An electron is accelerated so close to the speed of light that its (relativistic) mass is 1 kilogram.

[ Editor: the question was first put as "At about 20 9's c (that is,
  .99999999999999999999 times the speed of light), an electron has a
  mass of 1 kilogram.  What happens if that electron hits somebody?"
  The following quotes earlier replies in the thread, whose authors are
  not identified in the collected postings. ]

The "rest mass" of an electron is nearly 10^(-30) kg.  So in order to
reach near 1 kg, we'll need 60 nines after the decimal point above.  But
let's assume we did that.

|> Think the electron would carry a kilogram's worth of energy; on
|> striking the person you would have something like total conversion of
|> a kilogram of mass to energy.  Dunno what that would be in megatons
|> but it would be several.  Even if it managed to vaporize the person
|> out of the way before giving up all that energy, it would soon give it
|> up to other matter in the nearby neighborhood.  So, I figure not only
|> that person, but everything within a few kilometers of that person,
|> would be "knocked into next Wednesday."
|>
|> But the details do get interesting.  I don't _think_ the electron
|> could just drill a _tiny_ clean hole in the person--could it?

No, the major way of loss of energy of the electron would be the
"bremsstrahlung" [Editor: "bremsstralung" in the original] radiation it
gives away when it is slowed down by the nuclear electric field.  So the
process is radiation and not "knocking out particles to form a tiny
clean hole".

Although the processes are probabilistic, on an average, the electron
would lose two-thirds of its energy within about 50 cm of its travel
within a human body (my guesstimate based on some tables and some
approximations - might be good to within a factor of 2).

|> The energy release of this massive electron would on the order of
|> 9*10^16 Joules of energy (that is 9 followed by 16 zeros).  That
|> converts to 250000000000 kilowatt hours.  Yeah, you could run a city
|> on that for awhile.  If it could be harnessed.

[ Editor: 9*10^16 J divided by 3.6*10^6 J per kilowatt hour is
  2.5*10^10 = 25,000,000,000 kilowatt hours, a tenth of the figure
  quoted.  It is about 21 megatons (1 megaton = 4.2*10^15 J). ]

Well, I guess you would have spent that energy for accelerating the
electron to 1 kg..

|> A related question.  How much does a single electron weigh when
|> accelerated to the highest energy achievable with today's very best
|> particle accelerators, and could you feel a single such electron if
|> it hit you?

The largest accelerators of today can accelerate the electrons till
their energy becomes about 400,000 times its rest mass (give or take a
factor of 2).  So it is still less than 10^(-24) kg.  That is nearly
10^(-7) joules.

-- Amol Dighe <asdighe@yukawa.uchicago.edu>

I'm not so sure that Bremsstrahlung radiation would be the major loss
mechanism.  I believe in a human body, most of the energy would
dissipate through Compton scattering.  This means with an electron
travelling at this speed, if it doesn't just quantum mechanically tunnel
through you (a big probability of happening), it will knock so many
electrons out of your body, you'll probably explode from coulombic
forces!

>       Although the processes are probabilistic, on an average, the
>electron would lose two-thirds of its energy within about 50 cm of its
>travel within a human body

I assume you are using some sort of interaction cross section, but are
there really tables for such a high energy particle?

Here's another way to look at it, one gram of matter is capable of
boiling all the earth's oceans.  A one TON block of uranium if
COMPLETELY fissed would reduce its mass by about 1 gram.

[ Editor: both figures are far off.  One gram of mass is 9*10^13 J;
  heating sea water to boiling and evaporating it takes about
  2.6*10^6 J/kg, so one gram would boil about 3.5*10^7 kg (35,000
  tonnes) of water, against about 1.4*10^21 kg in the oceans.  Fission
  of a U-235 nucleus releases about 200 MeV out of a rest energy of
  about 235*931 = 219,000 MeV, roughly 0.09%, so a tonne completely
  fissioned would lose about 0.9 kg, not 1 gram. ]

The electron would "weigh" exactly the same as it would at rest.  The
concept of relativistic mass was abandoned some time ago, it is the
kinetic energy equation that changes with relativistic velocities, NOT
the mass.

-- Joel M. Therrien <jtherrie@tiac.net>

In article <5accu8$r0t@news-central.tiac.net>, jtherrie@pop.tiac.net
writes:

|> >   well, even if we consider the first "bremsstralung" photon, the
|> >Compton scattering mechanism dominates only at comparatively low
|> >energies - the energy of the photon should not be more than 5-6
|> >times the rest mass of an electron.  Here, where this factor is
|> >almost 10^(30), the most dominant process will be electron-positron
|> >pair production - and yes, I guess explosion is a distinct
|> >possibility.
|>
|> My suspicion is that the dominant energy transfer process at this
|> energy would be production of subatomic particles.

yes, agreed completely.  if you find such an electron, please let the
particle physicists know - it would help in showing the existence /
non-existence of many heavy particles.

so in fact, unless we know what heavy particles lurk out there (with
mass less than 1 kg), we cannot exactly predict what is going to happen.
the BR ("bremsstrahlung radiation") rate just tells us something that
will "definitely" happen - so if one says that the electron will lose
its energy within 50 cm due to BR, it might actually lose it much
faster due to the new particle creation.

-- Amol Dighe <asdighe@maxwell.uchicago.edu>