I, personally, don’t have any idea.

In the 1980s and ‘90s it was common for science writers to say “a point” or an object so small it didn’t even exist as we know things to exist today. In the 1990s, Dr. Robert Jastrow told me he thought the expansion began from an object that was about the “size of a basketball”.

In 1933, the British Astronomer, Arthur Eddington, said, “Initial radius of the universe before it began to expand = 328 megaparsecs = 1068 million light-years.”

But me, personally, I don’t know.

I think that right now, not too many science writers are talking about the beginning or the earliest “size” of the universe.

I had to think about that myself. He means "flat" in the sense of "not curved", or Euclidean space. So, a three-dimensional object like a ball can be embedded in flat space, and be "flat" even though its two dimensional surface is curved.

Not exactly.

The current model of The Universe, is of a Perfectly Flat 4 Dimensional Space-Time, that is then Curved into a Hyper-Sphere, around a Fifth, Unseen, Spatial Dimension.

In this way, the Seemingly Contradictory Equations allow us to Have Our Cake and Eat It Too, as it were.

This is because, The Surface of a Hyper-Sphere is Infinite in The Four Observable Dimensions, whil still being Finite in the Fifth, just as The Earth's Surface, while being Infinite in Length, Width, and Perhaps Time, is Wrapped around a Finite Extent, thus putting an Upper Limit, upon the Actual Surface Area.

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That “flat” term confused me too for a couple of years when I first started studying this stuff, then I began to realize they were talking about a possible 4th dimension of space.

So you do think the universe is “flat” (not a hypersphere) and is just a regular expanding curved 3-D sphere?

I wonder if we will ever find out? Seems to me that if it is already “infinite”, then it couldn’t “expand”. I can accept “space” being “infinite” and a “finite” amount of matter expanding into it.

But of course, it could be doing something very strange that we haven’t even thought of yet.

That's just it, the Part that is Expanding is Finite, however, as it Wrapped around a Fifth Dimension, it Appears to be Infinite.

Recent Studies have tried to prove this by comparing Sections of The Microwave Background, and trying to find Arcs of Repitition.

Unfortunately, the Background is SO Uniform, that this is Proving to be Very Difficult, to say the Least.

In fact, it may turn out that The Wrap Around Point, is Beyond our Visual Horizon, which would leave The Visible Universe occupying only a Fraction of a Much Larger Hyper-Spherical Universe.

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Not necessarily. It all depends on the geometry you're using. Classical Euclidean geometry, the stuff people learned in high school, allows for spheres. The thing to remember is that the sphere is a three-dimensional object with a surface and an interior volume. Within those three dimensions, all of Euclid's laws of geometry apply as normal. Parallel lines don't meet, the interior angles of a triangle add up to 180 degrees, and so on. We think of this geometry as flat because the axes are either going to be straight lines or a planar figure if you're using polar coordinates.

In *Riemannian* geometry those laws don't necessarily hold true. The basic geometric shapes that we find so intuitive exist, but they're warped by the fact that the geometry itself is curved. For instance, the surface of a sphere is a perfectly good *two-dimensional* Riemannian space. Lines that are parallel in one region of the surface are not necessarily parallel elsewhere (like lines of longitude being parallel at the Equator but intersecting at the poles) and the interior angles of a triangle don't have to add up to 180 degrees (you can get 270 on the surface of the Earth). Granted a sphere is the simplest possible geometry here, but more complex spaces are possible. Also, you can have curvature *without* wrapping the space around another dimension. In fact, you *only* need that extra dimension if you're trying to use Euclidean geometry to model the space.

The problem is that the human brain is not wired to visualize anything more than a two-dimensional curved space and it can only understand that by embedding it in a three-dimensional flat space. Current theory holds that the universe is a four-dimensionnal hypersurface whose curvature (gravity) is determined by the presence of matter and energy. We can model this as a surface in a five-dimensional Euclidean space, but I don't think that's inappropriate because that fifth dimension does not exist in any form we can experience. As such, it's best to invoke Ockham's Razor and discard the idea. Also, remember that the fourth dimension is *time* and, for whatever reason, time seems to be quite different from space. You can't embed time in a spatial dimension - it just doesn't work. (For the sake of argument, I'm ignoring the higher-dimensional theories floating around. If the universe has more dimensions, they may also be curved so the argument holds generally. Also, at least for now it seems that we can only directly interact with four of those dimensions - space and time - so my basic premise here should hold).

Which should be easy if the Big Bang was an explosive event. That would necessitate that the universe is essentially a huge, three-dimensional spherical cloud of matter that expands with time. We should, in theory, be able to find a point from which all galaxies are receeding, based on their redshifts.

Well, why does the amount of matter in the universe have to be finite? In fact, if the universe is a four-dimensional hypersurface it must have an infinite amount of matter to preserve the idea that it has no center and no edge. Otherwise, you could come to a point where you'd see lots of galaxies one direction and none in another. That violates the restriction that the universe must be uniform throughout its entirety. As long as matter and energy aren't being continuously created, there is no violation of energy and matter conservation. (Granted, spontaneous pair creation is an exception, but the Uncertainty Principle covers it).

No, the discussion is out there. The problem is that understanding the very early universe will eventually require us to finally get general relativity on the same page as quantum mechanics. Right now, those two theories are incompatible as there is still no way to get gravity to work on a quantum level. There is no experimental evidence of gravitons - or even gravity waves - and no generally accepted theory that bridges the gap.

Perhaps more importantly, the very early universe, by which I mean the Big Bang and the time shortly thereafter, poses a couple of huge questions that theorists find baffling, but intriguing. For instance, why is there no evidence of large amounts of anti-matter in the universe? If, as has been suggested, that some galaxies are made of anti-matter, why aren't they mixed within galaxies? Why didn't the galaxies and anti-galaxies annihiliate each other in the first place? Why do galaxies exist at all if the universe should be completely uniform? What is causing spacetime expansion to change speeds? What - and where - are dark matter and dark energy? I don't think I'm alone in thinking (and hoping) that the answers to these questions will help us understand the baby universe.

Can you explain what you mean by that? I’ve read that idea many times in many books, but I’ve never seen it explained in terms that I can understand. Why does gravity have to work on the ultra-small scale? Especially since the ultra-small particles are dealing with different kinds of fields and forces on the small scale.

When we clump a bunch of atoms together and call that a “mass”, then the overall mass works under the gravity laws, but why should the small-scale particles work under the large-scale gravity laws, when those small-scale particles have other fields to deal with?

Simple: those small particles still have mass and therefore should still have gravity. Neutron stars are a great example. As I understand them, the star's own weight causes protons and electrons to fuse into neutrons and the collective gravity of the neutrons then holds the star together, even though individual protons are very small objects and individual electrons are even tinier.

Keep in mind also that stars are mostly hydrogen - which essentially has the same mass as a proton. And yet, a star's gravity is strong enough to keep the hydrogen in. Nebulae are hydrogen gas (two protons) and gravity holds them together. Electromagnetism doesn't apply since both forms of hydrogen are electrically neutral and lack magnetic fields. The strong and weak nuclear forces don't extend beyond the individual nuclei, so they're irrelevant. If gravity can affect masses as small as a proton, why should it have a lower limit? What about the idea that so called 'WIMPs' - weakly interacting massive particles - account for the missing dark matter in the universe? Some of the particles in question aren't much bigger than a proton but taken as a whole have profound gravitational effects. Why should gravity stop just because you've taken something apart? Put another way, general relativity says that it should be possible for two neutrons to orbit a common center of mass in well-defined, completely predictable orbits. Quantum mechanics says that would violate uncertainty. Something has to give.

And that's one of the fundamental differences between general relativity and quantum mechanics. You're right that in some situations gravity is going to be overpowered by other forces, but that's not always the case. Either way, the gravity is still there. The cores of black holes may be point-like objects. However, if you have an electrically charged black hole, gravity is overpowering the electrostatic repulsion that should be causing the black hole to fly apart. Since that's happening on a small scale, quantum mechanical interactions *must* be involved. We're 99.9% positive that black holes exist, and yet there is no quantum mechanical theory of gravity that's been experimentally proven and no indication as to where the boundary between very large (GR) and very small (quantum) lies. Or, put another way, why should GR stop working when you get to the singularity when it works beautifully everywhere else in and around the black hole? Gravity *must* work on a quantum level, but there is no understanding of how it's affected by the uncertainty principle and the wave/particle duality of matter and energy.

The other big problem is that both theories offer distant explanations as to what gravity is. General relativity says that it's the curvature in spacetime. Quantum mechanics predicts that it's a force carried by gravitons. *Both* predict gravitational waves, although those have never been detected. This isn't as simple as saying that one theory is right and the other is wrong because gravity still *acts* like the other forces. If it's curvature, it still produces an effect analogous to unlike charges attracting each other. If it's a force, why does it work so differently than other fundamental forces (i.e., why is there no gravitational repulsion?)? Scientists keep looking for some way to explain these similarities and differences and neither theory seems to be able to bridge the gap.

Hope that helps.

Thanks for the info!

I don’t think I would say that “gravity stops” when things are taken apart. I’m thinking about something like a large electro-magnet that can overcome the pull of gravity by means of the pull of the magnetic field, and the magnet can hold a steel bar up in the air. Switch off the magnet, and the steel bar falls. With the magnet on, we are not doing away with the gravity, we are just overpowering it with a strong magnetic field.

It’s like a piece of cellophane. I can’t throw it away. It sticks to my hand and doesn’t fall because of an electric field at my hand. At close range to my hand, the electric field is stronger than the gravity field at that same place.

The “completely predictable orbits” you mention, would that be in the total absence of the other fields? Could the presence of the other fields, on the small scale, break up the “predictability” of the orbits of the Neutrons? Can we totally isolate the two Neutrons from all other fields? In large-scale space in our solar system, we don’t have other fields that are strong on a large scale, and so the gravity field dominates the large-scale motion of the planets. But wouldn’t the other fields be stronger at short distances on the small scale?

That's what I'm getting at, actually. The electromagnetic force is stronger than gravitation, but only over shorter distances. Nobody has any understanding as to why this is true.

In theory, yes to all of this. Neutrons are electrically neutral, so they don't interact with electric fields. They have no magnetic moment, so they don't interact with magnetic fields. As such, even if either type of field was present, they wouldn't make any difference whatsoever. The two neutrons aren't confined to the nucleus of an atom so the weak magnetic force. All we have are two neutrons in otherwise empty space - which isn't at all unlikely.

*But* the neutrons have mass and therefore they produce gravitational fields that tug on each other. It's not a strong pull by any means, but to the neutrons it's not negligible. Both general relativity and Newtonian mechanics saw that they should be able to rotate around a common center of mass - just like two stars of equal masses would. Calculating those orbits with those theories should be a simple matter of applying Kepler's laws and cruching the numbers.

The thing is, neutrons are small enough that you have to apply quantum mechanics. The two neutrons have wave-like properties that, because the neutrons are so small, can't be ignored. In fact, the longer the neutrons go without colliding with something (and the tiny amount of gravity we're talking here isn't going to be enough to do this) the more wave like they become. Neither general relativity nor classical mechanics has any way of dealing with this.

And then there's the Heisenberg Uncertainty Principle. At the risk of over simplifying it, the more precisely you meausre the neutron's velocity the less precisely you know the orbit, and vice versa. Well, to figure out the orbit you need to know the velocity of the neutrons. The catch is, when you measure the celocities you force the neutrons to collide with something that will change its position and therefore change its orbit. That change, according to quantum mechanics, is unpredictable whereas general relativity says that the change in orbit should be calculable. On the other hand, you could measure the distance between the neutrons and plug that into Kepler's laws. The inverse happens - you've changed the velocities and that will also change the orbit. Again, that change is unpredictable under quantum mechanics but deterministic under relativity and classical mechanics. Taking this a step further, it's not just a matter of the neutrons being so small that bouncing photons off of them to measure their position or velocity sends the neutrons flying. According to quantum mechanics, the neutrons don't actually have a specific, finite position or velocity until the photon hits it forcing it to take a proverbial stand. The longer they go without hitting a photon (or anything else, for that matter), the less specific their position becomes and the more *wave-like* they become. Neither relativity nor classical mechanics offer any explanation as to how that works, let alone how you can get two waves orbiting each other.

All that is very interesting. You need to write a book about it. You make more sense than most science writers who try to describe all this.

Not true!
1) The electromagnetic force is many orders of magnitude stronger than gravity. That is why an electromagnet can lift a steel bar against the gravitational pull of the entire Earth.
2) The range of the electromagnetic force is the same as that of gravity (infinite). The Earth is pulling from over 6000 kilometers away. The electromagnet is in contact (or very close to it) with the steel. The gravitational pull of the electromagnet on the steel is negligible and would be would be orders of magnitude less from 6000 kilometers away, but it would still be there (in the same ratio to its magnetic attraction).

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Good point - and bad wording on my part. ops: Perhaps a better way of looking at it might be that we don't understand why electromagnetic effects don't dominate over large scales but gravity does. To me at least it seems like there's something odd that the weakest of the fundamental forces (if it is a force) controls the way things move throughout the universe while, to the best of my knowledge, the effects of the electroweak force and the strong nuclear force are not observed over galactic scales.

The ratio of the strenght of the electromagnetic force to the gravitational force is not well-defined.

It's the GrapesOfWrath post that discusses the ratio with electrons, and protons, and asks about neutrons. ToSeek answers the question a couple posts later.

Well, don’t worry about that. If we always had to worry about our exact wording, we would always be afraid to say anything. What irritates me the most is physics books and textbook saying things that aren’t true, and that have never been true, and that obviously aren’t true.

That makes a whole lo