There's a new movement underay which looks at the time dimension moving relative to the spatial dimensions.
Moving Dimensions: http://physicsmathforums.com/forumdisplay.php?f=55
Time Vector: http://members.triton.net/daveb/
The Theory of Moving Dimensions
Dr. Elliot McGucken
mcgucken@jollyroger.com
In this paper I propose that the time dimension is moving relative to
the three spatial dimensions. Such a concept may be used to explain
physical phenomena encountered in relativity and quantum mechanics,
while offering a path for the unification of Quantum Mechanics and
Relativity.
Simply put, it is not possible to rotate an object into the time
dimension without that object gaining a velocity. Thus the time
dimension itself must be expanding relative to the three spatial
dimensions. Another way of looking at this is asking, "Why does
something always move when it is rotated out of the three spatial
dimensions and into the time dimension?" If someone can conduct a
Lorentz transformation on a ruler, and rotate it into the time
dimension without it moving through the three spatial dimensions, I
would very much like to hear about it.
Einstein's two postulates of relativity state:
I. The laws of physical phenomena are the same in all inertial frames.
II. The velocity of light in free space is a universal constant,
independendent of any relative motion of teh source and teh observer.
I propose that the two postulates may be expressed in an alternative
manner, by stating the following law of moving dimensions:
I. The time dimension is moving relative to the three spatial
dimensions.
This can be shown illustrated in several ways: Consider an expression
for the space-time interval of zero length, or of the null vector,
which traces a photon's path through space-time:
x^2+y^2+z^2-c^2t^2=0
or
x^2+y^2+z^2=c^2t^2
Which for one spatial dimension becomes
x^2=c^2t^2
or x=ct
by taking the derivative of both sides with respect to t, we get
dx/dt = d/dt (ct) = c
so
dx/dt = c
And hence the time rate of change of the spatial dimension relative to
the time rate of change of the time dimension is equal to the velocity
of light.
ct| /
| /
| /
| /
| /
|/_______________
x
Also, if we trace the path of a photon on a space-time diagram, the
only way for a photon to remain stationary in space time is to move at
the speed of light, or to keep up with the expanding time dimension.
The null vector, which represents a vector of zero length in
space-time, can only imply zero movement through space-time. Even
though a photon moves through space at a velocity equal to C, it stays
stationary in space-time. Is it not strange at first that in order to
remain stationary in space time, a photon appears move at the speed of
light through space? This is only because the time dimension itself is
moving relative to space.
Einstein proclaimed that all objects travel through space-time at c.
Even though we perceive a ruler along the x axis to be stationary, it
is yet traveling through space-time at the fixed speed of c, implying
that time is moving through it. Rotate it towards the y axis, and its
projection upon the x axis shortens, yet it still appears to be
stationary, and it is still traveling through space-time at the rate
of c. Rotate it into the time dimension, and it's projection along
the x axis still shortens, but now it begins to move through the three
spatial dimensions, while maintaining the fixed speed of c through
space-time. Again, we see it move through the three spatial
dimensions as it is rotated into the time dimension because the time
dimension is moving relative to the three spatial dimensions.
As Brian Greene points out in the Appendix to Chapter 2 of The Elegant
Universe, we note that from the space-time position 4-vector
x=(ct,x1,x2,x3), we can create the velocity 4-vector u=dx/d(tau),
where tau is the proper time defined by
d(tau)^2=dt^2-c^-2(dx1^2+dx2^2+dx3^2). Then the "speed through
space-time" is the magnitude of the 4-vector u,
((c^2dt^2-dx^2)/(dt^2-c^-2dx^2))^(1/2), which is identically the speed
of light c. Now, we can rearrange the equation
c^2(dt/d(tau))^2-(dx/d(tau))^2=c^2 to be c^2(d(tau)/dt))^2
+(dx/d(tau))^2=c^2. This shows that an increase of an object's speed
through space, (dx/d(tau))^2)^(1/2)= dx/d(tau) must be accompanied by
a decrease in d(tau)/dt which is the object's speed through time,
which also may be considered the rate at which time elapses on it's
own clock d(tau) or the proper time, as compared with that on our
stationary clock dt.
As an object moves through space, it is rotated into the time
dimension, and less wave fronts of time are allowed to pass through it
relative to a stationary object, which bears the full brunt of wave
fronts. Thus a moving clock will run slower, as all clocks are based
on the probabilistic emission and propagation of photons, and as a
moving clock catches up with the expanding wavefront of time, the
chance that a photon will be emitted without being reabsorbed is
diminished.
Thus it is shown that the spatial and temporal dimensions are moving
relative to one-another. The laws and equations of relativity and
quantum mechanics rest upon this fundamental nature of physical
reality.
Relativistic and quantum mechanical phenomena can be accounted for by
the underlying nature of the relatively moving dimensions. Time
dialation, relativistic length contraction, and the equivalence of
mass and energy can all be seen to derive from this concept of moving
dimensions. The statistical wave nature of matter and energy also
rests upon the relative motion of the underlying dimensions.
As one rotates into the time dimension, one becomes more orthogonal to
the spatial dimensions, and thus one's length contracts. And too, as
the time dimension is moving relative to the spatial dimensions, one
begins to move.
Wave-particle duality and quantum mechanical probabilistic behavior
can be accounted for by the relative motion between the dimensions, in
which both particles and waves exist. Feynman's many-paths integrals,
reflecting the notion that a particle travels all paths, can be
accounted for by the fact that until it interacts with other matter in
the three spatial dimensions, there is a probability that a particle
or photon may exist as a pure wave, rotated into the fourth dimension,
moving along with expanding time, independent of the spatial
dimensions. So it is that radiowaves may pass through walls, carrying
energy and thus mass.
The second law of thermodynamics (increasing entropy) can be accounted
for with the fact that all particles and matter have a chance of
existing in a dimension expanding at a constant rate, equally in all
dimensions, relative to the rest. The spherical symmetry of a photon's
wavefront may be viewed as the result of matter having been rotated
into the time dimension--the matter has become orthogonal to the
spatial dimensions, and it is now expanding along with time, equally
in all directions.
Einstein's second postulate, stating that the velocity of light is a
universal constant, holds to be true because the velocity of light is
merely the rate of propagation of a dimension relative to the other
dimensions. Although this relative rate of propagations between
dimensions may vary, we shall always interpret it as a constant,
because we are used to measuring the velocity of the propagation of
energy relative to the velocity of the propagation of energy, which we
write as c.
Relativistic time dialation occurs because as an object approaches the
speed of light, the object approaches the speed of the propagation of
energy. As time is measured with regards to the propagation of energy,
such as the emission of a photon (in an electrical circuit or a
mechanical spring) or or the occurence of a random event which
liberates energy, less time will pass for an entity which is
propagating at a rate which is close to the propagation of energy
itself. As an entity gains velocity, it is roated into the moving time
dimension, and it in a sense it catches up with the dimension.
Relativistic length contraction is always accompanied by an increase
in velocity, as the probability that each quantum of the object
resides in the time dimension is increased. Relativistic length
contraction can be accounted for by the fact that as an object gains
velocity its probabilistic wave function, or its essence, is rotated
into the time dimension, and thus it appears shorter from the
persepective of the three spatial dimensions. At the speed of light
the object would have to be a photon, so as to be completely absent
from the spatial dimension, as any presence or probability that a
particle is in the spatial dimnsion means that there is a probability
that the time dimension will expand without carrying it along, in
essence leaving it behind for that moment it exists in the spatial
dimension.
Moving Dimensions: http://physicsmathforums.com/forumdisplay.php?f=55
Time Vector: http://members.triton.net/daveb/