DARTH VADER wrote:
What exactly is electron tunelling?
When an electron is kept inside a closed container it is said that
there is a probablity of it tunneling through space-time and appearing
somewhere else between + infinity and - infinity.
How will it travell through space time ?

This is true, though not only of electrons, but for any quantum
mechanical object. Even things as large as animals and planets have
some probability of tunneling, though it gets pretty practically close
to zero for anything larger than an atomic nucleus.

Quantum mechanics goes like this: Given a system in state S at time
T, what state S' can be expected at T'? In classical physics the answer
is that S implies one and only one consequence, S'. In QM, however, an
entire spectrum of possible outcomes is possible. S at T implies, at
T', {...S1,S2,S3,...}. In fact there may be an infinity of possible
outcomes.

But not all possible changes of state have equal probability. Their
respective likelyhoods may be plotted on a graph:

P
R
O
B
A
B
I S8 S9
L S7 S10
I S6 S11
T S5 S12
Y S4 S13
...S1 S2 S3 S14 S15 S16...

The probability function is the absolute square of what's called the
'wave function' for the system in question, and the wave function is a
function of the relevant physical variables which define the system.
But let's say there's an electron trapped inside a magnetic toroid. (A
kind of donut shaped magnetic bottle, like they might use to store
anti-matter on Star Trek.) For the electron there's a wave function
that defines the likelyhood of it being detected within some spatial
interval. The peak of that function lies within the trap, but the left
& right tails of the curve extend a lot farther afield, in fact right
out of the trap itself. So there's some small probability of the
electron being detected outside. If so, then it's said to 'tunnel'
through the barrier, in a fashion never expected or allowed by
classical physics.

For a single such particle you might not reasonably expect to ever
detect it outside. But let's say the probability is 1/10^20 for a time
interval of delta-T. If you stuff the containment barrier with at least
10^20 electrons, then within a period equal to delta-T, you can
reasonably expect at least one of the electrons to tunnel through. This
is actually how alpha-radioactivity is understood to work. For atoms of
very large atomic number the nucleus is a large package of protons &
neutrons. The outer nucleons act as a barrier to the inner ones. But
they have a defined likelyhood of tunneling through and escaping. It
turns out to be respectably high for systems of two protons & two
neutrons. This is the alpha particle which tunnels.

And it's not precisely that, in standard QM the particle literally
travels through walls. It's more that the particle's position isn't
well defined to begin with. It exists *everywhere* within the area
addressed by its wave function. By placing a measuring apparatus within
an electron's region of possible locations, the electron is made to
either **** or get off the pot. So it ****s, meaning that it interacts
with the system comprising the device, and a location is registered by
the device.

-Mark Martin