Subject: Re: two postings
From: Shalender Singh
Date: Wed, 6 Dec 2006 21:30:57 -0800 (PST)
>> I vaguely recall that, in General Relativity,
>> inertia can be regarded as
>> related to gravity (inertia is to gravity as
>> magnetism is to
>> electrostatic force). Einstein even showed that
>> inertia gets distorted
>> in the neighborhood of massive rotating bodies
>> (pulling objects toward
>> the plane of rotation). I don't know whether this
>> has ever been verified
>> experimentally.
>>
>> Justin Smith
>>
Actually in more general terms inertia is 'resistance
to change'. General Relativity talks about inertial
entities, which have mass.
A inertial entity X is the one, which given 2 points
A, B in space-time, has to follow the topology of
space-time to travel from point A to B (in the purist
form, there exists a fibre of the bundle or a
space-time path between A to B and every inertial
entity follows it).
General Relativity transforms the problem of Dynamics
to the general problem of topology. It also says that
existence of any inertial object would itself modify
the topology of space-time...
One of the assumptions with which general relativity
starts is pre-existence of flat space-time topology
(euclidean meteric), which itself is a non-trivial
topology. So the concept of distance and path of
connection between any 2 points A and B pre-exists.
My question is a actually on more fundamental ground.
General Relativity assumes that there already exists a
flat space-time topology.
The string theory, which tries to unifies all kinds of
forces says that actually there are no point or
dimensionless entities, but themselves are a one
dimensional topological objects. Every fundamental
partical is a string. There is non absolute space-time
but all the strings in the universe interact to form
space-time.
For example if there are n fundamental particles
represented as 1-D sets A1, A2, ..., An then the
non-interacting universe of them is:
A1 X A2 X ... X An, which is n-dimensional. But
interaction, reduces no. of allowed states (That is
what is interaction by definition) so U or universe is
a subset of A1 X A2 X ... An. The topology of U
depends on how A1 X ... X An interact.
As it is seen that there is a assumption of 1-D
topology for every string and the overall topology of
universe U is also determined by rules of
interaction...
If we take 4-D space-time approach, the inertia or
resistance to change is actually equivalent to
existence of non-trivial topology of space-time. If
the topology of space-time was trivial then for
reaching from pt A in space-time to pt B in
space-time, there was non requirement of any path,
they would directly accessible. So there would be no
time...
So the string theory splits the problem of 4-D
absolute space-time topology to a more fundamental 1-D
topologies and thier interactions to incorporate more
types of interaction/forces (the interactions are in
physical terms forces and is accompanied by change of
energy!).
The question I ask is more fundamental. I ask why does
the non-trivial topologies exists (in other words
inertia)? Why even a string has a non-trivial topology
(or an ordered set or a 1-D structure). I content that
these questions arise because we always start with a
philosophical set-theoritical basis of 'absolute
existence', which means that anything which exists
must have a container.
So string is an ordered container of some elements
(may be states of string). The containership and
orderedness is a information, which comes from outside
of the string...
If we start from a different philosophical basis of
the concept of General Topology itself, which is
"Relative Existence" then the formal paradigm we will
get would explain current phenomena's and would give
extremely deeper insights and novel results in
physics.
So results like replicating space-time beating the
speed of light...
Shalender Singh