I shall simply have to plead ignorance on this one, but I was surprised nevertheless that I hadn't seen a competing explanation of the universe quite like this before. "How can it be that I've not heard a peep about something so ostensibly groundbreaking?" I wondered. Well, I haven't yet busied myself with reading any sort of refutation of this theory, and it's even harder yet to find follow up on the massive potential of such a description of the universe as this. As it stands, however, I can't help but predict that it was unable catch a lot of traction with cosmologists, but I'm wondering if anyone out there is/was familiar with this and can provide further information?
As an aside, what do we think about this idea, metaphorical plot holes and all? Clearly it doesn't address some of the protracted and lingering complexities that the BBT does, and yet it explains other core issues that the BBT does not. My interest has been piqued, but as much as I'd love to see big bang cosmology fall to the superfluous wayside - thus silencing men like William Lane Craig momentarily - I don't think I'll get too excited just yet.
So when you include quantum effects, the singularity is replaced by an area of spacetime where quantum gravity effects are important.
That is quite likely the case for the singularity in the past as the above quote from Hawking shows, but whether it is the case for the singularity predicted in the gravitational collapse of stars is a different question entirely. With the big bang singularity the small initial scale requires quantum gravity, but in the case of stars there is no similar requirement—hence "cosmic censorship." Does that conceal a new and different physics?
With the big bang singularity the small initial scale requires quantum gravity, but in the case of stars there is no similar requirement
Why do you think that? There would be a region of spacetime where quantum gravity effects are important, in a black hole.
When a star collapses into a black hole, the curvature of spacetime gets very large at the "singularity".
In GR this singularity is a point. But with quantum effects, there is unknown quantum gravity physics taking place at or near the "singularity".
That's what I presume Hawking intends when he writes:
With the singularity in the past the only way to deal with this problem seems to be toappeal to quantum gravity. I shall return to this in my third lecture. But the singularitiesthat are predicted in the future seem to have a property that Penrose has called, Cosmic Censorship. That is they conveniently occur in places like black holes that are hidden from external observers.
Well, if "quantum" effects are whatever happens at very very small length scales and GR is whatever happens in strong gravitational fields, then what happens at the singularity (or very near it) is quantum gravity. It might be something that doesn't look like either quantum theory as we know it or GR as we know it, but it has to integrate with them.
True you would never get a signal from the "singularity" in the black hole, but physics can perhaps deduce what is going on.
And yes there's a possibility that a rotating black hole might be a window to another universe. A rotating black hole would still have a singularity, but it would be a ring rather than a point. Very near to the ring the curvature tensor would get very large so there would be quantum gravity effects.
Actually you would eventually get a signal from the singularity inside the black hole when after gigantic eons, the black hole evaporates.
There are lots of proposals around for new theories such as loop quantum gravity and in some very recent applications to black holes there is no singularity inside. It will be interesting to see how it all falls out.
So often, early explanations of the natural world arise from anthropocentrism.
Euclid, for instance, built his geometry on a flat, unbounded plane, an abstraction of what he saw.
About 2K years later, his followers wanted to hurl Riemann and Lobachevsky from the profession.
Their offense? They built geometries on surfaces on which parallel lines are not everywhere equidistant.
In the June 2013 Scientific American, an article on Quantum Bayesianism opens with:
In the quantum realm, particles seem to be in two places at once, information appears to travel faster than the speed of light, and cats can be dead and alive at the same time.
Here is perhaps the shortest of all possible summaries: collapsed wave functions and Schrodinger's living and dead cat are figments of physicists' imaginations.
Readers here know my opinion of the BBT; it too is a figment.
About 2K years later, his followers wanted to hurl Riemann and Lobachevsky from the profession.
Their offense? They built geometries on surfaces on which parallel lines are not everywhere equidistant.
The full story is actually more interesting.The objections to non-euclidean geometry came from philosophers, not from mathematicians. Euclid's fifth postulate—the parallel postulate— had been viewed with suspicion for hundreds of years by mathematicians—not that they considered it false, but rather it was suspected of not being independent of the other postulates. Many vain attempts were made to derive it from the other four postulates.
Eventually in the nineteenth century it was realized that there are three possibilities:
1) given a line and a point not on the line there is one and only one line through the point which does not intersect the given line (euclidean geometry);
2) given a line and a point not on the line there is no line through the point which does not intersect the given line (elliptic geometry);
3) given a line and a point not on the line there are infinitely many lines through the point which do not intersect the given line (hyperbolic geometry).
The reason philosophers found non-euclidean geometries objectionable was Kant's thesis that euclidean notions of space and time are innate ideas in the human mind and therefore the most secure form of knowledge. The validity of alternate geometries challenged this fundamental premise and diminished euclidean geometry as the ideal of intellectual achievement. Dostoevsky in The Brothers Karamazov famously equated the discovery of non-euclidean geometry with evil.
Neither Lobachevsky nor Riemann suffered at the hands of fellow mathematicians. Lobachevsky did lose his university position as a result of political issues. The work of Bolyai, Lobachevsky, and Riemann on non-euclidean geometries was published in their lifetimes and they were well respected by colleagues. The controversy was entirely philosophical.
Dr. Clark, thanx for adding to my few words.
I dimly remember reading the story in Eric Bell's 1950-ish multi-volume history of math, titled as I recall, Mathematics, the Queen and Servant of Science.
BTW, I think elliptic geometry is valid on oblate spheroids too.
Kant's thesis that euclidean notions ... are innate ideas in the human mind.
Anthropocentrism, anthropocentrism. All is anthropocentrism.
There are easy to understand models of both elliptic and hyperbolic geometry. For eliptical geometry the sphere provides a model: the lines are great circles, which are geodesics on the sphere and any two great circles intersect.
The easiest model for hyperbolic geometry is the one given by Poincaré. The space of points is the interior of a fixed circle and the lines are the arcs of circles which meet the fixed circle orthogonally. The other common example is the pseudosphere, a surface of constant negative curvature obtained by rotating the tractrix around its asymptote.
Gauss was the first mathematician to consider non-euclidean geometries, Bolyai was the first to use the term non-euclidean, and Lobachevsky was the first to publish. It was immediately understood that this "solved" the problem of the parallel postulate.
Can the hyperbolic plane be isometrically embedded into R^4?
This would be a surface in 4-dimensional space, where the metric comes from the Euclidean metric in R^4, and the metric on the surface has constant negative curvature.
Apparently it's been proved you can't isometrically embed the hyperbolic plane into R^3, but you can into R^5.
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