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
    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:


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.


...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).


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.



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