User:David Relativistic

The Relativistic Perspective

The Entire Theory of Relativity is calculated/reasoned/viewed from a single perspective - from a real or NON-Relativistic view. But evaluation of any piece of Data cannot rely exclusively on an "ideal" viewpoint.

Consider: it is perfectly reasonable (in a theoretic ideal) to be in a Universe with two objects: you reside on the one that is not moving. You observe the approach of an object that seems to be moving towards you at the speed of light. The blue shift in the signal from a hydrogen fusion drive (as would be indicated by its spectral lines) indicates that the body is moving towards you at light speed. As it gets closer, it is observed that while all the shapes within the object match one another in their aspect, the aspect is somehow distorted. YOU KNOW that the object is moving, but instead of showing the Lorentz-Fitzgeral contraction, it is aspect is one of being elongated, not compressed. The hydrogen fusion drive should also not ever be blue shifted to that extent, because Relativistic effects would reduce the frequency through time slowdown.

It is then suggested that your body, not the observed one, is moving. If that were true, you could not use the Relativistic Equations, because they would be invalid from your perspective. It is then suggested that a group of equations for evaluation of data could be formulated. They would have their base in the fact that "Real Velocity" and "Relativistic Velocity" would have exactly the same proportions as MASS, TIME, & LENGTH. The shift in TIME, would mean an exactly proportional increase in velocity. That proportional increase would mean that equations FROM A RELATIVISTIC perspective are logically reasonable. This site will develop (step at a time) those equations, and examine the broader aspects of the fact that ALL relativistic suppositions should be made to account for the two different perspectives: Relativistic and Non-Relativistic All the equations will have been confirmed to be in agreement with the Classic Relativistic equations to more than 100 decimal places.

Let's start with the basics. The way the Relativistic time equation –

Time’=Time/(1-v²/c²)^½

– works is this: the faster you go, the closer the value [v] is to [c]. So [v/c] (or[v²/c²]) gets closer to one|1|. As a result the –

(1-v²/c²)^½

- expression gets closer to zero. It is a fundamental in mathematics that if the value of the denominator declines at a greater rate than the numerator, then the value of any fraction becomes greater. The faster you go, the greater the rate of Real time units passing, compared to those that would were you at rest. All of the expressions in classic Relativity theory deal with Real values.

But another valid expression for the Relativity time equation would be the inverse: to deal in Relativistic seconds. For both perspectives, if an object is motionless, there is no distortion. From the perspective of the moving object the Real seconds don't slow down and the Relativistic seconds don’t speed up. But when velocity increases relativistic distortion increases and from the Real Perspective, it apparently takes more and more Real seconds for a Relativistic second pass. But from the Relativistic Perspective (RP), it is fewer and fewer Relativistic seconds passing for each of the Real seconds. What observers on a Relativistic vessel would want to know is how many of their seconds pass for each Real. So they would employ equations that are the inverse of the Classic Einsteinian ones -

Relativistic_Seconds_{In_Motion} = Relativistic_Seconds_{At_Rest} * (1-v²/c²)^½

Velocity is directly related to time. If you were on a vessel where the faster you moved, the fewer seconds would pass, for you, the velocity would be distorted. At approximately a 2.1198528E+8m/s velocity, because fewer seconds passed, it would seem that you were going at the speed of light. This Velocity Distortion is exactly the same as the Time distortion – from the Relativistic Perspective fewer seconds pass – so (as is established in hundreds of SF stories) the faster you go. And of course, since your Relativistic Velocity will share the exactly the same proportion change as the Time; a doubling in Time would mean an apparent doubling in velocity for the person viewing from the Relativistic Perspective.

Relativity is a leading candidate for the most important and elegant relationship theory in the history of Science. “e=mc²” is likely the most famous (and important) equation of all time. The Relativistic equations introduced by Albert Einstein are not, though, a complete expression of that theory. They only examine relativistic distortions from a simple, undistorted perspective. Relativistic distortion determinations are all made from the [Real], non-Relativistic distorted velocity – a velocity that is perceived by outside observers to be limited to light speed. The units of measure are the same on both sides of the equation; length, mass, time, and velocity – they use what the value would be if the measuring device were not being distorted.

Though consider: you are on the business class of a Spaceship, desperately trying to overcome a schedule loss you were forced to accept going approximately 2.11E+8m/s. The distortion created by that velocity would slow time by a factor of approximately 1.414E0. So the velocity you would observe from how quickly you approached your unmoving clients – and the blue shift of the light ahead of you – would be your Real velocity multiplied by the time distortion: 2.11E+8m/s*1.414E0. From that blue shift, your velocity would appear to you to be approximately light speed: 299,792,458∗. It would also be what you perceived to be your velocity calculated from the distance you went divided by the time measured from your perspective.

In going to Alpha Centauri, you would measure that it took you 4.37 years (A. Centauri is 4.37 Light years away). But, for the annoyed customer at the Ternary Centauri system, it would appear that it took 1.414E0*4.37 – approximately 6.18 years. What you perceived/determined your velocity to be could not be used in the [1-v²/c²)^½] expression because it would tell you that the distortion should be facing would be infinite – or imaginary. “Relativistic” objects must use different distortion Formulas/values for evaluating the velocity they observe (from some perspectives), because that observed velocity is relativistically distorted. Those observations produce data that is relativistically distorted and so will require different evaluative tools/equations. The combination of the |Real| velocity and an unlimited time distortion means there is no theoretic limit to the apparent or |Relativistic| velocity – an unlimited Relativistic||Apparent velocity established in hundreds of SF stories.

Special Relativistic Perspective Distortion (SRPD) velocity equations determine directly the relationship between Real & apparent Relativistic velocity. Those equations may be limited in the sense that they do not consider General Relativistic Distortion, but all of Physics must be structured that way. Mr. Newton’s force equation (f=ma or a=f/m) does not allow for Dr. Einstein’s Relativistic mass distortions. That does not rob it of its validity. It is useful for making approximations without the confusion/alteration of relativistic effects. The same is true of the Classic Relativity equations for moving objects – that are also distorted by the General Relativistic twists. That does not mean they are not useful for evaluating/analysing Special Relativistic weight gains.

SRPD equations are derived from the time equation. In Classic Special Relativity, |Real| labels are always approximates. All observable objects in the Universe are in motion. Determining an exact would entail determining a point of zero velocity. That would be one in which in which an object moves less than the Planck Length constant within the Planck time constant - the inverse of c (light speed) or approximately 3.3356E-9. The time would be determined by a timing device (i.e. no measurable advance of time) produces no measurable/zero movement. The movement could be calculated by a three dimensional rotation in which a survey is done of observable objects. If there was movement present, the length distortion of the observation point would change on those rotations, meaning the observed objects would lengthen/shorten (whether they were moving or not, their distortion would remain the same Relativistically). More specifically, when the observing object turned 90°, the width||length of the observed object would exchange values. The described experiment would seem impossible methodologically now, but it is a viable ideal. Measurement of velocity from that point would give a “Real”, non-Relativistically distorted velocity. Once zero velocity were determined, a Robotic device could be left there as marker for zero velocity. It is a theoretic ideal, but it is a valid ideal – “F=GMm/r²” too, presumes just two bodies, with no intrusions and an exact measurement of the radius between the two objects. That isn’t true anywhere. Here on Earth, we have a very direct example of that three/four/five… body distortion: the tides: we may not be able to FEEL the 3/4/5/whatever gravitational force distortion but we see it in terms of the tides.

Thus, |Rest/Real| labels become more than theoretical concepts. Accepting Dr. Einstein’s equations would mean the relationship between Relativistic and non-Relativistic velocities is deducible (light speed is assumed to be 299,792,458 m/s; references to that are limitless to the reader in this age of the internet). And lets make more specific definitions of the Classic Time equation:

c - speed of light

Time - Real time perceived from the perspective of a body not moving

Time’ - Real time taken for the |Time| value to pass if the body were in motion

Velocity_Real - Real observed velocity from a non-Special Relativistic Perspective viewpoint under no distortion

The time distortion equation is:

Time’ = Time/(1-v²/c²)^½

The Classic relativistic time equation is entirely from the non-Relativistic viewpoint/Perspective – but the passengers on a moving body will not be conscious of a greater number of seconds/hours/days passing. What their perception will be is that more Real time units were passing outside their immediate perspective for each of their distorted time units. The inverse equation, the equation using the Relativistic values, the values perceived from a viewpoint under that Relativistic distortion, would show how many of distorted time units were passing for each of the undistorted time units. Fewer relativistic time units will pass for each of the non-relativistically distorted time units.

So what ARE the consequences of Relativistic distortions? That is, the mathematically defined consequences of those distortions? While this examination may seem overly obvious to some, we should remember that there have to be parallel consequences in General Relativity. Not for a personal experience of those distortions, but recognition that if those distortions exist, they will be observable in astronomic observations – and a more complete scientific examination of those consequences.

The time distortion is immediately perceivable: because fewer time units pass under Relativistic distortion, phenomena observed outside the distorted area will behave as though the observed time units were passing more quickly. Though time is a dimension in some senses, it is not in others. Length, width, and height are not dimensions that force movement along that dimension. While the perceived rate of movement through time can be altered (by either simple psychological distortions or more absolutely, by relativistic distortions) those altered rates are always local – and those alterations do not ever halt or (except in Science fiction stories) reverse the progression of time. The perception of the alterations will be that non-relativistic actions will appear to increase their speed because fewer relativistic time units will pass than will pass with non-relativistic actions. The non-relativistic actions will include the simple progression of activities on non-moving, non-distorted bodies, described earlier, but that progression will also include the motion through space; a value obtained from a non-relativistically distorted perspective. The relativistically slowed time rate will make it appear they move at a velocity distorted to an increased speed.

Consider the theoretic proposal of that you [the salesperson] are on a vessel moving at a relativistic speed. You are able to see both a clock on their vessel and a clock on the stationary base. The stationary base will use the methodology described earlier to establish its stationary status. Plug that velocity into the |Time| vs. |Time’| expression: [(1-Velocity_Real²/c²)^½]

So the increase in the number of seconds under relativistic distortion is determined. It is always necessary to use matching units on both sides of any equation to make it a valid view of whatever is being observed – undistorted seconds, or more generally, undistorted time units.

But you and the passengers on the moving object won’t perceive the greater number of seconds. What you see through outside observations – at least from your perspective – is that fewer seconds pass compared to the seconds from a non-moving base. For you and the passengers, the more fundamental unit to use is a relativistic time unit – the inverse of the Real or non-Relativistic time unit. If the distortion is a factor of 2, then when two “Real” time units pass on the non-moving stationary viewpoint, then one of those time units will pass on the moving Spacecraft/viewpoint: one “Relativistic” second/minute/hour/day for each two of the same in Real time. Again, we will use seconds for our time; almost all citations of the “c” velocity are done in m/sec or Km/sec. The above equation uses the number of how many undistorted seconds/time units pass from a perspective not distorted. [Time] shows how many seconds would pass were there no distortion – for an object not moving. [Time’] shows how many seconds pass would pass for the parallel length of time for the same moving, distorted body from the perspective of an observation point not under distortion – [Real] seconds. That distortion can be directly observed from the change in what’s being observed: the motions of non-Relativistic objects, of information transfer from the non-Relativistic site (i.e. the pace of computer Spam transfers), in any interaction the relativistic body has with the stationary base, the non-Relativistic perspective. The observations would use values perceived on the moving body in ratio to the values perceived in the same units for the non-moving observation point. There is even some evidence (not terribly well scientifically defined evidence) of mood swings in we humans depending on the lunar/solar position. All of those confusing data items do not invalidate the Gravitation equation even just one tiny Planck length.

The same would have to be true of Relativistic equations: we could never determine EXACT velocity, but that does not invalidate the equations. So let us do equation definition from the Relativistic perspective of a moving body, with a PRESUMED exactly defined movement. If you can’t/aren’t allowed to do that, then it very simply is NOT a valid scientific equation – we are not declaring the precision, we are reasoning from a theoretic viewpoint that PRESUMES an exact Uncertainty Principle ∆E∆t ≥h energy|time definition precision. Something as simple (and fundamental) as the Classic Gravity equation (F= GMm/r²) depends on exactly the same precision. There is no point in this Universe where the gravitational force is small enough to declare the equation precise to a Heisenberg degree – that perfection assumption does not invalidate it as an equation and theoretical tool. A re-write the equation to its inverse, to a form that will calculate the number of Relativistic seconds that pass for each Real or non-Relativistic second that passes for a body not moving. As was briefly examined in the introduction, the SRPD time equation is NOT:

Time_SRPD = Time_noSRPD/(1- Velocity_Real²/c²)^½

Again, that describes the non-Relativistic second relationship. Equations for manipulating data from the perspective of the Relativistic distorted locale would be the inverse:

Time_SRPD = Time_noSRPD*(1- Velocity_Real²/c²)^½

It is a fundamental recognized by all of Science/non-Academic that fewer Relativistic Perspective seconds pass with distortion Relativistic distortion. Defining the SRPD variables more specifically:

Time_noSRPD – seconds passing from a Relativistic Perspective – Relativistic seconds - under no distortion: the distortion factor is 1. The velocity accompanying that distortion would be a zero velocity, a point where any movement in any direction distorts linear dimensions in the view of outside objects; objects with no Planck level motion in any vector.

Time_SRPD – the lesser number of Relativistic seconds passing because of the distortion resulting from the motion the object is ::::in.

Again, Time_noSRPD also presumes there are no gravitational distortions. So the Time equation becomes:

Time_SRPD = Time_noSRPD*(1- Velocity_Real²/c²)^½

We can “mix” variables in the equation so that some measure units from a Relativistic perspective and some from a non-Relativistic perspective. The only crucial thing is that the units for any variable component value (seconds/metres/kilograms) are the same on both sides of the equation. For instance, a variable in “Relativistic velocity” would be in Relativistic seconds (so as to measure the perspective of time from the distorted object viewpoint) and Real/non-Relativistic metres, to measure movement in the Real world. It should be noted, though, that because of Relativistic distortion, the Real world is something APPEARS to have gotten longer from the Relativistic perspective (that’s why the stars elongate in all the “Next Generations” Star Trek’s) – it has not, it is simply the perspective of the viewer. So divide both sides with 1 Real noSRPD metre [1m_noSRPD]:

Time_SRPD/(1m_noSRPD) = (Timeno_SRPD/1m_noSRPD) * (1- Velocity_Real²/c^2)^½

Invert that:

(1m_noSRPD)/Time_SRPD = (1m_noSRPD)/Time_noSRPD) * (1- Velocity_Real²/c^2)_½

Make the TimenoSRPD variable more specific:

Time_noSRPD = 1mTime_noSRPD/VelocityTime_Real

So

VelocityReal = 1mnoSRPD/TimenoSRPD

And so

1mTime_SRPD/TimeSRPD = VelocityReal /(1-VelocityReal^2/c^2)^½

Define another variable name

Velocity_SRPD - velocity determined by dividing Real length metres by an SRPD viewpoint time value

The VelocityReal variable contains the combination of two values: 1 metre for the Real distance traveled and the number of SRPD undistorted seconds it took to travel that 1 metre. The VelocitySRPD variable would contain the parallel but in Relativistic time values: 1 Real metre for the distance and the number of relativistically distorted seconds to travel that Real metre. So a mathematic definition would be:

VelocitySRPD = 1mnoSRPD/TimeSRPD

So

VelocitySRPD = VelocityReal / (1-VelocityReal^2/c^2)^½

The Relativistic velocity is not a “Real” velocity either. It is the apparent velocity of the moving body from a viewpoint assumed to have no Relativistic distortion. But, everything in the Universe has some velocity. Determining points at rest (particularly when General Relativistic distortions are considered) is impossible under current theory/technology. Establishing the speed of light is done from a viewpoint having minimal/zero Relativistic distortion – and that velocity will be distorted as well. We know this from the simple fact that the Earth changes its direct, linear velocity by approximately twice its orbital velocity when it is on opposite positions in orbit – but our measurement of light speed does not change, even though the time distortion has changed. From that we then know that when the source of the light changes its time distortion, the light it produces changes velocity as well. While the determination of absolute velocity in a Relativistic Perspective Universe may always be impossible, it must be defined before it may be determined. Even then, it would only be definable/determinable at a given specific point, with determined values for both Special and General Relativistic distortion (this writer does not have the data or theory to make an assertion either way on that determinability), but the existence of relativity makes it a definable theoretical ideal, something not possible under Classic physics. Absolute Classic velocity can only be accepted to exist if you accept an existence of the aether: something now thought not to exist if you accept the legitimacy of the Lorenz-Fitzgerald experiments. As was in the variable definitions, a Relativistic zero velocity would be one where at a particular point in space any motion in any direction would slow the pace of time, or change the dimensions of objects independent of the moving object. That ideal would also presume that there were no mass objects within a vicinity that would change the GENERAL Relativistic factor by amount greater than that defined by than the Energy/time uncertainty equation (∆E*∆t ≅ h). All of those theoretical limits do not mean there is no theoretical ideal. If an equation only has value when it does not rely on theoretical ideals, then ALL of Science’s formal equations have to put into the reality recycle box (some other reality may find use for them).

So discard the prejudicing |Real| viewpoint and assume a theoretic, more descriptive one, for values under no or zero Special Relativistic Perspective Distortion (noSRPD). Zero velocity is no more determinate than absolute velocity, but it is mathematically definable. That “perfection assumption” is true for all physical constants/relationships ‘F=ma’ is an idealized criteria proposition. Forces acting upon a body can never be determined perfectly: estimated but not without some inaccuracy. Newton’s simple equation assumes an ideal; it did not include force/acceleration vectors. Two equal exactly opposite vector forces would mean no acceleration. That would not mean there was no force acting on the object. ‘F=GMm/r2’ is the same – there are always more than two bodies of mass, exerting forces with different energy and vectors. A simple example of that would be the gravitation between the Milky Way and Andromeda – M31. The gravity is very small (2.97E-13m/s^2), but that is still greater than the Planck constant by a factor of more than 2.0146E+21 – so while it is small, it cannot be ignored at the quantum level. Both equations, though, are valid for predicting Real actions and estimating forces on a body. So avoid using the prejudicing |Real| or |rest| designations and presume a velocity measured from an observation point with zero relativistic effects. The additional variable is not fundamentally different in any way, it simply defines some aspects of those |Real| or |rest| labels:

VelocitynoSRPD – velocity in Real meters/Relativistic seconds measured from a perspective under no Special Relativistic distortion.

From the velocity distortion equations, and setting the value of that variable:

VelocitynoSRPD = 1m/TimenoSRPD

Replacing VelocityReal with VelocitynoSRPD

VelocitySRPD = VelocitynoSRPD/(1-VelocitynoSRPD^2/c^2)^½ Equation 1

Invert the equation and define the value of VelocitynoSRPD in terms of VelocitySRPD:

VelocitySRPD2 = VelocitynoSRPD2 / (1-VelocitynoSRPD2/c2)

VelocitySRPD2 * (1-VelocitynoSRPD2/c2) = VelocitynoSRPD2

VelocitynoSRPD2 - VelocitySRPD2 * VelocitynoSRPD2/c2 = VelocitySRPD2

-VelocitySRPD2 - VelocitySRPD2 * VelocitynoSRPD2/c2 = -VelocitynoSRPD2

VelocitySRPD2 + VelocitySRPD2 * VelocitynoSRPD2/c2 = VelocitynoSRPD2

VelocitynoSRPD2 = VelocitySRPD2 + VelocitySRPD2 * VelocitynoSRPD2/c2

VelocitynoSRPD2 = VelocitySRPD2 * (1 + VelocitynoSRPD2 /c2)

VelocitynoSRPD2/(1+ VelocitynoSRPD2/c2) = VelocitySRPD2

VelocitynoSRPD2 = VelocitySRPD2 / (1+ VelocitySRPD2/c2)

So

VelocitynoSRPD = VelocitySRPD / (1 + VelocitySRPD^2/c^2)^½ Equation 2

The equations above were confirmed with the classic Relativistic time distortion equation: using it to determine VelocitySRPD and VelocitynoSRPD.

More equations can be then formulated, used for deductions of conditions for bodies at rest in time, length and mass. Relativistic/non-Relativistic ratios are always the same, whether they refer to time, mass, or length: they all use the same “1-v^2/c^2” expression. The ratio of distorted apparent SRPD velocity to noSRPD velocity (VelocitySRPD/VelocitynoSRPD) is identical for all Relativistic equations:

VelocitySRPD = VelocitynoSRPD /(1 - VelocitynoSRPD^2/c^2)^½

(1 - VelocitynoSRPD^2/c^2)^½ = VelocitynoSRPD / VelocitySRPD

And

VelocitynoSRPD = VelocitySRPD /(1 + VelocitySRPD^2/c^2)^½

(1 + VelocitySRPD^2/c^2)^½ = VelocitySRPD/VelocitynoSRPD

The Relativistic Perspective time equation can then be:

TimeSRPD = TimenoSRPD * (1-VelocitynoSRPD^2/c^2)^½

TimeSRPD^2 = TimenoSRPD^2 *(1-VelocitynoSRPD^2/c^2)

TimeSRPD^2 = TimenoSRPD^2 * (VelocitynoSRPD /VelocitySRPD)

TimenoSRPD^2 = TimeSRPD^2 / (VelocitySRPD /VelocitynoSRPD)

So

TimeSRPD = TimenoSRPD / (1+VelocitySRPD^2/c^2)^½ Equation 3

Again, the classic time equations (in terms of undistorted time units) would be the inverse:

Time’ = Time / (1 – VelocitynoSRPD^2/c^2)^½ Equation 4

And

Time = Time’ / (1 + VelocitySRPD^2/c^2)^½ Equation 5

SRPD velocity was confirmed determined using the Special Relativistic Perspective time equations, dividing the TimenoSRPD value into the TimeSRPD and using that proportion to calculate the Relativistic velocity. The non-relativistic velocity was derived from that relativistic value and compared the original SRPD velocity. Apparent SRPD velocity is immediately observable from within the vehicle, sharing the above relationship with the noSRPD velocity. The validity of observed Relativistic velocity is uncertain, but so is the “Real” velocity used in Classic Relativity equations.

Gravitational distortion and Special Relativistic distortion form part of our entire reality. Zero velocity can be estimated, but the time equations in Special Relativity theory mean that all velocities have relativistic factors. VelocityReal/noSRPD values used in any relativistic equation dealing with Real measured values are approximate, but are valid theoretic ideals. The terms should not be |relativistic| and |Real| but rather |relativistic| and |non-relativistic|. Any outside observed velocity is as valid as a relativistic velocity. The sole issue is the precision of the value. For lower velocities: |noSRPD|. For higher velocities |SRPD| is better, indicating the need for conversion to a non-relativistically distorted value, to make it more accurate – but neither aspect is absolute.

The remaining Relativistic Perspective equations can also be determined. The mass equations:

MassSRPD - mass of a body in kilograms from an SRPD velocity viewpoint under Special Relativistic distortion

MassnoSRPD - mass of a body in kilograms from an SRPD velocity viewpoint under no Special Relativistic distortion

MassSRPD = MassnoSRPD /(1-VelocitynoSRPD^2/c^2)^½ Equation 7

MassSRPD^2 = MassnoSRPD^2/(VelocitynoSRPD/VelocitySRPD)

MassSRPD^2*(VelocitynoSRPD/VelocitySRPD) = MassnoSRPD^2

MassnoSRPD^2 = MassSRPD^2/(VelocitySRPD/VelocitynoSRPD)

So then

MassSRPD = MassnoSRPD*(1+VelocitySRPD^2/c^2)^½ Equation 8

And the length equations

LengthSRPD – length of a body in meters under Special Relativistic distortion from an SRPD Velocity viewpoint

LengthnoSRPD – length of a body in meters when under no relativistic distortion from an SRPD Velocity viewpoint

LengthSRPD = LengthnoSRPD * (1-VelocitynoSRPD^2/c^2)^½ Equation 9

LengthSRPD^2 = LengthnoSRPD^2 * (VelocitynoSRPD/VelocitySRPD)

LengthSRPD^2 / (VelocitySRPD/VelocitynoSRPD) = LengthnoSRPD^2

LengthnoSRPD^2 = LengthSRPD^2 * (VelocitynoSRPD/VelocitySRPD)

So then

LengthnoSRPD = LengthSRPD * (1 + VelocitySRPD^2/c^2)^½ Equation 10

By current equations, the velocity can appear to reach or exceed light speed from the viewpoint of the moving body because of relativistic distortions. Distortions in observed bodies are then calculated with |(1 + VelocitySRPD^2/c^2)^½| for a moving viewpoint to calculate the Real velocity – the velocity without relativistic distortions. Relativistic Perspective equations determine relativistic distortions from moving observation points. Both equations will have their certainty distorted by the fact that with current technology/theory it is impossible to determine an exact VelocityReal value. Theoretically, it always will be.

Comparative value of the Classic Einsteinian Relativity equations and Relativistic Perspective equations is velocity dependent. Einsteinian equations are more appropriate for low speeds. Motion is relative in any observation point (planetary, stellar, galactic systems; and galactic groupings too. Even traffic jammed freeway systems: you can’t really know which one of you is closer to ‘c’) so it is impossible to know the exact value for velocity. If all observed objects show a large blue shift - including a point where that shift was highest – that would indicate a relativistic time shift because of the velocity of the measuring device. If that is not observed, assume the observation point is immobile and use Einsteinian equations. If neither aspect is sufficiently perceptible to establish scientifically legitimate data, a combination of the Einsteinian and the Relativistic Perspective equations could be used to estimate the speed and vector of the observing and observed points.

Relativistic equations determine relativistic values (velocity, time, mass, and length) from corresponding non-relativistic values. Relativistic Perspective converts those relativistic numbers back to the original non-relativistic values.

There is another distortion to consider: Lorentz-Fitzgerald contraction. When you move at a relativistic velocity, your physical existence does contract along the line of travel. It is unreasonable, though, to say that you will be directly conscious of “getting thinner”. All of the objects around would seem exactly as they were when you were at rest, because they are “losing thickness” at exactly the same rate you are. You would also not be conscious of either the mass or the time distortion. What will happen is that the world outside will seem distorted – that distortion will depend entirely on your direction of travel. All of those objects at a direct right angle to that direction of travel will elongate – just like they do in Star Trek (well, not in the original Star Trek, but in The Next Generation and all that followed).

The elongation reduces as your view moves forward or backward, until there is no distortion exactly in front or exactly behind you. It may be that this distortion is even detectable – by observing structures at great distances, and seeing if a compacting or elongation (because of the relativistic status) takes place because of the distortion. Again, the degree of that distortion can be determined from both the Real velocity and the relativistic velocity. The inverse is true: the degree of distortion observed from the moving body will be the non-Relativistic Distortion. Using the distortion observed will give you your non-Relativistic velocity, and in turn, your Relativistic velocity. That could be used as a check on the velocity you determine from the Blue shift of objects directly in front of you. That shift would be the Relativistic shift – because your time slowdown would make the waves appear to be at a higher frequency than their non-Relativistic value. You could use that to calculate both your Relativistic and your non-Relativistic (Real) velocity.

It will always be an estimate, but the Relativistic Perspective can always be estimated and be set as well. There is an interesting supposition to me made on any of the objects we observe: if they were really going at the relativistic velocities we observe them to, they NOT be exclusively moving directly away from us. EVEN if we were dead centre in the Universe, it is completely unreasonable to say that in light of the interactions with one another. That is something we KNOW happens – Galactic collisions are the most absolute, but there is a great deal of observed interactions of two Galaxy changing the direction of one another’s movement. Then from the distortion they would both possess, the objects would seem “flattened” to some degree, from some perspectives. Having them all appear exactly as they do, means that they are all going directly away from us, always. That is surely an unreasonable supposition, EVEN IF you accept the spatial expansion business. If anything, the spatial expansion hogwash supposition would impose EXACTLY the same sort of distortion – the space it is in expands, so it would seem to be getting thinner to us.

There are also additional General Relativistic equations that have to be examined. The equations do not contradict General Relativity either, but are equations from a General Relativistic viewpoint. The value of “Real” velocities and the apparent Relativistic velocities produced because of time distortion (Special or General) have exactly the same validity – or deniability.

There are two sites on the Internet that examine all the issues in Relativistic Perspective from a less academic standpoint. They are called http://www.david-relativistic-perspective.com/ & http://www.relativistic-perspective.com/