1. How can gravity bend light if photons are massless? Or If it is just curving space-time and bending the photon's path, does this mean that spacetime has mass?

2.

3. Photons only have zero rest-mass.

4. Gravity couples to the Stress-energy tensor, of which, mass is only one aspect. It also includes energy and momentum. Since the photon has both energy and momentum, it responds to a gravity field even though it is massless.

5. Originally Posted by schiz0yd
How can gravity bend light if photons are massless? Or If it is just curving space-time and bending the photon's path, does this mean that spacetime has mass?
Gravity cis the curvature of space, and so the photon has to follow that curvature.

If space was flat, like the long straight of a NASCAR oval, the photon would move in a straight line.

If space is curved, like at the ends of the NASCAR oval, the photon would be forced to follow a new path.

The photon itself would also cause the space around it co curve because it has both energy and momentum. Energy causes space to curve the same way that mass does because of the relation which tells us that energy and matter are equivalent.

6. This is from Wiki,

Gravity corresponds to changes in the properties of space and time, which in turn changes the straightest-possible paths that objects will naturally follow. The curvature is, in turn, caused by the energy-momentum of matter.

Paraphrasing the relativist John Archibald Wheeler, spacetime tells matter how to move; matter tells spacetime how to curve.
Would it be fair to say - spacetime has energy-momentum?

7. No, that doesn't sound right. Just because matter in spacetime has energy-momentum doesn't mean that spacetime itself would.

8. Originally Posted by MagiMaster
No, that doesn't sound right. Just because matter in spacetime has energy-momentum doesn't mean that spacetime itself would.
However, gravitational fields do have energy-momentum so that "gravity gravitates", and since gravity is really just curvature of spacetime in that sense spacetime does have energy-momentum.

9. Oh. I stand corrected then.

10. Yes, photons are considered massless. But they have an energy. The energy of a photon is determined by, . Or that is, the energy of the photon is equal to the product of it's wavelength, and Planck's constant. Then we take Einsteins equation for mass-energy equivalence, . Do a little algebra to get . And now the photon has an associate mass.
tell's us that mass and energy are not two different thing's. That indeed, they are variant expression's of a self-same thing. A rhinoceros is big, slow, obvious. The definition of mass. A mosquito is tiny, fast, hard to see. The definition of energy. But they are both one thing, biology. A photon move's in waves, energy. But it is a particle, mass. Thermodynamic's tell's us that temperature, is just the statistical average of atomic kinetic's for a particular sample volume. All of the existential is one coin, and mass is head's, and energy is tail's. Or, vice-versa.

11. how does mass curving spacetime differentiate from the aether theories of matter affecting the flow of the aether. sounds kinda similar.

12. Originally Posted by schiz0yd
how does mass curving spacetime differentiate from the aether theories of matter affecting the flow of the aether. sounds kinda similar.
The difference is that the aether was a material substance, space-time is not.

When it is said that space-time is "curved" it just means that the geometry is non-Euclidean. What is effected is how we measure space and time.

13. Originally Posted by Janus
The difference is that the aether was a material substance, space-time is not.

When it is said that space-time is "curved" it just means that the geometry is non-Euclidean. What is effected is how we measure space and time.
The geometry of what? it has to be 'something' if it's involved in an interaction. and since material substance is just as much made of the same thing as everything else, then spacetime would have to be made of the opposite of that, then. right? it interacts with energy but is not made of energy. this is confusing.

14. Originally Posted by schiz0yd
Originally Posted by Janus
The difference is that the aether was a material substance, space-time is not.

When it is said that space-time is "curved" it just means that the geometry is non-Euclidean. What is effected is how we measure space and time.
The geometry of what? it has to be 'something' if it's involved in an interaction. and since material substance is just as much made of the same thing as everything else, then spacetime would have to be made of the opposite of that, then. right? it interacts with energy but is not made of energy. this is confusing.
Nope.

Read a book on general relativity. Rindler's Essential Relativity, Special, General and Cosmological is about the least mathematically demanding of the genre.

15. I'm going out on a limb here, but. Think of space-time as a symbol representing a number set. The symbol itself has no particular value, but it's like a bin, full of numbers. If we take those numbers out, and do calculations with them, they return predictive results. We've used Space-time to accomplish something, but space time has no intrinsic existence. It's just an idea. It's a drawing of a bridge. There is no actual bridge, but there is the idea of one.
As for aether? Look up, Michaelson-Morley, ablation of starlight, and interferometer.

16. i know they are not technically the same thing and you are using the technical definitions of each one to prove this. i'm just saying the concept seems pretty similar; matter/energy acting upon a fabric/substance in the vacuum.

17. Originally Posted by GiantEvil
I'm going out on a limb here, but. Think of space-time as a symbol representing a number set. The symbol itself has no particular value, but it's like a bin, full of numbers. If we take those numbers out, and do calculations with them, they return predictive results. We've used Space-time to accomplish something, but space time has no intrinsic existence. It's just an idea. It's a drawing of a bridge. There is no actual bridge, but there is the idea of one.
As for aether? Look up, Michaelson-Morley, ablation of starlight, and interferometer.
Space-time is Lorentzian 4-manifold. General relativity as a subject is basically the differential geometry of such manifolds. That manifold is our universe. It is pretty real in that sense.

18. a mass falling into a black hole has force, but a photon allready is energy.

To give energy a force, one must divide with time:

mc^2/time = force.

But the photon allready has a force that determin it's path: F(release)

so a sideways gravity force would only change the energy in the photon approximately:

F*t(release)^2 + (F(gravity)*T)^2 = F*t(photon)^2

Since both forces are true, they add.

Then a black hole blueshifts radiation, and energy can escape from the black hole & I do mention that the blueshift is quant.

The slope down the black hole for the photon is F(gravity)*T divided with F*t(release)

Exactly how much this is can be read from the blueshift.

All a bit experimental, sorry.

19. Space-time is Lorentzian 4-manifold. General relativity as a subject is basically the differential geometry of such manifolds. That manifold is our universe. It is pretty real in that sense.
This is purely a question, cause' I don't know. Is the Lorentzian 4-manifold used as a frame of reference?

20. I'm sure DrRocket will correct me on this, but my understanding is that a frame of reference is the Euclidean 4-space equivalent to the manifold at a specified point.

21. Originally Posted by MagiMaster
I'm sure DrRocket will correct me on this, but my understanding is that a frame of reference is the Euclidean 4-space equivalent to the manifold at a specified point.
Yes that's pretty much right. In the same way that you can draw a tangent to a curve, you can set up local areas of flat space on curved manifolds. In these flat spaces the laws of Special relativity hold.

22. Originally Posted by GiantEvil
Space-time is Lorentzian 4-manifold. General relativity as a subject is basically the differential geometry of such manifolds. That manifold is our universe. It is pretty real in that sense.
This is purely a question, cause' I don't know. Is the Lorentzian 4-manifold used as a frame of reference?
No.

A Lorentzian manifold is a mathematical object that "locally looks like" 4-space with the Minkowski inner product used to define "distance".

4-space with the Minkowski metric is the basis for special relativity.

So a Lorentzian manifold is an object on which physics is locally approximated by special relativity. In special relativity one talks about frames of reference, which are just choices of coordinate systems that correspond to observers.

General relativity introduces the notion of curvature into the picture, which is what requires the notion of a manifold. So a Lorentzian manifold is a potentially curved structure on which physics is locally approximated by special relativity. That is how one handles gravity in the context of relativity. Einstein formulated the theory in terms of curvature of a Lorentzian manifold and the fact that it is Lorentzian reflects the melding of special relativity with gravitation. That is the diffrence between special relativity and general relativity.

23. Mr MagiMaster, sox, and DrRocket, thank you all for your answers. They all appear to agree, so I will accept them as authoritative. I think that I have a better understanding of manifold's now.
i know they are not technically the same thing and you are using the technical definitions of each one to prove this. i'm just saying the concept seems pretty similar; matter/energy acting upon a fabric/substance in the vacuum.
Yes, they (aether, Space-time) do seem similar. But, the simple observation that c will measure, regardless of the velocity of the observer, makes the concept of aether wholly null. I suspect the solution to this paradox lies in the rigorous definition of "manifold". I suspect you should start by investigating the geometric concept of "tangent". See below.
Yes that's pretty much right. In the same way that you can draw a tangent to a curve, you can set up local areas of flat space on curved manifolds. In these flat spaces the laws of Special relativity hold.

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