Matter, Space, Time, and Motion: A Unified Gravitational Perspective

Abstract

This article explores the links between space, time, matter and its motion in the essential context of the universe they constitute. Conventional and standard physics maintains a nearly dismissive separation between dynamics and the matter-filled universe and indeed between cosmic matter and a priori space-time while asserting their mutual influence in other physical situations through the Einstein equations of general relativity. This can be traced to the incompatibility between the special theory of relativity that rejects a preferred frame and the real situation of a single matter-filled universe in which observers in different states of motion have measurably different experiences. We will argue that the present position cannot be maintained consistent with empirical and physico-logical evidence. The historical fact that all our fundamental theories were formulated and completed before we acquired significant and crucial knowledge about the matter content of the universe and its gravity is contrasted with the unavoidable situation that all our empirical experience and dynamics happens in the presence of all other matter in the universe. A careful analysis leads to a new and necessary paradigm in which several of our notions and even fundamental theories involving space, time and matter need to be reformulated with cosmic gravity as the determining factor. This, when combined with some crucial experimental results, answers several open issues that have been debated for centuries in foundational physics.

Appendices

Appendix T

Here we summarize the essential theoretical results [1, 2, 8, 11], outlining the derivations that support the arguments in the paper. The conventional description of the properties of space and time under motion is contained in the Lorentz transformations (LT). This rejects Galilean relativity and replaces it with invariance of the homogeneity and isotropy of space. However this can be maintained only in empty space. Empty space is isotropic and homogenous and remains so in every moving frame. So, LT that keeps the isotropic and homogenous metric invariant is the valid description of motional transformations only in the nonexistent metaphysical empty space. The real space has matter—the charge of gravity—at an average density of $10^{-29}$ g/cc, which becomes a ‘current’ of the charge of gravity in every moving frame. Space becomes anisotropic with this flow, a physical vector potential proportional to velocity (which is in fact a part of the full 10-component symmetric tensor), $A_{i}/c=g_{0i}=v_{i}/c$ is generated, but LT cannot accommodate this anisotropy (see Fig. 14.1). Note that a similar electromagnetic vector potential would have been generated if the universe were slightly electrically charged. Not only the geometrical features, but also the ‘transformational features’ of space and time are to be determined by the matter around.

Fig. 14.1

Motion converts a nearly homogenous and isotropic distribution of matter into a matter-current generating relativistic anisotropic gravitational potentials or metric components. Only those motional coordinate transformations that reflect this are physically relevant and legitimate

This is all we need to see the solution to the age-old problem of pseudo-forces, inertia etc., and the real source of relativistic effects. The fact that there are no locally measurable physical effects of a constant vector potential field is then the statement of the principle of relativity and it is strongly tied to the observed homogeneity of the matter-energy distribution. Surprisingly, the Galilean transformations (GT) correctly gives us, along with the observed anisotropy, the most important relativistic feature of motion—time dilation! To illustrate this use a limited version of the actual Robertson-Walker metric, ignoring the very slow time evolution. GT specifies the coordinate transformations $x^{\prime }=x=vt$ and $t^{\prime }=t$. Physical spatial and temporal intervals can be deduced by including the metric in the moving frame. Under GT, the metric coefficients transform from $\left\{ g_{00}=-1,g_{0i}=g_{i0}=0,g_{ii}=1\right\}$ to $\left\{ g_{00}=-(1-v^{2}/c^{2}),g_{0i}=g_{i0}=v/c,g_{ii}=1\right\} .$ Nonzero $g_{i0},$ a gravito-magnetic potential, gives the observed anisotropy. The temporal duration in the moving frame is now $\sqrt{-g_{00}}dt^{\prime }=(1-v^{2}/c^{2})^{1/2}dt.$ GT indeed contains the physics of time dilation with v as the absolute velocity or velocity relative to the cosmic frame. Of course, the relative velocity of light is now Galilean, $c^{\prime }=c\pm v.$ Therefore, we also get the length contraction correctly.

This can also be treated in the language of gravitational potentials. It is well known that the Newtonian gravitational potential $\Phi _{u}$ at a point in this universe of size Hubble radius or so, evaluated using the observed matter-energy density, is numerically close to $c^{2}$. In moving frames, the relativistic potential will have velocity dependent ‘vector potential’ component

$$\begin{aligned} A_{i}=\frac{v_{i}\Phi _{u}}{c}\left( 1-v^{2}/c^{2}\right) ^{-1/2}=\gamma \frac{v_{i}\Phi _{u}}{c} \end{aligned}$$

(14.2)

leading to several large gravito-magnetic effects.

Though $g_{i0}$ is homogeneous in a uniformly moving frame, which implies the principle of relativity, if there an acceleration $g_{i0}$ becomes time dependent and the physical effect is a reactive force on the accelerated system,

$$\begin{aligned} F_{i}=-m_{g}\frac{dA_{i}}{cdt}=-\frac{m_{g}\Phi _{u}}{c^{2}}\left( \gamma a_{i}+\gamma ^{3}v_{i}(\vec {v}\cdot \vec {a}\right) \end{aligned}$$

(14.3)

In other words, the vector potential modifies the momentum (enabling generalizing to quantum theory) as $p^{\prime }=p-m_{g}A_{i}.$ We see that accelerating a body requires overcoming this cosmic gravito-magnetic reaction and hence a force $F_{i}$ which is the full relativistic form of Newton’s law of dynamics and the conventional inertial mass is just $m_{i}=m_{g}\Phi _{u}/c^{2}$. The law of dynamics is indeed gravitational, operative only because the universe is gravitationally charged, a connection that physics never imagined so far. Newton’s law is a relativistic gravito-magnetic consequence of cosmic matter and the analogue in electrodynamics is the Lenz’s law. We see that not just the conventional pseudo-forces in rotation, but also the very fact that a force proportional to mass is required to accelerate an object is a direct consequence of cosmic gravity, going a step deeper than Mach’s speculation on pseudo-forces in rotation.

Hence the ratio $m_{i}/m_{g}$ is universal. The equivalence principle is a necessary implication of cosmic gravity. Therefore, Newton’s law of dynamics and the equivalence principle have the same physical content and one implies the other through their cosmic gravity connection [11]. Needless to emphasize that both the centrifugal and the Coriolis forces follow as consequences of cosmic gravity, fully satisfying Machian speculations. The curl of $g_{0i}$ or $A_{i}$ is $2\Omega ,$which is the cosmic gravito-magnetic field $B_{cg}$ in any rotating frame and an object moving at velocity v will feel a gravito-magnetic force $F_{gm}(v)=m_{g}v\times 2\Omega .$ Thus Coriolis force is just the gravitational Lorentz force. The particular pseudo-force that Mach addressed, the centrifugal force is from the time dependence of the direction of $A_{i}$; $F_{c}=m_{g}A_{i}\frac{d\hat{A}}{dt}=mv^{2}/r$.

The other important effect is the coupling of cosmic gravity to spin, both classical and quantum. Spin is the current of the charge of gravity and all spin dependent physical effects should be traced to the gravitational interaction. The coupling is $s\cdot B_{cg}/2$. Cosmic relativity addresses this completely and derives a whole lot of observed and observable physical effects, ranging from geometric phases and spin valve effects on particles in chiral motion to purely quantum effects like the fractional quantum effect and spin-statistics connection [12].

Appendix E

1.1 The Relative Velocity of Light

In the context of the debate between absolute and relative, there is in fact just one crucial foundational postulate we need to test and verify for deciding one way or other. That is the nature of propagation of light. A paradigm in which there is a preferred frame that determines the ‘true’ velocity of light, the one-way velocity of light relative to an inertial observer moving relative to the frame at ‘absolute velocity’ v is $c\pm v.$ In contrast, the prevalent concept of space-time in physics derives from the postulate of the invariance of the relative velocity of light, which in turn rejects the idea of absolute rest, preferred frame and universal time. Then light takes the same duration to travel the relative distance L measured from the observer, independent of the velocity of the observer. If this could be directly checked, we can decide without ambiguity on the fundamental debate. The general premise is that this test is not possible because the measurement of duration requires two clocks separated by distance L, and their synchronization requires the very feature we are trying to ascertain. However, it turns out that this problem can be solved in an amazingly simple way [1, 13], once we break apart from the psychological shackles of classical two-way experiments like the Michelson-Morley experiment which are not decisive between the two alternatives. That the M-M experiment cannot decide the issue, contrary to common beliefs and statements is easy to prove. The expected signal in the M-M interferometer is proportional to the difference in two-way light travel time in the two arms;

$$\begin{aligned} \delta T=\frac{2L_{1}}{c(1-v^{2}/c^{2})}-\frac{2L_{2}}{c(1-v^{2}/c^{2})^{1/2}} \end{aligned}$$

(14.4)

This was observed to be zero. One explanation is that relative velocity of light is Galilean, but the arm $L_{1}$ that is along the direction of the velocity has a physical contraction of $L_{1}(1-v^{2}/c^{2})^{1/2}.$ The STR explanation is that there is no physical length contraction (and it is a coordinate effect that depends on relative velocities), but the relative velocity of light is an invariant constant and hence light takes time 2L / c in each arm, independent of the velocity of the interferometer. There is no way to resolve this ambiguity in any variation of the M-M experiment. One needs to find a way to compare one-way relative velocities.

The physical issue to determine by a measurement is the time taken to travel a distance L relative to the observer. Imagine a pre-defined light path with fixed length. One counts time when light starts from one end and it is clear that the time light takes to reach the other end does not depend on the shape of the light path. However, the second clock at the other end comes close to the first one when we loop around the path and one can dispense with the need for two clocks! If one chases any moving entity that is moving very fast on a looped one-dimensional path, one gets a crossing after a duration $\delta t=L/c^{\prime }$ where L is the distance around the loop and $c^{\prime }$ is the relative velocity, all measured relative to the observer. This can be measured with a single clock and the observer can continue to be on a inertial trajectory (unlike in the controversial Sagnac rotating experiment). The crucial point is that correctness of the experimental method can be tested on a known Galilean wave, like sound and then it becomes simply a comparison between sound and light in identical configurations (Fig. 14.2). The experiment with sound returns the expected result; the duration depends linearly on the velocity of the observer as $\delta t=L/(c-v)\simeq L(1+v/c)/c.$ The experiment with light returns the unexpected result; the duration, measured interferometrically, depends linearly on the velocity of the observer as $\delta t\simeq L(1+v/c)/c.$ Light is indeed Galilean! Its true velocity is determined in the cosmic rest frame (and not the ether of the 19th century). Irrespective of what one believes, a direct empirical test falsifies the fundamental postulate of relativity theories and also supports the existence of a preferred frame. The result itself cannot pin down what this frame is, but supplementary evidence unambiguously picks the cosmic gravitational frame as the determinant frame.

Fig. 14.2

When a wave-pulse is chased by an observer, the relative distance increases progressively, but the time taken to reach any point on the path can be determined with just one clock by looping the path around, while the observer is in inertial motion. The validity of the idea is tested by measuring the relative velocity of sound (left panel), which returns the expected Galilean dependence of the time delay on the velocity of the observer. The experiment is repeated with light in the same configuration and the result is similar, proving without ambiguity that light is indeed Galilean

It is important to mention that we have now completed several other experiments [12] involving currents and magnets in general relative motion and gyroscopes (gravito-magnets) in rotating frames, apart from analyzing several other experiments where particles with spin are transported along non-inertial trajectories, all of which unambiguously and firmly asserts that “phenomena of electrodynamics as well as of mechanics possess properties corresponding to the idea of absolute rest”.