The proof of mass vector.
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From: Ka-In Yen on 8 Mar 2007 20:12 On Mar 8, 11:06 am, "Eric Gisse" <jowr...(a)gmail.com> wrote: > On Mar 7, 5:07 pm, "yen, ka-in" <yenk...(a)yahoo.com.tw> wrote: > > > > > > > On Mar 3, 9:25 am, "Androcles" <Engin...(a)hogwarts.physics.co.uk> > > wrote: > > > > "Ka-In Yen" <yenk...(a)yahoo.com.tw> wrote in messagenews:1172884002.101304.55620(a)z35g2000cwz.googlegroups.com... > > > > Is it useful? > > > > > The proof of mass vector. > > > > The disproof: > > > http://mathworld.wolfram.com/VectorSpace.html > > > > When you find negative mass you can call it a vector. > > > Ergo, you are bonkers. > > > In 3D vector algebra of physics, linear mass density > > and surface mass density are vector; shortly, I call > > them mass vector. > > Prove it. You know, if what you say is true, it shouldn't be hard for > you to demonstrate it to be true when you derive the wave equation The proof of mass vector. The proof of mass vector. The proof of mass vector. The proof of mass vector. Introduction: In this paper, we will prove that linear mass density and surface mass density are vector, and the application of mass vector is presented. 1. The unit of vector. In physics, The unit of three-dimensional cartesian coordinate systems is meter. In this paper, a point of 3-D coordinate system is written as (p1,p2,p3) m, or (p:3) m and a vector is written as <a,b,c> m, or <a:3> m or l m<i,j,k> = <a,b,c> m where l=abs(sqrt(a^2+b^2+c^2)) is the magnitude of the vector, and <i,j,k> is a unit vector which gives the direction of the vector. For three reasons, a magnitude of a vector can not add to a scalar: i) The magnitude belongs to the set of vector; it's a portion of a vector. Scalar belongs to a field. ii) The magnitude is real non-negative number, but scalar is real number. iii) The unit of magnitude is meter, but scalar has no unit. This is a major difference between physics and mathematics. 5m+3 is meaningless. 2. Linear mass density is a vector. The mass of a string is M kg, and the length of the string is l m<i:3>. Where l m is the magnitude of the length, and <i:3> is a 3-D unit vector which gives the direction of the string. Then the linear mass density of the string is: M/(l<i:3>)=(M/l) (kg/m)<i:3> The direction, <i:3>, is not changed by "division", so we can move <i:3> from denominator to numerator. A direction is changed by -1 only. A proof is found in Clifford algebras: [Proof] k/<a,b,c>=[k<a,b,c>]/[<a,b,c>^2] =(k/l) <i,j,k> where l is the magnitude of <a,b,c>, and <i,j,k> is the unit vector of <a,b,c>. [Proof] 3. Surface mass density is a vector. A parallelogram has two vectors: l m<i:3> and h m<j:3>. <i:3> and <j:3> are unit vectors. The area vector of the parallelogram is the cross product of these two vectors. l m<i:3> X h m<j:3>= lh (m^2 )<i:3>X<j:3> = lh abs(sin(theta)) (m^2)<k:3> Where theta is the angle between <i:3> and <j:3>. <k:3> is a unit vector which is perpendicular to <i:3> and <j:3>. For AXB=-BXA, an area has two directions. We can divide the area vector by the length vector. lh*abs(sin(theta))<k:3>/[l<i:3>] =h<i:3>X<j:3>/<i:3> =h(<i:3>X<j:3>)X<i:3> (The direction, <i:3>, is not changed by "division", and the division is replaced by a cross product.) =-h<i:3>X(<i:3>X<j:3>) =-h[<i:3>(<i:3>o<j:3>)-<j:3>(<i:3>o<i:3>)] (where o is dot product.) =-h(cos(theta)<i:3>-<j:3>) =h(<j:3>-cos(theta)<i:3>) m The result is a rectangle, not the original parallelogram. We can test the result. h(<j:3>-cos(theta)<i:3>)Xl<i:3>=lh m^2<j:3>X<i:3> The magnitude of the area vector is conserved, but the direction is opposite. The mass of a round plate is M kg, and the area vector is A m^2<i:3>; then the surface mass density is M kg/(A m^2<i:3>)=M/A (kg/m^2)<i:3> 4. Mass vector in physics. Mass vector has been found in two equations: 1) the velocity equation of string. 2) Bernoulli's equation. i) For waves on a string, we have the velocity equation: v=sqrt(tau/mu). v is velocity of wave, tau is tension applying to string, and mu is linear mass density of string. We can rewrite the equation: mu=tau/v^2. In the above equation, the mu is parallel to tau, and both of them are vector. ii) Bernoulli's equation is: P + k*v^2/2=C (P is pressure, k is volume density, and v is velocity. Here we neglect the gravitational term.) Multiplying cross area vector A m^2<i:3> of a string to Bernoulli's equation(where <i:3> is a unit vector), P*A<i:3> + k*A<i:3>*v^2/2=C*A<i:3> F<i:3> + L<i:3>*v^2/2=C*A<i:3> (where F is the magnitude of force, and L is the magnitude of linear mass density.) These two equations are well used in the theory "Magnetic force: Combining Drag force and Bernoulli force of ether dynamics." For detail, please refer to my site: http://www.geocities.com/redlorikee
From: Eric Gisse on 8 Mar 2007 20:50 On Mar 8, 4:12 pm, "Ka-In Yen" <yenk...(a)yahoo.com.tw> wrote: [snip retardation] You are an idiot. The equations you keep using as examples were explicitly derived without such quantities in mind. I have gone through the derivations myself - have you?
From: Androcles on 9 Mar 2007 04:56 "Ka-In Yen" <yenkain(a)yahoo.com.tw> wrote in message news:1173402536.221189.303880(a)t69g2000cwt.googlegroups.com... > On Mar 8, 6:03 pm, "Androcles" <Engin...(a)hogwarts.physics.co.uk> > wrote: >> "yen, ka-in" <yenk...(a)yahoo.com.tw> wrote in messagenews:1173319658.500173.293520(a)8g2000cwh.googlegroups.com... >> > On Mar 3, 9:25 am, "Androcles" <Engin...(a)hogwarts.physics.co.uk> >> > wrote: >> >> "Ka-In Yen" <yenk...(a)yahoo.com.tw> wrote in messagenews:1172884002.101304.55620(a)z35g2000cwz.googlegroups.com... >> >> > Is it useful? >> >> >> > The proof of mass vector. >> >> >> The disproof: >> >> http://mathworld.wolfram.com/VectorSpace.html >> >> >> When you find negative mass you can call it a vector. >> >> Ergo, you are bonkers. >> >> > In 3D vector algebra of physics, linear mass denasity >> > and surface mass density are vector; shortly, I call >> > them mass vector. >> >> When you find a negative "denasity" (whatever that is), >> you can call it a vector. >> When you find a negative surface, you can call it a vector. >> Perhaps you simply don't know what English words mean, >> "denasity" is a new one on me. >> Is it a Chinese, Korean, Mongolian, Japanese word, what?- Hide quoted text - > > Sorry, it's neither Chinese, nor Korean, nor Japanese; it's TYPO. > I'm sorry too, I never did learn to speak TYPO or Gibberish. Dynasty? Tenacity? Tensity? I'm fluent in both English and American but spoken American often confuses "t" with "d", and "c" can be sybilant or guttural; it could be any of them, waddaya know... Maybe TYPO as variation of Ebonics. Do you speak Ebonics? I'm not fluent in that but I know enough to get by, bro'. I've met some boyz from the 'hood.
From: Androcles on 9 Mar 2007 05:11 "Ka-In Yen" <yenkain(a)yahoo.com.tw> wrote in message news:1173402746.622921.297240(a)8g2000cwh.googlegroups.com... > On Mar 8, 11:06 am, "Eric Gisse" <jowr...(a)gmail.com> wrote: >> On Mar 7, 5:07 pm, "yen, ka-in" <yenk...(a)yahoo.com.tw> wrote: >> >> >> >> >> >> > On Mar 3, 9:25 am, "Androcles" <Engin...(a)hogwarts.physics.co.uk> >> > wrote: >> >> > > "Ka-In Yen" <yenk...(a)yahoo.com.tw> wrote in messagenews:1172884002.101304.55620(a)z35g2000cwz.googlegroups.com... >> > > > Is it useful? >> >> > > > The proof of mass vector. >> >> > > The disproof: >> > > http://mathworld.wolfram.com/VectorSpace.html >> >> > > When you find negative mass you can call it a vector. >> > > Ergo, you are bonkers. >> >> > In 3D vector algebra of physics, linear mass density >> > and surface mass density are vector; shortly, I call >> > them mass vector. >> >> Prove it. You know, if what you say is true, it shouldn't be hard for >> you to demonstrate it to be true when you derive the wave equation > > The proof of mass vector. > The proof of mass vector. > The proof of mass vector. > The proof of mass vector. > > Introduction: > In this paper, we will prove that linear mass density and > surface mass density are vector, and the application of mass > vector is presented. > > 1. The unit of vector. > > In physics, The unit of three-dimensional cartesian coordinate > systems is meter. In this paper, a point of 3-D coordinate > system is written as > > (p1,p2,p3) m, or (p:3) m > > and a vector is written as > > <a,b,c> m, or <a:3> m > > or > > l m<i,j,k> = <a,b,c> m > > where l=abs(sqrt(a^2+b^2+c^2)) is the magnitude of the vector, > and <i,j,k> is a unit vector which gives the direction of > the vector. Err... I'm not sure what direction you think mass will take. http://mathworld.wolfram.com/VectorSpace.html 4. Existence of additive inverse: For any X, there exists a -X such that X+ (-X) = 0 Since the scalar always positive, given by "l=abs(sqrt(a^2+b^2+c^2)) is the magnitude of the vector" (a scalar). There is no such animal as negative mass. Ergo mass is not a vector. Proof failed.
From: Ka-In Yen on 9 Mar 2007 19:56
On Mar 9, 6:11 pm, "Androcles" <Engin...(a)hogwarts.physics.co.uk> wrote: > "Ka-In Yen" <yenk...(a)yahoo.com.tw> wrote in messagenews:1173402746.622921.297240(a)8g2000cwh.googlegroups.com... > > On Mar 8, 11:06 am, "Eric Gisse" <jowr...(a)gmail.com> wrote: > >> On Mar 7, 5:07 pm, "yen, ka-in" <yenk...(a)yahoo.com.tw> wrote: > > >> > On Mar 3, 9:25 am, "Androcles" <Engin...(a)hogwarts.physics.co.uk> > >> > wrote: > > >> > > "Ka-In Yen" <yenk...(a)yahoo.com.tw> wrote in messagenews:1172884002.101304.55620(a)z35g2000cwz.googlegroups.com... > >> > > > Is it useful? > > >> > > > The proof of mass vector. > > >> > > The disproof: > >> > > http://mathworld.wolfram.com/VectorSpace.html > > >> > > When you find negative mass you can call it a vector. > >> > > Ergo, you are bonkers. > > >> > In 3D vector algebra of physics, linear mass density > >> > and surface mass density are vector; shortly, I call > >> > them mass vector. > > >> Prove it. You know, if what you say is true, it shouldn't be hard for > >> you to demonstrate it to be true when you derive the wave equation > > > The proof of mass vector. > > The proof of mass vector. > > The proof of mass vector. > > The proof of mass vector. > > > Introduction: > > In this paper, we will prove that linear mass density and > > surface mass density are vector, and the application of mass > > vector is presented. > > > 1. The unit of vector. > > > In physics, The unit of three-dimensional cartesian coordinate > > systems is meter. In this paper, a point of 3-D coordinate > > system is written as > > > (p1,p2,p3) m, or (p:3) m > > > and a vector is written as > > > <a,b,c> m, or <a:3> m > > > or > > > l m<i,j,k> = <a,b,c> m > > > where l=abs(sqrt(a^2+b^2+c^2)) is the magnitude of the vector, > > and <i,j,k> is a unit vector which gives the direction of > > the vector. > > Err... > I'm not sure what direction you think mass will take. > > http://mathworld.wolfram.com/VectorSpace.html > 4. Existence of additive inverse: For any X, there exists a -X such that > > X+ (-X) = 0 > > Since the scalar always positive, given by > "l=abs(sqrt(a^2+b^2+c^2)) is the magnitude of the vector" (a scalar). > > There is no such animal as negative mass. Ergo mass is not a vector. > Proof failed. In 3D vector algebra of physics, velocity is a vector. <velocity> = <length> / time. Linear mass density is a vector too, <linear mass density> = mass / <length>. Surface mass density is a vector three, <surface mass density> = mass / <area>. |