Do we live in a 4D world?

[Rdivine]

I've always been intrigued by how four-dimensional objects can cast 3D shadows, can rotate around planes, and move upon a mirror image of itself.

Imagine a 2D world, completely flat, with people living on it ( flat as well ). The 2D world is bent into a 3-dimensional sphere, but the flat beings can't perceive it. They traverse the expanses and eventually come to the conclusion that their world is infinite.

 

What if we are those beings?

What if we are living in a 3D world, but bent into a 4D geometrical shape, just that we can't perceive it?

Are we actually living in higher spatial dimensions?

Can we visit the Fourth spatial dimension?

 

Keep in mind that when i say "4D" or four dimensions, i actually mean 4-dimensional euclidean space (space with 4 axes instead of 3), not 3-dimensional space and 1 dimensional time.

 

The implication is that our universe may actually be bent into a 4d shape through gravity, and we may perceive it as infinite, although it's not. Also, another implication is that we can actually (with enough power) warp spacetime into a 4d shape and cross from point A to point B instantly (similar to teleportation) and avoiding the distances that separate the two points.

[kerbiloid]

3-dimensional space is the only physical space with stable and closed orbits.
In case of any another dimensions number any particle/planet shall either fall on the core/star, or fly away to infinity.

So, even if there are >3 dimensions in our Universe, all of them except these known 3 should manifest their existance either on Planck or on Universe distances.

[Aladran]

I've seen in a documentary that you need to "live" in the Dimension above to be able to notice the dimension below.

 

Exemple, to be able to see the 1st dimension, you need to live in the 2nd, 1st Dimension is a line, to be able to see it you need to move, if not all you'd see would be a dot. By adding the 2nd dimension you could "move" in and other axis then see the line of the 1st dimension.

Same goes until the 4th, which is the dimension we're living in. The 4th dimension allows us to move and behold the first 3 dimensions, that we interpret as the world we see.

 

We can't see the 4th dimension, but we feel it, we feel it as the time passing by, it's this Time that allows us to navigate in the 3rd dimension. Remove the 4th dimension and the 3rd dimension wouldnt be visible since we would loose the sense of depth therefore see the world as a 2 dimensional picture.

The 4th dimension turns your picture into a movie 4th Dimension is another Axis, perceived by us as Time. Being from the 5th Dimension might look at a 4D object and think It's a small sphere on their table, but for us it's our whole Universe (MIB style)

So we're surfing on the world's 4th dimension, but that's only what we see. There would be a total of 11 dimensions (Maybe more)... but all the dimension above the 4th are meaningless for our day to day live.

Edited March 17, 2016 by Aladran

[luizopiloto]

we can move freely in 3 dimensions... but can we do it in the 4th dimension?

Edited March 17, 2016 by luizopiloto

[Aladran]

17 minutes ago, luizopiloto said:

we can move freely in 3 dimensions... but can we do it in the 4th dimension?

We are only moving along with it, like a feather in the wind.

[problemecium]

For some time now, cosmologists have been attempting to answer this very question, along with several others, via measurements of the properties of the entire visible universe.

If a group of flatlanders were living on a 3D sphere, they wouldn't be able to tell at first, but if they were to look very far into the distance (using 2D light that follows the sphere), they could see light that has traveled all the way around the sphere in a circle. There would also be cases where objects on the other side of the sphere would be visible in opposite directions.
Accordingly, cosmologists have searched for galaxies that are visible on opposite sides of the sky, or for motion patterns that suggest galaxies on opposite ends of the sky are interacting with each other, gravitationally or otherwise. Alas, so far no such phenomena have been found.

The flatlanders could also, with sensitive equipment, draw very long, straight, parallel lines and note that the distances between them decreased gradually, such that an infinitely long pair of lines should eventually converge. Models and tests show that this can happen in our universe with straight beams of light in the vicinity of massive objects, creating effects such as Einstein rings. Cosmologists have been looking for evidence that this occurs on the grand scale as well, but also to no avail - within the limits of our measurements, the fabric of spacetime appears perfectly flat with only miniscule possible deviation.

These separate observations indicate that the universe is not a closed 4D surface, or if it is, it must be much, much bigger than the visible universe - as in several orders of magnitude, the way the Earth was to ancient Mesopotamians who only knew of the Tigris-Euphrates basin.

[cubinator]

Yes, I think it's accurate to say our universe is the surface of a 4-dimensional...thing. Think of the rubber sheet analogy used to describe gravity. Our universe is a 3D 'rubber' sheet, warped by massive objects causing things like gravitational lensing and time dilation. We don't know exactly what shape it is though.

There are also many theories that there are higher dimensions tightly rolled up on a very small scale, like how where you might see a telephone wire from far away you would percieve it as a line, whereas an ant crawling on its surface would perceive it as a 2-dimensional cylinder, while an even smaller creature might see that it is really made up of lots and lots of tiny cylinders coiled up together. It's like how a piece of paper has width, although that doesn't become important except when you stack a lot of paper together, or when you have to peel it off some other surface, grabbing onto the tiny edge.

I don't think we could feasibly visit 4-dimensional space. First off, we don't know how to make anything leave the universe. It would cause some issues with the laws of thermodynamics. Second off, you would die. A space suit wouldn't help, because it doesn't protect you from the extra freedom of motion. All your blood would literally fall out. Think of a flatlander. He has blood running in 2D veins. If you were to pull him into 3D space without sandwiching him between two protective flat plates first, his blood would fall out from the extra dimension. The same would happen to you if you tried to leave our universe. It'd be like trying to contain water in a rubber band.

[Yourself]

18 minutes ago, cubinator said:

Yes, I think it's accurate to say our universe is the surface of a 4-dimensional...thing.

I'm no physicist, but what I do know leads me to believe that this isn't accurate.

Firstly, it's both time and space that warp, not merely space, so that's 4 dimensions to account for.  Also even though it's warped that doesn't necessarily indicate that the 4D "surface" that describes our universe is necessarily the surface of some 5D shape.  If I remember my differential geometry right that would be called an embedding, which isn't necessary to describe our universe.  And, in fact, there's certain things about an embedding of a surface in a higher dimensional space that would be outright impossible for use to measure from within that space.

That means that presuming that our universe is embedded within some higher dimensional space postulates certain properties which we cannot possibly observe, so I'd be reluctant to make the claim that it's true.

I'd trust more for someone like @K^2 to comment further since this seems more up his alley than mine.

[kerbiloid]

9 hours ago, luizopiloto said:

we can move freely in 3 dimensions

We can move freely in 2 dimensions, and also jump and duck.

[Bill Phil]

If we were in 4D space, then galaxies wouldn't be disks. Not to say that the geometry of the universe itself can't be a hyper sphere or something.

1 hour ago, kerbiloid said:

We can move freely in 2 dimensions, and also jump and duck.

We can move freely given enough force. If we're not on a planet, then any thruster will allow us to move freely in all three dimensions, albeit limited.

[kerbiloid]

34 minutes ago, Bill Phil said:

If we were in 4D space, then galaxies wouldn't be disks. Not to say that the geometry of the universe itself can't be a hyper sphere or something.

According to the Central force defintion and Bertrand's theorem, no stable orbits, galaxies and so on in a non-3D Universe.

That's obvious because the value of any central force is proportional to 1/R^N-1, where N is dimensions number.
In our 3D universe gravity and electrostatic forces are 1/R². This gives two symmetrical roots of equation which allows to have symmetrical and closed trajectories.
In any universe with N != 3 you will have an infinite spectre of not closed trajectories instead of orbits, which is just a chaos instead of regular structures.
 

Edited March 18, 2016 by kerbiloid

[PB666]

5 hours ago, kerbiloid said:

According to the Central force defintion and Bertrand's theorem, no stable orbits, galaxies and so on in a non-3D Universe.

That's obvious because the value of any central force is proportional to 1/R^N-1, where N is dimensions number.
In our 3D universe gravity and electrostatic forces are 1/R². This gives two symmetrical roots of equation which allows to have symmetrical and closed trajectories.
In any universe with N != 3 you will have an infinite spectre of not closed trajectories instead of orbits, which is just a chaos instead of regular structures.
 

Uhhhhh, you mean space-time, as in the 4th dimension is time?

In our universe it exhibit euclidian geometry in all directions, there is not evidence of hypergeometry beyond space time.

[K^2]

8 hours ago, Yourself said:

I'd trust more for someone like @K^2 to comment further since this seems more up his alley than mine.

*sigh* Yeah, but it's one of these topics which doesn't lead to anything good when discussed with lay-persons. Let me just drop a few bullet points, and for anyone who wants to understand this better, there are a few universities I can recommend.

Technically speaking, the idea of looking at our 3D space (or 3+1, really, because time) as a section, boundary, or some projection of space with higher dimension is related to Holographic Principle and various models involving this are sometimes known as holographic interpretations. The one that comes up most frequently as an example is the AdS5 which leads to the gauge/gravity duality.

The most important thing to understand about this is that no holographic interpretation produces better results than Standard Model. In fact, they can't even fully match SM. So far, they have all been just interesting mathematical models; at most, a different way to look at already understood physics. Kind of like gravity in General Relativity can be interpreted as consequence of Space-Time geometry, or it can be viewed as just another gauge field. Ultimately, all of the math is the same, but some interpretations are easier to grasp intuitively in certain contexts.

Nonetheless, there are still some very serious physicists who think that it's the key to Unified Field Theory. Again, not because it's inherently different, but because it's the same field theory seen from completely different perspective.

[kerbiloid]

26 minutes ago, PB666 said:

Uhhhhh, you mean space-time, as in the 4th dimension is time?

In our universe it exhibit euclidian geometry in all directions, there is not evidence of hypergeometry beyond space time.

No, I mean space. The very beginning of theoretical mechanics course. From the Action definition, then central forces in coordinate system and so on, about potential fields of central forces and particle trajectories in these fields.

[PB666]

11 hours ago, kerbiloid said:

No, I mean space. The very beginning of theoretical mechanics course. From the Action definition, then central forces in coordinate system and so on, about potential fields of central forces and particle trajectories in these fields.

So far as I have seen they are talking about less than 3 dimensions at quantum gravity resolution into space-time (long-long time ago in the murky inflation onset), and the possibility of other dimensions at the quantum scale, which we are pretty feckless in measuring. If you look at the feyman lectures, he basically combines all three dimensions of space into 1, a reference point at which c flows out. It produces 2 dimensional plots. Read K2s post. The critical problem is gravity quantum/gravity distinction, I keep making the point that gravity is a faux force, its actually space-times effect on intertia.

So lets go through the problem in laymans eyes. To start let me just premise the argument with a piece of dogma that resolution relies on multiple perspectives. Our perspective is on a particular comoving space-time that has a visibility (composite of many time components of space-time) of less than 10% of the comoving units of the universe. The boundaries of the visible unit our defined by the CMBR radiation which is Doppler shift tells us was about 13.8 billion years ago, it is uniform in all directions (pretty much) and denotes that our current largely (ignoring dark energy) expanding universe. Its' uniformity defines an inflationary state and this is the singular visible (inferred) perspective on that state.  Because we cannot see an edge to the universe in any direction, and because of the dating there is a secondary inference that comoving spatial frames (the relative average position and velocity vectors of averageing of four reasonably close galaxies in which there spatial positions are roughly tetrahedral) can be moving away from each other faster than the speed of light (c), and the best way of explaining this superluminal relative motion is via inflation (again excluding dark energies effect).

Now for some perspective, lets take a black hole, black holes communicate information via the Hawking radiation, and external energy communicates with it via absorbtion on its surface. It behaves as a singularity but we see a frequency (hv) being released. It sees incoming energy (again objects inside may still have structure, we simply cannot see the structure, we see the properties of the singularity). Note that gravity acts through the ability for energy to warp space-time. Mass energy equivilance allows this, so we can denote the energy of a black-hole by its gravitational attractions and via the radiation it releases. Us and black hole have two very different perspectives of each other, its as if the black hole lives in its own dimensions, but its simply a distortion of our dimensions by immense amount of energy. The energy is acting through something called gravitons which we have the poorest understanding of. So now lets look at something perilously bigger.

Imagine our universe's expansion

1. convert all mass to energy (its still maintains its gravitational attractions)

2. confine all the energy to one geometric point with no dimensions

3. Without dimension there is no space, and without space gravity become unitary, its quantum gravity - ta-da the only force in the universe.

4. since there is no space - ta-da- energy density is infinite.

That was easy, right [cough]. Well not exactly, because the universe as a singularity it may move around in other dimensions, for example virtual particles can move around in space and time and speeds greater than c, you can have all kinds of bizarre behaviors at the quantum scale. So what about our universe? Yeah, well we don't actually know. Then only thing is that its contents remain unidimensional, as a consequence the universe is timeless and spaceless in its origin from looking into the CMBR crystal-ball. This has consequences.

Ok so what happens next, well, errr, not so easy, layman computer malfuntion. S__t happens . . . . . . .inflation which really should be called hyperinflation because:

4. Space expands to faster than the speed of light in all directions (inferred above). Surprisingly the c-violation is not much of a problem, since quantum particles and disappear and reappear at places faster than c. As one quantum resolves into many, a probabilistic outcome is to spread energy according with the probability of where these sprites should be. Not too much of a problem.

5. There is no mass to confine anything (there is energy of the most exotic form), there cannot be mass because there is no space-time, mass relies on inertia and inertia has space-time as a premise. (i.e gravity is the warping of space-time). But an issue here is if there is no rest mass for the universe and quantum resolve into quanta how then is energy divided up, and the answer may be in phases.  There is actually a context here, since I can envision inflation as the end of this quantum/quanta resolution process, then the wave/particle nature of the energy exists pretty much as wave(s) until resolution thus can be divided evenly.   

Here is where there is a problem, space and time supposedly don't exist, so how can the singularity be flirting about in either. One possibility is extra-universal dimensions. Remember the black hole analogy, the black holes dimensions are a warped representation of ours from our perspective and vice versa. We cannot see the extra universal stuff (except maybe dark energy pouring in) and they cannot see whats going on in our universe (except our total energy - the faux pas here is what is the gravitational interaction - and hv- relies on space-time), it might need extra dimensions to inflate. 

6. The inflation stops and space-time [poof] exists. We havent a clue as to what gravitational constant was, I surmise that very shortly afterward that constant began equilibrating into something like our current constant. One of the reasons we don't know is that quantum gravity is still is the most dominant force in the universe. There are some who argue that warping of space time is a direct consequence to the resolution of the quantum universe, thats its a reflection of the process. This is important because did energy resolve uniformly across all comoving space, or did energy pour into the inflation and afterwards as some have suggested? If either are the case then we can pretty much infer that the gravitational constant was not. If energy was pouring into the universe, then where was it pouring from? if energy poured from a central point what retained it? If super-universal dimensions are the origin of 3D space then during inflation you could have something like hybrid dimensions of space to finally what we see. The alternative is that there are a set of dimensions that resolve at the quantum scale.

But if the layman asks the question of evidence, he would be pointed at a fairly uniform CMBR and told inflation has occurred, and thats is a very messy circular argument. 

What is needed here is a better understand of quantum gravity, what produces it, how does it warp space-time, etc. However the exotic birth of our universe is clothed in the CMBR, and from that point onward there is flat euclidian geometry of comoving space is all directions to the CMBR, there is no 'fish-tailing' of the universe as it might be expected with a 4th spacial dimension. So that if other dimensions exist they are acting on scales much much greater than the CMBR boundary. This can be happening, as I pointed out above our visible universe is a small fraction of the total universe, we cannot see the point of inflations center (either in time or space) nor the edge, if it exists.

 

 

 

 

Edited March 19, 2016 by PB666

[K^2]

12 hours ago, PB666 said:

I keep making the point that gravity is a faux force, its actually space-times effect on intertia.

Funnily enough, the central argument of Holographic Principle is that, "So is every other kind of force."