If the universe is infinite, does that mean that everything exists somewhere?

[Chalnoth]

And that old idea of monkeys typing Hamlet, given enough time, is nonsense for much the same kind of reason.

Not really, because that idea is based upon simple probability, and assumes that the monkeys are typing in a purely random fashion. If that's the case, then as time gets large enough, the probability that they successfully type hamlet will approach one. Of course, the time required to do that is unbelievably large.

 

[Freeman Dyson]

In an infinite universe, anything above zero probability happens an infinite amount of times. If the universe were infinite it would take an infinite amount of time to figure that out. The finite hides the infinite.

 

[Chronos]

About 3 minutes after the big bang the universe was cool enough for elementary particles [e.g., protons] to begin to form.

 

[ViewsofMars]

I'm going to play around with what you said Freeman. (I'm in one of those kind of moods today. I hope you don't mind. )

In an infinite universe [with dark energy], anything above zero probability happens an infinite amount of times [due to dark energy].

I've inserted within your thoughts my thoughts noted within the brackets.

If the universe were infinite it would take an infinite amount of time to figure that out. The finite hides the infinite.

Interesting. Two comments:

1. "However, the results of the WMAP mission and observations of distant supernova have suggested that the expansion of the universe is actually accelerating which implies the existence of a form of matter with a strong negative pressure, such as the cosmological constant. This strange form of matter is also sometimes referred to as the "dark energy". If dark energy in fact plays a significant role in the evolution of the universe, then in all likelihood the universe will continue to expand forever." (From NASA, Is the Universe Infinite?
http://map.gsfc.nasa.gov/universe/uni_shape.html)

2. "Since light travels at a finite speed, distant objects are seen as they existed in the past. We see the Sun not as it is now, but how it was eight minutes ago. (The Sun is eight light minutes away from the Earth). We see the nearby stars as they were several years ago. We see Andromeda, the nearest spiral galaxy as it was roughly 2.5 million years ago. Thus, the most distant objects that we see are the oldest objects that we can directly detect.

" Quasars are the most distant distinct objects that astronomers have been able to detect. In a region smaller than our solar system, a quasar emits more light than our entire Milky Way galaxy. Quasars are believed to be supermassive black holes, whose masses exceed that of a million Suns, and whose pull is swallowing gas and stars from their host galaxies. They shine brightly by converting the gravitational energy of the infalling material into light. The most distant quasars are seen at a time when the universe was one tenth its present age, roughly a billion years after the Big Bang." (From NASA- When Did the First Cosmic Structures Form?
http://map.gsfc.nasa.gov/universe/rel_firstobjs.html)

 

[Dmitry67]

No, of course not.

Some infinities are bigger than others, and the infinity of distinguishable configurations of things is a factorial kind of infinity that is always much, much bigger than the infinity of the number of things.

Think of building a universe as a collection of things, starting with a just a few. As your universe grows the number of ways the things can be arranged differently grows very much faster than their number. So all possible configurations (everything) is something that can never be realized. You needn't even struggle with the impossibility of imagining infinity. And that old idea of monkeys typing Hamlet, given enough time, is nonsense for much the same kind of reason.

Max Tegmark does not agree with you:

http://space.mit.edu/home/tegmark/multiverse.html

How many parallel universes are there?
Why must we have duplicates?

From Richard Reeves, valueprint@earthlink.net, April 18, 2003 14:23:31
Q: Given infinity, why isn't it equally plausible that the worlds within it would express infinite variety, rather than repetition
The answer is that there are only a finite number of possible states that a Hubble volume can have, according to quantum theory. Even classically, there are clearly only a finite number of perceptibly different ways it can be.

How rigorous is this?

From Bert Rackett, bertrckt@pacbell.net, Sat Apr 19 22:22:13 2003
Q: I very much enjoyed reading your Scientific American and Science and Uitimate Reality papers, but I am entirely befuddled about your estimates for likely distance of an identical environment. You claim that the volume may be completely defined by a (very long) list of binary values denoting the presence or absence of a proton, but this of course oversimplifies things.
A: Although classical physics allows an infinite number of possible states that a Hubble volume can be in, it's a profound and important fact that quantum physics allows only a finite number. The numbers I mentioned in the article, like 10^10^118 meters, were computed using the exact quantum-mecanical calculation, and the classical stuff about counting protons in a discrete lattice arrangement was merely thrown in as a pedagogical example to give a feel where the numbers come from, since that turns out to give the same answer.

Why must all regions have duplicates, not just one?
From Jeffery Winkler, jeffery_winkler@mail.com, Oct 13, 2003, at 0:58
Q: Just because something is infinite, does not mean that all possibilities are realized. The number pi is infinitely long, pi = 3.14159... and in that case, all combinations of digits are realized. However, the number 1/3, converted into a fraction, is also infinitely long, 1/3 = .33333... and in that case, all combinations of digits are not realized.
A: That's correct: infinite space alone guarantees only that SOME Hubble volume will have a duplicate, not that our own will. However, if (as in the current cosmological standard model) the cosmic density fluctuations originate from quantum fluctuations during inflation, their statistical properties DO guarantee that our (and indeed every) Hubble volume has a duplicate.
Is there a countable or uncountable infinity of universes?

Is it countable even with continuous wave functions?
From David Fotland, fotland@smart-games.com, August 3, 2003 21:09:49
You argued that the total number of possible states in a universe is finite, so if the total of all universes is infinite, then every possible universe must exist. I understand that quantum states have discrete vales, but the wave function is a continuous function. Can't the probabilities that give the possible locations of particles have any real value?
Interestingly, they can't: you can prove that in a finite volume, there's only a discrete number of allowed quantum wavefunctions. If the energy is finite, it's even a finite number.
But even a hydrogen atom has infinitely many states!
From Attila Csoto, csoto@matrix.elte.hu, Wed Mar 17 12:59:29 2004
Q: You say in your papers that the number of possible quantum states within the Hubble-volume is finite. I understand your argument, but there is a problem which puzzles me. If we single out one hydrogen atom in our Hubble volume, it has itself an infinite number of different bound states. So one could imagine a Hubble sphere next to ours which is the same as ours except that this hydrogen atom iis not in its ground state but in the next excited state, and in the next sphere in the next higher state, etc. These universes differ from each other by a tiny amount of energy but I don't think that this should matter. So, my question is: how can we have a finite number of possible quantum states in our sphere, if one hydrogen atom already has an infinite number of possible bound states?
A: There's infinitely many bound states if only space is truly infinite. There's in fact a beautiful old paper by Erwin Schrödinger deriving the exact solutions for a hydrogen atom in a closed finite Universe, showing that in this case, the number of bound states is finite.

 

[ViewsofMars]

Dmitry67, you have presented Max Tegmark whose last publication was from 2003, Richard Reeves (2003), Bert Rackett (2003), Jeffery Winkler (2003), David Fotland (2003), Attila Csoto (2004).

The year is 2009. We have come a long way since 2003-2004. You may wish to review the topic “offshoot from 'Theoretically how far can one see in the universe'” p.g. 3, and look at my contributions (msg’s 40 and 42) that have the most current evidence (2008 and 2009) that continues to support the Big Bang Theory, which is the standard model. I've provided the link below for you and others to explore.

I should also mention that Steven Weinberg on July 7, 2009 gave a lecture at CERN. He talked about inflation. Near the end of his presention he did say, "The world is really what we've always known, the standard model plus relativity." He wasn't trying to discourage string theorists yet he knows as a scientist that observations are essential if you are going to call it SCIENCE.

https://www.physicsforums.com/showthread.php?t=338032&page=3

 

[Dmitry67]

It appears that you are not familiar with the most important article: http://arxiv.org/abs/0704.0646 - really genious!
and year is 2007 - not 2003. Do you have any other arguments against his logic except the year of publication?

 

[ViewsofMars]

It appears that you are not familiar with the most important article: http://arxiv.org/abs/0704.0646 - really genious! and year is 2007 - not 2003.

Don't be curt or snippy with me. Dmitry67, I was going off the first link you gave when mentioning Max Tegmark. I didn't see this abstract you are now presenting on his website. The *abstract* by Max Tegmark is entitled, "The Mathematical Universe". As we know, math isn't science. Futhermore, it is a hypothesis of his.

Do you have any other arguments against his logic except the year of publication?

The year of publication is important as you will note with WAMP. I think it is important to see the current information. I've earlier provided you a link to another topic for you to review.

I know now that Max Tegmark's has a *hypothesis* that has been submitted to Cornell University. I'm sorry to disappoint you, but I'm not a fan of his "consciousness" and "parallel universes". I don't find his hypothesis in NASA. Also, hypothesis don't make it into internationally known peer-reviewed journals such as Science and Nature.

 

[Dmitry67]

At first, could you clarify what do you mean by "math isn't science"? Do you mean that we can't prove self-consistency of any axiomatic system, or something else?

 

[Chalnoth]

Dmitry67,

Yes, I've heard this argument about "copy universes" before. I don't think it necessarily holds.

Here is the problem, as I see it: quantum mechanics doesn't guarantee that absolutely everything happens. It just says that many things happen. For instance, let's say I take a simple harmonic oscillator, and prepare it in the following state:

$$\mid \psi \rangle = \frac{1}{\sqrt{2}} \mid E_1 \rangle + \frac{1}{\sqrt{2}} \mid E_2 \rangle$$

Here we have a system in a mixture of two states. If I take a measurement of the energy at t=0, I will obtain with 50% probability $$E_1$$, and $$E_2$$ with 50% probability.

Now step back and consider what I might be able to conclude if I didn't know how the state was prepared, but only am aware of my measurement of the state. For instance, if I measure $$E_2$$, what can I conclude about the original state? Can I conclude that $$E_3$$ was also represented? That some other "me" observed $$E_3$$ while I observed $$E_2$$? Certainly not! I do know that whatever state the system was in, it was in a specific state, and my measurement of $$E_2$$, while not ruling out the possibility of a component of the wavefunction inhabiting $$E_3$$, there is no reason to believe that $$E_3$$ was represented (or $$E_1$$, for that matter).

Therefore I claim that even with taking quantum fluctuations into account, I don't see why all possibilities need to be represented. Regions of the universe are still due to unitary evolution of a quantum mechanical wave function. They are still deterministically dependent upon the initial conditions. And so even though many things surely do happen, we can't say with confidence that all possible things do.

However, that said, I do think that it is entirely possible that all possible things do happen. I particularly like Tegmark's "mathiverse" idea, for instance. I just don't think we can conclude from what we know today that it's actually true that all things possible do happen.

 

[rasp]

If the universe is infinite, does that mean that everything exists somewhere, besides obviously impossible things like a star that contains oxygen but doesn't contain oxygen or a 4-sided triangle?

The answer to your question depends on what you mean by everything. If by everything you mean all that is, then everything fits into a finite Universe, an infinite Universe is not needed. If your definition of everything is what is existent and also on what doesn't exist but could exist, then an infinite universe doesn't help you, you need either a many world interpretation, or a Hilbert Space in QM.

 

[xantox]

Therefore I claim that even with taking quantum fluctuations into account, I don't see why all possibilities need to be represented.

Do you mean, by questioning the assumptions of ergodicity and equilibrium of the inflationary patches?

 

[Chalnoth]

Do you mean, by questioning the assumptions of ergodicity and equilibrium of the inflationary patches?

I'm pretty sure those are taken to be approximating assumptions.

 

[xantox]

I'm pretty sure those are taken to be approximating assumptions.

Yes, they are just assumptions – just making sure whether you agree that if they are true then "copy universes" would hold too, or if your argument was another one. Although those assumptions are supported by unitarity, quantum gravity effects such as backreaction on the metric could indeed subtly change the picture.

 

[Entropee]

I'm not sure anything in our universe at all can lead us to believe anything at all about a "different" universe. Just my opinion.

 

[Chalnoth]

I'm not sure anything in our universe at all can lead us to believe anything at all about a "different" universe. Just my opinion.

As long as we believe that the laws of physics are invariant of where you happen to be, yes, we can say some things about regions which are outside of our observable bubble.

 

[ViewsofMars]

Replying to Dmitry67, we have Math teachers and Science teachers. The two are distinctly different. Science is based on the scientific method, whereas Mathematics is not.

 

[Entropee]

As long as we believe that the laws of physics are invariant of where you happen to be, yes, we can say some things about regions which are outside of our observable bubble.

Yes inside our "observable bubble". I just meant that we have to reason to believe our universes laws of physics hold true in a different universe (whatever that means).

 

[Freeman Dyson]

"'the universe must go through a calculable number of combinations in the great game of chance which constitutes its existence . . . In infinity, at some moment or other, every possible combination must once have been realized; not only this, but it must also have been realized an infinite number of times."

-nietzsche

 

[Chalnoth]

Yes inside our "observable bubble". I just meant that we have to reason to believe our universes laws of physics hold true in a different universe (whatever that means).

Typically it just means something outside of our observable bubble. And while we may have reason to believe that there are different effective low-energy laws of physics, there are good reasons to believe that the fundamental laws remain the same no matter what.

 

[sokrates]

What are those good reasons to believe the laws of physics are the same outside our bubble?

I have a feeling whatever you'll argue is going to be exclusively about "observable" bubble, almost by def.

 

[Chalnoth]

What are those good reasons to believe the laws of physics are the same outside our bubble?

One way to look at it is that if there is stuff outside our observable universe (which there almost certainly is), then it was at one point connected to our observable universe. If it didn't follow the same fundamental laws when it was in contact, then you'd have a contradiction.

 

[Dmitry67]

I know now that Max Tegmark's has a *hypothesis* that has been submitted to Cornell University. I'm sorry to disappoint you, but I'm not a fan of his "consciousness" and "parallel universes". I don't find his hypothesis in NASA. Also, hypothesis don't make it into internationally known peer-reviewed journals such as Science and Nature.

Of course there is no proof for his hypotesis. But compare it to the Smolins evolving law: while Max Tegmarks works is quite strict and logical (and in his article he gave answers to most of the questions I found here, so it was enough just to quote his original work) Smolins evolving law is a pure handwaving.

Also, Max Tegmarks hypotesis has several falsifiable predictions so it can be testes in a future. I think this is the best we have for now.

 

[Dmitry67]

Dmitry67,
Here is the problem, as I see it: quantum mechanics doesn't guarantee that absolutely everything happens.

Yes, definitely, it is interpretation-dependent. In a local region "everything happens" only in MWI.

But interestingly enough, an argument about our distant 'copies' does not depend on MWI and even more, even if you insist that some possible configurations are never realized then there are even MORE copies!

Because if you fill the infinite void with all possible configurations, you will soon ran out of distinct ones (check Max Tegmarks Q&A I posted before). If you insist that only a subset of possible configurations is used, then you will run out of configurations even sooner!

 

[Dmitry67]

Replying to Dmitry67, we have Math teachers and Science teachers. The two are distinctly different. Science is based on the scientific method, whereas Mathematics is not.

You had probably bad teachers.
You agruments are strange: year of publication, your personal bad luck with teachers.

Can you point an exact place in max Tegmark's logic (in Q&A) which is wrong, as you believe? And explain, why do you think so?

 

[Dmitry67]

One way to look at it is that if there is stuff outside our observable universe (which there almost certainly is), then it was at one point connected to our observable universe. If it didn't follow the same fundamental laws when it was in contact, then you'd have a contradiction.

Yes.
It is more tricky in an accelerating expanding universe with consmological horizons. In such universe some places will NEVER be in causal contact with each other.

However, still you can define a sequence of intersecting bubbles B0...Bn, so if laws are different in B0 and Bn, there must be a bubble Bx (0<=x<=n) where both laws are effective at the same time.

The same argument applies not only in space but it time, law can not 'change' in time, for that reason I believe that Smolin's evolving law is a nonsense.

 

[Chalnoth]

Yes, definitely, it is interpretation-dependent. In a local region "everything happens" only in MWI.

No, I'm speaking purely in terms of MWI here. Even in that case, not everything necessarily happens. MWI just takes the unitarity of the wavefunction seriously: it evolves forward in time according to the equations of motion, with no collapse. This doesn't indicate that everything happens, just that many different things do.

I don't think you can take currently-known quantum mechanics and conclude that everything happens: you still have to add it in as an additional assumption.

Because if you fill the infinite void with all possible configurations, you will soon ran out of distinct ones (check Max Tegmarks Q&A I posted before). If you insist that only a subset of possible configurations is used, then you will run out of configurations even sooner!

Ah, yes, well, if the universe truly is infinite in extent, then obviously there will be an infinite number of copies. However, we don't know that the universe is infinite in extent.

 

[Chalnoth]

Yes.
It is more tricky in an accelerating expanding universe with consmological horizons. In such universe some places will NEVER be in causal contact with each other.

In the future. But in the past they would have been in contact (this would have been during the inflationary epoch for the most distantly-separated components of our universe).

The same argument applies not only in space but it time, law can not 'change' in time, for that reason I believe that Smolin's evolving law is a nonsense.

Well, I'm pretty sure that all serious considerations of evolving or otherwise changing physical laws are actually just talking about the effective low-energy physics. They tend to still rely upon an underlying fundamental theory that is quite invariant. But this isn't really saying something profound about our universe: Andy Albrecht and Alberto Iglesias showed a couple of years back that if you take a random, time-varying Hamiltonian, and simply invoke the clock ambiguity, you can always find a trajectory in this space that leaves the Hamiltonian time-invariant. That is to say, just the fact that we can change coordinates means that it's always possible to write down time-invariant laws of physics.

Here's one of their relevant papers:
http://arxiv.org/abs/0805.4452

 

[Dmitry67]

1
No, I'm speaking purely in terms of MWI here. Even in that case, not everything necessarily happens. MWI just takes the unitarity of the wavefunction seriously: it evolves forward in time according to the equations of motion, with no collapse. This doesn't indicate that everything happens, just that many different things do.

I don't think you can take currently-known quantum mechanics and conclude that everything happens: you still have to add it in as an additional assumption.

2
Ah, yes, well, if the universe truly is infinite in extent, then obviously there will be an infinite number of copies. However, we don't know that the universe is infinite in extent.

1 Agreed if everything = everything which does not violate any laws
So, everything does not mean that e can dacay, because it would violate the conservation of charge. However, if we monitor a single neutron then it can decay on the 1st second, 2nd, 3rd, ... So MWI insist that there MUST be copies observing a decay on any Nth second. If you say, "decay was possible on 55th second but that branch is actually missing" then you are adding something new, some 'branch scissors' and Ocamm is against you

2 What are the latest observational results?

 

[Chalnoth]

1 Agreed if everything = everything which does not violate any laws
So, everything does not mean that e can dacay, because it would violate the conservation of charge. However, if we monitor a single neutron then it can decay on the 1st second, 2nd, 3rd, ... So MWI insist that there MUST be copies observing a decay on any Nth second. If you say, "decay was possible on 55th second but that branch is actually missing" then you are adding something new, some 'branch scissors' and Ocamm is against you

Well, right, I'm not saying that. But I think my post #45 makes it clear what I'm talking about. Basically, whatever the latter configuration of the wavefunction is depends upon the former configuration, but as we only have information about our own component of the wavefunction, and don't necessarily have information about the former configuration, we can't necessarily say which other things happen.

2 What are the latest observational results?

Well, basically it comes down to the observed flatness and homogeneity of our universe. The observed homogeneity means that the universe extends significantly beyond what we can see (if it stopped, we should see some effect of that). This is brought down to something more objective with the average curvature, as with that we can make an approximate lower bound on the overall size of our universe. If we make the assumption that our universe is a sphere, for example, then measuring the curvature gives us limits on the size of that sphere. If it isn't a sphere, then it's likely much larger (though not necessarily). So we can get at least a rough lower-limit on the size by constraining the curvature, and so far we've constrained it to within about 1% from flat. From this we can get a very rough lower bound on the size at somewhere in the range of two orders of magnitude larger than our observable region.

 

[ViewsofMars]

Backing up Chalnoth's observations.

The Wilkinson Microwave Anisotropy Probe (WMAP) is a NASA Explorer mission that launched June 2001 to make fundamental measurements of cosmology -- the study of the properties of our universe as a whole. WMAP has been stunningly successful, producing our new Standard Model of Cosmology. WMAP continues to collect high quality scientific data.

WMAP's Top Ten

1. NASA's Wilkinson Microwave Anisotropy Probe (WMAP) has mapped the Cosmic Microwave Background (CMB) radiation (the oldest light in the universe) and produced the first fine-resolution (0.2 degree) full-sky map of the microwave sky

2. WMAP definitively determined the age of the universe to be 13.73 billion years old to within 1% (0.12 billion years) -as recognized in the Guinness Book of World Records!

3. WMAP nailed down the curvature of space to within 1% of "flat" Euclidean, improving on the precision of previous award-winning measurements by over an order of magnitude

4. The CMB became the "premier baryometer" of the universe with WMAP's precision determination that ordinary atoms (also called baryons) make up only 4.6% of the universe (to within 0.1%)

5. WMAP's complete census of the universe finds that dark matter (not made up of atoms) make up 23.3% (to within 1.3%)

6. WMAP's accuracy and precision determined that dark energy makes up 72.1% of the universe (to within 1.5%), causing the expansion rate of the universe to speed up. - "Lingering doubts about the existence of dark energy and the composition of the universe dissolved when the WMAP satellite took the most detailed picture ever of the cosmic microwave background (CMB)." - Science Magazine 2003, "Breakthrough of the Year" article

7. WMAP has mapped the polarization of the microwave radiation over the full sky and discovered that the universe was reionized earlier than previously believed. - "WMAP scores on large-scale structure. By measuring the polarization in the CMB it is possible to look at the amplitude of the fluctuations of density in the universe that produced the first galaxies. That is a real breakthrough in our understanding of the origin of structure." - ScienceWatch: "What's Hot in Physics", Simon Mitton, Mar./Apr. 2008

8. WMAP has started to sort through the possibilities of what transpired in the first trillionth of a trillionth of a second, ruling out well-known textbook models for the first time

9. The statistical properties of the CMB fluctuations measured by WMAP appear "random"; however, there are several hints of possible deviations from simple randomness that are still being assessed. Significant deviations would be a very important signature of new physics in the early universe

10. Since 2000, the three most highly cited papers in all of physics and astronomy are WMAP scientific papers.
NASA Official: Dr. Gary F. Hinshaw
Page Updated: Tuesday, 04-07-2009
http://map.gsfc.nasa.gov/

I've been taught by the most brilliant scientists! I'm done with this topic.

 

[rasp]

At first, could you clarify what do you mean by "math isn't science"? Do you mean that we can't prove self-consistency of any axiomatic system, or something else?

Can I jump in and say that it is my understanding that infinity is a mathematical concept which doesn't exist in the real world of science, but which may possibly exist (according to mathematical theories).

 

[Entropee]

One way to look at it is that if there is stuff outside our observable universe (which there almost certainly is), then it was at one point connected to our observable universe. If it didn't follow the same fundamental laws when it was in contact, then you'd have a contradiction.

I think maybe I didn't explain myself very well. I don't mean the laws might be different for things outside our observable universe, I mean outside our ENTIRE universe. Like I said before, "(whatever that means)". There may not be anything outside our universe, just an infinite number of dimensions we can't perceive.

 

[Chalnoth]

I think maybe I didn't explain myself very well. I don't mean the laws might be different for things outside our observable universe, I mean outside our ENTIRE universe. Like I said before, "(whatever that means)". There may not be anything outside our universe, just an infinite number of dimensions we can't perceive.

It's just a matter of describing things in the right way, then. Even if things vary, it's always going to be possible to describe them based upon some rules that do not. A good example here would be Tegmark's mathiverse: different universes based upon different mathematical structures are unified by the rule that all mathematical structures exist.

 

[Entropee]

Im going to look that up that sounds really interesting.