Deflected Space-Time-Mass Theory
Dr Weiguang HUANG
Abstract
We propose the deflected space-time-mass theory to release relationships among space, time, mass, energy and speed. It proves that moving objects appear heavier and compressed, their length, area and volume appear to contraction, and moving clocks appear to run slower by deflection of space-time-mass. It shows that space-time conservation and space-mass conservation, regardless of the object speed and space dimension.
1. Introduction
The Special Theory of Relativity (STR) first pointed out that observers of any two different coordinates who described "an event" such as time and space would get different results, which represented a breakthrough of the knowledge of space-time in human history. It has opened out the relation among space, time and motion. The Relativity Theory shows that space-time is curve.
Zhang Junhao and Chen Xiang [1-6] argued that space-time is
not curve by their gravitational theory on the flat space-time (Minkovsky’s
space-time) as the special relativistic gravitational theory.
Dr. Cui Silong [7] proposed
the Theory of Analytical Space-Time with two
hypotheses as principles: (I) the
area of space-time is invariant (Principle of a string), and (II) any two coordinates with relative speed
would deflect each other.
The theory completes Lorentz transformation with a factor of
two-dimensional or multi-dimensional rotation, obtains a new expression of
astro-object precession angular speed, gives two forecasts, demonstrates
Schrödinger equation with space-time rotation and concludes a space-time wave
panorama for Newtonian space, Relativistic space, quantum space and
black-holes. The theory will unify the foundations of Special Relativity,
General Relativity and Quantum Mechanics. He gave two forecasts: (1) 0.71c
space-time light cone vertex, and (2) Deflection of space-time
results in double refraction of light. From his first forecast, he
concludes that anything that has relative speed 0.71c to us is
invisible even though it moves in front of our eyes. The object can appear
again from its rear side when relative speed u > 0.71c.
This forms a phenomenon of light cone whose vertex point is 0.71c and
it may be demonstrated by measuring moving particles in lab. From his second
forecast, he concluded
that light from a moving system would produce a phenomenon of double
refraction. Light will split into two rays: one is ordinary ray co and the other is extraordinary ray ce. co spreads with the same speed in all
directions and follows the law of refraction whereas ce goes with a speed that is changeable in
different directions and varies on the relative speed of a moving system and
does not follow the law of refraction. Unfortunately, both forecasts are wrong because
there are mathematical errors in his mathematical deduction.
In this paper, we set up a model of deflected space-time-mass to release relationships among space, time, mass, energy and speed. We will point out Dr. Cui’s mathematical errors in his mathematical deduction. From our deflected space-time-mass theory, we conclude that space-time and space-mass are conservations, regardless of the object speed and space dimension, and show that space-time should not be curved.
2.
Space-Time Theory
2.1 One-dimensional Space-Time Theory
Let us introduce the Theory of Analytical Space-Time [7].
Definition: Given two right-angled coordinates (S') and (S), (S') is the moving coordinate and (S) is the observing coordinate. l' and t' in (S') indicate length and time upon the condition that (S') is in a stationary state relative to (S). If there is a relative motion between (S') and (S), we, being in (S), measure l ' and t' in (S'). The result of measurement is l and t, so l and t are all measured data [7].
Two hypotheses for the Space-Time theory [7]:
(I) Principle of invariant space-time area (Principle of a string)
Product of length l' and time t' in (S') and product of l and t in (S) are called space-time area S' and S respectively. The space-time area is invariant whether there is a relative motion between (S') and (S) or not. For any (l', t'), it must meet the equation: l' t' = l t.
(II) Principle of space-time deflection
If a moving coordinate (S') leaves or approaches the observing coordinate (S) with speed u (or u'), (S') deflects (S) from the direction of u (or u'), and the angle q of deflection results from the relative motion and its sine is proportional to relative speed u.
Therefore
sinq=u/c or sinq=u'/c'
where c is speed of light.
We get [7]
l = l' cosq (1-1)
t = t'/ cosq (1-2)
With principle (II): sinq =u/c, then eq. (1-1) and (1-2) are as follows [7]:
These two equations are the basic equations of the Special Theory of Relativity. We know that there is a definite meaning of the contraction factor: the deflection factor of space-time. It is the deflection of space-time that causes the contraction of a moving ruler and the delay of a moving clock.
By the way, we point out Dr Cui’s mathematical errors in his mathematical deduction of two forecasts [7].
1. He set x' = y' = c't' in his first forecast. It means that object speed is light speed, i.e. u = c. It leads to q = 90 degree. It is obvious wrong to conclusion of q = 45 degree. It should be that l = 0.707l’ and t = 1.414t’ when u = 0.707c.
2. He set c = c’ in his second forecast. It means that light speeds are the same. It is obvious wrong to get ce < c in his formula (1-32).
His Theory of Analytical Space-Time is valid in one-dimensional space only.
2.2 Two-dimensional Space-Time Theory
We extend above theory to two-dimensional space, i.e. area.
For any shape of an object, by double integration, its area A in (S) is defined as
A = òò dx dy (1-5)
Similarly, the area A’ in (S’) is defined as
A’ = òò dx’ dy’ (1-6)
Substitute eq. (1-1) into eq. (1-5), then it becomes
A = òò d(x’ cosq ) d(y’ cosq )
= cos2q òò dx’ dy’ (1-7)
Substitution
of eq. (1-7) with eq. (1-6) leads to
A = A’ cos2q (1-8)
For a given speed, the
value of cos2q is a constant. This
is relation between the area A in the observing coordinate (S) and the
area A’ in the moving coordinate (S’). It proves that the area of the moving object appears smaller due to
deflection of space-time,
but its shape is unchanged. This shows that the space should not be curved;
otherwise its shape should be changed.
2.3 Three-dimensional Space-Time Theory
Let us extend above theory to three-dimensional space, i.e. volume.
For any shape of an object, by triple integration, its volume V in (S) and V’ in (S’) are defined as
V = òòò dx dy dz (1-9)
V’ = òòò dx’ dy’ dz’ (1-10)
Substitute eq. (1-1) into eq. (1-9), then it becomes
V = òòò d(x’ cosq ) d(y’ cosq ) d(z’ cosq )
= cos3q òòò dx’ dy’ dz’ (1-11)
Substitution
of eq. (1-11) with eq. (1-10) leads to
V = V’ cos3q (1-12)
For a given speed, the value of cos3q is a constant. This is relation between the volume V in the observing coordinate (S) and the volume V’ in the moving coordinate (S’). It proves that the volume of the moving object appears smaller due to deflection of space-time, but its shape is unchanged. This shows again that the space should not be curve; otherwise its shape should be changed.
2.4 Space-Time Conservation
Combination of eq. (1-1), (1-8) and (1-12) leads to
l/l’ = Ö(A/A’) = 3Ö(V/V’) = t’/t = cosq (1-13)
then
l t = l’ t’ = ÖA t = ÖA’ t’ = 3ÖV t = 3ÖV’ t’ (1-14)
It shows that products of length, square root of area, or cubic root of volume with time are the same, regardless to the object speed and space dimension. We call it as space-time conservation.
If the shape is square, its area A is l 2, then from eq. (1-14), ÖA t = ÖA’ t’ becomes to lt = l’t’. Therefore, one-dimensional space is a special case of two-dimensional space.
If the shape is cubic, its volume V is l 3, then from eq. (1-14), 3ÖV t = 3ÖV’ t’ becomes to lt = l’t’. Therefore, two-dimensional space is a special case of three-dimensional space.
These show again that the shape of object is unchanged although its size, area and volume are reduced.
We can separate eq. (1-14) into
l t = l’ t’ (1-15)
At = A’t’ cosq (1-16)
Vt = V’t’ cos2q (1-17)
When u = Ö3/2 c = 0.866c or q = 60 degree, then t = 2t’, l = l’/2, A = A’/4, and V = V’/8. We call this speed as the speed of double time, the speed of half length, the speed of quarter area, and the speed of one-eighth volume.
3.
Space-Mass Theory
When an object with mass m moves to distance l, its motion energy F is defined as
F = ml
If we replace t and t’ in two right-angled coordinates (S') and (S) with mass m and m’, we get a relation similar to eq. (1-15):
F = ml = m’ l’ (3-1)
It shows that energy is
constant, regardless of the object speed. This is well-known conservation of energy.
Similarly, we get relations similar to eq. (1-14):
l m = l’ m’ = ÖA m = ÖA’ m’ = 3ÖV m = 3ÖV’ m’ (3-2)
It shows that products of length, square root of area, or cubic root of volume with mass are the same, regardless to the object speed and space dimension. We call it as space-mass conservation.
Substitution
of eq. (3-1) with eq. (1-1) leads to
m = m’ l’ / l
= m’ / cosq
q
= m’ / Ö(1- u2/c2) (3-3)
It proves that the
moving mass appear heavier due to deflection of space-mass. This is well-known mass equation in the
relativity theory.
The densities in (S) and
(S’) are defined as
D = m/V (3-4)
D’ = m’/V’ (3-5)
Combination of eq.
(1-12), (3-3), and (3-5) into eq. (3-4) leads to
D = D’ / cos4q (3-6)
It proves that a moving object
appears to compression due to deflection of space-mass. This is well known in the relativity theory.
When u = Ö3/2 c = 0.866c or q = 60 degree, then m = 2m’ and D = 16D’. We call this speed as the speed of double mass, and the speed of 16x density.
4.
Space-Time-Mass Theory
If we combine above space-time theory and space-mass theory into three-dimensional coordinate, we get a model of space-time-mass in three dimensions, where time is x-coordinate, mass is y-coordinate, and space is z-coordinate. When an object is moving, the moving coordinate (S') deflects the observing coordinate (S) in the z-coordinate, the angle q of deflection results from the relative motion, and its sine is proportional to relative speed u.
It is call as the deflected space-time-mass theory.
The theory proves that the contraction of a moving ruler, the delay of a moving clock, and heaver of moving mass, because the moving coordinate (S') deflects the observing coordinate (S), instead of space-time to curve. Not only do we realize that space, time and mass have been changed, but also space-time-mass actually deflect them all.
5.
Space-Time-Energy Theory
The space-time-mass theory is extendable, e.g. it can apply to space-time-energy. By principle of mass-energy equivalence, a relationship of energy E and mass is E=mc2, then the space-time-mass theory becomes to the space-time-energy theory by replacement of mass with E/c2. Therefore, the space-time-energy theory is similar to the space-time-mass theory.
6.
Conclusions
The deflected space-time-mass theory releases relationships among space, time, mass, energy and speed. It proves that moving objects appear heavier and compressed, their length, area and volume appear to contraction, and moving clocks appear to run slower by deflection of space-time-mass. It shows that space-time conservation and space-mass conservation, regardless of the object speed and space dimension. It indicates that space-time should not be curved; otherwise the shape of the object should be changed.
7. References
[1] Zhang Junhao and Chen Xiang , International Journal of Theoretical Physics, 29, 579, (1990 ).
[2] Zhang Junhao and Chen Xiang , International Journal of Theoretical Physics, 29, 599, (1990 ).
[3] Zhang Junhao and Chen Xiang , International Journal of Theoretical Physics, 30, 1091, (1991 ).
[4] Zhang Junhao and
Chen Xiang , International Journal of Theoretical Physics, 32, 609,
(1993 ).
[5] Zhang Junhao and
Chen Xiang , International Journal of Theoretical Physics, 34, 429, (1995 ).
[6] Zhang Junhao, Physics Essays, 10, 1, (1997).
[7] Cui Silong, Theory of Analytical Space-Time, (2000), http://publish.aps.org/eprint/gateway/epget/aps2000mar04_005/tast.htm