One of the ingredients in the approach to
quantum theory that I am
working on is called the path integral
and it is an approach to
quantum mechanics that was already set
out
and described by Dirac very early in
in the history of quantum mechanics and
it's something which
physicists use a lot in their everyday,
everyday work but hasn't
been taken up by the majority of physicists in
terms of interpreting the theory. The
basic idea behind the path integral is that 
if a particle is
measured to be at a particular position
at a particular time,
like there then,
to calculate the quantum amplitude
for it to be at a particular different
position at a later time,
there, you have to consider
all the possible space-time paths that
the particle can take between those two
space-time events.
Every single path is to be considered
a priority and each path has
its own amplitude which is a complex
number just,
and to calculate
the amplitude the total amplitude for going
from here to here
you add up all the
complex amplitudes one for each of 
the individual paths that the particles can take.
What you do with that number
that complex number, that's another
thing.
The standard
way to interpret this amplitude is to
say that the probability
that you measure the particle here given
that you knew it was there
to start with is given by taking the
amplitude
taking its absolute value
and squaring it and that's the
probability.
Why that is the probability
is that it's either a very deep question,
that's the rule and that gives us the
right answers when we come to
do experiments in the lab such as the
double slit experiment young slit
youngs slit experiment. Why you,
what the fundamental reason is for that
very
peculiar seeming rule which is add up
all the amplitudes take its absolute
value and square it
and why that should be the measure of how
likely it is for something to happen
is something which is either extremely deep
or is some kind of meaningless question.
I don't, I've
never understood never decided which
of those two it is.
The path integral interpretation is still
underdevelopment so
in that sense it's a little tricky to
compare it to
for example the Copenhagen
interpretation which has been around and
I guess roughly agreed upon by most
people. However,
in its, in the form that we have it the
path integral interpretation
deals with the physical world,
physical quantum world in itself
as it is. Whereas the Copenhagen
interpretation
does not have anything
to say about the quantum system.
The Copenhagen interpretation
gives you, is, it's a rule of thumb it's
a set of
rules for predicting the results of
experiments that you do on the quantum system
and it simply declines to say what is
really going on.
It declines to say anything about the
quantum system itself it just gives you
the predictions for what
the results your experiments
will be when you do experiments on the
quantum system but it
just is silent about the quantum systems itself.
So in that sense the path integral
does, it does what physics should do. It's
telling you about the physical
quantum world
whereas the Copenhagen interpretation
simply doesn't tell you anything
that so in that sense there's no
comparison the
path integral, it speaks to what
the physical world is.
To compare it to bohmian
mechanics
one would have to, the
the differences as far as they are both
developed
is that the path integral interpretation
is intrinsically relativistic
it doesn't require any
inertial frame any preferred frame to be
to be set down in its
fundamental formulation
in its intrinsically relativistic
you don't need any frame
for bohmian mechanics to be applied
to a relativistic system,
you need to have a preferred frame.
That preferred frame it turns out is not,
is not observable
but nevertheless in the fundamental
formulation of the theory it's there
you need to, you can't even write down
the formulation of the theory
without this background, without this
background
time coordinate. So it's there
physically but its somehow unobservable
in bohmian mechanics.
So which one would prefer in that
situation
is to me
I take relativity to heart and I
believe that,
that further Unity demands that we,
that the the quantum theory
should be
fundamentally relativistic rather than
somehow relativistic
for practical purposes.
