Spacetime and problem of 4th dimesion.

[Angelos]

Hi,

I know that this is probably the strangest thing for everyone, who started to think about relativity just few weeks ago, but how should I imagine 4th dimension? Many people say that thay can imagin it etc., but if you ask them for explanation they don't say anything usefull. Or other people say that you just add 4th dimension to the formulas and don't have to care any more, which I found pretty much stupid. I will be glad for every help...

 

[country boy]

Not a strange question at all. There is so much loose talk about the fourth dimension and how it is like the other three that it is no wonder the serious newcomer has a hard time with the concept.

See if this helps: If you are in a room and you want to give the location of your right hand, you can list three distances from a lower corner of the room - horizontal along one wall, horizontal out from the wall to a point under your hand, and vertical from the floor up to your hand. Those are the three spatial dimensions that your hand exists in. But if your now move your hand to another location, you have to give a new set of three distances for the new location at the later time. So the location of your hand also has a time associated with it that is needed to keep track of its motion. That's three space and one time dimension that your hand exists in.

Another example: When you call a cab you have to specify a location in both space and time: I will meet you on the corner of X and Y at 1 o'clock.

So, you see, we work in four dimensions all of the time.

 

[hayshed]

if you mean 4d space...

if you mean 4d space...then i well tell you about a book i once read. the book said that you can imagine 4d better by going a step down and inmaging that you are a flatlander. you are on on earth, and can only walk/swim around on its surface (so 2d) .u can however walk the whole length of the earth, all the time it seeming flat, yet u can walk right back 2 the same location from the oppistie direction u started in. basically the universe "bends" in a way we can't really understand, so we can go round in circles and such by appearing 2 go in a staright line.


all this may be wrong. don't judge me

 

[Mensoid]

What works for me, in rambling form.

The first three dimensions are rather easy, simply imaging a cube works for this. The way I look at the 4th dimension is to think of a line of cubes... It's rather simplistic but it works, the instant limitation is the resolution as you can't truly think of it in analog terms so much as digital terms. In other words, how can you really envision the real number line? You mentally assign a point to any level of divisions but not truly every point within. So back to the cubes, if we assign a resolution of Seconds to the 4th dimension we see an unending line of cubes each cube being a particular second. So when we give our 4 dimensional coordinates we say we're X,Y,Z in Cube t. When visualizing it it's kind of like a auto-lender ad I've seen on TV, the world of cars(cubes) shift to locate the 4th dimension then you use the first 3 to isolate a particular point within the cube. I'm a software developer so envisioning large numbers of dimensions is vital to some of my activities. The other advantage of this mental image is it can be extended to n dimensions, instead of a line of cubes you can picture a plane of cubes(5d), or a cubical group of cubes(6d), and then zoom out another level and have a line of cubical groups or cubes (7d)etc... Another envisioning technique to keep more to physics, is that once you identify the point in real space(3d) you then "zoom in" and see a line or plane of that are all the single 3d point, representing a 4th and 5th dimension. 4th being t, and 5th I guess for a lack of a better term dimension. I don't know if it accepted to think of a 5th dimension, going along the lines of every truly random event causes a split in the 5th dimension, I remember hearing of it from time to time. At any rate hope this helps.

 

[pmb_phy]

Hi,

I know that this is probably the strangest thing for everyone, who started to think about relativity just few weeks ago, but how should I imagine 4th dimension?

Its not easy to grasp 4-D spacetime. It best to learn how to work with it, solve problems with it and learn the language of it. Then it someone asks you if you know spacetime well enough to explain spacetime then you know spacetime decently enough ... buty I wouldn't trade Jennifer Aniston for it.

Imagining the 4th dimension is just as easiy as imagining time since that's what the 4th dimension is in some coordinates, time.
[/quote]
Many people say that thay can imagin it etc., but if you ask them for explanation they don't say anything usefull.[/quote]Notice how I'm not surprised by that observation? People can say they understand it by actually understanding it is all together an entirely different thing.

Or other people say that you just add 4th dimension to the formulas and don't have to care any more, which I found pretty much stupid. I will be glad for every help...

It sounds like they don't understand the significance about it all that well well aout it.

Please don't take my comments to be me making a statement that I'm an expert in spacetime. I will simply remain an okay artist on the topic and let it done either. I doubt be help more than that for the moment. But when I've finished my studies (which should take me into the summer until I finish some of the studies of these branches of science) I will be more knowledgeable about this in more detail. Meanwhile I'll be around using whatever knowledge that I have on that.

Pete

 

[Demystifier]

Those who say that they can really comprehend 4th dimension in a visual-geometrical (not purely algebraical) manner - lie!

 

[pervect]

Those who say that they can really comprehend 4th dimension in a visual-geometrical (not purely algebraical) manner - lie!

It's hard to say whether they are lying, but it's easier to say that it's not all that worthwhile, that the algebraic manner of understanding is actually more powerful.

One reasonably obvious way (I think) to represent a 4-d object is to have a 3-d volume with the fourth dimension visually represented as color.

It's not too hard to visualize some simple geometries this way, such as a hypercube. One can even count faces and edges in this way. It's a bit confusing if the two cubes of different color are coincident, so I'd recommend putting the blue cube inside the red one.

Eventually, a problem will become too complex for visual tricks like this to work, at that point one really needs to be able to understand it abstractly and mathematically.

 

[Ahmes]

These links might help:

 

[Demystifier]

These links might help:

They might help up to 4 dimensions. After that, they are meaningless and can only confuse you.