Would you say that it takes energy for a dimension (of any kind) to exist?

Ooooh! Tricky....
Well, I'd say yes with qualification. Try this:
Being scientific, what exists is what you can measure an effect of, else it is superfluous and we apply Occam's Razor chop chop. So if there is an extra dimension, we look for an effect of it's presence and compare that with the case if it wasn't there. Ok?
Good old gravity as per Newton ( and as a limiting case of General Relativity ) has an inverse square law for variation with separation of the force between two bodies. This is explicable as a geometric effect if you hypothecate a gravity 'flux' or field emanating from one of the bodies radiating outwards. The density of this flux as it crosses some unit area perpendicular to a line from the central body will also diminish as inverse square with separation. This follows from the surface area of a sphere being proportional to the square of it's radius, at least in a Euclidean model in 3 dimensions ( 'flat' 3D space ). Now if we assume another dimension like the other three ( spacelike ), and we assume that the field/flux also would radiate similarly into that dimension, then it follows that the inverse square law would not hold - in fact the force will diminish more rapidly as it 'leaks' away. Now any energy calculation of a second body moving in the field of the first is going to involve ( ultimately ) a summation or integration of the force along a given path. The reduced force strength with an extra dimension will alter that result, compared to not having that dimension. Essentially if the flux leaks away, so does the gravitational potential energy. A body will then fall inwards more slowly, gather less kinetic energy etc... so energy gets 'lost' into the extra dimension.
I know that's not quite what you asked, but it's the closest I can think of while staying with measurable phenomena. :-)

Aside: Such geometric thinking can suggest a prequel of general relativity within Newton's laws. What limited development of this thinking for a while was time itself. Predicting the path of a body from a given position in a gravitational field required knowledge of it's initial velocity. With a different velocity you get a different path. Thus the future evolution depended on the time rate of change of position ( velocity ) at that starting point, not upon the position alone. So if you are going to take a geometric approach, then you have to include time as a geometric element!

I have made this letter longer than usual because I lack the time to make it shorter ...

... and my other CPU is a Ryzen 5950X :-) Blaise Pascal

In referring to energy as a dimension let us exam this theory.The M Theory or what we call the String Theory. Time being one of the 11 dimensions (inluding Time,the three-dimensions and so on). Energy and dimenisions are based upon realities and membranes. Energy is what makes up these membranes. When membranes collide with each other they cause Big Bangs. Each membrane contains a universe and within that universe a reality. We must rationalize the connection between all strings (or dimenisons and realities).energy can often leak from one membrane to another, saying that particles not able to seen in our reality, but can be detected might be of another reality. It depends upon how close the reality or membrane is to ours. Therefore I hypothesize that there are more types of enrgy that are unknown to our reality until we dig deeper withi the M Theory.
Bloomfield College Student
Maurice Sherman

Would you say that it takes energy for a dimension (of any kind) to exist?

From the viewpoint of GR the answer would be no. A flat space would be empty but all of dimensions must be considered when defining the metric function.

Would you say that it takes energy for a dimension (of any kind) to exist?

If it helps, I'll list here what I've found to be excellent sources for pretty well the latest modern views on dimensional stuff. They're fascinating, very readable, don't require physics/maths degrees, and are not too expensive :
'Warped Passages' by Lisa Randall
'Hyperspace' by Michio Kaku
'The Elegant Universe' by Brian Greene
'Beyond Einstein' by Michio Kaku & Jennifer Thompson
'Flatland' by Edwin A. Abbott
'Sphereland' by Dionys Burger
They're all good but I think the first is the best, and you'll find the last two published as a single volume by Harper Perennial.
Cheers, Mike.

I have made this letter longer than usual because I lack the time to make it shorter ...

... and my other CPU is a Ryzen 5950X :-) Blaise Pascal

Even in M-theory the measurable properties of the embedded two-surface are defined by the coordinates in the dimensions of the embedding space. The embedding space is not modified by the embedded space.

Would you say that it takes energy for a dimension (of any kind) to exist?

From the viewpoint of GR the answer would be no. A flat space would be empty but all of dimensions must be considered when defining the metric function.

New here, just found this thread, and I remember something I learned some time ago. As I recall, there are empty (massless) universes in GR (e.g., De Sitter universe). They do not contain what we usually call energy, but their metric is different from zero. So I guess the answer would be indeed no. Although the De Sitter space is not flat.

Would you say that it takes energy for a dimension (of any kind) to exist?

I'd have to say no, because it's sort of like saying only the s-orbital in an atom exists if there's only one electron. There's still a p-orbital, even if it's empty. So I'd say there are N dimensions, however many necessary to resolve an event...

Would you say that it takes energy for a dimension (of any kind) to exist?

I'd have to say no, because it's sort of like saying only the s-orbital in an atom exists if there's only one electron. There's still a p-orbital, even if it's empty. So I'd say there are N dimensions, however many necessary to resolve an event...

I guess I risk being called a fastidious nitpick, but I'm not sure the analogy holds. The orbitals are there because the nucleus is there, not because the electrons ;-)

## Dimension question

)

Ooooh! Tricky....

Well, I'd say yes with qualification. Try this:

Being scientific, what exists is what you can measure an effect of, else it is superfluous and we apply Occam's Razor chop chop. So if there is an extra dimension, we look for an effect of it's presence and compare that with the case if it wasn't there. Ok?

Good old gravity as per Newton ( and as a limiting case of General Relativity ) has an inverse square law for variation with separation of the force between two bodies. This is explicable as a geometric effect if you hypothecate a gravity 'flux' or field emanating from one of the bodies radiating outwards. The density of this flux as it crosses some unit area perpendicular to a line from the central body will also diminish as inverse square with separation. This follows from the surface area of a sphere being proportional to the square of it's radius, at least in a Euclidean model in 3 dimensions ( 'flat' 3D space ). Now if we assume another dimension like the other three ( spacelike ), and we assume that the field/flux also would radiate similarly into that dimension, then it follows that the inverse square law would not hold - in fact the force will diminish more rapidly as it 'leaks' away. Now any energy calculation of a second body moving in the field of the first is going to involve ( ultimately ) a summation or integration of the force along a given path. The reduced force strength with an extra dimension will alter that result, compared to not having that dimension. Essentially if the flux leaks away, so does the gravitational potential energy. A body will then fall inwards more slowly, gather less kinetic energy etc... so energy gets 'lost' into the extra dimension.

I know that's not quite what you asked, but it's the closest I can think of while staying with measurable phenomena. :-)

Aside: Such geometric thinking can suggest a prequel of general relativity within Newton's laws. What limited development of this thinking for a while was time itself. Predicting the path of a body from a given position in a gravitational field required knowledge of it's initial velocity. With a different velocity you get a different path. Thus the future evolution depended on the time rate of change of position ( velocity ) at that starting point, not upon the position alone. So if you are going to take a geometric approach, then you have to include time as a geometric element!

I have made this letter longer than usual because I lack the time to make it shorter ...

... and my other CPU is a Ryzen 5950X :-) Blaise Pascal

## RE: Would you say that it

)

time, being the fourth dimension, and perpetually moving forward, must be or at least be affected by energy.

## RE: RE: Would you say

)

Spoken from the depths of ignorance.

THE MOTHER OF FOOLS IS ALWAYS PREGNANT

## In referring to energy as a

)

In referring to energy as a dimension let us exam this theory.The M Theory or what we call the String Theory. Time being one of the 11 dimensions (inluding Time,the three-dimensions and so on). Energy and dimenisions are based upon realities and membranes. Energy is what makes up these membranes. When membranes collide with each other they cause Big Bangs. Each membrane contains a universe and within that universe a reality. We must rationalize the connection between all strings (or dimenisons and realities).energy can often leak from one membrane to another, saying that particles not able to seen in our reality, but can be detected might be of another reality. It depends upon how close the reality or membrane is to ours. Therefore I hypothesize that there are more types of enrgy that are unknown to our reality until we dig deeper withi the M Theory.

Bloomfield College Student

Maurice Sherman

## RE: Would you say that it

)

From the viewpoint of GR the answer would be no. A flat space would be empty but all of dimensions must be considered when defining the metric function.

## RE: Would you say that it

)

If it helps, I'll list here what I've found to be excellent sources for pretty well the latest modern views on dimensional stuff. They're fascinating, very readable, don't require physics/maths degrees, and are not too expensive :

'Warped Passages' by Lisa Randall

'Hyperspace' by Michio Kaku

'The Elegant Universe' by Brian Greene

'Beyond Einstein' by Michio Kaku & Jennifer Thompson

'Flatland' by Edwin A. Abbott

'Sphereland' by Dionys Burger

They're all good but I think the first is the best, and you'll find the last two published as a single volume by Harper Perennial.

Cheers, Mike.

I have made this letter longer than usual because I lack the time to make it shorter ...

... and my other CPU is a Ryzen 5950X :-) Blaise Pascal

## Even in M-theory the

)

Even in M-theory the measurable properties of the embedded two-surface are defined by the coordinates in the dimensions of the embedding space. The embedding space is not modified by the embedded space.

## RE: RE: Would you say

)

New here, just found this thread, and I remember something I learned some time ago. As I recall, there are empty (massless) universes in GR (e.g., De Sitter universe). They do not contain what we usually call energy, but their metric is different from zero. So I guess the answer would be indeed no. Although the De Sitter space is not flat.

## RE: Would you say that it

)

I'd have to say no, because it's sort of like saying only the s-orbital in an atom exists if there's only one electron. There's still a p-orbital, even if it's empty. So I'd say there are N dimensions, however many necessary to resolve an event...

## RE: RE: Would you say

)

I guess I risk being called a fastidious nitpick, but I'm not sure the analogy holds. The orbitals are there because the nucleus is there, not because the electrons ;-)