Gravity Works Like This

I don't have a problem with this explanation of the deflection of light. It does, however, assume that space is flat and that the speed of light therefore varies. A different way to look at things is that space is curved and the speed of light remains constant. It's really just two ways of looking at the same effect.
I'm sorry James, but I must pick you up on that. Space isn't curved. See this Baez article: "Note: not the curvature of space, but of spacetime. The distinction is crucial". The two ways of looking at the same effect are inhomogeneous space ≡ curved spacetime, as per this paper. Sorry if that sounds nitpicky, but IMHO it is very important.

For example, in the animation above, we can explain the apparent slowing of the wavefronts that pass closer to the sun as due to their having to their not travelling in the two dimensions of the screen any more, but dipping "down" perpendicularly to the plane of the computer screen then up again, as they pass near the sun. The dip is greater for the waves passing nearer to the sun than it is for waves passing further away. The added component of the light's velocity perpendicular to the plane of the screen accounts for its apparent slowing in the plane of the screen. Adding up the components, the light still has its usual, constant speed.
You could. That's like looking at the bowling ball analogy from the top. But you can derive the bowling ball analogy from the equatorial-slice light clocks.

James R said:
This is a somewhat flawed, 3-dimensional analogy of what actually happens, of course. Because, in fact, that bending of the light perpendicularly to the plane of the screen doesn't really happen in that particular direction at all. The bending actually happens in the 4 dimensional spacetime around the sun, which is such that there's actually more space near the sun than there would be if spacetime was flat there. Light takes longer to travel through the space near the sun than it would if the spacetime there wasn't curved, and that accounts for the apparent slowing of the light (the Shapiro delay).
This is pretty much the "given" explanation provided by modern texts. What I'm essentially saying is this: that given explanation isn't in line with Einstein or the evidence. And it's wrong.

James R said:
The common ball-on-a-trampoline picture of curved spacetime near the sun or the Earth, which appears as your very first diagram in the opening post of this thread, gives an easy way to picture what is going on with the curvature, although it does that at the expense of dropping a spatial dimension from the picture.
And an easy way to understand that is that it's merely a curvature in your plot of equatorial-slice light-clock rates. A curvature in your plot of the speed of light.

Farsight:

I'm sorry James, but I must pick you up on that. Space isn't curved. See this Baez article: "Note: not the curvature of space, but of spacetime. The distinction is crucial". The two ways of looking at the same effect are inhomogeneous space ≡ curved spacetime, as per this paper. Sorry if that sounds nitpicky, but IMHO it is very important.

This is fine. I should have been more careful and written "spacetime" instead of "space".

This is pretty much the "given" explanation provided by modern texts. What I'm essentially saying is this: that given explanation isn't in line with Einstein or the evidence. And it's wrong.

Never mind Einstein, for now.

What evidence shows that it's wrong?

Those NIST optical clocks. There isn't "more space" nearer the floor. And nor is there infinite space at the black hole event horizon.

My main claim here is not wrong. Light curves and matter falls down because the speed of light varies with position. That's what Einstein said. That's what the evidence says.

And you've said nothing other than nay nay nay. You're a naysayer who cannot put together a counterargument. The NIST optical clocks can be simplified to this gif:

The speed of light varies with position. And for all your feather-spitting and tearful outrage, you have given us nothing at all.
A diagram is not an experiment or an equation. It does not prove your theory. And in fact it is contrary to the current prevailing theory.

In physics, a wave packet (or wave train) is a short "burst" or "envelope" of localized wave action that travels as a unit. A wave packet can be analyzed into, or can be synthesized from, an infinite set of component sinusoidal waves of different wavenumbers, with phases and amplitudes such that they interfere constructively only over a small region of space, and destructively elsewhere.[1] Depending on the evolution equation, the wave packet's envelope may remain constant (no dispersion, see figure) or it may change (dispersion) while propagating.

Quantum mechanics ascribes a special significance to the wave packet: it is interpreted as a "probability wave", describing the probability that a particle or particles in a particular state will be measured to have a given position and momentum. It is in this way related to the wave function. Through application of the Schrödinger equation in quantum mechanics, it is possible to deduce the time evolution of a system, similar to the process of the Hamiltonian formalism in classical mechanics. The wave packet is thus a mathematical solution to the Schrödinger equation.[2] The area under the absolute square of the wave packet solution is interpreted as the probability density of finding the particle in a region. The dispersive character of solutions of the Schrödinger equation has played an important role in rejecting Schrödinger's original interpretation, and accepting the Born rule.

So just what makes this happen?

My main claim here is not wrong. Light curves and matter falls down because the speed of light varies with position. That's what Einstein said. That's what the evidence says.

Ok, then please show us how this works in a simple example like the orbit of Mercury.

Ok, then please show us how this works in a simple example like the orbit of Mercury.

He cannot show you and is making false assumptions, especially the misleading bit about Einstein.
The speed of light is constant.....
Space and time are not absolute.

I'd be curious to see the math behind a single propagating wave moving tangentially through a field of graduated time rate differential (...err something)

Let me put it another way: the prism and gravity will both work on a single photon. This must be due to its wavelike nature. Farsight had a wonderful analogy with a swimmer in a pool of gelatin once but I want to understand the math.

cosmictraveler said:
So just what makes this happen?
It's because energy is quantised, and because of certain symmetries which are part of the structure of space and time when we treat space and time the same way, as orthogonal axes in R[sup]4[/sup].
What makes spacetime look like R[sup]4[/sup]? Or ordinary space, minus a time dimension, look like R[sup]3[/sup]? In fact they are isomorphic up to dimension, but there is no "energy" in R[sup]n[/sup].

He cannot show you and is making false assumptions, especially the misleading bit about Einstein.
The speed of light is constant.....
Space and time are not absolute.

OK, so he is either lying and can't show us a simple example or he isn't lying and he can do a simple example. I suppose it is up to farsight to show us whether or not he is lying. If he's been doing this for over a year, surely he has a simple example he can demonstrate.

OK, so he is either lying and can't show us a simple example or he isn't lying and he can do a simple example. I suppose it is up to farsight to show us whether or not he is lying. If he's been doing this for over a year, surely he has a simple example he can demonstrate.

It appears he has been doing it for 10 years or more....same old, same old.
Remember, forums such as this are the only outlet these people have...So they vent their anti mainstream, conspiracy nonsense frustrations out on us.

A diagram is not an experiment or an equation. It does not prove your theory. And in fact it is contrary to the current prevailing theory.
Read the OP on the previous thread in the series: The Speed of Light is Not Constant. Einstein said the speed of light is not constant, optical clocks go slower when they're lower, and the parallel-mirror light-clock is an optical clock. As for current prevailing, we do science using evidence, not by popular vote.

In physics, a wave packet (or wave train) is a short "burst" or "envelope" of localized wave action that travels as a unit. A wave packet can be analyzed into, or can be synthesized from, an infinite set of component sinusoidal waves of different wavenumbers, with phases and amplitudes such that they interfere constructively only over a small region of space...

...So just what makes this happen?
I don't know. But have a look at How Long is a Photon? by Drozdov and Stahlhofen : http://arxiv.org/abs/0803.2596

"...A single photon is conventionally thought as a ”wellenzug” (wave train) - a cut of (sinusoidal) harmonic oscillations - like the one shown in Fig.1..."

"...It appears more appropriate to consider a single photon like a real ultra-short pulse; the frequency is then understood as an inverse of the emission time instead of an ambiguous wave length..."

Farsight said:
My main claim here is not wrong. Light curves and matter falls down because the speed of light varies with position. That's what Einstein said. That's what the evidence says.
OK, then please show us how this works in a simple example like the orbit of Mercury.
No can do. And it won't change what Einstein said. And whilst I'm forever quoting Einstein, nor will it change the fact that the expression he gave for the Perihelion shift of Mercury was the same as Paul Gerber's. See wiki.

I'd be curious to see the math behind a single propagating wave moving tangentially through a field of graduated time rate differential (...err something)

Let me put it another way: the prism and gravity will both work on a single photon. This must be due to its wavelike nature. Farsight had a wonderful analogy with a swimmer in a pool of gelatin once but I want to understand the math.
You want Inhomogeneous Vacuum: An Alternative Interpretation of Curved Spacetime. You can access the full paper.

Here's that analogy:

Imagine a swimming pool. Every morning you swim from one end to the other in a straight line. But one day in the dead of night I truck in a load of gelatine powder and tip it all down the left hand side. This starts diffusing across the breadth of the pool, imparting a viscosity gradient from left to right. The next morning when you go for your swim, something's not right, and you find that you're veering to the left. If you could see your wake, you'd notice it was curved. That's your curved spacetime, because the pool is the space round a planet, the viscosity gradient is Einstein's non-constant gμν, and you're a photon. As to how the gradient attracts matter, consider a single electron. We can make an electron along with a positron from light, via pair production. Since the electron also has spin, think of it as light trapped in a circular path. So if you're swimming round and round in circles, whenever you're swimming up or down the pool you're veering left. Hence you find yourself working over to the left. That's why things fall down.

I'd be curious to see the math behind a single propagating wave moving tangentially through a field of graduated time rate differential (...err something)

Let me put it another way: the prism and gravity will both work on a single photon. This must be due to its wavelike nature. Farsight had a wonderful analogy with a swimmer in a pool of gelatin once but I want to understand the math.

That's about as close to the right math as language can get you. I figure the only difference is the limitations of both language and math in expressing a pi and a log into the imagination. The log being a graduated cylinder of time.

The diagram on the opening post is wrong. The plane does not just dip "downwards": the object pulls from EVERY direction because it has mass.

Farsight, that was a good opening post and it has been a good discussion thread. I understand what you are saying, and it is encouraging to see a few people actually discussing the topic, instead of dismissing it with disdain. The discussion posts are a tribute to your ability to put your ideas across. Thanks for the effort to stand up for what makes the most sense to you, and for making sense out of it for those who are open to it.

Thanks quantum_wave. I hope people get something out of this stuff. Note though that they aren't really my ideas. I quote Einstein, and others.

For the record, I started these threads in response to a challenge from brucep about black holes. So far there's been three, namely time travel is science fiction, which leads on to the speed of light is not constant, followed by this one. Hopefully everything is all very clear, and one thing leads to another in a simple step-by-step fashion. The next thread concerns the nature of black holes.

NB: the OPs are based on some "Science on Sunday" blog articles I wrote for an outlet called Bogpaper started by a journalist called James Delingpole. I've stopped writing for them now because the platform grew into something 100% political rather than the rounded "internet-newspaper" I was hoping for

I get my physics from Ancient Aliens.