From: Ronald Wong (ronwong@inreach.com)
Date: Mon Dec 20 1999 - 10:20:17 PST
Date: Mon, 20 Dec 1999 10:20:17 -0800 (PST) Message-Id: <l03102803b4832a642ddd@[209.209.18.52]> From: Ronald Wong <ronwong@inreach.com> Subject: Re: student question
Sarah Wise wrote:
>
>Hi everyone,
>
>A physics student of mine has a question that I can't answer! Could you help?
>Here he is:
>
>
>
>We're studying relativity and Einstein in class and I came across a
>question when we were discussing the mu meson particles. How would we know
>that mu meson particles have short lifespans when we can only know that it
>travels at the speed of life (and thus doesn't die because of the slower
>internal clock)?
>Thanks......
>
>
>
>Thanks -- Sarah Wise
>
Sarah:
Your student's question seems to have confused two different aspects of a
mu meson's behavior. The short life-span of a mu meson is not related to
the fact that "we can only know that it travels at the speed of life
(sic)".
At rest, half of a pile of mu-mesons will break down at random into more
elementary particles in 1.5 microseconds (one and a half millionth of a
second). This figure, 1.5 microseconds, is called the half life of the
mu-meson.
This short life-span has nothing to do with the fact that it can be found
traveling at very high speeds - including speeds close to that of light -
nor does it have anything to do with the amount of energy they possess at
rest (as was suggested in one of the responses to your question). It's just
the way mu-mesons behave when they are at rest. They break down randomly
into more elementary particles at the rate that they do because they are
what they are.
Also, if it "...thus doesn't die because of the slower internal clock" than
it would seem to imply that the mu-mesons are, in fact, "living" for a
longer period of time and thus DON'T have the "short lifespans" alluded to.
There seems to be some confusion in your student's mind about special
relativity and the role played by the mu-meson experiment conducted at MIT.
The MIT researcher took their gear up to a high mountain and collected
information about the mu-mesons that were being created as a result of
cosmic radiation colliding with molecules in our upper atmosphere.
Their apparatus did two things: 1) It counted the number of mu-mesons of a
specific energy that were brought to rest within their apparatus and 2) It
measured how long each of these stationary mu-meson took to decay into more
elementary particles (when captured, some took less than a couple of
microseconds to decay and others, of the same energy, took many
microseconds to decay).
They examined the data that had been collected for a specific period of
time and, knowing from previous studies that the mu-mesons were traveling
at about 99% the speed of light when they were captured, figured out how
many in their sample had lasted so long as mu-mesons that they would have
reached sea level if they hadn't run been stopped by the equipment (based
on the assumption that special relativity didn't apply).
They then went down to sea level and counted the actual number that arrived
during the same interval of time as that at the top of the mountain. They
discovered that there was more than 15 times the number that they had
predicted based on no relativistic effects!
The simplest explanation for this result would be to say that the fast
moving mu-mesons had a longer half life than those at rest and that was why
so many survived the trip.
Based on the discrepancy between the number observed and that predicted,
they could figure out experimentally how much longer the half life of the
moving mu-mesons must have been in order to get the experimental results
observed. The figure agreed quite well with that predicted when one applied
Einstein's special theory of relativity to a particle traveling at 99% the
speed of light - adding another feather to Einstein's cap. Apparently,
events do take longer to come about in a moving frame of reference than in
a stationary one.
Enough of this relativity stuff.
Cheers - ron
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