[From Bill Powers (970527.1222 MDT)]
Bruce Gregory (970527.1140 EDT)--
The order of events separated by a space-like interval depends
on the relative motion of the observers looking at the events.
Now what did I just say? If you imagine something happening on
the Sun "right now" there is no way we can can become aware of
the event in less than the light travel time from the Sun to the
Earth of eight minutes. This eight minute "dead zone" is such
that observers in relative motion would disagree as to whether
event A on the Sun occurred before or after event B on the
Earth.
But that is a simple problem, no more difficult than explaining why it
seems that a rifle bullet can arrive before one hears the sound of the
shot. If a flare occurs on the sun, anyone who knows about the speed of
light knows that its time of occurrance in the terrestrial frame of
reference corresponds to the clock time of the observation minus eight
minutes. Given a record of events on the earth and of events on the sun,
one can easily put them into proper correspondence, saying which occurred
before and after which. This isn't even a relativistic calculation.
As to _reversing_ the temporal order, that requires more than two inertial
frames; there is no way in which two events occurring in a single frame of
reference can appear to occur in the opposite sequence, as observed from
any other frame of reference moving or stationary in relation to the first
(as I understand the transformations).
One can, in general, determine the relative velocity between two frames of
reference, under the assumption that the laws of physics remain the same.
The wavelength of a particular spectral line of sodium, for example, is
assumed to be the same in any frame of reference; hence its doppler shift
gives the relative velocity. This allows us to apply the Lorenz
transformations to measures of length, mass, and time, and to correct
apparent measurements for the illusions created by relative velocity.
Each observer could predict what the other observer would
see, but events A and B could not be causally connected and
there is no sense in which A "really" precedes B, or vice versa.
Both observers would agree on the spacetime interval between A
and B, but each observer would divide space and time in
different ways. (Outside the "dead zone" however, before and
after have their conventional meaning. )
But you're speaking of naive observers who don't know that light takes time
to travel, and don't know about the apparent compression of space and time
due to relativistic effects. While intervals may be distorted, the
distortion is known and can be corrected for; there is no indeterminacy
here. Just as a French and an American observer can convert back and forth
between Celcius and Fahrenheit temperature readings, observers in different
inertial frames can convert back and forth between measurements of
everything, expressing them in terms of any single agreed-upon frame of
reference with respect to which "zero velocity" is defined.
When you say "actual", I suspect you mean "in a frame at rest
with respect to the object". This is what we normally think of
as the "actual" mass and length. But in my example no observer
at rest on the Earth or on the Sun can observe A and B during
the dead zone. I can look at my watch, but I have to wait eight
minutes to see what your watch reads (if you are on the Sun).
Yes, and then I add eight minutes to your watch reading before comparing it
with mine to judge whether it is set as mine is set. Relativity adds the
complication that the _rates_ our our watches can differ if we are in
relative motion, but that can also be corrected for by the factor sqrt(1 -
v^2/c^2). If I time events by your watch, I simply apply that correction to
get the true interval from the apparent interval. It's just like measuring
my voltage using your voltmeter; I have to know how yours is calibrated
relative to mine before I can convert your reading into my terms.
You are quite right about the laws of physics being the same in
all inertial frames. Einstein's genius was to realize that this
requirement demands that observers in relative motion partition
space and time differently. Each observer has a clear
"perception" of space and time, but these perceptions differ
depending on the relative motion. If I am traveling at almost
the speed of light with reference to you, we see the world very
differently. But the worlds we see are governed by exactly the
same laws of physics. That is, neither of us could perform a
laboratory experiment to determine which of us was "really" in
motion.
That's taken for granted: there is no objective reference frame for any
measurement (but one -- see below). This even holds for position: where is
the objective zero for measuring the spatial position of a star? It holds
for angle: where is the objective zero for measuring longitude? But the
lack of an objective zero doesn't prevent us from agreeing on one!
Incidentally, there is at least one measurement for which it seems that we
can establish a single objective reference frame: angular velocity. The
centripetal force required to hold two objects in circular motion around a
common center reaches a minimum at an angular velocity of zero. For nonzero
angular velocities of either sign, more force is required. While
relativistic corrections are needed to convert between magnitudes of
angular velocities in different inertial frames of reference, the zero
point is the same for all of them and can be determined completely within a
single inertial frame. An odd exception to relativity, if it's really true.
My main point is that since we know about relativistic effects, we can
correct our observations for them just as we do in calibrating any
measurements, and then we can once again speak of time and temporal
sequence in the same old ordinary terms. If, as in PCT, one is used to
thinking that we observe _perceptions_ rather than reality itself,
relativity ceases to be anything unusual.
Best,
Bill P.