Derivation of Lorentz Transformation

<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote"><i>Originally posted by Larry Burford</i>
<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote"><i>Originally posted by Thomas</i>
" ... but I think this could be due to the light propagating in the earth's magnetic field (which thus constitutes an absolute reference frame) ... "<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">

Earth's magnetic field, like Earth's electrical and gravitational fields, is a local phenomenon and therefore cannot be be used as absolute frame. The proper term when using any of them as a frame of reference is "locally prefered frame". Move to another planet, and you move to a different, and totally independent, locally preferred frame of reference.<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">
That's what I actually meant. I was not suggesting that the 'absolute' reference frame is the same everywhere.

<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote"><i>Originally posted by Larry Burford</i>
<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote"><i>Originally posted by Thomas</i>
" ... (although this might only apply in a vacuum and for sufficiently weak magnetic fields)."<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">

According to General relativity (which inherits its maximum speed limit and constancy of light speed for all observes from SR) the speed of light in a vacuum is a function of gravitational potential. The speed of light measured at two different altitudes (both above Earth's atmosphere on a very tall tower) will be different. Electric and magnetic fields do not seem to have any (detectable) impact, as judged by years of measurements of GPS signals looking for such things. (But stand by - newer and better GPS satellites, along with newer and better experiments, are in the planning stages.)<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">

That's obviously a matter of interpretation and presumes that GR is right. If you reject the possibility that light can be affected by gravity and assume instead that the 'gravitational bending' is caused by electric or magnetic fields that exist in the plasma halos around corresponding astronomical objects, then you can not say a priori that the data rule out the latter.
Obviously, clarity in this respect can only be achieved by less ambiguous observations, i.e. on the one hand by controlled laboratory experiments examining the bending of light (or not) in sufficiently strong electric field (gradients), and on the other by observations of the bending of starlight (or not) by massive objects that can be assumed to have a negligible plasma halo (e.g. the moon).
With regard to the Sagnac effect, note also that all experiments I am aware of were performed in the presence of the earth's magnetic field. The same can obviously also be said for Sagnac gyros on ships, airplanes and even earthbound satellites (and I am not aware of any interplanetary space probes that would have used Sagnac-gyros). So you actually don't know what the result of the experiments would be without a magnetic field.

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You make some good points, but consider this. Gravitational fields are extremely constant in both magnitude and direction over long and short periods of time.

Electrical and magnetic fields are extremely variable in both magnitude and direction over long and short periods of time.

Since we don't see any variations in things like light bending and clock rate changes, except those caused by moving the experiment or observation to a different place (IOW, to a different gravitational potential), it seems more likely that gravity is the cause.

Food for thought,
LB

But this gives me an idea. Hmmm. I'll do some research and see if it holds water. Thanks.

<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote"><i>Originally posted by Larry Burford</i>
<br />You make some good points, but consider this. Gravitational fields are extremely constant in both magnitude and direction over long and short periods of time.

Electrical and magnetic fields are extremely variable in both magnitude and direction over long and short periods of time.

Since we don't see any variations in things like light bending and clock rate changes, except those caused by moving the experiment or observation to a different place (IOW, to a different gravitational potential), it seems more likely that gravity is the cause.
<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">

Don't forget that for long and extended data sets (which are typically used for these kind of observations), any variations tend to average out.
Anyway, in some case like the Haefele-Keating experiment for instance, the results did not appear to have been so clearcut after all (see www.dipmat.unipg.it/~bartocci/H&KPaper.htm ). With regard to this particular experiment, I have actually suggested that the 'clock dilation' is caused by the Lorentz force associated with the motion of the airplane with regard to the earth's magnetic field; this should lead to a change of the atomic energy potentials and hence to a change of the transition frequencies; see my webpage www.physicsmyths.org.uk/discussions/relativity1.htm#dcooper (my reply to David Cooper about 2/3 down the page) for more.

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Hmmm. Interesting.

Sounds like it is time to break some hardware. (Experimental physicists tend to believe that until you break some stuff you aren't learning anything of value to mankind. Or yourself. The more expensive the stuff you break, the more you learn. If you can afford to fix it and try again.) Atomic clocks are widely availble from companies like HP. Magnetic fields (constant, variable, stationary, moving, and various combinations thereof) are very easy to generate in the lab. Or in the garage. If they are responsible for the effects currently attributed to gravitational fields you should be able to demonstrate this with relative ease. And collect a Nobel in the process.

Good luck. Keep us posted.

LB

Just in order to avoid any confusion: I have only corrected a typo in one of my earlier posts.

Thomas

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Just an update on this: I have discussed now the inconsistencies in the Derivation of the Lorentz Transformation in some detail on my Relativity Discussion Page . I think this should further clarify the matter.

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