Re: starship-design: Re: FTL travel

[Steve VanDevender <stevev@efn.org>]

Curtis Manges writes:
 > Steve VanDevender wrote:
 > >  > > It's no more dogmatic than any other physics text I've read;
 > >  >
 > >  > that's scary . . .
 > >
 > > I suspect that if physics texts contained the amount of philosophical
 > > hand-wringing needed to satisfy you, they'd be twice as big and even
 > > harder to read.
 > 
 > Pity's sake, Steve, I was trying to have some fun there. Excuse me
 > for failing to append the ;-) to it. And, no, I don't want
 > philosophical hand wringing (whatever that is) any more than I want
 > dogma, I want _information_, I want _instruction_, and I want it
 > clear, concise, and step by step, with each step explained fully, so
 > that when I'm done working through it, I have understanding and
 > confidence.

Sorry, it just wasn't apparent to me that your comment was meant in
fun.

I have seen different people approach teaching counterintuitive subjects
in different ways.  Some like to start with the theoretical basis and
work towards practical understanding only after the theory has been
completely explained.  Others may try to give at least some practical
understanding without explaining all the theory behind it first, the
idea being that intuitive understanding often comes from being able to
play with a concept even if you don't fully understand it yet.  Taylor
and Wheeler seem to prefer the latter approach.  If you read the whole
book you will find that they don't just wave something in front of you
never to explain it in full, but they do present some things as matters
of fact so you can practice working with them, then explain why things
happen that way later.

It also occurs to me that there is another book on relativistic physics
that I can recommend which you might like better: _Six Not-So-Easy
Pieces_ derived from Richard P. Feynman's Caltech physics lectures.  It
also has an excellent discussion of mathematical symmetry in physics in
the first couple of chapters.

 > > You apparently don't understand the idea of spacetime interval well
 > > enough to properly criticize it.
 > 
 > Again, I do understand what Lorentz did: he took a right triangle,
 > labeled "a" as space and "b" as time, or vise versa, applied
 > Pythagorean theorem, and got space-time as the hypotenuse, "c". Very
 > elegant, very simple.

Unfortunately I don't think you've fairly summarized what Lorentz did.

Lorentz originally derived the Lorentz transform to obtain a formulation
of Maxwell's equations of electromagnetism that would be invariant with
respect to velocity.  Only later did Einstein propose the (for the time)
radical idea that the Lorentz transform could be used to transform space
and time coordinates in general, producing predictions for high speeds
that would be very different from the then-conventional Newtonian
predictions.

Also note that the spacetime interval is _not_ Pythagorean; for a vector
(t, x, y, z) the interval is sqrt(t^2 - x^2 - y^2 - z^2), not the
hypotenuse sqrt(t^2 + x^2 + y^2 + z^2).  The negative signs make all the
difference; they are the underlying mathematical reason counterintutive
things happen in relativity, such as curved paths through spacetime
being shorter than straight ones.  The geometry of spacetime, even in
special relativity, is not Euclidean.

 > What I _don't_ understand is how he _got away_ with it. Here's how I
 > see it:
 > 
 > (1) time is not a property of space (otherwise you could answer the
 > question, "How many seconds are in a cubic meter?", or, for that
 > matter, even "How many seconds are in a meter?")

Even in unified units, "How many seconds are in a cubic meter?" is
meaningless, because the left-hand side would have units of distance
while the right-hand side has units of distance^3; you can't ask "how
many meters in a cubic meter", either.  However, there is an answer to
"How many seconds are in a meter?" -- there are 299,792,458 meters in a
second, so a meter is 1/299,792,458 seconds.

 > (2) time and space are, therefor, unlike terms

This is really what the "parable of the surveyors" that opens _Spacetime
Physics_ is about.  Pre-relativistic physics considered time and space
to be completely unlike and incomparable things, just as the daytimers
measured north-south distances in one set of units and east-west
distances in another.  Post-relativistic physics says that there's a
very nice way of expressing the relationships of relativity if you treat
time as another kind of distance coordinate, with the speed of light
(299,792,458 meters/second) as the conversion factor between units of
time and distance.  Then c is the unitless constant 1, velocities are
also unitless, and many things get simpler to express while remaining
mathematically equivalent.  Some textbooks use c * t explicitly in their
equations; Taylor and Wheeler happen to like a formulation where this is
expressed implicitly.

 > (3) the last I recall, it was illegal to combine unlike terms in an
 > equation
 > 
 >             therefor,
 > 
 > (4) the Lorentz space-time equation, and its resultant invariant
 > interval, are illegal.

Well, if you use faulty assumptions, you reach faulty conclusions.

Have you ever seen the Galilean transforms that are the Newtonian
analogue to the Lorentz transforms?  You might see that they also
combine measurements of time and distance using velocity as a conversion
factor:

x' = x - v * t
t' = t

Is that supposed to be illegal too?

If you read more carefully, you'll see that the unified-units
presentation of relativity does not mix measurements of time in seconds
and distance in meters -- units of time in seconds need to be multiplied
by c to obtain units of time in meters; one must measure both time and
distance in meters for things to come out right.  One can even choose to
measure both time and distance in seconds (by dividing distances in
meters by c) which is occasionally convenient too.