So my friend who lives on an Earth that is about 6,000 years old is possilbly completely correct with his pi = 3 idea.

– New Scientist, 17 April 1993, pp32-3.

Spacetime contracts around masses; the earth’s radius is contracted by 1.5 mm radially (the circumference or transverse dimension is unaffected, hence the fourth dimension is needed to keep Pi constant via curvature) by its gravitation. Time is also slowed down.

This is pretty obvious in cause - exchange radiation causes radial contraction of masses in general relativity, just as in special relativity you get contraction of moving masses. Take the Lorentz contraction, stick the Newtonian escape velocity into it, and you get Feynman’s simplified (1/3)MG/c^2 formula for gravitational radial contraction in general relativity (you have to put in the 1/3 factor manually because a moving object only has contraction in one dimension, whereas the contraction is shared over 3 dimensions in GR). The justification here is that the escape velocity is also the velocity acquired by an object falling from an infinite distance, so it is velocity corresponding to the kinetic energy equivalent to the amount of gravitational potential energy involved.

It’s obvious that spacetime is contracted by gravitation. Expanding space really just refers to the recession of masses, i.e., expanding volume.

All the experimentally or observationally confirmed parts of general relativity mathematically correspond to simple physical phenomena of exchange radiation in a Yang-Mills quantum field theory. (Ad hoc theorizing to model observations is not observational confirmation. E.g., dark energy speculation based on redshift observations, isn’t confirmed by the observations which suggested the speculation. A better model is that whatever exchange radiation causes quantum gravity when exchanged by receding masses, gets some kind of redshift like light due to the recession of masses, which weakens gravitational effects over large distances. OK, I know you don’t want to know all the correct predictions which come from this physics, so I’ll stop here.)

Thank you very much for the PDF link.

“Without introducing the concept of a topology change, there can be no real explanation of what happens when you reach the planck scale.”

Both the “dough & raisin” and the balloon analogies rely on describing the expansion of a 3-d manifold.

However, there is a distinction between inflation and the big bang.
You can explain inflation using a manifold, but as I understand it, if you project the process back to a planck-scale big-bang event, even this description breaks down. This follows strictly from the equations of Quantum Mechanics and Special Relativity.

The problem of course, is what leads to the debates going on between String theorists and Loop Quantum Gravity proponents at the moment.
I tend to think that underlying it, is a problem of philosophical conceptualisation, as much as mathematics.
Something along the lines that expansion of the universe and contraction are in someways dual/indistinguishable, which T-dualityin string theory points towards.

My own take on it is: - there’s no such thing as nothing.

See this succinct paper for the problem: -

http://arxiv.org/PS_cache/gr-qc/pdf/9610/9610066.pdf

Like many contemporary cosmologists, Menzel is a little more definitive about this than he really should be. When asked “What happened before the Bang?”, the correct answer is really “We don’t know. According to general relativity, space and time do not exist before the Bang, so there is no such thing as ‘before.’ However, we have no right to think that general relativity is correct in that regime, so… we don’t know.” Few people are sufficiently straightforwardly honest to give that answer.

But was it understood in 1932 that general relativity would eventually need to be replaced by a theory of quantum gravity, and that GR is likely to become significantly inaccurate at the Planck scale? Obviously a good physicist would consider the possibility that GR only worked in certain limits just like Newtonian gravity, but I’m wondering whether Menzel would have had any good sense of what these limits were likely to be, or why GR would be more likely to break down near the moment of the Big Bang than in any other circumstances.

Garth- “Is Dawkins Deluded?”
I’m an atheist, I can’t disagree too much with Dawkins, however his firebrand style of presentation on this topic could be better because he’s turned some people off. On the other side, I appreciate the Jesuits alot (and some are my friends) and I think that they could be important communication bridges to show fundamentalists the value of science. I also wonder if Dawkins has spent any time around the Jesuits. I suspect that they would get along very well (they might even make him laugh).

I was well aware of that fact!

So, is it Richard Dawkins who is Deluded?

Garth

The problem is that in our normal daily experience of the 3d world we use a perceptual ‘ruler’ that is only two dimensional, not three. If for example, our normal 3d world was expanding at a meter per second, we wouldn’t be able to perceptually tell this was occurring. A xyz ‘ruler’ would also be expanding and there would still be N units between two ‘things’, you need one more dimension for a proper perspective.

Question to Alex Nichols, can you explain a little further on:

Without introducing the concept of a topology change, there can be no real explanation of what happens when you reach the planck scale.

For a truly hilarious ‘bad’ bio of Lemaitre, check out Dan Brown’s Angels and Demons. He describes Lemaitre as a monk who wanted to prove the existence of God…

Without introducing the concept of a topology change, there can be no real explanation of what happens when you reach the planck scale.

This is what makes the analogies so imperfect and what most people find so hard to grasp.

Catholic Priest Proposes New Model for Creation

Returning to the main subject of the blog, does not the title provide a counter example of Richard Dawkins thesis that, as God does not exist, a scientist would recognise the fact?

Garth

Sad that people understood this in 1932 but there are still professional physicists who don’t get this simple point.

I’m sure you are familiar with Pythagoras’ theorem. You note that nowhere in that formula does anything depend on time.
Einstein’s big discovery was that this is actually wrong: the correct version of P’s theorem actually DOES contain a function of time. Thus the distance between two *stationary* objects naturally becomes a function of time. This time-dependence is what we call the expansion of the universe. That’s all there is to it. No balloons. No raisins. Though I too like raisins.

To get people to understand that the embedding of the surface is irrelevant is crucial but can again be done in the context of 2D geometry by pointing out the difference between intrinisic and extrinsic curvature (roll up a sheet of paper, still the same! on the sheet of paper you don’t notice any stretching! Doesn’t work with a sphere, etc…). But really this is the only caveat of the balloon.

I have been using 2D surfaces as lay-toy explanaitions for GR for a while with more success then with anything else. Especially for explaining how we can do physics with geometry (conceptually). I start out with pointing out that if you draw time and space as directions on a bit of paper stuff moves between points along the shortes connection between them. If they accept this then the idea of modifying the way things move by putting dents on the surface and changing what the shortest connection is becomes a fairly natural generalization (insert equivalence principle here). And then one can point out that for people on the surface extrinsic curvature is irrelevant since it doesn’t change what the shortest path is, so embedding is not important (mention klein bottle i.e. that it’s possibly even not embeddable in 3D). Then tell them that it’s really complicated because “matter tells spacetime how to curve and spacetime tells matter how to move”.

IMO this captures one of the central conceptual insights of GR.

At this point I can start explaining QM and how it’s probabilistic interpretation seems at odds with this geometric picture where there is no good notion of “now” and then they will truly and verily regret to have asked what this Quantum Gravity thing is.