Arthur wrote:.....
Because all equipotential lines of the gravitational field of a spherical body like the sun are bent curves, so the light beam is bent as well.
But please forget these fairy tales of "Curved space".
Greetings from Arthur Büttgen, Germany

Okay, but if space is not curved then the force of gravity is acting on the light, the photons which are massless according to current theory. Hmmm....

And greetings toyou Arthur!

From Physics In Minutes - 200 Key Concepts Explained In An Instant - Giles Sparrow

[ Gravitational lensing - Page 382 ]

One of the most useful predictions of general relativity is that gravitational fieldsdeflect the passage of light rays that pass nearby. This effect known as gravitational lensing cannot be fully explained by classical gravity [ since photons are massless
and should therefore be immune to Newtons law of universal gravitation ] but is a natural consequence of warped spacetime around massive objects such as stars

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It would be more accurate to describe spacetime as indeed warped and not curved as the latter implies symmetry and uniformity. This is not true because the degree of warp varies according to the mass of the body in question. The larger it
is the greater the warp / the smaller it is the lesser the warp. The most extreme occur at the event horizons of black holes
and the most extreme of those occur at the event horizons of supermassive black holes. But all stars and planets and moons exhibit some degree or other of warp relative to their size. Where there are no galaxies then spacetime will be relatively flat because of an absence of bodies capable of warping that specific region

So if it's not the force of gravity (the gravitational field) affecting the photons, then what is it that is warping. These last few posts bring out exactly the point of my initial question. Something is not jiving....at least for me....apparently not for others as well.

Take any three points and the triangle thereby formed. If the sum of the interior angles of said triangle is not precisely 180 degrees then space is not flat.

Simple.

kennyc wrote:
So if it's not the force of gravity (the gravitational field) affecting the photons, then what is it that is warping

Photons are massless particles and so cannot be affected but what is affected is the path they take. When light passes through a cluster galaxy anything beyond it such as another galaxy will appear distorted. This is because distorted light creates a series of rings at the point of the distant galaxy which are on the same path as the line from an observed point
and the two edges of the cluster galaxy. But a simpler way to explain this would be the distortion that water creates when
any object below its surface is viewed from above. It is not actually where it appears to be. The principle is the same as for gravitational lensing though the distances involved are far larger and the substance is light not water. Any type of distortion will result in a false image being projected between the observer and the object where it exists at any point within the path between the two. The example that Scott gave is however even simpler to understand although a purely hypothetical two dimensional one that does not automatically translate to four dimensional space but even so

Also remember that a further distortion can be caused by spacetime distance as it is not the same as physical distance. The spacetime distance between the Sun and the Earth for example is actually less than the physical distance between them. And as spacetime is a consequence of General Relativity which allows for gravity to distort orbits between bodies then there will always be some degree of distortion within galaxies because of the predominance of stars and planets. Only in space outside of galaxies will there be either zero or minimum distortion

Photons aren't massless, they have no rest mass. They still have mass associated with their kinetic energy, and this is indeed affected by gravity, hence gravitational red-shift.

I'd be interested to know what the difference between warping and curvature is.

I already explained the difference between the two. Curvature implies something nice and neat which is not the case in reality. The gravitational force exerted at the event horizon of a supermassive black hole is anything but nice and neat Anything that rips all matter apart and exerts a force so powerful that light cannot escape from it cannot be described
in such terms. Thus far more accurate to say that spacetime is warped rather than curved. Also as I already explained
the degree varies on the mass of body in question and so again is not uniform. Now it could be argued that this is mere
semantics and to a certain extent it is but warping is technically and linguistically the more accurate term of the two

Curvature implies something neat? Where?

To be fair I am thinking of it in two dimensional terms rather than four dimensional ones because it is easier to comprehend it as such. But the fact remains that it is not as nice and neat as drawing an asymptote on a sheet of paper. For one thing that does not take into account the force that can be exerted when at the event horizon or inside a white dwarf or at the centre of any galaxy which is as extreme as it gets. But something which is curved is neat and spacetime is not so that is
my reason for rejecting the definition in favour of warped and which is more accurate for the reasons I have already given

hackenslash wrote:Photons aren't massless, they have no rest mass. They still have mass associated with their kinetic energy, and this is indeed affected by gravity, hence gravitational red-shift.

I'd be interested to know what the difference between warping and curvature is.

Hmmm.....probably a much better thought (or something to think on) than the mirrors and hand-waving above. Thanks.

Red shift is due to velocity not gravity though.

surreptitious57 wrote:To be fair I am thinking of it in two dimensional terms rather than four dimensional ones because it is easier to comprehend it as such. But the fact remains that it is not as nice and neat as drawing an asymptote on a sheet of paper. For one thing that does not take into account the force that can be exerted when at the event horizon or inside a white dwarf or at the centre of any galaxy which is as extreme as it gets. But something which is curved is neat and spacetime is not so that is
my reason for rejecting the definition in favour of warped and which is more accurate for the reasons I have already given

Well space is at least 3 dimensional and the 'curvature' takes place in all of those dimensions -- that's part of why it is difficult to envision, but curved, warped, distorted, twisted....a rose by any other name...

kennyc wrote:Red shift is due to velocity not gravity though.

gravity can generate red-shift as well.

http://en.wikipedia.org/wiki/Gravitational_redshift

hackenslash wrote:

kennyc wrote:Red shift is due to velocity not gravity though.

gravity can generate red-shift as well.

http://en.wikipedia.org/wiki/Gravitational_redshift

True, but that only has a big effect when the light source is close to a black hole, so that there is a measurable increase in wavelength between emission and detection (assuming detection is not also near a black hole).

Indeed.

hackenslash wrote:Photons aren't massless, they have no rest mass. They still have mass associated with their kinetic energy, and this is indeed affected by gravity, hence gravitational red-shift.

The whole argument about the photon's mass it irrelevant. Even in Newton's theory gravitational acceleration doesn't depend on the mass of a test particle. That's why everything falls at the the same rate in vacuum.

But in General Relativity the amount of light bending is double of what Newton would have predicted, due to the spatial geometry:
http://www.mathpages.com/rr/s8-09/8-09.htm

hackenslash wrote:I'd be interested to know what the difference between warping and curvature is.

"Warping" would have been a better name for "intrinsic curvature", as it would not be confused with "extrinsic curvature".

kennyc wrote:So if it's not the force of gravity (the gravitational field) affecting the photons, then what is it that is warping.

The geometry of space-time, where light moves straight locally (geodesically).

Geometry of space affects light like shown here in the bottom picture:
http://www.physics.ucla.edu/demoweb/dem ... etime.html

Geometry of time (gravitational time dilation) affects light by effectively "slowing down" the lower part of a beam, so it bends down.

reksio wrote:

kennyc wrote:So if it's not the force of gravity (the gravitational field) affecting the photons, then what is it that is warping.

The geometry of space-time, where light moves straight locally (geodesically).

Geometry of space affects light like shown here in the bottom picture:
http://www.physics.ucla.edu/demoweb/dem ... etime.html

Geometry of time (gravitational time dilation) affects light by effectively "slowing down" the lower part of a beam, so it bends down.

Yeah, yeah, we've heard it before in this very thread, probably back on page one. .... I'm not convinced....as I'm sure I explained back there somewhere and maybe even recently....

kennyc wrote: I'm not convinced.

Not convinced of what?

kennyc wrote:

reksio wrote:

kennyc wrote:So if it's not the force of gravity (the gravitational field) affecting the photons, then what is it that is warping.

The geometry of space-time, where light moves straight locally (geodesically).

Geometry of space affects light like shown here in the bottom picture:
http://www.physics.ucla.edu/demoweb/dem ... etime.html

Geometry of time (gravitational time dilation) affects light by effectively "slowing down" the lower part of a beam, so it bends down.

Yeah, yeah, we've heard it before in this very thread, probably back on page one. .... I'm not convinced....as I'm sure I explained back there somewhere and maybe even recently....

Not to beat a dead horse here, kenny, but perhaps you need a more flexible notion of what a straight line is. OK, there's a wee pun there. Sue me. Let's imagine the universe without any mass in it. Then all the lines are straight straight lines.