Energy, mass and dimension.

[Daecon]

Something occured to me earlier.

 

If we lived in a Universe with 4 spacial dimensions instead of 3, then E=Mc(squared) would become E=Mc(cubed).

 

I think.

 

Would that be correct?

[ajb]

Why do you think this is the case?

[Severian]

No - that isn't true. Even in a 2d world (one time dimension, one space dimension) we would still have E=mc².

[[Tycho?]]

Why in the world would you think that?

[Farsight]

Transdecimal:

 

Energy is related to stress, which is force per unit area, and is the same as pressure. But it's not enough to think of pressure alone, you need to multiply by volume to get energy. This yields a dimensionality of:

 

(force / (distance x distance)) x (distance x distance x distance)

 

Cancel out the distances and you get force x distance, which you recognise as work, which has the same dimensionality as energy. In a four dimensional world, energy is still pressure x volume, but now the volume has an extra distance dimension. Distance is denoted by s, so the energy equates to:

 

E=Mc²s

 

In a two dimensional world energy is still pressure x volume, but now the volume has one distance less. So energy is force, equating to:

 

E=Mc²/s

 

But if we look again at pressure, in a four dimensional world maybe it's force per unit volume. That would shove us back to

 

E=Mc²

 

In a two dimensional world maybe pressure is force per unit length, which would again shove us back to:

 

E=Mc²

 

Hmmmnnn. Actually, I don't know. And I'm not even clear what a mass is in two or four dimensions. I think I'd better bow out and leave it to Severian. Sorry.

[Royston]

Errr, it would just change the value of energy in respect to the sum of mass and the speed of light, it has nothing to do with dimensions, you're just changing the value of the exponent.

[Daecon]

Well my reasoning is this:

 

If an object of 1m length in each direction were in a 4-dimensional Universe, it would be matter that is 1m... quadred? Instead of 1m cubed.

 

The same amount of matter would have an extra direction to extend in, and therefore an extra "level" of density for the same about of mass.

 

In our 3d Universe, if you imagine a... "m-brane" (I was going to say "thingy" but decided against it), that stretches 300'000 km across, and 300'000 km down, and it's depth equal to the amount of mass that an object has, the resulting (very wide, very tall) flat thing would give an approximation of how much energy is contained in that much matter (being the thickness of the "m-brane").

 

In a 4d Universe, the amount of energy contained in an object of any mass would be equal to a m-brane that was 300'000 km across, 300'000 km down, 300'000 km wide and however-much-mass deep/thick. (Having 4 spacial dimensions.)

 

(And yes, before people start bugging me about wide and across being the same thing, just go with it, okay?)

[ajb]

You can see that is must be [math]E=m c^{2}[/math] just on dimensional grounds. Just consider what the units on both sides of the equation.

[Daecon]

But surely an object would have more mass in a 4d Universe for any given volume, as it has an extra direction to extend in...?

[[Tycho?]]

But surely an object would have more mass in a 4d Universe for any given volume, as it has an extra direction to extend in...?

 

I dont think you are visualizing this properly. Or maybe its beacuse you are trying to visualize it.

[Daecon]

Can you elaborate?

[Daecon]

I don't mean taking a 3d object and putting it in a 4d Universe. I'm talking about a 4-dimensional object in a 4d Universe.

 

Comparing a 2d object with a 3d object, it would be like gaining "infinitely" more mass... wouldn't the same be true for comparisons between 3d and 4d?

[swansont]

Mass is a scalar, as is energy. Work is a dot product — it's not going to depend on the number of dimensions you have. The things that might get weird are the vector interactions, and fields. The manifestations of effects depending on the cross-product, surface integrals, etc. might be different; you'd have to work that out.

[Severian]

I don't mean taking a 3d object and putting it in a 4d Universe. I'm talking about a 4-dimensional object in a 4d Universe.

 

Comparing a 2d object with a 3d object, it would be like gaining "infinitely" more mass... wouldn't the same be true for comparisons between 3d and 4d?

 

I think I see your problem. You are getting confused by the difference between mass and density. An object of fixed density would clearly have more mass if it was extended into another dimension (since it has more volume), and thus it would store more energy. However, an object of fixed mass obviously doesn't have more mass, so doesn't have any more energy either.

 

To put this is equations:

 

In 3D, for a cube of length L, mass m = d L³ where d is the density.

So the enrgy contained in the mass is E = mc² = d L³c²

 

In 4D, for a cube of length L, mass m = d L⁴ where d is the density.

So the enrgy contained in the mass is E = mc² = d L⁴c²

[Daecon]

I think I see your problem. You are getting confused by the difference between mass and density. An object of fixed density would clearly have more mass if it was extended into another dimension (since it has more volume), and thus it would store more energy. However, an object of fixed mass obviously doesn't have more mass, so doesn't have any more energy either.

 

To put this is equations:

 

In 3D, for a cube of length L, mass m = d L³ where d is the density.

So the enrgy contained in the mass is E = mc² = d L³c²

 

In 4D, for a cube of length L, mass m = d L⁴ where d is the density.

So the enrgy contained in the mass is E = mc² = d L⁴c²

Ah, thank you. Now I see what I was getting mixed up. So it's the "m" part of mc² that changes, not the "c" part.

[swansont]

m changing has not been established.

[Daecon]

In 3D, for a cube of length L, mass m = d L³ where d is the density.

 

In 4D, for a cube of length L, mass m = d L⁴ where d is the density.

[swansont]

In 3D, for a cube of length L, mass m = d L³ where d is the density.

 

In 4D, for a cube of length L, mass m = d L⁴ where d is the density.

 

You've redefined density, though. Density is a derived quantity, not a fundamental one. The density could (and probably would) be changed and the mass remain constant.

[Daecon]

Take it up with Severian...

[swansont]

Take it up with Severian...

 

Severian explained the two cases. You've assumed one of them to be true with no evidence.

[Severian]

Well, you are talking at cross purposes. If you keep the density fixed and increase the volume then clearly the mass changes (this is the sense in which "So it's the "m" part of mc² that changes, not the "c" part").

 

But obviously the mass of an object is fixed, so really, if you 'stretch' it into an extra dimension, its volume increases and its density decreases to compensate. E=mc² still.

 

In other words, the energy is always proportional to the mass (for an object at rest), but is not necessarily proportional to the density.

[Adrogans]

Yeah, he just had the density mixed up with the mass I think.

[Daecon]

You're talking about taking an object from a 3D Universe and putting it into a 4D Universe, I'm taking about an object in a 4D Universe which has always been 4-dimensional.

[Ragib]

Tell me why another dimension would make every things energy multiply by c? Currently there are theories which incorporate up to 56 dimensions, and credible theories up to 11 dimensions. Yet those equations do not describe a universe with [math]c^8[/math] times as much energy as theories with 3 spatial and 1 time dimensions have.

[TriggerGrinn]

Something occured to me earlier.

 

If we lived in a Universe with 4 spacial dimensions instead of 3, then E=Mc(squared) would become E=Mc(cubed).

 

I think.

 

Would that be correct?

 

quantised relativity

Using math you can write things in many different dimensions. This does not mean they exist, nor that the do not exist.

 

A dimension is a thing that exists only in perception of our minds. According to all other things there is zero dimensions and infinite possisibilty.

 

That is, for a quanta, and its frame of observation, that position is zero dimensional point of possibility to other frames of reference.

 

The only place spacial conception exists is in a mind that has visual conceptability. All matter and energy simply obeys the constant of a frame/mind.

 

Consider for a moment that C is C in a frame, not c^2, not c^3 or any other version of c. You can use c in many values depening on an equation you write but that does not change what one observes does it.

 

Think for a moment about the law of c. It is constant no matter what inside a frame of observation.

 

But what is c? it is energy that connects other frames. If you are not connected to another frame you have no space or time or dimension around you.

Imagine being born blind and considering dimension.

Imagine being a billard ball in space (a single frame with nothing in motion relative to this ball) You have no velocity, nor mass, nor kinetic energy. There is nothing connecting you, better yet just considering being a mind in a unvierse with nothing else in it. Since in a billiard ball there is motion of atomic particles there still exists forms of energy via actions a distance, non observable, so better to imagine a your percepted mind in a empty universe and understand all laws of physics collapse.

You need two frames for something to happen.

 

Things occur between a minimum of two frames, and any change in one of those two minimum frames affects each frame equally, and oppositely.

 

If we consider [math]E = MC^2[/math] ;

The energy inside of mass that you see in another frame, will be measured to be equal to the square of C because, it must overcome all the forces in which hold the atom together, this 'requires' energy and at the same time must transfer that energy at C towards you 'the other frame'.

 

This does not mean you are capable to put to work the full value of the measured energy, the same way you can not make use of the full value of energy in moving objects.

 

Kinetic Energy = [math]1/2 m v^2[/math]

or

[math]K_e = \frac{(mv)(mv)} {2m} = \frac {p^2}{2m}[/math]

It requires #value energy to stop an object + #value energy to move an object, thus the Etotal is Kinetic Energy = [math]m v^2[/math] but you can only put 1/2 of any energy to work in one frame, because energy only exists because there is change between each frame, and the will always split that energy equally and oppositely, for a minimum of two frames.

 

Therefore, an object that is at rest has energy equal to the energy of the moving object. The object that is at rest can be considered to have [math]-K_e[/math] and the object in motion can be considered to have [math]+K_e[/math]. The so called Negetive energy is inertia, and it will slow the moving object, or stop it. The positive energy is the energy that will add velocity to the stopped object. When these objects collide the always exchange and equal value of [math]-K_e[/math] &[math]+K_e[/math]. The equal opposite action/reaction etc.

 

note that two frames disconnected or [math]\sqrt 2 [/math] form constant pythagoras constant, of 01.41 (pi= 03.141)

 

that is 1.41 "X" plane, and 1.41 "Y" plane.

 

A square root is two answers. Mathamically + and - , or geometrically 2dimensional plane, of x and y.

 

That is the distance between two positions that are squared. Aka the distance corner to corner of a square is equal to length x 01.41

 

and that this constant applies to the fact that all physics are formed from constants, that expand from a minimum of two frames. This is drawn as a right trangle with equal length sides. and a hypotinuse = 01.41 * length

 

C may infact expand out from this constant in some form or another but I have not yet looked into that.

 

Where as pi is the constant that occurs for a given length arm rotated around a center point one full revolution. The distance the oustide of that length arm travels devided by the length of the arm * 2 = pi

 

The reason for this is that a closed object like a trangle or a square, or a circle is a closed system, and an event in space is called a system. That event can only exist by a minimum of two frames which we call a closed system or apply to a shape.

 

Shapes form from a closed system between frames.