The peculiar results of an infinite universe

[ajtribick]

BlindedByTheLight, congratulations, you have identified one of the primary flaws in a strict positivist viewpoint - taken to its logical extreme it would end up denying the possibility of new results, which is obviously a Bad Thing.

However it is rather difficult to do experiments on unobservable objects (and I mean totally unobservable - even dark matter, if it truly exists, exerts a gravitational force and is thus observable). At best you can do a few thought-experiments (e.g. what would the universe be like if Planck's constant were a billion times larger, or something), but it soon starts to get divorced from reality and become at best philosophy, at worst outright fantasy.

As for your comments on causality, I don't mean to say Einstein's theories are the end result - maybe I shouldn't have used the light-cones point. But if you want to argue that information can be transferred faster than light, either show us faster-than-light information travel or an effect for which faster-than-light is required. Show us an effect where an event occurring outside the light cone affects an object in the light cone (say, a supernova beyond the edge of the observable universe).

Until then, discussion of the regions located so far away that their lightcone does not affect the observable universe is so much speculation. Again, if an event is unobservable and has no observable consequences, does it really matter whether it exists or not? If it is completely irrelevant to any possible observations, then I would go with the event not existing. While an unobservable supernova may seem reasonable, does an unobservable million-light-year-wide pink unicorn seem reasonable? Yet, if it is unobservable and remains unobservable that pink unicorn would still be consistent with the universe as we observe it.

Then again, if whatever ultimate theory we end up with requires a universe with unobservable regions (e.g. the theory requires an infinite universe to work), then in some way they are observable (if only by the universe working on a theory that requires their existence). Then again, this situation would be rather bizarre, and I'm not entirely sure if such a situation could arise.

I don't know about you, but I personally find the stuff we can actually observe to be rather more interesting than some unobservable limbo "beyond the universe".

[selden]

Supposedly an "inflationary period" took place not long after the Big Bang which was a spatial expansion which proceeded faster than light could travel an equivalent distance, making the existing universe larger than we can ever hope to see. However, my understanding is that since there has been only a finite time since the Big Bang the radius of the universe would still be finite.

I don't know what the speed and duration of the inflationary period are thought to have been. I suspect there are disagreements.

[ElChristou]

...Tell them what we DO know, show them the evidence that we DO have...

Mal, I'm quite ignorant on the topic, can you explain a bit more please? (I'm one of those boeotian believing in an infinite universe )

Edit:

Cross mail with Selden, is that the explanation you have?

[buggs_moran]

First off I will premise this post with a quote from Douglas Adams:

Infinite : Bigger than the biggest thing ever and then some. Much bigger than that in fact, really amazingly immense, a totally stunning size, real "wow, that's big," time. Infinity is just so big that by comparison, bigness itself looks really titchy. Gigantic multiplied by staggeringly huge is the sort of concept we're trying to get across here.

Now, here is my understanding and what I tell my students about infinity. The Universe (disclaimer: as far as I have learned) is most likely (2% error, WMAP) infinite (i.e. it will expand forever).

Time and space are linked. If time began 13.7 billion years ago, so did space and it has expanded ever since. The first electromagnetic particles we see left somewhere (in all directions) 1.296e23 km away and smacked into a telescope here 13.7 billion years later. This Hubble bubble we are in is essentially our local universe. Now, with some basic geometry we see that the Hubble bubble is 27.4 billion ly (GLY) in optical diameter. If travelers were to go to the very edge of our bubble instantaneously, they would encounter galaxies and stars that have evolved over the past 13.7 billion years. They can see a 27.4 GLY optical diameter sphere that has the Earth at it's edge, but Earth will not have formed yet from their perspective, nor will the Milky Way, they will see microwave radiation just like we do). We could then repeat the jump from that location another 13.7 GLY away and see the same thing, although at that point, Earth would not be in the universe yet (but it would have to, since we left it 2 jumps ago, hmm).

Even the bubble we're in is measurably bigger than we think. Optically, it's 27.4 GLY across. But in an inflationary flat universe, which we are currently thought to be in, it kept expanding. So we actually are at the center of a 156 GLY bubble in finite physical size. Even if we rushed towards 156 GLY from here, there would be another 156 GLY to go.

No matter where you are in the universe, light will be coming towards you from 13.7 GLY away, so it is optically finite, but spacially infinite and there is no edge to speak of. But I could be wrong.

Now, as I stated in the beginning, this is what I tell my astronomy students. It is a high school level course and they have all completed at least one year of algebra. From this thought experiment, my students get the feel for the possibility of an infinite universe. I tell them there are competing theories and ideas. I inform them about the debate between curved, flat, expanding, contracting, accelerating, dark matter/energy, multiple dimension, etc universes. That is why I end my lecture with "But I could be wrong."

I tell them we are like infants just from the womb, we haven't even mastered the knowledge of our own planet, there is always and will always be something new to learn and many times, what we teach and learn, may have to be tweaked a bit from time to time.

[selden]

Gentle folk,

I've been asked to make this more explicit.

As in another thread, I seem to need to remind you that emotional and potentially offensive phrasings are inappropriate. No matter how strongly you feel about a subject, that does not give you the right to attack personalities or to call people (even yourself) objectionable names.

Discuss the theory, not the person.

If you don't like a topic, don't respond to it.

Also, please remember that this is a public forum. We have many younger people subscribed to it. Abusive language is not appropriate.

Don't write things that you wouldn't want to be read by the people nearest and dearest to you, or by potential employers, for that matter. Searching the Web for what people have posted is one of the techniques being used to verify character references these days.

[fsgregs]

Steve:

THANKS for the link to your article from Scientific American. It is exactly what I was seeking, and in scientific terms, discusses the real possibility of infinite suns, infinite Earths, with infinite copies of you living in parallel universes, stretching across infinity.

For those of you who are interested in this topic , I recommend you read the article.

Thanks also to everyone who shared their thoughts on infinity.

Frank

[BlindedByTheLight]

Great stuff, Buggs (including the quote). Thank you.

Chaos, also thank you. I was not meaning to challenge the light cone-limits...just was asking if there were not legitimate theories out there that might. I really don't know - though I did read a fantastic book by Jaoa Maguizo (sp?) on the subject and he mentioned a few mechanisms about how FTL speeds could be achieved. I can sum up if you'd like me, too. But I really was just asking - not challenging.

I was simply pointing out two things: one, we may be mistaken about what can or cannot happen - thus, I would think theorists must be cautious to not limit themselves. If the limits are false... well, you know where that will lead. Nowhere.

Also...

<<Until then, discussion of the regions located so far away that their lightcone does not affect the observable universe is so much speculation>>

...I agree, speculation. But from what I understand, though science is hard and empirical in its execution, it also appears to require a very creative, free-flowing thought process in which new theories may gestate. And the creative process I do know something about. And I've seen amazing things come left-field out of the most INANE discussions. I suspect theory can work the same way -- IF we don't limit it. Thus I bristle when I hear judgements of pointlessness. The points are not always so apparent at first blush.

<<BlindedByTheLight, congratulations, you have identified one of the primary flaws in a strict positivist viewpoint - taken to its logical extreme it would end up denying the possibility of new results, which is obviously a Bad Thing. >>

Thanks! I mean... I think... Could you expand on your last sentence a bit about the logical extreme?

Steve

P.S. I apologize Selden (and to any I might have offended), if you are speaking to me.

[Telepath]

Frank,

One way to help your students to comprehend infinity is perhaps to get them to use their math skills. (Some consequences and paradoxes of an infinite universe may be exposed through mathematics)
For example:

1. In an infinite universe, anything (no matter how small the probability) is certain.

Code: Select all


1000 x 0.001 = 1
1,000,000 x 0.000001 = 1
...
<infinity> X <infinitesimally small probability> = 1  (ie. certainty)

2. In an infinite universe there are as many earthlike planets as there are stars.
Let's say (for arguments sake) that 1 in a thousand stars have earthlike planets...

Code: Select all

stars in the universe = <infinity>

number of earthlike planets = <infinity> X 0.001
                            = <infinity>

therefore, number of earthlike planets = number of stars in the universe = infinity

DISCLAIMER: I post this not in order to provoke the ire of those who would have us close our minds, but merely as a thought exercise for those who would like to open and exercise the minds of their students.

[BlindedByTheLight]

2. In an infinite universe there are as many earthlike planets as there are stars.

What if the space is infinite, but the matter is not? Though, mathmatically-speaking, would that also be a paradox? In that the ratio of the volume of the finite matter to to the infinite volume of space would basically be zero?

[fsgregs]

Steve and Buggs and Selden:

Thanks for your insight. You could not have said it better!!!

Telepath:

The problem with "math skills" in high school students today, is that in most of them, they have math skills that they do not know how to apply. They can do rote problems, but ask them to solve a word problem and most of them really freeze up, or get the answer wrong.

As an example, my Astronomy course in my HS is very popular. I draw good kids and have to turn a lot of them away. That said, I once gave my 160 high school juniors and seniors what I thought would be a trivial problem

Assuming the observable universe is a sphere centered on Earth, how long in years would it take Apollo 11 to depart from Earth and reach one "edge" of the known universe? I gave them (a) an estimate of the diameter of the Hubble Bubble (known universe) (~156 billion LY), (b) the distance in a LY (5.87xe12 miles), and (c) the speed of Apollo 11 (25,000 mph). I told them to ignore inflation and changing dimensions of space. Simply assume we are in the center of a sphere 156 GLY in diameter and solve the math problem. We kept it in English units instead of metric, cause American students have no conceptual image at all of metric units.

Obviously, they had to realize that they had to travel a radius distance (80 BLY), not the entire diameter (since they were leaving from Earth in the center). At the time, I assumed they would realize that.

Sadly, , only nine kids out of 160 got the correct answer! GOOD GRIEF! Of the 151 who did not, over 100 of them had no idea how to do the problem. I kid you not! The remainder used the diameter instead of the radius.

I blame this result on a paucity of applied word problems in math classes, and the laziness of many HS kids today. So many of them simply don't want to do the mental work.

Anyway, I am forever hopeful, so I will try some infinity math in the Autumn term and see what happens. Thanks for the suggestion.

Frank

[buggs_moran]

The problem with "math skills" in high school students today, is that in most of them, they have math skills that they do not know how to apply. They can do rote problems, but ask them to solve a word problem and most of them really freeze up, or get the answer wrong.

The truth is so painful... They have us teaching to these stupid tests on the rote problems that the kids have to pass before they can graduate...

Nice problem by the way. Can I use it? How are you going to teach infinity math to Algebra students? Exponentials, limits and series? I like limits personally. Good joke out there:



I do this problem to introduce them to exponential decay (plus you can link this to series and limits).

You're standing at the edge of the cliffs of insanity (in a perfect universe so the math works). The tips of your shoes are 1 meter away from the edge. You take a step half of the distance, then half of what's left, and half again, etc. Then I ask, do you ever reach the edge of the cliff? If so, when? Concept of infinitesmal (distance) and infinity (time) all at once.

As far as metrics go, c'mon we're one of three countries in the world that have the gaul to still use an archaic form of measurement. Let us stand with our brothers Myanmar and Liberia... Pretty dumb, isn't it...

[Telepath]

Frank,

I think you and your students may enjoy the story of the HOTEL AD INFINITUM: http://scidiv.bcc.ctc.edu/Math/InfiniteHotel.html



linked from this page: http://scidiv.bcc.ctc.edu/Math/infinity.html

[Telepath]

What if the space is infinite, but the matter is not? Though, mathmatically-speaking, would that also be a paradox? In that the ratio of the volume of the finite matter to to the infinite volume of space would basically be zero?

I guess another paradox, as that would mean that the average density of the universe is zero.

[fsgregs]

Telepath:

Fascinating article. Provides great room for whimsical thought

Frank

[Telepath]

I thought it was quite good too Frank.
IMO maths is always more interesting for students if presented in an interesting style like this. As a lot of students are bored by maths, if a problem is presented in the form of something they can relate to, it's possible for them to solve the problem using maths, before they even realise they're actually doing maths!
I don't know what level your students are at, but my suggestion would be to present each of the check-in situations as an exercise for your students to solve.
eg. You could start with housing the baseball player and perhaps show them how to solve that first case, and then get them to come up with the solutions to each of the progressively more difficult situations one by one (as their maths improves )

[Startyger]

The considerations of the universe aren't useless, the arguing may be. If something is, well, it is. If it isn't, well, it isn't. But, if we don't know... we have something to attain.

Many arguments are funny to me... "Does life need death to exist?" obviously, not.. it may use it to its own ends but, by definition... No. "Does Death need life to exist?" By definition.... Yes. Are these two things quantifiable? Yes and no lol... "Is the universe Inifinite?" if it is.. we'll never know! (except of course the Creator says, "Yes, yes it is." It would be the only thing then.. as big as the Creator LOL......dag. That too might explain its size.. now, back beyond the parenthesis..) If it is finite, then perhaps we'll know it.. one day, and wonder what lay beyond.

The question of Creation is doesn't preclude scientific understanding. Outside of Faith, (because, even History involves faith in the telling..) science might find the "fingerprints" of the Creator.. (hmm.. string theory.. or something similar?) ... the way investigators find the motive of a criminal. (Unless the criminal corroberates the results of deductive, and inductive analysis we're still going by 'faith' in what we have ascertained: Was that a picture of the man being choked.. or was his accused assailant merely holding the wound on his neck closed.. a picture can be worth a thousand of the wrong words...)

Science, has room for speculation... for our reasoning, until we have solid, and unquestionable evidence, is, essentially, speculation built upon or connected to some learned item. Sometimes the math seems crazy till you find the planet. Then, 'of course', math is infalible.. again. seriously, there should be a forum for speculation... but how can you quantify eternity? Isn't that the point... you don't? else a circle would cease to be.. round. LOL

[selden]

As Fridger and others have pointed out, speculative discussions (as opposed to questions about Physics and Astronomy topics) should be in the Purgatory forum.

Alternatively, as I've mentioned before, you should consider visiting web forums which concentrate on topics like that.

[Startyger]

I thought i said that.

[t00fri]

As Fridger and others have pointed out, speculative discussions (as opposed to questions about Physics and Astronomy topics) should be in the Purgatory forum.
...

[Sorry, I simply couldn't resist (exceptionally )]:

...which doesn't mean that VERY occasionally and more recently you might also come across some serious discussions about Physics and Astronomy in the Purgatory...

e.g. about the Topology of our Universe:
http://www.celestiaproject.net/forum/viewtopic ... sc&start=0

notably also here
http://www.celestiaproject.net/forum/viewtopic ... c&start=16

Startyger's post represents a vivid illustration that the Purgatory may these days be a "safer" place for serious P&A discussions ...

Bye Fridger

[Startyger]

What wasn't serious?