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Everything posted by steveupson
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Quantifying the Physical Property of Direction.
steveupson replied to steveupson's topic in Speculations
Of course it is if you're not willing to do the math. i need help with the math. -
Quantifying the Physical Property of Direction.
steveupson replied to steveupson's topic in Speculations
In the new function, the direction is the scalar quantity. -
Quantifying the Physical Property of Direction.
steveupson replied to steveupson's topic in Speculations
If this is a scalar quantity, then isn't it invariant? I honestly don't know the answer. This might be what I'm not understanding. -
Quantifying the Physical Property of Direction.
steveupson replied to steveupson's topic in Speculations
Correct, and equations are what? Unchanged. -
Quantifying the Physical Property of Direction.
steveupson replied to steveupson's topic in Speculations
I don't see how it can be the same, mathematically, since vectors and equations respond differently to Lorentz transformations. -
Quantifying the Physical Property of Direction.
steveupson replied to steveupson's topic in Speculations
I think that I already understand (sort of) what you are trying to get me to understand. Take a closer look. What is show is not rotation symmetry, it's rotation synchronicity. In two dimensions there exists a condition which causes translation-invariance. In three dimensions, this condition becomes translation-synchronous in much the same way, but with much different effect. I think you should see the equality where alpha is a function of E. This is true for every E. What we've shown is the equivalence of a triangle in plane geometry. Only here, as our relationship between the cardinal and ordinal directions change, the the relationship where alpha is a function of E also changes accordingly. This equality quantifies direction in a completely different way than how it is quantified using plane geometry. -
Quantifying the Physical Property of Direction.
steveupson replied to steveupson's topic in Speculations
Aha! I apologize for my impatience with you. I thought that you must have read the OP where I link to exactly that! Evidently no. I originally had the .gif displayed in the OP, but the moderators removed it, so as not to offend anyone here, I imagine. Go back the OP and click the link, then I think we'll be on the same page. On edit> better yet, go here to see it all on the same page. http://www.thephysicsforum.com/mathematics/9252-defining-new-function.html -
Quantifying the Physical Property of Direction.
steveupson replied to steveupson's topic in Speculations
Nothing else is in question. I agree wholeheartedly with all the other claims in your post. If we express direction as an equality, as an equation, then we don't need any coordinate system, do we? The reason we need the coordinate system is so that we can express the relationship between our reference and our direction. If this relationship is expressed as an equality instead, haven't we accomplished something completely different? -
Quantifying the Physical Property of Direction.
steveupson replied to steveupson's topic in Speculations
At some point I tire of the game. If you have derived the function and if you can express the new equality using algebraic terms, then why not just tell us all? If you can express the new equality using vectors, even better. Why the mystery? First I was wrong, now I'm pigheaded? Am I boring you? I don't think this is going to work this way. Why don't we simply find someone who is willing to graph the function? I am unable to upload the file containing the model, but perhaps someone has a suggestion about how it can be published here so that anyone who is interested can have a stab at it. -
Quantifying the Physical Property of Direction.
steveupson replied to steveupson's topic in Speculations
Correct. My problem is that even though I have the tools, I don't know which end of the shovel to hold. Can you show me? On edit> It's an equality. It's an equality. It's an equality. It's an equality. ..... Everyone seems to be saying that there is another way to express this equality using vectors. Can anyone express this equality using vectors? and being passing familiar with the number line -- I'm sure if I don't say passing familiar somebody here will say, "You have to know vector tensor shmelaculus in 15 triad synergies to really understand the number line. It's not even called that, it's called the real torticular space." or something to that effect -- http://www-m10.ma.tum.de/foswiki/pub/Lehre/ProjektiveGeometrieWS0607/chap5.pdf Do we know what an equality is? -
Quantifying the Physical Property of Direction.
steveupson replied to steveupson's topic in Speculations
What metric choice is chosen in the new model? Also, in my last post I asked how one would show me how to generate the tensor for the new model. Even though I followed your explanation, it didn't seem to respond to my question. I still don't know how one would do it. Can you show me? I sincerely appreciate your patience and you effort on this. It seems like we are talking past each other. If you could actually answer either of these two questions for me it would be extremely helpful in aiding my understanding. Understand, I don't want you to tell me how to do it, I want you to show me. Can you do it for me while I follow along with you? Or, it could be that you've taken me as far as you can using this approach for now. Maybe another approach would make a lot more sense to me. If I were to publish the Mathematica .cdf file again (it was previously published at Wolfram Community but then taken down without any explanation) perhaps someone here with skills that I don't possess can plot the function for us. If it were plotted for 45 degrees, then 44, and so on, and if those results were plotted together, then we could all sit around looking at those plots and wax philosophic about what, exactly, we're looking at. Someone might already know, once they see the graphic representation. -
Quantifying the Physical Property of Direction.
steveupson replied to steveupson's topic in Speculations
This is my question. I honestly need help on this. I guess anther way to go about it is to ask if you can explain to me how one would go about generating a nine quantity tensor for the model? The way that it looks to me, there is no 'information' about how these two directions relate to one another. Sure, you can pick some arbitrary reference frame, but how would you know that these two directions are 45 degrees to one another, other than by just declaring that it's so? The function is what makes them 45 to one another, not their orientation in any reference frame. In other words, without knowing how either axis is oriented in space, we know they are 45 to one another if they satisfy the equation. -
Quantifying the Physical Property of Direction.
steveupson replied to steveupson's topic in Speculations
Thank you, Mordred. That was much less painful than I expected it to be, and it fits perfectly with my understanding, too. Help me out with this, or at least let me know if anyone here can decipher what it is that I’m trying to say. Let the main axis of the new object lie along a line which is coaxial with a cardinal direction. Then, let the axis that is normal to the center of the small circle lie along a line which is coaxial with an ordinal direction. In the example used in the model, the directions of these two axes are oriented 45 degrees from one another in space. Also, the lines that are coincident with these axes lie in a plane, and are oriented at 45 degrees to one another in that plane. The basic underlying principle behind the new technique is to express the relationship between these two directions as a function which incorporates all three Cartesian directions (x, y, and z), simultaneously. The new function can mathematically replace the vector (two dimensional) in describing the same (almost) direction information. The new function actually appears to operate with even more ‘information’ which makes it communicative. When the cardinal direction and the ordinal direction in our model are reversed, the same arithmetic relationship between the two will still exist. The model that has been provided for a 45 degree relationship between two directions yields a different function from that in which this same model is used for defining a similar relationship between two directions that are not 45 degrees from one another. There is (should logically be) another additional function which will define the relationship between the 45 degree function and all of the other non-45 degree functions. An analogy would be how the trigonometric functions are used in plane geometry. A similar set of functions (as yet undefined) must exist for this geometry. If someone could help me express this function of a function algebraically then I think everyone would have a much better opportunity to make some sense of my gibberish. We shouldn’t have to derive the actual function in order to understand how this works. But, once these functions are derived then it should be possible to express direction in units using this method. Having come this far, it may be more useful to call direction and position relationships rather than properties, although I'm not quite sure what the difference is, technically. In which case, if we look at this relationship as something similar to a pointer in computer languages, then what we are talking about with this new technique would be similar to a pointer to a pointer. This new thing (the pointer to a pointer) is a quantity which is tied to the relationship between the two directions. On edit> maybe another way to say it is that it works without any metric tensor? -
Quantifying the Physical Property of Direction.
steveupson replied to steveupson's topic in Speculations
The way that I understand it to work, there is no "absolute" direction. I think this has been worked out already. There is the possibility of a "universal" direction instead. In other words, each particle (and position) shares a common property which determines the position and direction relative to all other particles. A good stepping off point would be to look at “The Physical Origin of Torque and of the Rotational Second Law” - Daniel J. Cross. There it is argued that rigid bodies cannot transmit torque, or some such (this is a gross oversimplification.) Although their observations are accurate enough, their conclusions seem to be very speculative. The other obvious conclusion would be that rather than having non-rigid bodies where position changes when acted on by a force, there could a scenario where the future of these particles changes first thereby allowing their direction to change rather than their position. Actually, because of the interaction between these two things (position and direction), both could probably be true, simultaneously. This is an example of how it could happen. What the new function seems to establish is a simultaneous reciprocal (commutative) relationship between discrete directions in three-dimensional space, and because it commutes, all directions must have a common element that ties them together. Alternatively, but equally as forceful, all positions must have a common element to tie them all together. Again, see the above mentioned paper by Daniel J. Cross in order to see a much better description of the issue in much clearer, and much more rigorous terms. Hello studiot, Welcome to the party! it's very reassuring to know someone here who understands how truly feeble I am when it comes to expressing things in standardized terms. And as for the explanation of the circulation of a vector field, I hope that you're pranking me. -
Quantifying the Physical Property of Direction.
steveupson replied to steveupson's topic in Speculations
Yes, this is the question. If it isn't a property, what is it? I don't know why it "should be" any certain way. I'm trying my best to make sense of a geometric reality that is defined by a new function that no one seems to be able to derive. As far as giving it a shot myself, such that I have a lot of skin in the game already, my attempt produced: α = cot ((1 – sin E) / sin E) = cot (1/sin E – 1) This makes no sense, not even a little... Edited to add> I do have a .cdf file that was used to create the animation, and would post it here, but I need some help with that. -
Quantifying the Physical Property of Direction.
steveupson replied to steveupson's topic in Speculations
Your first link has five appearances of the word "direction," none of which are in any form of table. Your second link does not even include the term "direction" at all. If some other word is being used instead, what is it? Being my first day here, I'm not sure if every semantic argument requires a response. I always try and form some type of response when asked a sincere question, but I'm sure it makes a lot of sense to turn this into a discussion of what a "table of physical properties" is. Maybe this should be asked. Is it ok to ask? -
Quantifying the Physical Property of Direction.
steveupson replied to steveupson's topic in Speculations
I am referring to any list of physical properties. The way that I understand it, the vectors that you mention are without any inherent magnitude, ie, they are not scalars. The object that I am talking about is unchanged by Lorenz transformation (it is an eqation) and therefore that would indicate to me that the quantity is a not a vector. This is my best attempt at asking some seemingly simple questions about physics are deceptively difficult. Try and make some allowances for my inability to convert this all to algebra, Although I have a passing familiarity with reading algebraic expressions, my ability to conjugate in that language is very limited. Observations can be made about other's research, it doesn't have to be original experiments, does it? In my particular case the research is fairly simple and consists of looking at lists of physical properties to see if they quantify a property called direction. It's simple enough, I would think. -
Quantifying the Physical Property of Direction.
steveupson replied to steveupson's topic in Speculations
I'm sorry, the other thread is about the math. Is there a Math/Physics forum where these two topics should be posted together? Edited for clairity> before making the claim that this is some pet theory, shouldn't we deal with the math? In other words, how can such a claim be made without math to support it? Second edit> how can making the simple observation that direction doesn't appear on any list of physical properties be consider a "pet theory?" It seems like a reality to me. Also, the only reason that I used the word maybe in my last post is because I make childish mistakes quite frequently. In this case the jargon that I am using is jargon that I'm not fully comfortable with. Your patience will be greatly appreciated. -
Quantifying the Physical Property of Direction.
steveupson replied to steveupson's topic in Speculations
The function itself does not seem to be understood at this time. It differs from the normal way the direction is expressed. Direction can currently be expressed as either a relationship between two or more vectors (Pythagoras), or as a relationship between circle and its radius (pi). In either event, direction is only expressed as a relationship that occurs in a plane. The new function defines direction much differently. Three (simultaneous) dimensions are required in order to create the model. This method is completely different from the method used where three planes are stacked orthogonality to one another. It isn't that the object rotates, rather the object occupies all of these rotations at once. Maybe. -
Unfortunately, all posts where Hans and I collaborated over at Wolfram Forums have been deleted without explanation. The original thread was there until yesterday. http://community.wolfram.com/groups/-/m/t/527829?p_p_auth=xWI25qyy Has anyone else run into this issue? Since I no longer have any way of contacting Hans (short of starting a new thread over there without knowing why the original has been removed), I cannot ask if he has figured it out yet. As of our last communication, he had not. The model was published more than two months ago.
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The physical property of direction does not appear on any list of physical properties. The reason for it not appearing on such lists seems to be unknown at this time, or least no accepted scientific source provides this reason. Without speculating as to what these reasons might be, there does seem to be a practical method that can be used in order to fill in this area of physics. There is a new model that illustrates the existence of a smooth function that establishes the relationship between two directions (orientated 45 degrees to one another) in three dimensions, simultaneously. It involves concurrent quantification of direction, without a metric, which can be understood as simultaneous finite rotations which commute in much the same manner as infinitesimal rotations commute in conventional plane geometry. This differs (mathematically and conceptually) from the usual (two dimensional) discrete finite rotations or infinitesimal rotations which are used to manipulate objects in Euclidean three space. In the new model, the relationship between the two directions is that they are 45 degrees to one another, but a similar model can be constructed for defining the relationship between any two directions. These are simply observations, not speculation. The new function is here: http://www.scienceforums.net/topic/95113-defining-a-new-function/
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Gratitude and credit go to Hans Milton for creating this model in Mathematica. http://community.wolfram.com//c/portal/getImageAttachment?filename=NSTF.gif&userId=93385 The first angle that we are concerned with is the elevation angle E. It is the angle that is formed between the equatorial plane (beige) and the elevation plane (yellow). The second angle is more complicated. It is formed between a plane of longitude (green) and a "tangent" plane (blue) which lies in a conical orbit. The construction of the longitude plane is not too complicated, but its orientation is very specific. The orientation of the longitude plane is such that it intersects a point on a small circle which is constructed on the surface of the sphere at a 45 degree angle. This small circle can be defined as a circle at the 45 degree latitude which has been tilted 45 degrees such that it intersects both the pole and the equator. The "tangent" plane lies along the surface of a cone formed by the sphere center and the 45 degree small circle. As the elevation angle E is varied, the position of this tangent plane changes such that it remains coincident with the intersecting point on the circumference of the small circle. If we call the angle that is made between the longitude plane and the tangent plane the angle α, then the object is defined by the function which expresses the relationship between the two angles, E and α. This function is the one that I have a lot of trouble with, for some reason or other. How is this function expressed? It should be mentioned that, although a sphere is used for construction of the animation that is shown here, there actually is no sphere involved in the function itself. In other words, there is no two-dimensional surface involving spherical excess, or anything like that. The sphere is simply used as an aid in visualizing how the object is constructed.