Does an "empty" hard disk drive (i.e. no or minimal data) have more or less
mass than a  "full" hard drive (i.e. full of data). I appreciate the
difference in the two masses may be absurdly small but I do need an answer..
of course this is with all other things being equal.

Data stored on the disk do not change it's mass.

 Bit's are stored by  changing magnetisation of small grains in the
recording medium.
http://www.tvhandbook.com/support/pdf_files/audio/Chapter6_1.pdf

 This is the same process (on microscopic scale) as magnetising a needle by
 rubbing it with a permanent magnet. The process does not adds or removes mass
to or from the object.

  Since you asked to include even the smallest changes in mass, we
need to consider the  energy content of  empty vs full disk. Increase
in energy by amount E will increase it's mass by amount E/ (c * c) - a
very small amount.

The writing of the disk requires energy, but that energy is not stored. 
Magnetisation of the grain is a bistable system
http://www-civ.eng.cam.ac.uk/dsl/Bistable_actuation/main_project_page.html
Writing  a bit is similar  to rolling a stone up the hill, across the top,
from one valley to another. So, energy delivered on the way up is
returned on the way down. So far answer is  still: Enefgy content is
not changed.
However, some of that energy will be dissipated as heat. Immediately
after recording, disk will be  warmer and therefore heavier (not in a
measurable way). But that temperature rise will equilibrate to
enviroment - so that change is not permanent.

Finally, there is an interaction of magnetic moments with each other
and with external magnetic field ( e.g. Earth magnetism).

Each magnetic dipole (a grain seen as small permanent magnet) has energy
which depends on orientation of the dipole relative to external field.
http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/magpot.html

By writing on the disk, the total number if dipoles on one direction,
(let's say) pointing North, changes. However, number depends on the pattern
written, and empty disk has a pattern written on it when disk is formated.

So, this very small change depends on the data, and also on the orientation of
the whole disk as a unit. Becouse of this last fact (dependence on the
orientation of the object) I would summarise answer as follow:

 Writing the data on the hard disk may change (increase or decrease)
total magnetic moment of the unit. That does not changes the mass of
the unit.
  However, orientation of the unit in external magnetic field will effect total
energy of the unit. If we include mass equivalent of that energy in the term
'mass of the unit', that quantity may go up or down as a result of recording or 
erasing (reformating the disk) of the data.


hedgie

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Request for Answer Clarification by osmosis99-ga on 16 Dec 2004 04:46 PST

Hedgie,

This is very comprehensive and clearly illustrated answer - I am
impressed. I have one follow up question with my layman's physics
knowledge. By magnetising a grain on the disk are you changing the
number of electrons on that grain or surrounding matter??

If so I would have thought the mass would change since electrons weigh
1/1850 (or that order) the mass of a neutron/proton and so it would
have an effect.

Thanks in advance,

Matthew

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Clarification of Answer by hedgie-ga on 17 Dec 2004 00:39 PST

Thank you.

  When you are charging an object, with static charge, as described here
http://www.unmuseum.org/exstatic.htm
 the number of electrons is increasing (or decreasing). 
Electron mass is much bigger then changes we accounted for in the answer.
To miss that would  be like counting pennies and missing pounds.

 When you are magnetising an object, number of electrons is unchanged.
 Only their spins flip. 
 What that means? Each electron can be seen as a small permanent magnet.
 More exactly as a very small coil. When electron is spinning, the
current    flows through the coil and coils becomes an electromagnet.
http://hyperphysics.phy-astr.gsu.edu/hbase/spin.html
http://www.ndt-ed.org/EducationResources/CommunityCollege/MagParticle/Physics/Magnetization.htm

Electrons are always spinning -- the tiny magnets are always there.
When material is magnetised, little permanent magnets get aligned 
(all up or all down) which encodes a bit. Number of magnets does not change.

 So, memory on the hard disk works like large number of those
'doctor in IN' or OUT sign. It is a configuration of the same objects
which encodes a bit as '0' or '1';

Hedgie

A very well constructed and illustrated answer pitched at exactly the
right level of granularity. I will definitely be using this service
again - perhaps for something more useful

"warmer and therefore heavier" should I think be lighter by a few
parts per trillion as the heat causes some out-gasing of volitiles
from the disk, and an occasional atom is thrown off the disk while it
is turning at high speed.  Neil

"Immediately after recording, disk will be  warmer and therefore
heavier"  As pointed out previously, this is simply untrue.  "Warmer
therefore heavier" is simply wrong.

Fermions (and gauge bosons) have a property called spin.  That is,
they have an inherent magnetic moment.  Electron magnetic moments have
magnitude of around one Bohr magneton, where a Bohr magneton is the
magnetic moment magnitude associated with angular momentum h.  You can
read more about this by looking up the Stern-Gerlach experiment.

Electrons have spin of +/- 1/2.  Effectively, one is "on" and one is
"off."  When data is written to the disk, electron spin is flipped.

Actually now that I think about it, the mass will increase slightly. 
And by slightly, I mean so small as to be immeasurable.