** “I have no need of that hypothesis” - LaPlace **

“Materialism”, “certainty”, “uniformity”, “induction”, “determinism”, “scientific law”, “universal causality” are as dead as god — the belief in them is no longer believable.

Nor, is a god hypothesis necessary. Was it only 200 years ago that LaPlace supposedly said this to Napoleon?

The brief rebuttal is

1.There is no such process as “induction” from “the facts” of nature.
2. There are no necessary empirical truths. (No science is certain.)
3. Every empirical statement must be falsifiable in principle.
4. To be part of science, an empirical statement must be testable, hence refutable.
5. “Materialism” is no part of science.
6. Mathematics makes models. Models, however refined, are not reality.

What follows from these now well-known propositions:

1. No part of science presupposes any “uniformity of nature.” (No faith needed!)
2. There are no “laws” in science — no need for a “law giver” or any “source.”
3. If any religion makes an empirical claim; then, it could be false.
4. In order to be considered scientific, empirical claims made by religion must specify conditions to test it — that is, show how it could be falsified.
5. “God” doesn’t do mathematics. Mathematics doesn’t “describe” or “explain” the world.

In practice, what does science have to say about arrogant religionists:

With respect to science vs. western bible-based monotheism, the relationship is strongly asymmetrical in favor of science. Science is the arbiter of which statements about the world, empirical statements, are or are not “known” — that is, are given the always provisional metalinguistic accolade, ‘true.’ (What is the value of truth — Nietzsche’s question is still important.)

True empirical statements are ‘methodologically fit’ according to the relevant testing procedures within science itself. This is the real meaning of ‘the scientific revolution’ — in what sphere is power vested?, who shall decide what is true?, and by what criteria?

Neither ‘ethical fitness’, as in Heraclitus and his Stoic followers, nor ‘theological fitness’, as in Plato and his xian followers, is any longer considered a viable principle for assessing the truth of an empirical statement.

Methodologically, whenever so-called “sacred” writings make claims about the natural world, they are subject to exactly the same forces of potential refutation as any other empirical claim. There is no “executive privilege” for god.

bipolar2
© 2007

http://www.nytimes.com/2007/12/18/science/18law.html?8dpc

Maybe both alternatives — Plato’s eternal stone tablet and Dr. Wheeler’s higgledy-piggledy process — will somehow turn out to be true. The dichotomy between forever and emergent might turn out to be as false eventually as the dichotomy between waves and particles as a description of light. Who knows?

I would like to argue for both alternatives, as two sides of a cosmic convection cycle, where the expanding energy of the quantum world is disconnected and discontinuous, random and microcosmic. But like heat it is always expanding. That it is like the future, invisible, but alway drawing us forward.
While the classic macrocosmic world we live in is reductionistically deterministic and lawful, orderly and mechanistic, but subject to entropy and gravity, it is collapsing and falling away into the past, even though it’s the only reality we can directly observe.
This relationship isn’t just about physics, but all sorts of processes can be understood in terms of the energy rising up, as the structured order slowly, or sometimes rapidly, crumbles. For those looking for guidance, Complexity Theory covers much of this ground, with its dichotomy of top down order and bottom up process/chaos. Those of us out in the larger world can see it in any number of ways. Rising unstructured youth and the crumbling order of age. Dynamic societies replacing prior civilizations. Political movements toppling as the ground moves under them.
Particles are energy that has started to contract and waves just wash over us. Like strings and their vibrations, we are always trying to put these two elements in the same equation and they just don’t fit. Maybe it’s trying to tell us something. Maybe Tao knows more then Moses.

that the transverse-moving mass will accelerate away from a given floor level in a free-falling elevator (since *you* claimed its “acceleration” was “different”, not me!) while the down-falling mass won’t, and yet still not “really” have usefully different accelerations (not in *any* perspective at all?)

Apparently you still haven’t really looked at what I wrote about the analogous situation with geodesics on a sphere. If you ever really think about that, and understand it — draw some pictures, do some calculations, whatever it takes for you to grasp it — you will stop harping on about this non-contradiction. There’s nothing further about this on the web page because I have no reason to remind a general audience that the equivalence principle is true, and is not contradicted by this (or any other) prediction of General Relativity.

No, I don’t have a PhD, just a BSc in Maths, but I taught myself GR from Misner, Thorne and Wheeler. The relativistic elasticity material on my web site is entirely orthodox, and as far as I can check is consistent with a PhD on the subject that I cite, but of course I can make no promise that everything is free of errors.

PS - You show savvy yet call yourself “a science fiction writer” - PhD but just didn’t get into the work? Just curious. And are you fully orthodox? I could almost swear, some of that stuff about accelerating elastic looks somewhat idiosyncratic. tx

I’ve written up my analysis of the planar mass here:

Weak-field GR near the centre of a light planar mass

If you ever succeed in getting anyone else who is competent in GR to consider this matter, it might be more productive to point them to this page than to offer them a paraphrase of my conclusions. I doubt you’ll find anyone else willing to wade through the detailed calculations, but anyone who actually knows GR will get as far as the bold-faced summary in the introduction and tell you that whatever the quantitative details, the qualitative statement here is obvious.

I’ll repeat what I noted earlier: the arxiv paper you found, The general relativistic infinite plane, also finds velocity-dependent accelerations in the static frame tied to the mass. The detailed formulas are different because the detailed space-time geometries are different, but the general phenomenon is, clearly, not absent even in solutions with exact planar symmetry.

Yes, that’s what we have, but no sensible thinker considers the objective results to be merely “an appearance” in any sane sense. Collapse is not “an axiom,” it is what happens.

This is an improper evaluation of the evidence. Again, the appearance of collapse is all that we can observe. This appearance can be described through one of two possible mechanisms:

1. There is actual collapse.
2. There is no collapse, but the underlying behavior causes observers to see collapse.

For many observations, these two are completely indistinguishable. Though one might expect that the underlying behavior might lead to subtle differences that may appear in some experiments (this appears to be the case with quantum decoherence), even without such differences one can determine which of the two hypotheses is more likely to be correct by asking which of the two requires fewer assumptions. The answer is that option two has one fewer axiom, and therefore is to be preferred by default.

If anything deserves to be called “hypothetical” it is the wave, not the collapse which is the “given.” We don’t even know what it means to say that the wave functions “exist” per se, but the collapses are little spots right there on a screen etc. How could “shut up and calculate” folks be brushed off so glibly, regardless of whether you agree with them?

Actually, we do know what it means to say that wave functions exist: it means that in between measurements, the particles in question obey the relevant wave equations. Through many repeated observations, we have demonstrated that this is correct, at least to a very good approximation.

QM without an “axiom” of collapse is, as I said, just waves staying waves forever and in one universe - if MW and decoherence say otherwise, then they are playing tricks with the logical and semantic framing of the issues.

Yes, QM without any axiom of collapse is just waves staying waves forever. Yes, there is just one universe. But due to the interactions that exist within quantum mechanics, observers that are described by the same quantum mechanics necessarily observe collapse: different components of the same wave function lose coherence with one another after many interactions, and are no longer capable of interaction.

This is very much like thermodynamics. Thermodynamics is an empirical set of laws that was derived directly from experiments. But we also know that thermodynamics can be derived by taking into account the specific properties of the individual components of the system and taking the large number limit. This derivation of thermodynamics from statistical mechanics shows us that, for example, the tendency towards equilibrium turns out to only be approximate. If you take a box of air, no matter the initial conditions it will tend towards a nearly uniform distribution. Provided the box is large and the air dense enough, statistical mechanics predicts that the deviations from uniformity will be so small or take so long that we will be incapable of detecting them.

The relationship between quantum decoherence and wave function collapse is exactly analogous to that between statistical mechanics and thermodynamics.

The experiments you mention are worth reflecting on, but I think they just show that the tendency to collapse (which is still an actual event each time) is a variable based on interactive parameters, not any big deal that.

And what is the mechanism for this? What is the underlying physics of this mechanism?

Quantum decoherence offers this without any additional assumptions. How many more assumptions will you add to the theory to replicate quantum decoherence just to avoid the many worlds interpretation?

The thing you have to recognize is that all we have are the results of experiments. That is, all that we can be sure of is the appearance of collapse.

Yes, that’s what we have, but no sensible thinker considers the objective results to be merely “an appearance” in any sane sense. Collapse is not “an axiom,” it is what happens.

The thing to do, then, is that when two different theories predict the same experimental outcome, we should apply Occam’s Razor: consider the theory with fewer hypothetical entities as the more likely.

If anything deserves to be called “hypothetical” it is the wave, not the collapse which is the “given.” We don’t even know what it means to say that the wave functions “exist” per se, but the collapses are little spots right there on a screen etc. How could “shut up and calculate” folks be brushed off so glibly, regardless of whether you agree with them?

QM without an “axiom” of collapse is, as I said, just waves staying waves forever and in one universe - if MW and decoherence say otherwise, then they are playing tricks with the logical and semantic framing of the issues. The experiments you mention are worth reflecting on, but I think they just show that the tendency to collapse (which is still an actual event each time) is a variable based on interactive parameters, not any big deal that.

PS: My regards to you and others for gracefully bearing the brunt of my orneriness and florid language at times. Oh - I want your opinion on the differential acceleration wrangle as well!

As for your second post, you’d probably like the sentiments in “The Fall of Freddie the Leaf” by Leo Buscaglia, which I favorably review in the Huckabee thread.

I might agree that people may not have any tendency to pose general “meaning of life” questions, but it seems perfectly clear that each of us is very much interested in the meaning and purpose of our own life. Of course, this meaning is whatever we make it to be: there is no meaning imposed externally. There is no objective meaning. Our purpose is what we choose it to be. And this is, I think, a far more uplifting sense of purpose than one imposed from the outside by some inexplicable deity.

Actually, meaning and purpose questions can be posed only in a religious framework (religion here indicates a system with Christianity as an exemplar); and cultures that don’t have religion (e.g., Buddhism is not a religion) don’t pose “meaning of life” questions.

Therefore human beings don’t have a natural tendency to look for meaning and purpose in the universe, because those questions did not arise universally, but only in religious cultures, simultaneous with or after the rise of the religion.

(The idea that religion is a human cultural universal is a nice piece of theology masquerading as knowledge, the argument is too big to fit in the margin, but the argument is now available on the web in the ebook here:

http://colonial.consciousness.googlepages.com/theheatheninhisblindness
)

Jason, talking about “the appearance” of collapse is sophistry. There *is collapse, by any honest accounting.

The thing you have to recognize is that all we have are the results of experiments. That is, all that we can be sure of is the appearance of collapse. The thing to do, then, is that when two different theories predict the same experimental outcome, we should apply Occam’s Razor: consider the theory with fewer hypothetical entities as the more likely.

And so, if quantum mechanics without an axiom of collapse can explain all experiments that show collapse, then it is highly unlikely for the axiom of collapse to describe reality. But fortunately, it doesn’t end there. In fact, quantum decoherence is not always a sudden deocherence: often the number of states that the interaction decomposes the system into is small enough, and the change is small enough, that the docoherence is merely partial instead of total. So we can see the “collapse” turn on slowly by carefully dialing the interaction that causes the decoherence. There is no way that this could happen with an axiom of collapse, as you either measure something or you don’t. There is no in between. And this has been tested.

Imagine this sentence said by a wizened old schoolmaster with spectacles, slowly drumming his smacking ruler against his palm, while a sheepish Neil stands there in an oversized British schoolboy uniform, looking at his own nervously shuffling feet and biting his lip.

Ok, don’t, because it’s silly. But I couldn’t help imagining it.

How does the appearance of collapse “violate all standards of empirical frankness”? There really is no question that quantum mechanics, without any axiom of collapse, has the appearance of collapse upon interaction of a wave function with the environment. Furthermore, we have seen this appearance of collapse turn on slowly through experimental tests.

And yes, this is a fully deterministic view of quantum mechanics. The randomness stems directly from the appearance of collapse, and is purely an artifact of us viewing the world from within the system described. The “frog” view, if you will, has this appearance of randomness, while the “bird” view has nothing of the sort.

I’ll make one last attempt to get you to actually think about curved spacetime and non-Cartesian coordinates.

Consider all the geodesics that pass through the north pole. That’s easy: they are the lines of longitude. Call longitude phi and co-latitude (the angle measured from the north pole) theta.

We can set up some nice coordinates in which these geodesics are locally linear. Define x = theta cos(phi), y = theta sin(phi). Geodesics are lines of fixed phi, phi=phi_0, so in our new (x,y) coordinates they will take the form y = tan(phi_0) x. In other words, they look just like straight lines. Taking the second derivative of y wrt x, we get zero. All geodesics look straight in this way, but note that we’re not just using the vacuous observation that “every smooth curve is a straight line to first order”. A non-geodesic curve passing through the north pole would not have the equation y = k x to second order; there would be a quadratic term as well.

You can perform an analogous construction in space-time. In place of geodesics through the north pole of a sphere, use geodesics through the event E in space-time where the world lines of two free-falling test particles intersect. The spacetime coordinates you get this way will let you describe every geodesic through E with a linear equation, with no quadratic terms. That’s what anyone inside a free-falling elevator would measure: all the test particles would be seen to travel along straight lines with uniform velocities.

Now, go back to the sphere, and look at all the geodesics that pass through another point: call it P, and place it at 0 degrees longitude, 45 degrees latitude (and 45 degrees co-latitude). Of course the north pole wasn’t special, and we could construct the same kind of nice x and y coordinates here that made the geodesics linear, with a bit more work, but we won’t do that. Instead, we want to know how the geodesics look using phi and theta as coordinates. On a map of a small region, latitude and longitude look almost Cartesian, so you might think you’d get linear equations for the geodesics in those coordinates too.

But you don’t. Suppose you take a geodesic that passes through P, and hits the equator at longitude phi_E. Close to P (phi=0, theta=45 deg), to second order in phi such a geodesic is described by:

theta(phi) = 45 deg + (1/2) cot (phi_E) phi + (1/4) cosec(phi_E)^2 phi^2

So not only is there a non-zero quadratic term, it’s different for different geodesics.

Of course the geodesics through P are no different from those through the north pole. They are still locally linear when described in sufficiently nice coordinates — the kind of coordinates a town planner might use if she doesn’t care about latitude and longitude but just wants to make distances and straight lines as easy to describe mathematically as possible.

But anyone who has a reason to insist on describing things in terms of the coordinates phi and theta will find that these geodesics are quadratic functions theta(phi), with different quadratic coefficients for different geodesics.

Equally, in the case of the falling test particles, anyone who is fixed relative to the planar mass and using coordinates in which the mass is stationary at z=0 will find z(t) for the falling test particles to be quadratic, and the quadratic coefficient in each case will be different.

This is neither “torturing semantics” nor logically contradictory. It is simply a description of different measurements made with different coordinate systems. Is the second derivative of co-latitude as a function of longitude different for different geodesics that pass through P? Absolutely. Do people travelling along these geodesics close to P observe any mutual “acceleration” as a consequence of this fact? Absolutely not; as far as they’re concerned, everything measurable is linear to second order.

If you understand (and preferably verify by your own calculations) what’s happening on the sphere, what’s happening in curved spacetime will no longer seem so strange.

40.

Jason, go and read and understand my critiques of the decoherence scam elsewhere on these threads (compare to what I just said about the equally wooly “multiple worlds” racket.) Specific localizations are what we actually observe, unless you are BSing us with that “illusion” and “appearing” conceit which violates all classic standards of empirical frankness. A wave which doesn’t collapse is just a wave, period, forever, not one or even a bunch of localizations (separated from each other by literally God only knows what – do you?) If they decohere, they would just forever stay “waves” which aren’t in the same relationship as before, unless you assume the consequences to begin with, that you were trying to prove. None of the mathematics of waves per se does or even *can* express or contain the localizations (since mathematical structures can’t produce true randomness, they are in effect “deterministic”! – so-called “random variables” are fiat entities of discourse about probabilities in general, not a genuine, formed machinery that can give us actual sequences.)

Collapses/localizations are a bizarre and logically absurd feature of the like-it-or-not *universe* we actually live in, for honest folk to acknowledge first and foremost even if *maybe* explainable in a sincere sense someday. Decoherence is a circular argument using the surreptitious putting in by hand of the very events it is presuming to explain.

BTW, what do you think of Greg Egan’s argument, first: that the acceleration of transversely moving bodies in the field of a very extended/”infinite” planar mass is higher than that of bodies falling straight down, and second: those kinds of accelerations really doesn’t matter for purposes of defining comparative acceleration in the equivalence principle, despite our clear ability to use that to show the distinction in terms of progression relative to a “floor”?

As for anyone “showing” that collapses can be incorporated into the deterministic wave function: I humbly submit (on the most general terms of proper semantics and logical hygiene) that he could not have done so.

He did. It’s called quantum decoherence:
http://en.wikipedia.org/wiki/Quantum_decoherence

That you call this “BS” in no way impacts the result. Take quantum mechanics, don’t include any wave function collapse axiom, and you get the appearance of wave function collapse as a result of interactions.

But I think you misdescribed the behavior of the particle with transverse motion.

You’re wrong. The equivalence principle says x=vt, y=z=0. These formulas are correct to second order in t: the instantaneous second derivatives of the elevator coordinates for the test particle are all zero, at t=0.

You’re making false assumptions about general coordinate systems when you claim this is incompatible with different second derivatives for the two test particles’ coordinates, in the coordinate system fixed to the planar mass.

Why don’t you try verifying the claims I made about geodesics on a sphere? You only need some simple vector geometry and calculus to do that.

(1) Consider two geodesics passing through the point P. Travel a distance s along each geodesic, arriving at the points Q and R respectively. Compute the great-circle distance from Q to R. Prove that its second derivative as a function of s, evaluted at s=0, is zero.

Hint: Without loss of generality, make P the north pole, and the first geodesic the prime meridian. The great-circle distance between two points on a unit sphere is the arccos of the dot product of the vectors from the centre of the sphere to the points. So I am asking for the second derivative wrt s of the function:

arccos[ (sin s, 0, cos s).(sin s cos r, sin s sin r, cos s) ]

where r is the constant longitude of the second geodesic (in radians), and the distance s we’ve travelled from the north pole gives us the co-latitude of both Q and R, because we’re assuming a unit sphere.

(2) Compute the latitude and longitude of Q and R, as functions of s [here it would be a loss of generality to put P at the north pole, so that makes the calculation a bit harder]. Compute the second derivatives of these latitudes and longitudes, evaluated at s=0. Note that in general these will not be the same for Q and R.

Once you believe both these results (and if you don’t currently believe them, do the calculations), then you ought to understand why there is no contradiction between the equivalence principle and the different coordinate accelerations of the test particles.