Naked Science Forum
Non Life Sciences => Physics, Astronomy & Cosmology => Topic started by: thedoc on 21/07/2013 08:30:02
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"mikesithole48 asked the Naked Scientists:
Is the universe finite or infinite and did it hve a beginning? Plus I'd love to understand about dark energy.
What do you think?
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"mikesithole48 asked the Naked Scientists:
Is the universe finite or infinite and did it hve a beginning? Plus I'd love to understand about dark energy.
What do you think?
There is no data to make that determination for certain. It remains only a possibility.
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"mikesithole48 asked the Naked Scientists:
Is the universe finite or infinite and did it hve a beginning? Plus I'd love to understand about dark energy.
What do you think?
Infinite and finite systems are complementary in nature. on paper Draw a large circle this is your FINITE boundary , then draw one 2 equilateral triangles so you have the star of david (sod) symbol. Now notice the two triangle inside your circle have now created 6 smaller triangles that make up the two larger ones. Draw Circles around each smaller triangle and add another opposite facing smaller triangle to your new smaller circles. So now you have smaller SOD's circling inside your larger one. Maybe you realize where this is going, but if not look at your smaller stars and notice even smaller triangles emerging where you can have even smaller circles.
You can do this to infinity , and never exit the initial boundary (First large circle) that you set for yourself. If each individual circle you can draw was a individual point to say store information, you would have infinite space for storing all information...This is a fractal principle that is found in nature. So now think about your infinite Star of David and notice or imagine that any direction you go inwards all points exist essentially in one single point. your first circle. So now you have a infinite fractal holographic universe.
Dark energy , dark matter, dark anything is basically "dark" because we cannot understand it . Dark energies and matter are forces added to universal equations to fix the fact that our observable universe is 99.99999% "EMPTY" Space. I quote "empty" because space is not empty its actually infinitely dense with primal energy (vacuum flux). The 0.000001% of the universe is the things we see. (electro magnetic frequency). The universe is blackhole on top of blackhole like the star of david infinity. We happen to exist in one such boundary embedded with infinite others. :)
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paper Draw a large circle this is your FINITE boundary
If space is bounded then there is no boundary. The space is finite but has no bound. The analogy often used in describing this is the surface of a balloon. The two dimensional surface of the balloon is analogous to our three dimensional space. Just as there is no boundary on the surface of the balloon there is no boundary in three-dimensional space.
Dark energy , dark matter, dark anything is basically "dark" because we cannot understand it.
That’s wrong. The term “dark” in “dark energy” refers to the fact that we can’t see it, that there is no interaction between dark energy and light (i.e. electromagnetic radiation). We only know it from its gravitational effects.
Dark energies and matter are forces added to universal equations to fix the fact that our observable universe is 99.99999% "EMPTY" Space.
This is wrong as well. Dark energy is that which is causing the universe to expand at an accelerating rate.
Where in the world did you learn about gravity? You’ve gotten everything wrong so far. If you haven’t studied physics then you shouldn’t go around acting as if you have. It will fill people’s heads with nonsense when they’ve come here to learn what physics really has to say about things, not what you’ve been posting from what you’ve dreamed up!
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oh yeah? 8D
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oh yeah? 8D
What kind of response is this? This is a serious discussion forum. It shouldn't be used to screw around with. We take time out of our day to help people understand physics. We're not here for you to make fun of.
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You can do this to infinity
This is not a criticism of the point you were making, this use of the term infinity is very common. My own feeling is that unbounded is less confusing than infinite, because there is no way in which infinity can be reached, even in theory.
Pete may well shoot this down, but I see no way in which something that is finite can become infinite.
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You can do this to infinity
This is not a criticism of the point you were making, this use of the term infinity is very common. My own feeling is that unbounded is less confusing than infinite, because there is no way in which infinity can be reached, even in theory.
Pete may well shoot this down, but I see no way in which something that is finite can become infinite.
Actually I agree with you. In fact the term infinite quite literally means without bound or something similar. See http://mathworld.wolfram.com/Infinite.html
However I disagree that something that starts out finite cannot become infinite. Call the distance between me and the finish line L. Let K = 1/L. Then when I reach the finish line K is infinite whereas it started out finite.
Consider the infinite Cartesian coordinate grid which maps out commoving coordinates. Let D represent the physical distance between two commoving coordinate lines. As time increases D increases. The distance to the end of the universe is the number of coordinate lines multiplied by D. Before the universe started to expand D = 0 and therefore the distance to the end of the universe was zero. But in the instant D became non-zero the size of the universe became infinite.
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You can do this to infinity
This is not a criticism of the point you were making, this use of the term infinity is very common. My own feeling is that unbounded is less confusing than infinite, because there is no way in which infinity can be reached, even in theory.
Pete may well shoot this down, but I see no way in which something that is finite can become infinite.
any finite area has infinite points of information embedded in itself.
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any finite area has infinite points of information embedded in itself.
Where in the world do you come up with this stuff? If you were tying to say that a point has information in it then you're wrong. Otherwise what information are you talking about tht pertains to this problem?
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Call the distance between me and the finish line L. Let K = 1/L. Then when I reach the finish line K is infinite whereas it started out finite.
I would not be so rash as to argue with the maths, Pete, but can you show me a physical example of any finite object that can actually become infinite?
If the Universe is finite, but expanding, it might expand for ever, but will it reach a point where one can say: "it is now infinite"?
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I would not be so rash as to argue with the maths, Pete, but can you show me a physical example of any finite object that can actually become infinite?
Nothing other than the universe.
If the Universe is finite, but expanding, it might expand for ever, but will it reach a point where one can say: "it is now infinite"?
No.
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any finite area has infinite points of information embedded in itself.
Where in the world do you come up with this stuff? If you were tying to say that a point has information in it then you're wrong. Otherwise what information are you talking about tht pertains to this problem?
if you have enough space between yourself and the earth the earth will appear as a POINT. As you go closer that 'point' shifts into many 'points'. A grain of sand appears in this dimension as a point. Same principle applies zoom into that sand grain and billions of more points emerge . ALL can thought of as INFORMATION. Infinity exist in every point.
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any finite area has infinite points of information embedded in itself.
Where in the world do you come up with this stuff? If you were tying to say that a point has information in it then you're wrong. Otherwise what information are you talking about tht pertains to this problem?
if you have enough space between yourself and the earth the earth will appear as a POINT. As you go closer that 'point' shifts into many 'points'. A grain of sand appears in this dimension as a point. Same principle applies zoom into that sand grain and billions of more points emerge . ALL can thought of as INFORMATION. Infinity exist in every point.
Then you weren't clear to begin with. You were talking about more than just a set of points and didn't say that
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No i wasn't.
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No i wasn't.
I didn't expect you to admit it. But I know as a fact that you weren't clear. It's evident in your vaugness in ypur post. But people have a hard time admitting their mistakes here and I can see that you're no different.
Since you don't have the abolity to see your own error I'll explain it. You claimed
any finite area has infinite points of information embedded in itself.
hwich is just plain false since it doesn't apply to [any area but only top very specific instances of area like the one you gave. If it truly applied to any area then it would apply to the unit area bounded between the lines x = 0, x = 1, y = 0 and y = 1. That area contains no information and therefore your statement is just plain wrong - QED.
And if you really knew what you were talking about then you'd understand that very simple argument. Show us that you're intelligent and just admit your error. Everyone makes them so we won't hold that against you. What we do hold against people is their inability to understand and/or admit their error.
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Pete, but can you show me a physical example of any finite object that can actually become infinite?
Although I said no at first I'd like to change my mind. If the universe started out as being zero in size and now has a flat spatial geometry (and observations are consistent with this) then the size went from finite (zero) to infinite.
Have you ever considered the energy in the field of a point charge like an electron. The energy is actually infinite!! :o The charge density is quite literally a Dirac delta function. That means it has infinite charge density where the electron is located. This is a famous and I believe unresolved problem in quantum theory.
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If the universe started out as being zero in size and now has a flat spatial geometry (and observations are consistent with this) then the size went from finite (zero) to infinite.
If the Universe has zero size, in what sense does it exist?
How do you define zero as a finite entity?
In fact the term infinite quite literally means without bound or something similar
If the Universe had a start, it is bounded in that direction. By your own definition, that is not infinite.
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In the hope that you didn’t really mean that you “hold against people [is] their inability to understand…” I shall press on. :)
Have you ever considered the energy in the field of a point charge like an electron. The energy is actually infinite!! :o The charge density is quite literally a Dirac delta function. That means it has infinite charge density where the electron is located. This is a famous and I believe unresolved problem in quantum theory.
I know little of the Dirac delta function other than that it appears to be a mathematical function, that may not really be a function at all. Am I right in visualising it as some sort of conical feature that tapers to “infinity”? If so, that seems like one of those mathematical “half-infinities” which cannot be truly infinite. Unbounded, perhaps, but infinite? Would it not be difficult to provide physical proof that it continued to infinity?
When you say it is an unresolved problem in quantum theory, does that mean that it is difficult/impossible to make sense of this infinity? Or is there another problem that I have not spotted?
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In the hope that you didn’t really mean that you “hold against people [is] their inability to understand…” I shall press on. :)
You’re correct. That doesn’t reflect what I meant to say. To me there’s a difference between saying “I don’t understand this.” or “I don’t have the knowledge and/or educational background to follow this.” And saying “I don’t care what your math says. In my opinion the result is not what every scientist or mathematician thinks it is.” The former is understandable, the later is arrogance. I don’t hold the first against someone but the second I do.
It's not as if any person can't learn to do some basic programing and write a numerical program to simply calculate the force at an arbitrary point inside the shell due to a point of mass which makes up the shell and using a reasonable approximation write a program to add up all the contributions from the shell and run the program. The only math needed is simple algebra and trignometry which can be learned rather easily. Or they can ask someone to do the math for them. However that's the problem isn't it? They just don't trust math for some reason. Although I've nbever seen anybody explain why other than those people who learn math anre all making the same mistake and they don't want to learn mistakes. I've heard that argument too many times. I find it very irritating. They all seem to think we loose some ability to think once we learn math and physics the hard way. Sheeesh! :)
I wish I was able to fully explain the self-energy problem, but at this stage of my life I don’t. I’m in the process of increasing my knowledge on certain things and right now I’m reviewing classical mechanics. Later on I’ll get to quantum field theory and particle physics. All I know now is that with mass renormalization one can only get so accurate with the calculation. When more terms in the calculation are added to make the answer more precise the accuracy gets worse, not better. That, as I understand it, is the problem. If you’d like I can get a better answer for you if the people I know who understand all this are willing to explain it to me in an e-mail.
Try looking up the term mass renormalization using Google.
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"mikesithole48 asked the Naked Scientists:
Is the universe finite or infinite and did it have a beginning? Plus I'd love to understand about dark energy.
Another chance to wheel-out this old link... :)
How can the Universe be infinite if it was all concentrated into a point at the Big Bang? ... ...The Universe was not concentrated into a point at the time of the Big Bang. But the observable Universe was concentrated into a point. The distinction between the whole Universe and the part of it that we can see is important.
From http://www.astro.ucla.edu/~wright/infpoint.html
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Another chance to wheel-out this old link
I found that explanation quite helpful when I was trying to sort the mechanism of expansion out in my head.
It does suggest that time and space, as well as galaxies, existed before the Big Bang. It also says that the BB did not trigger the expansion of the our Universe, so there seem to be some assumptions that may not readily be verifiable.
The distinction between the universe and the known universe is important. I tend to follow John Gribbin and use “Universe” for the known universe, “cosmos” for everything that exists, and “universe” for anything else.
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“I don’t care what your math says. In my opinion the result is not what every scientist or mathematician thinks it is.”
Sadly, this attitude is all too common, especially on some “would-be scientific” forums. I have a deep respect for mathematics and mathematicians; tinged with a little envy. :)
I accept that maths provides us with the best language for understanding the cosmos, but I suspect that any attempt to force the entirety of the cosmos into any sort of “mould”, mathematical or otherwise, could cause us to miss important factors.
In a discussion of Cantor’s work, John Barrow says:
“Gradually mathematicians lighted upon a new concept of existence. Mathematical ‘existence’ meant only logical self-consistency and this neither required nor needed physical existence to complete it. If a mathematician could write down a set of non-contradictory axioms and rules for deducing true statements from them, then those statements would be said to ‘exist’.”
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BTW, Pete, I hope you are coming back to the questions in #17 & #18. I'm seriously looking for answers, not just trying to score points. I lack the background knowledge to have any realistic chance of success in that area.
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It does suggest that time and space, as well as galaxies, existed before the Big Bang.
I sort of understood it has saying… If every point in an infinite universe is the centre of its own observable universe, then running the infinite model backwards results in a singularity at every point, in other words, an infinite expanse in a state of singularity. Correct me someone…singularity is a state not a point??
That is to say, we can’t understand the spacetime and physics when it’s in a state of singularity.
Winging it now… Our present understanding of spacetime and physics pops into existence with the big bang.
Bill S It also says that the BB did not trigger the expansion of the our Universe, so there seem to be some assumptions that may not readily be verifiable.
Since we can only understand anything after the BB and hence just before the state of singularity, then I think it's saying our understanding starts at the BB and shows it's been expanding since then, what happens to spacetime in a state of singularity is beyond current physics... I think.
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Bill, I can answer you on the Dirac delta function in quantum mechanics, but I'll leave relativity to Pete. The delta function is basically a mathematical tool to extend the idea of distributions over space to the case where everything is localized at one point. Imagine a quantum particle within a box in one dimension. If the particle has fixed charge of 1 unit and can be found anywhere within the box with equal probability, we can say that unit of charge is spread equally over the box. If the box is width L, the height of the function describing how the charge is distributed over space is 1/L. As we squeeze the box smaller and smaller, the particle takes up less space and the height of this function describing the charge goes up. As L decreases in width without bound (which corresponds to a particle at a particular point), the height of this function diverges to infinity, but it does so in such a way that the total area under the function is still 1.
It's not a true function and one reason for this is that, like the concept of infinity, defining a distribution this way is done in terms of limiting processes. The phrase "the height as L goes to zero" is not a number. Despite this, the rules of calculus allow this to be used in various expressions and for the most part physicists get away with treating it like a function with a few special (usually memorized) rules. Mathematicians are generally horrified by this. :p
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It does suggest that time and space, as well as galaxies, existed before the Big Bang.
I sort of understood it has saying… If every point in an infinite universe is the centre of its own observable universe, then running the infinite model backwards results in a singularity at every point, in other words, an infinite expanse in a state of singularity. Correct me someone…singularity is a state not a point??
That is to say, we can’t understand the spacetime and physics when it’s in a state of singularity.
Winging it now… Our present understanding of spacetime and physics pops into existence with the big bang.
The context in which you use singularity matters. Technically, it's a point where equations break down such that your mathematical quantity becomes undefined. I usually see this used to describe cases in general relativity where certain quantities diverge to infinity, meaning that at that point, the equations break down and things become undefined (since infinity isn't a number that you can plug into equations.) There is some debate on this, but I think most physicists (myself included) generally see singularities as a sign that our current models are incomplete rather than viewing them as a real physical object.
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Thanks JP, your explanation gives me heart to believe that, even at my age, it's not too late to gain some basic mathematical understanding. The problem is generally twofold; finding a simple enough explanation and then retaining it. :)
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To me unbounded speaks about the impossibility of me placing myself 'outside', looking in. In that way similar to the idea of a infinity to me. With a boundary on the other hand, speaking about a possibility of being 'outside', looking in. So from that point of view maybe infinity is the one I would lean to. How else would one define a boundary? If not assuming something existing, defining that boundary?
On the other hand you have gravity, becoming a intrinsic property, stating our observations of SpaceTime to 'bend' comes from inside, not relative us being 'outside' of SpaceTime, looking in to find it to bend. On the third tentacle, can there be observations from a 'outside'? If there can't be any such observations, How would one prove a boundary?
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The context in which you use singularity matters. Technically, it's a point where equations break down such that your mathematical quantity becomes undefined.
Would that be equations breaking down before or at the big bang?
we can’t understand the spacetime and physics when it’s in a state of singularity. ...
what happens to spacetime in a state of singularity is beyond current physics... I think.
JP, looking at the link I gave about an infinite universe…
Here http://www.astro.ucla.edu/~wright/infpoint.html (http://www.astro.ucla.edu/~wright/infpoint.html)
In the context my post was about an infinite universe…
If all points can be considered to be at the centre of their own observable universe,
then what happens in the context of an infinite universe when it is run backwards so that each observable universe ‘closes down’ to its respected point? How many points in an infinite universe? The equations break down ‘everywhere’? singularity everywhere? My sentence ‘an infinite expanse in a state of singularity’ could read as ‘an infinite expanse in an indefinable state.’ :)
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Good questions, lean bean. I'm not a general relativity expert but I'll answer to the best of my ability.
The big bang is generally called a singularity because our equations treat it as an infinitely dense state--that's an infinity and since infinity isn't a number we can't really get numbers out of our equations, so we say they're singular or that this is a singularity. I believe this happens at the big bang, as plugging in any finite numbers will likely get you a number out. The bigger question is what happens when you get "close enough" to the instant of the big bang. Is there some extremely large but finite density at which general relativity is not longer an accurate theory? I think most physicists believe so and that's why they're hunting for a theory of quantum gravity, which would cover the very tiny length scales that matter at those densities.
2) Yes, as I understand it the observable universe would be smaller in the past. This is because only so much time has passed since the big bang, so light can only have traveled so far to reach us. The less time between us and the big bang, the smaller region of the universe we can see. (Expansion plays a role as well, so we actually see stars that have since moved further away due to expansion). The closer you get to the big bang, the smaller the observable universe would be. At 1 picosecond after the big bang, assuming we could be there to "see" objects, we'd see things 1 light-picosecond plus whatever expansion had happened distance from us. (Obviously we can't necessarily imagine "seeing" things in this early universe since it was so hot and dense, so what we're really calculating is the maximum distance at which things can interact with each other since all interaction travels at the speed of light or less).
One of the toughest things for me to grasp about this was that if the universe is currently infinite in size, but has finite average density, the big bang could have been infinite in size with infinite density. It would still be a singularity because infinite density makes the equations break down. Maybe Pete can correct me on this, but I was under the impression that if the universe was finite in size (even at the big bang) it would still have to be infinite in size, and if it was infinite in size at the moment of the big bang, it would still be infinite in size.
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It's not a true function and one reason for this is that, like the concept of infinity, defining a distribution this way is done in terms of limiting processes.
One of the formal names for the Dirac delta function is distribution. The other formal name for it is generalized function since it can be defined as a map from functions to functions.
We use them in electrodynamics, quantum mechanics and classical mechanics. E.g. Poison's equation for the gravitational potential for a point mass is given as the Laplacian being proportional to the Dirac delta function (in 3 dimensions).
Fun stuff!
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I was under the impression that if the universe was finite in size (even at the big bang) it would still have to be infinite in size, and if it was infinite in size at the moment of the big bang, it would still be infinite in size.
Assuming your first "infinite" should have been "finite"; this is a major part of the line of reasoning I have been trying to follow. Namely that (physical) things that are finite, remain finite, and those that are infinite, remain infinite. For a few ecstatic moments I thought Pete agreed with me, but then his “Although I said no at first I'd like to change my mind” dashed my euphoria. Hopefully he will address your “impression”.
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The big bang is generally called a singularity ...
Were you aware that there is no event in the big bang which is actually called "the big bang"?
From Principles of Physical Cosmology by P.J.E. Peebles, Princeton University Press, 1993, page 6
If there were an instant, at a "big bang," when our universe started expanding, it is not in our cosmology as now accepted, because no one has thought of a way to adduce objective physical evidence that such an event really happened.
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I was under the impression that if the universe was finite in size (even at the big bang) it would still have to be infinite in size, and if it was infinite in size at the moment of the big bang, it would still be infinite in size.
Assuming your first "infinite" should have been "finite"; this is a major part of the line of reasoning I have been trying to follow. Namely that (physical) things that are finite, remain finite, and those that are infinite, remain infinite. For a few ecstatic moments I thought Pete agreed with me, but then his “Although I said no at first I'd like to change my mind” dashed my euphoria. Hopefully he will address your “impression”.
Ah yes, that should have been "infinite." I'm always wary of answering questions based on pop-sci books/websites and I don't know enough general relativity to answer the question definitively. But based on the pop-sci I have read, I haven't heard of a universe that's bounded (finite) becoming unbounded (infinite). In my limited mathematics, I don't know how it could happen, but the topology involved in GR is a bit beyond me.
As I've said before, I agree in spirit with your idea that "nothing finite can become infinite" but I disagree strongly with the statement itself. If you want such a statement to hold, you have to be precise. Pete gave the example of 1/(distance remaining) as you move between two points becoming infinite. Ligharrow gave the example of a series with infinite terms that sums to a finite number. These are certainly things. Perhaps they're abstract things, but you'd better state what you're precluding from your rule before you can claim it holds in all cases. I suspect that finding the exact dividing line of what it precludes will be very tricky.
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The big bang is generally called a singularity ...
Were you aware that there is no event in the big bang which is actually called "the big bang"?
From Principles of Physical Cosmology by P.J.E. Peebles, Princeton University Press, 1993, page 6
If there were an instant, at a "big bang," when our universe started expanding, it is not in our cosmology as now accepted, because no one has thought of a way to adduce objective physical evidence that such an event really happened.
I was using it in the hand-wavy pop-sci way that it's the limiting case as time since the universe started -> 0. My understanding (from pop-sci, as the equations are beyond me) is that this is a well defined limit, even though it's probably a non-physical state and it's unlikely that general relativity holds without quantum corrections. If there's a good reason why taking that limit doesn't work, I'd love to learn more.
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If there's a good reason why taking that limit doesn't work, I'd love to learn more.
Well my friend, I'll do my best to find out. I'm meeting a couple GR gurus this week and will bring it up. Anything in particular I should ask them or phrase the question?
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I'd be interested to know what cosmology says as you take the limit T->0, where T is the age of the universe. Does it predict an infinitely dense state we could tall "the big bang"? (This is almost certainly non-physical, but does GR predict it?) I've been led by pop-sci to believe that it does predict this "infinite density."
But my biggest question, stated above, is whether a bounded universe could become unbounded or if bounded must remain bounded for all time and unbounded must remain unbounded for all time. This ties into Bill's question on whether a finite universe can become infinite.
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I'd be interested to know what cosmology says as you take the limit T->0, where T is the age of the universe. Does it predict an infinitely dense state we could tall "the big bang"? (This is almost certainly non-physical, but does GR predict it?) I've been led by pop-sci to believe that it does predict this "infinite density."
But my biggest question, stated above, is whether a bounded universe could become unbounded or if bounded must remain bounded for all time and unbounded must remain unbounded for all time. This ties into Bill's question on whether a finite universe can become infinite.
I was talking to Alan Guth about this very thing. In cosmology as it is an unbounded universe cannot become bounded etc. If a universe is closed or open then they remain as such.
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If there were an instant, at a "big bang," when our universe started expanding, it is not in our cosmology as now accepted, because no one has thought of a way to adduce objective physical evidence that such an event really happened.
Pete gave the example of 1/(distance remaining) as you move between two points becoming infinite. Ligharrow gave the example of a series with infinite terms that sums to a finite number.
Absolutely right, undoubtedly mathematically sound, but has anyone adduced “objective physical evidence that such an event really happened”?
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Ah yes, that should have been "infinite."
Tricky stuff, this infinity. :)
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Pete gave the example of 1/(distance remaining) as you move between two points becoming infinite. Ligharrow gave the example of a series with infinite terms that sums to a finite number.
Absolutely right, undoubtedly mathematically sound, but has anyone adduced “objective physical evidence that such an event really happened”?
Now we're getting into the definition of "real," which is slippery. But I can move from point A to point B, so the quantity 1/(remaining distance) diverges to infinity. Similarly, the series is real--I can write it in notational form (though for obvious reasons I can't write it out explicitly).
The problem is that there's a huge class of finite things which can't become infinite, so I agree with you for the most part. But there's a smaller set of things that can, so I don't agree completely.