Re: Confirmation of Relativity

["William J. Larson" <bill_larson@CSI.COM>]

==>I think the two points of view for cosmic ray generated muons
==>is the best example.
Yup. I always assign this as homework and put it on the test.

Here are my lecture notes.
Sorry about the poor grammar, but they are lecture notes.  :-|

Muons as a Proof of Special Relativity

Muons are produced by cosmic rays in the upper atmosphere 200 km up
They are produced going about 99.99995%c.
(I made this up. Anyone know the correct number?)

The muon ½ life is 2 x 10^-6 s, so how far do they travel?
d = vt = 300,000 km/s x 2 x 10^-6 s = 600 m.
We detect them on Earth 200 km below. How?

99.99995 % c gives a gamma = 1000

So the muon sees the atmosphere length contracted by
L = L0/gamma
= 200 km/1000
= 200 m.
The muon sees only 200 m of atmosphere to cross
and they see themselves as able to travel 600 m before they decay
so they see themselves as making it.

But on Earth we still see the full 200 km. But we see
t = gamma x t0, i.e. we see the ½ life time dilated by
½ life = 1000 x ½ life = 2 ms
We see the muon now with a ½ life of 2 ms.

How far do we see that the muon can go in this 2 ms?
d = vt
= 300,000 km/s x 2 ms
= 600 km, so we also see that the muon can make it,
but for a different reason!

Dr. William J. Larson
Bill_Larson@csi.com
Institut Monte Rosa
Montreux, Switzerland

----- Original Message -----
From: Leigh Palmer <palmer@SFU.CA>
To: <PHYS-L@lists.nau.edu>
Sent: 2000 May 03 10:32 PM
Subject: Re: Confirmation of Relativity


> I think the two points of view for cosmic ray generated muons is the
> best example. I want to mention another that is of fairly recent origin.
> There is considerable interest now in measuring the distances to other
> galaxies using type Ia supernovae (Ia SNe) as standard candles. These
> supernovae are of an identifiable subclass distinguished from other SNe
> by their spectra and by the time evolution of their brightness (called
> the "light curve"). Principally because Hubble can reach deeper into
> the cosmos than Earth based telescopes could, but now augmented by the
> very large telescopes now being constructed, it has become possible to
> reach and detect Ia SNe in very distant galaxies. These galaxies show a
> large red shift which *can be* attributed to their rapid recession from
> our galaxy. Since the light curves of these SNe can be measured over
> the weeks to months following their discovery, these standard candles
> also constitute relatively reliable clocks moving away from us at high
> speed, and we can read the progress of time on these clocks. The time
> dilation effect has been seen now in some of the more distant of these
> Ia SNe, a verification of time dilation in a system of macroscopic
> scale over a relatively long time period.
>
> Those interested in looking further into this are directed to:
> astro-ph/9707260, astro-ph/9605134, and astro-ph/9602124.
>
> Leigh