Wonderful!
in [Physics]
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From: mpc755 on 30 Dec 2009 15:07 On Dec 30, 2:52 pm, moro...(a)world.std.spaamtrap.com (Michael Moroney) wrote: > mpc755 <mpc...(a)gmail.com> writes: > >On Dec 29, 7:14=A0pm, mpc755 <mpc...(a)gmail.com> wrote: > >> The Observer at M' knows the light is propagating at w through the > >> water at rest with respect to the embankment. The Observer at M' also > >> knows the light from the lightning strike at B/B' and the train are > >> moving relative to each other through the water at rest with respect > >> to the embankment at velocity ~ w+v(1-w^2/c^2) and the light from the > >> lightning strike at A/A' and the train are moving relative to each > >> other through the water at rest with respect to the embankment at > >> velocity ~ w-v(1-w^2/c^2). > > Amazing. You are actually using a more accurate approximation rather than > the known-wrong Gallilean you've been using all along until now. I do > want to point out that this approximation assumes a relatively small v, > you've beem using v=0.25 c so it may not be that accurate. But for now, > it will do. > > >Let's plug in some numbers to make this easier to conceptualize. > > OK. > > >A' and B' are each 1 light year from M'. Let's assume the light waves > >propagate in the water at rest with respect to the embankment at .75c. > >Let's also assume the train is moving at .25c relative to the > >embankment (which means the train is moving at .25c relative to the > >water at rest with respect to the embankment). > > OK. > > >The light wave from the lightning strike in the water at B/B' reaches > >M'. The Observer on the train measure to B' and determines it to be 1 > >light year from M'. > > OK. > > > The Observer on the train factors in the train is > >moving at .25c relative to the water at rest with respect to the > >embankment and factors in the light wave traveled at .75c relative to > >the water at rest with respect to the embankment > > OK. > > > and determines the > >light wave must have been created 1 year ago. > > Hey! I thought you wanted to plug in the numbers. You went back to the > known wrong Galilean, and ignored the formula in the post you quoted, > that you yourself wrote! > > FLUNK! > > I'll plug in the numbers for you. Light velocity from B' to M': > > W = w+v(1-w^2/c^2). W = (0.75c + 0.25c(1-(0.75c^2/c^2))) --> > W = 0.75c + 0.25c(1-0.5625) --> W = 0.75c + 0.25c * 0.4375 --> > W = 0.75 + 0.1094. W = 0.8594. > > Light velocity from A' to M': > > W = w-v(1-w^2/c^2). W = (0.75c - 0.25c(1-(0.75c^2/c^2))) --> > W = 0.75c - 0.25c(1-0.5625) --> W = 0.75c - 0.25c * 0.4375 --> > W = 0.75 - 0.1094. W = 0.6406 > > [snip incorrect conclusions based on wrong math] > > I'll let you fix your own work, now that you have the correct numbers. > > === > > However, as mentioned, the formula W = w+v(1-w^2/c^2) is an approximation > assuming v is nonrelativistic. Let's see some more accurate figures: > > u = (v+w)/(1+vw/c^2). For v=0.25c and w = 0.75c (B' to M') we get: > u = (1.0c)/(1+.1875) = 1.0c/1.1875 = 0.8421 c. > > For the opposite direction (A' to M'), v = -0.25c, so we have: > u = (0.75c-0.25c)/(1-.1875) = 0.50c/0.8125 = 0.6154. > > We see that v is large enough that the earlier approximation (based on a > nonrelativistic v) isn't that accurate in this case. It's off by several > percent. But you can use either pair of numbers. And what does all this have to do with the Observer at M' determining the simultaneity of the lighting strikes? The Observer at M' knows the relative velocity of the train and the light propagating towards M' from the lightning strike at B/B' is going to be greater than the relative velocity of the train and the light propagating towards M' from the lighting strike at A/A'. The only velocity of light that matters is the velocity w with respect to the water at rest with respect to the embankment. With your numbers above, plus factoring in the distance A' is from M' and the distance B' is from M', and factoring the difference in time between the light from B/B' arriving at M' and the light from A/A' arriving at M', and factoring in the trains speed relative to the embankment, giving the Observer at M' the speed of the train relative to the water at rest with respect to the embankment, the Observer at M' concludes the lightning strikes were simultaneous.
From: Michael Moroney on 30 Dec 2009 16:09 mpc755 <mpc755(a)gmail.com> writes: >With your numbers above, plus factoring in the distance A' is from M' >and the distance B' is from M' and factoring in the trains speed >relative to the embankment, giving the Observer at M' the speed of the >train relative to the water at rest with respect to the embankment, >the Observer at M' concludes the lightning strikes were simultaneous. Show the math.
From: mpc755 on 30 Dec 2009 18:04 On Dec 30, 4:09 pm, moro...(a)world.std.spaamtrap.com (Michael Moroney) wrote: > mpc755 <mpc...(a)gmail.com> writes: > >With your numbers above, plus factoring in the distance A' is from M' > >and the distance B' is from M' and factoring in the trains speed > >relative to the embankment, giving the Observer at M' the speed of the > >train relative to the water at rest with respect to the embankment, > >the Observer at M' concludes the lightning strikes were simultaneous. > > Show the math. The Observer knows the water is at rest with respect to the embankment. The Observer knows the light is traveling at 0.75c relative to the water at rest with respect to the embankment. The Observer knows the train is moving at 0.25c relative to the water at rest with respect to the embankment. The Observer measures to B' and notes it is one light year from M'. The Observer notes light from B' will travel at 0.8421c relative to the trains speed and the lights speed relative to the water at rest with respect to the embankment in the direction from B' towards M'. The Observer measures to A' and notes it is one light year from M'. The Observer notes light from A' will travel at 0.6154c relative to the trains speed and the lights speed relative to the water at rest with respect to the embankment in the direction from A' towards M'. The Observer at M' notes the time on the clock at M' when the light from the lightning strike at B/B' arrives at M'. Based on the light traveling at 0.8421c relative to the train and the light traveling relative to the water at rest with respect to the embankment, the Observer at M' concludes the lightning strike at B/B' occurred 0.75c from where M' is relative to the water at rest with respect to the embankment when the light from the lightning strike at B/B' arrived at M'. Since light travels at 0.75c in stationary water, the Observer at M' concludes the lightning strike at B/B' occurred one year prior to the light arriving at M'. The light from the lightning strike at A/A' arrives at M'. Based on the light traveling at 0.6154c relative to the train and the light traveling relative to the water at rest with respect to the embankment, the Observer at M' concludes the lightning strike at A/A' occurred 1.5c from where M' is relative to the water at rest with respect to the embankment when the light from the lightning strike at A/A' arrived at M'. Since light travels at 0.75c in stationary water, the Observer at M' concludes the lightning strike at A/A' occurred two years prior to the light arriving at M'. Since the clock at M' notes one year has passed between the light from B/B' arriving at M' and the light from A/ A' arriving at M', the Observer at M' concludes the lightning strikes were simultaneous.
From: mpc755 on 30 Dec 2009 18:13 On Dec 30, 4:09 pm, moro...(a)world.std.spaamtrap.com (Michael Moroney) wrote: > mpc755 <mpc...(a)gmail.com> writes: > >With your numbers above, plus factoring in the distance A' is from M' > >and the distance B' is from M' and factoring in the trains speed > >relative to the embankment, giving the Observer at M' the speed of the > >train relative to the water at rest with respect to the embankment, > >the Observer at M' concludes the lightning strikes were simultaneous. > > Show the math. The Observer knows the water is at rest with respect to the embankment. The Observer knows the light is traveling at 0.75c relative to the water at rest with respect to the embankment. The Observer knows the train is moving at 0.25c relative to the water at rest with respect to the embankment. The Observer measures to B' and notes it is one light year from M'. The Observer notes light from B' will travel at 0.8421c relative to the trains speed and the lights speed relative to the water at rest with respect to the embankment in the direction from B' towards M'. The Observer measures to A' and notes it is one light year from M'. The Observer notes light from A' will travel at 0.6154c relative to the trains speed and the lights speed relative to the water at rest with respect to the embankment in the direction from A' towards M'. The Observer at M' notes the time on the clock at M' when the light from the lightning strike at B/B' arrives at M'. Based on the light traveling at 0.8421c relative to the train and the light traveling relative to the water at rest with respect to the embankment, the Observer at M' concludes the lightning strike at B/B' occurred 0.75c from where M' is relative to the water when the light from the lightning strike at B/B' arrived at M'. Since light travels at 0.75c in stationary water, the Observer at M' concludes the lightning strike at B/B' occurred one year prior to the light arriving at M'. The light from the lightning strike at A/A' arrives at M'. Based on the light traveling at 0.6154c relative to the train and the light traveling relative to the water at rest with respect to the embankment, the Observer at M' concludes the lightning strike at A/A' occurred 1.5c from where M' is relative to the water when the light from the lightning strike at A/A' arrived at M'. Since light travels at 0.75c in stationary water, the Observer at M' concludes the lightning strike at A/A' occurred two years prior to the light arriving at M'. Since the clock at M' notes one year has passed between the light from B/B' arriving at M' and the light from A/A' arriving at M', the Observer at M' concludes the lightning strikes were simultaneous.
From: mpc755 on 30 Dec 2009 18:16
On Dec 30, 4:09 pm, moro...(a)world.std.spaamtrap.com (Michael Moroney) wrote: > mpc755 <mpc...(a)gmail.com> writes: > >With your numbers above, plus factoring in the distance A' is from M' > >and the distance B' is from M' and factoring in the trains speed > >relative to the embankment, giving the Observer at M' the speed of the > >train relative to the water at rest with respect to the embankment, > >the Observer at M' concludes the lightning strikes were simultaneous. > > Show the math. The Observer knows the water is at rest with respect to the embankment. The Observer knows the light is traveling at 0.75c relative to the water at rest with respect to the embankment. The Observer knows the train is moving at 0.25c relative to the water at rest with respect to the embankment. The Observer measures to B' and notes it is one light year from M'. The Observer notes light from B' will travel at 0.8421c relative to the trains speed and the lights speed relative to the water at rest with respect to the embankment in the direction from B' towards M'. The Observer measures to A' and notes it is one light year from M'. The Observer notes light from A' will travel at 0.6154c relative to the trains speed and the lights speed relative to the water at rest with respect to the embankment in the direction from A' towards M'. The Observer at M' notes the time on the clock at M' when the light from the lightning strike at B/B' arrives at M'. Based on the light traveling at 0.8421c relative to the train and the light traveling relative to the water at rest with respect to the embankment, the Observer at M' concludes the lightning strike at B/B' occurred 0.75c from where M' is relative to the water when the light from the lightning strike at B/B' arrived at M'. Since light travels at 0.75c in stationary water, the Observer at M' concludes the lightning strike at B/B' occurred one year prior to the light arriving at M'. The light from the lightning strike at A/A' arrives at M'. Based on the light traveling at 0.6154c relative to the train and the light traveling relative to the water at rest with respect to the embankment, the Observer at M' concludes the lightning strike at A/A' occurred 1.5c from where M' is relative to the water when the light from the lightning strike at A/A' arrived at M'. Since light travels at 0.75c in stationary water, the Observer at M' concludes the lightning strike at A/A' occurred two years prior to the light arriving at M'. Since the clock at M' notes one year has passed between the light from B/B' arriving at M' and the light from A/A' arriving at M', the Observer at M' concludes the lightning strikes were simultaneous. |