Moving Mirror Proves Einstein Wrong
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From: waldofj on 3 Jan 2010 16:01 On Jan 3, 3:53 pm, waldofj <wald...(a)verizon.net> wrote: > On Jan 3, 3:08 pm, waldofj <wald...(a)verizon.net> wrote: > > > > > >news:ea47baf0-a8f9-4f58-935d-812452ab275d(a)o19g2000vbj.googlegroups.com.... > > > On Dec 30, 7:36 am, "Androcles" <Headmas...(a)Hogwarts.physics_q> wrote: > > > > > I don't care about physical explanations, there is no mathematical > > > > explanation. Anyone handwaving their precious gamma around > > > > needs to derive it first. > > > > > gamma = sqrt[(c-v)(c+v)/c^2] > > > > actually gamma is the reciprocal of that function and deriving it is > > > easy. What's the big deal? > > > ======================================== > > > Go on then, show and tell. Just remember that the speed of light is > > > c in all frames of reference and so you can't use c+v or c-v without > > > being self-contradictory. > > > Ill derive it two ways, the first is the way it was taught to me in > > college, the second is a way I came up with myself. > > First: compute gamma by analyzing a light clock, two mirrors with a > > light beam bouncing between them. The mirrors are oriented so the > > light is moving parallel to the Y axis and perpendicular to the X > > axis. I will call the time it takes light to travel from one mirror to > > the other from the point of view of an observer that is stationary > > w.r.t. the clock T and the time from the point of view that is moving > > w.r.t. the clock T. Gamma is defined as the ratio between these two > > times. > > Gamma = T / T > > The distance between the mirrors is D and the moving point of view is > > moving with velocity V along the X axis. > > From the stationary point of view the time for the light to bounce > > between the mirrors is just D divided by the speed of light. > > T = D / C > > From the moving point of view the light traces out a diagonal path and > > a right triangle is needed to analyze this motion. The light path is > > the hypotenuse of the triangle and its length is the speed of light > > times the time it takes for the light to bounce between the mirrors, > > CT. The vertical leg of the triangle is the distance between the > > mirrors, D. The horizontal leg of the triangle is the distance the > > moving point of view moves in the time it takes for the light to > > bounce between the mirrors, VT. So from the Pythagorean theorem we > > have > > (CT)^2 = (VT)^2 + D^2 > > (CT)^2 (VT)^2 = D^2 > > T^2(C^2 V^2) = D^2 > > T^2 = D^2 / (C^2 V^2) > > T = D / sqrt(C^2 V^2) > > So > > Gamma = T / T > > Gamma = (D / sqrt(C^2 V^2)) / (D / C) > > Gamma = C / sqrt(C^2 V^2) > > Gamma = 1 / sqrt((C^2 V^2) / C^2) > > Gamma = 1 / sqrt(1 V^2 / C^2) > > > The second way I stumbled on to when I tried to derive the LTE from an > > idea I had. The first step was to find transformation equations that > > embodied the principle of the constancy of the speed of light (PCSL). > > It was so long ago I dont remember how I did it but I came up with > > this: > > X = X VT > > T = T VX / C^2 > > > So the reverse transform is > > X = X + VT > > T = T + VX / C^2 > > The next step was to see if these equations satisfy the principle of > > relativity (POR) > > In this case it means when the reverse transform is applied to the > > forward transform you should end up with > > X = X > > T = T > > > However when I applied the reverse transform to the forward transform > > I got > > X = X(1 V^2 / C^2) > > T = T(1 V^2 / C^2) > > > POR not satisfied. I realized if I could somehow get 1 / (1 V^2 / > > C^2) into the equations it would divide out. I also realized for the > > equations to satisfy the POR they had to be symmetrical, the forward > > and reverse equations have to have the same form. So I tried > > multiplying everything by 1 / sqrt(1 V^2 / C^2). This worked. The > > final equations are: > > X = (X VT) (1 / (1 V^2 / C^2)) > > T = (T VX / C^2) (1 / (1 V^2 / C^2)) > > X = (X + VT) (1 / (1 V^2 / C^2)) > > T = (T + VX / C^2) (1 / (1 V^2 / C^2)) > > > These are of course the LTE. They embody the PCSL and satisfy the POR > > and > > gamma is 1 / sqrt(1 V^2 / C^2). > > From this I realized the role that gamma plays in the LTE is to > > reconcile the PCSL with the POR. > > > Btw I didnt use c + v or c v here but you are wrong that the use of > > them (under certain circumstances) is self-contradictory > > oops! somehow sqrt dropped out of my copy/paste. Those LTE's should of > course be > X = (X VT) (1 / sqrt(1 V^2 / C^2)) > T = (T VX / C^2) sqrt(1 / (1 V^2 / C^2)) > X = (X + VT) (1 / sqrt(1 V^2 / C^2)) > T = (T + VX / C^2) sqrt(1 / (1 V^2 / C^2)) I'm getting to old for this. Once more X = (X VT) (1 / sqrt(1 V^2 / C^2)) T = (T VX / C^2) (1 / sqrt(1 V^2 / C^2)) X = (X + VT) (1 / sqrt(1 V^2 / C^2)) T = (T + VX / C^2) (1 / sqrt(1 V^2 / C^2)) I realize these are algebraically equivalent but I just like to keep the form consistent.
From: waldofj on 3 Jan 2010 16:29 On Dec 30 2009, 5:14 am, "Inertial" <relativ...(a)rest.com> wrote: > "waldofj" <wald...(a)verizon.net> wrote in message > > news:6a683279-f568-4167-81da-09183fb86d51(a)d20g2000yqh.googlegroups.com... > > >> > p xor q => p or q, dumby? Explain us what this is not true. > > >> Easy as 1,2,3, 4. > > >> 1) (FALSE xor FALSE) = TRUE > >> 2) (FALSE or FALSE) = FALSE > >> 3) (TRUE(from 1) => FALSE(from 2) ) = NOT TRUE > >> Happy now, moortel's rent boy? > > > just for the record: > > 1) (TRUE xor TRUE) = FALSE > > 2) (TRUE or TRUE) = TRUE > > 3) (FALSE(from 1) => TRUE(from 2) ) = NOT TRUE > > (FALSE => TRUE) = TRUE > > seehttp://en.wikipedia.org/wiki/Material_implication > > Gees .. you guys just don't know your logic. hey inertial, I never did thank you for the link. I was just correcting Androcles' use of the xor function. I didn't realize what => was. My teachings in logic, part of my CS curriculum in college didn't go that far. I like this stuff and I see I have some studying to do...... thanx
From: Inertial on 3 Jan 2010 17:23 "Henry Wilson DSc" <..@..> wrote in message news:pp22k5ptf1v81v0jlm2abjp6d0j2d42p9n(a)4ax.com... > On Sun, 3 Jan 2010 09:10:03 +1100, "Inertial" <relatively(a)rest.com> wrote: > >> >>"Henry Wilson DSc" <..@..> wrote in message >>news:1afvj5lapsqlrsl76hkcbnq14mr7fhiuda(a)4ax.com... >>> On Sat, 02 Jan 2010 13:23:35 -0800, eric gisse >>> <jowr.pi.nospam(a)gmail.com> > >>> >>>>Can >>>>you name ONE actual performed experiment that agrees with your claim >>>>that >>>>SR >>>>is wrong? >>> >>> Fizeau. >> >>Wrong > > see renshaw's paper. No need. SR completely explains Fitzeau.
From: Inertial on 3 Jan 2010 17:24 "waldofj" <waldofj(a)verizon.net> wrote in message news:08e49ba0-9c9c-4fb7-a2ff-7e1d388b6cc2(a)z7g2000vbl.googlegroups.com... > On Dec 30 2009, 5:14 am, "Inertial" <relativ...(a)rest.com> wrote: >> "waldofj" <wald...(a)verizon.net> wrote in message >> >> news:6a683279-f568-4167-81da-09183fb86d51(a)d20g2000yqh.googlegroups.com... >> >> >> > p xor q => p or q, dumby? Explain us what this is not true. >> >> >> Easy as 1,2,3, 4. >> >> >> 1) (FALSE xor FALSE) = TRUE >> >> 2) (FALSE or FALSE) = FALSE >> >> 3) (TRUE(from 1) => FALSE(from 2) ) = NOT TRUE >> >> Happy now, moortel's rent boy? >> >> > just for the record: >> > 1) (TRUE xor TRUE) = FALSE >> > 2) (TRUE or TRUE) = TRUE >> > 3) (FALSE(from 1) => TRUE(from 2) ) = NOT TRUE >> >> (FALSE => TRUE) = TRUE >> >> seehttp://en.wikipedia.org/wiki/Material_implication >> >> Gees .. you guys just don't know your logic. > > hey inertial, > I never did thank you for the link. I was just correcting Androcles' > use of the xor function. I didn't realize what => was. My teachings in > logic, part of my CS curriculum in college didn't go that far. I like > this stuff and I see I have some studying to do...... > thanx You are more than welcome.
From: Inertial on 3 Jan 2010 17:26
"Henry Wilson DSc" <..@..> wrote in message news:6132k5l90k7akhsl4hg1dfns658au2ht5p(a)4ax.com... > On Sun, 3 Jan 2010 09:07:54 +1100, "Inertial" <relatively(a)rest.com> wrote: > >> >>"eric gisse" <jowr.pi.nospam(a)gmail.com> wrote in message >>news:hhod94$nht$3(a)news.eternal-september.org... >>> ..@..(Henry Wilson DSc) wrote: >>> >>>> On Sat, 02 Jan 2010 12:19:51 -0800, eric gisse >>>> <jowr.pi.nospam(a)gmail.com> > >>>> If you accept that these two are fundamental dimensions then that might >>>> be >>>> OK.... but maybe the two quantities are themselves expressible in terms >>>> of >>>> other dimension about which we know nothing. >>>> >>>> So I would stick by my claim that the whole area is pretty vague, >>>> wouldn't >>>> you agree. >>> >>> What book did you study E&M from? >> >>I think we can extend the 'Henry doesn't know, doesn't care, and can't >>understand it" principle to many areas of physics, not just SR. He really >>needs a new hobby, one that a knows something about, cares about, and >>understands (if there is such a thing) because he is a failure at physics. > > Not interested in the two mirror problem, eh? No .. you're not really .. because we've shown you that it doe not refute SR nor show any internal or logical inconsistency. All you've done is shown that SR says different things to the theory you think is right, and that you don't know or care what SR actually says anyway (whether it is right or not). That does not refute SR. |