Quantum Singularity

[Robust]

Might any forum member here be able to describe for me in abbreviated form (or best web site for which) what the point of singularity is and its implications? A prime consideration, it would seem to me, might be in considering the oblateness of whatever the continuum under investigation.



"All things number and harmony." - Pythagoras

[Bo]

a singularity in principle is a mathematical concept. It means that a certain function isn't well defined on a certain point; this point is called a singularity. For example: 1/x isn't good defined for x=0.

Bo

[paultrr]

A gravitational singularity occurs when an astrophysical model, typically based on general relativity, predicts a point of infinite curvature. The term is closely related to the mathematical meaning of "singularity": a gravitational singularity occurs when the equations produce a mathematical singularity.

The Big Bang cosmological model of the universe contains a gravitational singularity at the start of time (t=0). At the "Big Bang Singularity," the model predicts that the density of the universe and the curvature of space-time are infinite.

Basically, a singularity is a point and from that point one gets infinities which tends to make any understanding or measurement at that specific point impossible. The one exception to this concerns a Kerr solution in which the singularity forms a ring.

Hawking's solution around this as far as cosmology goes was to impose the idea of an instanton in time. With such a model there is no T=0 point from the perspective of time. Many physicists believe that gravitational singularities are "unphysical", meaning that general relativity ultimately ceases to be an accurate description of gravity somewhere in the vicinity of what would otherwise be a singularity. This is where what is termed quantum gravity comes into play. However, Hawking's proposal is just one of many put forth at present.

[Robust]

Thanks!....I think the Kerr solution might be what I'm looking for. I'll check it out.


"All things number and harmony." - Pythagoras

[Bo]

A small refinement of the definition paultrr gave: in cosmological models, in a true singularity, not necessarely the curvature becomes infinite, but a quantity known as the Riemann curvature tensor (which is a function of the curvature basicly). There are cases (e.g. the schwarzschild radius of a black hole), where the curvature becomes infinte, but the Riemann tensor doesn't. Since it is the (contraction of the) riemann tensor that occurs in einstein equations, physics is still well defined here.

Can someone tell me what a kerr sollution is?

Bo

[DivineNathicana]

Also, it may be worth noting that according to string theory, the singularity would actually be around the h-bar diameter, and not infinitely small. And according to the likes of Hawking, it must always be shielded from the rest of the Universe by an event horizon to prevent cataclysmic consequences.

Both relativity and QM are necessary for describing singularities. This is probably the main reason they remain so enegmatic and are generally ascribed to hypothetical mathematical theory.

- Alisa

[gpdone]

Alisa,

You said a moutful... and I believe regarding your last statement, that is exactly where it belongs!

For Bo..Kerr solutions: http://www2.phys.canterbury.ac.nz/kerrfest/spin.html