"Michael has said much of what I want to say. The problem is purely
semantic - a question of what to call *real*. I too single out the *=
proper*
length of a "rigid" object and the *proper* period of a clock as use=
ful
invariant properties of certain objects. I have a problem when "pro=
per" is
used as a synonym for "real", rendering other length and period measu=
rements
unreal and only appearances. Is this real/appearance distinction res=
tricted
to only clocks and "rigid" rods?
I would indeed find this language more meaningful if one could give i=
t a
universal definition - ie. if one could define the "proper/real" tim=
e and
distance separations between two arbitrary events in space time. Thi=
s would
give the concepts "proper/real" a universal philosophical meaning rat=
her
than restrict the "reality" concept to events on the world lines of c=
locks
and "rigid" rods. "
I agree with this 100%, especially with the emphasis on the word "=
universal" (about definitions) in the second paragraph.
As I had suspected, and said in one of my previous messages, the d=
iscussion turns out to be semantic and is zeroing down onto basic def=
initions of what we mean when we say "mass", "time", or "real", for t=
hat matter. If John had said from the very beginning that a moving cl=
ock does not tick slower because "we" no longer want to call "time" w=
hat we measure to have elapsed in our Lab between its two ticks, only=
to preserve this term for the rest frame of the clock, then a questi=
on about the rate of the clock's tickings in any other RF would just =
loose its meaning, and there would probably be no discussion (at leas=
t I would not go into it). Terminology is a matter of taste. But even=
when choosing terminology, we must be careful for it not to be misl=
eading or too restrictive. I think the examples my Michael Edmiston i=
llustrate this point very well, and deserve more serious consideratio=
n.=20
The minor axis on the Saturn ring's projection is NOT the diameter=
of the Saturn's ring (here I agree with John 100%). In contrast, the=
projection of the proper time of moving clock onto the temporal axis=
of my Lab IS the time interval between its ticks in my Lab (here Joh=
n disagrees with me 100%.) But so far the aspect of reality called ti=
me is accessible to direct measurement in my lab, with clearly define=
d experimental procedure, and John has to state clearly that he does =
not agree with this conventional operational definition of measuremen=
t of property called time.=20
Nobody argues against the importance of the "proper" or "invarian=
t" characteristics of an object or process. But sometimes (and it is =
rather amusing in view of the way the whole discussion took) these "r=
eal" characteristics can only be found from the "less real" non-invar=
iant characteristics. For instance, the rest mass of a newly observed=
high-energy particle mc^2 =3D sqrt{E^2 - P^2c^2} can be inferred fro=
m the measurements of the particle's energy and momentum in our lab. =
Even more so for the cases when, as Bob has pointed out, we do not de=
al with something "solid". For instance, consider just two events in =
spacetime (say, two separate collisions). We can measure in our lab t=
he time interval and spatial separation between them, but these, bein=
g merely the "projections" of something really "real", are not really=
important characteristics, all the more so that they will be differe=
nt in another lab moving with respect to our. What is this "really re=
al" about the two events? The invariant 4-interval? To me it is beaut=
iful, elegant, but (in this case) abstract construction - definitely =
more abstract than real time and space separation between the events =
as observed and measured in my lab. One can say that we can find a sp=
ecial RF where these events are either simultaneous or occur in the s=
ame place, depending on the sign of the square of the 4-interval, and=
the corresponding distance (time) between these events would be thei=
r proper characteristics. Fine, but I could as legitimately argue tha=
t such a RF has a very minor advantage - only that of more simple exp=
ression for the 4-interval. Saying, that just because of this only th=
e corresponding distance (time) between the events in this special RF=
is "true" characteristic, whereas those in others are something lowe=
r in status, would be much of a stretch.
A couple of more examples. Imagine that the Earth became transparen=
t so that John and I (vacationing on the opposite sides of the globe)=
can see each other. I see John upside down, and he sees me upside do=
wn. We record the events, making photographs etc. We can then present=
our scientific evidence to a higher arbiter. What would the arbiter'=
s verdict be - who is really upside down? Here we do not have a situa=
tion when we can appeal to a special RF where corresponding character=
istic is a proper characteristic. If only proper is real, but there i=
s no "proper" here, then neither orientation is real in this case? I =
would rather say that either one is real, but neither is absolute.
I had once read about an exotic hypothesis that the whole universe =
was created in the collision of only two ultra-high energy particles.=
A proper rest frame of this system (admittedly coinciding with the o=
ne where the current background radiation is isotropic) was the one w=
here their net momentum was zero, and therefore neither of their ener=
gies was really energy. However, the net energy of current universe w=
here we live is energy, assuming that we live in its rest frame. Is i=
t that something real has been cooked up from something less real? Ar=
e we real?=20
Let us make this example even more exotic, assuming that the initia=
l particles were just two photons. The rest energy of each is zero; t=
he actual energy and momentum of a photon, being only a geometrical p=
rojection of the zero, surely cannot be considered as real energy and=
momentum (according to proposed new terminology). It follows that ev=
en if we still admit the reality of our world, then its "good, new" r=
est mass consists 100% of "bad, old" relativistic mass, and the same =
for its energy.=20
If relativistic energy and mass in E =3D mc^2 E are not really ener=
gy and mass, than what is this relationship about?
Only because "good, new" terminology is being currently used by maj=
ority (which statement has not been statistically confirmed), does no=
t necessarily mean that it is better than the "bad, old" terminology =
so effectively used in time of development of Special Relativity.
=20
Moses Fayngold,
NJIT
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