My question relates to the Big Bang theory of creation and quantum theory. Please help correct my understanding of the theories. My understanding is that the universe arose in a Big Bang out of a singularity. Quantum theory seems to come into play by explaining that even in a vacuum it is possible for particles to come into creation spontaneously. My understanding is that the Big Bang was such an event. What I don’t understand is if there is a fundamental difference between a vacuum, such as the vacuum between the galactic superclusters, and the nothingness that the Big Bang is expanding into. If a nothingness can have quantum fluctuations, how is it different than a vacuum?

A related question that I have that I think must be addressed with the first question is about the geometry of the universe. My understanding is that there are three spatial dimensions and one dimension of time. I have read other threads on this board, however, that the universe does not have an edge. How is this possible if there are only three spatial dimensions? If there are more than three, I can accept that I can’t visualize a 4D hypersphere. If there are only three, however, why is the question “What happens if you keep goin up?” a nonsensical question? Take our planet for example. If I start at the South Pole and travel along the z axis, I will reach the center of the earth and eventually the North Pole. But I can keep going at that point, up into the atmosphere and then into outer space. Why can’t someone at the edge of the universe ask the same question about going straight rather than curving back around? Is there a nothingness at the edge that prevents this?

Here are my simple-minded conceptualizations around those two questions, which those who know this field far better than I can feel free to correct or otherwise comment upon, but which I think are in principle correct.

Quantum fluctuations in a vacuum are a property of space, that which is constantly being created as a continuing consequence of the Big Bang. In fact they are a property of space and time. So they are fundamentally different than anything that could be postulated as a “cause” of the Big Bang which occurred in the absence of space, time, and indeed causation itself. They are at best an analogy.

The idea that the expanding universe has an “edge” seems to be related to the intuitive “explosion” model of the Big Bang, in which somewhere there exists a “center” in which it originally occurred, and an expanding outer sphere. But as pointed out on a previous discussion, this is not the correct model. It’s more like a 3D analog of the 2D surface of an expanding balloon, a balloon with dots on it (representing galaxies) that grow farther apart as the entire fabric (of space) expands. There is neither a center of expansion nor, for the same reason, an edge.

Doesn’t that imply a 4th spatial dimension, with the universe being a hypersphere? A sphere certainly has a center. What if I put some object inside the balloon before inflating it?

Edited to add. I’m sure the universe has to have some kind of shape. At the very least we can say that our area of the universe is a sphere with a radius of 13.82 billion light years.

You’re supposed to take the balloon analogy as limiting yourself to the surface of the balloon, and the earth’s north pole analogy as limiting yourself to the surface of the earth.

Leaving the surface and going “up” from the north pole is, strictly speaking, no longer going “north.” It’s a totally new direction, which longitude and latitude cannot describe.

It isn’t really an “argument,” but only a tool for envisioning the limits. Edwin Abbott’s “Flatland” is a charming version of this kind of imaginary way of thinking.

An ordinary vacuum is within a space within our universe. But the Big Bang’s singularity was not “within our universe.” It happened…um…nobody knows. Embedded in some higher-dimension space, perhaps.

String Theory is only barely able, mathematically, to model some of this, and, brother, the math is so way beyond anything we ever learned in school, it’s totally tons of depressing. (I can’t even do tensors!) So, at this point in cosmology, we have to take a lot on authority.

We don’t know that. The particles that come into existence spontaneously, do so because there is space for them to be in. The Uncertainty Principle says that position and momentum can’t both be known precisely, and the position part of that presupposes the space that you’re referring to. With the Big Bang, there was no space before (at least in some scenarios), so it’s not clear how to apply quantum uncertainty and vacuum fluctuations.

The Big Bang isn’t expanding into anything - it’s an expansion of space itself. You can’t think of it like there’s a larger, empty space and our universe is expanding into that. Our universe is all the space, and that itself is expanding.

No it doesn’t imply that, because (as Trinopus already mentioned) the balloon model is, again, only an analogy to get across the idea that things are moving apart because the fabric they are embedded in is expanding. One of the most intriguing theories for the expansion of space is one that says it’s just our perception, and that the “correct” model of the universe is a 4-dimensional one in which time and the three dimensions of space are all actually Euclidean dimensions. This is the Hartle-Hawking “no boundary” proposal for a Euclidean spacetime which posits that all instances of spacetime coexist concurrently in a finite but unbounded universe and that the “arrow of time” is merely an artifact of our perception.

It’s interesting that the math for the spacetime geometry inside a black hole suggests that the time dilation as you approach the event horizon will actually flip the time dimension with the radial spatial dimension once you cross the EH, placing the singularity not removed from you in space but in your immediate future time.

Does that mean a sphere is two dimensional, if any point on it’s surface can be described with two coordinates, the latitude and longitude? I feel like I’m missing something. Maybe I need to retake a geometry class

One conceptual problem is that space is not flat. Space itself is curved. In the same way the surface of a balloon has no edge because of it’s curvature, space itself has no edge because of it’s curvature.

IIRC, a vacuum can be described as anything from gaseous pressure less than ambient pressure at sea level (soft vacuum) through the near-total absence of air in outer-space (hard vacuum), through the complete absence of matter…to the total absence of matter AND energy: unattainable due to quantum fluctuations creating virtual particle pairs.

A sphere is definitely two dimensional and positions are described by latitude and longitude. A solid sphere (usually called a globe) is three dimensional; the third coordinate is depth. A 3-sphere is three dimensional by definition, but cannot be directly modeled in ordinary flat 3-space. It can be modeled in 4-space as the set of all (x,y,z,t) such that x^2 + y^2 + z^2 + t^2 = 1.

As far as the OP, nothingness would appear to be impossible due to quantum fluctuation, but a vacuum is certainly possible. Just has only virtual particles.

As noted, yes, the surface of a sphere is two dimensional.

What’s more useful to us, here, is that it is closed. You can never find an “edge” or “end” of the surface of the sphere; you just keep going around it.

The beautiful pseudo-Renaissance pseudo-woodcut engraving of the guy burrowing under the edge of the firmament…isn’t possible or valid. It has a naive attraction; it describes how we might think the universe works. But Einstein and Hubble and others went and spoiled the fun.

I think this analogy works: the center of the 4D hypersphere that is our universe is the location and time of the singularity that started the Big Bang. But that point does not exist in our 3D universe, just like the 3D sphere’s center doesn’t exist on the 2D surface of the sphere.

We cannot say that. More properly we can talk about the observable universe, which by one analysis is 45.7 billion light-years. (That analysis was in 2005 and I do not know what other work has been done on that since then.)

This analogy doesn’t work for topological reasons.

If we take the Universe to spatially have a topology of a 3-sphere, S[sup]3[/sup], (though note there’s no compelling reason that it should or should not have this topology), then the spacetime topology is R x S[sup]3[/sup]. This is because it only really makes sense to talk about a spatial topology Σ of a spacetime M, if M is globally hyperbolic and Σ is the topology of the Cauchy surfaces of M and hence M has the topology R x Σ.

So in other words of a geometrically and topologically spherical Universe doesn’t exist in spacetime, even as a singularity.