Total Posts:4|Showing Posts:1-4
Jump to topic:

Is a Poincare Recurrence Really possible?

R0b1Billion
Posts: 3,733
Add as Friend
Challenge to a Debate
Send a Message
4/28/2014 6:58:43 PM
Posted: 2 years ago
A Poincare Recurrence refers to the time it would take for a black hole with the estimated mass of the universe to randomly achieve a state in which it was identical to the way it is now. They use a black hole, I imagine, because it gives us a nice clean and simple way of imagining all that stuff without having to worry about lots of other variables. A simple example would be a box filled with particles. If we start all the particles in one corner (in a specific arrangement) and let it go, the particles will fly around endlessly. Although the chances of all those particles going back into the corner and being arranged identically to the start are low, they are non-zero and it is really just a matter of time before they do if left to randomly fly around indefinitely.

Similarly, the universe, if left for an infinite amount of time, will end up going back to the way it is now someday. In many googols of years all matter will thermalize into a homogenous soup and entropy will effectively "kill" any type of meaningful phenomenon. However, the uncertainty principle states that the energy state of each planck volume of space must be non-zero, which in turn means that energies must fluctuate and eventually, in say 10^10^56 years or so, energies will fluctuate just right so that there will be another big bang.

In this same fashion we may imagine that given an unimaginable amount of time, things will just happen to come back to exactly where they are now.

Is this conceivably possible? Would you go even further and say that every conceivable state of matter must be expressed if time is infinite? I am Okay with the first possibility, but not the second.
Beliefs in a nutshell:
- The Ends never justify the Means.
- Objectivity is secondary to subjectivity.
- The War on Drugs is the worst policy in the U.S.
- Most people worship technology as a religion.
- Computers will never become sentient.
PeacefulChaos
Posts: 2,610
Add as Friend
Challenge to a Debate
Send a Message
4/28/2014 7:25:44 PM
Posted: 2 years ago
At 4/28/2014 6:58:43 PM, R0b1Billion wrote:

A simple example would be a box filled with particles. If we start all the particles in one corner (in a specific arrangement) and let it go, the particles will fly around endlessly. Although the chances of all those particles going back into the corner and being arranged identically to the start are low, they are non-zero and it is really just a matter of time before they do if left to randomly fly around indefinitely.

Wouldn't this situation defy the second law of thermodynamics?

The only possible way for the molecules to arrange themselves exactly in their original position would for them to all simultaneously ricochet off one end of the box in such a fashion and in such an order that the original molecules go to the corner of the box they started at and in the positions they were originally in. Furthermore, the timing of such a situation would be absolutely crucial. If even half a second off, the molecules will have already moved and the formation would be broken. If the molecules were moving at different speeds, then it would be even harder to get them back into their original position.

It's so close inconceivably close to zero that it might as well be zero.
PeacefulChaos
Posts: 2,610
Add as Friend
Challenge to a Debate
Send a Message
4/28/2014 7:26:52 PM
Posted: 2 years ago
Edited. Not sure why it didn't italicize.

At 4/28/2014 6:58:43 PM, R0b1Billion wrote:

A simple example would be a box filled with particles. If we start all the particles in one corner (in a specific arrangement) and let it go, the particles will fly around endlessly. Although the chances of all those particles going back into the corner and being arranged identically to the start are low, they are non-zero and it is really just a matter of time before they do if left to randomly fly around indefinitely.

Wouldn't this situation defy the second law of thermodynamics?

The only possible way for the molecules to arrange themselves exactly in their original position would for them to all simultaneously ricochet off one end of the box in such a fashion and in such an order that the original molecules go to the corner of the box they started at and in the positions they were originally in. Furthermore, the timing of such a situation would be absolutely crucial. If even half a second off, the molecules will have already moved and the formation would be broken. If the molecules were moving at different speeds, then it would be even harder to get them back into their original position.

It's so close inconceivably close to zero that it might as well be zero.
R0b1Billion
Posts: 3,733
Add as Friend
Challenge to a Debate
Send a Message
4/28/2014 8:40:54 PM
Posted: 2 years ago
At 4/28/2014 7:26:52 PM, PeacefulChaos wrote:
Edited. Not sure why it didn't italicize.

At 4/28/2014 6:58:43 PM, R0b1Billion wrote:

A simple example would be a box filled with particles. If we start all the particles in one corner (in a specific arrangement) and let it go, the particles will fly around endlessly. Although the chances of all those particles going back into the corner and being arranged identically to the start are low, they are non-zero and it is really just a matter of time before they do if left to randomly fly around indefinitely.

Wouldn't this situation defy the second law of thermodynamics?

Entropy, for humans, is perhaps the most dependable principle one has for two reasons. The first is that humans are made up of biological processes (in turn based on physical processes) and our entire existence revolves around creating and maintaining more processes (i.e., transforming energy). Entropy is magnified during any type of energy transformation (any process of doing just about anything) and therefore whatever a human does, either directly or indirectly, only works to accelerate entropy. However, that isn't to say that entropy is always maintained no matter what. (explained more below).

The second reason is that we exist in short time-frames. One hundred years for a life, a few thousands for our entire historical civilization, perhaps a million for our history as a species and maybe a billion or two if we somehow find a way to perpetuate our existences to their fullest extents (using means that are as of yet completely unimaginable). But even billions of years are drops in the bucket for the time-frames for a Poincare Recurrence. One billion years is 10^9 years. I'm talking about 10^100,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000 years. This number is big. How big? It's impossible to express. If you wanted to WRITE this number, and you had the capability of writing so small that you could put a "zero" on every single atom that makes up the Earth (you had a really fine-point pen and lots of time on your hands) then you'd need a million Earths before you'd have enough atoms just to write the number down.

For these two reasons, entropy is no longer really a factor (explained further below).

The only possible way for the molecules to arrange themselves exactly in their original position would for them to all simultaneously ricochet off one end of the box in such a fashion and in such an order that the original molecules go to the corner of the box they started at and in the positions they were originally in. Furthermore, the timing of such a situation would be absolutely crucial. If even half a second off, the molecules will have already moved and the formation would be broken. If the molecules were moving at different speeds, then it would be even harder to get them back into their original position.

It's so close inconceivably close to zero that it might as well be zero.

Given normal time-frames that is true, but given 10^10^56 years, now any non-zero number becomes enormous.

This number also gives opportunities to sudden drops in entropy. The Uncertainty Principles precludes entropy from being absolutely infallible, and sudden drops in entropy happen all the time at the quantum level. If you wait 10^10^56 years, that's enough time for the chances of a huge, concerted drop in entropy which yields a very highly-ordered universe like ours. Entropy will continue to dominate the universe as it always does, but the extremely low (but non-zero) probability of it failing will manifest itself significantly on hyper-astronomical time-frames.
Beliefs in a nutshell:
- The Ends never justify the Means.
- Objectivity is secondary to subjectivity.
- The War on Drugs is the worst policy in the U.S.
- Most people worship technology as a religion.
- Computers will never become sentient.