The Fourth Dimension: Introduction to a Book

[disregardthat]

http://sprott.physics.wisc.edu/pickover/fourth.html

I just read this, and it makes no sense. In my opinion of the fourth dimension all that is written here is garbage. What do you get out of this?

It is an introduction to a book.

 

[mathman]

It is an attempt to describe a perfectly plausable mathematical construct (four dimensional Euclidean space) in layman terms. Although it is somewhat hokey, there is nothing particularly wrong with it.

Warning, it has nothing to do with general relatively or string theory.

 

[disregardthat]

Well, could you explain what he means of a four dimensional animal? A fourdimensional animal could NOT excist in our world. It must merely be a way of explaining how another dimension is.

 

[yenchin]

Don't take 4 dimensional animals seriously... it's just a way to enable laymen to understand higher dimensions by the use of analogy. Imagine a 2 dimensional flatland and you stick your your hands through flatland (assuming this is possible...) then the flatlanders will see 5 disconnected blob of fingers, more precisely, the cross sections of your fingers as they pass through the plane. And as time passes, they will observe that the 5 blobs converge to form a bigger blob (now your palm is passing through the plane) etc. So as analogy, if there are 4 dimensional animals come into our world, we would expect the same phenomena, but of course I doubt 4 dimensional animals, if they exist, will have any anatomy that we are familiar with :tongue:

 

[disregardthat]

Yeah, I get that. Well, I admit it was an ok way to make us understand the fourth dimension mathematical, but in our world we observe it as 'time'. So if there are 4d animals time must stand still for them, if you get me? Since if a 4d animal is capable of moving through the fourth dimension, it means that it can move through time.

That leads me to a question I have asked in another thread, unanswered: How come that the fourth dimension works as time, AND works as bending of the three dimensional space due to mass? I would understand if it worked as only bending of mass, but it is like we are moving along this 'line' that is added to the three dimensional coordinate system.

As you described in the 2d blob finger example, the flatlanders didn't observe, and therefore in their world the rest of the animal did not exist. So, how come that the three dimensional objects in the three dimensional coordinate system that we observe, exist at all 'times' as time pass by in the fourth dimension?

 

[yenchin]

Erm. No. By 4th dimension in my previous post, I meant the 4th spatial dimension, not the temporal one.

 

[mathman]

That leads me to a question I have asked in another thread, unanswered: How come that the fourth dimension works as time, AND works as bending of the three dimensional space due to mass? I would understand if it worked as only bending of mass, but it is like we are moving along this 'line' that is added to the three dimensional coordinate system.

The point I was trying to make in my previous remark is that the fourth (mathematical) dimension of Euclidean geometry is NOT the same as the time dimension of general relativity.

 

[DaveC426913]

I just read this, and it makes no sense. In my opinion of the fourth dimension all that is written here is garbage. What do you get out of this?

That is all very standard stuff in standard 4D talk. There are whole books devoted to the analogy between a 2D-vs.-3D and a 3D-vs.-4D world.

Read anything about "Flatland":

http://www.geom.uiuc.edu/docs/forum/polytope/"
http://www.pbs.org/wgbh/nova/elegant/dimensions.html"
http://www.rmcybernetics.com/science/physics/dimensions_2_dimensional_space.htm"
http://www.rmcybernetics.com/science/physics/dimensions_4_dimensional_space.htm"

 

[disregardthat]

Erm. No. By 4th dimension in my previous post, I meant the 4th spatial dimension, not the temporal one.

I wasn't questioning YOU, I was questioning the fourth dimension as it is in our world:uhh:

 

[yenchin]

You DID reply to my answer. And since you have further query, all I did is to further clarify that the forth dimension can be spatial or temporal depends on which one do you mean.

If there is a forth spatial dimension in our world, we won't notice it just like flatlanders can't see into the third dimension. That has nothing to do with the convention of time as the forth dimension in relativity.

 

[disregardthat]

Well, I was thinking of the most acceptet theory, general relativity...

And my questions was based on it's interpretion of the fourth dimension. Not of the silly 4d animals this guy talks about.

Anyway, how can time both be spatial bending AND time?

 

[DaveC426913]

Anyway, how can time both be spatial bending AND time?

Because Einstein's legacy to humanity is the knowledge that there is no such thing as '3D space' and ' 1D time', there is only '4D spacetime'.

 

[disregardthat]

Well, is there any explanation for it?

 

[yenchin]

I suppose when people talking about 4D animals (I agree it's crazy:rofl: ) or flatlanders, note that they also permit the animals/flatlanders to move around, have a rather decent life (If you read 'Flatland' you know what I mean), i.e. there is dynamics. Therefore a flatland is not just a 2D space, it is 2+1 spacetime, i.e. 2 spatial dimension and 1 temporal dimension. A silly 4D creature would therefore live in a 4+1 spacetime, 5 dimensions if you will in that sense. It is quite standard for people who talk about higher dimensions in the pure mathematical sense not to mention the time dimension (since they weren't talking about GR).

 

[gabee]

This kind of reminds me of the video my friend showed me the other day about imagining the 10th dimension (http://digg.com/videos/educational/Imagining_the_Tenth_Dimension_2 ). It looks like a bunch of baloney.

 

[Golfer]

seeing across dimensions

If there is a forth spatial dimension in our world, we won't notice it just like flatlanders can't see into the third dimension. That has nothing to do with the convention of time as the forth dimension in relativity.

I agree with this statement. First, our 3D world is electromagnetic {EM} in nature and EM does not exist in other dimensions. What little discussion I have seen implies that only gravity exists in other dimensions {up to and including the 11 dimensions of M Theory}. Gravity appears to be the active area in which to find evidence of other dimensions.

All discussions [I have seen] of what a 2 D person would observe of a third dimension is based on analogy. I would like to see a mathematical derivation. Has anyone seen such a derivation?

 

[Gigacore]

my lecture said how hard it is to understand the concept of 4th dimension. He compared 4th dimension to the time and he said there are 3 tense in the time, namely, past, present and future. So by this he says time kinda 3 Dimensional object. If there is a 4th tense..then that could be the 4th dimension of an object !

 

[stealthtank91]

Yeah, I get that. Well, I admit it was an ok way to make us understand the fourth dimension mathematical, but in our world we observe it as 'time'. So if there are 4d animals time must stand still for them, if you get me? Since if a 4d animal is capable of moving through the fourth dimension, it means that it can move through time.

That leads me to a question I have asked in another thread, unanswered: How come that the fourth dimension works as time, AND works as bending of the three dimensional space due to mass? I would understand if it worked as only bending of mass, but it is like we are moving along this 'line' that is added to the three dimensional coordinate system.

As you described in the 2d blob finger example, the flatlanders didn't observe, and therefore in their world the rest of the animal did not exist. So, how come that the three dimensional objects in the three dimensional coordinate system that we observe, exist at all 'times' as time pass by in the fourth dimension?

think the truth is that there is no such thing as time, only space. Time is an illusion created by our limited perception. the RATE of time is determined by how fast our mind processes information ( like for example with phsycodelics people feel like time is slowing down, because their mind starts processing info faster). Time is the 4 dimensional crossections of our 3 dimensional selfs. if you where to see your entire body in the 4th dimension, it would be like seeing your birth, death, and everything in between in a single instance infinitely. But really time is acually space. Its hard to explain but let's say you picked up a pencil and if you moved it, the pencil would leave a trail of itself behind it . The pencil in the fourth dimension (time as we call it) would acually take up more space than in the 3rd dimension because not only would it have: length, width, and height, but it would also have "moved" from one spot to another" which by looking at it from a 4D perspective would take up space from point (A) which was a desk let's say to point (B) which is the other side of the room. So the only way to imagine the pencil taking up 4D space is to imagine the pencil taking up the 3d space in point (A), point (B) and all movements/locations between point (A) and (B). So the pencil would look like a "snake like" entity in the 4th dimension ( or at least that's the only way we can imagine it)

> "|" < - pencil

DESK------------------>>>OTHER SIDE OF ROOM
Point A |||||||||||||||||||||| Point B
[1 sec.] [2 sec.] [3 sec.] [4 sec.] [5 sec.]
------------------------------------------------->>>

unfortunatly i can't show a better illistration but if this line was really a 3d pencil then u could measure its 3 dimensions, and also measure its size in the fourth dimension as "movement". Our bodies and everything else in the universe has more than 3 dimensions. and we only see "frames" if you will, of the fourth dimension which we call the "present" Memories are only info. that we collected as we move through the 4th dimension which we call the "past". Keep in mind that time is only created by our limited perception and the only way we could see the 4th dimension as a whole, is if our minds could hold an infinit amount of information at once, or at least enough info. to see your birth, life, and death as one instance.

 

[BigFairy]

Hi thanks for your posts

 

[stealthtank91]

no problem, just trying to help, it seems like every one that tries to explain the fourth dimension fails pretty bad at it :/ not sure if my explanation is top notch either, but what can you do. After all it is something that is beyond our full understanding.

 

[zankaon]

GRT formalism and Hubble expansion are orthogonal descriptions. That is, GRT formalism is describing PART of nature i.e. g.w.s geodesics etc. But we do not have superluminal expansion of a 4-cube, nor of just it's 3-faces. So for example, one can not mix Friedman description, solution of Einstein eq. with Hubble expansion i.e. expansion factor a as in Hubble parameter H. That unfortunately is an example of casino formalism! 'The fault, dear Brutus, is not in our stars, but in our' formalism. So we live in a 3-manifold; yet GRT formalism is a very good partial description.

 

[DRMOKADI]

Do u believe tht black holes exists

 

[stealthtank91]

i think that they do exist, in fact i think that there is one in the center of our universe where the big bang occured, and that's what's causing all the galaxies to spin. its quite possible that there is one in the center because when the big bang occured, there was a lot of mass in one spot which very well could have callapsed into a massive black hole, and whatever exerted far out enough, wasnt eaten by it but remained as gasses and formed into stars and planets, like ours.

 

[DaveC426913]

i think that they do exist, in fact i think that there is one in the center of our universe where the big bang occured,

There is no centre of the universe. Or, more accurately, the centre of the universe is everwhere.

Think about an inflating balloon. Every point on the balloon started in the centre. As the ballooon inflates, all parts of the balloon expand equally, no point on the balloon is special or can be considered the centre. (Note that while real balloons have mouths, an ideal balloon does not have to have a mouth.)

 

[stealthtank91]

that is not what i meant by the center of the universe, the universe is infinit, i know, but what i meant was the center of the overall mass in the universe, in other words the point of the big bang singularity.

 

[cristo]

i think that they do exist, in fact i think that there is one in the center of our universe where the big bang occured, and that's what's causing all the galaxies to spin. its quite possible that there is one in the center because when the big bang occured, there was a lot of mass in one spot which very well could have callapsed into a massive black hole, and whatever exerted far out enough, wasnt eaten by it but remained as gasses and formed into stars and planets, like ours.

that is not what i meant by the center of the universe, the universe is infinit, i know, but what i meant was the center of the overall mass in the universe, in other words the point of the big bang singularity.

Your posts are full of misconceptions:

1. There is no reason that the universe should have a 'centre,' whether this be a centre of mass, or a geometric centre. In fact, current observations suggest the opposite.

2. There is no one 'point' where the big bang occurred and, more importantly, there is no point of the 'big bang singularity.' The singularity is just mathematical shorthand telling us that our theory is not able to describe t=0. This is hardly surprising, since we don't have a quantum theory of gravity and, intuitively, such a theory would dominate at very very early times.

 

[DaveC426913]

that is not what i meant by the center of the universe, the universe is infinit, i know, but what i meant was the center of the overall mass in the universe, in other words the point of the big bang singularity.

As cristo points out:

The universe is not infinite.
The universe does not have a center of mass.
The Big Bang occurred everywhere, not at some point.

 

[stealthtank91]

As cristo points out:

The universe is not infinite.
The universe does not have a center of mass.
The Big Bang occurred everywhere, not at some point.

ok, thanks for the info. but how is the universe finite? can u explain this mathematically or give some kind of clarification. logically, dimensions stack on top of each other creating the fiber of existence. with this in mind dimensions are technically infinite (and considering time as the 4th dimension , {if it is}, then time has an infinite past and infinite future, just as the other spatial dimensions do) wouldn't this make the universe dimensionally infinite? sorry if i explained this in a confusing manner.

 

[DaveC426913]

ok, thanks for the info. but how is the universe finite?

can u explain this mathematically or give some kind of clarification. logically, dimensions stack on top of each other creating the fiber of existence. with this in mind dimensions are technically infinite

They are unbounded, that does not mean they are infinite.

For the sake of clarity, imagine a universe with one fewer dimensions than we're used to. Imagine we are two-dimensional creatures constrained to the surface of a 3 dimensional sphere.

On this spehere, we detect no boundary, our universe is unbounded. Yet it is not infinite.

 

[Tac-Tics]

The universe does not have a center of mass.

What is the evidence for this?

 

[DaveC426913]

What is the evidence for this?

It follows from the Big Bang model of our universe, which is pretty well corroborated. I do not know if there is any currently-considered model that posits a centre of mass. There is, basically, no reason in all our observations and models to believe there is one.

If you know of a model that does so, please share.

 

[Tac-Tics]

It follows from the Big Bang model of our universe, which is pretty well corroborated. I do not know if there is any currently-considered model that posits a centre of mass. There is, basically, no reason in all our observations and models to believe there is one.

If you know of a model that does so, please share.

What I'm asking is what physical phenomenon allows for a center-less universe. If the universe were up to classical mechanics, there would be a center (found by averaging the position of all matter, weighted by mass). Of course the world *isn't* classical, so if you suggest that there is no center, which nonclassical phenomenon is responsible?

I'm not doubting anyone, but I am curious to know how cosmologists know this.

 

[stealthtank91]

ok so as DaveC426913 says: that in anology to a 2d universe, our universe is like a sphere? so unless this sphere is constantly expanding, then we could start at one point in the universe, and keep going until we stop at the point we started am i right? I know its hard to image this in a 3D aspect, but how is this so? is our universe constantly expanding as in the available space to contain matter (dimensionaly)?

 

[DaveC426913]

What I'm asking is what physical phenomenon allows for a center-less universe. If the universe were up to classical mechanics, there would be a center (found by averaging the position of all matter, weighted by mass).

Having a centre somewhere requires having an edge somewhere else. There is no place in the universe where you are nearer to a boundary than anywhere else because there is no boundary. No matter where you were, you would get the same numbers for mass. Thus, no centre.

ok so as DaveC426913 says: that in anology to a 2d universe, our universe is like a sphere? so unless this sphere is constantly expanding, then we could start at one point in the universe, and keep going until we stop at the point we started am i right? I know its hard to image this in a 3D aspect, but how is this so? is our universe constantly expanding as in the available space to contain matter (dimensionaly)?

I'm not sure what sphere has to do with expanding.

Remember, in our 2D universe, we live only on the surface. While the 3D balloon may have a centre from which it is expanding, that is where the analogy breaks down. We are constrained tot he surface and the surface has no centre.

 

[Tac-Tics]

Having a centre somewhere requires having an edge somewhere else. There is no place in the universe where you are nearer to a boundary than anywhere else because there is no boundary. No matter where you were, you would get the same numbers for mass. Thus, no centre.

Such a definition of a center of mass doesn't rely on any sort of boundaries.

If you have two distinct objects, draw the shortest path between them, a geodesic with some length. If you divide that path into two halves, each with length proportional to the mass of the object, the point where the two halves meet is the average position of the two objects.

We can use a generalization of this kind of technique to find an average position of the objects weighted by mass.

Basically, what I'm asking is what is wrong with the above reasoning? The only points I can see are

1) that there may not be a unique shortest path between two objects. (On a sphere, this isn't the case with points on opposing poles, but these exceptional cases apply only to pairs of points can be probably be neglected). and,

2) Length is affected by relativity and is dependent on the observer.