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Spacetime metrics, the shape of spacetime.

Basically the spacetime metrics allow the calculation of distances in a coordinate system. They tell us about the "shape" of the space.

In Classical Mechanics the metric is Euclidean, 3D flat/square/constant, d=sqrt(x2+y2+z2)

In Special Relativity the metric is flat/hyperbolic/Minkowski, 4D, dependent on relative velocity , d=sqrt(c2*t2 - x2 - y2 - z2)

In GR the metric is Riemann, curved dependent on mass density, Differential Geometry tells how a given spacetime metric is related to the curvature of that spacetime. Basically, the curvature involves second-order derivatives of the metric. The Einstein Equation tells us how to calculate the spacetime curvature given the distribution of energy. In the end we have a set of second-order nonlinear partial differential equations for the spacetime metric. Once we solve those equations, we know how to measure distances in our spacetime. This is different from the other metrics in that given a fixed mass for the universe all parallel lines eventually meet and you have a closed finite spacetime. Non accelerating masses always travel in straight lines in this spacetime. To understand the path of a falling object in the normal sense we must map it back to the flat spacetime of SR.

We should expect relativity to fail on both micro and macro quantum scales due to quantum discreteness. High energy discriminates time and space only down to the Plank time and Planck length. A small integer values of Plack time and distance relativity can only be discrete, these continuous values predicted cannot be manifest. Lower energy discriminates vaster distances. The size of the spacetime interval manifest by the energy of a single Plank action is effectively the size of our universe. Small integer , n multiples of the Plank action discriminate this distance by 2n manifesting quantum discreteness on the galactic scale in addition to the micro scale.

Relativity does not fail in concept, that which is relative is still relative, but numerically it must fail. Its equations are continuous but the universe is discrete and composed of directed orderings of discrete change rates.

In Discrete Relativity we have local contractions (vacuum energy sinks, cold masses) defining a dynamic spacetime equivalent to GR, plus we have local expansions (energy sources), manifesting opposite curvatures or a positive cosmological constant which is not really constant and may be directional. It accounts for all acceleration, not just that due to gravity.

The Information System Model

The objective information model assumes only that the universe is one of the countable logical systems as defined by Turing. Just as we can enumerate all concievable mathimatical systems as the countable axioms of predicate calculus, we can enumerate all concievable logical systems. If the universe is in that set, then it is comprehensible. If it is not, study of it would be fruitless and thus far measurement has not contradicted the assumption that the universe is logical dispite the MythOfUncertainty.

We include the set of all communicating participants (senders and receivers of effects/signals) and consider the information theoretical possibilities for effects received to reveal the state of the sender, the local resulting state change of the participant, and subsequent emission comprising an information system.

We find that the system exhibits universal computing by equivalence to nand-delay networks. The quantum logical clockwork may be viewed as general purpose computation. This does not preclude the physical model of interacting differences, instead it provides a framework for modeling it. Everything is combined into a single mechanism of alternating differences which manifest energy as timespace intervals in units of Plank actions.

Quantum Mecxhanics is VERY close to the right answer, and the experimental facts of quantum mecanics can complete the model. But we cannot embellish nature with information not manifest by quantum interactions and be true to the information model. We do NOT embrace any of the various intepretations of quantum mechanics, just the measureable physical results it predicts.

The elemental information model only admits the existence of what may be measured. It does not presume the fundamental existence of fields or any other magical influences at a distance. Nor does it presuppose a continuuum or the existence of entities with particle or wave nature.

The Discrete Relativity Model

In quantum theory the entire universe represents a single state space. In relativity, state, as defined by momentum and position is relative, not absolute. In Discrete Relativity there exists a RelativeStateSpace for each participant in the InformationUniverse.

To understand the information of relativity, consider a simple thought experiment....

Suppose I pass you at half the speed of light (proper velocity) just as some light source flashes as it passes us both at some arbitrary speed.

We presume, based on experimental results that the speed that the light flash travels is relatively constant and independent of any of our motion.

By your clock, after one year, your buddy, at rest with respect to you, one light year away, receives the light. (fact)

But my buddy, at rest with respect to me, who passes your buddy at that instant and sees the light at the same time is only half a light year ahead of me as I am now half way between you and your buddy (fact)

How can it be that light speed is constant but the light traveled only half as far for me as it did for you in the same time interval????

It is impossible. Either, experiment is wrong, and light speed is not constant and independent of the motion of the source, or the time interval is not the same.

Either my light, or my clock must be slow. (fact)

Conversely I can consider myself and my buddy still, and you and your buddy traveling at half the speed of light in the other direction. There is no authority to say which one of us is really moving. By my clock, in half a year the light reaches the spot where our buddies cross. But how could it travel a light year between you and your buddy in only half a year? The only options are that the light is traveling twice as fast for you as it is for me or your clock must be running twice as fast as mine.

Experiment shows that the time interval is indeed not the same and confirms that light speed appears constant in any inertial frame to a good approximation. (fact)

There is no alternative. If light speed is constant, time must be relative to motion. There is no other logical solution and experimental results confirm both to a reasonable precision.

The remainder of special relativity is just a methodology to account for this fact in a covariant manner. It does as much, or more, to obfuscate the simple truth as it fudges reality to make everything come out right. It models the perceived distortions rather than the absolute reality. But mathematically it cannot be very wrong. There is no other means to reconcile constant light speed and relative motion except by relative time, which is, thankfully, confirmed by measurement.

Thus the assumption that light speed is independent of source motion is sufficient to justify the relative nature of time, and as a consequence, all the predictions of special relativity. It does not however justify all the misconceptions that special relativity seems to attract such as absolute mass increaces or length contractions etc.

The meaning of this, may be simply that all clocks are independent and the notion of absolute time is simply wrong. In discrete relativity we see how the tic tock of quantum interactions manifests time in this manner. Special relativity is not right all the time, but it is generally an excellent approximation.

The ordinary events defining space and time are photons, or exchanges of momentum between electrons which have only two witnesses the sender and receiver of the photon. The energy exchange is always in an integer number of Plank actions. The energy of the participating electrons is due to relative motion. Each observer agrees that the photon traveled at the speed of light from the high energy electron to the low energy electron. But they may disagree on which electron had the higher energy, since the energy is determined by their relative motion. When they disagree on which electron had the higher energy they must also disagree on which way the photon went. This makes the absolute path of the photon indeterminant in time. This effect can account for the relative nature of time.

In the macrocosm we all agree which way the photon went except at extremely high velocities, so we find the relative nature of time surprising. However measurement contradicts absolute time and the nature of the privative events that compose our world, I contend, seems to provide the reason.

Local orderings of actions manifest time but the primal constitute of energy is the action, Plank's action to be specific. Actions and lossless reactions unceasingly according to perspective. Actions across space need not be ordered in time except according to perspective.. It is not time or space or energy alone which is manifest by Planck actions, as these things are never manifest independently and manifest as all that is manifest is relative momentums and positions.

In the elemental information model energy is composed of frequencies of reversing differences. Differences reversing across time constitute masses, by me/c^2. Differences reversing across space free energy manifesting space, by xh*c/e at time independence intervals t1/fx/c.

A reversal may be a propagation across space, or a reflection manifesting position, depending on relative motion due to discrete effects. A clock is a tic toc, left right reflection. But moving rapidly relatively can lose lefts or rights, leaving only tics and no tocs, where nothing happens without a tic toc.

At .5c relative velocity there is an octave change in the relative rate of reversals or frequency by the Doppler shift. This is a doubling effect. Proper time is sqrt(2) as half the events are doubled. At .75c relative speed proper time is half the rest frame as all rest frame events are doubled. doubled events, tic without tocs or tocs without tics. This is a simple way to view the origin of the Lorenz factor in a discrete world.

The vacuum is the manifestation of occupied quantum states of low momentums. The vacuum manifests orderings of velocity changes, from which is projected our notions of velocities and positions which are illusional images in that they possess an existence which is relative, not absolute. They are merely a holographic projection, a second order discrete integral, of that which exists absolutely. As the zero point vacuum energy uniformly occupies lower momentum quantum states independent of relative motion, it has a nearly constant effect, manifesting the relative nature of motion. Only the changes in, or differences of differences are actually manifest where relative truth is a manifestation of perspective without independent manifestation.

Inertial Mass is manifest by the momentum exchanges associated with the velocity changes in the vacuum, both at the zero point and by those which are independently measurable.

See WhitescarverModel QuantumRelativity QuantumInterference QuantumTunneling QuantumEntanglement RelativeStateSpace MythOfTheContinuum MythOfUncertainty TheCaseOfTheElectronCollision

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