## Cluster Abell 2261 A "Local" Big Bang - the Abell 2261 Star Cluster

### A Special Relativistic Perspective

The proper determination of a Relativistic velocity (seen as greater because of the time distortion) means discarding the "Real" viewpoint and assume a theoretic, more descriptive one.  One for what the values would be were there no Special Relativistic Perspective Distortion (noSRPD).   While it is not said so specifically in the Classic theory, with “Relativistic” labels, but that is what a |Real| velocity is.  The speed measured from a viewpoint under no distortion – moving at a zero, or an immeasurably slow Planck level velocity.  That zero velocity is no more determinate than absolute velocity, but it is a valid mathematical perfection assumption that is true for almost all physical constants/relationships.  It is an ideal, but a valid theoretic ideal.

‘F=ma’ too, 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 an infinitesimal (2.97E-13m/s2), 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.  And the escape velocity, because it is a fundamentally different relationship calculated with a different equation, is much higher: approximately 3.75E+4m/s. Though they are valid for predicting Real actions and estimating forces on a body.  So avoid using the prejudicing |Real| or |Rest| designations and assume a velocity measured from an observation point with zero relativistic effects  – again, it is a presumed ideal.  Moreover, the time being measured is the time that passes from the perspective of the Relativistic object.  Fewer time units, not more.  The additional variable is not fundamentally different in any way, it defines some aspects of those |Real| or |Rest| labels.  There will be fewer Relativistic seconds passing as the distortion increases.  So instead of the "Classic" Special Relativity Time Equation:

Time' = Time/(1 - vReal2/c2).5

The Time variable is what Real time would pass for any event when there is no distortion. the |Time'| variable is for the amount of Real-time the same event would take when there is distortion.

The inverse would be the number of "Relativistic" seconds that would pass when there is no distortion |TimenoSRPD| and because time is slowing, fewer seconds will occur |TimeSRPD|.  We will also be more specific about the velocity calculating it with undistorted meters divided by the undistorted Time |vnoSRPD|.  So the equation becomes

TimeSRPD = TimenoSRPD*(1-vnoSRPD2/c2).5                        Equation 1

We will simply presume TimeSRPD & TimenoSRPD  are in seconds.  We will also define an noSRPD velocity: the number of meters traveled when divided by the greater number of undistorted Relativistic Perspective seconds |vnoSRPD|.  Set the vnoSRPD variable to 1 meter divided whatever TimenoSRPD it took to travel that meter.

vnoSRPD = 1m/TimenoSRPD

Divide both sides of Equation 1 with 1.0m

TimeSRPD /1.0m = TimenoSRPD/1.0m*(1-vnoSRPD2/c2).5

Inverting the equation

1.0m/TimeSRPD = (1.0m/TimenoSRPD) / (1-vnoSRPD2/c2).5

We have already defined vnoSRPDvSRPD would be the Relativistically distorted velocity

vSRPD = vnoSRPD/(1-vnoSRPD2/c2).5                                    Equation 2

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

vSRPD2vnoSRPD2 / (1-vnoSRPD2/c2)
vSRPD2 * (1- vnoSRPD2/c2vnoSRPD2
vSRPD2 vSRPD2 * vnoSRPD2/c2 vnoSRPD2
vSRPD2  vnoSRPD+ vSRPD2*vnoSRPD2/c2
vSRPD2  vnoSRPD2 * (1 + vSRPD2/c2)
vnoSRPD2  vSRPD2 / (1 + vSRPD2/c2)
vnoSRPD vSRPD / (1 + vSRPD2/c2).5                                    Equation 2

The equations above were confirmed with the classic Relativistic time distortion equation: using it to determine vnoSRPD  and vSRPD

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-v2/c2| expression.  The ratio of distorted apparent SRPD velocity to noSRPD velocity (vnoSRPD /vSRPD) is identical for all Relativistic equations:

vSRPD = vnoSRPD /(1 - vnoSRPD2/c2).5
vSRPD/vnoSRPD = 1/(1 - vnoSRPD2/c2).5
vnoSRPD/vSRPD = (1 - vnoSRPD2/c2).5

And

vnoSRPD = vSRPD /(1 + vSRPD2/c2).5
vnoSRPD/vSRPD = 1/(1 + vSRPD2/c2).5
vSRPD/vnoSRPD = (1 + vnoSRPD2/c2).5

Then because the RP Time variables are the inverse of the Classic |Time| variables, the Relativistic Perspective time equation can be the following:

TimeSRPD = TimenoSRPD * (1 - vnoSRPD2/c2).5                        Equation 3
TimeSRPD = TimenoSRPD /(vnoSRPD/vSRPD)
TimeSRPD = TimenoSRPD * (vSRPD/vnoSRPD)

So

TimenoSRPD = TimeSRPD * (1 + vnoSRPD2/c2).5                        Equation 4

The classic time equations (with undistorted time units) would be the inverse:

Time’ = Time / (1 - vnoSRPD2/c2).5                                   Equation 5

And

Time = Time’(1 + vSRPD2/c2).5                                       Equation 6

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 speed is uncertain, but so is the “Real” velocity used in Classic Relativity equations.

Gravitational Relativistic 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 speeds have relativistic factors.  VelocityReal/noSRPD values used in any relativistic equation dealing with Real measured values are approximate but are 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 speeds: |noSRPD|.  For higher ones |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 would use the more specific definitions.  |MassSRPD| would be the mass of a body in kilograms from an SRPD viewpoint under Special Relativistic distortion;  MassnoSRPD – the mass of the same body from an SRPD viewpoint under no Special Relativistic distortion

MassSRPD = MassnoSRPD /(1vnoSRPD2/c2).5                      Equation 7
MassSRPD = MassnoSRPD /(vnoSRPD/vSRPD)
MassSRPD = MassnoSRPD * (vSRPD/vnoSRPD)
MassnoSRPD = MassSRPD / (1 + vSRPD2/c2).5
Equation 8

And the length equations

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

LengthSRPD = LengthnoSRPD * (1vnoSRPD2/c2).5                      Equation 8
LengthSRPD = LengthnoSRPD * (vnoSRPD/vSRPD)
LengthSRPD = LengthnoSRPD * (vSRPD/vnoSRPD)
LengthnoSRPD = LengthSRPD / (1 + vnoSRPD2/c2).5
Equation 9

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 objects are then calculated with |(1 + vSRPD2/c2)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 vReal||noSRPD 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 & galactic groupings (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 significant 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.

Though the Lorentz-Fitzgerald contraction should be re-thought.  When you move at a relativistic velocity, it has always been reasoned that your physical existence does contract along the line of travel.  Though that does depend on the EM signal moving absolutely independently of the moving object - through a vacuum.  But for it to be absolutely independent of the environment through which it travels.  The Michelson-Morley experiment in the 1880's did not detect any motions for the experimental site, even though it was moving through a vacuum.  Though it could not have been a Quantum vacuum.  Perhaps the gas was undetectable with the sensing devices in the 1880's but that would not be a precision great enough for gas at Quantum levels.

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 be made on any of the objects we observe: what would they look like if they were really going at the relativistic velocities we observe them to, and they were NOT exclusively moving directly away from us.  Even if we were dead center in the Universe, it is completely unreasonable to say that in light of the interactions they have with one another.  That is something we KNOW happens – Galactic collisions are the most absolute, but there are many 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 an observed object is in expands, so it would seem to be getting thinner to us in some respect if anyone we observe were going in any direction other than directly away from us.

There are also additional General Relativistic equations that will 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.

* ALL of the equations in this paper have been confirmed in a table of velocities ranging from less than |1.0E-50m/s| to more than |c-1.0E-50m/s| to a precision greater than 100 decimal places. The speed of light is presumed to be 299,792,458m/s in this paper, but the reasoning used for its conclusions will work for any value.  It is an assumption necessary for a Universe with our light velocity, but the reasoning of this paper would work just as well for a Universe with a light speed as low as 1.0E-100m/s – or as high as 1.0E+100m/s.

A printable version of that velocities table is available on the Internet.

The table is at: Relativistic Space-Time Perspective Appendices

A Printable version of this Page is at: Special Relativistic Velocity Distortion

This site was authored by David G. Taylor

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