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Topic: For the readers of WM: Resources on empirical time to consider as
a foundation for mathematics

Replies: 10   Last Post: Mar 21, 2013 11:34 PM

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Posts: 1,968
Registered: 12/4/12
For the readers of WM: Resources on empirical time to consider as
a foundation for mathematics

Posted: Mar 20, 2013 3:26 AM
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In the post,


WM has made the remarks,

"This is deplorable because mathematic
like no other part of "arts"depends on

"Reality is the ultimate arbiter since
mathematics has been abstracted from

And in the post


he grounds the arithmetical succession
of elements relative to an "unfindable"
last line according to an analogy with
the progression of time

Everything that is in the list
1, 2
1, 2, 3
1, 2, 3, ..., n
is in the last line. Alas as soon as you try to fix it, it is no
longer the last line.

Think of the time. What is "now"? As soon as you try to fix it, it is

From the first set of quotes -- unless WM's
philosophical position on physics is non-material
physicalism -- one must interpret the second
quote as referring to "empirical, physical

I have asked WM to clarify his theories on time
so that his readers can judge the felicity of
his remarks. In view of the statements above,
one might expect his answer to reflect on current
trends in physics. So, to assist his readers,
I have prepared these resources.

The excerpted remarks by Craig Callender appeared
in the JUne 2010 issue of Scientific American.
They discuss the implication of reconciling general
relativity with quantum mechanics.

The first possible resolution mentioned in those
remarks is a "timeless" universe based on relational
quantum mechanics. It can be found at

The explanation that the notion of state (the temporal
evolution) has been replaced by relational exchange
of information between observers can be found on
page 11, and reiterated on page 14.

WM's readers are encouraged to visit the site

where they may inform themselves further
on these matters. Not every submission will
entertain a timeless physics. That is only

Papers recommended in the Callender article


"Newton's time may seem old hat
to us now, but a moment's
reflection reveals how astonishing
it is. It's many features --
order, continuity, duration,
simultaneity, flow, and the
arrow -- are logically detachable,
yet they all stick together as
the master clock that Newton
dubbed 'time'. This assembly
of features succeeded so well
that it survived unscathed for
almost two centuries.

"Then came the assaults of the
late 19th and early 20th centuries.
The first was the work of Austrian
physicist Ludwig Boltzmann, who
reasoned that, because Newton's
laws work equally well going
forward or backward in time,
time has no built in arrow.

"Einstein mounted the next assault
by doing away with the idea of
absolute simultaneity. According
to special relativity, what events
are happening at the same time
depends on how fast you are
going [...]

"And things only get worse in
1915 [...]. Gravity distorts
time, so that a second's passage
here may not mean the same as
a second's passage there. Only
in rare cases is it possible to
synchronize clocks and have them
stay synchronized. [...]

"Yet even in relativity, time
retains a distinct and important
function: namely, that of locally
distinguishing between 'timelike'
and 'spacelike' directions.
Timelike events are causally related.
[...] Spacelike events are causally
unrelated. [...]

"In a very precise sense, time
is the direction within spacetime
in which good prediction is
possible. [...]

"Quantum mechanics says that
objects have a much richer repertoire
of behaviors than we can possibly
capture with classical quantities
such as position and velocity.

"The theory's probabilistic
predictions require time to have
certain features. First, time
is that which makes contradictions
possible. [...]

"Second, the temporal order of
quantum measurements makes a
difference. [...]

"Third, a quantum state provides
probabilities for all of space
at an instant of time. [...]

"Canonical quantum gravity emerged
in the 1950's and 1960's, when
physicists rewrote Einstein's
equations for gravity in the same
form as the equations for
electromagnetism, [...] The
equation (dubbed the Wheeler-DeWitt
equation) utterly lacked a time
variable. The symbol t denoting
time simply vanished.

"If you take this result literally,
time does not really exist.

"[...] although general relativity
lacks a global time, it still
manages to describe change. In
essence, it does so by relating
physical systems directly to one
another rather that to some abstract
notion of global time. [...] Time
becomes redundant. Change can be
described without it.

"Getting rid of time has its appeal
but inflicts a good deal of
collateral damage. For one, it
requires quantum mechanics to be
thoroughly rethought.

"[...] Because time is so basic,
banishing it would transform
physicist's worldview.

"Even if the world is essentially
timeless, still it seems as
though it does have time in it.
[...] But canonical quantum gravity
already offers a more developed

"Known as semiclassical time [...]

"[...] The universe may be timeless,
but if you imagine breaking it into
pieces, some of the pieces can serve
as clocks for the others. Time
emerges from timelessness. [...]

"As interesting and startling as
this idea is, it leaves us wanting
more. The universe cannot always
be broken up into pieces that
serve as clocks, and in those
cases, the theory makes no
probabilistic predictions.
Handling those situations will
take a full quantum theory of
gravity and a rethinking of

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