The Universe: Finite or Infinite?

[TalonD]

If it is possible to concieve of something physical being infinite then there should be no problem with having a sphere who's radius and diameter are infinite,

This is over my head but if both the diameter and radius are infinite wouldn't the diameter have to equal the radius. And if the only the diameter was infinite wouldn't the circumference have to be greater than infinity?

I don't think it's meaningful to draw a distinction between radius and diameter like that. if you draw a circle there is one length acros it, that is diameter. Radius is just a subset of that disance. it can be used mathematically to determine circumference. I think if any of it is infinite then all of it is equally infinite. But as I said earlier, there is a such thing a some infinities being larger or smaller than other infinities.

Comparing infinite radius to infinite diameter seems almost like the old paradox of an arrow shot from a bow can never reach it's target because first it must travel half the distance, then half the remaining distance etc. etc. etc... ad infinitum.


but again, wheather our universe is curved, flat, finite or infinite has to do with the critical density... I think..

 

[Ike47]

...

but again, wheather our universe is curved, flat, finite or infinite has to do with the critical density... I think..

Sounds just like me, lol. I should put a disclaimer into a sig saying all my posts may be incorrect.

 

[phmovies101]

I have thought about this question all the time. I'm not PhD. Physicist, but I like to think about things like this. I'm sure if there is fact, or at least not yet, but I believe that this question brings about a belief in people. You have to decide what you think is the most reasonable.

My idea on this is not scientifically based, but maybe it could work. I believe in the big bang theory, and I believe in the finite universe. However, I do not like to believe in the fact that the universe is flat-ish. I think the objects in space are pulled around a center where the big bang was suppose to happen. Maybe there is an intense field of gravity and was produced by the massive explosion of the condenced particles. The area of space surrounding the site of explosion has no matter or particles. The force acting on the celestial objects is to far away to pull it toward the center. The universe is definitely expanding. If you can imagine on of those glass balls that has the tesla coil on the inside and shoots off beams of electricity. The Objects in space are dependant on the center. Thier rotation creates a sphere. Objects move infinitely until they are acted on by other forces. Matter is pushed outwards, but at the same time, rotating due to the intense amount of energy.

P.S. I don't expect you to believe this, but I did the best I could.

 

[Quisquis]

If it is possible to concieve of something physical being infinite then there should be no problem with having a sphere who's radius and diameter are infinite,

This is over my head but if both the diameter and radius are infinite wouldn't the diameter have to equal the radius. And if the only the diameter was infinite wouldn't the circumference have to be greater than infinity?

I have an experiment for you to try that might help you understand how if the radius of a sphere extending to infinity means that you have created a flat surface:

Take a piece of paper and roll it up into a cylinder. This cylinder has a defined radius. Now take the edges of the paper that you just rolled together and pull them apart. As you pull them apart, imagine that there's more paper filling in the gap so that you are creating a larger and larger cylinder. The radius is getting larger in your cylinder... now as you get closer and closer to having a flat piece of paper, your radius is expanding more and more... once you have a flat piece of paper again instead of a cylinder, you've reached the point where your radius has approached infinity.

So, in conclusion, if you have ANY curvature at all to your sphere, you have a finite radius.

Hopefully that clears things up for ya.

EDIT: I hadn't thought about this like that until now. That's sort of an interesting concept to think about actually. Thanks for giving me the chance to fire off some neurons. :-D

 

[eha]

space is endless in 3D, our universe has boundaries, there might be other universes, maybe there are so many different universes and they all occupy a certain volume within endless space. this is my opinion, frankly.

 

[Pjpic]

space is endless in 3D, our universe has boundaries,


That seems reasonable. Because, if It is not endless how could we ever be sure there wasn't something else past the boundary where nothingness started or past where a particular discipline was focused.

 

[x→∞]

Is the universe finite? (= implies a "Beyond")
Is the universe infinite? (= seems nonsensical, and counter-intuitive to "Big Bang" theory)

Finite does not imply boundary. Infinity and unbounded are two different concepts.

For example consider a spherical object. If you are a two dimensional creature embedded in the surface of a sphere, and you start moving in the same direction (you can only travel forward or backward and up and down since you are 2D), you would not find the end of the sphere, and since you are a two dimensional creature you would not have a brain to see a 3D object (because you don't need to), you would feel that you are traveling in a straight line. See that the area of the sphere is finite.

Now you are a 3D creature embedded in a 3D world. We would not see the boundaries of the universe just like the creature on the sphere. Only a higher creature outside our 3D universe, in a higher dimension, would be able to see the "finiteness" of our universe.

Therefore, we have no way of telling, we can only guess.

Even if traveling infinitely fast, you may or may not be able to reach a boundary where time and space would cease to exist. You could not go past this boundary because on the other side there is no time, and there is no space.

 

[Pjpic]

Finite does not imply boundary. Infinity and unbounded are two different concepts.

---- I don't quite understand why infinity and unbounded are different concepts. Because, in my understanding, infinity means 'without end' and unbounded means "without an ending".

See that the area of the sphere is finite.

--- In the example of a two dimensional creature living on a 3 dimensional sphere, the boundary is that which prevents the creature from moving off the surface of the sphere (that which prevents movement within the space which it is embedded). Even if the creature is not aware of it, it is still a boundary.


Even if traveling infinitely fast, you may or may not be able to reach a boundary where time and space would cease to exist. You could not go past this boundary because on the other side there is no time, and there is no space.

--- If there is a boundary that forms the end of the universe, it deals raises questions of nothingness (I think I read that constructive geometry considers 'nothing 'to be the inverse of 'infinte'). For example on the micro scale "nothingness" is often thought to separate two particles. Could that also be the case when thinking about a potenial nothingness beyond our universe (that the nothingness just separates us from other universes)?

 

[Chiclayo guy]

To a layman like me with absolutely no science background or training it seems incredibly simple. Space is a void. It is eternal and infinite. I’m content with that description. I don’t need to struggle with questions of where it came from or how it came about or what existed before. It simply is and always was. The universe is the physical matter occupying space. As I understand it, that physical matter all resided at one small central point some 14 billion years ago and has since expanded. I don’t have to deal with defining “small” or where that central point is/was located or how the physical matter got there. I have an image of both “small” and “central point” and am content with that. It’s a little harder for me to conceptualize matter as being eternal. As I see it space is ‘nothing’ and nothing doesn’t require a beginning or an end, but matter is ‘something’ and all the matter I’m familiar with has a beginning and an end, or at least changes form dramatically. Anyway to me it seems that whatever path is taken will ultimately lead to infinity and eternity because questions like “what was/is before or beyond ?” can be asked for…well…eternity.

 

[x→∞]

--- If there is a boundary that forms the end of the universe, it deals raises questions of nothingness (I think I read that constructive geometry considers 'nothing 'to be the inverse of 'infinte'). For example on the micro scale "nothingness" is often thought to separate two particles. Could that also be the case when thinking about a potenial nothingness beyond our universe (that the nothingness just separates us from other universes)?

By micro scale do you mean the Planck length? I understand what you are saying, you're right. All together, an infinite amount of seeming-to-us as being nothing (in reality being extremely tiny amounts of something) may add up to be quite a large amount of something? Or would the quantity/mass of that something be infinite as well, since it is found in an infinite amount of space, and there is an infinite amount of its particles?

 

[cragar]

could we say that there is only so much space but its a finite volume .
like an infinite series it goes on forever but it can converge to a finite area. A fixed number. So could space go on forever and have a finite volume.

 

[x→∞]

could we say that there is only so much space but its a finite volume .
like an infinite series it goes on forever but it can converge to a finite area. A fixed number. So could space go on forever and have a finite volume.

So according to what you said, space can contain a finite amount of matter (finite volume), although space itself is infinite? If the volume is finite, it must have a finite shape and boundaries in which the finite volume is contained. Then what is beyond those boundaries? It's impossible to tell, but theoretically speaking, what you are saying implies that there must be some sort of boundary.

 

[cragar]

there does not neccessarily have to be a boundry for example the improper integral from -inf to +inf of 1/(x^2+1) the bounds go forever i both directions but it has a finite area of (pi) 3.14 the limit as x approaches infinty of arctan(x) =pi/2 then multyply it by 2 cause we have 2 sides so we get pi . even tho the bounds go for ever we have a finite area .

 

[kenny30]

this is a question and not a reply.
when we look at very distant galaxi,we go back in time and we see the state of that galaxi supposing 12 billion years ago.
but 12 billion years ago the matter making the universe was very close to each other due to the theory of the big bang.
and here we are now looking at that galaxi 12 billion years later,looking at the light emitted by,that blob of matter when we were very close to it.and because the speed of light is ultimate and much faster than the matter making our beiing ,
(telescopes,eyes,brains,solaire systeme and galaxy ...Etc)that light should have passed by the matter that make us long time ago.

we should be moving with that light at the same speed,impossible!
is there a paradox or something wrong with big bang or the speed of light theories.

 

[Gan_HOPE326]

Hmm... I'm not 100% sure of what I'm going to say cause I'm not a physicist, but

this is a question and not a reply.
when we look at very distant galaxi,we go back in time and we see the state of that galaxi supposing 12 billion years ago.
but 12 billion years ago the matter making the universe was very close to each other due to the theory of the big bang.
and here we are now looking at that galaxi 12 billion years later,looking at the light emitted by,that blob of matter when we were very close to it.and because the speed of light is ultimate and much faster than the matter making our beiing ,
(telescopes,eyes,brains,solaire systeme and galaxy ...Etc)that light should have passed by the matter that make us long time ago.

we should be moving with that light at the same speed,impossible!
is there a paradox or something wrong with big bang or the speed of light theories.

I think this could be because speed of light limitation doesn't apply to universe expansion. During the "inflation" universe should have expanded actually faster than light. Lightspeed is a limitation due to our space-time construct: expansion is the creation of that same space-time. Then, after all, probably 12 billions year ago that galaxy was already very far from us - 'cause the universe experienced its biggest expansion in its first moments. If it was, say, 8 billions LY from us, then it took 8 billion years for light to reach our former position - but in the meanwhile, we went a little further. So it took a little more and so on - finally, it's 12 billion years. More or less ...

Or maybe the universe definitely is a curved, finite one (meaning, with curved, it has a "Riemann" or spherical geometry), and light just went round and round since it came to us... again. Maybe we're just looking our own galaxy how it was 12 billion years ago, after its image turned the whole universe. Ok, this is madness .

 

[honzik]

Hi,
Finity of the universe for me doesn't mean that it has finite volume but that it is space-ly bounded (ie. there exists distance D that every two points in the universe have distance between them lower than D).

I think that a) inflation theory implies finite universe or b) I don't understand inflation theory.

So to be able to discuss about inflation we have to define what we understand under this term. Or to be less strict - what are the exhibitions of inflation.

The first and major question of all is:

(*) Did inflation took place in the whole universe (no matter whether it is finite or infinite)?

I think both possible answers (yes or no) can lead into contradiction if we suppose the universe is infinite. But please answer the question first to lead our discussion in one direction only.

Thank you very much.

Honzik

 

[TalonD]

Hmmm..

b)

 

[kenny30]

thanks to Gan_HOPE326 for answering my question.
i think the concept of inflation that u described should apply not only to space but to time too i guess.
so in this case cosmologist will be having another problem in giving our universe an age which is between 13.5 and 13.7 billion years old.
because if there is an inflation in time,the flow of time in the early universe would be much different than the flow of time in the actual universe .
i mean a second won t be a second as we know it know ,
and a year won t be a year as we know it now.
so the universe could be 20 or 30 billion years older or more
and probably the constant of speed of light could have been much different than the (c)
as we know it in the actuel universe .but who knows.?

 

[DevilsAvocado]

thanks to Gan_HOPE326 for answering my question.
i think the concept of inflation that u described should apply not only to space but to time too i guess. so in this case cosmologist will be having another problem in giving our universe an age which is between 13.5 and 13.7 billion years old.
...

I'm just a layman (not avocado, nor advocate ), but I think I can help you.

This question about light from very old (and at that time near) "objects" almost drove me crazy , before I found the logical answer on Wikipedia. Inflation could be some part of the answer, but the real "heavy" thing here is Einstein's General Relativity, which describes gravity as a geometric property of spacetime (the curvature of spacetime).

The key thing to understanding this, is that the light from very old objects, actually were emitted at an angle of 45° towards Earth, and furthermore had to work its way "upstream" the expansion of spacetime.

I strongly doubt that speed of light (c) has varied... That's the only constant thing Einstein left for us to hold on to...

Here is the link (including nice pictures):
http://en.wikipedia.org/wiki/Expanding_universe#Understanding_the_expansion_of_space"

 

[DevilsAvocado]

Dear Pjpic,
George Jones who is both a PF mentor and someone with academic specialization in cosmology effectively answered the question. But you couild reasonably ask for more elaboration and say that what you've been able to find in your other readingon it is either:
1. not spelled out in simple language, or
2. too contaminated with noise and disagreement about the meaning of words.
So I'll make a stab at clarifying for you.

I think what Mattex is asking is if you could freeze expansion at the present instant of cosmological time and then were able to wander freely around and explore all of space,then would it turn out to have infinite volume or would it have finite volume?

...

(Perhaps I'm throwing stones in a glass house, with this question...? marcus, you have to excuse me for this... )

But I think the real "forbidden" question here is - What is the universe expanding into?

I.e. mattex & Pjpic are very "polite", but I guess the (traumatic) underlying problem/question is - what the heck is that extremely generous "thing" providing bigger and bigger "living room" for our maniac accelerating universe. (Packman seems like a nice guy in comparison)

(Please note; I'm NOT religious at ALL)

We can get lost in formal discussions about finite versus infinite, flat versus open/closed, etc. And if we calculate with spacetime and gravity (GR) - it becomes impossible to just talk in words about where we are and what is now, and what happened first, etc.

So, the one thing we surely can agree on (in words), is that our observable universe is expanding at accelerating rate. This no-one can deny.

Thus, if our universe is finite - there MUST be "new room" for this expanding monster at almost twice the speed of light. Where does this "new room" come from??

And if our universe is infinite - there MUST be "extra room" for this expanding monster at almost twice the speed of light. Where does this "extra room" come from??

I know it's "forbidden" to talk about things that we never ever will be able to come in contact with. But if guys like http://en.wikipedia.org/wiki/Multiverse" can talk about Multiverse and "bubbles" we never ever will be able to come in contact with...? Why can't I talk about what we are expanding into??

You can twist this as much as you want. The bottom-line is that our universe is like BIG expanding aquarium (with some stupid fishes = me) in a room that is providing more and more space for the aquarium.

In my head this construction doesn't work! It's not a real thing... And the thing that finaly makes me throw up is – WHAT THE HECK IS OUTSIDE THIS LIVING ROOM?? HELP!

(I'm not crazy... yet... )

 

[Gan_HOPE326]

WHAT THE HECK IS OUTSIDE THIS LIVING ROOM?? HELP!

(I'm not crazy... yet... )

But I'm not sure this question really makes sense... think of it: the universe being "bigger" means, more or less, it has "room for more matter". What determines matter's dimensions? Mainly, Planck's Constant, from which we can deduce an electron's cloud vastness, and then how big an atom is. And the constants which determine the intensity of the four interactions, then (consequently) the speed of light, and so on. The "scale" of our universe is all comprised into this kind of stuff. But, they're all internal laws to OUR universe, right? So, why should our universe need "space" to expand? It's just that it can "contain more matter" second after second.
Plus, expansion is a temporal concept: but if we want to take a look to our universe from outside, it's got to be four-dimensional (or even worse...). Then, its shape is already determined in all of the four dimensions: the space for the future, bigger versions of our universe is already booked!

 

[Dmitry67]

And if our universe is infinite - there MUST be "extra room" for this expanding monster at almost twice the speed of light. Where does this "extra room" come from??

No.
Take an infinite line: -inf .. +inf
every point on that line is defined by the real number X

Now expand this line to 200%: every point on then new line will be 2*X
All distances now doubled.

Where did the line expand into? :)

In mathematics, you can not use the naive common sense measurements of 'space', 'volume', etc to compare infinite sets. For infinite sets, there are other methods (cardinality for example).

Note that even the law of conservation of mass/energy is not applicable tot he WHOLE universe (even it is valid in every small region)

 

[Dmitry67]

I know it's "forbidden" to talk about things that we never ever will be able to come in contact with. But if guys like http://en.wikipedia.org/wiki/Multiverse" can talk about Multiverse and "bubbles" we never ever will be able to come in contact with...? Why can't I talk about what we are expanding into??

You can talk about it in the context of superstrings, the BULK, and the multidimensional "landscape"

So yes, you can talk about it.

But, it is possible that there are NO other entities except our universe. Mathematically, the curved spacetime does not require it to be 'embedded' into some more highly dimensional euclidean space.

It is just curved, for us it is easier to understand to when we look at it 'from the outtside', but it is just a limitation of our brains. Flat/euclidean space is not more 'natural' then curved space; we just got used to it in our everyday life, so it got hardwired in our brains.

 

[Gan_HOPE326]

Note that even the law of conservation of mass/energy is not applicable to the WHOLE universe (even if it is valid in every small region)

Really? I thought this had to be one of the few things we could hold for certain. I mean, except for instantaneous quantum fluctuations (like virtual particles being born and disappearing in the blink of an eye). You mean mass can be created - or disappear? Under what circumstances?

 

[Dmitry67]

The problem is that when you take 'time slices' of the universe say, ‘the whole Universe Now’ or ‘the whole universe 1 year after the Big Bang’, these ‘slices’ do not form valid rest frames. So the conservation laws are not applicable to such entities – I repeat – laws are not VIOLATED, they are just NOT APPLICABLE. So no particles magically 'created' from nothing or disappeared into nothing.

So, if you look at the universe from any observer perspective, mass/energy IS conversed, but you observe just a tiny bit of the Universe and in different times (you see very far objects on their early stage of the evolution).

If you take the Cosmology point of view, which is really a ‘God’s eyes view’, or ‘Bird’s view’ in the terminology of Max Tegmark, then the picture becomes simpler, but energy is not conserved there.

For example, when our Universe becomes 10 times bigger, the matter becomes 1000 times less dense. But the radiation becomes 10’000 times less dense! In the Bird’s view, the extra energy is gone. For any observer, we just see it more and more red-shifted when we look further and further.

 

[Gan_HOPE326]

The problem is that when you take 'time slices' of the universe say, ‘the whole Universe Now’ or ‘the whole universe 1 year after the Big Bang’, these ‘slices’ do not form valid rest frames. So the conservation laws are not applicable to such entities – I repeat – laws are not VIOLATED, they are just NOT APPLICABLE. So no particles magically 'created' from nothing or disappeared into nothing.

So, if you look at the universe from any observer perspective, mass/energy IS conversed, but you observe just a tiny bit of the Universe and in different times (you see very far objects on their early stage of the evolution).

If you take the Cosmology point of view, which is really a ‘God’s eyes view’, or ‘Bird’s view’ in the terminology of Max Tegmark, then the picture becomes simpler, but energy is not conserved there.

For example, when our Universe becomes 10 times bigger, the matter becomes 1000 times less dense. But the radiation becomes 10’000 times less dense! In the Bird’s view, the extra energy is gone. For any observer, we just see it more and more red-shifted when we look further and further.

Right, I didn't think about that.

Which makes me think something different... I'm expanding space, so distances increase as well. If two bodies have, say, gravitational potential energy -U, after the universe has expanded tenfold it's got to be -U/10, and this is rough, since I'm not using Einstein's general relativity, but just classical gravitation. Here energy pops out of nothing. Can't it be that the missing energy from radiation goes here, to potential energy for the interactions? Id est, that radiation pressure is just the force which gives the work needed to expand universe, creating new space? If so, mass/energy conservation would still hold.

 

[DevilsAvocado]

But I'm not sure this question really makes sense...
...
But, they're all internal laws to OUR universe, right? So, why should our universe need "space" to expand? It's just that it can "contain more matter" second after second.
Plus, expansion is a temporal concept: but if we want to take a look to our universe from outside, it's got to be four-dimensional (or even worse...). Then, its shape is already determined in all of the four dimensions: the space for the future, bigger versions of our universe is already booked!

Thanks Gan_HOPE326, for taking the time to try to answer this 'impossible' question.

I know this is a 'little bit' outside the mainstream cosmology, and extremely difficult to 'talk' about. Ned Wright gives this explanation in his FAQ - http://www.astro.ucla.edu/~wright/cosmology_faq.html#XIN":

"This question is based on the ever popular misconception that the Universe is some curved object embedded in a higher dimensional space, and that the Universe is expanding into this space. This misconception is probably fostered by the balloon analogy which shows a 2-D spherical model of the Universe expanding in a 3-D space. While it is possible to think of the Universe this way, it is not necessary, and there is nothing whatsoever that we have measured or can measure that will show us anything about the larger space. Everything that we measure is within the Universe, and we see no edge or boundary or center of expansion. Thus the Universe is not expanding into anything that we can see, and this is not a profitable thing to think about."

This is perfectly clear to me. And the odds to get the Nobel Prize in studying "the thing outside" our universe, is not outstanding. The Holy Grail of this question is this line:

"Thus the Universe is not expanding into anything that we can see, and this is not a profitable thing to think about."

This is also perfectly clear to me. Why should a professional scientist spend valuable time on this 'impossible' question? There are thousands and thousands other questions with much better prognosis for a real solution... Reasonably - this is 'stupidity' and a waste of time (for a pro).

But for me, as a layman, it's extremely interesting and fun to speculate about. And it doesn't cost me much (in status or money).

I also have come to the conclusion that "the thing outside" probably must have extra dimensions, additional to our four-dimensional spacetime. But I'm not sure I can follow your reasoning all the way:

"... the space for the future, bigger versions of our universe is already booked!"

Take a look of http://upload.wikimedia.org/wikipedia/commons/3/32/Embedded_LambdaCDM_geometry.png" (Lambda-Cold Dark Matter) cosmological model, showing one dimension of space and one of time (the red line is the path of a light beam emitted by the quasar about 13 billion years ago and reaching the Earth in the present day).

How can we state that geometrical status of our universe in 13 billion years from now "is already booked"!?

I could be wrong? But doesn't this mean that our universe is perfectly deterministic?? This is NOT what the QM-guys (quantum mechanics) are telling us?? We can make very good mathematical predictions, but noting is absolutely written in stone - about the future?

So, how can we state anything 100% sure about our universe in 13 billion years from 'now', and how can the 'future space' already be "booked"??

(An easy way to get rid of this problem is to say - Yeah, yeah Dude! And what do we know of the determinism in "the thing outside"!? Absolutely nothing, nada, zero, zip! )

Another thing that often pops up in this kind of discussions is "extra dimensions". But I'm not sure this satisfies me. Take one thousand extra dimensions, and you still have the problem of a physical reality that seems (in some way) impossible...

Dmitry67 (thanks!) talks about "the Cosmology point of view, which is really a ‘God’s eyes view’, or ‘Bird’s view’" (and I like that very much!). Now with this view - visualize our observable universe - 14 billion parsecs (46.5 billion light-years) at least. And according to Alan Guth (founder of the theory of cosmic inflation), the entire Universe could be at least 1023 to 1026 times as large as the observable universe.

Imagine the enormous amount of matter/energy in our giant universe. And recall that only 4% of the universe is ordinary matter/energy that we can see - 96% we cannot see (Dark Matter & Dark Energy).

How on Earth can this extremely 'heavy thing', that is our universe, just 'float around' in some weird nothingness? That furthermore doesn't exist!? And at the same time provides more 'room' for our extremely fast 'expanding giant'??

This is an absolutely mind-blowing thought - no matter how many dimensions you add to this scenario - you always run into the 'irrational wall'. To me it seems as an impossible construction: A never-ending series of a "Russian Nested Doll"-reality. If you find the answer for "one doll", then instantly a new question needs to be answered - Okay, AND what kind of "doll" is this one 'floating' around in??

My guess is that our brains are not developed enough (yet ) to comprehend this 'recursive reality loop'. Or... the universe and our existence is a fundamentally impossible construction that really cannot exist - in the way we percept the world...

(And I still claim; I'm not crazy... yet... )

(Dmitry67, thanks! I'll be back...)

 

[Gan_HOPE326]

I also have come to the conclusion that "the thing outside" probably must have extra dimensions, additional to our four-dimensional spacetime. But I'm not sure I can follow your reasoning all the way:

"... the space for the future, bigger versions of our universe is already booked!"

Take a look of http://upload.wikimedia.org/wikipedia/commons/3/32/Embedded_LambdaCDM_geometry.png" (Lambda-Cold Dark Matter) cosmological model, showing one dimension of space and one of time (the red line is the path of a light beam emitted by the quasar about 13 billion years ago and reaching the Earth in the present day).

How can we state that geometrical status of our universe in 13 billion years from now "is already booked"!?

I could be wrong? But doesn't this mean that our universe is perfectly deterministic?? This is NOT what the QM-guys (quantum mechanics) are telling us?? We can make very good mathematical predictions, but noting is absolutely written in stone - about the future?

So, how can we state anything 100% sure about our universe in 13 billion years from 'now', and how can the 'future space' already be "booked"??

(An easy way to get rid of this problem is to say - Yeah, yeah Dude! And what do we know of the determinism in "the thing outside"!? Absolutely nothing, nada, zero, zip! )

Thanks to you, for popping out such a mind-breaking question. As for you (a layman), for me (actually, right now, a PhD student in Physics... but in a completely different field. And anyway, my life changed a lot and in unpredictable ways since my first post in this topic. Another demonstration that the universe definitely isn't deterministic ) this kinda speculation is fun. Anyway, what I meant was not about universe being deterministic or not... Even if it's quantum-mechanical, our universe (I'd like to point out I'm saying our. If we believe in the many-worlds interpretation of QM, universe doesn't evolve randomly, it's just that there's a lot of them) has a past, a present, a future. Time is really a convention, a dimension perfectly equivalent to others (try reading Julian Barbour's work... look for his "Platonia" website. He's got some interesting ideas up his sleeve!), so it's not like our universe is a three-dimensional one evolving through time. Our universe is a four-dimensional thing, it's us that we're seeing it frame-by-frame. Like an avi file: the whole lot is there, it occupies a certain space on your hard-disk; different frames may occupy different space because of the compression algorithm, but the total is fixed. Seeing it in a time sequence doesn't mean it stops occupying all of his size. That's more or less what I meant with "space already booked". I don't think that when a physics says trying to answer to this question isn't proficient he means he can't make a living out of it, it's just that it's "gnoseologically" not proficient. It's beyond our knowledge; more or less like debating if God exists or not. You can go on with similar debates for thousands years, but you just won't get an answer, cause, even if it exists, it's not for us to know. Or so it seems.

 

[DevilsAvocado]

Thanks to you, for popping out such a mind-breaking question. As for you (a layman), for me (actually, right now, a PhD student in Physics... but in a completely different field. And anyway, my life changed a lot and in unpredictable ways since my first post in this topic. Another demonstration that the universe definitely isn't deterministic ) this kinda speculation is fun.

Thanks again. Yeah, this forum definitely determine the indeterministic nature of the universe (and soon I'm going to be classified as an hopelessly incorrigible topic hijacker ).

This question is probably, as you say, "beyond our knowledge". But then again, we do have Max Tegmark, Sean Carroll, Multiverse and "bubbles"! If you could crack that nut - why not crack mine!?

I see you are into QM Many-worlds interpretation. Personally I don't like that solution. It's cheating. You can explain anything with that:

- Why can't I understand "the thing outside" our universe?
- Ohh, but you can! It's just happened that the "QM-one of you", that DID understand this, was split into another world in the same second you found the solution! Sh*t happens!

Julian Barbour is an interesting man, ...on a very thin line... I think... even as a layman I react when he says:

"If all distances in the universe were doubled over night, nothing would tell us this had happened."

Huuum... is this really true?? I think that the guy who measure the distance to the Moon every day is going to sh*t in his (new big 2x) pants, if this happened - since the laser beam (speed of light) would take twice the time yesterday, to make it to the Moon and back!

Maybe you're AVI-analogy is the real movie of our universe. Time is weird. Everyone who has been in love and to the dentist (but not at the same time!) knows this for sure. Or as my hero says:

The only reason for time is so that everything doesn't happen at once -- Albert Einstein

 

[DevilsAvocado]

No.
Take an infinite line: -inf .. +inf
every point on that line is defined by the real number X

Now expand this line to 200%: every point on then new line will be 2*X
All distances now doubled.

Where did the line expand into? :)

In mathematics, you can not use the naive common sense measurements of 'space', 'volume', etc to compare infinite sets. For infinite sets, there are other methods (cardinality for example).

Note that even the law of conservation of mass/energy is not applicable tot he WHOLE universe (even it is valid in every small region)

Dmitry67, thanks for taking the time to answer. Your answers were what I hoped fore from a real math-pro.

I realize that infinity is not a 'problem' for a mathematician. Even I can grasp mathematical infinity:

A = 1;
while (A > 0) {A++}

This code will continue forever and variable A will grow bigger and bigger and bigger (i.e. if you have the right 'hardware').

But can we really convert this to our physical world?? More and more and more and more and more and more and more energy/matter ... forever and ever and ever and ever and ever... ?

I could be out, knee-deep in the "Amateur Guessing Swamp" - But I thought that if you get infinity large (e.g.) energies in an equation, describing our universe, then something must be wrong with that equation?? (Or did I just drown in the "swamp"!?)

You can talk about it in the context of superstrings, the BULK, and the multidimensional "landscape"

So yes, you can talk about it.

But, it is possible that there are NO other entities except our universe. Mathematically, the curved spacetime does not require it to be 'embedded' into some more highly dimensional euclidean space.

It is just curved, for us it is easier to understand to when we look at it 'from the outtside', but it is just a limitation of our brains. Flat/euclidean space is not more 'natural' then curved space; we just got used to it in our everyday life, so it got hardwired in our brains.

This is so damn interesting! I do understand that very beautiful mathematical equations (Einstein/GR?) don't require our universe to be 'embedded' into something more. But just think about it for a sec or two - without the equations:

Our Universe; 46 billion light-years of 4% ordinary matter and 96% DM & DE (and maybe 1000 times as large in the cosmic inflation model)... Could ALL this stuff just 'HANG' out there?? Surrounded by nothingness that doesn't exist!? A nothingness providing more 'room' for our extremely fast (~2c) expanding universe??

Does this really look like a physical working picture for you?

 

[Chronos]

The observable universe appears to be temporally finite.

I do not see how a temporally finite universe can be infinitely large. A temporally finite universe can be unimaginably large, but, not infinite. Olber's paradox, imo, suggests an infinitely old universe should be in thermal equilibrium. This is not observed - e.g., :

Molecular Hydrogen in a Damped Lyman-alpha System at z_abs=4.224
http://www.arxiv.org/abs/astro-ph/0602212
. . . The high excitation of neutral carbon in one of the components can be explained if the temperature of the Cosmic Microwave Background Radiation has the value expected at the absorber redshift, T=14.2 K.

http://babbage.sissa.it/abs/astro-ph/0012222
The microwave background temperature at the redshift of 2.33771
Authors: R. Srianand (IUCAA, Pune), Patrick Petitjean (IAP, Paris), Cedric Ledoux (ESO, Munich)
Comments: 20 pages, 5 figures, accepted for publication in Nature, Press embargo until 1900 hrs London time (GMT) on 20 Dec 2000

The Cosmic Microwave Background radiation is a fundamental prediction of Hot Big Bang cosmology. The temperature of its black-body spectrum has been measured at the present time, $T_{\rm CMBR,0}$ = 2.726$\pm$ 0.010 K, and is predicted to have been higher in the past. At earlier time, the temperature can be measured, in principle, using the excitation of atomic fine structure levels by the radiation field. All previous measurements however give only upper limits as they assume that no other significant source of excitation is present. Here we report the detection of absorption from the first {\sl and} second fine-structure levels of neutral carbon atoms in an isolated remote cloud at a redshift of 2.33771. In addition, the unusual detection of molecular hydrogen in several rotational levels and the presence of ionized carbon in its excited fine structure level make the absorption system unique to constrain, directly from observation, the different excitation processes at play. It is shown for the first time that the cosmic radiation was warmer in the past. We find 6.0 < T_{\rm CMBR} < 14 K at z = 2.33771 when 9.1 K is expected in the Hot Big Bang cosmology.

 

[Dmitry67]

1 But can we really convert this to our physical world?? More and more and more and more and more and more and more energy/matter ... forever and ever and ever and ever and ever... ?

2
I could be out, knee-deep in the "Amateur Guessing Swamp" - But I thought that if you get infinity large (e.g.) energies in an equation, describing our universe, then something must be wrong with that equation?? (Or did I just drown in the "swamp"!?)

3
Does this really look like a physical working picture for you?

1
As a proponent of Mathematic Universe Hypotesis,
http://arxiv.org/abs/0704.0646
- this is very good reading,
I don't see any difference between physical and mathematical.

2
For that reason Newtonians gravity theory was not valid, because when applied to the infinite Universe, you got infinities. In General Realitivity you don't run into infinities even for the infinite Universe.

3
If a theory is a) self-consistent, b) is compatible with the observations I don't see reason to cry all the time "wow, but wait, the whole Universe is hanging in the nothingness! or wow, but it is infinite!" :)

 

[Dmitry67]

Our Universe; 46 billion light-years of 4% ordinary matter and 96% DM & DE (and maybe 1000 times as large in the cosmic inflation model)... Could ALL this stuff just 'HANG' out there??

Yes, it can, without any help of the turtles :)

 

[Gan_HOPE326]

I see you are into QM Many-worlds interpretation. Personally I don't like that solution. It's cheating. You can explain anything with that:

- Why can't I understand "the thing outside" our universe?
- Ohh, but you can! It's just happened that the "QM-one of you", that DID understand this, was split into another world in the same second you found the solution! Sh*t happens!

Julian Barbour is an interesting man, ...on a very thin line... I think... even as a layman I react when he says:

"If all distances in the universe were doubled over night, nothing would tell us this had happened."

Huuum... is this really true?? I think that the guy who measure the distance to the Moon every day is going to sh*t in his (new big 2x) pants, if this happened - since the laser beam (speed of light) would take twice the time yesterday, to make it to the Moon and back!

About the first thing: I'm not really into the many-worlds intepretation, meaning I don't really have chosen my way to look at QM. I was taught the Copenaghen interpretation, of course, so it still has deep roots in my mind; and I don't think that objective-collapse intepretations are really satisfactory. I find the many-worlds a definite possibility that I just don't want to discard. But, it's true, it seems quite easy. It's more or less admitting in this field too our inability to really understand the truth. But if we keep on surrendering at every single tiny difficulty...

But I think what Barbour says is absolutely true. He's not saying he's just pulling apart the moon, so its distance is doubled. He says "double every distance". It's like drawing something on a rubber sheet, then pulling it making it larger. You can see the difference because you're not part of the sheet; but if you were on it, with your deformed eye you'd see deformed rays of light that, on your point of view, would travel exactly at the same speed (but, seen from outside the sheet, they'd appear to travel faster). The scale factor between what's inside the universe and what supposedly is outside of it doesn't matter at all, simply because there's no known interaction between the two, so you can't make comparisons.

 

[Dmitry67]

DevilsAdvocado, regarding the QM ManyWorlds you are a victum of popular junk about the MWI.

1. There are no 'MANY' universes in MWI - everything happens in the same universe, just some parts of the omnium (almost) loses an ability to communicate forming 'branches'
2. When I make an experiment with different outcomes, I don't 'split' the whole Unvierse. The effect propagates at speed of light (or slower) via experimentally observed process called 'Qunatum Decoherence'
3. MWI does not make any additional assumptions expect we already have in QM. In that sense it is minimalistic. It does not even postulate the existence of the other branches: all that is derived using the standard QM stuff + Quantum Decoherence

 

[DevilsAvocado]

About the first thing: I'm not really into the many-worlds intepretation, meaning I don't really have chosen my way to look at QM. I was taught the Copenaghen interpretation, of course, so it still has deep roots in my mind; and I don't think that objective-collapse intepretations are really satisfactory. I find the many-worlds a definite possibility that I just don't want to discard. But, it's true, it seems quite easy. It's more or less admitting in this field too our inability to really understand the truth. But if we keep on surrendering at every single tiny difficulty...

But I think what Barbour says is absolutely true. He's not saying he's just pulling apart the moon, so its distance is doubled. He says "double every distance". It's like drawing something on a rubber sheet, then pulling it making it larger. You can see the difference because you're not part of the sheet; but if you were on it, with your deformed eye you'd see deformed rays of light that, on your point of view, would travel exactly at the same speed (but, seen from outside the sheet, they'd appear to travel faster). The scale factor between what's inside the universe and what supposedly is outside of it doesn't matter at all, simply because there's no known interaction between the two, so you can't make comparisons.

Okay, now I'm really confused...?

http://en.wikipedia.org/wiki/Copenhagen_interpretation#Nature_of_collapse"
"So if an electron passes through a double slit apparatus there are various probabilities for where on the detection screen that individual electron will hit. But once it has hit, there is no longer any probability whatsoever that it will hit somewhere else. Many-worlds interpretations say that an electron hits wherever there is a possibility that it might hit, and that each of these hits occurs in a separate universe."

Is it my brain that has split into impossible many QM-states?? Or... isn't the Copenhagen interpretation <> Many-worlds interpretation...??

I follow your reasoning about Barbour. But didn't he miss one very important factor? Doesn't Barbour also have to double the speed of light, for example, if the distance between Earth and Moon has doubled, and you want the same result as yesterday?? Or, Barbour has to decrease the speed of our atomic clocks to half?? But that's maybe comes automatically? From the increased (doubled? quadrupled?) gravitation of a doubled-sized Earth... (even if it seems like a too big 'effect' for a layman...)

And further more. Doesn't Barbour have to redesign ALL of the four fundamental interactions of nature, In the Standard Model of particle physics, the strong and weak nuclear force etc? If the all distances in the atom also get doubled??

A practical example: If our Sun would double in size overnight, and Barbour doesn't adjust the laws of physics accordingly, we would know something strange had happened last night! The Sun 2.0 would burn its fuel much faster, and hence would die much quicker. And the end of the Sun 2.0 would be a whole different enchilada, than the end of Sun 1.0!

Please, tell me I'm right on this one? I suddenly feel a clear mind!

 

[Dmitry67]

Copenhagen interpretation <> Many-worlds interpretation
Copenhagen interpretation (together with the 'collapse') is almost abandoned in 21th century. So forget about the 'collapse'

 

[DevilsAvocado]

Okay Dmitry67, thanks! I'm working on your other replays. I'll be back.

 

[Gan_HOPE326]

I follow your reasoning about Barbour. But didn't he miss one very important factor? Doesn't Barbour also have to double the speed of light, for example, if the distance between Earth and Moon has doubled, and you want the same result as yesterday?? Or, Barbour has to decrease the speed of our atomic clocks to half?? But that's maybe comes automatically? From the increased (doubled? quadrupled?) gravitation of a doubled-sized Earth... (even if it seems like a too big 'effect' for a layman...)

And further more. Doesn't Barbour have to redesign ALL of the four fundamental interactions of nature, In the Standard Model of particle physics, the strong and weak nuclear force etc? If the all distances in the atom also get doubled??

A practical example: If our Sun would double in size overnight, and Barbour doesn't adjust the laws of physics accordingly, we would know something strange had happened last night! The Sun 2.0 would burn its fuel much faster, and hence would die much quicker. And the end of the Sun 2.0 would be a whole different enchilada, than the end of Sun 1.0!

Please, tell me I'm right on this one? I suddenly feel a clear mind!

No, that's the point. Doubling distances means doubling everything: light speed is 3e8 meters per second, but in such a 2.0 universe, the very concept of "meter" would be doubled. It's not about enlarging objects: it's about stretching the fabric of space itself. That's why he says that nothing changes: or better, you could say it's even meaningless to think such a concept, because, how can you tell Universe 2.0 is twice the size of Universe 1.0 if you don't have anything external to the universe to measure it?

P.S. if we're talking about doubling linear distances, anyway, volumes, and then, roughly, masses, would be multiplied per 8. Yet still, since gravity goes as mass/square of radius, a "double radius" Earth, provided it had the same density than ours, would have a doubled gravitational force. And here's the trick: in Barbour's hypotesis, Planck constant, dielectric constant, Newton's gravitational constant etc. would change as well; as a result, we'd have an Earth made of bigger (less dense) atoms, with different laws, etc., so that its gravity wouldn't change from the original value.

 

[DevilsAvocado]

And here's the trick: in Barbour's hypotesis, Planck constant, dielectric constant, Newton's gravitational constant etc. would change as well; as a result, we'd have an Earth made of bigger (less dense) atoms, with different laws, etc., so that its gravity wouldn't change from the original value.

Okay Houston, I Read You Loud and Clear!

But as "Cranky Layman" I still argue that Barbour maybe should express his hypothesis in this way:

"If all distances, scales and (physical) constants in the universe were doubled over night - nothing would tell us this had happened."

This I will have for breakfast tomorrow!
(i.e. if the QM-guys do high-five as wel)

With all the respect for Barbour (and your interest in his theory), it does make me 'nervous' when he tries to visualize Eternity with this "thing" (that looks like a drying rack to me)...

http://www.youtube.com/watch?v=WKsNraFxPwk"

(Says the man who 'believes' Extra-Universal Space! )

 

[DevilsAvocado]

1
As a proponent of Mathematic Universe Hypotesis,
http://arxiv.org/abs/0704.0646
- this is very good reading,
I don't see any difference between physical and mathematical.

2
For that reason Newtonians gravity theory was not valid, because when applied to the infinite Universe, you got infinities. In General Realitivity you don't run into infinities even for the infinite Universe.

3
If a theory is a) self-consistent, b) is compatible with the observations I don't see reason to cry all the time "wow, but wait, the whole Universe is hanging in the nothingness! or wow, but it is infinite!" :)

- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
1) I love Max Tegmark :!), he is a brave man and the Grand Master of Mind-Blowing Theories!

• TOE - Theory of Everything
• ERH - External Reality Hypothesis
• MUH - Mathematical Universe Hypothesis
• CUH - Computable Universe Hypothesis

Tegmark probably has more intelligence in his left pinky TOE than I have in my whole brain, and obviously I cannot comprehend all of his Mathematic Universe Hypotesis.

But then again, I am the DevilsAvocado and I did complete my course at the http://www.youtube.com/watch?v=kQFKtI6gn9Y" , and therefore I naturally going to have objections about this.

"If a future physics textbook contains the TOE, then its equations are the complete description of the mathematical structure that is the external physical reality. We write is rather than corresponds to here, because if two structures are isomorphic, then there is no meaningful sense in which they are not one and the same."

Huum, isn't this 'maneuver' a little bit too easy to 'replace' the physical reality with math? Isomorphic is mainly a mathematical 'tool' (right?) for mapping between objects... isn't that 'cheating'?

Example: If you have a complete technical drawing of a house, and make a complementation with all scientific knowledge about the material, down to quarks - then Tegmark could call the technical drawing and the physical building isomorphic, right? But can Tegmark take his family and move into that Technical Drawing?? I say no.

"Wigner argued that 'the enormous usefulness of mathematics in the natural sciences is something bordering on the mysterious', and that 'there is no rational explanation for it'."

I DO admire all people who use extremely advanced mathematics to investigate and explore the world. They are my heroes!

At the same time, I think there is a little risk of losing perspective and getting 'lost in translation', and fall in love with the 'pure magic' of the tools you are working intensely with. For me, as layman, it feels extremely awkward that the physical world doesn't really exist - it's just equations...

In Erwin Schrödinger's book - What Is Life - from 1944 (old stuff I know! ) he wrote as a section header in Chapter 1:

PHYSICAL LAWS REST ON ATOMIC STATISTICS AND ARE THEREFORE ONLY APPROXIMATE

And if I'm not wrong; there is NOT today ANY mathematical equation that can describe what really goes on in the QM-world. All we calculate are probabilities, right? And Heisenberg's uncertainty principle doesn't give us much hope of ever getting rid of this 'trauma', right? So, how can (mathematic) approximations ever be the real physical world we live in??

Another side of this coin could be the EPR paradox, and the fact that Alain Aspect 1982 (almost?) performed a validation of Bell's theorem (Bell inequality). The world is random by nature. As far as I know, mathematics is NOT random by nature?

Tegmark's solution to banish randomness:
" ... so that the final state is a superposition of observers obtaining all outcomes, then in the limit of infinitely many bits, almost all observers will find their bit strings to appear perfectly random and conclude that the conventional quantum probability rules hold."

Huum, "a superposition of observers obtaining all outcomes" = Many-worlds interpretation ...??

If so, I not like...

The final objection is completely homemade, and feel free to laugh out loud!
What's the most natural geometric shape in the universe? Yes, circles/spheres. Not quadrates/triangles. What is the natural mathematic tool for handling circles and spheres?

3.14159265358979323846264338327950288 ... ... ... ... ... ... ... ...

Just a layman 'feeling' - but shouldn't ∏ be more 'exact/natural', if the Mathematical Universe Hypothesis is correct...??


- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
2) Is the reason for NOT running into infinities even for the infinite Universe, the fact that we can never get out of our local light-cone (event-horizon)? Or is this 'embedded' more 'fundamentally' in GR?


- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
3) "b) is compatible with the observations"... Hehe, this is the Holy Grail of avoiding difficult questions! Business as usual, everything (observable) works, without any help of the turtles!

 

[DevilsAvocado]

Yes, it can, without any help of the turtles :)

Turtles all the way down
I think I've found the solution... The last turtle is not that big, and he has all the information at the fingertip!

 

[DevilsAvocado]

DevilsAdvocado, regarding the QM ManyWorlds you are a victum of popular junk about the MWI.

1. There are no 'MANY' universes in MWI - everything happens in the same universe, just some parts of the omnium (almost) loses an ability to communicate forming 'branches'
2. When I make an experiment with different outcomes, I don't 'split' the whole Unvierse. The effect propagates at speed of light (or slower) via experimentally observed process called 'Qunatum Decoherence'
3. MWI does not make any additional assumptions expect we already have in QM. In that sense it is minimalistic. It does not even postulate the existence of the other branches: all that is derived using the standard QM stuff + Quantum Decoherence

Okay, thanks for info.

And how do we relate Qunatum Decoherence to Tegmark's:
"a superposition of observers obtaining all outcomes"

To me it sounds like every observer is going to have their own bit...??

 

[Dmitry67]

DevilsAdvocado, regarding your objections, how do you know if you are living in the virtual reality or real reality? "complete technical drawing of a house" is not a good example for "virtual reality". So you can't live there.

The second part of your objections are rather constatation of fact that we don't know the 'Ultimate', TOE equations. Yes, this is true. But we hope we'll learn them soon.

And precise and deterministic laws of physics can lead to the appearence of randomness (MWI, BM)

 

[Dmitry67]

Okay, thanks for info.

And how do we relate Qunatum Decoherence to Tegmark's:
"a superposition of observers obtaining all outcomes"

To me it sounds like every observer is going to have their own bit...??

It depends on how you define the "observer"
After the schoedinger cat experiment:

You + closed box with 1/2 dead cat + 1/2 alive cat

So you can never see the superposition of cats
you get decoherenced with the box literally after you exchange few photons, and the system evolves into

1/2 Happy you observing alive cat + 1/2 Sad you observing dead cat

 

[DevilsAvocado]

DevilsAdvocado, regarding your objections, how do you know if you are living in the virtual reality or real reality? "complete technical drawing of a house" is not a good example for "virtual reality". So you can't live there.

The second part of your objections are rather constatation of fact that we don't know the 'Ultimate', TOE equations. Yes, this is true. But we hope we'll learn them soon.

And precise and deterministic laws of physics can lead to the appearence of randomness (MWI, BM)

Thanks. Virtual reality is cool, and could be one explanation for the "turtle problem". Can we be absolutely sure about the vastness of our universe in that case? I mean, is there any way to tell for sure (CMB, etc)?

TOE is very thrilling. I can't wait.

A deterministic law of physics sounds a little 'disturbing'. I like my free will...

 

[DevilsAvocado]

It depends on how you define the "observer"
After the schoedinger cat experiment:

You + closed box with 1/2 dead cat + 1/2 alive cat

So you can never see the superposition of cats
you get decoherenced with the box literally after you exchange few photons, and the system evolves into

1/2 Happy you observing alive cat + 1/2 Sad you observing dead cat

Yes, but then again Tegmark's MUH has a problem to banish the randomness in the Geiger counter?
Or, Curiosity Killed The Cat??

 

[Dmitry67]

In MWI free will is compatible with determinism.

Virtual reality is cool, but this is not what Max meant. The idea of Matrix is too popular, but what he is saying is much deeper.

Let me ask you - how you can tell the mathematical system from a physical one?

 

[Dmitry67]

Yes, but then again Tegmark's MUH has a problem to banish the randomness in the Geiger counter?

MUH is unrelated to Schroedinger cat problem
MWI is.
Randomness is an illusion.
Both branches (deterministically) exist
Observer is each branch thinks that the outcome was random.

 

[DevilsAvocado]

In MWI free will is compatible with determinism.

Virtual reality is cool, but this is not what Max meant. The idea of Matrix is too popular, but what he is saying is much deeper.

Let me ask you - how you can tell the mathematical system from a physical one?

Well, I guess if we accept the possibility that we and the universe are a running simulation, then the mathematical system setting the rules, must be more real than the actual simulation!?

And I guess there is NO way to find out if we are real real, or simulated real, i.e. if the 'programmer' did his job.

If this is true; how can we ever find TOE?? The 'programmer' must be an idiot if he programmed his own 'weakness'?

If we are not simulated, then I say my Technical Drawing is a pretty good indicator.

Another (old) question that pops up in my head; Nick Bostrom is almost sure we are in a simulated reality, and that it's impossible to tell the difference between real reality and simulated reality.

Hence the (mathematical) simulation system/rules/programming must be 'govern' from outside the simulation, right? How can the 'simulation governors' (and here goes my turtles again! ) be absolutely sure they are not simulated as well?? And so on, and so forth, in all eternity... (And, does this make any 'real' difference...??)


Finally a new nut for you to crack:
If we are in a simulated reality - how you can tell a 'real' mathematical system that works, from a simulated mathematical system that is simulated to work?