Conservation Of Energy In The Fourth Dimension

[dieadderalls]

The other day while considering the concept of energy conservation, I found myself wondering: can energy be conserved in the fourth dimension, and possibly all subsequent dimensions, which could account for the complexity of experimental readings?

 

Prove me? Disprove me? I'm interested in finding the truth.

[granpa]

yes it would be conserved in any number of dimensions.

 

what complexity?

[CraigD]

Welcome to hypograhy, dieadderalls! :) Please start a thread in our introductions forum to tell us about yourself and your interests.

 

The other day while considering the concept of energy conservation, I found myself wondering: can energy be conserved in the fourth dimension, and possibly all subsequent dimensions...

You can use classical mechanics – Newton’s laws of motion – with any number of non-compact, measurable spatial dimensions. This is because it has 3 basic quantities – time, mass, and length – and length uses the general Pythagorean metric –

 

[math]d_{a,b} = \sqrt{ \sum_{i=1}^n (a_i - b_i)^2 } [/math]

 

– which works in any number [imath]n[/imath] of dimensions.

 

So derived classical mechanical principles such as conservation of momentum and energy would be the same in 1, 2, 3, 4, or more dimensions.

 

If the 4th or above spatial dimensions are compact or un-measurable, we might find through experiments failure of conservation laws in 3 dimensions. For example, kinetic energy in the usual 3 spatial dimensions might “spin up” a body, accelerating it in a compact 4th dimension. If this 4th dimension is un-measurable, kinetic energy would appear to unaccountably vanish, violating conservation of energy.

 

... which could account for the complexity of experimental readings?

I don’t know what “complexity of experimental readings” you mean. Can you give an example, or provide a link to a paper or article giving one?

 

There are some speculations that un-measurable, non-compact 4th and higher dimensions might be able to explain why gravity is so much weaker than the other fundamental forces by asserting that gravity, but not the other forces, can propagate through the higher dimensions. (see, for example Brane-World Gravity, 2010 Maartens and Koyama)

[dieadderalls]

Welcome to hypograhy, dieadderalls! :) Please start a thread in our introductions forum to tell us about yourself and your interests.

 

 

You can use classical mechanics – Newton’s laws of motion – with any number of non-compact, measurable spatial dimensions. This is because it has 3 basic quantities – time, mass, and length – and length uses the general Pythagorean metric –

 

[math]d_{a,b} = \sqrt{ \sum_{i=1}^n (a_i - b_i)^2 } [/math]

 

– which works in any number [imath]n[/imath] of dimensions.

 

So derived classical mechanical principles such as conservation of momentum and energy would be the same in 1, 2, 3, 4, or more dimensions.

 

If the 4th or above spatial dimensions are compact or un-measurable, we might find through experiments failure of conservation laws in 3 dimensions. For example, kinetic energy in the usual 3 spatial dimensions might “spin up” a body, accelerating it in a compact 4th dimension. If this 4th dimension is un-measurable, kinetic energy would appear to unaccountably vanish, violating conservation of energy.

 

 

I don’t know what “complexity of experimental readings” you mean. Can you give an example, or provide a link to a paper or article giving one?

 

There are some speculations that un-measurable, non-compact 4th and higher dimensions might be able to explain why gravity is so much weaker than the other fundamental forces by asserting that gravity, but not the other forces, can propagate through the higher dimensions. (see, for example Brane-World Gravity, 2010 Maartens and Koyama)

 

Thank-you so much!

 

When I say complexity I mean the seeming randomness of some results, the variability of answers; even in really similar conditions. That could be attributable to other forces we are not aware of, but I remember doing experiments in high school and everybody would get different results even though they were performing the same test. So by complexity I mean the way that results vary so widely (even if widely is a variation at ten decimal places, that is a huge change when the experiments should all be exactly the same).

 

I hope that makes more sense :3