Quantifying the Physical Property of Direction.

[Strange]

Thank you Strange. You have no idea how envious I am.

 

 

You could have done it yourself in a few minutes. But, as usual, you expect everything to be done for you.

Maybe you need to offer a prize as an incentive (as there is no reason for anyone to reverse-engineer this animation for you).

 

$1,000 for the first person to come up with the equation?

Edited May 22, 2016 by Strange

[steveupson]

 

 

You could have done it yourself in a few minutes.

 

I still need two more at 30 and 60 degrees.

 

That might illuminate some things.

 

I would think |pi/2| might be a sine curve.

Edited May 23, 2016 by steveupson

[steveupson]

 

We ask this question a lot. You are one of very few who want to deal with the math.

 

 

You are suggesting that it should be, which is not part of mainstream science. Direction is not a property of the particle, per se, since that will change with a choice of coordinate system.

 

Direction is a property of the points adjacent to the particle.

 

(which is another way of saying "coordinate system")

Edited May 24, 2016 by steveupson

[Mordred]

I believe the definition of property has already been given this thread.

 

 

physical property - any property used to characterize matter and energy and their interactions

property - a basic or essential attribute shared by all members of a class; "a study of the physical properties of atomic particles"

 

Direction doesn't qualify as a property.

 

A coordinate system isn't physical, it's a tool used to describe the physical. ( you can arbitrarily use any coordinate system to describe any interaction, field etc )

Edited May 24, 2016 by Mordred

[steveupson]

I believe the definition of property has already been given this thread.

 

 

physical property - any property used to characterize matter and energy and their interactions

property - a basic or essential attribute shared by all members of a class; "a study of the physical properties of atomic particles"

 

Direction doesn't qualify as a property.

 

A coordinate system isn't physical, it's a tool used to describe the physical. ( you can arbitrarily use any coordinate system to describe any interaction, field etc )

 

 

I don't understand what you mean. The classic double-slit experiment is used to explain the wave-particle relationship by looking at the direction of travel of photons. Surely, you're not saying that this direction of travel isn't real? I don't know what you mean.

 

And I agree with you about the coordinate system. It all has to do with how we go about mapping physical things into that system.

 

Anyhow, whether it's a property or not, direction changes when performing relativistic transformations using the standard method.

Edited May 24, 2016 by steveupson

[Mordred]

There is a difference between polarization and direction. Just because one can predict which direction an object will go doesn't mean that direction is a property.

 

Lets put it another way, just because an object or particle moves a certain direction in relation to an influence doesn't mean the direction itself is a property.

 

A good example being a pool ball. We can easily predict which angle and direction the ball will travel upon being hit or hitting another object.

 

However the direction travel of the ball requires other influences.

 

An intrinsic property doesn't require other influence. Ie intrinsic angular momentum,charge, rest mass etc. ( though mass is debatable as its due to field interaction) it's accepted as a property as all electrons have the same rest mass. In any particle species all members have the same intrinsic properties.

 

In simplistic terms a property is something we can use to classify and identify with all members of a species.

 

Lets look at those pool balls again.

 

List the properties that every pool ball shares in common.

Edited May 24, 2016 by Mordred

[Strange]

 

I don't understand what you mean. The classic double-slit experiment is used to explain the wave-particle relationship by looking at the direction of travel of photons. Surely, you're not saying that this direction of travel isn't real?

 

 

Surely the whole point of this experiment is that you don't know the direction of travel (or, at least, of you do then you don't get interference).

[swansont]

 

Direction is a property of the points adjacent to the particle.

 

(which is another way of saying "coordinate system")

 

 

Yes, direction is a property of the coordinate system. Which you are free to choose.

[steveupson]

There is a difference between polarization and direction.

 

The difference between direction and polarity (orientation) seems to be symmetrical with the difference between length and line (distance).

 

We don't treat these properties as having any symmetry in the normal system.

List the properties that every pool ball shares in common.

 

All of them, except position (direction x distance).

 

Surely the whole point of this experiment is that you don't know the direction of travel (or, at least, of you do then you don't get interference).

 

 

Correct, that's what I'm saying. Not knowing some parameter. Therefore, since it can be parameterized, it's a property.

 

 

Yes, direction is a property of the coordinate system. Which you are free to choose.

Since the coordinate system is a mapping of reality, then we can capture different information if we use a coordinate system that shares the same curvature as spacetime. This can be accomplished by expressing direction as an invariant quantity.

Edited May 24, 2016 by steveupson

[Strange]

Correct, that's what I'm saying. Not knowing some parameter. Therefore, since it can be parameterized, it's a property.

 

It is not a property of the object (whether photon or pool [billiard] ball) though. It is observer-dependent. In other words, it can be changed arbitrarily by choosing different coordinates.

[swansont]

 

Since the coordinate system is a mapping of reality, then we can capture different information if we use a coordinate system that shares the same profile as curved spacetime.

 

 

I'm not sure what that means.

 

If you can transform from one coordinate system to another, there is no information in one that is absent in the other.

[ajb]

If you can transform from one coordinate system to another, there is no information in one that is absent in the other.

 

This really is a core principle of physics. It is known as the 'gauge principle', which says that nothing meaningful should depend on your choice of coordinates.

[steveupson]

 

It is not a property of the object (whether photon or pool [billiard] ball) though. It is observer-dependent. In other words, it can be changed arbitrarily by choosing different coordinates.

 

Yes, but this is also true for any line or length that we use in order to find its position. We describe distance in units. We can give these units the attribute of being scalar quantities, depending on how we want to apply them.

 

This assignment (where distance units are the scalar quantity and direction is the vector quantity) is totally arbitrary. I know that doesn't sound right, but it is. The conventional method doesn't allow for this possibility because there's no way to assign the attribute of being a scalar quantity to direction, we can only do that with distance.

 

Direction is expressed as the orientation between two objects. This orientation can only be expressed in non-dimensional units using the conventional method. Because of this (mathematical) fact, it is not possible (mathematically) to assign a scalar attribute to direction.

 

If, however, direction were expressed in a manner where actual, dimensional, units are used, such as |pi/x|, then we will be able to assign a scalar attribute to those units.

 

 

I'm not sure what that means.

 

If you can transform from one coordinate system to another, there is no information in one that is absent in the other.

 

This isn't really like that. It is a coordinate system where additional geometric equalities are used.

 

So far, I only know how to use the system in order to define direction as an invariant quantity under that geometry.

 

Although I am sure that the new geometry is completely compatible with conventional geometry, I also know that once a scalar or vector attribute has been assigned to something (either direction or distance, but not both) in a particular application that it isn't trivial to undo that assignment.

[Strange]

This assignment (where distance units are the scalar quantity and direction is the vector quantity) is totally arbitrary.

 

This really doesn't make much sense. (As I am sure has been explained before.)

 

 

The conventional method doesn't allow for this possibility because there's no way to assign the attribute of being a scalar quantity to direction, we can only do that with distance.

 

If it has direction then BY DEFINITION it is a vector.

 

 

If, however, direction were expressed in a manner where actual, dimensional, units are used, such as |pi/x|, then we will be able to assign a scalar attribute to those units.

 

1. Why do you think that?

 

2. How do you intend to do it? (You keep making vague claims that this is possible/meaningful. It is time for you to get specific.)

 

 

So far, I only know how to use the system in order to define direction as an invariant quantity under that geometry.

 

Please show, in detail, how you do that.

[steveupson]

This really is a core principle of physics. It is known as the 'gauge principle', which says that nothing meaningful should depend on your choice of coordinates.

 

I agree with that. The "idea" of direction being part of the coordinate system is what is immutable. I'm not saying this part correctly, I know, but there's a lot of resistance or push back to what I'm trying to say, whether I say it correctly or not.

 

Some things, like the use of a coordinate system and how critical that is, are questions that I haven't really explored. You have to understand that all of this math (it's a lot) is being done in my head. We really need a lot of extra horsepressure in order to look much deeper into that question.

 

One thing that I can tell you is that as I've been brought along by studiot, and others, I've looked at the material that's been recommended to me and it has been a wonderful experience for me. I appreciate everyone who has joined the conversation, especially the skeptics, because this is the kind of thing that anyone with a solid grounding in physics should be very skeptical of.

 

There has only been one case where I haven't seen that it's possible to "transform" either a principle or a technique into something that can be true in the new system. That one thing that blew up was the stuff about swirl. I've given up on trying to figure out why that was, but I'm thinking that it has something to do with the inherent or assumed or implied calculus (I don't know what terminology is used). I can't figure it out without a lot of help.

[Mordred]

The above doesn't change the fact that distance or direction are both relationships. Not properties by definition.

 

Even in coordinate systems and mathematics not all relations count as properties.

 

For example there are four mathematical properties which involve addition. The properties are the commutative, associative, additive identity and distributive property.

 

In terms of shapes example properties are for example

 

The interior angles of a triangle always add up to 180°

The exterior angles of a triangle always add up to 360°

Edited May 24, 2016 by Mordred

[steveupson]

The above doesn't change the fact that distance or direction are both relationships. Not properties by definition.

 

Even in coordinate systems and mathematics not all relations count as properties.

 

For example there are four mathematical properties which involve addition. The properties are the commutative, associative, additive identity and distributive

 

Aha, I see what you mean.

Your argument is substantive, not simply semantic.

 

Please show, in detail, how you do that.

 

The model that has been prepared by Hans Milton shows, in detail, exactly how it is done.

[Mordred]

I'm a firm believer one must look and study why certain terminology is used and why. These terms aren't arbitrary. It may seem insignificant but proper terminology should always be applied as more often than not the terminology provides clues into key relations. In particular within the definition.

 

If you can show a mathematical property that can be applied to direction following the mathematic or coordinate definition or even the physics definition.

 

Then you might be on to something. However simply trying to apply a terminology without a proper correlation is pointless.

 

Aha, I see what you mean.

Your argument is substantive, not simply semantic.

 

 

The model that has been prepared by Hans Milton shows, in detail, exactly how it is done.

The model by Han Milton is extremely simplistic. Anyone can see that, it does nothing to suggest direction is a property.

 

At best Hans animation simply shows the properties of trigonometric functions.

Edited May 24, 2016 by Mordred

[Strange]

The model that has been prepared by Hans Milton shows, in detail, exactly how it is done.

 

Then can you use that model to generate some useful results?

 

Or are you just making a wild guess based on some pretty animations?

 

You have to understand that all of this math (it's a lot) is being done in my head.

 

Then you need to put it down on paper so it can be properly reviewed.

 

I suspect what is really going on is that have some vague mental images of "something" that you think is significant. But because it is vague and not mathematical, I doubt it has any substance or validity.

[Mordred]

Here is a list of properties of trigonometric functions

 

http://www.analyzemath.com/trigonometry/properties.html

[steveupson]

If you can show a mathematical property that can be applied to direction following the mathematic or coordinate definition or even the physics definition.

 

The model by Han Milton is extremely simplistic. Anyone can see that, it does nothing to suggest direction is a property.

 

 

You have to do the math. It looks simplistic, sure, but the function that the model returns has not been derived as of yet.

 

It's been weeks, no, actually months, since this model has been up on the web.

 

I'm sure that other people than myself have had a crack at it, some of whom have some actual skills in this area.

 

One of the statements that Hans made concerning the model is that it is an intrinsic function of Mathematica to automatically return the angles.

 

Then can you use that model to generate some useful results?

 

Or are you just making a wild guess based on some pretty animations?

 

 

Then you need to put it down on paper so it can be properly reviewed.

 

I suspect what is really going on is that have some vague mental images of "something" that you think is significant. But because it is vague and not mathematical, I doubt it has any substance or validity.

 

 

It HAS been put down on paper. Print out the .cdf file. If you know how to use the program (I don't) then you can look for yourself.

[Strange]

 

 

You have to do the math.

 

No. YOU have to do the math. You claim it will show something new and insightful. It is up to you to support your claims. No one else is going to waste time on it.

 

What makes you think that this animation has the significance that you claim?

 

It just shows some planes being rotated around the surface of a cone. One thing that isn't clear is what it means by the angle between two planes. I decided that the easiest way to define that is in terms of the surface normals, which are vectors.

 

You are looking for a trigonometric relationship between two planes. This will give a result in standard mathematical terms (lengths, angles, vectors, etc.) There is no magic here.

 

 

It HAS been put down on paper. Print out the .cdf file. If you know how to use the program (I don't) then you can look for yourself.

 

Funny. But also untrue:

 

One of the statements that Hans made concerning the model is that it is an intrinsic function of Mathematica to automatically return the angles.

 

So it ISN'T in the cdf file. It is implicit in Mathematica. So now you want people to reverse engineer the code (*) for Mtahematica to solve your non-existent problem.

 

(*) Illegal in some jurisdictions.

[studiot]

 

steveupson

So far, I only know how to use the system in order to define direction as an invariant quantity under that geometry.

 

I'm sorry this makes me think you are just pulling technical sounding words out of the air and stringing them together.

 

Please try to understand their meaning, and then use them properly.

 

It really does aid communication.

 

Invariant means, well that it does not vary, in any coordinate system.

 

 

You cannot have something invariant in only one coordinate system.

Edited May 24, 2016 by studiot

[ajb]

The "idea" of direction being part of the coordinate system is what is immutable.

I don't see that you have a reasonable notion of 'direction' that has any invariant meaning.

 

In differential geometry (which is my speciality), informally we use 'direction' to mean picking one coordinate from a local coordinate system: eg, the x-direction where I have picked local coordinates (x,y,z...). An almost identical notion is to pick a vector at the point in question. This is actually an invariant notion, but by picking local coordinates we can always make this vector just d/dx.

 

One could think of 'direction' as being as being defined by the coordinates on the tangent bundle of the manifold in question. The fibre coordinates at a point can be thought of as specifying a vector. This I think is the best you could hope for and defines 'infinitesimal directions'.

 

 

Some things, like the use of a coordinate system and how critical that is, are questions that I haven't really explored.

As I think I may have said, nothing fundamental can depend on your choice of coordinates. However, some calculations maybe easier in certain coordinates.

 

You have to understand that all of this math (it's a lot) is being done in my head.

Get it on paper! (I have to, its my job!)

[steveupson]

Would someone who understands mathematica please graph 30 and 60 degrees between the cardinal and ordinal axes?

 

90 degrees is not necessary as that would produce a sin curve.

 

If someone would actually take the effort and do the math, then you'd see.

 

I have done the math. I see how the function behaves. I already understand it.

 

First the argument was that there is no function.

 

Now, strange has graphed the function and the argument becomes, yeah, but it ain't nothin special.

 

Someone please take the effort to graph the function at 30 and 60 degrees.

 

 

I can't (for various reasons) or else I would.

 

30 or so pages of Q&A shows that there is an interest.

 

Eh not help me out a little?

Get it on paper! (I have to, its my job!)

The model IS the function.

 

It IS on paper.

 

It's a protractor. Every angle has a different curve. It's usefulness will be more apparent once graphs are produced for several different angles.