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Ben the Ignorant

Infinite repetition or infinite variety?

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This question has been bothering me for years. Assuming the Universe is infinite in size and/or duration (and doesn't become a Big Crunch or a Big Freeze), will every situation repeat itself because there is an infinite amount of time to allow the probability to manifest itself? Is there already a copy of me living the same situation in a twin room, on a twin planet, with every detail being identical down to the position of every dust grain, every droplet of water in the clouds, every subatomic particle?

In an infinite place the probability for identical situations becomes 100%? In an infinite time, same? Or does infinity make infinitely diverse situations that never repeat themselves?

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My personal belief is that it is Infinite and that every possible eventuality can, will, has and does happen. 

Of course I may be wrong but I'll won't live long enough to see it not happen. 

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Infinite time and finite size implies repetition.

Infinite size and finite time does not imply repetition. It is actually much more complicated than that as there are different types of infinities.

Take for example number scale - we can say that it goes onto infinity when we move to the right - there are infinite amount of numbers larger than 1 (and sequential for that matter - for any number there are infinite amount of larger numbers). However, there is infinity right here in our "backyard". Take interval 0-1 - there are infinite amount of numbers there as well.

In infinite size universe, you can get infinite number of copies of the same event / setup, but problem is "surroundings". Can we say for certain that infinite number of same events have the same things happening "to the left" and "to the right"? Where do we draw a boundary saying we observe this configuration only and whatever lays beyond boundary has no influence on configuration of the system?

 

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Posted (edited)

My understanding (i.e. probably incorrect) is that the current evidence points to the universe being of a finite (but unmeasurable) size and that it has been evolving since its creation 13.8 billion years ago.  It will continue to evolve, with eventually every bit of energy and mass turning into a low energy state - the heat death of the universe.  If correct, this would lead to the conclusion whilst the universe would theoretically exist for an infinite time and continue to expand at an ever-increasing rate, it could not play out all potential scenarios before the present star-forming stage finished. 

However, if you subscribe to the multiverse theory that we live in just one of an infinity number of possible universes, then there could be an infinite number of exact copies of our universe, and an infinite number of all other possible universes, duplicated an infinite number of times and that has always been the case! :icon_scratch: :icon_scratch:

Of course, the problem with all of this is that, with the discovery of 'dark energy', it is highly possible that our current fundamental understanding/ideas of how the universe works, and indeed what it is, may well be completely wrong! 

Therefore, as any theory we have of the universe is provisional and possibly completely wrong, and the fact that I can only surmise that my existence is simply down to the consequence of a 13.8 billion year old chain of random quantum events, the best thing I can do is leave the theorising about the true nature of the universe to people MUCH cleverer than me and celebrate the wonder of my meaningless existence with another pint of Old Speckled Hen.  ?

Cheers

Edited by michaelmorris
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Actually we have no idea if universe is infinite in spatial extent or finite.

Only piece of evidence we now have is limits on lower size in case of certain topologies. Our measurement of curvature points to very flat universe - curvature is less than very small number. This for example tells us that if we live in positively curved space - radius of curvature must be very large and hence universe can't be smaller than certain size.

I want to expand on my previous answer and case of finite time and infinite universe.

I thing that two same events are not possible in strict sense in finite time and infinite universe, precisely due to surroundings. In order to have two truly same events they need to have exact surroundings. But if we take event A and event B and draw a line between them, one event will have its own copy "to the left" and other will have its own copy "to the right" - so they are not the same - they can be differentiated by this.

Only way to get exact copy of event in infinite universe is to have infinite number of exact copies - like periodic function, whole universe would need to be one periodic function - and it would always be in state of infinite number of copies. Probability for this is infinitesimally small.

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I recall this video from way back touching on the subject. I'll leave it to the cosmologist to elaborate. To me it seems to ask some more questions that leaves me scratching my head, but it is an interesting gedanken-experiment nonetheless.

  

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The LCMB concordance model supports a Universe that is and always has been spatially infinite. It started at a finite time in the past but is unbounded in the future.

It may be wrong but that is the current consensus.

Regards Andrew 

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This quote for wiki article on shape of the universe explains quite a bit:

Quote

The curvature of the universe places constraints on the topology. If the spatial geometry is spherical, i.e., possess positive curvature, the topology is compact. For a flat (zero curvature) or a hyperbolic (negative curvature) spatial geometry, the topology can be either compact or infinite.[14] Many textbooks erroneously state that a flat universe implies an infinite universe; however, the correct statement is that a flat universe that is also simply connected implies an infinite universe.[14] For example, Euclidean space is flat, simply connected, and infinite, but the torus is flat, multiply connected, finite, and compact.

In general, local to global theorems in Riemannian geometry relate the local geometry to the global geometry. If the local geometry has constant curvature, the global geometry is very constrained, as described in Thurston geometries.

The latest research shows that even the most powerful future experiments (like SKA, Planck..) will not be able to distinguish between flat, open and closed universe if the true value of cosmological curvature parameter is smaller than 10−4. If the true value of the cosmological curvature parameter is larger than 10−3 we will be able to distinguish between these three models even now.[15]

Results of the Planck mission released in 2015 show the cosmological curvature parameter, ΩK, to be 0.000±0.005, consistent with a flat universe

Thing is that we don't know, and our current measurement says it's very close to 0 but does not exclude both small positive or small negative value for curvature.

For positive curvature we will have finite universe. For 0 and negative curvature we can either have infinite universe if we stick to cosmological principle (isotropic and homogeneous) or we can have finite universe if we abandon idea of cosmological principle (like in torus which is flat in terms of curvature - curvature is 0, but it is multiple connected, meaning it is not isotropic - there are preferred directions).

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Though, it cannot exactly repeat - entropy always increases (laws of thermodynamics) and so at any point in the future, there is a different universal state. 

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1 hour ago, vlaiv said:

 

Thing is that we don't know, and our current measurement says it's very close to 0 but does not exclude both small positive or small negative value for curvature.

 

The problem is you can never show it is zero exactly by any real world set of measurements. FAPP it is flat to scales well beyond the size of the observable universe. Unless, that is, the whole LCMB model is discredited. 

Regards Andrew 

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2 hours ago, vlaiv said:

In order to have two truly same events they need to have exact surroundings.

So the two same events should be two same whole universes, is that possible in the Multiverse case?

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4 minutes ago, Ben the Ignorant said:

So the two same events should be two same whole universes, is that possible in the Multiverse case?

The whole set  of multiverse theories is extremely speculative. 

You could safely believe anything about them without fear of evidence proving you wrong! ?

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2 hours ago, andrew s said:

a Universe that is and always has been spatially infinite. It started at a finite time in the past

In that case, did the Universe itself start at a finite time in the past, or only its content?

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17 minutes ago, Ben the Ignorant said:

In that case, did the Universe itself start at a finite time in the past, or only its content?

In normal usage the Universe is everything there is so the Universe is its content.

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You could say that the Universe is repetitive, it builds stars>planets>life>mobile phones by the bucket load :D

Alan

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Does time repeat itself past the big crunch?  I love this segment of a Futurama episode:

 

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The current view is there will not be a big crunch (nor to a anticipate the next question) a big rip. Views may change with new data.

Futurama is possibly not the best source of serious science. ?

Regards Andrew 

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Can't contribute to this discussion as the whole subject boggles my brain too much!!  ?

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Posted (edited)
1 hour ago, Alien 13 said:

You could say that the Universe is repetitive, it builds stars>planets>life>mobile phones by the bucket load :D

Alan

That can only be done locally and sustained for short periods as it would contradict the 2nd law of thermodynamics if continued throughout the Univers for all time. But hay ho who knows it might turnout to be false.?

Regards Andrew 

PS in any case all we could see via our telescopes would be phones taking selfies, not star, planets etc just phones.

Edited by andrew s
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2 hours ago, Ben the Ignorant said:

So the two same events should be two same whole universes, is that possible in the Multiverse case?

We really need to start by defining what constitutes same events. If we jump strait ahead to "there is my double, and your double and they are having this same conversation" thing, it pays to think of regular earth twins. We know that same genetic makeup does not generate same persons. Sometimes very similar, but never the same. Would they be the same identical people if they had exactly the same history (all events in their lives unfolded in exact same way)? This tells us very important thing about two systems being the same - they need to have same history. So it's not the event as such that we need to think of being the same, but whole trajectory in configuration space.

I have to admit that I have no clue what Multiverse is, nor how it's modeled / imagined, what ever.

My best guess is that multiverse is just universe that is so wast and because of inflationary period some sections of universe are no longer in causal contact with others and have "evolved" in different ways (different physics and the reset). I'm also aware of eternal inflation proposal - where local universes are regions where inflation ceased for some time (???) but the rest of universe is inflating at same crazy speed (???)

Seriously weird stuff.

1 hour ago, Ben the Ignorant said:

In that case, did the Universe itself start at a finite time in the past, or only its content?

Time is also "content" of universe - no reason to think that time should exist separately from universe (other content of universe) - so we can't even speak of universe coming to existence at some point in past. We can only speak of time past since time (along everything else) came into existence (or transitioned to this state of affairs - not sure if we can distinguish between the two).

53 minutes ago, andrew s said:

The current view is there will not be a big crunch (nor to a anticipate the next question) a big rip. Views may change with new data.

Futurama is possibly not the best source of serious science. ?

Regards Andrew 

Ha! Big rip :D

Anticipation of an event will not make it go away :D

I was under impression that accelerated expansion of universe facilitates the big rip? We now have strong indication that we are in accelerated expansion phase.

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13 minutes ago, vlaiv said:

 

I was under impression that accelerated expansion of universe facilitates the big rip? We now have strong indication that we are in accelerated expansion phase.

If you take the big rip as being that the scale factor goes to infinity in a finite time then it depends, based on the LCMB model, on the equation of state for dark matter which is :

w = p/ρ   ( with c=1) only if w < -1. 

Best current view is w = -1.006 +/- 0.045 which  is consistent with Λ being the cosmological constant w = -1 hence current consensus view is no big rip.

As always room for both options in the error bars.

Regards Andrew

 

Regards Andrew

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Interesting question, if infinite and those possiblities surely exist than you may rest easy knowing someone exactly like you or an infinite number of you's are covering this question in excess as we speak, if not than you are just you and with no other you's around and you get total credit for this brilliant question. Either way this turns out, best of Luck and Clear Skies of course ?

                           Freddie...

 

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Having one twin or infinite twins, past twins or future twins sounds too weird and downright creepy to be the case, taking intuition as a clue when little else is reliable.

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Posted (edited)
4 hours ago, Gina said:

Can't contribute to this discussion as the whole subject boggles my brain too much!!  ?

Me too, Gina. And I can never forget a wonderful statement by an eminent physicist (very eminent but I can’t remember his name ?) who said: ‘For a mathematician infinity is just a very big number; for a physicist it is an abomination!’

Still mind-boggling but I love the differentiation.

EDIT: Michio Kaku, US theoretical physicist.

Edited by Floater
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4 hours ago, Gina said:

Can't contribute to this discussion as the whole subject boggles my brain too much!!  ?

I could contribute barely more than the first question.

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