I think Robert Cohen's questions of whether his muon examples are equivalent
to the original question, is yes... they are equivalently bad questions.
The SR problem is the "when."
In a previous post I stated this might be a question of semantics. "When"
could mean "at a specific time." If that is what is meant, then as Denker
and I have pointed out, these questions are meaningless, inappropriate, (or
in John's words "tilt... game over.")
However, some people interpret "when" to mean "for the same measurement" and
a time correlation is not implied. "When I measure the muon lifetime I get
this, and when you measure the muon lifetime you get that." In this latter
statement I am implying we measured the same natural phenomenon, but we did
not measure it at the same time.
Unfortunately Robert's muon example also has problems in the actual physical
measurement process. How do you measure the lifetime of a muon if you only
have one muon and you don't know when it was created? You either need to
witness two events (creation and decay) or you need to have a collection of
muons for which you measure the decay rate and know how many muons there
are, or you need to measure the muon flux (of a steady beam) at two
different locations. In the example, the wording "passing through my
detector" doesn't provide the requisite data.
I would phrase the muon example this way. Peter is in the rest frame of
beam of muons. Peter and the muons are moving at 0.9 c with respect to me.
Peter observes muons near him decaying, and from the decay rate and number
of muons present he calculates the average lifetime to be t(life)-Peter.
Some of the muons are going through two detectors I have set up some
distance apart. By comparing the muon flux in each detector, and from
knowing the detector separation and muon-beam velocity I calculate the
average lifetime to be t(life)-me. Please compare t(life)-Peter to
t(life)-me.
The way I phrased it I think I can calculate a valid answer. The way Robert
asked it I have to respond that I don't understand. The way he asks it I
don't even understand the physical process of how I measured the muon
lifetime nor how Peter measured the muon lifetime.
If my detector detected a muon, that muon is gone, it's no longer part of
the beam. I'm not sure how Peter detected this, but if he somehow could see
it, and I detected it in my detector, then we both detected it die at the
same time because we were coincident in space and time (at my detector) when
we say it interacted with my detector.
Perhaps we are playing a "thought experiment" in which we can somehow see a
muon with our eyes without disturbing the muon. In this case I don't want a
detector, I just want a reference point that I see the muon pass. Peter,
the muon, and I are all simultaneously at the reference point and we
synchronize our clocks at that point. Sometime later that muon decays and
we both observe it. If Peter recorded the time of decay as 1.00
microsecond, what time did I record for the time of decay. Here we are back
to talking about two specific events and we can calculate what times we each
wrote down for each event and we can each calculate a delta-t between the
events.
Michael D. Edmiston, Ph.D. Phone/voice-mail: 419-358-3270
Professor of Chemistry & Physics FAX: 419-358-3323
Chairman, Science Department E-Mail edmiston@bluffton.edu
Bluffton College
280 West College Avenue
Bluffton, OH 45817