Can We Mathematically Define Physical Impossibility in an Infinite Universe?

[Loren Booda]

In an infinite physical universe, can we describe mathematically physical impossibility, or are such constraints (e. g., Heisenberg uncertainty principle, constant speed of light, energy and momentum conservation) for finite space only?

 

[HallsofIvy]

Whether the universe is finite or infinite has nothing to do with
" Heisenberg uncertainty principle, constant speed of light, energy and momentum conservation", etc.

 

[Chi Meson]

Originally posted by Loren Booda
In an infinite physical universe, can we describe mathematically physical impossibility, or are such constraints (e. g., Heisenberg uncertainty principle, constant speed of light, energy and momentum conservation) for finite space only?

Chaos theory indicates that there is plenty of room for infinite possibilities and infinite complexity while still operating within fixed parameters.

 

[Loren Booda]

HallsofIvy,

Please read Chi Meson's response.

 

[chroot]

Chaos theory is just a branch of determinism that deals with systems that are very sensitive to initial conditions. I see no connection between chaos theory and any sort of infinite-ness.

- Warren

 

[Chi Meson]

Chaos theory also is useful for developing models of complex, interacting particles. The choas part is due to the non-predictable nature of outcomes due to the impossibility of measuring the initial conditions.

One of the neat things about chaos theory is fractals which are, specifically, images produced by very simple algorithms. Fractals have infinite complexity although they exist within a finite space.

Chaos theory has been used to answer the old atronomy paradox (I forgot whose paradox this is). IT was thought that if the universe was infinite, and the distribution of stars was random, then there should be light coming from every point in space, and the night sky would be very bright.

This paradox was solved already in several other explanations (light is absorbed by dark matter is the most obvious one). BUt it is false to assume that there is a random distribution of stars. Galaxies and clusters are formed according to specific rules, and this is why a number of repeating shapes keep appearing. Galactic formations are perfect examples of fractal images (but then again, so is nearly everything).

My point is, by saying that there is infinite space, and infinite possibilities, it does not necessarily follow that there be an infinite set of rules and constants. THere could be an infinite number of universes, but there does not have to be an infinite number of universal laws.

 

[chroot]

Originally posted by Chi Meson
One of the neat things about chaos theory is fractals which are, specifically, images produced by very simple algorithms. Fractals have infinite complexity although they exist within a finite space.

In the exact same way that there are an infinite number of points on the real number line between any two given points. So?

Chaos theory has been used to answer the old atronomy paradox (I forgot whose paradox this is). IT was thought that if the universe was infinite, and the distribution of stars was random, then there should be light coming from every point in space, and the night sky would be very bright.

You're thinking of Olber's paradox, and it has nothing whatsoever to do with chaos theory.

This paradox was solved already in several other explanations (light is absorbed by dark matter is the most obvious one).

This was the first suggested solution, but it is a red herring. Given infinite time, the dark matter would absorb enough energy to be just as radiant as the stars themselves.

The accepted solution to the paradox is that the universe is either not infinitely old, or not infinitely large. Modern cosmology assumes the universe is neither infinitely old, nor infinitely large.

BUt it is false to assume that there is a random distribution of stars.

On the contrary, that assumption seems quite true. In fact, it's one of the most basic assumptions of cosmology -- that, at large enough scales, the universe is homogenous.

Galaxies and clusters are formed according to specific rules, and this is why a number of repeating shapes keep appearing. Galactic formations are perfect examples of fractal images (but then again, so is nearly everything).

I don't see any connection between galaxies and fractals. The type of fractals you seem to be interested in are the coastline- and fern-type fractals, like the Mandelbrot set. They are just examples of images with similar structure at all scales. Real galaxies do not exhibit this behavior in any respect -- they are very different at different scales.

My point is, by saying that there is infinite space, and infinite possibilities, it does not necessarily follow that there be an infinite set of rules and constants. THere could be an infinite number of universes, but there does not have to be an infinite number of universal laws.

Okay?

- Warren

 

[Chi Meson]

Yeeow!

I have to concede that I did not do a good job at making my point, although I don’t concede the point. It is not such an important point anyway, nor is it my own, so rather than defend it further and have Chroot drill through everything I say, I’ll just let it flounder there like a trout full of holes.

I must say, however, that it was in my general astronomy class in sophomore year (1984) where my professor brought up the subject of fractals in regards to galaxies and Olber’s paradox. I suppose if I had taken notes I could have done a better job recounting the explanation.

 

[Loren Booda]

HallsofIvy

Whether the universe is finite or infinite has nothing to do with "Heisenberg uncertainty principle, constant speed of light, energy and momentum conservation", etc.

Y'all refer to your May 2003 Scientific American article Parallel Universes by Max Tegmark, specifically "Level IV: Other Mathematical Structures," on page 49 and following. There he gives an argument for mutable laws of physics in an infinite universe.

 

[HallsofIvy]

Loren Booda wrote
HallsofIvy,

Please read Chi Meson's response.

I did. He said effectively the same thing I did. What is your point?

 

[Loren Booda]

According Max's Sci Am article, those "fixed parameters" elsewhere in an infinite universe need not be of laws and constants familiar to our local physics.