LTE
in [Relativity]
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From: glird on 17 Jul 2010 15:23 On Jul 16, 4:07 pm, dlzc <dl...(a)cox.net> wrote: > Dear glird: > > On Jul 16, 11:53 am, glird <gl...(a)aol.com> wrote: > > > It is said that the Lorentz Transformation > > Equations (LTE) have been experimentally > > confirmed by many different experiments. I > > would appreciate it if someone would provide > > a list of all the experiments that did so. > > Doubt that this is all of them, but Tom Roberts made a very nice list > that maps from theory to quantifiable observation via application of > the LT: > > http://www.physics.adelaide.edu.au/~dkoks/Faq/Relativity/SR/experimen... > > David A. Smith Thank you, David. His list will be very helpful. glird
From: Jonathan Doolin on 17 Jul 2010 15:44 On Jul 16, 8:48 pm, Tom Roberts <tjroberts...(a)sbcglobal.net> wrote: > xxein wrote: > > Does anyone out there know how velocity addition > > works to describe how we measure it besides a math? What is the > > physical reason? > > Consider a pointlike object moving with constant velocity v along the x axis, > and plot its x position vs time t. You'll get a straight line with a slope of v. > Now do the same for 2v, and get a straight line with slope 2v. In such a graph, > relative velocity is a rotation of the axes, and by considering the angle > related to the relative velocity, not its slope, it's clear that in Galilean > relativity when composing relative velocities the angles merely add (when > plotted on a Euclidean piece of paper). > > In relativity there is also an angle associated with relative velocity, called > rapidity. When composing relative velocities, their rapidities add. But this is > hyperbolic geometry, and when plotted on a Euclidean piece of paper the angles > corresponding to the rapidities do not simply add, they combine in such a way > that the sum of angles never exceeds 45 degrees (= the invariant speed of the > Lorentz transform = the speed of light). > > If you think this is far fetched, remember that v is the slope of the relative > velocity, not an angle. Look up the formula for composing two Euclidean > rotations in terms of the slopes of lines and you'll find a formula quite > similar to the Lorentz addition of velocities, differing only in a sign. > > You'll also find that composing two large-enough slopes can > flip the sign of the line's slope. That's highly unphysical > when applied to relative velocities.... > > As for "why" hyperbolic geometry applies rather than Euclidean geometry, that is > outside the realm of science. In the world we inhabit it just does. > > > I know what it is but I doubt that anyone else does. > > Such hubris! Such cowardice! > > Tom Roberts Thanks, Tom. I was wondering about something related. Since if you take the unit circle, x=cos(theta) y=sin(theta), the arc length of the unit circle is the same as the angle in radians. Is the arc-length of the unit hyperbola x=cosh(theta), y= sinh(theta) also equal to its angle? It seems like it ought to be, but I can't figure out the path-integral. I just wondered, because then you can say that the rapidity change is equal to the arc-length of the unit hyperbola, just the same as rotation angle is the arc-length of the unit circle. Jonathan Doolin
From: Androcles on 17 Jul 2010 15:53 "Jonathan Doolin" <good4usoul(a)gmail.com> wrote in message news:e7d38138-7ca0-446a-893f-603a443cdcde(a)r27g2000yqb.googlegroups.com... On Jul 16, 8:48 pm, Tom Roberts <tjroberts...(a)sbcglobal.net> wrote: > xxein wrote: > > Does anyone out there know how velocity addition > > works to describe how we measure it besides a math? What is the > > physical reason? > > Consider a pointlike object moving with constant velocity v along the x > axis, > and plot its x position vs time t. You'll get a straight line with a slope > of v. > Now do the same for 2v, and get a straight line with slope 2v. In such a > graph, > relative velocity is a rotation of the axes, and by considering the angle > related to the relative velocity, not its slope, it's clear that in > Galilean > relativity when composing relative velocities the angles merely add (when > plotted on a Euclidean piece of paper). > > In relativity there is also an angle associated with relative velocity, > called > rapidity. When composing relative velocities, their rapidities add. But > this is > hyperbolic geometry, and when plotted on a Euclidean piece of paper the > angles > corresponding to the rapidities do not simply add, they combine in such a > way > that the sum of angles never exceeds 45 degrees (= the invariant speed of > the > Lorentz transform = the speed of light). > > If you think this is far fetched, remember that v is the slope of the > relative > velocity, not an angle. Look up the formula for composing two Euclidean > rotations in terms of the slopes of lines and you'll find a formula quite > similar to the Lorentz addition of velocities, differing only in a sign. > > You'll also find that composing two large-enough slopes can > flip the sign of the line's slope. That's highly unphysical > when applied to relative velocities.... > > As for "why" hyperbolic geometry applies rather than Euclidean geometry, > that is > outside the realm of science. In the world we inhabit it just does. > > > I know what it is but I doubt that anyone else does. > > Such hubris! Such cowardice! > > Tom Roberts Thanks, Tom. I was wondering about something related. Since if you take the unit circle, x=cos(theta) y=sin(theta), the arc length of the unit circle is the same as the angle in radians. Is the arc-length of the unit hyperbola x=cosh(theta), y= sinh(theta) also equal to its angle? It seems like it ought to be, but I can't figure out the path-integral. I just wondered, because then you can say that the rapidity change is equal to the arc-length of the unit hyperbola, just the same as rotation angle is the arc-length of the unit circle. Jonathan Doolin ===================================== The arc length of an ellipse of eccentricity 1 (a circle) is 2pi. The arc length of an ellipse of eccentricity 0 ( two straight lines) is 4. What is the eccentricity of an ellipse of arc length 5? 6?
From: glird on 17 Jul 2010 16:07 On Jul 16, 6:39 pm, xxein <xxxx...(a)gmail.com> wrote: > On Jul 16, 2:53 pm, glird <gl...(a)aol.com> wrote: > >>< It is said that the Lorentz Transformation Equations (LTE) have been experimentally confirmed by many different experiments. I would appreciate it if someone would provide a list of all the experiments that did so. > > >< xxein: Don't worry about it. Experiments are measuremental observations and affects. They are put into a math form without regard to really understanding the physic that caused them to be observed and effect in this way. > "Physics" is the study of the mathematical equations that summarize the results of experiments. Those results are always quantities, without regard to the nature of the things so measured. >< Oh wow! There is a --- formula. Does it explain what is really happening or is it just a math wysiwyg? The Lorentz transformations are fine, but when you math-shortcut them to SR (and its postulates), you strip the essence of the physic out of it. What you call "physic" I call "Metaphysics"; which is the study of the underlying realities that physics quantifies. > I told you this before (in some fashion) but you decided > that it was too much for you to try to understand. BS! > And now an appeal. Does anyone out there know how [the LTE!!] work --- besides a math? What is the physical reason? Geez! Doesn't anybody know how to think logically of the physic beyond the archaic scientific method? I have a complete metaphysical theory concerning the structure of everything in the universe, and how its mechanisms work. I know where Einstein made mathematical errors in his 1905 paper that prove he neither derived the LTE nor understood what they rest on and impose(and that neither does any physicist!). But HOW,other than by studying the observations that fit a given set of equations, can you prove that the underlying metaphysics is "this" rather than "that"? glird
From: glird on 17 Jul 2010 17:14
On Jul 17, 4:07 pm, glird <gl...(a)aol.com> wrote: > ><HOW, other than by studying the observations that fit a given set of equations [such as the LTE], can you prove that the underlying metaphysics is "this" rather than "that"? Here, from notes at the end of "The Universe", is what led me to ask for the list: ______ 7/10/2010. The speed of light will always be c, when measured by a Q,q,q-contracted self-esynched system, regardless of the value of its own velocity wrt the etheric matrix of the parent unit. Examples: For v = .6c, Q = .64. Let a ray go from x = 0 to x = 1. It will take Qx/(c-v) = .64/.4 = 1.6 seconds to reach x = 1 and Qx/(c +v) = .64/1.6 = .4 seconds to get back; so the round-trip will take 2 seconds. The one way outbound time will be t - vx/c2 = 1.6 - .6 = 1 second as marked by the self-synched system. For v = .5c, Q = .75. Let a ray go from x = 0 to x = 1. It will take Qx/(c-v) = .75/.5 = 1.5 seconds to reach x = 1 and Qx/(c+v) = .. 75/1.5 = .5 seconds to get back; so the round-trip will take 2 seconds. The outbound time will be t - vx/c2 = 1.5 - .5 = 1 second as marked by the entrainment-synched system. In both cases, as in all others, the speed of light will be c = dx/ dt = 1 light-unit/second as plotted that way. Complication: Suppose the moving systems density has changed within the closed physical system that shrunk by Q,q,q. Then the speed of light will also have changed within it! (See 1] M&M; 2] the Pan Am experiment; 3] my smoke one, 4] the demo that clocks run faster at a higher altitude in a g-field; 5] the size of a proton is a function of the weight of a circling thing such as a muon versus an electron. For the latter, the proton is about 4% smaller. ("To their astonishment, the scientists detected x-rays at an assumed proton radius of 0.8418 femtometers4 percent smaller than expected." NYTimes) Given that there is no such thing as a really stationary system, the new purpose is to prove my recent hypothesis: ANY system may be take as the viewing system, and relative to it ALL other systems will appear to be shrunken by q,1,1; and their times will appear to run slower by q; which is WHY the LTE have been experimentally confirmed. As of now, it is easily seen that if two Q,q,q;1 deformed systems, moving in opposite directions at the same speed wrt an ABSOLUTELY stationary middle system, plot each other, since their lengths are identically deformed, unit-rods in the perpendicular directions are and will appear identical in both systems, so phi(+/- v) = 1, and when measured with their esynched clocks, their identical lengths in the axis of motion will appear q contracted, and the identical rates of their clocks will be measured by the other as running q-slow. Rather than hypothesize that therefore, if we dispense with a really stationary system, we can let any one of these Q,q,q shrunken ones be taken as stationary etc, I want to PROVE it is correct in reality, not just in mathematics. Q 1: How u gonna prove that a q-contracted vertical unit-rod that is . 8 units long, will appear to be 1 unit long as measured by ALL differently moving systems, REGARDLESS of the variable values of v? !!!! 7/11: There is no way for a physical system to be a universally extending frame of reference! The cs attached to one can extend only as far as _it_ does. Examples: The Earth extends to the limits of its own matter-unit; which moves in the cs centered on the Sun; which moves in a cs centered on the Milky Way, etc all the way up and down. The Pan Am experiment, and others, proved that. Therefore it is impossible for a q-contracted vertical unit-rod that is .8 units long to be 1 unit long as measured by ALL differently moving systems, REGARDLESS of the variable values of v. Think about that and you will slowly understand it. Once you do, you will know why Einstein gave up almost his entire STR apparatus in order to construct GR. The only thing he kept was his Esynched clocks. He didnt know that clocks would esynch themselves. (Esynched clocks are set by *E*insteins method; and esynched clocks automatically get the identical local-time offsets via *e*ntrainment.) Complication: If a cs cant extend past the limit of its own referent, then WHY have the LTE been experimentally confirmed? To answer that question we will have to look at the ways in which it was done. The object of that is to show that the experiments were restricted to within the frame of reference of matter-unit Earth. ______ At a quick glance, as of now, those that fit the LTE were indeed VERY local; and those that weren't local did NOT fit STR's claim that ANY system can be taken as "stationary". glird |