View Full Version : How can the universe be "infinite" in any way ?

apolloman

2011-May-20, 10:54 AM

Something I just can't get my head around...

When researching the BB, I've heard/read numerous times that in the so called beginning (or just after) the universe was infinitely small, infinitely dense and with infinite energy.

This makes no sense to me. I'll start with the size first.

If the universe was infinitely small at some moment in time and then it grew by a google-fold a moment later, it would still be classified as being infinitely small, right ? So, no matter how much expansion took place, it would always be infinitely small. Well that can't be right, as the universe is most definitely not infinitely small (excuse the repetition) today.

What am I missing ?

apolloman

2011-May-20, 10:57 AM

obviously the title thread should read "how can the universe be infinite in any way"

Jeff Root

2011-May-20, 11:32 AM

There isn't much reason to think that the Universe was ever

infinitely small or infinitely dense, and there is some reason

to think it was not. The infinitely small and infinitely dense

notion comes from how the Big Bang was first discovered:

by tracing the cosmic expansion backward through time.

All the galaxies are seen to be getting farther and farther

apart, so at one time long ago the matter they are made of

must have all been in a much smaller volume. Extrapolate

far enough back in time, and all the matter must have been

at a single point. No physics that we know of can prevent

this predicted "singularity". However, it conflicts with the

predictions of quantum mechanics. As near as I can tell --

and probably, as near as anyone can tell -- something

happened which resulted in the Big Bang. What that

"something" was is completely unknown, although there

are many ideas about possibilities. I think that the event

must have taken some time (everything else takes time

to happen -- why not the Big Bang?), which means that

the extrapolation is wrong. Pretty much everyone agrees

that the extrapolation is wrong, but nobody knows what

to replace it with, so the default statement is just to say

that if you extrapolate back far enough, you reach a point

in time when everything was in the same place.

However, I'm not the best person to answer your question

of how the Universe could be infinite, since I am certain

that it cannot be infinite. At least, the part of the Universe

which resulted from the Big Bang and is participating in

the ensuing cosmic expansion. The Universe as a whole

might be infinite, in my view, but in that case only a part

of it (an infinitesimally small part, I guess) could be the

result of the Big Bang.

-- Jeff, in Minneapolis

apolloman

2011-May-20, 11:55 AM

Hi Jeff,

Thanks for the reply, thats pretty much how I see things as well... which is why these commonly used notions of infinities and singularities are confusing and, to me, misleading.

Aside from clashing with QM, shouldn't simple logic (as explained in my example above) also induce an understanding that any infinity/singularity is a mathematical non-sequitur ? Having said that, I am aware that QM and many other things in physics defy logical thinking so I'm probably way off track.

Quoting JEff : "The Universe as a whole might be infinite... "

Again, statements like these loose me.

The HST looks out to approx. 13.8 billion light years where it sees the first stars/galaxies forming (I might be off with the distances but bear with me) and it sees this in all directions. If that is the case, how can there be another part of the universe (the whole you are referring to) that we aren't seeing ??? Wouldn't this entail that we should see, in some part of the sky, a patch of the universe that at a distance of 13.8 billion years doesn't show the first stars/galaxies forming ?

I hope thats put clearly enough to answer.

Strange

2011-May-20, 12:14 PM

The first thing that struck me was the fact you are using "common sense arithmetic" (specifically, multiplication) in your argument. Sure, if something was zero size (infinitely small) and it doubled in size then it would still be zero sized. But what if it grew by 1 inch (or 1 Planck unit) then it would no longer be zero sized. So I don't really see the logical paradox you do.

But, more importantly, as Jeff says, the big bang theory is about the evolution of the universe not its creation. We don't know if it started out from nothing (o at least, something zero sized) or if it bounced back from a collapsing universe or one of the other alternatives...

The part of the universe we can see is almost certainly not all of it - parts of it have expanded away so fast light from there has not reached us yet; there are other parts from which the light will never reach us. Beyond that it might come to and end. Or it might go on forever. We don't (can't) know.

profloater

2011-May-20, 12:17 PM

a difficult question to answer but why would infinity be more difficult to think about than beginnings and endings? if a situation repeats itself, for example, endlessly, that is a form of infinity. If you imagine a nothingness, that has to extend to an infinity or it becomes something. If all change in a system stops, it will be like that for ever. Is that so hard to imagine? These ruminations tell us nothing about what we actually experience, you cannot prove anything about infinity by imagination.

noncryptic

2011-May-20, 12:25 PM

how can there be another part of the universe (the whole you are referring to) that we aren't seeing ???

At ~13.7B ly we see the surface of last scattering/the origin of the Cosmic Microwave Background. That is an opaque plasma. (we don't actually see stars there)

It might eventually be possible to probe it by means of gravitational waves and/or neutrinos, but for the time being it puts a hard limit on how far out / how far back we can see.

If there would be no surface of last scattering then an observation limit would be caused by the fact that galaxies very far out are receding from us faster than the speed of light, so there'd be no way to see those.

Jeff Root

2011-May-20, 12:27 PM

Everything we know about infinity is by imagination, and we

do know quite a bit about it, as a mathematical concept.

-- Jeff, in Minneapolis

apolloman

2011-May-20, 12:34 PM

Sure, if something was zero size (infinitely small) and it doubled in size then it would still be zero sized. But what if it grew by 1 inch (or 1 Planck unit) then it would no longer be zero sized

Strange, I'm not a bright spark so have patience but this is precisely my point. It makes no sense at all (to me) for anything of zero size to exist because no matter what you did to it, it will always stay that size. Following that logic, the universe (or the part we can see) is not zero-size today therefore it was never zero-size.

I really really don't understand how something infinite (small or large) can become something finite simply by adding/deducting a finite number to it (the 1 inch example in your reply). Eg. if I have an infinite number of apples and take one, 10 or a million away, I will still have an infinite number of apples. The same should apply with the universe; if at some moment in time, it was infinitely small and then grew by 1 inch or 10 million trillion times, it will always remain infinitely small.

Therefore I come to the conclusion that the universe was never infinitely small.

Strange

2011-May-20, 12:34 PM

Everything thing we know about infinity is by imagination, and

we do know quite a bit about it, as a mathemetaical concept.

I'm not sure. I can't imagine it; I can only understand it though the mathematics!

apolloman

2011-May-20, 12:39 PM

Strange, something strikes me as completely confusing... I can increase the size of an infinitely small apple by any magnitude and it will remain infinitely small but if I increase it by 1 inch it actually acquires a definite size... how can this be ?

Strange

2011-May-20, 12:46 PM

It makes no sense at all (to me) for anything of zero size to exist because no matter what you did to it, it will always stay that size. Following that logic, the universe (or the part we can see) is not zero-size today therefore it was never zero-size.

That sounds like a sort of Zeno's paradox in reverse. If you have an apple (say) and cut it in half and half again, it will never be zero sized. On the other hand, if you remove one tenth then another tenth it will be gone in 10 steps. How many leaves does a tree start out with? Zero, then two and eventually hundreds.

I really really don't understand how something infinite (small or large) can become something finite simply by adding/deducting a finite number to it (the 1 inch example in your reply).

Well, I wasn't specifically talking about the universe, just the principle. I think that if the universe is infinite it must have always have been infinite. On the other hnad, there are an infinite number of integers, each just one bigger than the previous :) (and they start from zero).

Therefore I come to the conclusion that the universe was never infinitely small.

I think you are making the common mistake of assuming the universe should only do things that make sense to you ...

apolloman

2011-May-20, 12:50 PM

I think you are making the common mistake of assuming the universe should only do things that make sense to you ...

I don't think I am... I'm not playing spoilt brat who wants his own way... I'm really only trying to understand and accept.

Astron

2011-May-20, 12:52 PM

Strange, I'm not a bright spark so have patience but this is precisely my point. It makes no sense at all (to me) for anything of zero size to exist because no matter what you did to it, it will always stay that size. Following that logic, the universe (or the part we can see) is not zero-size today therefore it was never zero-size.

I really really don't understand how something infinite (small or large) can become something finite simply by adding/deducting a finite number to it (the 1 inch example in your reply). Eg. if I have an infinite number of apples and take one, 10 or a million away, I will still have an infinite number of apples. The same should apply with the universe; if at some moment in time, it was infinitely small and then grew by 1 inch or 10 million trillion times, it will always remain infinitely small.

Therefore I come to the conclusion that the universe was never infinitely small.

It's not you it's every human that can't understand the infinite, it's just doesn't fit to our nature for anything to be infinite,at least that's my opinion on this.

It's general more acceptable to say that "everything was once an infinite small spot" than say "everything was in a state that we don't have a clue how it was and we possibly never learn"

The more you try to understand infinite in every aspect of science the more you'll get frustrated.

apolloman

2011-May-20, 12:54 PM

a difficult question to answer but why would infinity be more difficult to think about than beginnings and endings? .

They're pretty much on the same level to me, Profloater, I'm just focusing on the notion of infinity at the moment

Jeff Root

2011-May-20, 12:54 PM

Quoting Jeff : "The Universe as a whole might be infinite... "

Again, statements like these loose me.

The HST looks out to approx. 13.8 billion light years where it

sees the first stars/galaxies forming (I might be off with the

distances but bear with me) and it sees this in all directions.

If that is the case, how can there be another part of the universe

(the whole you are referring to) that we aren't seeing ??? Wouldn't

this entail that we should see, in some part of the sky, a patch

of the universe that at a distance of 13.8 billion years doesn't

show the first stars/galaxies forming ?

It may be that the entire Universe came from the Big Bang, or it

might be that the Big Bang only involved a small part of a much

larger -- possibly infinite -- Universe. In the latter case, which

is what I was referring to before, there would be no visible sign

of the "rest of the Universe". As it is, what we can see is most

likely only a very small part of everything that came from the

Big Bang. Measurements of the cosmic expansion and the

distribution of galaxies suggest that those galaxies continue

to distances much farther than we can ever see. What I was

talking about was what might be beyond even that -- a part of

the Universe that had no involvement in the Big Bang.

Anything that might be in that Great Beyond is hidden from us

by distance, by the cosmic background radiation which fills the

sky, coming at us from 13.7 billon years ago, and possibly by

the shape of spacetime, which may close us in a bubble which

nothing can enter and from which nothing can escape.

-- Jeff, in Minneapolis

Strange

2011-May-20, 12:55 PM

I don't think I am... I'm not playing spoilt brat who wants his own way... I'm really only trying to understand and accept.

It wasn't meant in a bad way - sorry if it came across like that - its just that the universe doesn't have to adhere to our "common sense" or "logic". It is amazing that we can understand (and accept) so much of how the universe works. When it comes to quantum theory or relativity, one might be able to understand the math, but that doesn't mean it will "make sense" or even be easy to accept. My reaction to some other the "weirder" aspects of the universe is pretty much, "whatever".

Strange

2011-May-20, 01:06 PM

I'm just focusing on the notion of infinity at the moment

To get a handle on the mathematical concept (which I think helps more generally) take a look at Cantor's diagonal argument (http://en.wikipedia.org/wiki/Cantor%27s_diagonal_argument) - one of the things that defines "beauty in mathematics", in my opinion. (Not sure the wikipedia article is as clear as it could be; here is another description: http://planetmath.org/encyclopedia/CantorsDiagonalArgument.html)

apolloman

2011-May-20, 01:06 PM

strange, no, it didn't come across "in the wrong way" ... I just wanted to be sure of coming across "the right way". :razz:

I'll check out the link, thanks.

And thanks Jeff for your replies as well.

I'll be back for more !!!

Strange

2011-May-20, 01:10 PM

Does the descretness (is that a word?) of spacetime come into play in any way ?

As far as I know, spacetime is not known to be discrete; I think relativity treats it as continuous. Some theories of quantum gravity may not do. But I can see your point that it would put a lower limit on the steps by which the initial universe could grow. But then, perhaps, so does the existence of fundamental particles. But we are in the realms of speculation here ... not something I am comfortable with.

cosmocrazy

2011-May-20, 01:15 PM

Try and get the notion of "infinitely small" out of your head and just image zero size, you may find this easier to imagine. At the beginning there was no time, or space, so there was no room for size. For whatever reason space and time hand in hand began (for want of a better word). As soon as space and time as we know it comes into existence then so does size, as we know it.

Strange hit upon this with his analogies about the apple and tree.

Jeff Root

2011-May-20, 01:19 PM

It makes no sense at all (to me) for anything of zero size to

exist because no matter what you did to it, it will always stay

that size.

Imagine a mathematically perfect cone, which tapers to a point.

The point has zero size. Does it exist? Yes, in the imaginary

mathematical sense, it does exist. That is exactly the case

with the Big Bang. We can trace everything backward in time

to a mathematical point. We can't go any farther back. That

point in time is the singularity. Just as a cone spreads out

from its point, the Universe spreads out from the singularity.

Following that logic, the universe (or the part we can see) is

not zero-size today therefore it was never zero-size.

...

if at some moment in time, it was infinitely small and then

grew by 1 inch or 10 million trillion times, it will always remain

infinitely small.

If something of zero size grows by 1 inch, then it has a size

of 1 inch. How big were you one hundred years ago?

I really really don't understand how something infinite (small or

large) can become something finite simply by adding/deducting

a finite number to it (the 1 inch example in your reply). Eg. if I

have an infinite number of apples and take one, 10 or a million

away, I will still have an infinite number of apples. The same

should apply with the universe; if at some moment in time, it was

infinitely small and then grew by 1 inch or 10 million trillion times,

it will always remain infinitely small.

Those are two different, separate problems you are talking about.

One is the problem of how something that has zero size can

become larger than zero size. The other is how something of

zero or finite size can become infinite in size (or the other way

around: how something infinite can become finite). The first

happens all the time. The second doesn't seem possible to

me, either.

-- Jeff, in Minneapolis

noncryptic

2011-May-20, 01:21 PM

Imo the issue of zero size isn't really an issue because nowadays hardly a cosmologist can be found who 'believes' the universe started from zero size.

"Singularity" follows from General Relativity, but...

"General Relativity is not the final word when it comes to gravity, we know this because it predicts singularities. General Relativity says there are places in the universe where the equations of General Relativity do not apply.

The Big Bang is one of those places. The Big Bang is not the necessary beginning of space and time, it is just the place where General Relativity breaks down."

- Sean Carroll (cosmologist), on the arrow of time

~15:00

Sean Carroll on the arrow of time (Part 2)

dec 2009

http://www.ted.com/talks/sean_carroll_on_the_arrow_of_time_part_2.html

apolloman

2011-May-20, 01:33 PM

Imo the issue of zero size isn't really an issue because nowadays hardly a cosmologist can be found who 'believes' the universe started from zero size.

"Singularity" follows from General Relativity, but...

"General Relativity is not the final word when it comes to gravity, we know this because it predicts singularities. General Relativity says there are places in the universe where the equations of General Relativity do not apply.

The Big Bang is one of those places. The Big Bang is not the necessary beginning of space and time, it is just the place where General Relativity breaks down."

- Sean Carroll (cosmologist), on the arrow of time

~15:00

Sean Carroll on the arrow of time (Part 2)

dec 2009

http://www.ted.com/talks/sean_carroll_on_the_arrow_of_time_part_2.html

My point exactly, lets stop invoking infinities and singularities as they are not the right terms to use... although we apparently haven't found the right ones as yet

apolloman

2011-May-20, 01:45 PM

One is the problem of how something that has zero size can become larger than zero size. The other is how something of

zero or finite size can become infinite in size (or the other way around: how something infinite can become finite). The first

happens all the time. The second doesn't seem possible to me, either.

-- Jeff, in Minneapolis

So "zero size" means it has no size at all. Add an inch to it, it becomes 1 inch in size. Thats clear. No qualms there.

"Infinitely small" means it has a non-descrete size which is precisely that, infinitely small. Do anything to it, and it remains inf. small.

As a consequence, I come to the conclusion that the universe had no size at all, came into existance and inflated (ok, in really broad terms). Therefore, at some time in its history, it was of a definite finite size which then inflated to what we see today.

apolloman

2011-May-20, 01:47 PM

And, Jeff, I've come to another conclusion that I completely misread your reply... let me go over that again. Doh.

Strange

2011-May-20, 01:48 PM

"Infinitely small" means it has a non-descrete size which is precisely that, infinitely small. Do anything to it, and it remains inf. small.

Ah, OK. To me "infinitely small" and "zero size" are exactly the same thing, by definition (see also, the old "is 0.999... equal to 1" thread). So that is another source of confusion (that comes from using words for math, I guess).

apolloman

2011-May-20, 02:20 PM

And, Jeff, I've come to another conclusion that I completely misread your reply... let me go over that again. Doh.

No, I did read it correctly and come to the same conclusion or rather :

So "zero size" means it has no size at all. Add an inch to it, it becomes 1 inch in size. Thats clear. No qualms there.

"Infinitely small" means it has a non-descrete size which is precisely that, infinitely small. Do anything to it, and it remains inf. small.

As a consequence, I come to the conclusion that the universe had no size at all, came into existance and inflated (ok, in really broad terms). Therefore, at some time in its history, it was of a definite finite size which then inflated to what we see today.

Ken G

2011-May-20, 03:42 PM

To me, the OP really comes down to saying "I don't understand the first moment of our universe." There is nothing wrong with not understanding that, no one does, you're not supposed to. The Big Bang is a model of the evolution of the universe starting at some fairly arbitrary point where our physics begins to make sense-- it is not a model of what happened before our physics makes sense. Some are disconcerted that we can't make sense of the origin itself, but personally, I think that is the most brilliant aspect of the entire Big Bang paradigm-- it doesn't explain the origin, it explains why we cannot explain the origin. Of course, the Big Bang may one day be replaced by a theory that does explain the origin, but if that happens, it won't be the Big Bang any more. And what's more, I'm not sure I'd be glad-- not being able to understand the origin makes perfect sense to me.

profloater

2011-May-20, 03:46 PM

Maths is always a model. Have you come across Goedel's incompleteness theorem? I have to presume the universe is a real phenomenon but real zeros and real infinities are not necessarily what the maths say, that's why the maths has so called singularities. If you accept the language of Maths you have a different understanding which can be manipulated in many ways but it is hard or impossible to form word pictures or graphics to represent that understanding. According to quantum theory a probability function can spread out through all space, as Feynman said the maths works but it's really hard to understand why.

Hornblower

2011-May-20, 04:06 PM

Let's remember that the cosmos is what it is and does what it does, and it does not care whether or not mortal humans such as ourselves understand it or can describe it in words. These ongoing difficulties give us something that keeps inquisitive physicists busy with healthy research.

noncryptic

2011-May-20, 05:02 PM

I think the OP's question arises from popular misunderstandings about what the current scientific insights are, in this case regarding the beginning of the universe.

I think these misunderstandings are caused in no small part by oversimplification of science by the popular media, helped by poor science education (outside of academia).

For all i know it is indeed a popular misconception that science thinks the universe once was zero size (came from a singularity).

The issue here isn't whether or not it makes sense that the universe once was zero size - the issue is that science doesn't think the universe ever was zero size.

If you heard on a science program that the universe came from a singularity, that statement was either incomplete, out of context or overly simplified (even scientists do that sometimes).

Ken G

2011-May-20, 07:39 PM

If you heard on a science program that the universe came from a singularity, that statement was either incomplete, out of context or overly simplified (even scientists do that sometimes).

I think the correct statement that science programs should make would be not that the universe "came from a singularity", but rather, extrapolating physics, as we now know it, backward in time leads inexorably to a singularity if you use relativity, or a contradiction if you use a combination of relativity and quantum mechanics. So you get to choose between one of the four choices when you extrapolate our current physics backward in time:

1) a singularity

2) a contradiction

3) some unknown new physics

4) something unknowable as physics

Take yer pick, at this moment no one on the planet has any idea which of those is the most correct way to think about the "singularity."

caveman1917

2011-May-20, 08:34 PM

or a contradiction if you use a combination of relativity and quantum mechanics

Could you elaborate where exactly the contradiction lies? Do you mean the word in the exact mathematical sense?

ETA: btw, welcome back :)

noncryptic

2011-May-20, 09:15 PM

Take yer pick, at this moment no one on the planet has any idea which of those is the most correct way to think about the "singularity."

I beg to differ.

Is it not true what Carroll says, that the very fact that GR predicts a singularity means GR does not apply in situations where it does predict a singularity? Isn't it like applying Newtonian mechanics to calculate the orbit of Mercury: it can be done but we know it's wrong?

That's at least one idea about how to think about the singularity wrt the big bang and black holes.

And is it not true that we know we don't know all about how the universe works? That makes "unknown new physics" rather plausible.

In the mean time to most laymen it is not clear that "singularity" actually means "we don't know" or "unknown new physics".

slang

2011-May-20, 09:43 PM

Time and space are funny stuffy. As in, they just don't behave the way we'd expect intuitively. I mean, how weird is it that lengths and time are not the same for observers moving with respect to each other? It's hard enough, if not impossible, to envision how that can be.. is it that strange to discover that we're not equipped with a brain that can easily envision the extremes of the universe? That our (well, us regular dudes and dudettes, not you Einsteinian guys!) brain just says "HALT! ERROR! 'infinite!' .. This cannot be!?!?".

Jeff Root

2011-May-21, 12:11 PM

Is it not true what Carroll says, that the very fact that GR

predicts a singularity means GR does not apply in situations

where it does predict a singularity? Isn't it like applying

Newtonian mechanics to calculate the orbit of Mercury: it can

be done but we know it's wrong?

It is like applying Newtonian mechanics to calculate the orbit

of Mercury: It is right but not complete. There is more going

on than Newtonian mechanics knows about, so its predictions in

extreme situations are not as good as those given by general

relativity.

I think general relativity applies to the beginning of the

Universe as well as it applies to any other time, but there

is more going on than general relativity knows about, so its

predictions in extreme situations are not as good as they

would be if we took into account the other things that are

going on.

We don't know the mechanism of the Big Bang. It will require

new physics, which will modify predictions of general relativity

just as radically as general relativity modifies predictions of

Newtonian mechanics.

-- Jeff, in Minneapolis

danscope

2011-May-21, 05:19 PM

And to the original OP , "How can the Universe be infinite in any way ? " , one can easily surmise ..." How can it not be? "

' Best regards,

Daniel

noncryptic

2011-May-21, 06:23 PM

How can it not be? "

Nature doesn't seem to do a lot of infinite or zero.

It would be unusual, so i think it's a valid question: "how can it be?"

astromark

2011-May-21, 08:43 PM

I love these questions and its why I come here...

Its great to see 'KenG' back and great to see so much good science being said here.

The answer is in the first few posts by 'Jeff Root' and 'Strange'...

but it does require a understanding of principles to comprehend it all

Infinitely small is a concept that the physics we know does not lend itself to.

That single point of a 0 point is a concept only. I note that it took until post 21 and 'Cosmocrazy' to clear that.

A point of some importance to my understanding 'might' help.

That at the early universe time was not as we would know it.

If you can imagine the image of that cone Jeff gave us, of where the point was the single arity

Time did not yet exist. If you can grasp that concept your question vanishes... There may never have been a beginning.

AND one further concept is to consider that .. As the Universe might be 'finite but unbound.'

That concept is my understanding of the mainstream view.

I have a leaning towards Jeffs other than we can ever know... principal.

Noclevername

2011-May-21, 08:53 PM

To our minds it's "impossible" to be in more than one place at once. It's "impossible" for something to both exist and not exist. Yet in physics, these things happen constantly. Sometimes what happens on one scale is counterintuitive to those of us who live and observe on a completely different scale.

noncryptic

2011-May-22, 09:49 AM

To our minds it's "impossible" to be in more than one place at once. It's "impossible" for something to both exist and not exist. Yet in physics, these things happen constantly. Sometimes what happens on one scale is counterintuitive to those of us who live and observe on a completely different scale.

True, that has been observed and it fits with the best theories.

Otoh infinite universe and zero-size anything, although those fit the theories, have not been observed.

So imo argumentation in favor of infinite universe and/or physical existence of singularities requires more than "sometimes" or "why not?".

baskerbosse

2011-May-23, 11:59 AM

One is the problem of how something that has zero size can

become larger than zero size. The other is how something of

zero or finite size can become infinite in size (or the other way

around: how something infinite can become finite). The first

happens all the time. The second doesn't seem possible to

me, either.

It seems to me that the question itself is beside the point.

The universe still remains zero size to photons, while it's quite possibly infinite for anything with mass.

Suppose there was no mass at the big bang, does the size of the universe even have any meaning?

If energy is all there is, perhaps space OR time cannot exist? It has to be zero..

Peter

noncryptic

2011-May-23, 01:14 PM

Suppose there was no mass at the big bang, does the size of the universe even have any meaning?

If energy is all there is, perhaps space OR time cannot exist?

Peter

According to Relativity, energy and mass are equivalent, and are closely tied to space and time.

"The previously separate ideas of space, time, energy and mass were linked by special relativity..."

http://abyss.uoregon.edu/~js/ast123/lectures/lec09.html

cosmocrazy

2011-May-23, 01:22 PM

It seems to me that the question itself is beside the point.

The universe still remains zero size to photons, while it's quite possibly infinite for anything with mass.

Suppose there was no mass at the big bang, does the size of the universe even have any meaning?

If energy is all there is, perhaps space OR time cannot exist? It has to be zero..

Peter

This is a good point, and hits on relativity.

But the question is worth asking because we are here to ask! If there was no mass then there wouldn't be a need for time and space to make room for it, so the universe could be, and well.. most likely would be zero size (as we know it). But like most questions of this type they tend to invoke deep philosophical questions in the process.

The bottom line is, the universe has size, mass and us here to prove it!

What we want to understand is where did it all come from, why and how? The current physics suggests from an extremely, if not infinitely, small size. If this is correct we then ask how this process began, works and for what reason?

caveman1917

2011-May-23, 01:37 PM

Suppose there was no mass at the big bang, does the size of the universe even have any meaning?

If energy is all there is, perhaps space OR time cannot exist? It has to be zero..

Vacuum solutions (ie no matter) exist, perhaps the most famous cosmological one is de Sitter space.

Ken G

2011-May-24, 01:35 AM

Could you elaborate where exactly the contradiction lies? Do you mean the word in the exact mathematical sense?

The contradiction is that the equations of relativity assume that there is such a thing as a spacetime metric on an arbitrarily small spatial scale, but quantum mechanics says that some scales are so small that they cannot be given physical meaning without resorting to extremely high energies. Those energies, when plugged back into general relativity, would induce black holes instead of a smooth spacetime. This problem appears at the "Planck scale". So if you extrapolate some physical distance in the current universe backward in time until it was the size of the Planck length, you could no longer given that distance a physical meaning that is consistent with quantum mechanics. That's the contradiction you encounter before you ever get to a singularity.

csmyth3025

2011-May-24, 03:45 AM

Originally Posted by baskerbosse

Suppose there was no mass at the big bang, does the size of the universe even have any meaning?

If energy is all there is, perhaps space OR time cannot exist? It has to be zero..

Vacuum solutions (ie no matter) exist, perhaps the most famous cosmological one is de Sitter space.

Aside from the hypothetical de Sitter space which, essentially, postulates a universe with energy but no matter, there is the actual big bang cosmological model by which the number of photons per nucleon in the early universe can be estimated:

It is estimated that there must have been about two billion photons present for each nucleon.

(ref. http://www.scienceandreason.net/oq/oq-co008.htm#nucleosynthesis )

By this estimate, even the universe that we live in has but a very small smattering of matter in it compared to the electromagnetic energy that it contains.

Chris

Ken G

2011-May-24, 03:51 AM

I beg to differ.

Is it not true what Carroll says, that the very fact that GR predicts a singularity means GR does not apply in situations where it does predict a singularity?I didn't say there isn't a singularity, the four choices I gave were around the best way to deal with the singularity. Relativity yields a singularity, and quantum mechanics replaces it with a contradiction. We don't know if this is any kind of improvement, because we don't know if quantum mechanics works and relativity doesn't, we only know that relativity doesn't work. We also don't know if we can replace both quantum mechanics and relativity with some other new physics, or if physics itself is incapable of addressing the origin of the universe. Hence, we are left with those four possibilities, with no way to know which way to go.

And is it not true that we know we don't know all about how the universe works? That makes "unknown new physics" rather plausible.Yet there are basic paradoxes about using physics to discern an origin of the laws of physics. There simply might not be any new physics that can do that.

Ken G

2011-May-24, 04:01 AM

By this estimate, even the universe that we live in has but a very small smattering of matter in it compared to the electromagnetic energy that it contains.

No, the energy in the universe is now thought to be about 70% dark energy and 30% rest mass energy, with very little photon energy.

caveman1917

2011-May-24, 04:40 AM

Those energies, when plugged back into general relativity, would induce black holes instead of a smooth spacetime. This problem appears at the "Planck scale".

Isn't a black hole spacetime smooth everywhere except at the point of the singularity itself?

Why would the problem appear before that at the planck scale?

I assume you're using heisenberg's principle of \Delta t \Delta E or conversely \Delta p \Delta x to show that a minimal small time or spatial scale doesn't make sense unless you're giving it that huge energy. But if that energy is big enough to give a black hole, why does the problem in GR start at the planck scale instead of at a single singularity point as is expected from a standard black hole manifold?

caveman1917

2011-May-24, 05:03 AM

I can see that the planck radius is that radius for which follows that the energy inside due to quantum effects equals the energy needed for it to be a black hole.

What i'm having trouble wrapping my head around is why that would be a problem, when plugged back into GR, to make the spacetime smooth.

One could argue that the spacetime is closed of by an event horizon there. But the absolute horizon is global, and for example in the case of an asymptotic de sitter space undefinable. And the apparent horizon in the schwarzschild metric can be removed by a coordinate change.

I guess i can't readily see why, even if there's a mini black hole there with a planck radius, it would give a problem in making the spacetime smooth (at least up until the point of the singularity itself).

Ken G

2011-May-24, 05:55 AM

I assume you're using heisenberg's principle of \Delta t \Delta E or conversely \Delta p \Delta x to show that a minimal small time or spatial scale doesn't make sense unless you're giving it that huge energy. But if that energy is big enough to give a black hole, why does the problem in GR start at the planck scale instead of at a single singularity point as is expected from a standard black hole manifold?Yes, that's the idea. You're saying that any point particle is in effect its own little black hole, and can still interact normally with other particles on larger scales, so what's the big deal with the Planck length. But the problem isn't in the innate size of the particle, it is in the scale of its wave function, relative to the scale of its event horizon. If you take a thermal radiation field and compress it arbitrarily (say by running time backward), general relativity only knows about the energy density there, and its equations present no problems until you get to the singularity. But there are actually quanta there if one uses quantum mechanics, so we have a new wrinkle-- the arbitrarily compressed thermal radiation field not only has a huge energy density, it also has a huge energy per photon. When the Schwarzschild radius of each photon exceeds the distance between photons, you don't have a medium of "space" through which the photons can move, you have a universe of overlapping black holes with a completely fragmented spacetime. In short, the problem is not that the event horizons are so small, it is that they are so big-- compared to the distance between photons. At least, that's my impression of the situation-- for a more complete description, you'd need a real quantum field theorist (which I am not)-- the only trouble is, ten such theorists might give you ten different descriptions of life at the Planck scale!

baskerbosse

2011-May-24, 12:01 PM

Vacuum solutions (ie no matter) exist, perhaps the most famous cosmological one is de Sitter space.

Ah, that looks interesting! Especially de Sitter Universe. (-when am I going to find time to learn some maths? -Sigh..)

I still don't get how you measure size without matter?

Seems like measuring time without movement..

Does the answer lie with deSitter..? Looks like a tough one to tackle..

Peter

Ken G

2011-May-24, 01:42 PM

I still don't get how you measure size without matter?

Seems like measuring time without movement..

There couldn't be size without matter, there couldn't even by physics without matter. But in a de Sitter universe, the matter isn't contributing in any important way to the gravity of the universe as a whole. Instead, the matter is treated at "test particles", which means its motion probes the nature of spacetime without affecting the nature of spacetime. It would be the way we like to think of physicists-- as "flies on the wall" of a universe that is ambivalent to their presence.

caveman1917

2011-May-24, 02:38 PM

You're saying that any point particle is in effect its own little black hole, and can still interact normally with other particles on larger scales, so what's the big deal with the Planck length.

I didn't have point particles in mind, or even particles per se.

I was thinking about the "fuzzy energy blob" that happens to be inside its own schwarzschild radius. My reasoning is that, since all geodesics inside a black hole point straight towards the singularity, there doesn't seem to be a problem with this "spatially extended" energy since it will collapse to a single point immediately anyway. That's why i could see pointlike singularities happening, but not any fragmented spacetime beyond those points. The interior of a schwarschild black hole is stable, even if you disturb it badly with a huge distributed energy, it will immediately re-establish itself.

But the problem isn't in the innate size of the particle, it is in the scale of its wave function, relative to the scale of its event horizon.

I assume you mean that the spatial distribution of that energy is as big as the event horizon? If that's what you mean, that's indeed what i was considering, but by the above paragraph dismissed as a fundamental problem.

When the Schwarzschild radius of each photon exceeds the distance between photons, you don't have a medium of "space" through which the photons can move, you have a universe of overlapping black holes with a completely fragmented spacetime.

The first question is wether we really have any event horizons there. An event horizon is defined as the boundary of that section of spacetime not in the causal past of future null infinity. Since we know we can actually see the photons now (which is the situation we "turned the clock on"), this suggests they were never behind any event horizon. How would they have escaped from beyond their event horizons to get to us here and now?

By the second law of black hole mechanics we can also say that there were all those overlapping event horizons, and they grew to encompass our entire observable universe so we are still within one huge black hole. That way us seeing the photons don't represent them going out to future null infinity. But wether the distinction is meaningful is quite another matter, so we might as well use the former one.

All in all i can see how you'd get a spacetime with a bunch of naked pointlike singularities, but not how you'd get a fragmented spacetime beyond those points.

I know there must be a problem there, but i just can't see how you'd get an issue with the general smoothness of the manifold except for a couple of points.

caveman1917

2011-May-24, 02:40 PM

Ah, that looks interesting! Especially de Sitter Universe. (-when am I going to find time to learn some maths? -Sigh..)

I still don't get how you measure size without matter?

Seems like measuring time without movement..

Does the answer lie with deSitter..? Looks like a tough one to tackle..

Peter

I suppose it's the difference between mathematically describing a model of the universe, vs actually being in such a universe making measurements.

Mouser

2011-May-24, 03:00 PM

According to big-bang papers I have read, in pre-inflation universe, space-time (itself a constituent of the current universe) did not exist.

In the absence of space-time, the notion of infinitely small is a whole different notion, I would think.

If we extrapolate to the big-rip (given current inflation notions and observations tend to shy away from big-crunch), if space-time rips apart along with the rest, then infinitely large also looses it's meaning.

I entertain the notion that the pre- space-time and post- space-time universe ought to have the same properties. Ie, no size etc. Wether right or wrong, it lessens my headaches on the subject. :think:

csmyth3025

2011-May-24, 06:33 PM

Originally Posted by csmyth3025

By this estimate, even the universe that we live in has but a very small smattering of matter in it compared to the electromagnetic energy that it contains.

No, the energy in the universe is now thought to be about 70% dark energy and 30% rest mass energy, with very little photon energy.

You are, of course, quite right. I should have phrased that statement in the past tense - for our very young, radiation dominated universe:

Initially, the energy density of radiation was much larger than that of matter. However, at some point, since radiation density decreases faster than matter density, the latter overtook the former, the universe became "matter dominated", and it has and will remain so. We might ask at what point the transition from radiation dominance to matter dominance occurred. The answer is that it depends on both Ω (or curvature) and on the present value of the Hubble parameter H. Given the best current observational evidence that Ω = 1 and H is about 70 kmps/Mpc, the time works out to 47,000 years (1.5×1012 seconds), and the scale factor was 2.8×10-4. Since redshift z and scale factor are related by z = 1/a - 1, this corresponds to a redshift of about 3570.

(ref. http://www.scienceandreason.net/oq/oq-co008.htm#models )

Interestingly, the de Sitter model of the universe that has been discussed in the last few posts seems to be a viable candidate for describing our universe as it might become far into the future:

It models the universe as spatially flat and neglects ordinary matter, so the dynamics of the universe are dominated by the cosmological constant, thought to correspond to dark energy in our universe or the inflaton field in the early universe. According to the models of inflation and current observations of the accelerating universe, the concordance models of physical cosmology are converging on a consistent model where our universe was best described as a de Sitter universe at about a time t = 10 − 33 seconds after the fiducial Big Bang singularity, and far into the future.

(ref. http://en.wikipedia.org/wiki/De_Sitter_universe )

Chris

Ken G

2011-May-24, 08:46 PM

I assume you mean that the spatial distribution of that energy is as big as the event horizon? If that's what you mean, that's indeed what i was considering, but by the above paragraph dismissed as a fundamental problem.

It's still a fundamental problem, because the purpose of a spacetime is to provide a medium against which we can do physics on particles. If the scale we need to talk about to do physics on particles requires energies associated with those particles that create event horizons larger than the scale on which we are trying to do physics, then we can't do the kind of physics we need to do-- we can't talk about the motion of the particles or their interactions with other particles. Instead, the situation is just as you say-- every time we start trying to talk about a spacetime through which the particles could move or interact, we find the curvature of the spacetime is so tiny that the only motions allowed are right into singularities. We don't even know where to put the singularities, because the quantum mechanical wave function does not have that kind of spatial precision in the first place. It just doesn't work as a spacetime on which you could try to do quantum mechanics, so if quantum mechanics is indeed the right way to do physics (I doubt it on those scales, but many others seem to think it is), then you have to drop general relativity at that scale. You're going to have to drop general relativity anyway, as all roads lead to singularity when extrapolating backward in time.

Of course, another matter is that we are not just talking about GR, we are talking about GR with a cosmological principle. That almost certainly breaks down long before you get to the Planck scale, so again we see the need for new physics. The indispensable value of the cosmological principle is then seen as yet another reason why the way we do physics in the first place is probably not going to be up to the task, so for that and many other reasons my personal suspicion is choice #4. It's not a popular choice because it sounds like giving up, but if it's the truth, then it's just how it is.

The first question is wether we really have any event horizons there. An event horizon is defined as the boundary of that section of spacetime not in the causal past of future null infinity. Since we know we can actually see the photons now (which is the situation we "turned the clock on"), this suggests they were never behind any event horizon. How would they have escaped from beyond their event horizons to get to us here and now?Oh yes, there's no question that general relativity plus the cosmological principle is wrong there. But that doesn't tell us what is right-- maybe general relativity is right and we never need scales anything like that, because we are simply overusing the cosmological principle to make that extrapolation. Or maybe general relativity is wrong but so is quantum mechanics. Or maybe physics itself is wrong when you extrapolate it to an origin, or maybe we'll figure it all out eventually. Those are the four choices I mentioned above.

All in all i can see how you'd get a spacetime with a bunch of naked pointlike singularities, but not how you'd get a fragmented spacetime beyond those points.What physics will tell you where the pointlike singularities turn up? Smoothness of the manifold is required to be able to even talk about a "point" in physical terms. In quantum mechanics, there is no such thing as a physical point, there are only idealized contributions to some mathematical integral in a "position basis", unless there is the infinite energy needed to make an exact position measurement.

caveman1917

2011-May-24, 09:36 PM

If the scale we need to talk about to do physics on particles requires energies associated with those particles that create event horizons larger than the scale on which we are trying to do physics, then we can't do the kind of physics we need to do

But how do you know they create event horizons? It looks to me as though the situation suggests they don't, at least not an absolute horizon in the standard black hole sense. Perhaps coordinate horizons, but they should be removable with a suitable coordinate choice.

What physics will tell you where the pointlike singularities turn up?

I would assume the spherical symmetry of the schwarzschild solution might provide those means. If the energy is high enough to be within its own schwarzschild radius, the schwarzschild radius could be used to pinpoint the singularity.

Do you perhaps have a mathematical reference on this? Not necessarily the cosmological aspect, but the general aspect of trying to do physics near the planck scale, and specifically how quantum factors mess up the smoothness of the manifold. Maybe i'd more clearly see the issue when it's worked out mathematically.

Ken G

2011-May-25, 04:49 PM

But how do you know they create event horizons? It looks to me as though the situation suggests they don't, at least not an absolute horizon in the standard black hole sense.The issue isn't so much horizons, as curvature. But either way you slice it, the gravity would be so strong that interactions between particles would be impossible. To say a particles is in a box the size of Planck length is to a gravitational curvature that makes that box its own tiny universe, it curves back on itself. That would be OK if there was some kind of background spacetime for the black hole to move through, just as real ones do, but the Planck scale is the interparticle spacing scale that we are talking about, so there's no smooth background spacetime for the curled-up pockets to move through.

Maybe a better way to say all this is that if we extrapolate the GR equations with the cosmological principle, we get back to a point when the temperature is so high that as soon as you quantize the particles, they each get kT of energy, which is in turn too much energy to allow the particle to have a wave function. The scale of the wave function is supposed to be h/p which here is hc/kT. When that scale is larger than the Schwarzschild radius of the particle, so GkT/c4, we have a contradiction because the curvature of the spacetime does not allow the uncertainty principle to hold any more. Solving for T says the kT cannot go above h1/2c5/2/G1/2 without encountering this contradiction.

I would assume the spherical symmetry of the schwarzschild solution might provide those means. If the energy is high enough to be within its own schwarzschild radius, the schwarzschild radius could be used to pinpoint the singularity.Quantum mechanics does not allow you to pinpoint the singularity. There's uncertainty in its location, but at the Planck scale, the uncertainty in the location of the singularity is larger than the curvature associated with the singularity. It's sort of like in quantum mechanics, you cannot say that a wave function is just an uncertainty about the true location of the particle-- there needs to be interference effects that actually allow the particle to be at any of those places. So you can't say you really have a singularity and you just don't know where it is, you have to say the singularity really is in some sense at all those places-- but that's not consistent with general relativity, since GR makes no provision for gravitational superpositions.

Do you perhaps have a mathematical reference on this? Not necessarily the cosmological aspect, but the general aspect of trying to do physics near the planck scale, and specifically how quantum factors mess up the smoothness of the manifold. Maybe i'd more clearly see the issue when it's worked out mathematically.I was able to google up this: http://people.bu.edu/gorelik/cGh_FirstSteps92_MPB_36/cGh_FirstSteps92_text.htm. In it, you will find somewhat different approaches by Bronstein, Klein, and Wheeler (in sections 4 and 5), and although it's hard to see just what the differences are, they all seem vaguely similar to the argument I'm presenting here. Whether or not any of this is rigorously true I really couldn't say-- it all has the flavor of rough scaling analyses.

caveman1917

2011-May-25, 11:05 PM

I was able to google up this: http://people.bu.edu/gorelik/cGh_FirstSteps92_MPB_36/cGh_FirstSteps92_text.htm. In it, you will find somewhat different approaches by Bronstein, Klein, and Wheeler (in sections 4 and 5), and although it's hard to see just what the differences are, they all seem vaguely similar to the argument I'm presenting here. Whether or not any of this is rigorously true I really couldn't say-- it all has the flavor of rough scaling analyses.

Thanks.

Would i be right in thinking that it is not so much the high value of the curvature, but the uncertainty of it that is the problem?

Basically that \Delta g / g \rightarrow 1 as l \rightarrow l_p.

Where for electromagnetism you can measure the field accurately by keeping the charge/mass ratio low, this is impossible for the gravitational field due to the equivalence principle stating that gravitational mass equals inertial mass, so there's nothing you can do about that ratio in that case.

In other words, you cannot get around the back-reaction between measurement device and system being measured.

Since the speed of light is given by the slope over the geometry, the uncertainty in the speed of light goes like the uncertainty in the metric.

\Delta g / g = 1 \implies \Delta v_c / v_c = 1.

This completely breaks down causality, and thus any physics at the planck scale.

Is this about right?

If it is, i understand. I was thinking too much about the proverbial black hole and the high (but definable) geometry involved with a black hole, as opposed to the problem of an undefinable geometry.

Ken G

2011-May-26, 05:51 PM

Thanks.

Would i be right in thinking that it is not so much the high value of the curvature, but the uncertainty of it that is the problem?

Basically that \Delta g / g \rightarrow 1 as l \rightarrow l_p.I think it's both-- I'd bet that delta-g / g ~ 1 at pretty much the place where the curvature equals the spread in the wave function. So there are lots of ways of saying what ends up being the same thing-- the concept of a metric has to be married with the concept of the fundamental uncertainty of a superposition, in ways that have not yet been done, when you get to the Planck scale.

Where for electromagnetism you can measure the field accurately by keeping the charge/mass ratio low, this is impossible for the gravitational field due to the equivalence principle stating that gravitational mass equals inertial mass, so there's nothing you can do about that ratio in that case.Yes, I think that's an interesting insight, it's probably another way of saying what ends up amounting to the same issue at the Planck scale.

This completely breaks down causality, and thus any physics at the planck scale.

Is this about right?Yes, I suspect the fundamental problem involves causality. Both GR and QM respect a principle of causation (even if the QM version invokes a weird concept of a wave function), and that's what frays at the Planck scale. Most likely, the universe itself does not require such a fundamental principle, causation itself may emerge on scales above the Planck scale, but everything we do in physics is so reliant on the concept of causation that it might require reconstructing physics itself to accomodate its breakdown. But even that presupposes we could ever do experiments at the Planck scale, which is unlikely-- so all we ever need is the emergent theory which will always break down too early in the Big Bang. I say live with it. We never really had any business extrapolating the cosmological principle that early in the first place (remember that inflation comes after the Planck era).

If it is, i understand. I was thinking too much about the proverbial black hole and the high (but definable) geometry involved with a black hole, as opposed to the problem of an undefinable geometry.Yes, I think the definability is the crucial issue. The deepest principle of physics is that we can define what we are talking about, and when even that breaks down, we have a real problem! We often rely heavily on a separation of scales-- we can talk about a soccer ball made up of atoms only because the size of a soccer ball is so much larger than the size of an atom. Time and space require clocks and rulers that can function within that time and space, and at the Planck scale, none of that works. That's why I say the most brilliant thing of all about the Big Bang model is that it tells us why physics doesn't have to explain the origin-- because it explains why physics can't.

caveman1917

2011-May-26, 11:01 PM

We never really had any business extrapolating the cosmological principle that early in the first place (remember that inflation comes after the Planck era).

On the other hand the problem doesn't just show up in cosmology but in trying to do physics on small scales in any context, so i'm not sure we can blame the cosmological principle. The webpage you linked to derives it in minkowski with a weak linear gravitational field added to it.

caveman1917

2011-May-26, 11:10 PM

My QM is at the level of a toddler so i'm just guessing about this, but i have a follow-up question.

I suppose one could look at it as spacetime itself fluctuating as by the normal quantum fluctuations of the vacuum. Because at the planck scale the influence of those fluctuations on the geometry becomes too great to ignore, we get an undecidability of the structure of spacetime at that scale.

But does this not mean that quantum fluctuations cannot be gaussian? Since we know that the spacetime described by them at that scale gives rise to a specific behaviour on greater and greater scales.

Ken G

2011-May-27, 12:40 AM

On the other hand the problem doesn't just show up in cosmology but in trying to do physics on small scales in any context, so i'm not sure we can blame the cosmological principle. The webpage you linked to derives it in minkowski with a weak linear gravitational field added to it.Yes, it comes up outside of cosmology in theory, but not in anything we can observe. Personally, I feel all physics theories should be regarded as effective theories rather than fundamental ones-- we should always expect our theories to emerge as consequences of deeper ones that we have little chance of discovering without some direct observational evidence. Certainly this has always been true throughout the history of physics. Cosmology is the place where there are observable consequences of the Planck scale, because the universe on all scales would have been at that scale at some point (if indeed the cosmological principle were applicable down to those scales). But if the cosmological principle is purely a post-inflationary principle, then the universe we now observe might not be extrapolatable earlier than the inflationary epoch. In other words, there might have been some global physics at play, different from a Big Bang expansion, that has left no testable trace on our local piece, the "true" Planckian universe pre-inflation might have completely covered its tracks, and the only way we could ever re-encounter that "true" physics would be to have observations at the Planck scale, which is basically unthinkable.

Ken G

2011-May-27, 01:12 AM

I suppose one could look at it as spacetime itself fluctuating as by the normal quantum fluctuations of the vacuum. Because at the planck scale the influence of those fluctuations on the geometry becomes too great to ignore, we get an undecidability of the structure of spacetime at that scale.I believe some efforts along those lines have been attempted, but I really don't know much about them. They can't have been too successful yet, or we'd hear more about them.

But does this not mean that quantum fluctuations cannot be gaussian? Since we know that the spacetime described by them at that scale gives rise to a specific behaviour on greater and greater scales.I doubt it could be strictly Gaussian, but maybe approximately so-- I really don't know!

iantresman

2011-May-27, 04:52 PM

I always assumed that the Big Bang did not assume that the initial universe was infinitely small (equivalent to zero size), but that the size was immeasurable. If we consider a universe with no photons and no particles, what references are there to measure against?

cosmocrazy

2011-May-27, 08:34 PM

I always assumed that the Big Bang did not assume that the initial universe was infinitely small (equivalent to zero size), but that the size was immeasurable. If we consider a universe with no photons and no particles, what references are there to measure against?

Its a popular concept that prior to the BB (if that in its self has any real meaning) there was no space or time. If this is true then "size" at this point is irrelevant. Also we are unable to measure smaller than the Planck scale (again if that in its self has any real meaning). So what we can say is the universe appears to have started out extremely smaller than could be imagined or from zero size (before space-time)

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