[David Cooper]

It's no coincidence. The thing is, GR doesn't actually explain why matter falls down. It doesn't actually say why an object acquires some given speed, which is escape velocity when you flip things round. However it's very easy to understand if you think about the wave nature of matter and stuff electron diffraction and spin. Just simplify the electron to light going round and round, then simplify it further to light going round a square path. The horizontals bend in the gravitational gradient, and the electron falls down. It's similar if you accelerate the electron in gravity-free space. Sadly you never seem to see any texts which combine relativity with the wave nature of matter.

That's a useful way of looking at things. Where do you get your knowledge from, because I'd like to explore the source.

[JohnDuffield]

That's a useful way of looking at things. Where do you get your knowledge from, because I'd like to explore the source.

A whole rack of different places, ranging from old papers by the likes of Maxwell and Einstein, to newer papers and articles  that tend not to get much publicity. See for example http://arxiv.org/abs/physics/0512265 and S A Goudsmit talking about the discovery of electron spin: "When the day came I had to tell Uhlenbeck about the Pauli principle - of course using my own quantum numbers - then he said to me: "But don't you see what this implies? It means that there is a fourth degree of freedom for the electron. It means that the electron has a spin, that it rotates". Also see magnetic moment and the Einstein-de Haas effect which "demonstrates that spin angular momentum is indeed of the same nature as the angular momentum of rotating bodies as conceived in classical mechanics". However if you were to ask a contemporary particle physicist about this, he might say the electron is a point particle, that its spin is not a real rotation, and that gravity is all down to gravitons flitting back and forth.

NB: note that only the horizontals bend downwards, which is why  light is deflected twice as much as matter.

[David Cooper]

Thanks John - I'll follow all of those up.

[JohnDuffield]

There's loads more interesting material out there. IMHO an interesting read is On Vortex Particles by David St John. He's a recent physics PhD. It isn't peer reviewed or anything, but it gives a wealth of information going back to Thomson and Tait, which arguably goes back to Maxwell's theory of molecular vortices. The gist of it is that the electron is a spinor which is akin to a cyclone. The positron is a similar spinor with the opposite chirality which is akin to an anticyclone, and counter-rotating vortices attract. I really ought to write a paper on it. I was talking to the SPIE  guys about this, but I can't go to San Diego in August.

[jeffreyH (OP)]

On the Hubius Helix.

Read, enjoy and maybe provide all the proofs required.

http://www.quora.com/What-do-physicists-think-of-the-hubius-helix-model-of-electron-structure

[jeffreyH (OP)]

Strangely John there is a Mr John Duffield and a Mr Stuart J Duffield at SPIE. Which one are you? Doesn't this get confusing over who wrote what. One may easily think one Duffiled wrote something when in fact it was the other. That would be unfortunate.

[jeffreyH (OP)]

John you aren't going to claim to be an authority on spinors are you? How much group theory do you know? This is an honest question and I think it deserves an honest answer. If you are going to be making these claims and representing yourself as an authority, where people might actually be convinced that they are learning established physics from you, then put up or shut up. It is hard enough to learn physics without being waylaid by bogus claims. You do every enthusiastic amateur an injustice by doling out spurious information simply to boost your status in the eyes of others.

[jeffreyH (OP)]

Last night I watch the Horizon programme on the BBC about the search for the gravitational waves from the big bang. Alan Guth was one of the physicists included. He propose the theory of inflation right at the start of his career. Finding those waves will tell us a lot more about the big bang and validate Alan's theory. The guys set up telescopes at the pole and spent 3 years recording CMBR from a dark spot in the sky. Then after 3 years they found the data wasn't accurate enough. They then went away and built a better telescope and spent several more years looking for the b mode signal of the early gravitational waves. They found something that looked like the signal and spent more time analyzing it and ruling things out until they were confident in announcing it. Then it was shown that at least 50% of it and maybe 100% of the signal was due to dust. That is physics.

[jeffreyH (OP)]

For anyone interested in the signal there is information here;

http://background.uchicago.edu/~whu/intermediate/Polarization/polar6.html

[jeffreyH (OP)]

The thing that crosses my mind about the equation

g = c^2/(2[r_s+n]*SQRT(1-r_s/[r_s+n]))

is how would this relate to the Bekenstein bound

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

and the chandrasekhar limit

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

If a connection to the black hole entropy can be found that would be a positive step. With the chandrasekhar limit it may be possible to put a lower and upper bound on possible black hole masses. In respect of the big bang this could be very important if the idea of a singularity is to hold.

[JohnDuffield]

Jeffrey: David Simmons-Duffin was being overly hostile. Take a look at the picture on the quora page. Then note that the Dirac spinor is a bispinor, and have a look at Dirac's belt on Mathspages:

"In contrast, the Mobius strip is a non-orientable surface, because a right-handed figure, moved continuously around the loop until arrive back at its starting point, becomes left-handed. An object must be translated around the loop twice in order to be restored to its original position and chirality. In this sense a Mobius strip is reminiscent of spin-1/2 particles in quantum mechanics, since such particles must be rotated through two complete rotations in order to be restored to their original state...

I'm John Duffield. I don't know any Stuart J Duffield. I'm not claiming to be an authority on spinors or group theory, I'm just telling you about things that aren't in the popscience/student books/articles/etc you've been reading. Do not think that something is "spurious information" or isn't "established physics" just because you don't know about it. The vast bulk of what I tell you about is established physics. I didn't invent the word spinor, and I didn't write the Wikipedia article or put this picture on it:

Last night I watch the Horizon programme on the BBC about the search for the gravitational waves from the big bang. Alan Guth was one of the physicists included. He propose the theory of inflation right at the start of his career. Finding those waves will tell us a lot more about the big bang and validate Alan's theory. The guys set up telescopes at the pole and spent 3 years recording CMBR from a dark spot in the sky. Then after 3 years they found the data wasn't accurate enough. They then went away and built a better telescope and spent several more years looking for the b mode signal of the early gravitational waves. They found something that looked like the signal and spent more time analyzing it and ruling things out until they were confident in announcing it. Then it was shown that at least 50% of it and maybe 100% of the signal was due to dust. That is physics.

The Horizon producers pulled their punches, and didn't say anything about the orchestrated hype that put people's back up. See Physicist Paul Steinhardt Slams Inflation, Cosmic Theory He Helped Conceive. And note this: that "first light" dates from 300,000 years after the big bang. How can that tell you anything about the first nanosecond after the big bang? The universe was a seething maelstrom of plasma for a third of a million years. It would be like putting those sonic standing waves into a blender.

[jeffreyH (OP)]

John, how do you validate anything if you don't understand it? You now say you are not an authority on spinors. What exactly DO you know about them?

Bispinor on wikipedia.

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

Have you even looked at the equations in there? You have group mapping, transformations and the SO(3;1) group all mentioned.

You can find information on orthogonal groups here:

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

Try reading it.

"Equivalently, it is the group of n×n orthogonal matrices, where the group operation is given by matrix multiplication, and an orthogonal matrix is a real matrix whose inverse equals its transpose."

"The determinant of an orthogonal matrix being either 1 or −1, an important subgroup of O(n) is the special orthogonal group, denoted SO(n), of the orthogonal matrices of determinant 1. This group is also called the rotation group, because, in dimensions 2 and 3, its elements are the usual rotations around a point (in dimension 2) or a line (in dimension 3). In low dimension, these groups have been widely studied, see SO(2), SO(3) and SO(4)."

What about symmetries? Does that ring any bells?

[jeffreyH (OP)]

Now then John what type of matrix has its inverse equaling its transpose?

[jeffreyH (OP)]

Jeffrey: David Simmons-Duffin was being overly hostile. Take a look at the picture on the quora page. Then note that the Dirac spinor is a bispinor, and have a look at Dirac's belt on Mathspages:

"In contrast, the Mobius strip is a non-orientable surface, because a right-handed figure, moved continuously around the loop until arrive back at its starting point, becomes left-handed. An object must be translated around the loop twice in order to be restored to its original position and chirality. In this sense a Mobius strip is reminiscent of spin-1/2 particles in quantum mechanics, since such particles must be rotated through two complete rotations in order to be restored to their original state...

I'm John Duffield. I don't know any Stuart J Duffield. I'm not claiming to be an authority on spinors or group theory, I'm just telling you about things that aren't in the popscience/student books/articles/etc you've been reading. Do not think that something is "spurious information" or isn't "established physics" just because you don't know about it. The vast bulk of what I tell you about is established physics. I didn't invent the word spinor, and I didn't write the Wikipedia article or put this picture on it:

Last night I watch the Horizon programme on the BBC about the search for the gravitational waves from the big bang. Alan Guth was one of the physicists included. He propose the theory of inflation right at the start of his career. Finding those waves will tell us a lot more about the big bang and validate Alan's theory. The guys set up telescopes at the pole and spent 3 years recording CMBR from a dark spot in the sky. Then after 3 years they found the data wasn't accurate enough. They then went away and built a better telescope and spent several more years looking for the b mode signal of the early gravitational waves. They found something that looked like the signal and spent more time analyzing it and ruling things out until they were confident in announcing it. Then it was shown that at least 50% of it and maybe 100% of the signal was due to dust. That is physics.

The Horizon producers pulled their punches, and didn't say anything about the orchestrated hype that put people's back up. See Physicist Paul Steinhardt Slams Inflation, Cosmic Theory He Helped Conceive. And note this: that "first light" dates from 300,000 years after the big bang. How can that tell you anything about the first nanosecond after the big bang? The universe was a seething maelstrom of plasma for a third of a million years. It would be like putting those sonic standing waves into a blender.

That article correctly states that Paul Steinhardt helped refine the theory years after Alan Guth conceived it. Don't put your own slant on things and try to rewrite history. So what if he objects to it. HE has a right to. Someone may well come up with a better theory. That is what physics is all about.

[jeffreyH (OP)]

If we take the mass of the chandrasekhar limit and then calculate its Schwarzschild radius an equation can be formed thus:

g = c^2/[2r_s+L/2]

The value for g that we then get is 299788351 which just about equals the speed of light. To find the lower limit of a feasible black hole we need to vary the parameters until this acceleration is as near to the surface of the event horizon as it is possible to get. This may or may not equal 1 Planck length.

CORRECTION: c/2 has been modified to L/2 to represent the distance traveled by light in one 1/2 second. You just can't add a velocity to a distance.

[jeffreyH (OP)]

If the limit on the lowest mass of a black hole coincides with the acceleration at one Planck length from the horizon being equal to the speed of light then that would relate directly to black hole entropy and the Bekenstein bound.

[SorryDnoodle]

We are all familiar with the escape velocity of a black hole as being equal to c.

If that were the case, wouldn't light escape?

Yes of course...........I should have said "escape velocity greater than c." But greater by only the smallest degree.

Would't escape velocity be proportional to the mass of the black hole, in other words; A very small black hole being very close to c but a super massive black hole very much great than c?

If not, why?

[jeffreyH (OP)]

We are all familiar with the escape velocity of a black hole as being equal to c.

If that were the case, wouldn't light escape?

Yes of course...........I should have said "escape velocity greater than c." But greater by only the smallest degree.

Would't escape velocity be proportional to the mass of the black hole, in other words; A very small black hole being very close to c but a super massive black hole very much great than c?

If not, why?

A black hole traps light at its event horizon. That is why it is called an event horizon because we cannot retrieve any information beyond the horizon. As the radius of the event horizon increases so does the mass but the density of the gravitational field decreases proportionally. If the escape velocity at the event horizon exceeded c then it would no longer be the event horizon. In that case the event horizon would be larger in radius.

You can find details here.

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