energy applies to the total energy of a system, not just to single particles moving through a gravitational field. An example of when the energy of a particle changes when its moving through a gravitational field is when the gravitational potentials, i.e. the g_uv, are time dependent.

The derivation of this fact can be found in A First Course in General Relativity - 2nd Ed. by Bernard Schutz, page 176

I put it on my website at http://home.comcast.net/~peter.m.brown/gr/conserved_quantities.htm

If some of those cosmology texts say gravitational field energy is negative, they're at odds with Einstein, ...

They most certainly are not!

...the energy of the gravitational field shall act gravitatively in the same way as any other kind of energy

Just because the energy of a gravitational field acts the same way as other energy, it doesn't mean it has the have the same value of energy.

You claim that there's no such thing as negative energy in physics. I think that you don't know what energy is.

[JohnDuffield]

That's true, but for non-experts like me some explanation of what Einstein meant by (for example) the last sentence of John's quote would be of great value.

He meant what he said. Light curves in the room you're in because the speed of light is spatially variable. The speed of light near the floor is less than the speed of light near the ceiling. If it wasn't, your pencil wouldn't fall down.

[PmbPhy]

Light curves in the room you're in because the speed of light is spatially variable. The speed of light near the floor is less than the speed of light near the ceiling. If it wasn't, your pencil wouldn't fall down.

So what? Everyone who knows GR knows this. So long as you know that this is not about infinitesimals. PhysBang was correct when he said

It is one thing to recognize that the coordinate speed of light changes over finite distances. It is another thing to deny that the speed of light is constant over infinitesimal regions.

He's much better than you at physics. You'd better listen to him.

[JohnDuffield]

Do you know how to calculate the mass of a particle when it's in a gravitational field?

You don't calculate it, you measure it. And I will reiterate: when you send a 511keV photon into a black hole, the black hole mass increases by 511keV/c². You know this.

See? This is what I mean by the errors you keep making. There's no reason to assume that the energy of any particle, including photons, is conserved when its moving through a gravitational field.

I'm not making any errors, and you know it. Because in your article you said this:

"The total energy of a photon moving through a gravitational field is constant."

They most certainly are not!

Yes they are. Einstein made it crystal clear that gravitational field energy is positive. It causes more gravity.

This is a good example of your poor understanding of what you read. Just because the energy of a gravitational field acts the same way. Just because it acts the same way as other energy it doesn't mean it has the have the same value of energy. That's just plain dumb.

No, it's a good example of my understanding. When two bodies fall together some of their mass-energy is converted into kinetic energy which ends up being radiated away into space. We're then left with a mass deficit. People then refer to binding energy as negative energy, but there's no actual negative energy present, just less positive energy. The conservation of energy books balance.     

You claim that there's no such thing as negative energy in physics. I think that you don't know what energy is.

I know what energy is. See post #7 here where on 19/09/2013 you said this:

"My objection with French here is that he gives the impression that energy "exists" whereas physics uses it merely as a bookkeeping scheme which requires no physical system."

It does exist. Matter is made from it. Ah, I see you've changed your tune, because in your article you say this:

"This means that there is a flow of energy going around the electron. What is it that's actually flowing? All we can do at this point is give it a name. And the name we give it is energy." Have you been reading my Energy Explained?

[Bill S]

Another naïve question.

Light in a vacuum travels at “c”.

Light in a medium appears to travel more slowly, but this is because the photons interact with atoms in the medium (I know that’s an oversimplification).  Between atoms, light still travels at “c”.

Light slows in a gravitational field.  Unless gravitons are physically real, there is nothing in a gravitational field to take the place of atoms in other media. 

What slows light in a gravitational field?

[PhysBang]

What slows light in a gravitational field?

The causal structure of spacetime?

I think I need time to come up with a better answer.

[JohnDuffield]

Light slows in a gravitational field. Unless gravitons are physically real, there is nothing in a gravitational field to take the place of atoms in other media. What slows light in a gravitational field?

The altered properties of space. In mechanics a shear wave travels at a speed v = √(G/ρ) where G is the shear modulus of elasticity and ρ is density. In electrodynamics the an electromagnetic wave travels at a speed c = √(1/ε0μ0) where ε0 is the permittivity of space and μ0 is the permeability.

[yor_on]

I would call it different definitions Bill. SR describes a 'flat universe', and assuming a perfect vacuum you have 'c'. GR describes gravity. A photon 'interact' with gravity. f you let go of a propagation, then it can be defined to the way a field interact, which makes it simpler. Not when it comes to how this 'field' is constructed though, and how you want to consider its 'dimensions' 'infinite stretch' etc. But it let us free from the discussion whether a photon path is 'bent' or 'slowed down' from the eye of the beholder. We're so used to motion, we see it everywhere, and when we measure a 'speed of light' we automatically start to discuss paths and 'weak experiments' proving that concept. But you don't really need it, you only need a logic giving those excitations an expression that also can be translated into a 'speed'.
==

what I think one need to see there is that the description no longer is solely about 'speeds' and 'paths', but more about 'timings', as expressed through that possible 'field'. It's somewhat of a bother how to think of this field, as we have real observer dependencies existing, making my observation differ from yours. Also it's somewhat of a huddle trying to define it as 'deterministic', or not. Myself I would expect it to be microscopically probabilistic and macroscopically defined from observer dependencies though, just as the universe we think us see normally. So 'non linear' to me, and if you use time symmetries, also non linear both ways. If there is a symmetry that is.

The last one is weird, but it has its own logic. As long as you have a way to record every outcome 'everywhere' (and at all 'times') you can disregard that statement. but if you don't have that ability, then you will find the past bifurcate into possibilities, just as the future can be seen to do, until it becomes a 'now', as in you observing that specific outcome. If the universe is non linear though, then I don't see how we ever will be able to know all outcomes. And if that is true for a future, then that 'future' also is my 'now', and 'past'.

Ever heard of 'the fog of war'? How about 'the fog of history'

[PmbPhy]

What slows light in a gravitational field?

The causal structure of spacetime?

I think I need time to come up with a better answer.

The answer is that gravitational time dilation causes light to slow down. Think about it and you'll soon realize why.

[PmbPhy]

The altered properties of space. In mechanics a shear wave travels at a speed v = √(G/ρ) where G is the shear modulus of elasticity and ρ is density. In electrodynamics the an electromagnetic wave travels at a speed c = √(1/ε0μ0) where ε0 is the permittivity of space and μ0 is the permeability.

All wrong.

[PmbPhy]

You don't calculate it, you measure it.

I can't believe this!!! The mass is calculated using the theory of relativity. One measures the mass and compares it with what the theory predicts. But in all cases one can calculate what the mass should be. In fact sometimes you actually cannot measure it, you have to calculate it.

[jeffreyH (OP)]

Being the OP I would like to pose a further question. Would the decrease in energy of the photon moving away from a gravitational field source be linear over distance? That is would the decrease in the gradient be a straight line?