The Physics of The Minuscule 27
Roland Piquepaille writes "The Economist says that "physicists have worked out how to look at the smallest sizes and shortest time that some of them believe can exist." It starts by comparing the quantum theory, which states that space and time are grainy, to the theory of relativity, which assumes that space is continuous. The well-documented article then looks at several current research projects trying "to reconcile quantum theory with relativity, and thus produce a grainy theory of quantum gravity." In particular, it looks at a paper by Richard Lieu and Lloyd Hillman, published by the Astrophysical Journal Letters, "The Phase Coherence of Light from Extragalactic Sources." Check this column to know more about their work and what their contradictors are saying -- plus a quote from Albert Einstein -- or read the original article for even more details."
Ah, you poor misguided fools! (Score:2)
smallest sizes and shortest times, indeed (Score:4, Funny)
So physicists have so little to do they're investigating the sex life of geekus unattractiveus, the common Slashdotter?
Shouldn't they be spending that grant money on smething useful, like Total Information Awareness of what the Goatse man is up to (or had up him)?
Work in progress... (Score:3, Funny)
not grainy, but rather DIGITAL (Score:3, Interesting)
Using Moore's Law, we could probably come up with a virtual reality equivalent to the real word given 10,000 years or so.
Re:not grainy, but rather DIGITAL (Score:5, Informative)
Re:not grainy, but rather DIGITAL (Score:4, Interesting)
IANAP (yet, still studying) however there appears to be a great deal of evidence pointing towards our universe being nondeterministic. This means that chaos theory in the simplistic, naive sense isn't really valid. The butterfly effect assumes some level of determinism (it is based on the idea of cause and effect, and sensitivity to initial conditions). If you throw nondetermism (constantly random factors) into the equation, the "butterfly effect" can be drowned out. Even if you have *PERFECT* information on the current state of the system, it doesnt' help you much because its behavior is still the result of many stochastic processes.
Put another way, imagine a tree of all possible universes starting with the one we are in right now. This tree represents the set of all possible futures (nearly infinite, if quantum physics is indeed correct that our universe is nondeterministic). Now, if you make some change to the starting universe, if you go far enough into the future the two trees will end up looking identical (that is, in some universes the probabilities align to exactly cancel out the change, and this is of course symmetric).
So if you want to look at possible futures, you really have to look at it in a probabilistic fashion, and for that you don't need perfect information, because IT DOESN'T REALLY MATTER.
Chaos theory is great and all, but take it out of context and it can really mislead you.
Re:not grainy, but rather DIGITAL (Score:2)
Re:not grainy, but rather DIGITAL (Score:3, Interesting)
It is true in an absolute sense, however you should know that there is a difference between how one quantifies an extremely small number of things and an extremely large number of things. A statistical description of 2 or 3 discrete objects is nearly meaningless, however if one has, say 10^100 somethings (such as discrete future universe states) then it makes sense to talk in terms of statistics (50% of the future universes have Bob being alive, rather than dead). I said nearly infinite because I was suggesting that the number was finite, but very large, large enough that for most forms of analysis, the discrete possibilities could be treated as a continuum.
I suppose that terms like "nearly infinite" are simply a matter of perspective and perhaps not as mathematically precise as I should have been. It was, however, 2:35 in the morning so I was very tired.
Cheers,
Justin
Oh, and by the way, there is no "very largest number short of infinity". Infinity is a tricky thing, there are different kinds of infinity [mathforum.org]. Given any real number x, you can apply an operator O which adds an arbitrary positive constant to x to get a new, necessarily larger number x'. Thus, if you tell me you have found this "largest number" I can apply this operator and get an even larger number, thus invalidating the idea that x was the largest number.
Re:not grainy, but rather DIGITAL (Score:2)
Re:not grainy, but rather DIGITAL (Score:2)
Another point I forgot to add last post is that you do *NOT* in any way need all the matter in the universe to store all the information in the universe. The amount of information in the universe is equal to its entropy, and until the heat death of the universe (if that is indeed what will happen) the amount of entropy in the universe is less than it could be. That means a "smaller" universe containing less mass/energy could have the same entropy and thus encode the same amount of information as is in our current universe. This is why lossless data compression works.
Another thing to consider is that if you subscribe to the copenhagen interpretation of physics, quantum information about a particle doesn't exist until it's measured, a sort of "lazy evaluation" in the way the universe works. Provided the number of observers capable of causing this collapse of the wave function was small, one could simulate the universe with far less information than actually exists.
Also, it's possible to store many many pieces of information in the wave function of a single electron, through quantum superposition. So a device that simulated the known universe could be much smaller than the universe it is simulating.
Cheers,
Justin
Interesting article about that idea... (Score:1)
grainy? (Score:1)
Grain implications (Score:5, Insightful)
Will Zeno's Paradox [mathacademy.com] no longer be a paradox since it would no longer be about traveling an infinite series of infinitely small distances but rather traveling a large finite number of miniscule 'space grains'?
Could the relativity of time be more about different sizes of 'time grains' and a little less about where an observer might be standing? The rate of passage of 'time grains' being universally constant but the size of the grains dependant on local conditions?
Our minds are in a maze full of dark and twisty passages. (At least mine is.)
Re:Grain implications (Score:5, Interesting)
Sigh. pi is a mathematical constant, so it is what it is independently of physics. It just happens to be useful in physics.
Re:Grain implications (Score:2, Interesting)
Re:Grain implications (Score:2)
Graininess being assumed (which I do, along with a belief in Many Worlds and other semipsychotic things) then somewhere off in the far distance, the final digit in 1/3 is flickering back and forth between 3 and 4 (and once in a while other digits, too). So yes, it DOES have a last digit, but you have to be extraordinarily careful about when and where you ask what it is, lest your answer differ from what Nature is handing out at that time and place. The neverending series of 3's is just mathemetician's sloppy way of evading the issue in the name of "precision" even when no such thing actually exists in the FINAL analysis.
Re:Grain implications (Score:1)
It does in trinary. Irrational numbers cannot be fully expressed as a "decimal" in any base.
More interestingly, I don't think you could make "effective pi" rational. Try drawing circles of different sizes on a grainy medium, like say, pixels on a screen.
Re:Grain implications (Score:5, Informative)
Interesting question, but I'm afraid not. Pi is a mathematical abstraction, defined [wolfram.com] as the ratio of a circle's circumference to its diameter. These are idealized, mathematical circles and lines. If you were looking at real circles and lines in practical applications, you would truncate after a few dozen decimal places at most. Given that we have computed billions of decimal places, the distinction between the abstract and practical is important to remember.
Will Zeno's Paradox [mathacademy.com] no longer be a paradox since it would no longer be about traveling an infinite series of infinitely small distances but rather traveling a large finite number of miniscule 'space grains'?
This was resolved when analysis (calculus) was formalized. Read more about it at MathWorld [wolfram.com].
Could the relativity of time be more about different sizes of 'time grains' and a little less about where an observer might be standing? The rate of passage of 'time grains' being universally constant but the size of the grains dependant on local conditions?
There are some good books out there that are accessible to anyone with a bit of knowledge about relativity and quantum mechanics. See my tangentially related post [slashdot.org] for some reading references. I particularly enjoyed Smolin's book [amazon.com].
Re:Grain implications (Score:2)
So if we are looking at practical real world implementations of Pi vs. the abstract mathematical concept, and space is in fact grainy and we know the grain size, then wouldn't we know exactly at what decimal place Pi stops being real and becomes abstract only? I think that would be fairly cool to draw a concrete line between the concrete and the abstract with respect to Pi. Math could certainly use more well defined boundaries between the abstract and Reality. That was my point, I had no illusions about changing the abstract mathematical definition.
[Zeno's paradox] was resolved when analysis (calculus) was formalized. Read more about it at MathWorld.
My oh my you are condescending. I know all about integrals and derivatives thanks. Just insert "no calculus required" into my comment. That was the whole point. You wouldn't need calculus if you could just count the grains of space. My mistake leaving it up to the reader to think outside the curve.
Re:Grain implications (Score:1)
This damn nicotine patch is way too small.
Not to mention it tastes terrible and is hard to light.
Re:Grain implications (Score:2)
Interestingly enough, the Stade Paradox, mentioned on the same page, seems relevant to the whole 'grainy' picture of quantum mechanics that the original poster suggests would solve Zeno's dichotomy motion paradox.
I'm still a bit confused about how calculus resolves the dichtomoy motion paradox, though. Yes, we can calculate that certain infinite geometric series will converge, but don't we do so by looking just at the series and not at the infinite number of items in that series? That is, don't we solve the problem precisely by not performing the infinite number of calculations that would be required without calculus? If so, I don't see how this actually resolves the paradox, which is a paradox precisely because, according to our notions of being and motion, we must actually go through the infinite number of steps involved: we are not allowed to just look at the series as a whole, but must go through it.
Put another way, Zeno's motion paradox was not that we can't calculate such a series: he was not so foolish as to say that a body travelling one mile per hour will take anything other than one hour to travel one mile; it was not a mathematical paradox. It rather dealt with whether mathematical concepts, or any human concept, such as space or being or motion, are applicable to the world: can there actually be a body travelling at one mile per hour? We might think things move, but our definition of movement is paradoxical, and so what we call movement can't actually be what's going on.
But like I said, I simply haven't seen an explanation for why this is otherwise.
Grainy, eh? (Score:1)
what quantum theory says... (Score:5, Informative)
It's important, when someone talks about discrete space or time, to ask what the hell they mean. In quantum mechanics, a particle's displacement is something you can measure (always with some uncertainty; an error margin, if you will); it is possible that there is only a (very large!) discrete set of possible answers, though the actual sizes would be so small that even in most quantum mechanical measurements space would appear to be continuous.
Time is somewhat different as it's not a measurable quantity; you can only express the propogation of a system through time. Can you only propogate in discrete chunks?
In quantum field theory, space and time are parameters, making spacetime quantization easier to discuss, but certainly not an inherent assumption!
While discrete space and time are important ideas that are being investigated, the current formulation of quantum mechanics that is taught at schools and used in research does not state this. On the contrary, the incorporation of Hilbert spaces into quantum mechanics has happened specifically because space is not discrete.
Look at the preprint in the arXiv (Score:2, Informative)
The phase coherence of light from extragalactic sources - direct evidence against first order Planck scale fluctuations in time and space [lanl.gov]
You might also find this previous paper interesting by the same authors:
Stringent limits on the existence of Planck time from stellar interferometry [lanl.gov]
the op-ed page (Score:2)