# B What does 4 D spacetime look like?

#### wolram

Gold Member
I imagine Earths gravity well as a vibrating bubble, vibrating because all the other planets disturb it , then the galaxy as a seething mass of bubbles, then gravitational y bound galaxies as conjoined bubbles, I know this may be wrong but I can not imagine any thin else.
What does 4D space time look like?

#### pinball1970

Gold Member
I imagine Earths gravity well as a vibrating bubble, vibrating because all the other planets disturb it , then the galaxy as a seething mass of bubbles, then gravitational y bound galaxies as conjoined bubbles, I know this may be wrong but I can not imagine any thin else.
What does 4D space time look like?
We see in three dimensions so I don't think your question has any physical meaning

#### wolram

Gold Member
We see in three dimensions so I don't think your question has any physical meaning
Surly we have width, height , length and time thus 4 dimensions

#### Grinkle

Gold Member
We see in three dimensions
I certainly do.

Surly we have
In my opinion you can't change the verb "see" to "have" and continue as though the objection has been addressed.

#### Ibix

Surly we have width, height , length and time thus 4 dimensions
Yes. But it doesn't "look like" anything. You can draw visualisations of parts of it - for example the "rubber sheet" model of gravity should show Flamm's hyperboloid, which is a surface in Euclidean space that has a 2d metric that is the same as a 2d spacelike slice through a diameter of the Earth. But note how many caveats and limitations I put in there. And it's still wildly misleading because it's the curvature in the timelike planes that is important. And you can't draw that because null lines just can't be done right in Euclidean space.

There are any number of visualisations of specific spacetimes, such as Minkowski diagrams, Kruskal diagrams, Penrose diagrams. All of them show only a reduced amount of information (2 or 3 dimensions only) and all of them are schematic to some degree or other - notably because the behaviour of null intervals simply cannot be replicated on a Euclidean surface.

There simply is nothing that spacetime "looks like" because nothing is a 4d pseudo-Riemannian manifold, except spacetime.

#### pinball1970

Gold Member
Surly we have width, height , length and time thus 4 dimensions
Grinkle and Ibix have made the technical points, analogies take you so far then stop being useful.

We exist in four dimensions but see in three.

Space time has three spatial dimensions and one of time but you don’t “see” time you experience it (trying not to stray into wishy washy)

Great example of how this sort of thing can be misconstrued

My friend was proudly showing off her “4D” image of her baby scan a few weeks ago.

I explained to her that it was in fact a 2D image because the dimensions of the photo were length and width, that’s it.

The baby has three dimensions and the image has apparent depth (3rd dimension) because of the contours light and shade of the image.

The image was taken from a still from a short video of the baby, the baby is moving through time (4th)

Nice sell from imaging team though.

#### AgentSmith

What does 4D space time look like?

How could we possibly know what it looks like? I have tried to imagine a block universe, and came up with a 4-spheroid with lots of pulsating "pimples" that come and go, due to QM. Its nothing but my imagination. The movie Transtellar probably did better.

#### arydberg

The best example is a book called "Flatland" Where creatures live in 2 dimensions and cannot conceive the third dimension. To them things simply disappear and re- appear.

Staff Emeritus
What does 4 D space time look like?
Look out the window. That's what it looks like.

#### Bosko

Gold Member
I think that universe is "spherical" and I am trying to explain how it looks like
If you draw the circle . That is 1D sphere in 2D space... formula $$x^2+y^2=t^2$$ ... t -the radius is time
If you draw the sphere . That is 2D sphere in 3D space... formula $$x^2+y^2+z^2=t^2$$

The universe is 3D sphere in 4D space ... formula $$x^2+y^2+z^2+u^2 =t^2$$

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#### Ibix

I think that universe is "spherical"
Do you have a reference for this? As far as I know current consensus is that the universe is spatially flat, and the maths you are showing does not seem to me to match a closed FLRW universe in any case.

#### Bosko

Gold Member
Do you have a reference for this?
No. It is just as simple as possible explanation of the idea of the universe width closed, finite geometry and constant curvature.
and the maths you are showing does not seem to me to match a closed FLRW universe in any case.
I put scale factor (radius) a(t) = t , and at present =1. The curvature 1/t , also =1 now. All is simplified as much as possible
FLRW metric will be correct under those conditions, I hope so.
As far as I know current consensus is that the universe is spatially flat,
It is the same as far as I know also, but if the universe is either flat (Euclidean ) or "hyperbolic" it has to have the border.
It doesn't look logical to me that universe have any border.

Light should travel the same amount of time and distance from point A to B as from point B to A.

If me and you are at point A (Earth, Solar system in Milky Way galaxy) and the universe have the border.
Let's find the closest to us, the point B on the border.
The CMB radiation coming from all directions . Let's pick the point C in the same direction of the point B.
A................................................................................................C..................B

Let's go back in time of when the whole universe emitted CMB we are observing today.
Acmb...................Ccmb.......Bcmb

Light needs the same amount of time and distance to go from Ccmb to A as light ray from Acmb to C.
CMB radiation from Bcmb is come to B but also in opposite direction to the point D
A.............D..................................................................................C..................B

Point A have to be left of the point D in order that any CMB come to it from B direction.
Point A have to be in area which size is the same as size of the universe when CMB have been emitted.
It is very small area and probability that our universe have a borer is very low.

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#### Ibix

I put scale factor (radius) a(t) = t , and at present =1. The curvature 1/t , also =1 now. All is simplified as much as possible
FLRW metric will be correct under those conditions, I hope so.
If that was supposed to be a metric it needs coordinate differentials (dx, etc.), not the coordinates themselves. And if you want to set the scale factor to a constant then it either isn't a description of our universe, or it only applies over a short enough timescale that the scale doesn't change.
if the universe is either flat (Euclidean ) or "hyperbolic" it has to have the border
Current models treat it as infinite in spatial extent. No border is necessary.

#### ScientistAlexandrus

Well,we can't really know what a 4 Dimensional Hyperspace "looks" like as of now. That's because we are still trapped in the three and hence the fourth isnt yet imaginable as you are asking here. The evolved natural sensory systems and all the components'/particles' interactions are in 3D particles so we can't imagine the 4th Dimension Naturally like that.

#### Ibix

The evolved natural sensory systems and all the components'/particles' interactions are in 3D particles so we can't imagine the 4th Dimension Naturally like that.
You seem to be mixing models here. If spacetime is 4d as usually modelled then we are all embedded in it and are also 4d. It's certainly true that our perceptual system does not lend itself to imagining a (3+1)d manifold, but that's not because we're made of "3d particles".

#### ScientistAlexandrus

You seem to be mixing models here. If spacetime is 4d as usually modelled then we are all embedded in it and are also 4d. It's certainly true that our perceptual system does not lend itself to imagining a (3+1)d manifold, but that's not because we're made of "3d particles".
I didn't mean we are made of 3D particles and that's the reason. The physical interactions that facilitate us our senses,especially basic vision is 3D is what I meant. The OP asked what does this 4D spacetime look like. I think we need to delve deeper into Quantum and Particle Science and Physics to know or even get an idea or even imagine a 4th Dimension.

#### PeterDonis

Mentor
The physical interactions that facilitate us our senses,especially basic vision is 3D
The physical interations aren't 3D, they're 4D. They happen in spacetime, not space.

#### Ibix

The physical interactions that facilitate us our senses,especially basic vision is 3D is what I meant.
This doesn't make sense. You can - in a limited sense - model individual interactions as events, which are zero dimensional. Otherwise you need to treat them (and certainly your perceptual system as a whole) as extended in space and time, meaning that they are four dimensional.
I think we need to delve deeper into Quantum and Particle Science and Physics to know or even get an idea or even imagine a 4th Dimension.
The maths we have is a perfectly good description of it. It's just not something you can readily visualise.

#### Bosko

Gold Member
I you spend 8 minutes siting that is 8 minutes distance in 4th dimension=time .
That is the same as traveling to the Sun 8 light minutes in 3 spatial dimensions.
We are in 4 dimensional world.

#### jbriggs444

Homework Helper
I you spend 8 minutes siting that is 8 minutes distance in 4th dimension=time .
That is the same as traveling to the Sun 8 light minutes in 3 spatial dimensions.
We are in 4 dimensional world.
If you travel from Earth to the Sun at 99% of the speed of light in a straight-line (geodesic) path, the length of the space-time interval that you traverse between starting and ending event will be approximately one minute.

We live in a 4 dimensional world with a pseudo-Riemannian geometry.

#### Ibix

I you spend 8 minutes siting that is 8 minutes distance in 4th dimension=time .
That is the same as traveling to the Sun 8 light minutes in 3 spatial dimensions.
Careful. The distance to the Sun in Sun centred inertial coordinates and eight minutes are kind of the same - the sign on the interval is opposite. But, as jbriggs444 points out, the interval along a path you could follow is typically very very different from eight minutes.

#### Deepblu

We can't visualize 4D space (4 directional dimensions) but I always imagined that if we are looking at an object moving in a 4D space then it can scale up or down in size while it is moving and it may disappear then appear suddenly, violating normal physical sense, that is only in my own imagination nothing scientific in my description.

#### Ibix

We can't visualize 4D space (4 directional dimensions) but I always imagined that if we are looking at an object moving in a 4D space then it can scale up or down in size while it is moving and it may disappear then appear suddenly
The thing to remember is that it's 4d spacetime we are talking about. What you seem to be talking about is viewing a 3d slice of a 4d space, where objects are free to pass in and out of the slice we view, as in Abbott's Flatland story. But spacetime puts a lot more restrictions on you, partly because time is already accounted for. So stuff moving freely in and out of the 3d slice you see is not really possible.

I don't think it can be visualised. But it is rather different from four spatial dimensions, which are not relevant to physical reality.

"What does 4 D spacetime look like?"

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