Re: [Phys-L] Big Bang

[John Denker <jsd@av8n.com>]

On 03/14/2013 06:38 AM, Anthony Lapinski wrote:
> I'll be teaching cosmology next month in my (high school) astronomy class.
> The book I use discusses inflation and that the volume of the universe
> during the Big Bang was less than the size of a proton! How can this be? I
> realize the universe had a "hot" and "dense" beginning, but isn't there a
> limit to how closely matter (made up of particles) can be packed together?
> Particles take up space, so how could an object -- let alone the entire
> universe --  have essentially "infinite" density (zero volume)?

To answer the specific question that was asked:  The basic answer
is no, there is no limit.  The reason is that the equation of state
says that at super- high temperatures, most of the energy will be
in the form of radiation, not "particles" let alone "objects".  It
is only at a later (i.e. cooler) stage that we see the formation of
particles with nonzero mass.

More generally, even at low temperature, there is no limit to how
much you can squeeze something.  It might require enormous pressure,
but it can always be done.

The so-called "hard sphere" model of a not-quite-ideal gas is just
a model, and not even a very good model.  The Lennard-Jones model
is much better.  The size of an atom can easily be worked out in
terms of the balance, namely the pressure of a degenerate electron
gas versus the Coulomb interaction with the nucleus.  Squeezing
the atom just raises the pressure in a completely routine prosaic
way.  Similarly the size of a neutron star can be understood in terms
of equilibrium, namely the pressure of a degenerate neutron gas versus 
the gravitational interaction.  We are definitely not talking about a
hard sphere;  it's just pressure.
   http://www.av8n.com/physics/degeneracy.htm

On 03/14/2013 10:10 AM, Anthony Lapinski wrote:

> So how do you get a finite amount of mass into essentially zero volume?
> Everything has volume!

It is not true that everything has a /fixed/ volume.  It would be 
better to say that everything obeys the laws of physics.  At the
fundamental level, everything is quite squishy.  The macroscopic
classical notion of solidity and sharp boundaries is only an 
approximation.

========

> Unless I am mistaken, the current thinking is that the universe is finite.

I'm not convinced it's finite ... and even if it were, this would be
conceptually separate from the issue of expansion.

> The book I use discusses inflation and that the volume of the universe
> during the Big Bang was less than the size of a proton! 

Yuck!

As I see it, the smart way to introduce the idea of expansion of the
universe is *not* in terms of size.  Instead, emphasize the following
idea:
  Particles(*) are moving away from each other, moving at a rate 
  proportional to their initial separation.        [1]

When you say it that way, the statement is completely independent of any 
notion of size.  Note that local velocity is an intensive quantity, and
density is a intensive quantity, so there is no way you can the observed
expansion /by itself/ to infer anything about the size.

Here's a movie of how it works, with some discussion:
  http://www.av8n.com/physics/expansion-of-the-universe.htm

Everything that follow is IMHO too much detail for the introductory
discussion;  I mention it here as a cautionary tale, to convince you
that you do not want to drag "size" into the introductory discussion:

  As a *separate* matter, piled on top of the notion of expansion, you 
  might  be able to use additional information, perhaps a specific detailed 
  theory of gravitation, to infer a size-scale; however
    a) This is IMHO definitely not a reasonable pedagogical starting place.
     It is important to understand the basic geometrical meaning of
     expansion before one tries to connect it to other theoretical ideas.
    b) The theories that connect density and expansion to size are quite
     sketchy.  Experts argue endlessly about the details.

  First of all, it is entirely possible to have an open universe with no
  overall size whatsoever, and to still observe expansion.  Law [1] can
  perfectly well apply everywhere in an infinite open universe.  It is 
  an intensive law.

  Secondly, even if you find that the universe is curled up with some
  length-scale R, you cannot be sure that it has intrinsic size R or
  even 4 π R.  It could be curled up like a scroll, such that in-universe
  distances could be enormous compared to the radius of curvature.