Just checking--this science reporting at phys.org is incorrect, correct?

Article here: http://phys.org/news/2015-02-big-quantum-equation-universe.html

Passage in question here: “In the beginning, everything in existence is thought to have occupied a single infinitely dense point, or singularity.”

But I believe I have been educated (here and elsewhere) to understand that the above sentence is false. Yet here I see it again repeated at what I think is a respectable site, right?

Is it false or not?

What I’ve been taught in the last few years is that the view is actually that everything in existence once existed in an infinitely dense state*, but not all at a single point.

Is that right?

*Whether it was actually infinite or some kind of ‘divide by zero’ infinite I’m not sure–if actually then I am not sure how it is possible for it to have made any kind of transition to non-infinite but this is a digression.

I don’t see how it’s possible to be infinitely dense over a non-infinitesimal volume. That would seem to lead to uncountably infinite mass, but someone can surely correct me on this. Perhaps all of the universe was concentrated in one Planck volume, because sizes below this do not make sense to talk about?

Infinity squared is still countable. You don’t get uncountable (IIRC) until you raise some number to an infinite power.

Let’s not quibble over orders of infinity. The claim that you cannot have infinite density over an positive volume would have infinite mass. Now this is not impossible, provided the universe now has infinite volume (and finite density). But if I understand cosmic inflation properly, the volume got very large very fast, but didn’t get to be infinite.

However, from reading The First Three Minutes, I came away with the impression that nothing at all is known about the universe before 10^{-37} seconds (I may have the time wrong, but it was something absurdly small) and by that time the size was not infinitesimal and the density not infinite.

Any statement about The Beginning is in the realm of “not even false”. We can talk about conditions at any time after The Beginning, but it’s problematic to try to extrapolate that to The Beginning itself. For instance, we can say that for any two given points, as we run time backwards, those points get closer together, such that the limit of that distance as t -> 0 is 0. But we can also say that at any given time, the Universe is infinite, so the limit of its size as t -> 0 is also infinite. One can’t really reconcile these two statements, so there must be some sort of discontinuity in at least one of them, and we can’t say which.

[insert deity here] said, “Let there be light,” and there was light. They saw that the light was good, and They separated the light from the darkness.

So there it is - A single photon first with no mass and no density.

I think the mistake here is not that they said something that was false, but that they said something like it’s a fact, when it’s not known to be a fact.

According to my understanding, we can understand the physics that describe what the universe was like when it was very small - I’ve heard the visible universe at the size of a grapefruit. But saying what happened even before that is speculation at this point, because quantum physics and relativity physics get to the point where they contradict each other and we don’t know which is right, or if it’s something else entirely.

Well, we could in principle develop a quantum theory of gravity that could take our extrapolations back to earlier times. Doubtless we’d still encounter some other gap in our understanding further back yet, but we could in turn come up with new models and techniques to break through that barrier, too, and so on. But I don’t think it’s possible, even in principle, to go all the way back to t=0.

Wouldn’t a Theory of Everything do that? Are you saying that a ToE is impossible in principle?

I am certain that a Theory of Everything is impossible in principle.

As Chronos rightly points out the question doesn’t have a precise answer. The assumption is that general relativity is a theory about smooth manifolds, but a manifold can’t be smooth where the curvature tensor blows up like it does at the big bang singularity. Therefore the theory literally breaks at this point, though what is meant by ‘breaks’ can be interpreted in a variety of ways philosophically.

That said I think it is better to think of the singularity as infinite denseness rather than a single point of infinite denseness. To give a little justification you can do what is called a conformal mapping and map curved cosmological spacetime onto flat Minkowski spacetime whilst still preserving the “spacetime angles” (but not “spacetime distances”). When you do this you find that any standard cosmology doesn’t conformally map onto the whole of Minkowski spacetime , but only part of it and the singularity doesn’t map to a point in Minkwoski spacetime, but a slice of time,such as that defined by the clock of an inertial observer at a given instant of their time.

Why bother to do this? Well conformal transformations preserve causal structure, so it tells you that there is a hard limit to how far you can see (i.e. there exists an observable universe for each observer bounded by a particle horizon) which is defined by your past light cone at the “singularity time slice”.