From: roberts@CMR.NCSL.NIST.GOV (John Roberts)
Newsgroups: sci.space
Subject: Re: Relativity
Date: 4 Sep 92 11:21:50 GMT
Organization: National Institute of Standards and Technology
	formerly National Bureau of Standards


-From: vincent@reg.triumf.ca (pete)
-Subject: Re: What is the speed of light measured from?
-Date: 3 Sep 92 12:44:00 GMT
-Organization: dept. of theophysics and cosmogyny

-stgprao@st.unocal.COM (Richard Ottolini) writes...
->vincent@reg.triumf.ca (pete) writes:
->>Neglecting the engineering problems of high speed travel through an
->>imperfect vacuum, you can travel light centuries in subjective
->>hours if you accelerate long enough. If you arrive at the Andromeda
->>galaxy 2 weeks after leaving earth, you could be justified in
->>thinking you travelled faster than c. It's just that the rest of 
->>the universe will have aged 2x10^8 years.
-> 
->No. You would not feel you are going faaster, but the universe got smaller
->and slower.  These are stardard result of Special Relativity.

-*sigh* ...I should just learn to keep my mouth shut.
-OK consider: you've accelerated to .99999 c relative to your 
-original frame. Tangential to your world line at that instant
-is an inertial frame, in which your speed is instantaneously 0.
-Now consider this new frame to be the rest frame, and your
-velocity relative to it is small, but steadily increasing as
-you continue your constant acceleration. Clearly, a newtonian
-approximation of your situation considered from this frame
-will conclude that you continue to experience the full force
-of your acceleration, just as you did when you first started
-from your initial rest frame. That is, just because you are
-traveling at nearly c relative to your initial frame doesn't
-mean that in your frame you sense your acceleration decreasing.
-And you have absolutely no reason to model the universe outside
-as getting smaller. That's just silly. 

But length of objects in other frames of reference *does* decrease by the
factor of the Lorenz contraction, same as passage of time. (And effective
mass increases by one over this factor.) If you're in a fast spaceship,
and you use a Doppler radar to determine your velocity relative to the
objects around you, you will always get a value less than c. If it's
going to take an hour of subjective time (at constant velocity) to
reach the Andromeda galaxy then any measurement of the distance to the
galaxy will put it at less than one light-hour.

There are several factors which have to be considered, and which are
often left out of popular accounts of relativity:

 - There is often considerable confusion between what can be observed
   within a particular frame of reference and what a person in that frame
   of reference would see. For the single observer, the lightspeed delay
   of information on its way to the observer has to be taken into account.
   Contrary to popular opinion, it's possible to set up a coordinated time
   system throughout a frame of reference, and it's valid to say that
   two events within a given frame of reference that took place a great
   distance apart were simultaneous. Simultaneity between two different
   frames of reference has no meaning. (A "frame of reference" includes 
   all the objects in the universe that are motionless with respect to
   one another.)

 - Special relativity only applies directly to objects that are not
   undergoing acceleration. For something that's accelerating, you need
   general relativity, which has much harder math. People often throw in
   acceleration when it's not needed as part of a thought experiment on
   special relativity. Even with acceleration, you will never observe
   anything that will lead you to believe that you're moving faster than
   the speed of light with respect to anything else. A single observer
   may still see some interesting effects due to the previously-mentioned
   lightspeed delay in receiving information. For instance, if a spacecraft
   is moving toward Earth at nearly the speed of light, its position as
   you observe it will appear to translate toward the Earth at a much greater
   rate than the speed of light. However, blueshift measurement will show
   that it's actually traveling slower than light, and if you set up
   a network of observers through your frame of reference with synchronized
   clocks, they will show that the spacecraft is moving slower than light.

John Roberts
roberts@cmr.ncsl.nist.gov