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Dimensions

Imagine that suddenly our world has turned to a $$\text{two dimensional world}$$. Assume that all the living beings have turned in to simple shapes(for understanding the concept clearly). And you've turned into a triangle.

You completely forgot what $$\text{three dimension}$$ is. It's been $$\text{3 days}$$ since your existence in this new world, everything seems very normal for you. You've been meeting other shapes everyday and everything is normal.

One fine day, you see a meteor in the night sky which falls before you. You go closer and find that it's not a meteor at all, but it's a sphere. But as you've forgotten all about $$\text{the three dimensional world}$$, you treat it as a circle only.

But, something from your hearts suggests that it's not a sphere. Suddenly, the sphere comes alive. It tells you what $$\text{the three dimensional world}$$ is. You understand the difference between, both the worlds. The new dimension $$\text{depth}$$, has created a completely abnormal world.

So, we can conclude that we cannot say that "a $$\text{the four dimensional world}$$ doesn't exist. Though it may seem impossible, we have got to accept it. As in the story, you can only understand the next dimension clearly, only if an object from that world comes to explain you what it actually is.

Physics claims that there are $$\text{ten dimensions}$$! we only experience three spatial dimensions in our universe, when super string theory, for instance, claims that there are ten dimensions — nine spatial dimensions and a tenth dimension of time!

The only thing is that we are not able to perceive them. So here's the question, can an object living in a particular dimension see the next dimension? Or is it confined to the same dimension? If so why or why not?

$$\text{Comments are open! Feel free to express your views.}$$

Note by Sravanth Chebrolu
1 year, 11 months ago

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An active field of study in string theory is the subject of dualities, which is about demonstrating a mathematical equivalence between two or more respresentations. Probably the most famous is the M-Brane representation, which uses 11 dimensions, which has been shown to be equivalent to 5 other string theory representations that each have 10 dimensions. Still controversial is work underway to show a duality between an early bosonic string theory, which uses 26 dimensions and a particular symmetry in general relativity, which only has 4.

The point is, it's not true that our physical universe necessarily can only have one particular number of dimensions. It could be described as having different numbers of dimensions, depending on which model you want to use to describe it, the models being mathematically equivalent, i.e., interchangeable.

And then we have quantum physics. In any textbook of quantum physics, it's invariably treated in 4D space, usually relativistic 4D spacetime, so one gets the impression that quantum physics has 4 dimensions. Well, not really. The concepts of quantum physics actually threatens to throws out the concept of dimensionality altogether, and that only as an approximation we seem to exist in a 4D space. That was one of the big reasons why Einstein, whose life's work rested on the mathematical exactitude of curved 4D spacetime geometries, hated quantum physics so much. Quantum physics seems to make a mockery of the idea of such mathematically precise notions of spacetime geometries---whatever dimensions it may have.

Theoretical physicists now tend to treat dimensions like space and time as "emergent properties", in pretty much the same way why are planets like Earth are round. Earth is round because it is the natural consequence of gravity pulling together scattered matter into the least potential energy configuration, but the universe did not start with round planets. Likewise for properties such as time, space, and dimensions.

You always have something new :D

Least potential energy state huh? That's a very interesting way to put it.

Just to comment, I really don't think the fact that the Universe cannot be represented elegantly - i.e. as Einstein wanted it - is a bad thing. In fact, I find elegance in complexity. Simple as possible, not simpler. Imagine when we have the full picture - like, Theory of Everything, and beyond! It's like discovering what the square root of $$-1$$ is - and all it's implications. Or what $$\frac{0}{0}$$ is (<<DUNNO). Or better, what $$x$$ is in $$|x|<0$$ ;). Or rather, when you think you've figured out all of chess with so many books on the topic, and then someone invents a chess computer and busts your ass 1000/1000 times xD

To figure out the Universe, perhaps, we'll need intelligence beyond that allowed by our biological brains. We need... $$\huge{\text{2045}}$$.

Or maybe it isn't intended to be known. Just like the simultaneous knowledge of the position and momentum of a particle ^.^ · 1 year, 11 months ago

Eh, but maybe I did not answer the question directly, which is whether or not "beings in some n-dimensional space can see things in a n+1 dimensional space". But if beings can perceive things in a n+1 dimensional space, then they are going to believe they're in that n+1 dimensional space. As a matter of fact, the "holographic universe" theory (theories, actually) suggests that maybe we could be existing in an universe of fewer dimensions that we perceive of it having. · 1 year, 11 months ago

Michael Mendrin sir, i have posted this following note since a long time. i wanted someone's views on it. seeing your profile you seem to be the best person to ask to. Could you please check the following note. note · 1 year, 11 months ago

Thanks a lot for commenting sir! As you've mentioned about different universes, do you believe in $$\text{parallel universes?}$$ · 1 year, 11 months ago

Okay, I "believe" in parallel universes in the same way I "believe" that time travel is possible. Quantum physics does suggest time travel is possible for quantum information, i.e., quantum events in the future can actually influence quantum events in the present. But that doesn't mean I think it's possible for humans to travel through time in a time machine. Likewise, parallel universes is a mathematical way of looking at or explaining certain quantum phenomenon, in that quantum does behave as if there are multitudes of concurrent parallel universes. But that does not mean I believe that we have humans and civilizations living in parallel universes, a highly popular science fiction idea. Can I make Schrodinger's cat interfere with itself much like how physicists can already make atoms behave like light? In theory, I can, but in practice it requires exceedingly difficult conditions be first met before such a thing is possible for something as large as a cat--maybe not likely at all in this universe.

Interestingly enough, though, physicists now seem to have some evidence that dark matter that seems to exist in our universe could be "complex", i.e. self-interacting and possibly capable of forming its own atoms. This is not the same kind of parallel universe as suggested by quantum physics, but it does open the possibility that there could be parallel complex matter in a galaxy--the closest thing to the popular idea of parallel universes. · 1 year, 11 months ago

Ha ha ha! Yes sir, the recent science fictions suggest weird things about parallel universes. Even then I think, mathematically speaking, the probability of their existence is very low.

I'd seen a program on discovery science speaking the existence of parallel universes. I really got mesmerized by the show, and thought of asking the community here about their opinions, thanks for sharing your view sir! I respect it. $$\huge\ddot\smile$$ · 1 year, 10 months ago

Thanks For Mentioning me @Sravanth Chebrolu ^_^

According to me, It's a matter of thinking. It depends.Any person would be able to imagine the Next dimension if he/she has a strong thinking power.

For example, When We construct the 2 dimension Cartesian Plane, We're able to See it and figure it out completely. But, When We imagine Octants or the 3D Plane, Some People are able to imagine it Vividly, Some are not.

As far as I am concerned, I have never been able to imagine a 4th Dimension. I just can't Think What could Possibly be a 4th Dimension.

I would love to see Other Geniuses on B'ant Commenting on this discussion. · 1 year, 11 months ago

I would also love to see the master minds commenting here! · 1 year, 11 months ago

First, thanks for mentioning me for this topic ^.^

As with all concepts, comprehension depends on intelligence. For me personally, it took about a year of here-and-there thought to comprehend higher dimensions. But as of right now I still cannot comprehend 4D space. I've never tried. I can only treat 4D as 3D space and 1D time - 5D as 3D space and 2D time, etc. At 7D, I treat 6D as a point and introduce a different parameter - universal properties (see movies below). Well if I try I bet I will - for a later time.

The main problem in comprehension of higher dimensions comes from the fact that - assuming this applies to all dimensions (probably not) - whatever the dimension the entity resides in, it tries to base any higher dimension off of its own. And this can cause problems. For example, if we were originally flat-landers - i.e. 3D (2D space 1D time), we'd treat the 3rd spatial dimension as just more space - stacking planes. Like, what's the point? It'd make as much sense to us as it is to have a 4th spatial dimension - i.e. stacking cubes. Stacking cubes is just more cubes - nothing new, right? The trick is, we do not easily acknowledge the difference between spatial and temporal dimensions.

(A higher dimension is built by "stacking" of the lower dimension. Stacking points (0D) makes a line, stacking lines makes a plane, etc. As you can see above, the "4th D" seems like a mere "extension" of 3rd D. But this is not so, just like 3rd D is not a mere extension of 2nd D - as a flatlander would perceive).

The key is to imagine stacking your own dimension in a continuum. What I mean is, what does it MEAN to have a stack of many planes? We easily recognize that as a 3rd Dimension - the cube, if you will. But to a flat lander, this makes no sense. More planes is just more space to move in two degrees of freedom - just like to us, stacking cubes means simply more space to move in three degrees of freedom - almost like adding water to a fish tank. But the cubes we're adding aren't simple extensions of the system we reside in. There are three ways to look at XD - purely spatial, purely temporal, and spacetime. 4D from a space-time perspective can be viewed as 3D space and 1D time - easy. One can visualize this as a tape - that is, each point on the 1D time LINE represents a different state in 3D space. On the best possible film, there would be $$10^43$$ frames per second (one frame per Planck time (which is derived from shortest distance divided by fastest speed - Planck length/speed of light)). That is, for our Universe. So that is a new way to visualize 4D - 3D spaces stacked one after another in a continuum, but the continuum is temporal - i.e. it operates on space. But what about 4D space?? THIS is the challenge. We have to visualize the additional cubes not as mere extensions, but as the SPATIAL continuum of one system. This is known as a tesseract. FOUR degrees of freedom. And as of right now, I'm sad to inform you, I CAN'T DO THAT. But I'm sure with EDUCATION I will. Independent research always rules.

So yeah basically it all depends on intelligence. No biggie here. I guess I'll easily prove my point here with an example: I know there's something about matter turning into "pure information" upon entering a black hole - and thus become 0 dimensional, or even 2D. Bottom line is, it doesn't matter where you put my brain, as long as knowledge is conserved, so is my comprehension. Put me in 2D, I'll still know what 3D is. ALRIGHT?!

But before all, we must acknowledge that those "dimensions" are mere MODELS - attempts at representations of reality. It makes absolutely no sense to even imagine 2D beings because we by no means know how those entities would behave - if at all - or if they can even exist. Same goes for higher dimensions. Heck, I even remember Mr. Mathopedia telling me how all dimensions can be shown to be equivalent or something. Then he went on about 400 dimensions and stuff. Oh my neurons >.<

I'd like to suggest the two following movies:

Flatland

Imagining the 10 dimensions

For those with not a lot of time on their hands I suggest the second movie for it is purely educational. I did not get to see the first one but it looks really interesting - especially after watching the second. Then... I should put second first? Ah whatever meh sloppy :D · 1 year, 11 months ago

Thanks for replying sir. It was very informative(lengthier than I'd expected someone to write)! So, we should consider dimensions as models which help us to visualize the world we are living in, right? Or simply, they act as the visual aids for us. . .

So, what do you conclude, can a person living in the $$n^{th}$$ dimension be able to visualize and clearly perceive the $$(n+1)^{th}$$ dimension?

P.S: I think that's $$10^{43}$$ frames per second. $$\huge\ddot\smile$$ · 1 year, 11 months ago

Like I said, it all depends on intelligence. A mathematician's mind is perhaps the best for such purpose ;) · 1 year, 11 months ago

Sir, can you give your views on the existence of parallel universes? · 1 year, 11 months ago

Not necessarily parallel, but the multiverse sure is real. The best super-advanced book on that subject is The Road to Reality, a book by Dr. Roger Penrose. IT'S NOT AN EASY READ!!!

For something easier, try my playlist

100% worth of your educational time. Unless you have deadlines/work, of course.

Cheers · 1 year, 10 months ago

Thanks sir! I will surely see to it after my exams. · 1 year, 10 months ago

Good of you to point out the distinction between "parallel universes" and "multiverses". Moreover, there's even a distinction between quantum "parallel universes" and dark matter "parallel universe", the latter being a relatively new field of inquiry, as I have noted in my comment in here. · 1 year, 10 months ago

@John Muradeli sir, @Michael Mendrin sir @Brian Charlesworth sir, @Rohit Gupta sir, @Swapnil Das, @Nihar Mahajan @Mehul Arora, I would love to see your comments here! · 1 year, 11 months ago

Hi Sravanth, Thanks for mentioning me!

As per the views of Theoretical Physicists whom I admire, like Michio Kaku, 26 dimensions exist as per bosonic string theory! It may be that they are right. The only thing we require to understand these superdimensions is to stretch our thinking to a higher extent.

Coming to my opinion, It also might be possible that infinite number of dimensions or even no dimensions exist! Recent research has predicted that even time is an illusion!If it really is, then why not the dimensions? · 1 year, 11 months ago

Ah! you deserve to me mentioned!

Yeah, if time's considered as an illusion, then why not the dimensions? Can you express your feelings on parallel universes? · 1 year, 11 months ago

Hmm... Controversial topic!

Researchers of string theory(Actually even I want to be one!) confirmly state that Parallel Universes exist. They say that they can confirm this result with their calculations. As per my thinking... Oh, really confused! See, two things come to my mind. Firstly, if such worlds exist, why don't we have visitors from there? Secondly, for the support of the theory, I think the people out there are even researching if parallel worlds exist!

Oh, a third thought also! I read that parallel universes are possibly made up of antimatter and have everthing opposite to us, so is the world the mirror image of this? If yes, what would happen if the two men from the different universes meet? Will that result to the annihilation of the Universe? · 1 year, 11 months ago