If I have a particular CD, say "The Wall" by Pink Floyd, and my friend
has also bought a copy, is there a way to uniquely identify each
physical disc, or proof of ownership?

Not that I am aware of

Write your name on yours with a Sharpie.

I also don't think there's anything about the CD or DVD itself that
would distinguish otherwise identical units. (Obviously, there could
always be some external identifier--like a receipt, or a name tag, or
whatever else.)

But it may be worth realizing that as RFID tags become more common,
they may be able to more uniquely identify individual items. (My
understanding, though, is that RFID tags are not yet in common use on
individual items, but are being used to help track cartons and
shipping containers.)  But I could be wrong...

Thank you for your comments everyone.  I appreciate the time and
effort.  What I am trying to get a better understanding of is the
legalities of CD music ownership.  If i buy a CD, I can legally rip
the music to MP3 for my own use, correct?  This is based upon the
premiss that I have purchased the disc to begin with and am making a
copy for backup or use on my portable MP3 player, comupter, etc... 
This is whether i paid $15 for that CD in a store, or $1 at a garage
sale.

1. Assuming this is all accurate, if i asked a friend to rip the music
to MP3 format for me, and i paid him $2 to do this, is that ok?  I
assume yes because i physically own the disc, and if the nusic
industry lawyers came after me or my friend we would be within our
rights.

2. What if he used his own copy of the disc to do the actual burning? 
Again, I assume that is ok, because we both own the disc.

What if in the above scenarios, i subsequently lost, sold, or
destroyed the physical disc?  Now, an act that was presumed legal at
the time of transaction is seen as illegal because i can't prove i
owned the original disc...  is this true?  I could keep my receipt if
the original CD was bought in a store, but what if it was a gift,
traded for, bought at a garage sale, or just found?  Is prosecution
imminent, or possible in this case?

" lost, sold, or destroyed the  [original] physical disc? "

  lost and sold  are two very different cases:

 Most software licenses allow owner to make a backup copy - and use it when
 original is lost or destroyed. If original is sold, use of the backup copy
 is clearly a piracy.

Case of music CD is more complex:


Digital watermarking (while not widespread) allows copyright owner to
distinquish  the 'apparently identical' copies and trace and proove
copying.

http://en.wikipedia.org/wiki/Digital_Rights_Management

 It is even not clear that 'transfering the content to different format' e.g.
 converting LP into a MP3 to use in a car is legal. It would depend on 
 wording (of implied) licence. In practical situation, that is not prosecuted,
 as long as no selling (including barter) is involved.  If you (or your friend)
 make a significant amount of money, when copying any copyrighted materials,
 you are likely to attract attention of lawyers and courts.

Hello slm2112-ga,

I found that music CDs have serial numbers built into them which can
be read with downloadable software.

Serial Number: "A set of characters that uniquely identifies a single
unit and can be used for traceability and warranty purposes. It does
not normally refer to the use of a single identifier for a batch or
lot composed of multiple units."
SOURCE: http://www.bridgefieldgroup.com/glos8.htm

Software: 
"Designed initially for the digital imaging bureau as a way of
controlling documents issued on cd. This software allows you to
capture the hard-coded serial number that exists on every cd that is
written. When you issue a cd for distribution, you can check at any
time that the cd in circulation is indeed the cd that you initially
distributed, simply by reference to the serial number that is embedded
in every cd. You can even capture the serial numbers of you audio cd
collection." http://www.aptrio.com/Business/Applications/capture-cd-serial-number-2673.html

Also there is code available to get the serial number (differentiated
from the UPC code), for example:
http://www.delphi32.com/info_facts/faq/faq_313.asp

While I am not 100% confident, I am not convinced that cds do not have
unique serial numbers. There is no clear evidence to support my view
though, serial number could be used more as a synonym for product
number (with different cds having the same serial number).

tisme-ga