EXACTLY

It's a little complicated, but the arithmetic isn't done with the current radius of the observable universe. You use the cosmological event horizon, which has an upper limit of 62 billion light years - photons from beyond this point can never reach us due to the accelerating expansion of the universe.

If there is infinite space in the universe (and recent calculations do suggest that this is the case), that still does not mean that there is infinite matter. I think that information is defined by degrees of freedom, and there can be no more information stored in a given object than there are degrees of freedom in that object. The states of these degrees of freedom fully define a given system, so if there is a finite amount of "information" in a region of space, then the potential continuity or infinite precision of space in that region is irrelevant.

Even if there is an infinite amount of matter spread throughout infinite space, most of it is moving away from us faster than the light it is emitting, which will never reach us. If we're trying to understand why we are experiencing infinity here and now, then it seems to me that infinite space does not account for that. Perhaps space is infinitely complex on the smaller scales, but then the Bekenstein bound seems to thwart this idea (Maybe the bound is wrong).

elaborate on this complicatedness.

and also this STILL doesn't prove or point to a finite universe.

If the universe is expanding, and will conceivably do so forever, then it is only bound in the realm of time, which we don't really have a firm grasp of anyway. Outside the universe, where TIME is thought not to exist, the universe is at once infinite, finite, minute AND non-existent! There's a conundrum - beyond the realm of time the universe can be said to be all those things at once, including infinite, in which case there is no "outside the universe" - MEANING THERE IS NO PLACE TO HAVE NO TIME.

And there is. And there isn't. And there is, and there isn't. But that is our polar mind attaching itself to simple binaries for the sole reason that we are not equipped to imagine different contradictory states co-existing, the non-existence of time or the notion of infinity itself.

Now I am going to have a coffee to try and clear out the cobwebs of confusion I have introduced to my own mushy grey abacus.


Cheers,

JJJjjJJjJbBBbBBbBbaAaaAAAaAaAaArrRRRrRrRrRRrKkKkkkKKk

"elaborate on this complicatedness"

Dark energy currently makes up 70% of the universe. As the universe accelerates, this will go up to 100%. A universe dominated by dark energy can be approximated by de sitter space. The cosmological event horizon can then be treated in the same way as the surface of a black hole (actually, a black hole turned inside out). This allows us to use the Bekenstein-Hawking formula to do the calculation.

The Bekenstein-Hawking formula is:

S = A/4A0

Where A0 is the planck area and A is the surface area of the cosmological horizon. The radius of the cosmological horizon is 62 billion light years (or 10^25 m) and A0 = 10^-70 m^2. Placing these numbers in the formula gives the answer of 10^120 bits.

"and also this STILL doesn't prove or point to a finite universe"

It's not a mathematical proof, it's an argument based on known physics.

hehe. good luck!!

"A cosmological horizon is a measure of the distance from which one could possibly retrieve information" Wikipedia

But what makes you think there is nothing beyond that?

PS: You obviously know more about astrophysics and cosmology than me but I believe philosophy, abstract logic and intuition just as powerful tools for exploring reality.

Whether there is something beyond that is of no consequence to us. We could never know and it could never affect us. It is completely irrelevant to anything we may be experiencing here in the universe.

But that doesn't mean it doesn't exist. And surely it could effect us via gravity (although they don't know how this works yet right?) or tachyons (although these are theoretical)?

Gravity waves travel at the speed of light. Tachyons on the other hand... The Bekenstein bound (which I can't really say I'm sold on yet) relates the maximum energy to mass. Tachyons have imaginary mass, so the upper bound on information would be a complex number. What is complex information?

Don't get me wrong, I make plenty of assumption in claiming that infinity does not exist here and now. My assumptions could all be wrong... They probably are wrong. Even if the Bekenstein bound is true, it only accounts for information that is contained in a region of space at a given time. As far as I can tell, it does not account for transient information. In other words, a single bit can convey infinite information per second if it is flipped on and off infinitely fast. How many bits can be contained in a given region of space says nothing about the temporal complexity of the information in that space (Perhaps I am misusing the term "information" here).

Here's a nice paper on this topic by Seth Lloyd at MIT.

Computational Capacity of the Universe

"Merely by existing, all physical systems register information. And by evolving dynamically in time, they transform and process that information. The laws of physics determine the amount of information that a physical system can register (number of bits) and the number of elementary logic operations that a system can perform (number of ops). The universe is a physical system. This paper quantifies the amount of information that the universe can register and the number of elementary operations that it can have performed over its history. The universe can have performed no more than 10^120 ops on 10^90 bits."

Wow. Nice find! I'll take a look when I get the chance.