Properties of the fourth dimension

[twpatry]

I am new to this forum so I apologise if I am saying stuff that has been said a thousand times.

I have based my thinking about the fourth dimension on the patterns in the relationships between the first three dimensions (plus the zero dimension or point). By developing an understanding of the patterns between higher and lower dimensions, I have sort of come up with a general idea of what the fourth dimension would be like. Nothing new I think but I would like to talk about it anyways and see what others have come up with.

For example, every surface in four dimensional space would be three dimensional.

The third dimension is completely flat when seen from the fourth dimension.

Purely three dimensional substance would be insubstantial compared with four dimensional substance.

What do you think and what are some properties of the fourth dimension that you have come up with?

Tim

[jinydu]

Yes, those things have already been said many times. For more properties of the 4th dimension, you can take a look at the website, tetraspace.alkaline.org

[houserichichi]

For example, every surface in four dimensional space would be three dimensional.

That's right - but it's a very difficult concept to imagine. Also, the boundary of a surface would be 2-dimensional within 4-space, which is different from the 1-dimensional boundaries we experience here in our existence.

The third dimension is completely flat when seen from the fourth dimension.

Again you're right, but don't think of flat as in what we percieve the word to mean. A being in four dimensions wouldn't see a flat surface that only has a left-right, up-down combination of motions...they would see exactly what we see, but to THEM that would be "flat" because they have another degree of freedom to move in.

Really, it's all playing with words when describing the fourth dimension in this way...just remember that the words we use to describe "boundary", "surface", "flat", etc are the same mathematical descriptors, but have very different physical interpretations when switching to 4-space and beyond.

[RQ]

Purely three dimensional substance would be insubstantial compared with four dimensional substance.

Purely...

I'm sure there are a lot of nonpure 3D/4D objects in that 4D universe ay.

[andyMan]

3 dimensional surfaces in the 4th dimension is true, but it can be misleading. Be careful not to fall into the trap of thinking you can make a 4D shape by making a box, and then just making the a bigger box, and putting the smaller box in the bigger box, making the stuff round the outside of the smaller box a 3 Dimensional area.
(It can sound a bit silly expressed there but it's hard to explain)

This is wrong because when you consider the 2 dimensional equivalent, you get a square inside a square, which does make an area around the smaller square 2Dimensional, but it is not a 3Dimensional shape.

[RQ]

We aren't actually making the 4th dimension, it's just a representation, since a higher dimensional space cannot exist within a lower one and vice versa. The surface of a 4D object is 3D and thus is infinitely many of them stacked in the 4th dimension to make it, thus individually they don't exist.

[typo91]

i dont see why there are sooo many 3d concepts trying to demonstrat 4d...

what about this idea...

Place a piece of dice in front of you. now think about it... its 3d?

no, cause if it was 3d it would be a massless cube with no compisition, and wouldn't even reflect light so you couldn't see it... but a piece of dice must be defined by more then 3 dimensions...

it has mass

it has composition

2 critical definements that must be declaired in order to measure/prove (in math) that you have indeed a pice of dice on your desk.

mass is a time based varuable is it not? Can't measure the pull of gravity without a time unit right?

so there you have it, mass is the 4th dimension, and matter composition is the 5th!

btw Energy is actually the 5th, as all matter values convert to Energy valus thanks to Einstien....

Well i am glad i could answer all your questions, your welcome!!

[houserichichi]

I don't even know what to say...yes, a die has mass and composition, but think about what you're saying. Mass results in warping of spacetime (as far as relativity goes)...gravity doesn't pull a mass down, gravity is a result of mass.

A die is composed of atoms which are in turn composed of leptons and quarks. Both of these "things" have mass, so a die has mass as a whole. We see a die because it DOES reflect light...if there's no light to reflect (turn them off) you no longer see it.

Mass is not time based, it's fundamental.

Thanks for answering all our questions typo :wink:

[PWrong]

It sounds like you're using the definition that a dimension is the number of points needed to describe an object.

i.e. a particle in our universe has a position in space, which requires 3 dimensions, a position in time, which requires an additional and also mass and energy, which make two more dimensions.

However, the number of dimensions has to be the smallest number possible. If the value of one attribute depends on another, then it doesn't count as a dimension

I'll use some physics formulas to demonstrate that an object only really has 4 dimensions.

E=Fs
F=ma
E=mas

i.e.

Energy = force * displacement
Energy = mass * acceleration * displacement

Now, by E=mc[sup]2[/sup], we know that energy and mass are proportional.

Acceleration is the derivative of velocity with respect to time, and velocity is the derivative of displacement WRT time. So acceleration must be dependent on position and time.

Now, I'm not too good at differential equations, but I think this shows that both energy and mass are dependent on position and time.

By the way, the above equations result in something slightly odd.
E=mc[sup]2[/sup], and E=mas
c[sup]2[/sup] = as

This would imply that acceleration is inversly proportional to displacement, so the harder you hit the accelerator, the less distance you can drive.

But I don't think it applies because relativistic acceleration means something different to newtonian acceleration.

[Keiji]

I thought you knew about the [sup] tags, PWrong...

I don't see how you can combine Newtonian physics and Relativity. You can't just "choose" one of them or the other :?

[PWrong]

I usually don't bother with the tags if it's only a few equations. But I will from now on.

I don't really know the equations for relativity. But I think equations like E=mas are still the same for both theories.

The difference is that in relativity, E includes both kinetic energy and the energy provided by the mass. So maybe it should be
E = mc[sup]2[/sup] + mas, or something.

It probably gets confusing because mass also increases as you approach the speed of light.

But the important thing is that energy is still a function of space and time, so it can't count as a dimension.