The end of time

December 2, 2005 10:44 PM

How do we know the mathematical models of physics — equations modeling the universe — apply across the universe, to data we collect about the universe that may be billions of years old? (What would be the process for verifying this?)

By extension, is there general, metaphysical consensus in the physics community if mathematics is solely an invention of the mind, or is it a piecemeal discovery, a revelation, about the universe?

Thirdly, given Hawking radiation which leaks outside of a black hole, is that information statistically random — and can said information be collected, and therefore useful for, say, a one-time pad? What is the rate of emission, for example, in relation to the size of said black hole?

posted by Rothko to science & nature (22 comments total)

To question 1: We don't, I believe it's an assumption that we make. The only reasonable assumption we can make is that the laws that govern our little corner are the same laws that govern everything. However, we test this assumption every time we look at distant galaxies, and it has yet to fail.

Regarding question 2, some Googling turned up this interesting essay, but I don't have a definitive answer. Maybe some physicist MeFite will.

The information content of a black hole appears to be lost when it evaporates, as under these models the Hawking radiation is random (containing no information). - Wikipedia

Honestly, these are interesting discussion topics but you might do well to just Google them.
posted by knave at 11:15 PM on December 2, 2005

How do we know the mathematical models of physics — equations modeling the universe — apply across the universe, to data we collect about the universe that may be billions of years old? (What would be the process for verifying this?)

The models are developed from the data so they'd kind of have to. (Until we collect more data anyway)

is there general, metaphysical consensus in the physics community if mathematics is solely an invention of the mind, or is it a piecemeal discovery, a revelation, about the universe?

Mathematics is a system for describing the universe, based on a way of describing the interaction of measurable variables. Like any tool, it's only as good as the operator. Because mathematics is based on describing interactions and outcomes we can use it to infer information about unmeasured variables. This doesn't make mathematics itself a revelation, but properly applied it can revela information, certainly.
posted by fshgrl at 11:22 PM on December 2, 2005

1. Its an assumption but one that seems consistent with observations (e.g. based on light received from the rest of the universe) Mathematical models of the Big Bang go on to accurately predict the Hydrogen-Helium abundance. The predicted Cosmic Microwave Background was there, also as predicted.

2. Consensus on metaphysics isnt needed to move forward. See Mathematical Realism vs. Platonism


3. Sure but why do you need a black hole when general radiation is itself statistically random (see Hotbits) As for the latter, Google is your friend.

I'll think you'll get better answers if you do some groundwork first yourself. All these are pretty broad topics.
posted by vacapinta at 11:22 PM on December 2, 2005

Revela= reveal.
posted by fshgrl at 11:23 PM on December 2, 2005

Mathematics is a system for describing the universe

I think a lot of mathematicians would disagree with you there. Mathematics is, at its purest, the exploration of an abstract mathematical universe. That physicists come along later and use those tools to model physical phenomena is a kind of afterthought.
posted by chrismear at 11:36 PM on December 2, 2005

Also, in response to your first question, Rothko: I'm not sure what your confusion is. You've got some data; you've got a theory; you test the data against the theory. That's how you verify it. What difference does it make if the data is from a tabletop experiment that's running in front of you, or from a satellite that's collecting radiation that's millions of years old?
posted by chrismear at 11:39 PM on December 2, 2005

No confusion, just thinking of an idea for a story and wanted to get some direction on current knowledge. I don't entirely trust Wikipedia. Thanks for all informed input.
posted by Rothko at 11:51 PM on December 2, 2005

Look up "problem of induction" for some philosophers' opinions on the question.
posted by shoos at 12:03 AM on December 3, 2005

How do we know the mathematical models of physics — equations modeling the universe — apply across the universe, to data we collect about the universe that may be billions of years old? (What would be the process for verifying this?)

Warning: I am not a physicist, but I spent some time going through my old chat logs with a physicist friend in order to answer these. If my answers are wrong, blame him.

Basically, we don't. The principle of universality is one of the implicit assumptions of the scientific method, and from a Creation 'science' standpoint, one of their favorite weak points.

While things like CMB radiation have been accurately predicted prior to confirmation of their existence (as was the gravitational lensing effect Einstein predicted), we also have anomalies that point towards our models not applying everywhere.

Probably the biggest fundamental problem in physics right now - gravity, basically - stems from the problems we're seeing with how it applies in a cosmic scale. There are major problems with the rate of universe expansion, gravitational cohesion of galaxies, and quirks like the Pioneer anomaly. These problems are what resulted in the theories of 'dark matter' and 'dark energy', which while quite plausible, are at this point essentially fudge factors used to bring our observations of distant galaxies in line with what we can clearly observe back here at home about falling ball bearings and high-precision observations of planetary orbital mechanics. While there's a much more solid backing to dark matter and dark energy than, say, the 'aether' of yesteryear that light supposedly propagated through, it's still a byproduct of our models failing the test of universality.

By extension, is there general, metaphysical consensus in the physics community if mathematics is solely an invention of the mind, or is it a piecemeal discovery, a revelation, about the universe?

I'm not sure what you're getting at, here.

What is the rate of emission, for example, in relation to the size of said black hole?

The less massive a black hole, the more quickly it loses mass.
posted by Ryvar at 12:18 AM on December 3, 2005

How do we know the mathematical models of physics ... apply across the universe...

This is currently a testable question being pursued by cosmologists and physicists; the former work to verify the laws are the same over grand distances, the latter are working to verify the laws are invariant as time evolves in the lab.

[is] mathematics is solely an invention of the mind, or is it a piecemeal discovery, a revelation, about the universe?

My feeling is there is no such general consensus, at least among physicists. The answer one gets may depend heavily on whether one asks an experimentalist or a theorist. My answer: "in practice, I've never at all had to care."


...and can said information be collected, and therefore useful for, say, a one-time pad? What is the rate of emission, for example, in relation to the size of said black hole?

There are much, much more efficient random number sources for use as one-time pads. See, for instance, Quantum Key Distribution which marries the generation and distribution of one time pads securely in one step. That's a trick you can't do with a black hole. In general, the less massive a black hole, the faster it is predicted to radiate.
posted by fatllama at 12:37 AM on December 3, 2005

By extension, is there general, metaphysical consensus in the physics community if mathematics is solely an invention of the mind, or is it a piecemeal discovery, a revelation, about the universe?

In engineering we talk about delta functions - they are defined as infinite at the origin and zero everywhere else. A delta function is also defined to have an integral of one, which is to say the area under the infinitely high peak with infinitesimal width has a finite value. According to an engineering prof. I had, the delta function was ignored by mathematicians for a long time because it has such an awkward definition (infinity x 0 = 1), but it was used by engineers and physicists because it worked. The point is, math and physics feed off each other, but the relationship is poorly defined. I can talk more about why it turns out to work even though the math is so degenerate...

Ryvar: Probably the biggest fundamental problem in physics right now - gravity, basically - stems from the problems we're seeing with how it applies in a cosmic scale.

I think it is worth adding to this... The problems Ryvar mentions don't necessarily have anything to do with a Theory of Everything - which would unify gravitational theory with electromagnetic theory. A lot of physicists seem to think that solving the problems and finding a ToE are one and the same, but a lot don't. Any attempt to draw implications from the existence of the problems is mere conjecture.
posted by Chuckles at 1:49 AM on December 3, 2005

maybe you've seen it already, but there's an example from astronomy here, where i tried to explain one way in which we constrain how physical constants might change over cosmological time.
posted by andrew cooke at 4:21 AM on December 3, 2005

Rothko: How do we know the mathematical models of physics — equations modeling the universe — apply across the universe

We don't and we can't. Looking at (light from) stars assumes that the entire universe is visible to us. Assume the universe is divided into two parts. One part, A, where we are, follows Ruleset A; the other part, B, follows Ruleset B. At the interface between A & B, most information is either lost or "converted" to the appropriate ruleset. Only way to know is by traversing the interface.
posted by Gyan at 4:37 AM on December 3, 2005

there's no need for an interface. an extreme extrapolation of gyan's argument is to say that just beyond where we can physically travel it's a system of projectors, pulleys, wires etc that "fakes" everything we observe. parhaps run by a guy with flowing white hair.

putting it in pseudo-scientific terms with "interfaces" and "rule-sets" is a little misleading, because there's nothing to support such a model of the universe any more than the one i gave. in particular, we have no evidence of things changing to "fit in" with local rules.

for example, if you take a pair of scales to the moon, where gravity is lighter, they don't change so that you still read the same weight as on earth. there's no automatic compensation for the new "rule set" (lower gravity).

closer to home, you can use exactly the same argument over time. there's absolutely nothing to say that physics won't change tomorrow so that everything is completely different, or that it was completely different yesterday, but we have been given false memories, false environments, etc.

there is no answer to hard scepticism except to point out that it's something we ignore all the time and, as a consequence, apparently make and do some amazing things (maybe we're only imagining that everything outside our heads exists, but if i assume it does then i can go build an atomic bomb....)

but i don't think that's what you were asking about. i think you were addressing a more interesting argument, which is along the lines of - "could we detect changes in physics if it continued to generally hold true, but has small perturbations (typically in the value of certain physical "constants") over extreme distances?"
posted by andrew cooke at 4:59 AM on December 3, 2005

andrew cooke : "in particular, we have no evidence of things changing to 'fit in' with local rules."

The whole point is that there would be no evidence if 'fitting in' was going on. So its absence isn't an indicator of anything.

andrew cooke : "maybe we're only imagining that everything outside our heads exists, but if i assume it does then i can go build an atomic bomb"

This is off-topic, so I'll leave it at this: Even if everything exists in your head, that doesn't mean that all rules are elastic.
posted by Gyan at 5:19 AM on December 3, 2005

The less massive a black hole, the more quickly it loses mass.

To be precise, the more quickly it loses relative mass, because the mass loss is proportional to the surface area, and smaller spherical objects have a higher surface to volume ratio.

In terms of validating physical constants over long periods of time, Alex Meshik and co have done a lot of good work on a rash of 2-billion+ year old naturally chain reacting nuclear reactors. Analyzing the fossil evidence of these reactors can tell you a surprising amount about the values of some fundamental constants way back when. It is interesting to speculate that for some planets formed from different starstuff, entire regions of their surfaces may be "hot" for long, long periods of time.

Meshik A. P., Hohenberg C. M. & Pravdivtseva O. V. Phys. Rev. Lett., 93. 182302 (2004)

There's also some work on analyzing the extent and invariance of the fine structure constant, a value that's used a lot in electromagentic calculations.

Barrow JD (2005). Cosmological bounds on spatial variations of physical constants, PHYSICAL REVIEW D, 71(8): 083520-1–083520-7.

Tzanavaris P, Webb JK, Murphy MT, Flambaum VV, Curran SJ (2005). Limits on variations in fundamental constants from 21-cm and ultraviolet quasar absorption lines, PHYSICAL REVIEW LETTERS, 95(4): 041301-1–041301-2.
posted by meehawl at 8:38 AM on December 3, 2005

How do we know the mathematical models of physics — equations modeling the universe — apply across the universe, to data we collect about the universe that may be billions of years old? (What would be the process for verifying this?)

I feel like most of the answers here skirt the point, which is that this is not a question that can be asked of a scientific theory. Science is a methodology not of proving, but of falsifying. We can only ask "how do we know that the models do not apply across the universe." And the answer to that is, as many people did point out above, based on all the data we have collected, the theories fit.

If some new data comes to light that doesn't fit, the theories will be changed to accomodate the new data such that it is all consistent. The beauty of science is not that theories are infallible, but that they can be adjusted to take into account new data, such that they will always fit.

A good example is Einstein's Special Theory of Relativity. Newtonian physics were fine for describing things of speeds that we observe everyday, but when applied to things that were very close the speed of light relative to the observer, Newtonian physical models broke down. Einstein solved this by applying the Lorentz transformations [1/((u^2/c^2)^1/2) where u = velocity and c = the speed of light)] to the Newtonian equations. When speed is very low, in ranges in which we move, or even cars or trains or planes, the Lorentz Transformation is essentially a multiplier of 1, which means the Newtonian model fits close enough. For their time, when no one really considered something moving at the speed of light, they were great, and could model two trains moving toward each other at x velocity for y hours as you would think about on a middle school physics test. As speed increases toward light, though, the multiplier increases toward infinity, changing the Newtonian result, and giving an answer that fits with observations. A change was made, and now we have a better theory.

I realize that this is a horrible approximation of the Special Theory, and the physicists here will probably flog me, but the essence of the molding of an older theory to fit new data is there.
posted by The Michael The at 8:41 AM on December 3, 2005

applying the Lorentz transformations

Irish physicist FitzGerald came up with the contraction idea first. Lorentz proposed a more rigorous framework, which Poincaré perfected. Had his dodgy health issues not led to premature death by embolism, it's possible that Poincaré's publications on relativity preceding and mirroring Einstein's might have received more PR.
posted by meehawl at 9:11 AM on December 3, 2005

"By extension, is there general, metaphysical consensus in the physics community if mathematics is solely an invention of the mind, or is it a piecemeal discovery, a revelation, about the universe?"

The physics community, as a rule, is relentlessly realist and in so being are inclined to a sort of Platonism, an idealism complementary to their realism. For them, mathematics are "real" insofar as they are a necessary attribute of a description of the physical universe. While a physicist may expect that any given exercise in pure mathematics is likely to be useless; he or she is not that surprised when it turns out to be useful in the end. The math is "there" because the universe is there.

In contrast, the vaguely "official" stance of the mathematics community nowadays is quite definitely that math is formal and certainly not "ideal". In the same way that the physics community has good reasons for expecting something in math to be a reflection of the actual nature of the universe (because in their experience, it has been), the mathematics community has learned that a physical intuition that is as a practical matter a form of idealism has consistently been misleading while a formalistic view has consistently been validated.

In a fascinating chapter of their book, Mathematicians Phillip Davis and Reuben Hersh in their book "The Mathematical Experience" confide that while as a matter of pure intellectual rigor modern mathematicians are formalists, secretely in their heart of hearts they remain idealists, believing they are mapping the territory of truest universe, that of pure mathematics.

Anyway, physicists do not consider these questions, at least not professionally or publicly. Your questions are squarely in the realm of philosphy which almost without expection every physicist I've known eschews or even ridicules. They are pragmatic. They believe in the principle of universiality because it's simply impractical not to. They believe the universe is comprehensible. A philosopher will tell you, however, that there's no really good reason to believe that the universe is, or must be, comprehensible. Not as a point of rigor. As a practical matter, of course. In this way physicists are very practical—that's why they are not mathematicians or, God forbid, philosophers.

This is also why there is a contemporary schism between scientists and philosophers of science. Kuhn stands tall in the philosphy of science these days while, in contrast, many or most physicists (wrongly) see Kuhnism as kin to postmodernist claptrap. I myself am quite certaintly not postmodernist but I do find most physicists I've known to be what I call "naive realists". (In other words, positivists.)
posted by Ethereal Bligh at 11:25 PM on December 3, 2005

Your third question is tied up with one of the most vexing puzzles of quantum gravity. That puzzle can be roughly described as follows: suppose I throw an encyclopedia into a black hole, and then wait a long time until the black hole completely evaporates. Where did the information in the encyclopedia go?
If the answer is "the information has vanished from our Universe", then this process seems to violate some bedrock principles of quantum mechanics. Since this violation is unpleasant, people have tried various ways to rescue the information; one proposal is that the information is somehow subtly encoded into the Hawking radiation (despite the fact that Hawking's original calculation doesn't show any signs of that.)
There is a huge literature on this issue, and it's led to a lot of exciting developments, but it is not fully settled; so I'd say the honest answer to "is the radiation statistically random?" is "maybe".
posted by em at 8:56 PM on December 4, 2005

suppose I throw an encyclopedia into a black hole, and then wait a long time until the black hole completely evaporates.

Is this meant literally, or as allegory so that regular people can understand? (or be extra confused by it...)

See, in my day to day life I can destroy information... The display on my monitor for example. You could argue that when I turn it off I can still guess at what it was showing just before I turned it off, but you can't very well argue that the current state of the monitor can reveal every state it has ever been in for all history...
posted by Chuckles at 11:12 PM on December 4, 2005

What I mean more precisely is that if we have some system that is governed by quantum mechanics, then time evolution in that system is supposed to be unitary -- in particular, you never have 2 initial states which wind up in 1 final state. (This is true in classical mechanics too.)

The puzzle is that if you throw any object into a black hole, and that object has some entropy (say, a box of gas), the information about which state it was in seems to disappear -- so you have several possible states in the past, all mapping to the same state in the future.

The situation with your computer monitor is different -- we might well believe that all the information about what was displayed there before you turned it off is still in the Universe somewhere.
posted by em at 8:17 AM on December 5, 2005