The thing about physics is that once you understand one thing, it’s easy to understand the next. A while back I was explaining that time travel is science fiction because clocks "clock up" motion. Once you understand that, it’s easy to understand that the speed of light is not constant. There no actual time flowing in an optical clock. It goes slower when it's lower because light goes slower when it's lower, just like Einstein said. Then once you understand that, it’s easy to understand gravity. You’ll be familiar with the bowling-ball analogy. The Earth is likened to a bowling ball in a rubber sheet, like this:
GNUFDL image by Johnstone, see wikipedia
You probably know already that one problem with this picture is that the Earth looks like it’s being pulled down by gravity. It’s no good using gravity to explain gravity, that’s circular. But the picture isn’t totally wrong. Imagine you’ve placed a whole lot of parallel-mirror light-clocks in an equatorial slice through the Earth and the surrounding space. When you plot all the clock rates, your plot resembles the rubber-sheet picture because clocks go slower when they’re lower. Then the curvature you can see relates to Riemann curvature which relates to curved spacetime. And yes, you measured those clock rates, so yes, it’s a curvature in your metric. But it’s important to remember that the curvature is just a curvature in your plot of clock rates, and those clocks measured the motion of light through space. So what the rubber-sheet analogy is really depicting, is the varying speed of light.
It’s also important to note that the clocks nearer the Earth don’t run slower because your plot is curved. In other words, they don’t run slower because spacetime is curved. Spacetime is an abstract mathematical space, and it is static. It’s the plot, the map, and the map is not the territory. Spacetime is not what space is. The clocks run slower when they’re lower because the space down there is different. That’s because a concentration of energy in the guise of the matter of the Earth “conditions” the surrounding space, the effect of this diminishing with distance. Einstein talked about this in his 1920 Leyden Address, where he also talked about inhomogeneous space. That’s the physical reality that underlies curved spacetime. And like I was saying in the speed of light thread, he didn’t say light curves because spacetime is curved. He said light curves because the speed of light varies with position.
I don’t know if you know, but there’s another couple of problems with the rubber-sheet picture. One is that it depicts tension instead of pressure. Einstein’s stress-energy tensor has an energy-pressure diagonal, and to envisage pressure you need to step up from a rubber sheet to three-dimensional space. Imagine it’s like some gin-clear ghostly elastic jelly, then you insert a hypodermic needle and inject more jelly to represent the mass-energy of the Earth. The surrounding jelly is pressed outwards rather than being pulled inwards. The other problem is that the Earth is spherical, which really muddies the water when we’re talking about Einstein’s inhomogeneous space. To get past that, we need to zoom in a little, like this:
Image credit: NASA (I removed the moon and added the lattice lines)
The height of each square relates to your clock rates. Remember they’re light-clocks, so the height of each square relates to the speed of light at that position. And because the speed of light varies from top to bottom, a beam of light going across the picture will curve like a car veers when it encounters mud at the side of the road. Like this:
Hence Professor Ned Wright’s Deflection and Delay of Light wherein "the delay experienced by light passing a massive object is responsible for the deflection of the light”. That’s easy to understand. And of course, once you understand why light curves, it’s easy to understand why matter falls down. There’s only one other thing you need to know about, and that’s the wave nature of matter. You can make an electron along with a positron out of light waves in pair production. And you can diffract an electron. Plus in atomic orbitals electrons exist as standing waves. So just think of an electron as light going round and round. Then you can simplify it to light going round a square path. Try drawing it, like this:
Now imagine it’s in a gravitational field. The vertical parts of the path are still vertical, but the horizontal parts bend down a little. So the electron falls down. Like this:
In essence the reducing speed of light is transformed into the downward motion of the electron. You can diffract protons and neutrons too, so the same principle applies to matter in general. From this you can even understand why the general-relativity deflection of light is twice the Newtonian deflection of matter. It’s because for matter, only the horizontals bend down. Yes, it’s pretty simple really. But as for why this isn’t common knowledge, I don’t know. It should have been common knowledge for about three hundred years, because in Opticks queries 20 and 21 Newton said this:
"Doth not this aethereal medium in passing out of water, glass, crystal, and other compact and dense bodies in empty spaces, grow denser and denser by degrees, and by that means refract the rays of light not in a point, but by bending them gradually in curve lines? ...Is not this medium much rarer within the dense bodies of the Sun, stars, planets and comets, than in the empty celestial space between them? And in passing from them to great distances, doth it not grow denser and denser perpetually, and thereby cause the gravity of those great bodies towards one another, and of their parts towards the bodies; every body endeavouring to go from the denser parts of the medium towards the rarer?"
That’s Newton telling you why light curves, and it's pretty much what Einstein said. And in Opticks query 30 Newton said "Are not gross bodies and light convertible into one another?" So I imagine he had an idea about why matter falls down. I hope that now you do too. Understand time, then the speed of light, and then gravity is easy. And so it goes. It's like pulling a thread with Einstein's name on it, and out comes a string of pearls.
Oh, and one of them is called black holes.
GNUFDL image by Johnstone, see wikipedia
You probably know already that one problem with this picture is that the Earth looks like it’s being pulled down by gravity. It’s no good using gravity to explain gravity, that’s circular. But the picture isn’t totally wrong. Imagine you’ve placed a whole lot of parallel-mirror light-clocks in an equatorial slice through the Earth and the surrounding space. When you plot all the clock rates, your plot resembles the rubber-sheet picture because clocks go slower when they’re lower. Then the curvature you can see relates to Riemann curvature which relates to curved spacetime. And yes, you measured those clock rates, so yes, it’s a curvature in your metric. But it’s important to remember that the curvature is just a curvature in your plot of clock rates, and those clocks measured the motion of light through space. So what the rubber-sheet analogy is really depicting, is the varying speed of light.
It’s also important to note that the clocks nearer the Earth don’t run slower because your plot is curved. In other words, they don’t run slower because spacetime is curved. Spacetime is an abstract mathematical space, and it is static. It’s the plot, the map, and the map is not the territory. Spacetime is not what space is. The clocks run slower when they’re lower because the space down there is different. That’s because a concentration of energy in the guise of the matter of the Earth “conditions” the surrounding space, the effect of this diminishing with distance. Einstein talked about this in his 1920 Leyden Address, where he also talked about inhomogeneous space. That’s the physical reality that underlies curved spacetime. And like I was saying in the speed of light thread, he didn’t say light curves because spacetime is curved. He said light curves because the speed of light varies with position.
I don’t know if you know, but there’s another couple of problems with the rubber-sheet picture. One is that it depicts tension instead of pressure. Einstein’s stress-energy tensor has an energy-pressure diagonal, and to envisage pressure you need to step up from a rubber sheet to three-dimensional space. Imagine it’s like some gin-clear ghostly elastic jelly, then you insert a hypodermic needle and inject more jelly to represent the mass-energy of the Earth. The surrounding jelly is pressed outwards rather than being pulled inwards. The other problem is that the Earth is spherical, which really muddies the water when we’re talking about Einstein’s inhomogeneous space. To get past that, we need to zoom in a little, like this:
Image credit: NASA (I removed the moon and added the lattice lines)
The height of each square relates to your clock rates. Remember they’re light-clocks, so the height of each square relates to the speed of light at that position. And because the speed of light varies from top to bottom, a beam of light going across the picture will curve like a car veers when it encounters mud at the side of the road. Like this:
Hence Professor Ned Wright’s Deflection and Delay of Light wherein "the delay experienced by light passing a massive object is responsible for the deflection of the light”. That’s easy to understand. And of course, once you understand why light curves, it’s easy to understand why matter falls down. There’s only one other thing you need to know about, and that’s the wave nature of matter. You can make an electron along with a positron out of light waves in pair production. And you can diffract an electron. Plus in atomic orbitals electrons exist as standing waves. So just think of an electron as light going round and round. Then you can simplify it to light going round a square path. Try drawing it, like this:
Now imagine it’s in a gravitational field. The vertical parts of the path are still vertical, but the horizontal parts bend down a little. So the electron falls down. Like this:
In essence the reducing speed of light is transformed into the downward motion of the electron. You can diffract protons and neutrons too, so the same principle applies to matter in general. From this you can even understand why the general-relativity deflection of light is twice the Newtonian deflection of matter. It’s because for matter, only the horizontals bend down. Yes, it’s pretty simple really. But as for why this isn’t common knowledge, I don’t know. It should have been common knowledge for about three hundred years, because in Opticks queries 20 and 21 Newton said this:
"Doth not this aethereal medium in passing out of water, glass, crystal, and other compact and dense bodies in empty spaces, grow denser and denser by degrees, and by that means refract the rays of light not in a point, but by bending them gradually in curve lines? ...Is not this medium much rarer within the dense bodies of the Sun, stars, planets and comets, than in the empty celestial space between them? And in passing from them to great distances, doth it not grow denser and denser perpetually, and thereby cause the gravity of those great bodies towards one another, and of their parts towards the bodies; every body endeavouring to go from the denser parts of the medium towards the rarer?"
That’s Newton telling you why light curves, and it's pretty much what Einstein said. And in Opticks query 30 Newton said "Are not gross bodies and light convertible into one another?" So I imagine he had an idea about why matter falls down. I hope that now you do too. Understand time, then the speed of light, and then gravity is easy. And so it goes. It's like pulling a thread with Einstein's name on it, and out comes a string of pearls.
Oh, and one of them is called black holes.
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