Is the universe entirely predictable, or is it based in probability?

[Sylickon]

Could i predict what everything in the universe will look like in 10 million years using formulas, or is that impossible due to probability?

 

[WannabeNewton]

If you are talking strictly in terms of classical GR then yes you can use initial value data to predict the large scale structure of the universe indefinitely given that the worldline you are following does not fall out of the domain of dependence of the surface you started with i.e. as long as it does not come in contact with a singularity or such.

 

[bcrowell]

Hi, Sylickon,

Welcome to PF!

WannabeNewton's answer is the one I would have given off the cuff, but since s/he beat me to it, I'll try to add some more nuance.

There are various reasons why we can't make perfect predictions of the future:

-Quantum mechanics has randomness in it, but as WannabeNewton has pointed out, this is irrelevant if you just want an answer within the framework of GR.

-There can be randomness due to exponentially growing sensitivity to initial conditions. This is why weather is random, in the sense that nobody can tell from measurements today whether it will rain a year from now. http://en.wikipedia.org/wiki/Lyapunov_time

-In GR, when a singularity is not hidden behind an event horizon, we can't predict its effect on the entire universe. As John Earman of the University of Pittsburgh puts it, anything could pop out of a singularity, including green slime or your lost socks. As far as we know, the Big Bang singularity is the only such singularity. http://en.wikipedia.org/wiki/Cosmic_censorship_hypothesis

-Ben

 

[Chalnoth]

Could i predict what everything in the universe will look like in 10 million years using formulas, or is that impossible due to probability?

Well, that sort of depends.

If you want to take the bird's-eye view of the universe, then all physical laws that we know so far are perfectly predictable: as long as you have the full state of the universe at one time, you can, in principle, compute the full state of the universe at any other time.

But this isn't what we can do, because we cannot view the universe from the outside. Instead, we view it from inside. And inside the universe, quantum decoherence ensures that information about the full state of the universe is continually being lost to the environment. We interpret this information loss as probability: we can't know which information in a quantum experiment is lost until we do the experiment and see. So even though the fundamental laws are, so far, completely deterministic, the behavior we actually observe, even given perfectly knowledge of our universe, turns out to have a degree of unpredictability. We can still say, "If I do quantum experiment X 10,000 times, the average result will be A," but I usually can't say, "If I do quantum experiment X once, the result will definitively be A."

 

[bcrowell]

If you want to take the bird's-eye view of the universe, then all physical laws that we know so far are perfectly predictable: as long as you have the full state of the universe at one time, you can, in principle, compute the full state of the universe at any other time.

But this isn't what we can do, because we cannot view the universe from the outside. Instead, we view it from inside.

Well, all you need to know about is the initial conditions in the past light-cone of the event you're trying to predict. You don't need to know initial conditions for the whole universe.

 

[Shovel]

Well, all you need to know about is the initial conditions in the past light-cone of the event you're trying to predict. You don't need to know initial conditions for the whole universe.

If you extrapolate backwards in time to the big bang, as you approach t=0, any two points will become arbitrarily close together and thus be in each other's light cone.

 

[Chalnoth]

If you extrapolate backwards in time to the big bang, as you approach t=0, any two points will become arbitrarily close together and thus be in each other's light cone.

That's actually not true. In fact, in the classical big bang, the exact opposite happens: the closer you are to the big bang, the less of the universe is in the past light cone. This has to do with the fact that in the classical big bang, the expansion early-on is slowing down. When you have an expansion rate that is slowing down, the past light cone tends to include more and more of the universe as time progresses. This is known as the horizon problem, and is one of the problems that inflation was proposed to address.

 

[Cosmo Novice]

Could i predict what everything in the universe will look like in 10 million years using formulas, or is that impossible due to probability?

If U was flat and spacially infinite then I don't see how this could ever be possible - as it would not be possible to see what everything looks like right now, so by extension determining future states is impossible.

On another note Also whilever there are intelligent sentiences that make conscious decisions this could effect U dramatically. For example on a small scale our radio signals are being broadcast out into space etc. etc. Over time this would cause more and more disruption over what may be expected without conscious decisions affecting U.

Very interesting question i think. )

 

[bcrowell]

If you extrapolate backwards in time to the big bang, as you approach t=0, any two points will become arbitrarily close together and thus be in each other's light cone.

"Initial" doesn't mean the Big Bang. (It can't mean that, because the Big Bang is a singularity, so it's not an event in spacetime at all.) "Initial" just means any spacelike surface cutting across the past light-cone.

 

[Chalnoth]

"Initial" doesn't mean the Big Bang. (It can't mean that, because the Big Bang is a singularity, so it's not an event in spacetime at all.) "Initial" just means any spacelike surface cutting across the past light-cone.

Right, so, in that sense it's a somewhat confusing name. The point is that if you take a slice of the universe in time (for your favorite choice of time coordinate, whatever that is, and were able to know perfectly the state of the universe across that entire slice of time that lies within your past light cone, then you could in principle calculate everything else that happened since then that you can potentially observe.

 

[bcrowell]

Right, so, in that sense it's a somewhat confusing name. The point is that if you take a slice of the universe in time (for your favorite choice of time coordinate, whatever that is, and were able to know perfectly the state of the universe across that entire slice of time that lies within your past light cone, then you could in principle calculate everything else that happened since then that you can potentially observe.

Agreed -- modulo all the other issues listed in #3.