_{1}

^{*}

Through reevaluating the physical significance of Hubble law, we propose the concept of spatial relativity and make two postulates: 1) Distance is equivalent to motion; 2) Hubble radius

In 1929, Hubble announced his discovery in astronomical observation [_{H} need to obey different additions, but indeed they are also linked by the Hubble relation u_{H} = Hr (H Hubble constant). This means that, as long as H is constant, it would inevitably lead to the observational contradiction. Specially, if distance is doubled, the recession velocity determined by HL will be doubled (even greater than the speed of light c), u_{H} (2r) = Hr, whereas by the Lorentz velocity addition, due to the body at position 2r moving with a velocity Hr as measured in the cosmic rest frame S' at r, and the velocity of S' relative to the earth reference S reading Hr, it seems to be equal to

To avoid the contradiction, we raise HL to the status of a postulate, and stress the equivalence of distance and motion. It shows that, for being equivalent to motion, the cosmic distance should obey the same addition as velocity. Starting from this, we develop the theory of relativity into a unified form, in term of which spatial geometry, kinematics and cosmic electrodynamics are to be understood. The modified spatial geometry can help us to construct a static cosmological model with neither a beginning nor end of time, and hence no need to define initial conditions. In our model, the universe is appearing as a finite 3-dimensional ball of radius _{0} = H^{−}^{1}), just corresponding to the physical horizon. The properties of the model are discussed and some new results are presented.

Basic consideration. In cosmology, the cosmological principle is always regarded as a theoretical cornerstone [

To find the way out of the impasse, we extend the content of the relativistic principle: no experiment can definitely single out one of frames of reference is “truly” stationary or at “absolute” origin, while the others are “truly” moving or in the off position. This means the physical relativity is not only reflected in motion, but in space, namely the cosmic space has the relativity too. Therefore, the difficulty that had to be resolved amounted to choosing amongst two alternatives: 1) Distance and velocity obey different additions, and something was wrong with HL; 2) There is a new principle valid for cosmological observation. The first possibility should be thrown out due to many observational evidences supporting HL. The second is our final choice: physical laws are the same in every part of our universe, or, no experiment can detect the “absolute” position of a frame. Hereby, we make two postulates:

Postulate I. Physics in a still frame at position r in relativistic space is equivalent to physics in an inertial frame moving with velocity Hr in rigid space (i.e. Euclidean space).

Postulate II. Hubble radius

By the two, the cosmological and relativistic principles can be stated uniformly as that: the universe does not possess any privileged positions or frames. Once the idea is included in this framework, all the frames, whether in remote distance or motion, are now on equal footing. Importantly, ^{−}^{18} s^{−}^{1}, we get

To illustrate the consequences of our postulates, we reassert that HV is only quantitatively equal to the velocity of a particle passing though distance r in time interval T_{0}, but indeed represents a virtual velocity for its being unable to cause any displacement. So that, if assuming there exists a kind of displacement

, (1)

where

transformation

that, two events observed by observer S' to be simultaneous (

Accordingly, the transformation for 4-position

, (2)

This is a remarkable and general result, which in the case of

Effects of spatial relativity. Until now, we have only concerned the spatial relativity, but need to look at its kinematics. The reason is that, according to the usual view if given a speed, an object will move without bound i.e. up to and then beyond the horizon range. This implies, if accepting the transformation above, it will transform a real position into imaginary. To avoid the problem, we must distinguish two type velocities in physics, the first is a virtual velocity, called HV

Now, we emphasize only the frames of moving with constant FV relative to a free particle can be treated as the inertial ones, which would strongly suggest us to modify the Newton inertia law as that: the inertial nature of free moving object is no longer to keep usual velocity, but FV constant. Therefore, the spacetime geometry could be derived from the assumption that there exist rigid coordinates _{D} representing the relative speed of photon flying away from the horizon, like the separation speed of two reverse motion photons. In fact, the FV of light measured by any observer in any position, without exception, is c.

What is the physics behind the spatial relativity? The answers are time dilation―a distant clock appears to run slow, and length contraction―a distant object appears to contract. Physically, to interpret time dilation, we consider a rest light clock of ticking away the time by light-pulse bouncing back and forth between proper length L_{0} (see _{0} with DV

Correspondingly, a length will get shortened in sight line when measured by a distant observer. Shown as _{0}. Whereas for observer S, the pulse distance becomes L, and the total round time

Developed relativistic principles. Now, it should be restated that, the universe appears the same in every direction from every point in FV space, and the statement encourages us to develop Einstein’s postulates as:

The principle of relativity Physical laws have the same form in all frames of reference moving with constant FV with respect to one another.

Constancy of FV of light. The FV of light is independent of the motion and position of its source.

The moving behavior of material objects will be influenced by, and consistent with the FV transformation between different frames. The transformation for 4-velocity

, (3)

which in the case of

Let us examine the point O' at position r in frame S, its proper distance should be

when

For simplicity, we rewrite the 4-coordinate interval as

Relativistic Dynamics. As an extension of usual momentum, the FV 4-vector

This is very the Hubble relation.

For free particle, we can naturally think of its FV momentum conservation, namely

, (6)

The result shows, even for a free particle, it will be subjected to an effective damping force

An interesting step is to introduce the 4-momentum inertia

Cosmic electrodynamics. It is natural that, the electrodynamics of moving bodies could be in agreement with the developed relativistic principles, under which all the problems in electrodynamics could be discussed. In particularly, when we say Maxwell equations (ME) are covariant, we eventually must specify the transform properties of the electromagnetic fields E and B. Namely, under the FV Lorentz transformation, not only the space and time coordinates will change, but also the electromagnetic fields. The transform formulae for ME are somewhat simpler when written in the Heaviside-Lorentz system of units, of which the rigid coordinate form is [

where

Using these rules, we can check the covariance of equations of electromagnetism. The approach can provide us all the knowledge of cosmic electrodynamics, the key point is to transform the involved quantities into relativistic space. For example, by Equation (7) we get the Coulomb field

for

In modern cosmology, our universe is described as a surface of 4-dimensional sphere, whose contracting or expanding in the direction of the 4-radius would give all the dynamical properties of cosmic system [

To introduce

In this way,

Therefore, for our universe of

which requires

Now, by analogy with the modified Coulomb field (9), we write the Newtonian gravity in relativistic space as

From which we see that, accompanying with the usual gravity

It shows that, for the Newton universe, the widespread existence of repulsive interaction can just resist the gravitational collapse, namely

By the transformation of volume element_{0} is the background mean number density near us. The total number of galaxies within radius r in relativistic space reads_{0} within radius

Finally, Equation (5) also tell us the apparent variation of temperature of cosmic blackbody radiation with redshift,

As presented above, BBM maintains the existence of the causally disconnected regions in cosmic space, and this is clearly contrary to the spirit of physical unification. Here, we show that, the difficulties can be overcome by proposing the sameness of distance and motion, and adopting instead a principle of relativity for cosmic mechanical and electromagnetic processes and by assuming the independence of the FV of light on the velocity and position of the source. Importantly, application of the developed principles can naturally lead to a detailed description of relativistic phenomena, and thus it can provide a consistent theoretical expression to the spatial geometry and material motion both at cosmological distance and in local space―all in a complete agreement with observations. This expression has numerous conceptual differences with the traditional ones, and thus possesses more explanatory power.

To sum up, our developments can be given as followings:

1) The starting point of this work is to propose the spatial relativity by raising the postulate status of HL, which would require the new spacetime geometry adapted to the modified inertia law.

2) A unified form of relativity theory has been derived from the FV relativistic principles: a) Physical laws have the same in all FV inertial frames; b) FV of light is constant. And the unified can give a satisfactory account of the phenomena of kinematics.

3) By the definition of 4-position

Reviewing the overall scenario and its implications, what is most remarkable is that the developed theory will bring a significant change to physics. Especially, our cosmological model based on the concept of spatial relativity can differ so much from the standard picture, and lead to the current universe without employing more extra assumptions.

Qiankai Yao, (2015) The Spatial Relativity and Its Physical Consequences. Open Access Library Journal,02,1-8. doi: 10.4236/oalib.1101286