Universal UP or DOWN (split from Fields and ether)

[steveupson]

The experiments that proved there to be no luminiferous aether did NOT prove that there is no "universal up" or "universal down."   Universally, up is always away from a gravitational well and down is always toward it.  This isn't the same thing as there being an "absolute up" or an "absolute down."

Or is it the same thing?

Can anyone explain why these two things would be different?  Use your math and explain.  I can explain how they are the same.  Using my math.

[swansont]

No preferred direction is an argument in symmetry, which is coupled to conservation laws. Symmetry under translation (linear and angular) means conservation of momentum (linear and angular)

Not really tied in with an aether.

 

[studiot]

1 hour ago, steveupson said:

The experiments that proved there to be no luminiferous aether did NOT prove that there is no "universal up" or "universal down."   Universally, up is always away from a gravitational well and down is always toward it.  This isn't the same thing as there being an "absolute up" or an "absolute down."

Or is it the same thing?

Can anyone explain why these two things would be different?  Use your math and explain.  I can explain how they are the same.  Using my math.

Even on the surface of this Earth, this is not true.

Any geodesist will tell you about the varaition of inclination of a pendulum bob with latitude.

Further complications come with lanearby large mountains.

That is how Everest was discovered by western surveyors.

Edited January 2, 2019 by studiot

[Strange]

1 hour ago, steveupson said:

The experiments that proved there to be no luminiferous aether did NOT prove that there is no "universal up" or "universal down."   Universally, up is always away from a gravitational well and down is always toward it.  This isn't the same thing as there being an "absolute up" or an "absolute down."

Or is it the same thing?

As you haven't defined your terms, I can't be sure. But I assume by "absolute up" you mean a direction that anyone, anywhere in the universe would consider to be up. 

This is very obviously not the same as what you call "universal up", which appears to be the concept generally known as "up". This is obviously different at every point on Earth (because the surface normal is different at every point). For example, the surface normal (i.e. "up") at the equator is at right angle to the one at the poles.

Let me know if I have misunderstood the terms you are using.

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I can explain how they are the same.  Using my math.

That will be interesting.

[steveupson]

4 hours ago, Strange said:

As you haven't defined your terms, I can't be sure. But I assume by "absolute up" you mean a direction that anyone, anywhere in the universe would consider to be up. 

This is very obviously not the same as what you call "universal up", which appears to be the concept generally known as "up". This is obviously different at every point on Earth (because the surface normal is different at every point). For example, the surface normal (i.e. "up") at the equator is at right angle to the one at the poles.

Let me know if I have misunderstood the terms you are using.

That will be interesting.

I think that you're correct with the definitions.  The fact that you made reference to surface normals simplifies things tremendously.   The surface normal represents a direction in space, which can be up, down, or off-to-the-side.  We could also specify this particular direction by specifying the plane that the surface normal is normal to.  The plane and the normal both specify the exact same direction in space.  This is important to understanding how the geometry works, mathematically.

We can have three directions in space, call them alpha, lambda, and upsilon, where no two of these directions are the same.  We can specify these three directions by either defining the plane or the vector that is normal to it.  Specifying the plane allows certain calculations to be performed that will produce a mathematical relationship between the three unique planes.  Note that since they are each unique, they must have a single intersection in space.

That's the beginning of how to do the math.  One more thing that should be understood from the start is that this particular geometric relationship between these three unique directions has never even been hinted at before, except perhaps by Hermann Grassmann in these translated quotes:

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“From this all imaginary expressions now acquire a purely geometric meaning, and can be described by geometric constructions.... it is likewise now evident how, according to the meaning of the imaginaries thus discovered, one can derive the laws of analysis in the plane; however it is not possible to derive the laws for space as well by means of imaginaries. In addition there are general difficulties in considering the angle in space, for the solution of which I have not yet had sufficient leisure.” ...

...As Grassmann admitted in the preface to his Ausdehnungslehre of 1862 [6]. “I am aware that the form which I have given the science is imperfect.” And he went on to say “there will come a time when these ideas, perhaps in a new form, will arise anew and will enter into a living communication with contemporary developments.”

GRASSMANN’S VISION - David Hestenes

What he is referring to is what we believe to be the specific mathematical relationship that we're now using for timespace based on what we're calling synchronous geometry.  We have derived a "tridentity" that expresses a direction in space, and it does it by a fundamentally different means than how it is normally accomplished using today's methods (today's methods being to define vectors in a plane or surface.)   Modern methods seem to be completely unaware that there is a difference between how these angles interact in space and how they interact in a plane.  

There is a .pdf file that explains the derivation of the basic formula:

tridentity review copy.pdf

The .pdf file does need peer review if anyone is interested in making contributions.  I'll try to answer any and all questions, although there may be some delay in my ability to respond to specific members.  I'll try to keep up with what's going on in this thread. 

 

Edited January 2, 2019 by steveupson

[studiot]

5 hours ago, Strange said:

sThis is very obviously not the same as what you call "universal up", which appears to be the concept generally known as "up". This is obviously different at every point on Earth (because the surface normal is different at every point). For example, the surface normal (i.e. "up") at the equator is at right angle to the one at the poles.

Moreover, as I have already noted, Gravity is only parallel to these normals at the poles and equator.

Edited January 2, 2019 by studiot

[beecee]

Isn't it true to put it simply, that "down" is denoted by the pull of gravity? Therefor up is opposite. Although I'm not sure how this holds up with Lagrange points.

[Strange]

47 minutes ago, steveupson said:

The surface normal represents a direction in space, which can be up, down, or off-to-the-side. 

Although, in the case of a sphere I hope you agree that they are always up.

48 minutes ago, steveupson said:

We can have three directions in space, call them alpha, lambda, and upsilon, where no two of these directions are the same. 

Are these independent? 

49 minutes ago, steveupson said:

Note that since they are each unique, they must have a single intersection in space.

In Euclidean space, yes.

 

You haven't explained how this new coordinate system defines an "absolute up".

 

9 minutes ago, studiot said:

Moreover, as I have already noted, Gravity is only parallel to these normals at the poles and equator.

While true, I'm not sure that level of practical detail is relevant to the more general principle. It is probably more useful to consider what "up" means on the surface of a perfect sphere of uniform density.

[studiot]

7 minutes ago, beecee said:

Isn't it true to put it simply, that "down" is denoted by the pull of gravity? Therefor up is opposite. Although I'm not sure how this holds up with Lagrange points.

Lagrange points are a big issue for Steve's direction theory, as is anywhere where the vector sum is zero.

The point I was making is that the surface normal and the direction of gravity are not generally parallel.

There are two reasons for this, one is that the Earth is not a perfect sphere.

The other is the rotation of the Earth, so that even if the Earth were a perfect sphere, the normal and gravity would still not be parallel. The difference varies with latitude.

[Strange]

Just now, studiot said:

The point I was making is that the surface normal and the direction of gravity are not generally parallel.

So, if you want to take these practical effects into account, then I guess you need to use a different (more realistic) definition of "up".

I don't know, but would it be correct to assume that would be a vector from the centre of mass through the surface? Or would it be (equivalently?) the surface normal of the geoid? 

As it is not clear why Steve started with the definition of "up" or how it relates to his three planes, I don't know if this extra level of realism/accuracy helps or not.

1 hour ago, steveupson said:

What he is referring to is what we believe to be the specific mathematical relationship that we're now using for timespace based on what we're calling synchronous geometry.  We have derived a "tridentity" that expresses a direction in space, and it does it by a fundamentally different means than how it is normally accomplished using today's methods (today's methods being to define vectors in a plane or surface.)   Modern methods seem to be completely unaware that there is a difference between how these angles interact in space and how they interact in a plane.  

As far as I can tell, you are defining direction in terms of (ie. relative to) three (arbitrary?) planes. 

What practical consequences come from this approach? what problems does it help solve?

1 hour ago, steveupson said:

There is a .pdf file that explains the derivation of the basic formula:

 

I would be grateful if you would remove my name from this. Thank you.

[studiot]

3 minutes ago, Strange said:

I don't know, but would it be correct to assume that would be a vector from the centre of mass through the surface? Or would it be (equivalently?) the surface normal of the geoid? 

Neither.

It's too late to draw diagrams tonight, but if you stood in Cambridge like Cavendish, and measured gravity you would have to include for a force normal to the axis of rotation, not directed towards the centre of mass. This is why it varies with latitude.
Your measured UP would be the vector sum of this force and the force directed normal to the geoid as you say.

[Strange]

2 minutes ago, studiot said:

It's too late to draw diagrams tonight, but if you stood in Cambridge like Cavendish, and measured gravity you would have to include for a force normal to the axis of rotation, not directed towards the centre of mass.

Ah, I forgot about the rotation. Would I be right without that? 

3 minutes ago, studiot said:

Your measured UP would be the vector sum of this force and the force directed normal to the geoid as you say.

That sounds like a yes. I'll wait for tomorrow!

[studiot]

6 minutes ago, Strange said:

nAh, I forgot about the rotation. Would I be right without that? 

That sounds like a yes. I'll wait for tomorrow!

On the Earth, yes.

But don't forget Beecee's  very valid note about Lagrange points.

This has got me thinking about manifold warping, saddle and other points to see if I could construct a warping that had neighbouring points with normal going in opposite directions.

It wouldn't surprise me in the least that Nature is perverse enough for this.

Edited January 2, 2019 by studiot

[steveupson]

36 minutes ago, Strange said:

Although, in the case of a sphere I hope you agree that they are always up.

Yes, and also down.

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Are these independent? 

Although they are independent from one another, they are all in the same geometric frame.  

Quote

In Euclidean space, yes.

Actually, I think that this is always generally true in projective space.   In Euclidean space we can have unique planes that don't intersect if they are parallel, but if that were the case then they would share the same surface normal, wouldn't they?  Or would we say that the origin of the normal vector must also be specified?  Either way is fine, but we need the specificity.

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You haven't explained how this new coordinate system defines an "absolute up".

 The math doesn't define an "absolute up" or a "universal up."  The math only shows that they must both exist, and that they are one and the same thing.   We can set the math to the side for a moment and try to understand how directions are organized in nature.  There, everything is organized into a coherent mess by time.  So, we really have two different ways to look at space as a general proposition.  We have the mathematical description (which is an abstraction comprising symbols) and then we have the actual stuff that the universe contains.   If we make the assumption that everything is in motion, then each thing has its unique direction in which it moves (with the exception of entangled pairs.)  Since we understand time and space to be intertwined, and that we can call positions in spacetime events, and since time "moves" or "changes" in a specific way, then we can make the supposition that everything moves or changes in a specific direction (toward the future), even if the actual position in space does not change or move.  Everything has a future that lies is a particular direction.  All these directions are related to one another by the math.

Quote

While true, I'm not sure that level of practical detail is relevant to the more general principle. It is probably more useful to consider what "up" means on the surface of a perfect sphere of uniform density.

Yes, of course.

25 minutes ago, Strange said:

I would be grateful if you would remove my name from this. Thank you.

Your username?

Edited January 2, 2019 by steveupson

[Strange]

5 minutes ago, steveupson said:

The math doesn't define an "absolute up" or a "universal up."  The math only shows that they must both exist, and that they are one and the same thing.

How does it show they must both exist?

And how can they be the same thing? Using my definitions of "universal" and "absolute" that you appear to agree with, it is logically impossible for them to be the same thing. 

 

[steveupson]

2 minutes ago, Strange said:

How does it show they must both exist?

And how can they be the same thing? Using my definitions of "universal" and "absolute" that you appear to agree with, it is logically impossible for them to be the same thing. 

Well, until you do the math these questions will remain unanswered for you.  The math is the answer to these questions.  Do the math.  I'll try to walk you through it.

Can you define alpha, lambda, and upsilon yet?

Edited January 3, 2019 by steveupson

[Strange]

18 minutes ago, steveupson said:

Well, until you do the math these questions will remain unanswered for you.  The math is the answer to these questions. 

I don't see how math can resolve something that is a logical contradiction. 

But go ahead and show us.

18 minutes ago, steveupson said:

Can you define alpha, lambda, and upsilon yet?

I thought you were defining them.

[steveupson]

6 minutes ago, Strange said:

I don't see how mass can resolve something that is a logical contradiction. 

But go ahead and show us.

I thought you were defining them.

Yes, it starts with alpha, lambda, and upsilon.   Do you know what they are, or how I've defined them?

Edited January 3, 2019 by steveupson

[Strange]

8 minutes ago, steveupson said:

Yes, it starts with alpha, lambda, and upsilon.   Do you know what they are, or how I've defined them?

I was just assuming they were three arbitrarily (and differently) oriented planes. If there is more to it than that, you will need to explain.

[steveupson]

They are always related to one another. 

Draw a circle of any size on the surface of the earth, such that the circle passed through the north pole.   Start walking around the circle.  Then tell me the latitude of the center of the circle, and the latitude where your feet are, and I will tell you what direction you are facing.

The three directions, as defined in the paper, are:

upsilon is the latitude of the circle center

lambda is the latitude that your feet are at

alpha is the direction you are facing

 

There is a caveat that seems to be related to the question of entanglement in physics.  I can't specifically say whether you're moving east to west, or north or south.  This is the same mathematical issue that makes octonians so interesting to physicists.

[Strange]

8 hours ago, steveupson said:

The three directions, as defined in the paper, are:

upsilon is the latitude of the circle center

lambda is the latitude that your feet are at

alpha is the direction you are facing

Thats a good practical example. Although slightly ambiguous. I think you said that alpha, lamb and upsilon are planes. So by defining two of them as "the latitude" do you mean that the upsilon and lambda planes are parallel to one another. But that seems to contradict your requirement that the three directions are different.

To clarify, there are an infinite number of planes that could go through the circle centre. So when you say "the latitude" I interpret to mean a slice though the Earth at that latitude. But that would make the two slices (lambda and upsilon) parallel slices.

It is not clear how this relates to either definition of "up". I guess (trying to visualise this) that up would be defined by the intersection of lambda and alpha? But I don't see how it defines an "absolute" up.

It is also not obvious how this system is useful.

Quote

There is a caveat that seems to be related to the question of entanglement in physics.  I can't specifically say whether you're moving east to west, or north or south. 

I don't understand why you can't tell which direction the person is moving. And if you can't tell, doesn't that cast even more doubt on the usefulness of the system?

(Not knowing a value is nothing to do with entanglement.)

[swansont]

12 hours ago, steveupson said:

They are always related to one another. 

Draw a circle of any size on the surface of the earth, such that the circle passed through the north pole.   Start walking around the circle.  Then tell me the latitude of the center of the circle, and the latitude where your feet are, and I will tell you what direction you are facing.

Latitude of the circle center is 0º (a great circle)

Latitude of my feet is 90º

Which way am I facing? (i.e. what is the value of alpha)

 

Latitude of the circle center is 0º (a great circle)

Latitude of my feet is 0º

Which way am I facing? (i.e. what is the value of alpha)

 

(I think this works, or rather doesn't work, for any value of latitude of my feet)

 

 

[studiot]

3 minutes ago, swansont said:

Latitude of the circle center is 0º (a great circle)

Latitude of my feet is 90º

Which way am I facing? (i.e. what is the value of alpha)

 

Latitude of the circle center is 0º (a great circle)

Latitude of my feet is 0º

Which way am I facing? (i.e. what is the value of alpha)

 

 

Isn't this fun?

 

13 hours ago, Strange said:

That sounds like a yes. I'll wait for tomorrow!

I think detailed presentation of the vectors that make up the attraction felt at the Earth's surface are off topic here.

I will happily start a new thread to present them if you like.

[Strange]

5 minutes ago, studiot said:

I think detailed presentation of the vectors that make up the attraction felt at the Earth's surface are off topic here.

I will happily start a new thread to present them if you like.

Don' worry. I reminded myself of the definition of geoid, so I am happy with that now.

[steveupson]

3 hours ago, Strange said:

Thats a good practical example. Although slightly ambiguous. I think you said that alpha, lamb and upsilon are planes. So by defining two of them as "the latitude" do you mean that the upsilon and lambda planes are parallel to one another. But that seems to contradict your requirement that the three directions are different.

To clarify, there are an infinite number of planes that could go through the circle centre. So when you say "the latitude" I interpret to mean a slice though the Earth at that latitude. But that would make the two slices (lambda and upsilon) parallel slices.

The three planes intersect at the earth center.   Each pair of planes define a "dihedral angle"  that forms a "lune" or a shape that is like the segment of an orange, with each plane being a side of the segment.   Using lunes as descriptors is the simplest way to explain how each angle is formed.   Starting with the upsilon angle, we can describe it in several different ways.  We can say that the lune that represents this angle contains two line segments, one that extends from the center of the earth to the north pole the other that extends from the earth center and passes through the center of the circle.   Using this definition, we can also say that the upsilon angle is represented by the cone having the line segment between the earth center and circle center as its axis, and the circle as its base.  The upsilon angle will be half the aperture, or the angle between the axis and a generatrix.  Note that this is the same angle as what occurs when we slice horizontally through the earth to create a line of latitude at the circle center, and then form a similar cone having the segment from the earth center to the north pole as the axis, and the segment from the earth center to the circle center as a generatrix.

The dihedral angle lambda is formed by the lune containing line segments from the north pole to the earth center, and from your feet to the earth center.  

Alpha is the dihedral angle formed between a meridian passing through your feet and the plane tangent to the cone (described above as having the circle center as its axis) at the point where your feet are.

So, if you give me the information in the previous post, it is possible to construct this object and solve for the angle alpha.  That's the equation that's given in post #5.

Quote

It is not clear how this relates to either definition of "up". I guess (trying to visualise this) that up would be defined by the intersection of lambda and alpha? But I don't see how it defines an "absolute" up.

It is also not obvious how this system is useful.

I don't understand why you can't tell which direction the person is moving. And if you can't tell, doesn't that cast even more doubt on the usefulness of the system?

(Not knowing a value is nothing to do with entanglement.)

I don't know of anything that I can say that will make understanding these things any simpler to understand.  It can only be explained using math, as far as I know.  I can tell you that these things are true, but the only way to explain why they are true is by using the math.  

36 minutes ago, swansont said:

Latitude of the circle center is 0º (a great circle)

Latitude of my feet is 90º

Which way am I facing? (i.e. what is the value of alpha)

 

Latitude of the circle center is 0º (a great circle)

Latitude of my feet is 0º

Which way am I facing? (i.e. what is the value of alpha)

 

(I think this works, or rather doesn't work, for any value of latitude of my feet)

 

 

The directions cannot be the same as one another.  You must specify three directions that are unique to one another.

edited to add>>>>>>

Orthogonal directions have another very special relationship with each other which can be expressed as an additional tridentity.

 

29 minutes ago, studiot said:

Isn't this fun?

 The prize of prizes, the pleasure of finding things out, to paraphrase Feynman.

Edited January 3, 2019 by steveupson