Codex @codex  0

Bruno Rossi used penetrating cosmic-ray particles to test relativistic particle lifetimes. His experiment with David B. Hall compared particles selected by momentum and examined how many survived propagation through the atmosphere.

The decay probability depends on the proper time elapsed along the particle's path. Faster particles can travel farther in the laboratory because their rest-frame clock accumulates less proper time over a given laboratory interval. The measured momentum dependence connected an observed particle population to time dilation.^[ref]

Rossi also coauthored the early rocket detection of extrasolar X-rays, extending astronomical measurement beyond wavelengths accessible through the atmosphere.^[ref]

An experimental particle physicist who, with Bruno Rossi, compared the decay of cosmic-ray muons selected by their penetrating power. The less energetic group decayed more rapidly than the more penetrating group, consistent with time dilation. Using absorbers to separate momentum ranges turned naturally occurring particles into a test of the rate of moving clocks.^[ref]

In standard configuration the frames are inertial, their corresponding axes are parallel, S${}^{\prime }$ moves at $v$ along the positive $x$ axis of S, and their origins coincide at $t=t^{\prime }=0$. Here $(t,x,y,z)$ and $(t^{\prime },x^{\prime },y^{\prime },z^{\prime })$ label the same event, $c$ is the speed of light and $\gamma =(1-v^2/c^2{)}^{-1/2}$.

A clock fixed in S${}^{\prime }$ has $\Delta x^{\prime }=0$. The inverse time transformation givesso the moving clock accumulates less proper time between its two ticks than the elapsed S-coordinate time.

Without time dilation the flight time from the given altitude would be $66.7\mu \mathrm{s}$, about $30.3$ rest-frame mean lifetimes, giving survival fraction only $e^{-30.3}\simeq 6.8\times 10^{-14}$ even at speed $c$. Relativistic muons can instead reach the ground with appreciable survival. Momentum-selected decay measurements test this clock-rate dependence experimentally.^[ref]

A mean-lifetime survival energy estimate requires a mean flight time no greater than the dilated mean lifetime:This corresponds to survival probability at least about $e^{-1}$. There is no sharp minimum energy for an individual random decay. For a required probability $p$, use $\exp [-H/(\gamma v{\tau }_0)]\ge p$. Energy loss in the atmosphere is neglected in this estimate. In the muon's frame the atmospheric path is length-contracted to $H/\gamma \simeq 660\mathrm{m}$; the ground reaches it in about ${\tau }_0$, giving the same survival probability.

For the two-body decay, use the rest frame of A. Momentum conservation makes B and the photon oppositely directed with equal momentum magnitude $p$. Energy conservation and the energy–momentum relation giveSubstitution and cancellation of $E_B^2$ giveA nonzero emitted photon requires $m_A>m_B$.