Are there an infinite number of copies of the solar system?

[fmichel04]

To my knowledge, it is still a mystery if the universe is finite or infinite in size.

Assume the universe is infinite in size.

Does it imply that there exist an infinite number of copies of our solar system in the whole infinite universe?

I presume that the answer depends whether the solar system can be defined by discrete or continuous data. If there exists only a finite number of states to describe the solar system, I would guess that the same pattern is repeated an infinite number of times in an infinite universe. If a continuous model is needed to describe the solar system, I would guess that there exists somewhere in an infinite universe planetary systems as close as possible to the solar system, but not exactly equal to it. Is that right?

Thank in advance for your answers.

 

[marcus]

Personally I don't assume, in my own thinking, that the universe is spatially infinite. I've seen data in several places suggesting that it might have a slight positive curvature and be spatially finite----like the 3-sphere.

But you are right that it is unknown. the finiteness issue is unresolved.

So let's assume space infinite for the sake of discussion. And it is usual to suppose matter is approximately uniformly distributed. cosmologists normally assume "homogeneous and isotropic".

so assuming for the time being that we have this infinite universe with pretty much the same amount of matter everywhere, on average, then I think WHAT YOU SAY IS THE MOST REASONABLE PICTURE.

In such a universe there would be other regions the size of our Hubble volume (or take some other convenient volume) which have the matter particles distributed as closely as you please to how they are distributed here. So these regions would have an eerie resemblance to our own. they would be extraordinarily rare, unimaginably rare, but yet despite the rarity there would be an unlimited number of such regions.

an unlimited number of regions where, for example, there is a Mcdonald's right down the block and Paris Hilton shows her fanny to the photographers. If you were God you would doubtless wish to immediately destroy such a universe, but it follows plausibly from your assumptions.

 

[Janus]

Also with an unlimited number of such regions you would have Earths which varied from our Earth in some detail or another. An Earth where Gore won the 2000 election or an Earth where Sherlock Holmes existed as an actual person. In fact, any variation of Earth and its history that doesn't violate the laws of physics would exist.

 

[TR345]

If the universe is infanite and there is an infinate Earth look alikes, then there would exist at all times the Earth at all of its stages of development. So there would be infinity Earth's of the future, and more interestingly people of the future. Eventually the people would abandon the planet and use advanced technology to survive in space. And with infanite time they may make their way to distant solar systems in search of valuble recources. Eventually a trillion year old race of future like Earth people would maybe find one of those other Earth like planets. Not to mention the assortment of inteligent life from other planets. Given infinite time and infinite races of people. How long would it be before the infinite universe becomes infinitly overpopulated with intelligent life.

 

[Chronos]

An infinite universe is illogical. We live in an observationally finite universe. What might exist beyond those bounds is metaphysics, not science.

 

[ganstaman]

An infinite universe is illogical. We live in an observationally finite universe. What might exist beyond those bounds is metaphysics, not science.

How is an infinite universe illogical? Note that your second two sentences are not an answer to my question.

As for this being a question of metaphysics and not science, I can only say with my limited knowledge that you might be correct now. However, I wouldn't discount the idea that having an infinite universe would have some implications in our observable region that we could one day test. That is, infinite and finite universes don't necessarily have to appear the same to us.

 

[hellfire]

To my knowledge, it is still a mystery if the universe is finite or infinite in size.

Assume the universe is infinite in size.

Does it imply that there exist an infinite number of copies of our solar system in the whole infinite universe?

I presume that the answer depends whether the solar system can be defined by discrete or continuous data. If there exists only a finite number of states to describe the solar system, I would guess that the same pattern is repeated an infinite number of times in an infinite universe. If a continuous model is needed to describe the solar system, I would guess that there exists somewhere in an infinite universe planetary systems as close as possible to the solar system, but not exactly equal to it. Is that right?

Thank in advance for your answers.

Jaume Garriga and Alex Vilenkin have worked on this topic. You can find a nice popular description of their ideas in Vilenkin's book "Many Worlds In One". They assume a spatially infinite, homogeneous and isotropic universe. Moreover, they argue that the possible configuration space of matter is finite, which would lead to infinite copies as you have mentioned. If you drop the assumption of a finite configuration space, infinite copies do not necessarily follow. Vilenkin gives a "proof" of the finiteness of the configuration space of matter within causally connected regions: they argue that the Heinsenberg uncertainty relation for matter forces to a "coarse-grained" description of the universe within a finite causally connected region. To me, that proof does not seem to be conclusive, an it seems to me that a rigorous proof should make use of a quantum theory of both, matter and gravitation. That aside, the fundamental question of finiteness of space remains open. I can hardly figure out how to find any experimental or theoretical proof about an infinite space. You can find a technical discussion on which the book is based in: http://arxiv.org/abs/gr-qc/0102010

 

[xantox]

To me, that proof does not seem to be conclusive, an it seems to me that a rigorous proof should make use of a quantum theory of both, matter and gravitation.[/url]

The Bekenstein-Hawking formula for the entropy of a black hole may be used to constrain the maximum number of states in a given volume.

 

[hellfire]

The Bekenstein-Hawking formula for the entropy of a black hole may be used to constrain the maximum number of states in a given volume.

The Bekenstein bound, yes, thanks for the enlightening remark.

 

[Burning-thunder]

An infinite universe is illogical. We live in an observationally finite universe. What might exist beyond those bounds is metaphysics, not science.

It's illogical for us to percieve it all, but not illogical to exist. As the question is assuming the universe is indeed infinite then I'd say that percieving the infinite isn't a problem.

I would actually argue that this doesn't mean there are an infinite number of copies, for there are an inifinite amount of combinations of planets when you consider the particles that make them. For example, one particle may be an infinitely small distance away from one atom than in another seemingly perfect solar system, and this small difference is enough to make the two different.

Argh, I really didn't explain that very well but I hope you guys get my point.

 

[xantox]

I would actually argue that this doesn't mean there are an infinite number of copies, for there are an inifinite amount of combinations of planets when you consider the particles that make them. For example, one particle may be an infinitely small distance away from one atom than in another seemingly perfect solar system, and this small difference is enough to make the two different.

This is true in classical Newtonian mechanics, but false in quantum mechanics. And as it was famously said, nature is not classical, dammit.

 

[setAI]

An infinite universe is illogical. We live in an observationally finite universe. What might exist beyond those bounds is metaphysics, not science.

it is science because we can make quantifiable predictions: the sciences of statistics/physics and chemistry predict that in an infinite spatial universe there will be an exact copy of you 10^{10^29} meteres away- this is testable through simulation on a very powerful computer as well as in principle a very long trip to verify

 

[Burning-thunder]

This is true in classical Newtonian mechanics, but false in quantum mechanics. And as it was famously said, nature is not classical, dammit.

Sorry, but my knowledge of Quantum is a little sketchy. Are you (or rather, is quantum) suggesting that space can't be divided into infinitely small chunks, and that there's a limit?

Scary.

 

[Burnsys]

And, does it have any implication in the law of consevation of energy? i mean, what's the big deal of conserving energy if anyway it will be always infinite, i could create or destroy energy and there will always be the same amount of it: Infinite

 

[TR345]

On that same note, how could energy ever be conserved if it isn't infinate. If energy is always conserved then what happens to it at the end of time in a finite universe? Does a finite universe imply creation of energy, and therefore destruction of energy as well? Or does conservation only work in the universe as we know it today?

 

[xantox]

Are you (or rather, is quantum) suggesting that space can't be divided into infinitely small chunks, and that there's a limit?

The fundamental explanation follows from the coarse-graining of the position x momentum of each particle as described by the Heisenberg uncertainty principle, implying that the number of states for a given energy of the system is always finite.

And, does it have any implication in the law of consevation of energy? i mean, what's the big deal of conserving energy if anyway it will be always infinite, i could create or destroy energy and there will always be the same amount of it: Infinite

There are no implications, since conservation of energy is local. Eg, if you are now in a room and later you are no longer there, then conservation of energy says that you must have left through some door in the meantime.

 

[keinve]

assuming the universe is infinite... yes. there would be infinite copies of the solar system. and in quite a few of these, doctor who would exist. and family guy. and futurama... in a thousand years. halo, in about 500 years.

 

[Pippo]

To my knowledge, it is still a mystery if the universe is finite or infinite in size.

Assume the universe is infinite in size.

Does it imply that there exist an infinite number of copies of our solar system in the whole infinite universe?

I presume that the answer depends whether the solar system can be defined by discrete or continuous data. If there exists only a finite number of states to describe the solar system, I would guess that the same pattern is repeated an infinite number of times in an infinite universe. If a continuous model is needed to describe the solar system, I would guess that there exists somewhere in an infinite universe planetary systems as close as possible to the solar system, but not exactly equal to it. Is that right?

Thank in advance for your answers.

I would simply say that the solar system is the demonstration that solar systems can exist in the universe, I would include the life in it.

 

[sysreset]

Does there exist an infinite number of copies of our solar system in the whole infinite universe?

I presume that the answer depends whether the solar system can be defined by discrete or continuous data.

I think our solar system would be defined by continuous data. Too many random collisions have occured, too much chaotic motion, to "quantize" our solar system into a discrete model, IMO.