APOD: Multiverses: Do Other Universes Exist? (2010 Nov 14)

[Céline Richard]

So if i write a trajectory X(a, b, c, d), where a, b, c, d are variables, and if i follow such a trajectory, thus i can travel into a space with 4 dimensions?
It is fascinating, thank you
I can't imagine such a travel, but it is funny to see how far maths can go in this example, because we could add as many dimensions as we would like to!
Have a very good day, thank you for all your answers,
Céline

[Chris Peterson]

So if i write a trajectory X(a, b, c, d), where a, b, c, d are variables, and if i follow such a trajectory, thus i can travel into a space with 4 dimensions?

Yes. If you use more conventional variable names, your trajectory (really, your position) would be a function of (x, y, z, t) - the three spatial and one temporal dimension that define space-time. Indeed, you find just these four variable (or their transforms) in many practical trajectory and orbit problems.

Mathematically, you could use any number of variables. Take away z and you'd be working with a trajectory on a plane- easy to visualize. Add another variable w and you'd have a trajectory in four spatial dimensions. Easy to handle mathematically, not so easy to visualize, though! Our brains are the product of evolution in an environment with three spatial dimensions, so it's not surprising that visualizing more is a challenge.

[NoelC]

Actually, i can imagine a 3D-Universe, but not a fourth dimension.

Something that might help...

It's really not hard to imagine a 4th dimension. If you consider the passage of time the traversal of a dimension, just think about moving around in your (ever changing) surroundings. Voila, 4 dimensions. The passage of time crosses all the other 3 dimensions, no? If you remember what happened yesterday, you are mentally simply moving through the 4th dimension.

Now for the "bake your noodle" question: Is there some Entity outside this 4 dimensional reality we call home Who can turn a shuttle and traverse time in either direction, much as we operate a DVR?

-Noel

[Céline Richard]

Thank you a lot !

Now, i know how to write a trajectory in a 4 dimensions space-time When i have written my trajectory, i think my letters were likely to be taken for constantes, while we are looking for variables.
Our world is a 3 dimensions one, indeed...
Nevertheless, if we include time, thus we have 4 dimensions? So when we count dimensions, don't we take into account time?

I guess we have to use time in our representations, because space is linked to time in relativity. Moreover, i hardly imagine a world without time, or it would be an "eternity". Unfortunately, as i didn't study relativity, i wonder why time is linked to space... Maybe i have to study more to understand it. Otherwise, please, could anyone give me a few explanations?

I can "travel" until yesterday, crossing the other three dimensions, that represent space, so i get a 4th dimension! It is very helpful. Actually, the idea of "crossing" are interesting, because the 3 dimensions of space don't cross each other. In the string theory, maybe all those strings can cross each other, i don't know at all, do you?

Thank you again, have a very nice day!

Céline