topics: |  science | history | philosophy | temporal

Asymmetry and irreversibility in time

The nature of time has been a starting point for much human thought about the universe.

Morris opens by pointing out that "What is time?" is a question that may not be as trivial as it first seems to us in a world where we take time as given, as the substratum on which life thrives!!

St. Augustine: What then, is time? If no one asks me, I know what it is. If I wish to explain it to him who asks, I do not know. p.8

In civilization after civilization, we encounter myths of the cyclicity of the universe - all will be destroyed, and re-creeated again. Eternal recurrence : Pythagorieans, Stoics, Neoplatonics, etc. 10

How did we shift from a cyclic to a linear view of time?

ch4 : Calculus and the idea of determinism

Galileo struggled with the problem of the nature of motion for decades.  Of
all the q's facing him, the one he found most difficult was: what is the
nature of instantaneous velocity?

For years, he thought this concept was nothing but mathematical fiction, if
not a contradiction in terms.

Constant speed is easy - ball covers 4m in 2s at constant rate ==> vel = 2 m/s
Avg speed is also ok; ball dropped from 64' reaches ground in 2s
==> avg vel = 32 ft/s

but how fast is the ball moving 0.5 sec after it is dropped?  there can be no
notions of distance moved in an instant - in an ideal "instant", the ball
does not move at all!

Galileo never did come up with an adequate definition of instantaneous
velocity.
To handle the q, he proposed a view in which a body attained a certain
instantaneous velocity, and then continued moving at that same speed [itals
mine].

But he should not be criticized for using such a muddled definition; in fact,
he deserve praise for attempting to deal w quantities that were changing in
time, and arriving at the correct formula, v = at, without using any of the
mathematical tools that were developed later to deal with rates of change.


moves to the theory of linear time, and then to the notion that velocity is a
function of time (Galileo) that introduced time as an element in science.

Newton saw time as forming a steady linear background
to the universe:

    Absolute, true and mathematical time, of itself, and from its own
    nature, flows equably without relation to anything external, and by
    another name is called duration.
	   - Newton, towards start of Principia tr. Andrew Motte (209)

Evolutionary theories broadened the horizons of time considerably, followed
by modern notions like thermodynamics (entropy and irreversibility), and then
relativity altered it in ways that we are still not trying to relate to.

Five arrows of time

This brings us to how time is viewed in different disciplines - the five
arrows are five views of asymmetry in time, four arising in physics:
   1. thermodynamic,
   2. cosmological (expansion of the universe, curvature in space, etc.),
   3. nuclear K-meson arrow (normal nuclear reactions - e.g. beta reactions
        involving antineutrinos - may be reversible - though whether
        reverse betar reactions really occur is not clear.  But surely
        k-meson decay is irreversible.)
   4. the electromagnetic arrow - seems quite complex, depdneing on the
        Wheeler-Feynman theory on time-reversed radiation

And the fifth arrow is from our own minds:

   5. psychological arrow, arising due to our subjective awareness of a "flow"
	of time, particularly the phenomenon of "now" - is it subjective or
	is there some inter-subjectivity or objectivity?  E.g. a baseball
	being hit is seen by everyone in the stadium, who can then agree that
	their "now"s for the baseball hit is shared [is it?].  Given this,
	there may be objective elements in this now as well.  But it is not a
	mathematical instant.  Also the passage of time is subjective -
	sometimes is passes fast, sometimes slow.

[For more on how the brain constructs its model of objective and subjective
time, especially "now", see Robert Pollack's
Missing Moment: How the Unconscious Shapes Modern Science, chapter 3.

Feynman's theory of antimatter

Feynman's theory of antimatter = matter reversing in time.  The clash of the
electron and the positron is nothing but the same electron suddenly reversing
itself in time.  At the microscopic level, there is no notion of entropy,
since entropy is only definable for the aggregate, a collection of
individuated entities.  Also, this reverse time idea may be applied to an
explanation of "charge" in general (p. 124-128)

The probability of a glass falling on the ground and breaking are high.  On
the other hand if the glass has ~ O(10^25) atoms, then the probability of the
fragments of glass that are on the floor joining up back together again and
forming a glass in my hand is ~ O(10^{10^25}) [AM: well, may be a bit less if it
isn't shattered into atomic smithereens, but ok let's go on].  10^{10^25} is so
big that if we had 10^10 the number of books we had to day all the pages
would not be suff to write down the this number. p. 129

If avg density of the universe < 5 x 10^-27 kg/m^3, then curvature is -ve,
universe is infinite in topology.  If density > 5 x 10^-27 kg/m^3, curv is
+ve, like a shere, and all lines are bounded (a ray of light will return
where it started, in many billion light years).  The density cannot be
measured well enough but may be less than this, as low as 10% even.
p. 173-174

Gravity: the presence of massive objects - causes the universe [space-time] to
be curved.  If the curvature is +ve, then both time and space is bounded.

[Karl Popper:] scientific theories can never really be proved to be correct.
The most that one can do is to attempt to falsify them by looking for
experimental disproofs.  The theories in which we have confidence are the
ones that have survived numerous attempts at falsification. 143

Links

Also: check out this review.

Also, the Stanford Encyclopedia of Philosophy has an excellent page on
Thermodynamic Asymmetry in Time.

---bio
Richard Morris has a PhD in theoretical physics, and is tha author of
Dismantling the Universe and Evolution and Human nature.