Expanding Universe question - need help for teaching

[fsgregs]

Hi folks:

I am about to begin teaching Astronomy to over 150 high school seniors. Some of them are very bright (fortunately) and will be anxious to catch their teacher in a faux pax. I have a question regarding the expanding universe I really need an answer on.

As we've been told, the universe and the space it occupies is continuing to expand and inflate. Although the rate is slower than it was during the Big Bang, it is nevertheless expanding into .....

Galaxies are getting farther apart and in fact, recent evidence suggest the rate of expansion is accelerating, forcing normal matter further and further apart.

Here is the question. Since all of space is expanding, that includes the "space" not only between the galaxies, but the space enveloping the atoms that make up our bodies. In short, our bodies are inflating, getting spacially bigger as the very space of the universe within us expands and spreads apart. Naturally, since everything around us is expanding/inflating at the same rate, we don't notice anything at all. Everything appears to occupy the same spacial dimensions. However, if we are inflating .... at what speed are we doing so? Is our local/immediate universe swelling (so to speak) by millions of ???? per hour? Are we blowing up like a Pilsbury doughboy at 50% the speed of light ... becoming gargantuan in relation to our relative size the day before??? Exactly what can I say to my students to give them a visual description of exactly how their personal space is expanding??

Any help you can give me would be greatly appreciated.

Thanks

Frank G

[don]

Are we blowing up like a Pilsbury doughboy at 50% the speed of light ... becoming gargantuan in relation to our relative size the day before??? Exactly what can I say to my students to give them a visual description of exactly how their personal space is expanding??

Frank, you really have a way with words. Your students must love you!

Your description made me think of the Ghost Busters movie that had the giant marshmellow guy in it. What an image!

I'm sure someone here will give you a proper answer. Until then...

According to (http://curious.astro.cornell.edu/question.php?number=346): "The satellite mission WMAP has produced in the past couple of months some new and exciting results! Among other things, it has enabled astronomers to calculate the value of the Hubble constant. They find a value of 71 km/s/Mpc, within 5% of error." Earlier in the answer, they wrote, "(which means that for each Megaparsec (Mpc), galaxies appear to be receiding at 71 km/s, one Mpc being equivalent to 3.2 million light years)."

-Don G.

[Evil Dr Ganymede]

Isn't it that the further things are away from us, the faster the apparent expansion is? So we're not 'expanding' ourselves, it's just that things very far away are receding from us more quickly?

[granthutchison]

Frank:
The current expansion rate translates to a linear increase in dimensions of about 0.000000008% per year.
Fridger will no doubt correct me if I'm wrong, but I'd be surprised if our atoms are getting any bigger: the forces that hold atoms together are very strong, and any change in size would require an alteration in some fundamental constant like Planck's constant. That in turn would mean that atoms behaved differently in the past, and so we'd be able to detect that difference in distant galaxies when we looked at them today - but there's no evidence of a systematic variation in fundamental constants with the age of the universe.
So the expansion of space must effectively slide "past" the existing atomic and molecular structures, and only becomes evident on huge scales, at which the cohesiveness of the universe is very weak (because gravity is very weak).

Grant

Oops. Missed a zero on my first typing.

[Guest]

Oh. And another more obvious reason that we can't be expanding at the same rate as the Unverse: if that were so, we would have no perception that the galaxies were moving apart, because our idea of a megaparsec would be getting bigger at exactly the same rate as the galaxies were moving apart, and the galaxies themselves would be getting bigger to scale with the increasing distance. Our impression would be of a static Universe.

Grant

[julesstoop]

Only if the speed of light would increase similarly as well.

[granthutchison]

Only if the speed of light would increase similarly as well.

I should have made that clear - thanks. But the speed of light is known to at least 10 digits, so if wasn't scaling along with the Universe in Frank's "incredible swelling boy" scenario , we would long since have detected a systematic variation in lightspeed locally.

Grant

[fsgregs]

OK, I can accept what appears to be a logical assumption; namely that we can't be expanding much at all or our atoms would have long ago spread out beyond the ability of the strong nuclear force to hold our quarks together in the nucleus (as protons and neutrons) and we, the earth and most normal matter would have ceased to be cohesive. Plank's Constant does appear to be stable.

That being said, Hubble's Constant, which Astrophysicists all take as reasonable and which Don quoted, suggests that at the farther reaches of the observable universe, galaxies are receding from us (due to the inflation of space, not their own speed within normal space), at something like 50% the speed of light. However, Einstein's Special Relativity view points out that everything is relative. If you were in one of those distant galaxies, it would be us (the Milky Way) that appeared to be expanding/inflating at 1/2 C.

Thus, how can space expand at such an incredible pace, yet the microspace between our atoms not be expanding virtually at all? Does space somehow "know" if a fundamental particle is present to slow down its expansion?


Frank

[granthutchison]

Thus, how can space expand at such an incredible pace, yet the microspace between our atoms not be expanding virtually at all?

Particles aren't nailed down to space and obliged to move with it - otherwise we would all be stuck like flies in amber. Everything is free to move under the influence of whatever force it's subjected to. So you can imagine two objects a couple of metres apart, tethered by a bit of elastic, floating in empty space. After a year, the intervening space has expanded by a few nanometres. Is the elastic able to counteract this expansion? Sure - the objects simply acquire a velocity towards each other of a nanometre or so per year through the expanding space, as a result of the increased tension created in the elastic. So, as I say, the expanding space slips past the objects embedded in it, because they are tethered to each other by various forces. (The thermal battering your component molecules are withstanding at present without stretching out of shape makes the tiny, slow drift of the expansion of space trivial by comparison.)
Only on the huge scale of separate galactic clusters can the spatial expansion overcome the forces of mutual attraction, because gravity is an exceedingly weak force at those distances.

Grant

[granthutchison]

Note added after rereading your text:

If you were in one of those distant galaxies, it would be us (the Milky Way) that appeared to be expanding/inflating at 1/2 C.

The Milky Way wouldn't be "expanding/inflating at 1/2C" it would merely be receding at 1/2c - and that would be because the tiny proportional expansion in the huge distance between ourselves and the distant galaxy adds up to a very large displacement per year. But anywhere in the Universe the expansion is tiny when measured over short distances - think what "71km/s per megaparsec" means when scaled down to a velocity measured between two objects a few metres (or nanometres!) apart.

Grant

[fsgregs]

Grant, THAT is what I needed. I understand my confusion between recessional velocity and expansional velocity. Now if I can only work through all those zeros to work down to subatomic scales vs expansion rates ...... to come up with an expansion value at the size of an atom.

Thanks for your insight.

Frank

[don]

Howdy Frank,

Once you have cancelled out all those zeros on either side of the equation, would you mind posting your results for the rest of us? Enquiring minds want to know.

As a side note, here is the Stay Puft Marshmallow Man *before* the universe began expanding (he's only 300 microns in size).

[billybob884]

Your description made me think of the Ghost Busters movie that had the giant marshmellow guy in it. What an image!

The stay-puff marshmellow man!

[fsgregs]

Sigh .... OK ... here goes.

If the universe is expanding at a rate of 71 km/sec over a distance of 1 million parsecs, how much is it expanding within our bodies over a microscopic distance of say, 1 micron (which is a distance a high school senior can picture with some coaxing (just barely) )?

1 parsec = 3.26 light years
1 megaparsec = 3.26 million LY
1 light year = 9.460 x e12 km.
Hubble constant = ~ 71 km/sec
1 km = 1 e9 microns

therefore

(3.26 e6) * (9.460 e12) * (1 e9) = 3.084 e28 microns of distance in Hubble's constant units.

or saying it another way, the universe expands at the rate of 71 km/sec, over a distance of 3.084 e28 microns.

What is the rate (speed) of expansion over a 1 micron distance?

71 km = 71 e9 microns, so

71 e9/3.084 e28 = 2.30 e-18 microns per second, which is

0.000000000000000023 microns/sec. This is the speed at which we are expanding internally over a distance of one micron (approximately), via the expansion of the universe.

So, if this is the rate of expansion, how many years would it take for 1 micron of space within us to move/expand 1 micron away from its neighboring space?

Setting up a ratio, 2.3 e-18 / 1 sec = 1 micron / x (in years)
Solving for x yields: 4.34 e 17 secs, or 7.9 billion years.

If my calculations are correct, it will take two adjoining 1 micron spaces in our bodies 7.9 billion years to expand one micron in distance through the expansion of the universe. Good grief! No wonder we don't notice anything

The odds that I got this right the first time around are small. What do you think? Is it correct?

Frank

[t00fri]

Hi all,

Frank's question about whether the expansion of the universe has
consequences also within the microcosmos is certainly a
good one. It tests some basic understanding of what's going on and thus
it might even be a suitable question for advanced student examinations;).

Let me start off by reminding you about the range of the fundamental
forces that we know and which determine the dynamics in the
microcosmos:

1) strong interactions: ("Quantumchromodynamics (QCD)").
----------------------------------------------------------

They involve the force that binds quarks in protons, neutrons, pions etc.
The range of QCD is about the size of the proton or 10^{-13}cm = 1
fermi! Beyond 1 fermi the strong force is not felt anymore!

2) electromagnetic interactions ("Quantumelectrodynamics (QED)").
----------------------------------------------------------------
They act only on electrically charged matter, hence since matter is on
average neutral at distances beyond the size of atoms, we do not feel
electromagtnetism either at larger distance (on average).

3) weak interactions ("Quantumflavordynamics (QFD)").
------------------------------------------------------
Even much shorter range, of the order 1/M_W where m_W is the high mass
of the weak gauge boson ~ 80 GeV!

Now, let us turn to the fourth force,

gravity
--------

This is the only interaction that despite its weakness, has truely
infinite range, and hence acts even on very large distances!!


Standard BigBang (SBB) (inflationary) cosmology is the theory about
the large scale behaviour of the Universe, not at all about
what happens in the microcosmos where the other three forces would
have to be switched on!! The SBB treats a nearly perfectly
homogenuous and isotropic Universe under the influence of gravity
alone, which gives a good fit to the present
observations provided we average over sufficiently large distances.

The single dynamical quantity describing the broad features of the SBB
is the "scale factor" a(t), which obeys the famous "Friedman equation"

(d/dt a(t)/a(t))^2 =8 Pi/3 rho(a(t)) -k/a^2(t),

in units where M_Planck=hbar=c=1, rho(a) = the energy density and k is the curvature of the universe. The lhs of the equation is nothing but the square of the Hubble parameter at time t!

The Friedman equation is a differential
equation (remember high school?) that can be solved for a(t) once rho(a) is determined through the equation of state.

The solution for the scale factor a(t) as function of t determines the
overall expansion of the Universe.

Now we are ready to answer Frank's question:
---------------------------------------------------------------------
The Friedman equation only contains the effects of gravity at
sufficiently large scales where all other known forces are not acting
anymore according to 1)-3) above! The intrinsic assumptions of
homogeneity and isotropy clearly only hold in the Universe after
averaging over sufficiently large distances.
-----------------------------------------------------------------------

So nobody needs to worry whether the gaps between his/her teeth will become larger with time;-))

Bye Fridger

[fsgregs]

Dear Fridger:

Thanks for the detailed reply. While I don't pretend to understand all of your argument, I thought Hubble's constant, the inflation of the universe and of space itself was a consequence of the Big Bang and not a consequence of gravity, the strong or weak forces or electromagnetism? I realize folks are trying for the unified theory. I also know there appears to be an inverse relationship between gravity and the expansion of space, however, I did not realize that velocity of expansion could be canceled by any of the forces over atomic distances.

Frank

[t00fri]

Dear Fridger:

Thanks for the detailed reply. While I don't pretend to understand all of your argument, I thought Hubble's constant, the inflation of the universe and of space itself was a consequence of the Big Bang and not a consequence of gravity, the strong or weak forces or electromagnetism? I realize folks are trying for the unified theory. I also know there appears to be an inverse relationship between gravity and the expansion of space, however, I did not realize that velocity of expansion could be canceled by any of the forces over atomic distances.

Frank

Hi Frank,

I am afraid you quite misinterpreted what I wrote. I have just pointed out that at large scale the strong, electromagnetic and weak forces are irrelevant since these act only at short distances. Only if you were to answer your question about consequences in the microcosmos you would have to consider them!

For the large scale expansion of the Universe, however,
only gravity matters. The framework is /of course/ Einstein's general relativity, where the geometry of space-time is a dynamical degree of freedom! The Friedman equation specializes the setup to a BigBang initial condition.

The dynamical evolution of the Universe is then given by Friedman's equation, along with the equation of state. Shortly after the BigBang, the Universe is first dominated by relativistic matter ("radiation dominated"), later it is dominated by non-relativistic matter ("matter-dominated").

In the first case one finds rho ~ a^-4, a ~ sqrt(t)
in the latter, rho ~ a^-3 and a ~ t^2/3.

So the scale factor a(t) of the Universe and thus the time evolution of the Hubble parameter is completely given at all later times....

Bye Fridger

Ps: added later: The BigBang initial condition formally corrsponds to vanishing scale factor at "t=0", a(0)=0, which would in fact amount to infinitely big energy density (see above, rho ~ 1/a^4). But clearly, very close to the BigBang, largely unknown quantum phenomena take over, whence one cannot sensibly go to a(0)=0.

Very short times after the Bang, when a(t) is very small, of the order of the inverse energy scale where all forces are believed to unify, then all forces matter as well! Particle physicists are most interested in this stage. You might have heard about the very well known book on cosmology by Nobel prize winner and father of the Standard Model, Steve Weinberg: "The first 3 Minutes", for example.

I am sure you also are aware about the most well known reasons why the above simple SBB based on the Friedman equation actually does not work satisfactorily and correspondingly has led people to require an intermediate stage of "inflationary (exponentially strong) expansion". These reasons run under the names of: Flatness Problem, Horizon Problem , Homogeneity Problem and Monopole Problem. They largely arise from analysing the structure of the solution of Friedman's equation which turns out to require extreme finetuning of the initial conditions to match our present day observations...

Bye Fridger

[granthutchison]

Solving for x yields: 4.34 e 17 secs, or 7.9 billion years.

Frank, there are about 365.2422*24*60*60 = 3.16e7 seconds in a year. So your final figure comes out to 13.7 billion years. It was kind of implicit in my original back-of-the-envelope, one-significant-figure calculation (if I'd been able to type the number of zeros correctly!): the inverse of a 0.000000008% linear increase per year comes to 12.5 billion years, the length of time it would take for any spatial distance to grow by its own length (at least, outside the constraints Fridger gives).
(The reason my answer differs from yours is that I used simple rounded values in my calculation: 3e8m/s for the speed of light, 3e7 for the number of seconds in a year, and so on.)
Of course, in that vast time period the Hubble "constant" will change hugely (the universal expansion will accelerate, in current thinking), so the simple derived figure is inaccurate - you'd be better sticking with a tiny percentage change per year, I think.

Grant