# The Naked Scientists Forum

### Author Topic: Could we calculate the diameter of the universe at the moment of the big bang?  (Read 7592 times)

#### Richard Arrett

• Guest
##### Could we calculate the diameter of the universe at the moment of the big bang?
« on: 05/11/2010 09:30:05 »
Richard Arrett asked the Naked Scientists:

Question.  Assuming all the matter and energy of the universe is in the form of quarks at the moment of the big bang.  Assume everything is packed together as tightly as possible (to the planck length limit).

Can we calculate the diameter of a sphere of all of the matter of the universe, at the moment of the big bang?

If so - what is it?

What do you think?
« Last Edit: 05/11/2010 09:30:05 by _system »

#### Pikaia

• Full Member
• Posts: 81
##### Could we calculate the diameter of the universe at the moment of the big bang?
« Reply #1 on: 05/11/2010 11:23:13 »
The universe seems to be infinite in size, both now and at t=0. It certainly isn't spherical because a sphere has a surface, and an inside and an outside, but talking about the surface of the universe, and an inside and outside is nonsense. So your question is invalid.

http://www.astro.ucla.edu/~wright/cosmology_faq.html#RB

#### BenV

• Neilep Level Member
• Posts: 1503
##### Could we calculate the diameter of the universe at the moment of the big bang?
« Reply #2 on: 05/11/2010 11:32:42 »
He's asking a question with some assumptions, so I think this is a perfectly valid question.  I don't know how to answer it though!

#### Bill S

• Neilep Level Member
• Posts: 1828
• Thanked: 12 times
##### Could we calculate the diameter of the universe at the moment of the big bang?
« Reply #3 on: 05/11/2010 14:55:57 »
Pikaia - I need some help here!
Quote
The universe seems to be infinite in size, both now and at t=0.
Do you mean "infinite" or "boundless"?

Quote
It certainly isn't spherical
If it is infinite it makes no sense to talk of it as spherical; but it could be boundless and spherical.

Quote
talking about the surface of the universe, and an inside and outside is nonsense
If it is infinite, talking of an outside is nonsense, but, surely, everything is inside.
If it is only boundless, there could be something outside.

The original question requires that we accept the B B as the beginning of the Universe. If it had a beginning it must be finite.

#### Pikaia

• Full Member
• Posts: 81
##### Could we calculate the diameter of the universe at the moment of the big bang?
« Reply #4 on: 05/11/2010 15:24:35 »
Do you mean "infinite" or "boundless"?
It is probably both. There are theories involving weird geometry in which the universe is finite but unbounded, but they are thought to be unlikely (eg the dodecahedral model, in which the faces are joined together).

Quote
If it is only boundless, there could be something outside.
How would you go from the outside to the inside without crossing a boundary?

Quote
The original question requires that we accept the B B as the beginning of the Universe. If it had a beginning it must be finite.
I don't think the question does assume that the BB is the origin of the universe - it could be infinitely old, with the BB representing the end of a collapse.
Also, why couldn't the universe be infinite in size when it began? If it is infinite now then it must have been infinite a finite time in the past.

#### Bill S

• Neilep Level Member
• Posts: 1828
• Thanked: 12 times
##### Could we calculate the diameter of the universe at the moment of the big bang?
« Reply #5 on: 05/11/2010 20:03:42 »
Quote from: Pikaia
There are theories involving weird geometry in which the universe is finite but unbounded
Why the need for weird geometry?  Surely, if the Universe had a beginning, it is finite.  It might go on expanding for ever (unbounded), but it could never become infinite.

Quote
How would you go from the outside to the inside without crossing a boundary?
Ours might not be the only universe.  If there are others, it would not be possible to pass from one to another without crossing a boundary, but that would not mean that the other universes could not exist.

Quote
I don't think the question does assume that the BB is the origin of the universe - it could be infinitely old, with the BB representing the end of a collapse.
Bouncing universe?  BB would still be the beginning of the universe we perceive.  How would we know that earlier universes were "the same universe" as our's, or even that they occurred as a sequence, rather than all at once?
Quote
why couldn't the universe be infinite in size when it began? If it is infinite now then it must have been infinite a finite time in the past.
I have no problem with the second part of this.  In fact I would go further and say that if it is infinite now, it must always have been infinite.
I'm not clear about the first bit, though.  Are you using "infinite" as though it were synonymous with "unbounded"?

#### Pikaia

• Full Member
• Posts: 81
##### Could we calculate the diameter of the universe at the moment of the big bang?
« Reply #6 on: 05/11/2010 20:29:39 »
Quote
Why the need for weird geometry?  Surely, if the Universe had a beginning, it is finite.  It might go on expanding for ever (unbounded), but it could never become infinite.
Here is one weird geometry that has been proposed, although a Euclidean universe seems more likely:
http://physicsworld.com/cws/article/news/18368
The universe may or may not have had a beginning, it depends on which of the various theories we are talking about.

Quote
Bouncing universe?  BB would still be the beginning of the universe we perceive.  How would we know that earlier universes were "the same universe" as our's, or even that they occurred as a sequence, rather than all at once?
Here is one promising theory:
http://www.scientificamerican.com/article.cfm?id=big-bang-or-big-bounce

" ... time may have extended before the bang. The prebang universe may have undergone a catastrophic implosion that reached a point of maximum density and then reversed. In short, a big crunch may have led to a big bounce and then to the big bang."

Quote
Are you using "infinite" as though it were synonymous with "unbounded"?
I am using "infinite" in the sense of an infinite straight line.

#### Bill S

• Neilep Level Member
• Posts: 1828
• Thanked: 12 times
##### Could we calculate the diameter of the universe at the moment of the big bang?
« Reply #7 on: 05/11/2010 21:02:23 »

Quote
I am using "infinite" in the sense of an infinite straight line.
The infinite straight line, like the infinite series, is a mathematical construct which has no "reality" outside the, presumably finite, minds of mathematicians.

#### Pikaia

• Full Member
• Posts: 81
##### Could we calculate the diameter of the universe at the moment of the big bang?
« Reply #8 on: 05/11/2010 22:17:02 »
Quote
The infinite straight line, like the infinite series, is a mathematical construct which has no "reality" outside the, presumably finite, minds of mathematicians.
That doesn't mean that it is an invalid way of describing the universe. We think about the universe in mathematical terms all the time!

If we travel in a straight line then there are three possibilities:
1. we come back in a loop to where we began - ie a weird geometry,
2. we come to an end - but what does it mean to talk about the edge of the universe? What would it be like?
3. We continue for ever, ie the infinite universe, which seems to be the best bet.

#### Don_1

• Neilep Level Member
• Posts: 6890
• Thanked: 7 times
• A stupid comment for every occasion.
##### Could we calculate the diameter of the universe at the moment of the big bang?
« Reply #9 on: 06/11/2010 13:58:36 »
Can I add my 2 penny worth, for what it's worth.

Tuppence, obviously, fool

I think what Richard's question boils down to is what the size of all the compressed matter in the universe would have been at the instant of the Big Bang.

Let's not get into any discussion about the BB theory, you must just accept the theory for the sake of the question.

So to come to a guesstimate, we first need to know how much matter is in the universe. OK, that's it, I'm lost!

#### syhprum

• Neilep Level Member
• Posts: 3822
• Thanked: 19 times
##### Could we calculate the diameter of the universe at the moment of the big bang?
« Reply #10 on: 06/11/2010 20:20:43 »
It is common to refer to the size as that of a pineapple, presumably compressing the apparent mass of the observable universe to Planck density.

#### Bill S

• Neilep Level Member
• Posts: 1828
• Thanked: 12 times
##### Could we calculate the diameter of the universe at the moment of the big bang?
« Reply #11 on: 07/11/2010 01:01:03 »
Quote from: Pikaia
That doesn't mean that it is an invalid way of describing the universe. We think about the universe in mathematical terms all the time!

Perhaps because it is the easiest way to think about the Universe, and it is undoubtedly very valuable.  However, there is just a chance that there is more to the Universe, or the cosmos, than we can find in our mathematics.  Infinity may provide us with an example of that.

Quote
We continue for ever, ie the infinite universe, which seems to be the best bet.

Boundless, but not necessarily infinite.

#### RichardArrett

• First timers
• Posts: 1
##### Could we calculate the diameter of the universe at the moment of the big bang?
« Reply #12 on: 08/11/2010 18:48:58 »

I was imagining all the matter and energy in the universe coming together at the moment of the big bounce.

I was assuming that the laws of physics as we understand them today are still in effect.

Which would mean that the very tightest you could pack the matter and energy would be to cram a planck mass into a space of planck length.

I had read at wipedia that the mass of the universe is estimated to be on the order of 10 to the 60th planck masses.

I computed the volume of a sphere of diameter planck length.
Density is mass divided by volume so I assumed you could add the volume of all of the 10 to the 60th planck masses into the volume of one sphere.

When I solved for the radius I got:

r = cubed root of (lp/2 * 1060)  (just solving for r in the equation for volume.

This equals .0004 meters (approximately).

So if all of the mass of the universe (10^60 planck masses) was packed into a volume of 1 planck mass per planck length sphere - I compute the radius of the universe to be about .0004 meters.

This seemed way to small to me - so I thought I would ask the Naked Scientists.

So, yes - for my question I am assuming that all the matter and energy comes back together for a big bounce - but cannot pack closer together than the planck length.

#### Don_1

• Neilep Level Member
• Posts: 6890
• Thanked: 7 times
• A stupid comment for every occasion.
##### Could we calculate the diameter of the universe at the moment of the big bang?
« Reply #13 on: 09/11/2010 10:41:24 »
I was assuming that the laws of physics as we understand them today are still in effect.

This may not be the case. So much matter under such gravitational force would result in pressure we cannot imagine. I see no reason why the laws of physics should apply in such conditions. Of course, I could be wrong.

#### Bill S

• Neilep Level Member
• Posts: 1828
• Thanked: 12 times
##### Could we calculate the diameter of the universe at the moment of the big bang?
« Reply #14 on: 09/11/2010 14:49:04 »
Quote from: RA
This seemed way to small to me

Why does this seem too small?  Many scientist believe that a singularity could occur in which all this matter would be crammed into an infinitely small space. You will probably realise from my other posts that I have problems with the infinitely small, so I would be interested to know your thinking on this.

Quote from: Don 1
I see no reason why the laws of physics should apply in such conditions

Nor do I, but I suppose we have to make some assumptions in order to progress in areas where no direct evidence is available.  I think you are right, though, to make this point, because it is all too easy to let assumptions evolve into "facts".

#### JP

• Neilep Level Member
• Posts: 3366
• Thanked: 2 times
##### Could we calculate the diameter of the universe at the moment of the big bang?
« Reply #15 on: 09/11/2010 15:09:17 »

I was imagining all the matter and energy in the universe coming together at the moment of the big bounce.

I was assuming that the laws of physics as we understand them today are still in effect.

Which would mean that the very tightest you could pack the matter and energy would be to cram a planck mass into a space of planck length.

I've never seen the planck units cited as being the ultimate limit for anything.  All I've read is that the Planck units are basically where quantum theory and gravity would have to cooperate--and that we don't have a theory for how that would work.  I'm not sure there's a good reason to assume that you can't pack things denser than 1 planck mass/1 planck volume.  It's just that we couldn't predict from our current quantum theory how things would behave there.

#### imatfaal

• Neilep Level Member
• Posts: 2787
• rouge moderator
##### Could we calculate the diameter of the universe at the moment of the big bang?
« Reply #16 on: 09/11/2010 16:33:29 »
Richard - not sure of your sums either!

If one planck mass goes into one planck length cubed then volume = 10^60 planck lenghts cubed.  cube root of 10^60 is 10^20 - so your sphere has a very rough radius of 10^20 planck lengths which is 10^-15 metres.  More importantly look at JP's point - a planck lenght radius sphere can definitely hold a planck mass - because that is the definition (swartzchild radius of planck length black hole has mass of planck mass)

#### QuantumClue

• Hero Member
• Posts: 613
##### Could we calculate the diameter of the universe at the moment of the big bang?
« Reply #17 on: 15/11/2010 09:32:16 »
The diameter of the universe was pointlike during the initial condition of the universe, or the first moment in time (which is very small) perhaps even smaller than the Planck Time . This would mean there really is no diameter.

#### Bill S

• Neilep Level Member
• Posts: 1828
• Thanked: 12 times
##### Could we calculate the diameter of the universe at the moment of the big bang?
« Reply #18 on: 15/11/2010 15:45:42 »
Quote from: QuantumClue
perhaps even smaller than the Planck Time
We regard the photon as the quantum of energy; there are no smaller packets of energy.
Is it not also reasonable to regard Plank time as the quantum of time, in which case time would not come in smaller packets?

#### Olympus

• First timers
• Posts: 4
##### Could we calculate the diameter of the universe at the moment of the big bang?
« Reply #19 on: 15/11/2010 17:55:52 »
This idea that the universe poped into existence from a minutely small point whether a planck mass is a little hard to accept. You could then ask the question what were the conditions prior to the expansion event. The key to explaining the origin lie with understanding the unity theory of gravity and it's existence prior to the big bang. !

#### Bill S

• Neilep Level Member
• Posts: 1828
• Thanked: 12 times
##### Could we calculate the diameter of the universe at the moment of the big bang?
« Reply #20 on: 15/11/2010 18:40:37 »

Quote from: Olympus
This idea that the universe poped into existence from a minutely small point whether a planck mass is a little hard to accept.
Is it the popping into existence that is difficult to accept?  Consider the possibility that all the matter and energy of the Universe were packed into that small speck; then it would not have to come into existence, it would already be there.  OK, so that's hard to accept as well, but if you think about it enough it can make more sense.  What's more, it could put a few scientists' hackles up, which might be fun.

#### QuantumClue

• Hero Member
• Posts: 613
##### Could we calculate the diameter of the universe at the moment of the big bang?
« Reply #21 on: 15/11/2010 22:13:17 »
This idea that the universe poped into existence from a minutely small point whether a planck mass is a little hard to accept. You could then ask the question what were the conditions prior to the expansion event. The key to explaining the origin lie with understanding the unity theory of gravity and it's existence prior to the big bang. !

I think my point being was, that physics necesserily breaks down at the singularity. There maybe many phenomenon of the beginning of time we may discover in time to come.

#### Bill S

• Neilep Level Member
• Posts: 1828
• Thanked: 12 times
##### Could we calculate the diameter of the universe at the moment of the big bang?
« Reply #22 on: 15/11/2010 22:36:47 »
Quote from: QuantumClue
physics necesserily breaks down at the singularity
Obviously a singularity can exist in theory, but has anyone established that it is a physical possibility?

#### Pikaia

• Full Member
• Posts: 81
##### Could we calculate the diameter of the universe at the moment of the big bang?
« Reply #23 on: 16/11/2010 00:06:42 »
A singularity is simply somewhere that an infinity occurs, it need not be a point in space.
The Big Bang was a singularity that occurred throughout space, with the density virtually infinite. The universe was not a point at t=0 - that is the fault of popularised descriptions of the BB, which compare it to an inflating balloon, but that is a very misleading analogy - the universe is not curved, is not finite, and it is not expanding into a larger space.

#### Bill S

• Neilep Level Member
• Posts: 1828
• Thanked: 12 times
##### Could we calculate the diameter of the universe at the moment of the big bang?
« Reply #24 on: 16/11/2010 01:04:58 »
Quote
A singularity is simply somewhere that an infinity occurs, it need not be a point in space.
The Big Bang was a singularity that occurred throughout space, with the density virtually infinite.
"somewhere that an infinity occurs". To me that sounds like a contradiction in terms.  Surely, by its very nature, an infinity must be everywhere, and include everything; unless you are talking about a Cantor type mathematical infinity, which is a very different "creature".
The BB must have happened throughout space, that I can see, as we are assured that space and time were created in the BB.
The question of running the expansion of the Universe backwards, and the identity of a "virtual infinity" feature in another thread so there is no point in repetition.

#### The Naked Scientists Forum

##### Could we calculate the diameter of the universe at the moment of the big bang?
« Reply #24 on: 16/11/2010 01:04:58 »