## The puzzle of time
We can refer to moments in time. The physicist speaks of Objectively, t, again I write down a description.
Every fact that I have written down about time _{2}t
is still true about time _{1}t, even though those facts may not
all apply to time _{1}t, they still apply to time
_{2}t. So, if those facts are still true about
_{1}t, then why is _{1}now no longer at time
t?_{1}Let's examine this puzzle a little more carefully. What causes any
particular time to be So consider a maximal catalog of
causes in the objective universe, a world book containing all
objective information about every point in space-time, from the origin of the
universe until its end. This world book will catalog my looking at my
watch at time It is now noon.It will catalog my looking at my watch at time t
and saying _{2}it is now 12:05.Objectively, there is no conundrum at all--clearly I am allowed to make those two statements at those two different times, but, subjectively, something in the universe changed. That is, from the objective standpoint of the world book, the situation
at time ## An analogyConsider the act of reading a book. I might, at some time, look at the
page numbers. I might say I am on page 205, I could call that p. It would be no trick for the author to have
written those margin notes. Those are the objective trappings of my
journey through the pages of the book. Indeed, most books are published
with page numbers. The descriptions associated with the various pages do
not change, depending on whether we are reading them or not. But, as
readers, we do have a subjective perspective that changes._{2}## A mistakeThe mistake that the concept of Subjectively, we know that, given the universe, we have a subjective
perspective on time, we call now. I'll write that as t. Note, that it only begs the question to say that
it evaluates to _{2}t at time _{1}t
and to _{1}t at time _{2}t. To say
that is to insist that the function must be written _{2}Now(U,
t in the first case and as _{1})Now(U,
t in the second case--in other words that the quality
of _{2})now-ness is independent of U. More generally,
however, we can say that we must write Now(U, x
and _{1})Now(U, x where _{2})x and
_{1}x are independent of _{2}U. In either case,
we have shown that the passage of time is independent of the objective
aspects of the universe.To put this in terms of the book analogy, suppose consider the page we
are on as p. To say
that it evaluates to page _{2}p when we are reading
page _{1}p is to insist that the function in that case
must be written _{1}Page(Book, p, in other words to
accept that the page we are on enters independently of the book
itself._{1})## The arrow of timeNote that the above discussion is not that closely related to the
question of the arrow of time. That problem is concerned only with why
physics is asymmetric with respect to time. This approaches a subjective
question about time when the discussion gets to such things as Time proves to be asymmetric with respect to such things as entropy increase and wave function collapse. Intuitively, maybe the irreversible increase in the entropy of statistical ensembles, in fact, arises from the implications of wave function collapse in chaotic systems. ## Time travelGiven that the passage of time is not an objective concept, it is a
little strange that physicists sometimes talk about time travel.
Objectively, what this means is not that the subjective awareness of
(Updated: 2004-03-29) |