Another Big Bang Question: The Universe's Minimum Size

pohjonen’s thread on the Big Bang (Do all of the scientists accept the Big Bang? reminded me of a related question I’ve been meaning to ask:

Observationally, how small must the universe have been at its smallest? To say that it had been the size of an atom, e.g., would require extremely accurate measurements of the motions of all the galaxies, an accuracy we certainly don’t have. What is the largest minmimum size of the universe in the past which is consistant with measurements?

I’m not certain I follow the question.

Before the Big Bang there was a singularity…an infinitely small, infinitely dense point.

After the Big Bang I would suspect the smallest size the Universe could be while growing would equate to the Planck Length and go up from there.

If you are asking how small the Universe could be and actually still have defined galaxies I have no idea or even if such a thing could be answered.

It was a really big bang, wasn’t it?

Whatever size the universe is is dependent on how old it is.

Lets say that the universe is 15 billion years old.
Light is the fastest velocity there is.
Then the universe = or < 15 billion light-years in radius,
or from center to edge (This is assuming that the universe is a 3D sphere…4 dimensions is another matter).

Strictly speaking, there was no “before”.

Time began at the moment of the Big Bang.

It’s an unsatisfactory conclusion, because half my brain tells me that “before the Big Bang” is a meaningless question, and the other half says, “Yeah, but…”

What <b>ZenBeam</b> is asking, I believe, is, based on ovservation of galaxies today, and extrapolation of their position into the past, how small can we definitively state (within the accuracy of our measurements) that the universe was at an early time. In other words, is it possible to give each galaxy an arrow representing their measured velocty (including direction) reverse that arrow to indicate travel into the past, and have all these arrows come together within a sphere of some size? Or are our observations so gross as to just limit us to saying that there is a general trend of moving apart today, so there must have been a general condition of being close together previously?

I, of course, am not in any way trying to imply that evidence for the big bang might be shoddy. I am aware of much good evidence for it. But I believe I have captured the gist of the question. And a damn good question, I might add.

-b

Assuming that the Universe is flat or open (as now seems to be the case), you can’t assign a size to the whole thing, because it’s always been infinite. The best you can do is compare the size of portions of it. Think of it as an infinite sheet of graph paper, with the individual boxes expanding. We can say that the grid squares (and thus, presumably, the whole paper) doubled in size from one time to another, but we can’t say absolutely how big the paper is.

Now, then, let’s say the question is “what fraction of its current size was the Universe, at its smallest?”. That’s a meaningful question, but unfortunately, I don’t have an answer readily available. I’ll see if I can find something.

bryanmcc’s interpretation of my question is the correct one.

Especially the last sentence. :wink:

Chronos: perhaps I could have phrased that better as “visible universe.” Twelve or fifteen billion lightyears radius, perhaps. Can the current measured position and velocity of those galaxies all be extrapolated back to place them in a volume the size of a system? galaxy? cluster? singularity? (That’d be some pretty impressive measurements! :wink: )

ZenBeam: I call 'em like i see 'em. :slight_smile:

-b

There is something odd going on with this thread.

Whach-a-Mole seems to have quite nicely (with one tiny error noted by Slip Mahoney) ZenBeam’s question.

And then there is all this weird cruft coming in afterwards.

Take bryanmcc’s query:
“In other words, is it possible to give each galaxy an arrow representing their measured velocty (including direction) reverse that arrow to indicate travel into the past, and have all these arrows come together within a sphere of some size?”

Ummm, “direction”??? The galaxies are NOT, repeat NOT travelling away from a supposed center of explosion in our 3 dimensional space. We cannot in our normal world view draw arrows towards the center of the Big Bang explosion.

Think of it this way: I want you to point:
North, now East, then Up, and finally along the +axis in the fourth dimension. (If you can do it, you must be a hit at parties.)

ZenBeam’s question is no different from asking:
“Gee, I’m going 60mph in my car now, but I was stopped a few minutes ago. What was the smallest speed I was going?”
Answer: 0. If you want smallest non-zero speed then we got a few hours of Planck constant discussion ahead of us. Just think “exactly just tiny enough to measure”. Cf. Whack-a-Mole.

Remember, the galaxies took quite a while to form after the BB. The universe really was fantastically small within a fantastically small short time after the BB.

And I thought my kids grew fast.

I realize that. But I don’t believe I ever said or implied that. Astronomers have measured speeds and headings for various galaxies, correct? Then one should be able to extrapolate those speeds and headings (assuming they haven’t changed a great deal) back into the past. This should place them, at some arbitrary point in the past, within a certain volume. Extrapolate back to yesterday, and the galaxies in the visible universe all lie within a sphere of radius (approx.) 12-15 billion lightyears. Extrapolate back five or ten billion years, and that sphere will be some smaller size. Of course, at some point, our imperfect measurements will have errors too large to be ignored, and further extrapolation would result in galaxies passing obliquely, rather than all collapsing to a point. At this point, this particular line of reasoning towards the Big Bang breaks down (because it looks as if the galaxies all just merely flew past each other), and we must move on to other inferrences about the initial state of the universe (i.e., the CMB radiation, etc.).

If one carried out this extrapolation (or if the universe were actually collapsing) it would LOOK like all the galaxies were collapsing onto ours. We would have the erroneous impression that we were at the center. Just as today it seems that all galaxies are moving away from immovable us. But this would look the same from any vantage point in the universe. Alien astronomers in other galaxies would measure velocities relative to their position, and would extrapolate backwards as if the galaxies all began at their starting point. And in fact, the expansion started at every starting point. The question is simply how accurate are current measurements of galactic velocity, and what kind of direct calculation of earlier sizes of the visible universe are possible.

-b

Zenbeam - I think the answer is “that’s not known”. I’ve heard widely varying estimates from a point to a pea. My impression is that modern physics can’t describe that early condition. Maybe a theory of quantum gravity can. Anyway, like Chronos was saying, even if it was the size of a pea, if you were inside it (how could you not be?), you would still perceive it as infinite (well, boundless) because space would be curved back on itself. If you could travel it (ignore inflation for a moment), you’d be back at your starting point.

Actually there is no such measurement. It’s easy to measure the radial velocity (velocity towards or away from us) of distant objects by measuring the Doppler shift of thir light. But to measure transverse (sideways) velocity, you need to take a high resolution photograph, wait for a period of time, take another photo and see if it’s moved. With current telescopes, this only works for nearby stars. As far as I know, we have zero information on transverse velocities of galaxies.

Now that is a good point. I hadn’t thought of that. Thanks scr4! In that case, it will look as if every distant galaxy is moving exactly away from us, and, therefore, would’ve been exactly on top of us in the past. There goes that problem. Thanks again!

-b

A hypothetical person asks:
“At one time my car was stopped. It is now going 60MPH. Observationally, how slow must my car have been going at its slowest? To say that it had been moving at the rate of an atom width per hour, e.g., would require extremely accurate measurements of the motions of my car, an accuracy we certainly don’t have. What is the largest minmimum speed of my car in the past which is consistant with measurements?”

The answer: Measurements have very little to do with it. That fact (or assumption) that it was once stopped and it is now moving quite fast means that the car at some time was moving at all in between speeds. Knowing that the car is currently going 60.0000000000MPH or 60.0000000001MPH is completely irrelevant.

Same thing with the universe. If we assume it’s size was once zero and it is now billions of light years across automatically means it was once 1 mile (or 1 inch or 1 atom) in size. The main issue to scientists is when was it a mile (or inch or atom) in size.

Note in particular that whether or not the other galaxies are perceived to be moving “exactly” (bryanmcc) away from us or not is also not relevant. (For one thing, there is relative proper motion. A few close galaxies are moving closer to us. All the galaxies in our local group are moving in mutual orbit around each other. And then there’s motions within our supercluster, etc.)

The lower-dimensional view of our universe is to consider an expanding soap bubble. Our galaxies are just amazingly tiny dots on the bubble. Observers on the surface of the soap bubble only know about their two dimensions. They cannot measure anything in the dimension orthogonal to the surface.

Imagine if all the galaxies on the soap bubble were not statically stuck at one place on the bubble but swirling around like the rainbow colored lines on a real soap bubble. Measuring just these swirling motions tells you very little about the how fast soap bubble is expanding.

In the real universe, we measure the motions and distances of a lot of galaxies so we can average out the irrelevent swirling motions.

And could scr4 explain the meaning of “transverse”? It certainly cannot mean “along the axis of expansion” since that is 4th dimensional and obviously cannot be photographed. If it refers to “motion in either 2 dimensions not along the axis pointing to us” then said motion is irrelevant to universe expansion and not necessary to measure for these purposes.

And you came up with this assumption from where? Perhaps you read it somewhere, but how has it been shown that the universe was once arbitrarily tiny? Your car analogy has the same problem: you assume “At one time my car was stopped”. The universe was never observed when it had zero size, so how is it known that it was? There is a huge leap from the statment the universe is expanding, and therefore was smaller in the past to the statement the universe is expanding, and therefore was smaller in the past, and therefore had zero size at some point in the past.

Transverse with respect to the line of sight from Earth to the galaxy.

Regarding the transverse galactic velocities, you could make the (in my mind reasonable) assumption that the Milky Way holds no special place in the universe, and therefore any variations in velocity from an ideally expanding universe would be the same in the two transverse directions as in the radial direction. If we know the typical difference between how fast distant galaxies are actually moving away from us versus how fast they are expected to be moving away from us, we’d have an estimate of the typical transverse velocity.

The change in speed has relatively little to do with it. If you had an overhead view of a parking lot full of cars all moving apart from one another, you could back calculate their speed to see how close they all were to each other at arbitrary points in the past. And if you want to assume constant accelleration for the cars, you can throw that into the calculation, too. You could tell by this method whether the cars had all started off touching each other at the center from a dead stop, or whether they had all whizzed past each other and are now emerging. Not to suggest that the galaxies actually all swung past each other and were flung out, but you get the idea.

Imagine an exploding hand grenade. Theoretically, you could measure the speed and heading of each individual piece of shrapnel and back-calculate to the original object, or at least the approximate size thereof. Yes, the universe doesn’t have a center like that, but since all points percieve the expansion in the same way, we can act as if it does.

Granted. But for the point of this question, we have explicitly chucked that assumption out the window. We all know that much evidence (of several different types) points to the fact that the universe was once extremely tiny, but the OP wants to know what is the smallest size one could determine strictly from measurements of galactic motion. Back to the hand grenade analogy, the back-calculation wouldn’t get you down to a single point, because the individual components aren’t moving directly away from each other. There is some lateral motion.

Actually, it is exactly what is important in regards to the OP. If they are observed to be moving exactly away from us, the answer to the OP is that the measurements indicate a very small volume indeed. If they are observed to be moving almost exactly away from us, then the errors in our measurements would indicate a larger volume for the young universe. And this would be ignoring (or compensating for) motion of close galaxies gravitationally bound to our own.

scr4 correctly pointed out that Doppler measurements only measure the vector component of velocity directly towards or away from us. The transverse component of galactic motion would be orthogonal to the radial component. And it is the combination of these that would tell us the “true” motion of the galaxy relative to ours, and is necessarry to answer the OP. Unfortunately, as pointed out by scr4, this requires taking a picture of a galaxy, and then waiting for it to move. This takes a bit of a while, and pretty much makes the OP impossible to answer. (Or else, since the galaxies are observed to be heading directly away from us, revalidates ftg’s assumption and indicates that the initial size of the universe indicated by direct observation is zero (although the validity of this is somewhat in question as we know that we are completely ignoring all non-radial components of galactic velocity).)

-b

I don’t want to “stunt” the thread, so reasonable, explicity made assumptions are fair game.

Strictly speaking, measured Doppler shifts don’t necessarily give radial velocity. If the galaxies were zipping transversely at a great enough speed, the relativistic time dilation could account for the red shifts. We’d currently be at the minimum volume. It’s not very likely, but that’s one extreme.

The other extreme is to just assume the universe was a point at one time, so the minimum size is zero.

In between is the interesting territory: What minimal, resaonable assumptions can be made that reduce the minimum size?

Even if the transverse galactic velocities are assumed zero, the radial velocities would have to be just so for all the galaxies to reach the same point at the same time. The radial velocity measurement errors would bound how small the visible universe could definitely be said to have been. This volume is probably not much different than if you assume the transverse velocities had the same typical errors as well.

And if anyone knows what assumptions lead to the accepted conclusion of zero initial size (or Planck length), that would be interesting also. I have this sneaking suspicion it eventually comes down to aesthetic reasons: “Well, we know based on lots of different evidence that the visible universe must have been no larger than a galaxy (or the Earth, or a pumpkin), so why not a point.”

I can see this turning into another hammer/feather thread, but I’m going to complicate it anyway (and, to be even less help, I won’t have any answers).

The problem as described seems to be discounting any interaction between the masses of the universe. If you were actually to trace the vectors backward, you would be moving toward a time when these bodies were close enough together to change each other’s motion gravitationally.

So, it becomes much more difficult to figure the motions of galaxies once they are near enough to one another to represent the dreaded 5-billion-body problem.

Read this very carefully.

The question in the OP is inherently flawed. It makes a significant mistake in assuming that the motion of galaxies in 3d can in any way shape or form be used to determine their previous position in 4d.

Repeat: The motion of a galaxy that we see is completely unrelated to its “original” position in 4d space near the time of the Big Bang.

Poster after poster to this thread keeps making this fundamental mistake.

Go back to the Bubble Universe analogy. Take the galaxies on the surface of the bubble, draw vectors for each galaxy on the surface of the bubble that points in the opposite direction of its current motion on the surface of the bubble.

All of these vectors are tangent to the bubble and therefore not a single one passes thru the interior of the bubble let alone passes near the center of the bubble.

In 3d, hardly any pairs of these vectors would come close to intersecting.

And from the point of view of observers in the bubble universe, these vectors correspond to arcs of great circles. The complete great circles themselves would not all interesect at two points (like lines of longitude on the earth). They would appear to be like an extremely messy ball of twine. Intersections all over the place.

Knowing “exactly” these great circle arcs is utterly useless in finding the center of the bubble if your universe is 2d.


So, you measure exactly the proper motion of some far off galaxy. You get a vector in 3d. This vector is orthogonal to the vector pointing from the galaxy to the 4d BB start point. All our vectors in 3d are orthongal to the 4th dimensional axis.

We cannot point to anyplace in the universe and say: “That’s where it all started.” It’s orthogonal to anything we see see, measure or calculate.

A bubble being cannot point to the center of its bubble. Anything it points to is always at a right angle to the center of the bubble.


Running the motion of galaxies backwards, they all converge not so much because of their motion in 3d but because the space between them is getting smaller. The great circle arcs on the surface of the bubble get closer and closer together.

BTW: Asking a question about the size of the universe in the Big Bang model but not allowing the assumption of the size once being zero is like asking about the diameter of the earth but not allowing the assumption that it is round and not flat. The Big Bang models (standard, inflationary, etc.) all start with a size 0 universe.