Can dimensions be limited, or is the universe really infinite?
By Engineer Saviour – Blaze Labs
From our point of view, the universe seems to be infinite, and it seems that it’s not only infinite but even ever expanding. Now that you should be able to understand how our seemingly 3D space time universe can all fit in a 4D hypersphere, which in turn can fit on a surface of a 5D hypershere and so on, where a difference in time is equivalent to a different point within its volume, you can understand why the universe as seen by a 3D observing creature/mind has no limits.
Just imagine one of those 2D creatures who cannot understand what is height in the z direction and put him on the surface of a sphere. He would walk round and round searching for an edge for ever, and finally he may conclude and even prove that the path is infinite. Same applies to a 1D creature going round a simple circle, and therefore same applies to us 3D creatures living and travelling around in a 4D universe! In general we can say that a creature with n x D observation capability, will observe an (n+1)D dimension universe as infinite. We also learn that for an n x D observer, the only way to observe a universe of a higher dimension than himself is to ‘walk around it’ and memorise.
A 1D creature cannot understand what is a circle other than observing all the points making it up, one by one. Similarly a 2D creature cannot understand what is a sphere other by observing the flow of circles making it up. We see that in all cases, walking around, or observing the flow through time, is necessary to observe a higher dimensional space.
The question is, how can we know how many dimensions is the universe made up from. All the arguments mentioned above can be applied to any dimension and would imply the possibility of an infinite dimension space. But mathematics shows us that there are yet unknown reasons for which an ultimate dimension may be reached. One very interesting curve is the plot of surface area of hyperspheres of different dimensions, shown below. One would easily think that as we go higher in dimensions, the surface area of the nsphere would increase at each stage, and yet, something very strange occurs, as a maxima in its surface area is reached at the 7th dimension. Could this indicate the real ultimate dimension of the universe?
Dimension

Volume

Area

1

2.0000

2.0000

2

3.1416

6.2832

3

4.1888

12.5664

4

4.9348

19.7392

5

5.2638

26.3189

6

5.1677

31.0063

7

4.7248

33.0734

8

4.0587

32.4697

9

3.2985

29.6866

10

2.5502

25.5016

What would an n x D observer see if the universe in which he lives in is his own n x D dimensions ? – the answer is ‘a still, or static (frozen in time) spatial shape of n x D dimensions’. A 2D creature does not need to move around the circle to recognise it or know anything else about it, and a 3D creature does not have to flow through circular slices of a sphere to recognise a sphere. Note that the actions move and flow both require the time dimension to make sense, but recognise is an act that reacts to the shape of a static structure and needs no time. For an n x D observer, the ndimensional universe is static, lifeless, and does not change through time, but has all the knowledge of what’s within all lower dimensions. Let’s name this ultimate n x D observer as the universal observer. For the universal observer, time does not exist, since both himself and the universe are the same thing and neither himself nor the universe is effected by time in lower dimensions, and from a lower dimensional observer point of view he can be said to be existing from eternity to eternity.
For those mathematically minded, let’s take a car accelerating in a road. If we integrate the observed acceleration m/s^{2} with respect to time we get a car driving at a velocity measured in m/s. We have thus moved the motion of the car one dimension up with respect to time. If we integrate further the velocity with respect to time, we get the total distance covered in metres, no time. So did the road distance exist before or after the car started acceleration? As you see the ‘road’, the time independent dimension is NECESSARY for all other actions (differentiations with respect to time) to take place, and hence the universe should be limited in its number of dimensions, with the highest dimension being time independent, and being the universal observer itself.
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Nick
Difficult stuff to understand, but you explain it very well. Nicely done.
Louis B. Fournier
Thanks for some OUTSTANDING web pages!
RMCybernetics
It seems quite reasonable. It is quite possible though that we will never truly understand and we will have to make do with out best guesses!
constantine
Just wish i could psell roppolly
Constantine.
Thank you for that article. most enlightening.
Should his prediction of a theory find favour. then it would seem is simply entropy. not (im gussing here) a forth spacial dimension. obvioulsy there will be other spacial dimensions just time aint one of them.
how does that sit with other theorys? I know standing wave theory would probably work just fine with that.
can i ask your view. im not sure about everything he says in that article. but my gut reaction is that its possibly a huge leap in the right direction.
but i might be biased as it sits happily with a bunch of stuff i have tried to postulate before.
RMCybernetics
Take a look at this Theory of time
RMCybernetics
Yes, to be omnipotent would be quite boring. Mystery and learning is great!
Yes, I mean parallel universes.
constantine
by parallel I assume you don’t mean spacial dimensions.
what is wrong with envisiging our universe as a buble (n dimesional whatever) in a soup of others, much like a partcle that pops into existance in space. for all we know the everything from the big bang, to the end of the last photon in a googleplx of googleex years is to multiverse the tiny span bettween a particle pairs creation and anialation.
maybe the big band was just that,
just a thought.
ps. could particle entanglement be proof of dimensions below “1” like bellow the line come what ? a dot? or what about dimesions spacialy eqivelent to 1 2 3 etc. mirror the graph and take it the othe way. looks like a wave…..
constantine
had a flip thru most of those, but as a non mathmatition (cant even divide well) standing w
ve is the only one that makes sence to me.
much of this talk though reminds me of a friend who asked me why pie could not be a whole number, its like building a sphere out of strait lego bricks (the bricks being our maths) a perfect circle has in theyory an infineite number of “POINTS” any atempt to discribe any part of a circle will involve infinty, so we need pye.
that’s really what we are doing here, we can keep adding bricks, like you can kerp on calculating pye to ever decreasing points, but the surphae will never be smooth, and therr will always be little bits we don’t know. and I hope its always so. to know verything woild be so Borring.
e
RMCybernetics
“maybe it can receive energy from “outside””
Some newer theories suggest that the weakness of gravity (relative to other forces) is due to it being shared by parallel dimensions.
Please remember that this is theoretical physics. Not all people would agree on the same answers to your questions. You really need to read about some of the different theories. Try looking for papers or books on the following..
Einstein’s theory of relativity
Einstein’s theory of special relativity
String theory
MTheory
Supersymetry
constantine
hope you answer previous. but can i please ask you to also consider the following.
if a particle is a wave in space, which has curled space about it, on at least 4 dimensions probably more so its analougus to an n dimensional bubble containing a bit of space with a wave in it)… that paticle can recieve energy from a photon, and re admit it, it can also receve enough energy to change the wave and stay in a higher energy state until it has cause to pass that energy on and resume its previous state. but from the inside, it would appear the wave was going on and on forever
now consider the universe in a simaler way, maybe it can recieve energy from “outside” which to us inside would seem like an increase in expasion (energy of waves.) but the energy will posibly get passed on at some point. it does make sence and answers why the universe seems to act in certain ways.
constantine
ok. if the observeable dimensions, are acelerating in expansions, then either the time spacial dimension is also expanding, one would imagine that if time was expanding, the reletive view it would give us is… what? the viewable expasion would seem to slow down? what if the time spacial dimension was shrinking? surely the speed of light would appear (in a vacume) to increase? but we know its not. there fore i would asume the time spacial dimension is expanding. while time may be reletive generaly, as a spacial dimension its is as fact and absolute as any other dimension, and its expansion along with the other 3, or 4 if you count space itself seems to explain this mysteious slowing down of light and speeding up of expansion.
ok.. what am i missing
RMCybernetics
Spacetime is warped by the presence of mass/energy. Time is relative so universally it can’t slow down or speed up as there is not other reference to compare to.
PS. I didn’t answer some of your most recent questions as I partially answered n other posts. Besides, its getting hard to keep track. Maybe posting your questions on one page would make it simpler.
constantine
thanks for that. should have read it befrore making other posts.
ok. how does this work… time is affected by mass and energy, universal expansion appears to be getting faster, the speed of light apears to be slowing down, ….it all points to something..
universally is time slowing down? meaning one day it could stop? maybe all the waveforms will be absorbed by space, the bubble of reality pops and time for a new big bang. sound good?
RMCybernetics
Actually travel does not require any energy at all. Energy is only needed for acceleration (a change in speed or direction). I really don’t know the answer to that, but I would expect it is analogous to momentum in that some event set us off in this direction and we will just keep going. Also remember time does not flow equally throughout the universe. More gravity or more speed ‘slows’ time down. This effect has to be compensated for in satellites because they are often moving so fast relative to the earth for very long periods.
constantine
hi rm. can u just give an answer, (complex as you like….i wont understand but will be comforted) why are we moving through time at all. travel through the other dimensions requiers energy, dosnt time?
Rebecca Boone
Thanks for this outstanding, free for all blog! I happened to read it trying to find a concise mathematical definition of “dimension.” No luck so far, but I like the idea of dimension being simply what one “sees.” That makes me wonder, what then might two, three, four and more “see?”
If every 1’s total time and energy amounts to a functioning universe, albeit restricted in its domain and range, what about antecedent and successive 1s? Digitization of functionally limited universes (math’s continuum of real numbers) may be reducible to computer science’s binary system of 0,1 (viz. 1 is either nothing or 1 is something). If every 1 is simply something and not nothing, where does an infinity of subsequent “numbers” fit in?
I suggest that every 1 may “see” itself as simply doing time — the only dimension that “counts” (as in “once upon a time… so and so happened). How big, small, short, long, or expansive is your life (assuming you have a life that is something and not nothing)?
Surely there’s no such “dimension” as a partial life, a fraction of a life, a divided life, or even a “blind” life?
If what we see is what we get by way of life’s “dimension,” how do You and I accommodate one another visually?
I have worked out a logic (based on Frege’s deep insight into sense and reference) that reduces “numbers” to mothers as something and sons as something else (daughters are the same something as mothers).
So far, I’ve found no way to work math’s obsession with dimension into my either/or assertion that, if anything, 1 as a “functioning number” must “see” itself as either fe/male or male. At bottom, where ends meet, what difference does dimension per se make when it comes to correctly understanding numerical functions? What makes no sense to me is dimension as size, number of coordinated points, direction of possible motion, extent of function or action, or whatever — partial differential “equations” anyone?
The correctness or incorrectness of what humans “see” surely comprises all possible mathematical disputes. In particular, how correctly do sons see their mothers’ spacetime means and ends, and vice versa? In general, how correctly do males see their own spacetime lives’ means and ends relative to the spacetime lives (and functions) of fe/males?
Being something instead of nothing becomes endlessly complicated, numerically speaking, it seems. Yet, by factoring in gender differentiation as a numerical fact, I see much of math suddenly clarified. I dream of seeing my construct of gendered numbers introduced in junior high school when girls and boys are most keen to learn how numerical existence actually works.
I am 88 years old and still attend the MAA and AMS joint meetings. The 2010 meeting will be in San Francisco. See you there!
Your name there is here
could time and energy be one in the same thus the universal constant making up part of every other dimention?
constantine
ok rm here is a challange for you
assume for a momment. that multiple realities are just wishfull thinking for those who wish to belive that even there wishfull thinking is there own and not predetermined.
that whole sentance sorta goes against the idea but assume.
then look on time in the same way a 2d guy would look at the sphere.
assume the identity on the nd observer
he has no concept of time and therfore vry likely no consept of what we call rational thought.
it dont seem to make much sence. but its interesting to let your mind rest there.
i was thinking. the earlyer quote about the ball passing through a pice of paper…. a ball never would.
so if the universe is passing throgh a dimension we can only perseve as time. WHY is it. whats pushing it through. the universe is expanding they say. but only if you have a sence of time.
there is something else going on here. i cant even guess at what. but either the universe is moving through a dimension that existed before it did (from our time locked view…unlikely)
or the dimension, and us with it. is being dragged through the universe. by what? motion needs energy. for anything to move through the universe in any other direction need energy. you cant push the ball though paper without it. (and without distroying the paper) so the amount of energy needed for all this forth dimensional travel we are doing without realising it must take a bit.
tell me im not mad please.
oh bring back the other realitlies i feel safer now.
constantine
rm
thanks for that post. it was what i was trying to say in others.
i like the idea that we move bettween time indipendant realiteis as we make decisions allowing freedom of will in a universe of static forth dimension.
if so. that could be called moving sideways in time and would mean we can give time another axis and theres a missing dimension for you.
however. i would hate to “belive” in this consept just cos i cant handle the idea that there isno free will.
but then if there isent. what im tyoing here. the electrons which send the info to the server and the ones that take it to you screans. even the photons which take it to your eyes. are all part of those particles “strings” they were allways gona do that and nothing could change it.
so i can ramble in pease knowing im destined to.
philosphy and scince make intereting bed fellows. but bother need eachother.
who knows what einstien might have done if he wasent hung up on the “god wouldnt do that” way of thinking.
but then withhout his faith would he have amounted to anything.
sorry rambling.
mods please edit if necessary.
but anyway. think we have a dimension candidate tere.
RMCybernetics
Not a time frozen state but a time independant one. Problem is to function as a human you need personal time. You would have to exsist in some version of reality all on your own to observe it independantly.
The fate idea depends on your opiniion really. It could be true, or we could all be unknowingly moving between very similar alternate realities continuously or every time we make a decision. This would elliminate the idea of having a predetermined fate.
varsha
so it can be that there is the so called fate and the obsever can see it all from the time frozen state..
RMCybernetics
If you went back in time you would go to an alternate reality that would be identical to the onbe of yor past except for the presence of your time traveling self. To go bck on your same time line you would just have to reerse your prsonala time and go back to a point in the past. you would therefore not be aware of it at all.
varsha
can we ever go back time? or will time ever move back in future?
RMCybernetics
I think you mean “You’re retarded”. Quite ironic and very amusing.
You obviously missed the whole point of this series of articles. You shouldn’t worry about America becoming dumber, it is just you. Cheers!
smartscience
your retarded. time is not a dimesion. Also if a 2D creature lives on a sphere then it is 3d not 2D. A 2D creature would live on a 2D planet. It can go left or right and jump. If it lived on a sphere it would have no surface to walk on below it, only the sphere behind it. Be smart when you say stuff. This paper is almost completly wrong. Stop telling false information cause then those people pass it on. Then america just gets dumber and dumber. Next time please say that this is only your thoughts. Thanks!
custennin
that is a fantastic consept and causes my mind no end of fun trying to imagine it. hoever is it not true that all infinite lines meet the on beginning in infinity? also you remember the old question. “if i stand 5 meters from a wall, and take a one meter step. then a .5 meter step and every step is half the distance of the one before. how many steps to reach the wall. answer, the journey is infinite.” but at some point your gona bump your nose
Shukmani
If you take a plane with perpendicular lines originating on its surface and extending into 3d space both below and above the plane and then you warp the x axis downward from the (0,0) point forming a hyperbola and then do the same for the y axis but only upward the plane becomes a saddle shape.
What happens to the perpendicular lines though? They are no longer perpendicular from our three d point of view and in fact are no longer parallel to each other.
Because the perpendicular lines are no longer parallel … one would think that the lines must converge and actually cross each other or on the other hand diverge away from each other.
I postulate this is not the case but that there is infinite space inwards for the lines not to converge.
What this describes is warped space where you can imagine each perpendicular line coming off the warped plane … which remains parallel but not i n three dimensions … a model to represent a higher spatial dimension.
Gravity warps space in such a manner but instead of leaving or 3 dimensional space which is stable to experience higher dimensions we choose to feel it as a force against or physical form.
constantine
Much of what you said here makes scence. however though the universal observer (lol sounds like a god) has no scence of time and lives in a static universe. no time? then is he from his own point of view eternal? did he start a the moment the universe was created or if hes eternal was the universe created? just as i can look a 2 dimensional drawring of a circle and understand it for what it is. surely the universal observer would be able to see the dimensions beneath him and have and understanding of time. or would it see the lower dimensions as a blurr and not be able to tell one momment from another,
as someone with s keen interest but is not a scientist. your post is the first i have read that makes the other dimensions seem plausable. however im still not certain they are not higher dimensions but simply over looked ones. imagine a scocioty (stealing from douglas adams here) that lived in a world with no stars in the sky or whatever. basicaly a scocialy that had never had a reason to look up. everything they needed was on the ground. who acted like your 2 dimensional creatures on a sphere. then one day . something falls out of the sky and they look up. the extra dimension needed to make there sandles into shoes was always there. just over looked. also we need more tempral dimsion. so far i can move forward ( and in theory backwards. ) why cant i move up and down in time? and most importantly ( for science fction buffs) why not move sideways in time? please rebuff my silly ideas. but do it so we can go away and sah “ahhhh thats why”