A Question for Cjlr
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17-09-2015, 12:42 PM
RE: A Question for Cjlr
(17-09-2015 07:04 AM)The Organic Chemist Wrote:  Right, the adults. He ready answered your question. I understood him, did you?

He did answer my question and then he asked a question of his own. He wanted to know my rationale for claiming in 4d space a dust cloud would not collapse into a single disk. Did you miss his question?.....Cause that is what we are discussing now.
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18-09-2015, 09:41 AM
RE: A Question for Cjlr
(17-09-2015 09:58 AM)ZoraPrime Wrote:  
(17-09-2015 03:23 AM)Heywood Jahblome Wrote:  Rotation is not a vector. It is a process that combines two orthogonal directions. We say that process rotates around the a particular axis, say Z, because it isn't the dimension being combined. In 3d space Once you define an axis, rotation is the combination of the remain two dimensions but this isn't really a vector even though we often think of it as being one. There is no quantity having a specific direction as well as magnitude.....there is no vector.

You really haven't shown that in 4d space rotation in the XY plane and rotation in the ZW plane can ever be combined mathematically into a single planer rotation. So my claim still seems to be true. In 4D space a dust cloud would not collapse into single accretion disk.

In general, angular momentum can be represented as a bivector, which is for all intents and purposes, an (anti-symmetric) matrix*. By Noether's Theorem, this bivector is conserved, and the addition for bivectors is the same vectors (you add component by component). As such the equation L[sub]system[/sub]=constant still holds true. If you're saying we can't find an operation that involves rotating XY and ZW... we can. You just multiply the corresponding rotation matrices for XY rotation and ZW for one operator. Lastly, the fact that angular momentum in 4D has six components doesn't change how in 4D a dust cloud would collapse into a single accretion disk (or the 4D Euclidean equivalent thereof). On the contrary, the same argument for 3D for why a accretion disk forms (angular momentum is constant by Noether's theorem) is the same argument in 4D for why a accretion disk forms (angular momentum is constant by Noether's theorem). The fact the bivector has more components doesn't change that argument.

Nevermind the whole fact that 4D Euclidean space never shows up anywhere, so this whole discussion is moot on that.


*if want to be pedantic, I have to say it's isomorphic to an antisymmetric matrix, but that's a detail since isomorphic is the mathematicians way of saying "practically equivalent."


_____________________

It's occurred to me that I think you're getting concerned over the word "disk." Yes, a 4D Euclidean "disk' (in the sense of how we're using it) spans over two planes. However, there's no word for "flat object that confines itself to particular plane(s)." We'd call them disks, even if they span two planes. It's like becoming concerned because someone uses the word "spherical symmetry" when discussing 4D Euclidean space and insisting "it's not a sphere, it's a hypersphere, so we should call it hypersherical symmetry." I'm calling it an accretion disk, even if it spans two planes, because I don't see why the fact it spans over two planes instead of one plane matters when it's orientation in space (i.e. the 4D angular momentum bivector) doesn't change.

Thumbsup

If it weren't obvious, I was trying to leave out mathematical detail, because HJ hasn't studied it and thinks his feels are on equal footing.

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18-09-2015, 09:42 AM
RE: A Question for Cjlr
Or to summarise the thread -
Heywood: So, can I make up my own physics rules?
cjlr: No. What you made up isn't valid, and even if it was, it wouldn't prove anything.
Heywood: Are you sure? I want to make up my own rules. Can't I?
Zora: Fuck no.

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18-09-2015, 10:40 AM (This post was last modified: 18-09-2015 10:50 AM by Heywood Jahblome.)
RE: A Question for Cjlr
(14-09-2015 02:26 PM)cjlr Wrote:  Spin refers to angular motion about a single axis. That's how it's defined - it can't be anything else.

In 3D space angular motion occurs about a single axis. In 4D space angular motion occurs about two invariant axis planes.

Quote:Every rotation in 3D space has an invariant axis-line which is unchanged by the rotation. The rotation is completely specified by specifying the axis of rotation and the angle of rotation about that axis. Without loss of generality, this axis may be chosen as the z-axis of a Cartesian coordinate system, allowing a simpler visualizaton of the rotation...

Quote:....Analogous to the 3D case, every rotation in 4D space has at least two invariant axis-planes which are left invariant by the rotation and are completely orthogonal (i.e. they intersect at a point). The rotation is completely specified by specifying the axis planes and the angles of rotation about them. Without loss of generality, these axis planes may be chosen to be the uz and xy planes of a Cartesian coordinate system, allowing a simpler visualizaton of the rotation.

https://en.wikipedia.org/wiki/Rotations_...dean_space

The only place I have read anything to indicate that in 4D space a dust cloud would collapse into disc is here. Sorry if I am little skeptical....for all I know your just some internet crackpot.
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18-09-2015, 10:50 AM
RE: A Question for Cjlr
(18-09-2015 10:40 AM)Heywood Jahblome Wrote:  
(14-09-2015 02:26 PM)cjlr Wrote:  Spin refers to angular motion about a single axis. That's how it's defined - it can't be anything else.

Except that it isn't. In 3D space angular motion occurs about a single axis. In 4D space angular motion occurs about two invariant axis planes.

ZoraPrime just told you why you're wrong, in more explicit language than I used. My plain English allowed ambiguity; the maths don't.

(18-09-2015 10:40 AM)Heywood Jahblome Wrote:  
Quote:Every rotation in 3D space has an invariant axis-line which is unchanged by the rotation. The rotation is completely specified by specifying the axis of rotation and the angle of rotation about that axis. Without loss of generality, this axis may be chosen as the z-axis of a Cartesian coordinate system, allowing a simpler visualizaton of the rotation...

Quote:....Analogous to the 3D case, every rotation in 4D space has at least two invariant axis-planes which are left invariant by the rotation and are completely orthogonal (i.e. they intersect at a point). The rotation is completely specified by specifying the axis planes and the angles of rotation about them. Without loss of generality, these axis planes may be chosen to be the uz and xy planes of a Cartesian coordinate system, allowing a simpler visualizaton of the rotation.

https://en.wikipedia.org/wiki/Rotations_...dean_space

You don't seem to understand the difference between a rotation - the single operation - and angular momentum of e.g. a collection of space dust.

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18-09-2015, 11:12 AM (This post was last modified: 18-09-2015 11:18 AM by Heywood Jahblome.)
RE: A Question for Cjlr
(18-09-2015 10:50 AM)cjlr Wrote:  ZoraPrime just told you why you're wrong, in more explicit language than I used. My plain English allowed ambiguity; the maths don't.

ZoraPrime's conclusion is disputed.

Quote:One notable feature, related to the number of simple bivectors and so rotation planes, is that in odd dimensions every rotation has a fixed axis – it is misleading to call it an axis of rotation as in higher dimensions rotations are taking place in multiple planes orthogonal to it. This is related to bivectors, as bivectors in odd dimensions decompose into the same number of bivectors as the even dimension below, so have the same number of planes, but one extra dimension. As each plane generates rotations in two dimensions in odd dimensions there must be one dimension, that is an axis, that is not being rotated.

https://en.wikipedia.org/wiki/Bivector

In 3D space there is one dimension that is not being rotated....hence clouds can collapse into discs. In 4D space all dimensions are being rotated and no disc would form. You and ZoraPrime are simply mistaken.
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18-09-2015, 11:39 AM
RE: A Question for Cjlr
(18-09-2015 11:12 AM)Heywood Jahblome Wrote:  You [cjlr] and ZoraPrime are simply mistaken.

Laugh out loadLaugh out loadLaugh out loadLaugh out loadLaugh out load

Given their credentials, it is much more likely that you are mistaken. What are your credentials, by the way?
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18-09-2015, 11:43 AM (This post was last modified: 18-09-2015 11:46 AM by cjlr.)
RE: A Question for Cjlr
(18-09-2015 11:12 AM)Heywood Jahblome Wrote:  
(18-09-2015 10:50 AM)cjlr Wrote:  ZoraPrime just told you why you're wrong, in more explicit language than I used. My plain English allowed ambiguity; the maths don't.

ZoraPrime's conclusion is disputed.

You don't even understand what he's saying.

(18-09-2015 11:12 AM)Heywood Jahblome Wrote:  
Quote:One notable feature, related to the number of simple bivectors and so rotation planes, is that in odd dimensions every rotation has a fixed axis – it is misleading to call it an axis of rotation as in higher dimensions rotations are taking place in multiple planes orthogonal to it. This is related to bivectors, as bivectors in odd dimensions decompose into the same number of bivectors as the even dimension below, so have the same number of planes, but one extra dimension. As each plane generates rotations in two dimensions in odd dimensions there must be one dimension, that is an axis, that is not being rotated.

https://en.wikipedia.org/wiki/Bivector

Yes, very cute, you can copypasta wiki.

(18-09-2015 11:12 AM)Heywood Jahblome Wrote:  In 3D space there is one dimension that is not being rotated....hence clouds can collapse into discs. In 4D space all dimensions are being rotated and no disc would form.

... But that's a statement you pulled from nowhere. "All dimensions are being rotated" in 3D space just as much as in 4D space. Or they aren't in either. Or anything. It's quite possible to construct situations in which the initial conditions are different, but then what's the point?

You wouldn't get a disk - if by 'disk' you mean 2D entity in 3D space - because no shit you wouldn't. This is literally and explicitly what ZoraPrime said to you, which is why I said you didn't understand him:
(17-09-2015 09:58 AM)ZoraPrime Wrote:  It's occurred to me that I think you're getting concerned over the word "disk." Yes, a 4D Euclidean "disk' (in the sense of how we're using it) spans over two planes. However, there's no word for "flat object that confines itself to particular plane(s)." We'd call them disks, even if they span two planes. It's like becoming concerned because someone uses the word "spherical symmetry" when discussing 4D Euclidean space and insisting "it's not a sphere, it's a hypersphere, so we should call it hypersherical symmetry." I'm calling it an accretion disk, even if it spans two planes, because I don't see why the fact it spans over two planes instead of one plane matters when it's orientation in space (i.e. the 4D angular momentum bivector) doesn't change.

...

(18-09-2015 11:12 AM)Heywood Jahblome Wrote:  You and ZoraPrime are simply mistaken.

Can you explain how?

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18-09-2015, 12:16 PM
RE: A Question for Cjlr
(18-09-2015 11:43 AM)cjlr Wrote:  You don't even understand what he's saying.

Why bother understanding, when it's more fun to just make stuff up? He does not want to understand. He wants to make believe.

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18-09-2015, 12:23 PM (This post was last modified: 18-09-2015 12:28 PM by ZoraPrime.)
RE: A Question for Cjlr
(18-09-2015 10:40 AM)Heywood Jahblome Wrote:  In 3D space angular motion occurs about a single axis. In 4D space angular motion occurs about two invariant axis planes.

Which, no one is disputing. Invariant angular momentum in 3D Euclidean space can be specified with one coordinate along the z-axis; angular momentum in 4D Euclidean space needs to be defined by two coordinates corresponding to orthogonal planes that intersect at a point.

And please stop dropping the word Euclidean. If your OP is any indication of where you want to take, the fact that there's still only three Euclidean dimensions (the usual three dimensional space we all know and maybe love) in any hypothetical model of physics means that anything discussed in this thread is irrelevant to the real-world.


Quote:The only place I have read anything to indicate that in 4D space a dust cloud would collapse into disc is here. Sorry if I am little skeptical....for all I know your just some internet crackpot.

And this is where your posts go to shit.

Because I honestly think you're getting confused over the word "disc," I will call the 4D Euclidean equivalent that's confined to two planes (instead of one plane/about one axis) a hyperdisk to avoid ambiguity.

The reason why a dust could collapses into a 3D Euclidean disc is because angular momentum is conserved. Similarly, the dust in 4D Euclidean space will still collapse into a hyperdisk because angular momentum is still conserved.

The conservation of angular momentum, like the other two conservation laws (energy and linear momentum), can be derived through Noether's Theorem. In short, if a system's Lagrangian (or more precisely, action) is invariant about a rotation, then angular momentum is conserved. I will take time explaining this, since I think you're not clear what needs to be invariant under rotations.

For angular momentum to be conserved, the system's Lagrangian that needs to be invariant under rotations. The Lagrangian is defined to be Kinetic Energy minus Potential Energy. To say that the Lagrangian is invariant under rotations mean that the kinetic energy term and potential energy time do not change under rotations. This isn't a difficult procedure to do, since for a gravitational potential, both kinetic energy and potential energy are determined by vector norms. I.e., kinetic energy is one-half times the mass times the vector norm squared of velocity; potential energy is (the sum of) constant times some masses over the norm of distance. Rotations, by construction, are designed to keep norms unchanged. So the Lagrangian is unchanged by rotations.

This may sound confusing, because doesn't the angular momentum conservation "bias" a system along a particular direction? Yes, it biases the system along a particular direction but not the Lagrangian. The reason is because the angular momentum the system has for all times is determined by the initial conditions. Two systems can have the same exact Lagrangian but two completely different initial conditions.

Therefore, a system in 4D Euclidean still will collapse into a hyperdisc by angular momentum conservation.

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And you've delayed answering this question: what the fuck is the point of this thread anyway?
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