Re: The spinor nature of spacetime - Fictitious motion in a Minkowski spacetime

Albertito wrote on Fri, 05 Dec 2008 10:49:20 -0800:

On Dec 5, 4:28 pm, "Juan R." González-Álvarez
<juanREM...@xxxxxxxxxxxxxxxxxxxx> wrote:
Albertito wrote on Fri, 05 Dec 2008 07:47:41 -0800:





On Dec 5, 2:30 pm, "Juan R." González-Álvarez
<juanREM...@xxxxxxxxxxxxxxxxxxxx> wrote:
Albertito wrote on Fri, 05 Dec 2008 04:49:02 -0800:

In an ordinary Euclidean 3-d manifold a body can travel from point
A to point B in a finite time, because of the existence of point B
along all the path followed by the body. Had not existed the
destination point B, it would have been impossible for the body to
travel from A to B, in finite time, obviously. This fact is not
that obvious in a Minkwoski spacetime.

Minkowski spacetime is a weird construct. A reference frame in it
has three spatial coordinates a one time coordinate, so a point is
called an event (x,y,z, - ct), where c is the standard invariant
speed of light in a vacuum. Here, the time coordinate has a
peculiar behavior, it is endowed with a kind of flow, such that a
body can't stay fixed in it. We can achieve a body remained fixed
in a spatial location (x,y,z), but the price to pay is that the
time coordinate will run at a constant non-null rate. A body in
event S=(x,y,z,-ct) can't travel to event S'=(x',y',z',-ct'). Why?
because the event S' does not exist when the body in S starts its
motion, nor exist along the followed path. The destination spatial
point (x',y',z') exists, obviously, but the coordinate time -ct'
is missing. A body can't travel to a four-point (event) that still
doesn't exist. Ok, you can represent that destination event in a
graph, but that representation doesn't make the point be real, so
the motion from S to S' is just a fictitious motion. We would say
that the time coordinate has less degrees of freedom that the
spatial ones, and this is called 'irreversibility of the arrow of
time'.

Ignoring, some remarks you make about Minkoski spacetime. The
difficulties to embrace the observed 'irreversibility of the arrow
of time' with the consideration of time as coordinate is well-known.

Precisely this and other limitations of Einstein [#] concept of
'time' are the basis for the development of relativistic theories
with *absolute* time, where Newtonian *strong* concept of time is
recovered.

One popular approach of this kind is described in

http://en.wikipedia.org/wiki/Relativistic_dynamics

and literature described therein. See also some basic expressions in

http://canonicalscience.blogspot.com/2007/08/relativistic-
lagrangian-...
limitations_20.html

[#] Relativists have always confounded time with clock rate.

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Hi Juan, thanks for your comments.

Yes, I already am aware of that approach (hypothesis II in
relativistic dynamics). The model I'm proposing might be called
hypothesis III. Rather than two temporal variables, a coordinate
time, and an evolution parameter, I propose a 3-d spatial symmetry.
IOW, the physical space would be endowed with two opposite sides or
faces, such that material particles could be located by means of
those two symmetric points, each one in the relative opposite side.
This leads to interesting implications:

1. The more accurately you can measure the
position of a particle in 3-d spatial position, the more
inaccurately it is in the temporal 3-d side.

example: suppose you can measure the position of a particle at
location (x,y,z) with uncertainties (dx,dy,dz). This means that its
symmetrical temporal location (x',y',z') is also endowed with
uncertainties (dx',dy',dz'), such that there is an intrinsic relation
between them as,

dx dx' + dy dy' + dz dz' > = l_p^2 = G h_bar / c^3, (l_p = 1
Planck
length)

Neither a coordinate time nor an evolution parameter are needed,
because we are dealing now with two opposite and symmetrical sides in
a complexified spacetime.

2. We can change Schrödinger equation to include this
symmetry, and by doing so, we include automatically a new
relativity
into it.

3. The irreversibility of the arrow of time is assumed,
since it is clear that the norm of temporal coordinates
(x',y',z') is always a positive real value

t = sqrt(x'^2 + y'^2 + z'^2).

Reversibility implies that it can be t<0, which is forbidden in my
model, because t can only be the square root of a positive real
number.

Regards

With the danger that you will ignore my advice :-) I will encourage you
to study literature before looking as reinventing the wheel and
repeating old errors already corrected in print.

You may think that people has not ideas, but believe me people had/has
*many* ideas, both trivial and revolutionary, and they are archived in
specialised literature.

Moreover, you are doing new mistakes. E.g. your claim to solve the
reversibility paradox by prohibiting "t<0" means that you do *not*
understand the problem:

http://www.canonicalscience.org/en/researchzone/time.html

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Juan, I like to reinvent the wheel, it's funny :-)

Well you ignored my advice as predicted.

It is your time. I spend part of my free time in USENET hunting. I find
that more funny. I catch a big troll in recent days and I am preparing
the article blog "Catching a big troll" about that :-)

One question, is your troll's chat program still available? Probably I
will link to it.

Partly, because the
current mainstrean wheels seem to be squares rather than wheels :-)

It is clear, at least for me, why the reversibility paradox is resolved
in my model. It is easy to grasp. Pose a particle at location S_0 =
(x_0,y_0,z_0) in your frame of reference. where x_0, y_0 and z_0 are all
real values. That particle has also a symmetry temporal point S_0'=
(x_0',y_0',z_0'). Now, let that particle to move from S_0 to S_1 =
(x_1,y_1,z_1), in a time interval

t = sqrt[(x_1' - x_0')^2 + (y_1' - y_0')^2 +
(z_1' - z_0')^2],

where the temporal coordinates at S_1 are

S_1' = (x_1', y_1', z_1').

So, you always get a time interval t > 0.

A reversibility would mean that we could get a time interval t < 0, but
that's impossible since we are performing all measurements within the
same frame of reference, and all the temporal coordinates are real
values. IOW, the distance between two different points is always a
positive length.

If you now reverse the motion from S_1 to S_0, you do not get a time
reversal, because that particle has to travel the same distance in the
same positive time interval. That is what an arrow of time means (i.e
positive length between two temporal points).

So, Loschmidt's paradox is unfounded, since if you reverse velocities,
you are not reversing time. If you were able to attain a negative
distance between two points, then Loschmidt's criticism to Boltzmann's
H-Theorem would be well-founded. But, as said above, the distance
between two different points is always a positive length.

As said you do not understand the problem. Sorry to say this but your
'solution' is both invalid and useless. I will add nothing more.


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