Re: Expansion of space, total energy source.

A bunch of interesting and deep questions - to which we don't really
know the answers!  Fortunately we can at least say something interesting
about these issues...

1a)  Energy source for the Big Bang?
     Do we have to worry about this question? - maybe the universe
   was started off with a big lot of energy and it didn't "come"
   from anywhere.  On the other hand, it is true that the universe
   seems to be expanding at something close to its "escape velocity" -
   in other words, it may just have enough energy to keep expanding
   for ever.  If this were exactly true (technically, we'd say that
   the matter density was critical or Omega=1) then as the age of
   the universe got bigger, the kinetic energy AND the potential 
   energy would reduce, eventually tending to zero.  This would
   mean that the kinetic energy, in some sense, always balances 
   the potential energy, so the total is zero and we certainly 
   don't have to worry about where zero energy comes from!
   (Actually, the latest observations suggest this isn't the
   case)

1b)  Visualising a "time" before time, space and matter existed?
     The basic picture we have of the Big Bang (based on Einstein's
   theory of General Relativity) has the universe starting at a particular
   point and nothing, not even time itself, "before" that.  Obviously 
   this is very difficult, perhaps impossible, for human's to imagine.
   However, there are good reasons for believing that General
   Relativity can't carry on working right back to the first 
   fraction of a second (less than 10 to the power -43 of a
   second to be more precise), when the density and temperature
   were very extreme.  The hope is that we will eventually find
   a better theory (it already has a name, quantum gravity, in 
   anticipation!) which will allow us to probe beyond that point
   and may well not have the neat cut-off in time which General
   Relativity requires.  Unfortunately, the bad news is that our
   present efforts to discover such an improved theory suggest it
   will be even more weierd and hard to visualise than the theory
   it will replace!

2a)  Does empty space expand?
     That's certainly one way of looking at the expansion of
   the universe, that in a sense the matter stays put while the
   space expands between the particles of matter.

2b)  How can something that's infinite become larger?
     Ah yes, this is a tricky old question which people wondered 
   about long before it had any relevance to the Big Bang theory!
   The modern mathematical practice (developed originally by
   Cantor in the last century) is to regard to infinite sets as
   "equivalent" if they can be paired off one by one.  For
   example (I think Galileo, or maybe Kepler, once pointed this
   out) consider the positive counting numbers (the "Natural" numbers)
   and their squares:
     1   2   3   4   5  ...and so on to infinity
     1   4   9   16  25 ...etc  
   Now Cantor would say these infinite sets of numbers are 
   equivalent since for every one on the top line there is a 
   partner on the bottom line.  But notice that in fact, all the
   numbers on the bottom line are included in the top line, plus
   a whole lot more!  So despite all those "extra" numbers, both
   sets have the same infinity-worth of members.

   Similar arguments can be made for the decimal ("Real") numbers
   and can also show that they are a bigger infinity (greater
   "cardinality") than the natural numbers.

   What does this have to do with the universe?  Simply it says
   that mathematically (and GR is a mathematical theory) it's
   possible for an infinite space to expand without producing a
   bigger infinity!

2c)  Can time end?
     The same (GR) equations which predict time had a begining also
   predict an end in some circumstances.  This only happens if
   the matter density is greater than critical, so that the universe
   is not expanding fast enough to overcome the attraction of gravity.
   In which case, at some time in the future it would cease expanding
   and then begin to contract, ending in a "Big Crunch".  Again, current
   observations suggest this is not the case for our universe.

   However, even if the universe goes on for ever, we think there
   are many places within the universe where time may come to an
   end, and these are in black-holes which have "singularities" at
   their centres!