Hi Jesse,
On 7/22/2011 8:03 PM, Jesse Mazer wrote:
On Fri, Jul 22, 2011 at 4:54 PM, Stephen P. King
<stephe...@charter.net <mailto:stephe...@charter.net>> wrote:
Hi Jason,
None of those papers address the concern of narratability that
I am considering. In fact they all assume narratability. I am
pointing out that thinking of time as a dimension has a big
problem! It only works if all the events in time are
pre-specifiable. This also involves strong determinism which is
ruled out by QM. See
http://plato.stanford.edu/entries/determinism-causal/#StaDetPhyThe
for a general overview
But the link notes that strong determinism is *not* ruled out by QM:
"So goes the story; but like much popular wisdom, it is partly
mistaken and/or misleading. Ironically, quantum mechanics is one of
the best prospects for a genuinely deterministic theory in modern
times! Even more than in the case of GTR and the hole argument,
everything hinges on what interpretational and philosophical decisions
one adopts. The fundamental law at the heart of non-relativistic QM is
the Schrödinger equation. The evolution of a wavefunction describing a
physical system under this equation is normally taken to be perfectly
deterministic.[7] If one adopts an interpretation of QM according to
which that's it—i.e., nothing ever interrupts Schrödinger evolution,
and the wavefunctions governed by the equation tell the complete
physical story—then quantum mechanics is a perfectly deterministic
theory. There are several interpretations that physicists and
philosophers have given of QM which go this way. "
The many-worlds interpretation, which many on this list are presumably
sympathetic to, is an example of a deterministic interpretation of QM.
In fact many-worlds advocates often argue that not only is it
deterministic, but it's also a purely local interpretation, which
doesn't violate Bell's theorem because the theorem makes the
assumption that each measurement yields a single unique result,
something that wouldn't be true in the many-worlds interpretation. For
more on how MWI can be local, see these papers:
http://arxiv.org/abs/quant-ph/0103079
http://arxiv.org/abs/quant-ph/0204024
Umm, did you notice the words "non-relativistic" in the paragraph? Most
QM formalisms treat time as if it where Newtonian and thus carry over
the idea of time as an absolute well order of events. This is equivalent
to the notion of a global synchronization that I am arguing against.
Even MWI does not help because in it one is taking constructions that
exist in Hilbert space and assuming that they are ordered a priori. This
does not follow logically because one needs to chose a basis within
which an ordering follows and absent this choice there is no ordering.
The idea that time is a dimension assumes that the events
making up the points of the dimension are not only isomorphic to
the positive Reals but also somehow can freely borrow the well
order of the reals.
Not sure what you mean by this, events at a spacelike separation
aren't "well-ordered" in time, are they? Only if one event is in the
light cone of the other (a timelike or lightlike separation) will all
frames agree on the time-ordering, that's just a consequence of the
relativity of simultaneity.
Sure, let us focus on the space-like surfaces. Does a unique order of
them exist? No. This is the foliation problem that I mentioned below.
Also, that situation where "all frames agree on the time-order" assumes
that the ordering already exists. I am asking about how it got there in
the first place.
at
http://physics.stackexchange.com/questions/2710/what-does-foliation-mean-in-the-context-of-a-foliation-of-spacetime
Hiatus wrote:
"If you want to solve equations of motion to describe the time evolution
of a system, either classically or quantum mechanically, you need to
impose initial condition at one point in time, and then under some
conditions the entire evolution of the system (forward and backwards) is
determined. This is the type of things physicists do all the time.
Now, general relativity is a theory of spacetime, so it is not clear
that any spacetime manifold will have well-defined evolution of the sort
I described, where the conditions at a spatial slice at one point in
time (called Cauchy surface) determines the system everywhere. For that
to be true there has to be a way to separate what is the time direction
at every point in spacetime.
If this can be done you express the spacetime as a series of spatial
slices which evolves in time (called foliation of spacetime), and you
have now a problem which amounts to describing how those spatial slices
evolve, which is a traditional initial value problem which physicists
know and love. Manifolds for which this can be done are called globally
hyperbolic, and those are the ones which are easier to discuss, though
there are well-known examples of spacetimes which are not globally
hyperbolic.
Once you find one way to do it, one "foliation" of spacetime, usually
there are many other ways, but the difficulty is usually in finding one
way that works everywhere (it is always possible to do that separation
only in some region of spacetime, but that exercise is not useful since
you want to predict what happens everywhere, at any point in time)."
The block universe idea assumes a unique and global ordering of
events, the actual math of SR and GR do not!
Why do you think the block universe idea assumes a unique ordering? It
doesn't, not for pairs of events with a spacelike separation. For such
events, the question of which event occurs at a later time depends
entirely on what coordinate system you use, with no coordinate system
being preferred over any other. Similarly, on a 2D plane the question
of which of two points has a greater x-coordinate depends entirely on
how you orient your x and y coordinate axes, even if you restrict
yourself to Cartesian coordinate systems. And the whole idea of block
time is that time is treated as a dimension analogous to space, so
it's not surprising that there could be situations where different
coordinate systems disagree about which of two events has a greater
t-coordinate, with no coordinate system's answer being more "correct"
than any other's.
So the block universe does or does not assume a "time dimension"? If it
does then that "time dimension" is equivalent to a unique ordering of
events such that events are labeled with values in the positive Real
numbers, other wise known as the Real line. The point here is that for
this to obtain then all of the events must be such that their position
of that Real line is defined from the beginning. How, exactly, was this
ordering determined at the 'beginning"? This question as not asking
about what coordinate systems have as their particular t, x,y,z values;
it is about the construction of the block universe itself. Consider the
famous words of Laplace:
"We may regard the present state of the universe as the effect of its
past and the cause of its future. An intellect which at a certain moment
would know all forces that set nature in motion, and all positions of
all items of which nature is composed, if this intellect were also vast
enough to submit these data to analysis, it would embrace in a single
formula the movements of the greatest bodies of the universe and those
of the tiniest atom; for such an intellect nothing would be uncertain
and the future just like the past would be present before its eyes."
—Pierre Simon Laplace, /A Philosophical Essay on Probabilities/
This is the block universe idea. Given that we now known, per QM,
that the positions, momenta and other observables cannot be
simultaneously given for 'all items' in the universe, how can we still
think that the universe just exists as a fixed and eternal 3,1
dimensional 'block'?
My claim is that the idea that time is a quantity like space
only works in the conceptual sense where we are assuming that all
events are chained together into continuous world lines.
Not really, just as you can have a collection of points on a 2D plane
without continuous lines joining them, so you could potentially have a
collection of events in spacetime that are causally related but don't
have a continuous series of similar events between them. Sort of like
if you took vertices on a Feynman diagram to be events, and understood
the lines joining them to just express causal relationships, not
worldlines.
No, that requires that a basis be chosen for that particular Feynmann
diagram. At best we can map between bases and causal structures that
obtain from those but this does not generate a 3,1 dimensional universe
like structure at all.
It is impossible to define a unique Cauchy hyper-surface of
initial (final) data that completely determines all of the world
lines in the space-time block in a way that is consistent with QM.
What specific source are you getting that claim from? I checked the
first link you posted after it:
I was trying to not write a book.... What is a Cauchy surface?
http://en.wikipedia.org/wiki/Cauchy_surface
"a plane in space-time <http://en.wikipedia.org/wiki/Space-time> which
is like an /instant/ of time; its significance is that giving the
initial conditions <http://en.wikipedia.org/wiki/Initial_conditions> on
this plane determines the future (and the past) uniquely.
More precisely, a Cauchy surface
<http://en.wikipedia.org/wiki/Hypersurface> is any subset of space-time
which is intersected by every non-spacelike
<http://en.wikipedia.org/wiki/Spacelike>, inextensible curve
<http://en.wikipedia.org/wiki/Curve>, i.e. any causal curve
<http://en.wikipedia.org/wiki/Causal_curve>, exactly once."
Since we know from QM that the values of the initial conditions are
subject to the Uncertainty principle, this results in the impossibility
of defining the set of initial (or final) conditions. The determinism
that we find in QM is a determinism of the unitary evolution of the wave
function. It is not an entity that exist 'in' spacetime therefore one
cannot borrow its deterministic property for spacetime.
http://www.scientificamerican.com/article.cfm?id=was-einstein-wrong-about-relativity
...but it didn't say anything like that. I'd rather not read through
all your links to find the basis for this particular statement, so can
you tell me exactly where I should look?
When we add to this difficulty the fact that QM does not allow
us to consider all observables as simultaneously definable,
because of non-commutativity and non-distributivity of
observables; the idea that events are representable as
pre-specifiable partly ordered sets from the Big Bang
singularity's event horizon into the far distant future falls flat
on its face.
Not sure what you mean by "pre-specifiable", again can you tell me
which specific link I should look at to understand what you're saying
here? Anyway, the fact that some observables don't commute isn't
really a problem for local determinism in the many-worlds
interpretation. "Observables" are understood to correspond to a
specific set of basis vectors (eigenvectors of the operator for that
observable) which can be used to express any quantum state vector as a
weighted sum of eigenvectors (the weights are complex amplitudes, and
you square these amplitudes to get probabilities of each eigenstate in
to the "collapse the wavefunction" version of measurement). The fact
that some observables aren't simultaneously definable basically just
means that an eigenvector of one observable can't simultaneously be an
eigenvector of the other, but if you take the wavefunction as
fundamental as in the many-worlds interpretation, this shouldn't be a
big deal because there is no longer the concept that the quantum state
must "collapse" onto an eigenstate with each measurement. Instead the
quantum state vector just evolves deterministically forever, and as
the second of the two papers I posted above says, you can break the
quantum state down into a set of local field operators at each point
in space, whose time-evolution is determined by local differential
equations (which I take to mean that nothing outside a point's past
light cone affects the value of the field operator at that point).
Jesse
Wave functions do not exist 'in' spacetime. Additionally, the
diffeomorphism invariance (also known as general covariance) of GR does
not allow any particular meaning to "a point in space", so the idea that
'a time-evolution is determined by local differential equations..."
fails because the mapping that one has to use to identify a particular
set of field operators with each point of spacetime is not invariant
with respect to diffeomorphisms.
"That this requirement of general covariance, which takes away from
space and time the last remnant of physical objectivity, is a natural
one, ..."*^
<http://en.wikipedia.org/wiki/Background_independence#cite_ref-2>*
Einstein's Equivalence Principle, Einstein's physical space and
Observational Validity of the Schwarzschild Solution
<http://www.hongshe.org/hongshe/1954_files/cylopoem.htm>^"
See:
http://en.wikipedia.org/wiki/Background_independence#Diffeomorphism_invariance_and_background_independence
for more.
So as far as I can tell, the block universe is an idea left over
from classical physics that simply does not work. Why it still is
considered as viable is a mystery to me.
Onward!
Stephen
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