Does Infinity exist in nature

[vuquta]

I guess that one should also point out that we do have divergent quantities for second order phase changes. A good example is the ferromagnetic transition, here the heat capacity diverges to infinity.

 

My understanding is generally if infinities occur then either we need "new physics" or a phase transition has occurred.

 

Is it possible the impossibility of the simultaneous observation of the wave and particle properties of an electron proves the existence of infinity?

[cypress]

If you travel across the surface of the Earth in a straight line, you will never reach an edge. Nevertheless, the surface of the Earth is not infinite. There are geometries that allow the universe to be finite despite being unbounded.

 

Except perhaps as a mathematical exercise in limits, It does not seem possible to travel on a closed spherical surface in a straight line in a real sense. A sphere is not an example of an unbounded finite geometric shape. I suppose there are mathematical models that represent finite space that remain unbounded in this sense, but like infinity, they both exist as mathematical concepts. Neither seem to have an analog in nature.

[Sisyphus]

Except perhaps as a mathematical exercise in limits, It does not seem possible to travel on a closed spherical surface in a straight line in a real sense. A sphere is not an example of an unbounded finite geometric shape. I suppose there are mathematical models that represent finite space that remain unbounded in this sense, but like infinity, they both exist as mathematical concepts. Neither seem to have an analog in nature.

 

I suppose by "in a real sense" you mean in the sense of 3D Euclidian space. That's true, as a literal sphere is an analogy for a 2D universe using 3 dimensions, so as to make it easier to grasp. It is not a perfect analogy, nor is it meant to be literal. However, it is very much true that nature is not simple Euclidian space, so the intuitive notions of what does and does not exist in nature are wrong. This is what general relativity is all about.

[ajb]

Is it possible the impossibility of the simultaneous observation of the wave and particle properties of an electron proves the existence of infinity?

 

How?

[cypress]

I suppose by "in a real sense" you mean in the sense of 3D Euclidian space. That's true, as a literal sphere is an analogy for a 2D universe using 3 dimensions, so as to make it easier to grasp. It is not a perfect analogy, nor is it meant to be literal. However, it is very much true that nature is not simple Euclidian space, so the intuitive notions of what does and does not exist in nature are wrong. This is what general relativity is all about.

 

Is there a literal example of this that is real in the sense that it is observed and confirmed? I suspect that, like infinity, these mathematical constructs don't have analogs in reality.

[Sisyphus]

Is there a literal example of this that is real in the sense that it is observed and confirmed? I suspect that, like infinity, these mathematical constructs don't have analogs in reality.

 

The shape of the universe remains unknown, so no, nothing is confirmed. There are many possibilities being considered, and such a "spherical geometry" is in fact one of them, being the simplest case of negative average curvature on the largest scales. There are also several possibilities in which it is infinite in extent. They aren't simply mathematical constructs - that space is not simply Euclidian on all scales is very much observed and confirmed. Though, obviously, the universe only has one shape, so most possibilities are necessarily wrong.

 

I suppose the closest you could come to a "literal example" would be inside the Schwarzchild radius of a black hole, in which any straight line in any direction points "inwards." A true example would be impossible in our universe, as it would literally be its own universe.

[vuquta]

vuquta, on 19 August 2010 - 11:54 PM, said:

 

Is it possible the impossibility of the simultaneous observation of the wave and particle properties of an electron proves the existence of infinity?

 

 

 

How?

 

Neither are finitely decidable.

[PlatinumZr0]

It's funny to think infinity has an endpoint. Like something can be infinitely big but not infinitely small. Looking at it with basic geometry, Ray AB stops at A, but passes through B to continue on to infinity. Naturally, infinity cannot exist for the sole reason that universe is still expanding so it has a definite and finite border, even though that border changes every second. The real question is "is there anything beyond our universe?" if so, then infinity has a higher chance of existing. Also, we can look at atoms, and subatomic particles. If each has something inside it, like a quark, and the quark has something inside it and so on and so forth, infinity would exist. When You say infinity, you usually think number, distance, or size. But what about time. When was the start of time? The Big Bang? Sure. But when is the end. Keep thinking...