Hypotheses,
conjectures, postulates & principles arising.
In
this work it was discovered that for the path of particle to be considered
physically real, that its time component must be purely real or imaginary in
both Schwarzschild coordinates and in proper time. In the case of proper time
it can not be established if the path is physically real without consideration
of the transformation to Schwarzschild coordinates. This strongly suggests the
conjecture that for a path to be physically real, it has to be mathematically
purely real or imaginary in all coordinate systems under any valid
transformation. It is further conjectured that paths that are described by a
complex time variable that has both none zero real and imaginary parts,
identifies the path as not being physically real.
It
was also discovered that the most logical conclusions were reached when the
coordinate time of a particle is only treated as going forward in time.
Mathematically, velocity expressed as (dr/dt) can be interpreted two ways. The normal
interpretation is that negative velocity means going in the negative spatial
direction in a positive time interval so that (dr/dt) means (-dr)/(dt). However there is nothing mathematically invalid as
interpreting negative velocity as meaning going forward in the spatial
direction in a negative time interval so that (dr/dt)
means (dr)/(-dt). Of course
in normal physics we would never interpret velocity that way and our everyday
experience would back that up. However, it is perfectly mathematically valid
and the only way to resolve the dilemma is to propose the principle that the coordinate
time interval dt is only
ever positive. This might seem so obvious, that it not worth mentioning in
polite company. However, it situations where we can not make direct
experimental measurements, such as below the event horizon of a black hole it
is not so obvious. In fact the conventional physical interpretation of the
velocity of light below the event horizon light is treated as going backwards
in time and it is shown in this work, that making that assumption results in
many unsolvable logical paradoxes. These errors could have avoided by using the
simple postulate that coordinate time only ever advances.
Another
observation in the new interpretation is that a particle can never escape its
future light cone in static spacetime. Again this might be seem
obvious but it has been ignored by many physicists over the years. If they had
accepted that simple principle they would not have made the mistake of
concluding that a physically real particle can cross the event horizon because
doing so requires the particle to escape its own future light cone.
Another
principle that is violated in the conventional interpretation of black holes is
that an object can never exceed the local speed of light. Again, if physicists
had paid attention to that simple principle they would not have got the
conventional physical interpretation so wrong.
Einstein
showed us the way in his elegant Special Theory of Relativity of how to go about
constructing a theory. Rather than proving some assumptions that may have been
difficult to prove in isolation, he took them as self evident truths
(postulates) and then applied them to see where it took him. If the results
were self consistent and did not lead to logical contradictions then it was a
good indication that the original assumptions were valid. This approach proved
very successful. The work done here in this website is by contrast a little
convoluted and multi threaded and possibly difficult to follow. A better
approach (with hindsight) might have been to take a lead from Einstein and
start with some simple postulates.
The
preamble to this section suggests some candidate postulates which are now summarised
here:
1)
A physically real
particle can never exceed the local speed of light.
2)
A particle can
never escape its own light future light cone in static spacetime.
(Each successive future light cone is
completely enclosed by the previous future light cone of the particle.)
3)
A region of space
can never have infinite mass density.
4)
Coordinate time
intervals between events are always positive and purely real.
5)
Under any valid
transformation the time component of the motion of a particle is always purely
real or purely imaginary.
6)
An observer never
perceives the motion of a particle as going backwards in coordinate time.
7)
A photon or
particle with mass can not be in two widely separated locations at the same
time.
(Quantum fuzziness not withstanding)
8)
A photon can not
arrive at its destination before it has been emitted.
Note:
It is acknowledged that some of the postulates in this list are a simple
reformulation of others in the list.
Now,
by choosing any one of these proposed postulates from the list as a reasonable
assumption, it can be shown that the conventional physical interpretation of
black holes is in error. Choosing any one of these postulates
and applying them as a principle, results in all the others in the list as
being logical conclusions as they are all intimately interrelated.
Gravity
tells time how to tick and time tells gravity which way is up.
)
2008 KevPegrume