Thanks for you clarifications on this Mitch, to which I add a few more:
> [John K Clark, to Omega]
>
> > I agree that there is no way, absolutely no way Einstein would say there was
> > " a zero spacetime interval" between Earth and the virgo cluster, but what
> > about Cramer? If Cramer were to say there was a zero time difference between
> > earth and what we see in the Virgo cluster then time does not change, it also
> > stops being a useful concept, but I still see the symbol "t" , for time in
> > his equations, and he sure doesn't treat it like a constant equal to zero.
Actually this is exactly what Einstein would say. The general formula for
spacetime interval is:
s^2 = x^2 + y^2 + z^2 + (ict)^2, x, y, z, and t all being real.
> > If the spatial distance to the Virgo cluster is zero then the concept of
> > distance never changes and is always equal to zero, but you see the symbol
> > "L" for length in his equations and he sure doesn't treat it like a constant
> > equal to zero.
Relativity remember, distances in both space and time are relative to the
reference frame your in. From the perspective of a lightlike reference frame,
they are all exactly zero.
> > If there was " a zero spacetime interval" between Earth and the virgo cluster,
> > then all of spacetime would be a single mathematical point, points have no
> > internal structure so the idea of spacetime would not be a useful concept.
>
> Well, the answer to this problem is that distance is path-dependent. If
> you take a spacelike path from here to the Virgo cluster, the spacetime
> length isn't zero, but if you proceed along Earth's future light-cone
> to a point where it intersects the Virgo cluster's future light-cone,
> and follow a lightlike trajectory backwards in time into the Virgo cluster
> itself, you've travelled on two paths, each of which has spacetime "length"
> of zero.
The same applies on past-light cones too. All points on any given light cone,
both past and future portions together are relativistically local on lightlike
reference frames and all exist with no spacetime interval. This is the heart
of the paradox.
> I think bidirectional local causality is an ingenious idea, but what
> bothers me about the transactional interpretation when it's compared to,
> say, Bohm's theory, is that it doesn't really have an exact mathematical
> formulation yet. Cramer suggests that you could decompose a wavefunction
> into advanced and retarded components which altogether constitute a
> back-and-forth-in-time "causal sequence", but nowhere that I have seen
> does he propose a formula or an algorithm for such decomposition.
Supposedly, and I think this is Cramer's word on this, that his trans-
actional interpretation is mathematically identical to orthodox quantum
mechanics, and becomes obvious when one starts using the relativistically
necessary second order differential equation for time.
Unlike the first order differential equation for time that non-relativistic
QM uses, second order equations will automatically provide answers that
are bidirectional with time. In the formal interpretation, these backward
in time answers also carry negative energy, and so nothing really weird
comes from it except for the clarity that 50% of all microcausality is
happening as a result of advanced action.
> Something I'd like to figure out: how the operation of quantum computers
> would be understood in the transactional interpretation. Would it be
> that the readout operation retrocausally determines which computations
> are performed...? John Cramer has e-mail, I'll ask him what HE thinks.
One could say that the time and energy necessary for intermediate cal-
culations is being "borrowed" from the quantum vacuum and then payed back,
but a probably better way to describe it would be as some form of closed
timelike loop that holds up so long as the wavefunction remains coherent.
Still even this doesn't describe well an advanced action system such as
this. I'll ponder this a bit and see if I can come up with a real good
metaphor that describes what's going on.
-- In the Ecstatic Service of Life -- Omega