Twins Paradox doesn't add up with light
in [Relativity]
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From: Darwin123 on 10 May 2010 13:17 Darwin123 09 May 2010 The following is a direct quote from Einstein On the Influence of Gravitation on the Propagation of Light, by Albert Einstein in The Principle of Relativity, by H.A. Lorentz, A. Einstein, H. Minkowski, and H. Weyl. (published 1923) Page 107 If we call the velocity of light at the origin of the co-ordinates c_0, then the velocity of light at a place with gravitational potential phi will be given by the relation, c=c_0(1+phi/c^2) (3) The principle of the constancy of the velocity of light holds good in this theory in a different form from what usually underlies the theory of relativity. The "usual form" means in the inertial frame. However, the traveling twin is in an accelerating frame, not an inertial frame. He knows he is accelerating because his accelerometer says zero acceleration. From the traveling twin standpoint, the stationary twin is in a positive gravitational potential. So from the traveling twin viewpoint, c>c_0. The stationary twin can use the "usual" principle of the speed of light. He knows he is not accelerating because his acclerometer says zero acceleration. So the stationary twin sees the traveling twin in a zero gravitational potential. So phi=0 and c=c_0. Your calculations are valid for the stationary twin only. I assume that you know first term undergraduate calculus. If you want to confirm some of the results yourself (like I did) without knowing a great deal about general relativity, try the following. Use the complete Lorentz transformation for time: t'=t(1+vx/c^2) Differentiate t' by t. In other words, find dt'/dt. Substitute in the dynamic acceleration, g, where g=dv/dx. Also set g as in Newton's Law. g=F/m where F is the corresponding external force (i.e., F is the "effective gravitational field") on the appropriate twin and m is the mass of the twin. You will find dt'/dt in terms of both velocity v and external force F. I think you will find the formula useful. Please let us know when you are done finding dt'/dt.
From: Darwin123 on 10 May 2010 13:29 On May 10, 1:17 pm, Darwin123 <drosen0...(a)yahoo.com> wrote: Correction. I forgot the gamma. > I assume that you know first term undergraduate calculus. If you > want to confirm some of the results yourself (like I did) without > knowing a great deal about general relativity, try the following. Use > the complete Lorentz transformation for time: > t'=t(1+vx/c^2)/sqrt(1-v^2/c^2) > Differentiate t' by t. In other words, find dt'/dt. > Substitute in the dynamic acceleration, g, > where > g=dv/dx. > Also set g as in Newton's Law. > g=F/m > where F is the corresponding external force (i.e., F is the "effective gravitational field") on the appropriate twin > and m is the mass of the twin. > You will find dt'/dt in terms of both velocity v and external > force F. I think you will find the formula useful. > Please let us know when you are done finding dt'/dt. gamma=sqrt(1-v^2/c^2). It is an unavoidable part of the Lorentz transformation. I corrected the corresponding formula above. c=speed of light in an inertial frame. v is the speed of the traveling twin. t is the time in the inertial frame of the stationary twin. t' is time in the traveling twin frame. Note that dt'/dt has a dependence on F and m. This is usually left out of introductory courses on relativity. Did I answer your original question in the OP?
From: Darwin123 on 10 May 2010 16:18 On May 10, 1:29 pm, Darwin123 <drosen0...(a)yahoo.com> wrote: > > I assume that you know first term undergraduate calculus. If you > > want to confirm some of the results yourself (like I did) without > > knowing a great deal about general relativity, try the following. Use > > the complete Lorentz transformation for time: > > t'=t(1+vx/c^2)/sqrt(1-v^2/c^2) > > Differentiate t' by t. In other words, find dt'/dt. > > Substitute in the dynamic acceleration, g, > > where > > g=dv/dx. > > Also set g as in Newton's Law. > > g=F/m > > where F is the corresponding external force (i.e., F is the "effective gravitational field") on the appropriate twin > > and m is the mass of the twin. > > You will find dt'/dt in terms of both velocity v and external > > force F. I think you will find the formula useful. > > Please let us know when you are done finding dt'/dt. > > gamma=1/sqrt(1-v^2/c^2). It is an unavoidable part of the Lorentz > transformation. I corrected the corresponding formula above. > c=speed of light in an inertial frame. > v is the speed of the traveling twin. > t is the time in the inertial frame of the stationary twin. > t' is time in the traveling twin frame. > Note that dt'/dt has a dependence on F and m. This is usually left out > of introductory courses on relativity. > Did I answer your original question in the OP?
From: Darwin123 on 11 May 2010 19:46 On May 11, 2:32 am, "Inertial" <relativ...(a)rest.com> wrote: > "Darwin123" <drosen0...(a)yahoo.com> wrote in message > > news:119fa2bd-f990-455f-8071-cdea9453059d(a)k29g2000yqh.googlegroups.com... > > > > > On May 11, 1:25 am, "Inertial" <relativ...(a)rest.com> wrote: > >> "Darwin123" <drosen0...(a)yahoo.com> wrote in message > > >>news:4a209de4-f68d-4729-a656-f501a3ad6231(a)s29g2000yqd.googlegroups.com.... > > >> > On May 10, 5:52 pm, "Androcles" <Headmas...(a)Hogwarts.physics_z> wrote: > >> >> "Darwin123" <drosen0...(a)yahoo.com> wrote in message > Did you see his old assertion that there is a smallest finite positive > number? .. he claimed it is the non-zero difference between 0.999.... and > 1. Bahaha No I didn't. However, I saw a similar claim by another nut. "Thomas E. Phipps" is another crazy man who writes books "refuting" relativity and other physics. In one of his books, he claims that the small angle formula in trigonometry is wrong. this is the claim that to first order, for A<<1 in radians, sinA=A. Note, this is a first order formula. How did he prove it wrong? He used his calculator, which he is very proud of. He made a table of values where A gets smaller and smaller. He found it leveled off at some value. Did I hear you say, "truncation error"? Yes, the truncation error will do that. I collect psychopaths. By definition, that makes me one too. Sorry.
From: Inertial on 11 May 2010 20:37
"Darwin123" <drosen0000(a)yahoo.com> wrote in message news:cc5e3a8c-d47d-4750-94b2-83e88ee2c9f8(a)a21g2000yqn.googlegroups.com... > On May 11, 2:32 am, "Inertial" <relativ...(a)rest.com> wrote: >> "Darwin123" <drosen0...(a)yahoo.com> wrote in message >> >> news:119fa2bd-f990-455f-8071-cdea9453059d(a)k29g2000yqh.googlegroups.com... >> >> >> >> > On May 11, 1:25 am, "Inertial" <relativ...(a)rest.com> wrote: >> >> "Darwin123" <drosen0...(a)yahoo.com> wrote in message >> >> >>news:4a209de4-f68d-4729-a656-f501a3ad6231(a)s29g2000yqd.googlegroups.com... >> >> >> > On May 10, 5:52 pm, "Androcles" <Headmas...(a)Hogwarts.physics_z> >> >> > wrote: >> >> >> "Darwin123" <drosen0...(a)yahoo.com> wrote in message > >> Did you see his old assertion that there is a smallest finite positive >> number? .. he claimed it is the non-zero difference between 0.999.... >> and >> 1. Bahaha > No I didn't. However, I saw a similar claim by another nut. > "Thomas E. Phipps" is another crazy man who writes books > "refuting" relativity and other physics. In one of his books, he > claims that the small angle formula in trigonometry is wrong. this is > the claim that to first order, for A<<1 in radians, > sinA=A. > Note, this is a first order formula. How did he prove it wrong? He > used his calculator, which he is very proud of. He made a table of > values where A gets smaller and smaller. He found it leveled off at > some value. > Did I hear you say, "truncation error"? Yes, the truncation error > will do that. Oh dear > I collect psychopaths. By definition, that makes me one too. Sorry. Always good to have a hobby :):) |