# 10^80 particles in observable v unobservable universe

1. Jun 20, 2012

### robertjford80

Here is a chart showing the unobservable universe

The green lines indicates the part we can see. My question is that figure that gets thrown around, there are 10^80 particles in the universe, is that for observable or the unobservable universe.

2. Jun 20, 2012

### nicksauce

10^80 is for the observable universe, as the unobservable universe is probably [maybe?] infinite.

3. Jun 20, 2012

### robertjford80

that the unobservable universe is not infinite is something i feel very strongly about. it's quite simple: the universe began at a definite time in the past and it is bounded by the present, so there is a boundary on the past and the present, hence finite. Second argument: in an infinite universe there is an infinite amount of matter which would overwhelm the cosmological constant thus causing the universe to implode into a big crunch. third, you can't do any measurements in an infinite universe because all quantities are infinite, thus there is no way to determine if space is flat. fourth, although this is an argument from authority, take a look at the graph, it clearly shows the unobservable universe to be not infinite but finite at roughly 46 billion light years. fifth, you can't calculate probabilities in an infinite universe, the odds of all events happening are infinite. sixth, as olbert demonstrated in the 1830's in an infinite universe the sky would be filled with light from every angle.

4. Jun 20, 2012

### nicksauce

A timelike boundary does not imply a spacelike boundary.

Plainly false. The Friedmann equations show that the big crunch only results in universes with positive curvature (i.e., finite universes)

Just do your measurement in some local patch. Why does the rest of the universe matter?

You are way off-base here. 46 Glyr is the size of the **observable** universe.

I don't think this makes any sense.

This is true for an infinitely old universe, but is solved by a finite age universe. If the universe is of finite age, there we can only have received light from so far away, so the sky will not be filled with light from every angle, regardless of whether or not the whole universe is infinite.

5. Jun 20, 2012

### robertjford80

Sure it does. Go back to first year physics. Take the following equation:

D = RT, distance equals rate times time. You're arguing the D is infinite. How do you get D to be infinite? Either R or T has to be infinite. What's the R of the universe? It's the Hubble constant, 75 km/s/MPc. What's the T of the universe. It's 13.75 by. Hence D is finite.

That's ridiculous. I have a feeling that you're talking about the multiverse for which there is no evidence. It's the universe as a whole that matters. Let's say my local patch was the solar system and someone else's local patch was the system of Alpha Centauri, clearly our measurements would be in disagreement.

Look at the chart again. It's that curved green line that represents the observable universe.

What is the probability that I'm a random word generator? How do you determine the probability of something? You take the number of events divided by the probability space. in an infinite universe there is an infinite number of random word generators, moreover, the space in which it can happen is infinite, so you can't determine the probability of something happening.

Last edited: Jun 20, 2012
6. Jun 20, 2012

### DaveC426913

Yes you can.

While it is probably true that, in an infinite universe, all things that can happen will happen, so what? our cause and effect is still limited to our own light cone.

Show me one example where something that happens 1030 light years away has any effect on our calculations or physical universe here.

7. Jun 20, 2012

### phinds

Yes, but the universe really doesn't care what you think, and as nicksauce has pointed out, your logic is seriously flawed.

Your inability, or unwillingness, to accept that the universe might have STARTED OUT infinite (weird as that does seem), is your limitation, not the universe's. Just because it was a lot smaller 14+ billion years ago does NOT imply that it was finite.

8. Jun 20, 2012

### robertjford80

Probability at least can be debated. The following however cannot:

Take the following equation:

D = RT, distance equals rate times time. You're arguing the D is infinite. How do you get D to be infinite? Either R or T has to be infinite. What's the R of the universe? It's the Hubble constant, 75 km/s/MPc. What's the T of the universe. It's 13.75 by. Hence D is finite.

I would like an answer to the above.

9. Jun 20, 2012

### robertjford80

I'm not saying: I feel strongly about X therefore X is true. I'm saying that X is true, I think it's important. A lot of people think it's false, and I care deeply about this misconception.

For you as well, phinds, I would like an answer to this:

D = RT, distance equals rate times time. You're arguing the D is infinite. How do you get D to be infinite? Either R or T has to be infinite. What's the R of the universe? It's the Hubble constant, 75 km/s/MPc. What's the T of the universe. It's 13.75 by. Hence D is finite.

This is just a bald assertion. You've got no reason for this statement of faith.

10. Jun 20, 2012

### DaveC426913

I'm not. I'm simply poking holes in the flawed logic that's been presented.

11. Jun 20, 2012

### DaveC426913

As is yours. "It is finite" is a statement of faith. You can't apply things like D=R/T to the universe.

More correctly, we think it's probably finite.

12. Jun 20, 2012

### Number Nine

This betrays an ignorance of basic probability. You can certainly calculate probabilities that way when dealing with a finite sample space, but calculus allows us to deal with infinite (or uncountable) probability spaces very easily. The normal distribution itself is, of course, defined over the reals...

You're assuming here that the universe began with radius zero and that expansion involves the increase in radius over time, but this isn't true. Expansion, in the context of the bang bang, refers to metric expansion, which is very different.

13. Jun 20, 2012

### Dickfore

14. Jun 20, 2012

### robertjford80

You're going to have to show how metric expansion implies an infinite space.

Also an infinite universe conflicts with standard inflationary cosmology. Here's a quote from Lisa Randall

You can't double the size of the universe if it is infinite.

I also want to get back to the density parameter. You can't calculate the density of an infinite universe. Such statements as the universe is 4% ordinary matter, and 24% dark matter are meaningless because in an infinite universe there is an infinite amount of matter.

Last edited: Jun 20, 2012
15. Jun 20, 2012

### robertjford80

You're just asserting that you can't apply things like D = RT to the universe. You're going to have to provide some reason why our common sense intuitions should be suspended. If you look at the chart above, it clearly asserts that the size of the universe is 46 billion light years. It doesn't require faith to believe that a finite number times a finite number equals a finite number.

If it's more probable that the universe is finite then we're in agreement. Of course there's always a small probability that the universe is infinite but that's not what we're arguing and that's not what nicksauce asserted.

16. Jun 20, 2012

### Number Nine

No, you're completely missing the point here. Your argument was as follows: the expansion of the Universe involved the Universe beginning with finite size and increasing in radius over time, therefore the current size of the Universe must be finite. You grossly misunderstand the notion of inflation in Big Bang cosmology; and your argument fails utterly when expansion is understood as metric expansion.

Brilliant! It's incredible that a century's worth of physicists and mathematicians have simply overlooked this fact. If only we had a mathematical framework that allowed us to deal with infinite processes; it's a shame that Isaac Newton didn't think of one...

No, it doesn't. That chart very obviously describes the radius of the observable universe as 46 light-years. It even has a nice caption saying "visibility horizon" above the bar reading 46 light-years. How have you failed to notice this?

17. Jun 20, 2012

### Dickfore

Hey OP, imagine a (infinite) plane. Next, imagine the plane stretching evenly. If you drew two points on it, they would recede from eachother. So would any two arbitrary points. Did the size of the plane increase? Next, imagine two distant points and a light signal emanating from the first one towards the second one. If the points are sufficiently far apart, the distance between them would increase by more than the distance traverseed by the light. In this fashion, we arrive at an observable region around each point. Does this region increase?

18. Jun 21, 2012

### robertjford80

You still haven't explained how metric expansion implies an infinite space.

This is just an assertion. Why don't you demonstrate how you can calculate that the universe is made of 4% ordinary matter when in an infinite universe it should be infinite.

It's the green line that marks the observable universe. You can't observe something 46 billion light years away because only 13.7 billion years have passed. How have you failed to notice this?

19. Jun 21, 2012

### robertjford80

Above are self-consistent statements but you have not shown that those statements describe reality. Nor have you shown how they do not conflict with standard inflationary cosmology:

Further, you have yet to explain how a finite number times a finite number equals an infinite number.

Last edited: Jun 21, 2012
20. Jun 21, 2012

### Number Nine

I'm tempted to dismiss this as deliberate ignorance. As I've already clearly explained to you, the notion of metric expansion was brought up because you misunderstand what expansion means in the context of big bang cosmology. You argued that the universe must be finite because its radius has expanded at a finite rate since its origin. Your argument is flawed because your premise is wrong; expansion has nothing to do with an increase in the radius of the universe.

How can you say that 50% of positive integers are even if there are infinitely many positive integers? You would need some sort of magic!

Infinitude doesn't negate the existence of ratios or probability; I can't imagine why you think it would. There are infinitely many natural numbers and infinitely many primes, but we can still calculate the probability that a randomly selected number less than n is prime (even taking the case where n goes to infinity), and that probability is finite (or do you dismiss complex analysis as well?)

Honestly, have you ever even encountered a normal distribution? We do probability over infinite sample spaces all the time. It's trivial. You would be aware of this if you had even the slightest knowledge of elementary mathematics.

Why would he? It's irrelevant to the discussion.

Last edited: Jun 21, 2012
21. Jun 21, 2012

### robertjford80

Number nine,

So do you concede that the chart states the unobservable universe is 46 bly across?

You're just asserting that the premise is wrong. You don't have any reasons for why the universe is infinite. You also have yet to comment on the Lisa Randall quote which states that the size of the universe doubled.

What determines the size of the universe other than the Hubble constant and its age? Both of those numbers are finite.

You tell me. You're the one that is asserting that the amount of ordinary matter is 4% in an infinite universe.

Less than n is not infinite. Sure, we can calculate the probability of primes less than n but not more than n.

You have a flawed analogy. The ratio of primes to non primes is not analogous to determining the density of an infinite space. To determine the density of space you need to know how large the space is. You can't determine how large infinity is.

If this is true, then what are they? You can't tell because you're just guessing that the odds of a prime below 9 digits is more or less similar to the odds of a prime above 9 digits. In order for the density of the universe to be calculated it has to be in principle calculable if not calculable practically. You can't get an exact number with infinity. Infinity divided by infinity equals infinity.

Give me an example.

You're just asserting that it's irrelevant. If the size of the universe is not determined by the hubble parameter and its age, then what determines it.

22. Jun 21, 2012

### nicksauce

Look it's irrelevant what the chart says, or what you think it says. I know 46 Glyr is the radius of the observable universe because it's a simple calculation I've done many times before.

$$ds^2 = -c^2dt^2 + a^2(t)\left(dr^2 + r^2d\Omega^2\right)$$

The maximum distance (and hence the spatial boundary of the observable universe) will be represented by radially travelling photons, so choose ds^2=0, and d\Omega=0, and you get

$$dr = c\frac{dt}{a(t)}$$

$$R = c\int\frac{dt}{a(t)}$$

$$R = c\int\frac{da}{\dot{a}(t)a(t)}$$

Then use the Friedmann equation

$$\left(\frac{\dot{a}}{a}\right)^2=H_0^2\left(\Omega_Ma^{-3}+\Omega_{\Lambda}\right)$$

to replace $\dot{a}$ and you get

$$R = \frac{c}{H_0}\int_0^1\frac{da}{a^2\sqrt{\Omega_Ma^{-3}+\Omega_{\Lambda}}}$$

Choose H_0 = 72km/s/Mpc, $\Omega_M=0.28$, $\Omega_{\Lambda}=0.72$. Put into Wolfram alpha http://www.wolframalpha.com/input/?...rom+0+to+1+of+(1+/+(x^2*sqrt(0.28x^-3+0.72))) and you get the 46 billion light years.

23. Jun 21, 2012

### Number Nine

No. As is explained above, that number refers to the observable universe.

The premise is wrong because your definition of "expansion" is incorrect; this has been clearly explained to you already. Research metric expansion.

Yes, so what? Odd numbers constitute 50% of the integers. The fact that there are an infinite number of integers is irrelevant.

As I already very clearly explained, we can easily take the limiting case as n goes to infinity. Any introductory treatment of the prime number theorem will explain this to you.

I'm going to go right ahead and accuse you of being deliberately ignorant, here. Why? Because right in my previous post I gave you the example of the normal distribution, whose domain is the reals. You've really never encountered basic probability theory before, have you?

Last edited: Jun 21, 2012
24. Jun 21, 2012

### IsometricPion

The universe as we know it was to hot and dense until ~300,000 years after the big bang for light to propagate through it freely. Therefore, the light that has taken the longest time to reach us was emitted at that time, it is the cosmic microwave background (CMB). The density of matter in the universe is approximately constant everywhere we know of on scales larger than ~300 Million light-years. General relativity (GR) predicts that the universe will either expand forever or eventually contract back to a singularity, depending on the average density of mass-energy (and the nature of dark energy). Only if the average mass-energy was enough to make the universe contract would GR predict that the universe is finite (at least in the simplest possible geometries ref. Wikipedia- Shape of the Universe).

The 46 billion light-years that the image refers to is the co-moving distance to the CMB (Wikipedia- Distance measures (cosmology)). This is the distance that the matter emitting the CMB would be from us if the universe's expansion were frozen today and measured (though by today it would have formed galaxies and such). The green line presumably indicates the path that light we see as the CMB took to reach us. The light from any object we observe today followed the "same" green path (starting at a point closer to the present of course). So, where the blue line that ends up at 10 billion light-years crosses the green line indicates the co-moving distance from us (looks like about 6 billion light-years) at the time light we see today left objects which today are at a co-moving distance of 10 billion light-years (i.e., roughly 7.5 billion years ago). When the light we see today as the CMB was emitted the matter emitting it was at a co-moving distance of about 42 million light-years. This seems to be the sort of information the posted chart conveys.

Any figure for the number of particles in the universe is an extrapolation from the known density and properties of matter to large scales (which seems to be valid on the largest scales). For a universe that is approximately flat on large scales the total mass-energy density must be about 9.7x10-27 kg/m3 (Wikipedia- Friedmann equations) if 4% of that density is ordinary matter then that part would have an average density of about 3.9x10-28 kg/m3. Most of this mass density would be in the form of protons and neutrons for a number density of about 0.23 m-3. 46 billion light-years is about 4.4x1026 m, so the co-moving volume today of the part of universe we can see is about 3.5x1080 m3. This yields about 8.1x1079 particles. Since most of the universe is made of hydrogen and helium there are a similar number of electrons to yield a total of about 1.7x1080 particles.

So, it would appear that 10^80 is a reasonable estimate for the number of particles (of ordinary everyday matter) in the part of the universe we have seen via light. It approximately corresponds to the number of particles at any given time between the line labeled "Us" and the blue line that ends at 46 billion light-years.

Note that anything that is a density in the above calculations is a local (or intrinsic) quantity and is well-defined no matter how big the rest of the universe is. At present there is no way to know how big the part of the universe we can't see is; there may not be much of it we cannot see, we might only be able to see a tiny fraction of the universe, or it could be infinite. Wikipedia- Observable universe describes everything I have said and more.

Last edited: Jun 21, 2012
25. Jun 21, 2012

### robertjford80

This is lifted from the wiki article that isometricpion references who was rather kind and polite about the whole thing, I cannot say the same thing for you, number nine:

This website puts the size of the whole universe at 93 billion light years
http://scaleofuniverse.com/

I'm aware that many mainstream physicists believe the size of the whole universe is infinite. For instance here's Stephen Hawking:

I have not yet heard any decent reason why anyone would think it is infinite and when I say infinite I mean that there is no limit on how many particles, planets or stars it has. If you're talking about a different kind of infinity that you're committing the fallacy of equivocation.

I'm not sure there any point in debating with you, number nine. You use insulting language such as:

When you're opponent starts to use language like that he's doing it to cover up the weakness of his position.

You also fail to answer my points. I can't debate with someone who will not answer the questions I put to him. I asked you to prove how metric expansion implies that space is infinite and you failed to do that. There is nothing in metric expansion that makes space infinite. This is lifted from the wiki article on metric expansion:

D= RT still applies you just have to calculate rate differently, that is you have to factor in how much space expands while you're crossing over it. The product of two finite numbers is still finite.

I've also asked you three times for an explanation of this quote:
It's been my experience that when they refuse to answer a point the first time they rarely answer it when you ask them again.

I asked you to go ahead and calculate the probability of a number being prime and you didn't but said that someone else has done it.

Odd numbers are abstract objects they are true by definition. You can't compare abstract objects with concrete objects. There are 50% odd numbers by definition. You can't say:

"I can calculate the odds of an abstract entity, therefore I can calculate the odds of an empirical entity."

Odd numbers are in no way comparable to concrete, ordinary matter. The ratio of a finite patch of space to infinite space is practically zero. Your sample size of the what you can observe compared to what you think exists is next to nothing. It would be ludicrous to extrapolate from an extremely tiny sample to the whole infinite universe if there is an infinite universe.

I'm talking about an example in the real world not an example from the abstract world of mathematics that doesn't exist. Go ahead and tell me the probability of finding a certain type of matter in a universe of infinite size and I'm not talking about the matter restricted to our light cone. I want you to calculate the density of matter in an infinite universe.