Time to end all misconceptions for ever!

[Qfwfq]

Goodness! Surely you didn't take that seriously now!

 

Experience shows space as being 3-dimensional, apparently homogenous and isotropical and time as being homogenous. Lorentz covariance and the minkowskian geometry of space-time are confermed experimentally. We can't exactly choose these things arbitrarily. Proper time is proper time, the square of it for the interval between a pair of space-time points is given by the metric and is a scalar. It doesn't slow down. The same interval just has different coordinates for different reference frames.

 

A mathematical concept requires no experimental verification, it isn't required to represent anything real, it may or may not describe something physical.

 

What do you mean by being, or not being, a physical entity?

[WebFeet]

Goodness! Surely you didn't take that seriously now!

No I didn't.

 

The post would have been better if I had said we have rather than you.

 

What do you mean by being, or not being, a physical entity?

I was referring to the relationship between Space and Time and that although it has been clearly shown that there is a relationship, does this constitute a real fabric?

 

A mathematical concept requires no experimental verification, it isn't required to represent anything real, it may or may not describe something physical.

 

Here's an alternate mathematical concept that may interest you.

 

A right angled triangle.

The vertical side is Energy, the horizontal is mass and the hypotenuse is the relationship.

The angle opposite mass is permeability and the one opposite energy is permittivity (the out angle is density)

 

The angle between Energy and the vertical is velocity, so you can put the thing in motion and see what happens.

 

Have a play with it.

 

How many of the fundemental laws of physics can you find?

[maddog]

No, it hasn't, don't worry WebFeet, we can still arbitrarily choose it to be whatever manifold we like, without any need for experimental corroboration.

 

I know most people choose 1 + 3 dimensions with real coordinates and Minkowski's metric but you can choose for there to be 3 time and 7 space coordinates, for example, perhaps with some of these being real, some complex and one or two quaternionic. With an imaginative metric, it might even be a lot more fun. not to mention global topology. How about 3 or 4 of the spatial dimensions being closed Möbius style?

Qfwfq,

 

I have a question on this since you say we can arbitrarily choose how to compose our manifold whatever

way we desire. How about not being just 1 + 3 dimensions but being but having a composition of two

separate manifolds where a special transformation between them.

 

One manifold is in 1 + 3 dimensions ( 1 scalar, 3 vector or 4 Vector) with all real components and

One manifold is in 1 + 7 dimensions (1 scalar, 7 vector or 8 Tensor) with at least all complex components,

though maybe quaternionic or of a field from the Essential group E8.

 

Were a construction of these two manifolds conjoined, one manifold would be seen as rolled up to the

other or complex to the other so to not be visible. Since this would be symmetrical, one could

construct a metric on either manifold that would appear "real" distances within its own manifold yet

not when attempting measure from one manifold to ther other. I also created in essence two

independent time coordinates (which could be viewed as time is complex for all frames - modulus |t|).

 

With such a construct would I be able to use such a construct as this view the four forces as a unified

force viewed geometrically like in gravity. Kaluza Klien model made an attempt with EM and Gravity

using 5 real dimensions (1 being rolled up -- yet real). Gravity would be the one force that effects

both manifolds directly yet the other forces would require some intermediary field not so far found

to go between. I know this might sound strange. This does have some symmetry qualities and has

some mathematical basis. Then could this geometry have both a string theory (or M-theory) and

LQG theory laid onto it. Just curious. ;-)

 

Maddog

[Qfwfq]

A right angled triangle.

The vertical side is Energy, the horizontal is mass and the hypotenuse is the relationship.

The angle opposite mass is permeability and the one opposite energy is permittivity (the out angle is density)

Reminescent of, but not quite matching up with, Lorentz-covariant dynamics in which:

 

m^2 = E^2 - p^2.

 

Have a play with it.

The angle between Energy and the vertical is velocity, so you can put the thing in motion and see what happens.

The angle between Energy and the vertical is zero, since you said the vertical side is Energy. ;)

[Qfwfq]

Is there a Möbius type topology in the Kaluza Klien model too? Just curious. ;-)

[WebFeet]

The angle between Energy and the vertical is zero, since you said the vertical side is Energy. ;)

 

While it's a right angled triangle, it can be viewed as at rest.

 

If you move the energy side away from the vertical, it can be viewed as in a different reference frame. The difference being the velocity - the angle between energy and the vertical.

[Qfwfq]

Vertical and horizontal. Sure you don't mean time axis and space submanifold?

 

Is your triangle meant to represent the equation m^2 = E^2 - p^2 or what? Your description isn't very clear.

[WebFeet]

Vertical and horizontal. Sure you don't mean time axis and space submanifold?

No, it's not a graph. Time and space are not the axis.

The vertical and horizontal are references. The value of the velocity angle indicates the difference in reference frames.

As for the horizontal, I have yet to determine quite what moving mass off the horizontal actually means.

 

Is your triangle meant to represent the equation m^2 = E^2 - p^2 or what? Your description isn't very clear.

No it isn't. If anything the triangle represents the equation E=MC^2.

 

The triangle is a set of relationships, primarily that between Energy and Mass.

The internal angles represent Space and its properties.

 

Eample

Take a right angled triangle, any values you like. Now decrease the mass, as if in a stronger gravitational field. The new values of the angles now represent the new region of space.

[maddog]

Is there a Möbius type topology in the Kaluza Klien model too? Just curious. ;-)

Qfwfq,

 

Not sure if this was directed at me. To answer, I never thought of putting a flip on

the inside dimension. Since in Kaluza Klien model the internal extra dimension was

to represent the EM field potential, by expessing this a complex field (i.e. using

complex numbers), I would think you could create an inside flip somehow. I think

to do a proper job though would require 2 extra dimensions where the internal

formed a 2-brane. There you could create Möbius like surface. Kewl !! ;)

 

Maddog

[Qfwfq]

Not sure if this was directed at me.

Of course it was. I was pulling your leg!!! You appeared to have taken me seriously when I was pulling WebFeet's leg!

 

If the closed dimension is locally perpendicular to any spacelike or timelike direction, wouldn't that Möbius flip have rather odd implications about locality, to say the very least?

[Qfwfq]

No it isn't. If anything the triangle represents the equation E=MC^2.

Equation which I write as E = m and which, apart from non-physical signs, is just the other equation in the zero momentum case i. e. in the rest frame.

 

Eample

Take a right angled triangle, any values you like. Now decrease the mass, as if in a stronger gravitational field. The new values of the angles now represent the new region of space.

Transcendental meditation? The things you say often don't match up, but angles representing regions of space is even more of an oddity. I've heard of projective geometry but, although I've never really studied it, I'm not quite sure even it could give a sense to what you say now. What's the geometry that you are reasoning in called?

[WebFeet]

Transcendental meditation? The things you say often don't match up, but angles representing regions of space is even more of an oddity. I've heard of projective geometry but, although I've never really studied it, I'm not quite sure even it could give a sense to what you say now. What's the geometry that you are reasoning in called?

Use the triangle and refer back to PV, you will see that permittivity and permeability are consistant.

[Qfwfq]

How do the angles represent regions of space?

[WebFeet]

How do the angles represent regions of space?

As I said, the triangle represents relationships.

The angles don't necessarily have to represent space, they simply represent the relationship between energy and mass.

 

With the space example, remember using PV not GR, the amount of energy in a mass is determined by the refractive index (permittivity) of where the mass is. If the mass is moved to a different position in space, the energy will remain constant, but the amount of mass will be determined by the refractive index in the new position.

If you use the triangle to represent these, the different refractive indicies are represented by the sine value of the permittivity angle (and because it's a right angled triangle, the permeability will show the inverse change).

[Qfwfq]

I see. It was difficult to interpret the way you worded things. I haven't looked up PV since these discussions, what you say now gives me the impression it isn't what I previously made it out to be from these discussions.

 

Has this been checked out for the whole of the standard model, or only for electrodynamics?

[WebFeet]

I see. It was difficult to interpret the way you worded things.

Phew...

I haven't looked up PV since these discussions, what you say now gives me the impression it isn't what I previously made it out to be from these discussions.

I'd be interested to know what your new impression is.

 

Has this been checked out for the whole of the standard model, or only for electrodynamics?

As I said, the angles simply represent the relationship between energy and mass.

If the mass were to represent a gas and premittivity, the pressure, you will find that it is consistant with Boyle's law. If you take premittivity to represent the frequency of an object, then the effect of increasing the energy on the frequency is experimentally verifiable.

 

It would appear to be a standard set of common relationships.

 

It's been looked at by a few academics. The general opinion is that it's either a fundemental tool OR it's an interesting toy.

[maddog]

Of course it was. I was pulling your leg!!! You appeared to have taken me seriously when I was pulling WebFeet's leg!

 

If the closed dimension is locally perpendicular to any spacelike or timelike direction, wouldn't that Möbius flip have rather odd implications about locality, to say the very least?

Not that I mind a little leg lengthening. ;-) I was actually hedging. Cause what you were asking was

suspicious. However, assuming it was a valid question, I thought of a way to answer it. Since then I've

been contemplating some multiple dimensional surfaces of dim n embedded in a space of n+1 dimensions

and thinking how to create a Möbius hyperspere of some higher than 3 dimensions. Hmmm. I remember

that Twistor Theory uses complex dimensions for spatial coordinates yet only uses the modulus |z| in any

distance metric.

 

As for the odd flip, I have been thinking about that already for a long time. You should be aware that

the phase angle for an electron complete a full circle at 4*PI and NOT 2*PI. This means an electron

turns around twice to turn around once. What is it doing the other half of the circle ? Could that be the

flipped side ??? Hmmm ?

 

BTW, I have done some projective geometry to me WebFeet isn't making much sense. So I am glad you

have found a way to comprehend what he is attempting to say. Maybe you could explain it to me...

 

Sorry, I haven't been back to read these earlier. I been dealing with a few urgent issues at work the

last couple days.

 

Also, for expectation values in QM, I understand that one can use either eigenvector on either side of

the expectation value to write out the Schroedinger wave equation. So say you pick the right side,

what phenomenilogically happens to the other eigenvector ? How quaint that the since the operator H

is Hemitian and want to find <x>

 

<x> = <x* H x> where x* = complex conjugate of x.

 

What if <x* and x> are related yet not within the same space. Can the operator be a Tensor and still

be Hermitian ? If so, would be able to compute a quantum gravitational field by directly combining the

Schroedinger equation and the G field Riemmanian Metric Tensor as an Operator (possibly made

Hermitian if possible). I get a lot my thinking in the thinking room. ;)

 

Maddog