Null Gravity?

I just love this science forum. Thanks to everyone. Big plus for Einstein crunchers.

Ooooh .... a corker of a question there Bill. :-)

Classical GR says the density is infinite there. Well, Newton also for that matter. That's a hint that we can't legitimately make any genuine interpretive statement from theory. It's best to say "don't know" here rather than give a figure, or even say infinite gravity or whatever. Leave it as a patch of ignorance to be safe.

Such points in the theory are known by the mathematical term 'singularity', a type of naughtiness ( more or less the difficulty produced when you divide a number by zero ) that some functions have at certain points. It's not just gravitational theory that mentions singularities, these are know to occur in the mathematics of many other areas of physics also.

Sometimes it is not an especial problem for a theory overall but rather for the way a physical situation has been modelled in some example to which theory has been applied, and in particular by choice of a coordinate scheme to define a scenario. A good example of that is the event horizon of a black hole which has singularity features only evident with certain choices of reference frame. The difficulty may be 'transformed away' eg. by taking the viewpoint of an object descending into a black hole. Nothing especial happens at the Schwarzschild radius in that case. The central singularity remains with any/all choices of frame and is if you like a more general roadblock to understanding.

It is of great note that quantum mechanics has this blessed ability to prevent some reasons for singularities occurring. The core idea here is that one can't really pin down positions and movement simultaneously for any entity ( and regardless of whether you label said entity a 'particle' or a 'wave' ). The machinery of QM prevents 'one thing sitting atop another', and hence the sort of stacking up and totalling of things without bound. There must be some separation of things. I guess with a quantum theory of gravitation that would enforce an upper limit on densities.

So the Heisenberg Uncertainty Principle, which is usually disdained for it's imprecise undercurrent, can come into play to protect a theory from yielding singularities. Well that's a rough take on it at least.

[aside]There is a trick used often with quantum field theories called 'renormalisation'. This is a tactic that essentially excludes certain infinite sums from being performed ( as a mathematical procedure ), and that reflects back onto the modelling as only assessing quantities above a certain scale size. Very roughly speaking if you don't look too close around the region of some point then you can't manufacture a singularity ...

... Feynman admitted this was 'sweeping infinity under the rug'. He found in quantum electrodynamics that some parts of a calculation would have a sum which totalled to infinity. The very same sum ie. the mathematical expression, appeared in several places. He decided to simply replace that crappy term with a ( finite ) value as measured by experiment. This divided QED calculations into two parts : that which gave sensible results and that which gave the silly ones. Calculate the sensible bits, straight up ignore the bad bits by replacing them with a valid number from the real world. This is not terrible, more to the point it is a recognition that below a certain distance scale we don't know what is happening, but we can accept a 'summary' of behaviour that occurs at that difficult scale.

So that's sort of like producing a profit & loss statement for a company without going into finer details of it's operations. If you own a group of companies then look at said group in toto by manipulating the various profit/loss statements of each. Anyone who has either dealt with an accountant and/or read The Hitch-hikers Guide To The Galaxy series knows that much useful work can come forth from the minds of accountants ... :-)[/aside]

Cheers, Mike.