A Special Relativistic Perspective

The proper determination of a Relativistic velocity (seen as higher 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 explicitly 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 a theoretic ideal.

‘F=ma,’ too, is an idealized criteria proposition.  Forces acting upon a body can never be determined precisely. They can be 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/r^2’ is the same – there are always more than two bodies of mass, exerting attractions 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.  The time 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 - v_Real²/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 |Time_noSRPD| and because time is slowing, fewer seconds will occur |Time_SRPD|.  The velocity is calculating by dividing undistorted meters by the undistorted Time |v_noSRPD|.  So the equation becomes

       Time_SRPD = Time_noSRPD*(1-v_noSRPD²/c²)^.5                        Equation 1

We will simply presume the Time_SRPD & Time_noSRPD, variables to be in seconds.  A noSRPD velocity is Meters travelled by of undistorted Relativistic Perspective seconds |v_noSRPD|.  Set the v_noSRPD variable to 1 meter divided whatever Time_noSRPD it took to move that meter.

       v_noSRPD = 1m/Time_noSRPD

Divide both sides of Equation 1 with 1.0m

       Time_SRPD /1.0m = Time_noSRPD/1.0m*(1-v_noSRPD²/c²)^.5   

Inverting the equation

       1.0m/Time_SRPD = (1.0m/Time_noSRPD) / (1-v_noSRPD²/c²)^.5   
                            
We have already defined v_noSRPD; v_SRPD would be the Relativistically distorted velocity.

    v_SRPD = v_noSRPD/(1-v_noSRPD²/c²)^.5                                    Equation 2

Invert the equation and define the value of Velocity_noSRPD in terms of v_noSRPD:

     v_SRPD² = v_noSRPD² / (1-v_noSRPD²/c²)
     v_SRPD² * (1- v_noSRPD²/c²) = v_noSRPD²
     v_SRPD² - v_SRPD² * v_noSRPD²/c² = v_noSRPD²
     v_SRPD²  = v_noSRPD² + v_SRPD²*v_noSRPD²/c²

     v_SRPD²  = v_noSRPD² * (1 + v_SRPD²/c²)
     v_noSRPD²  = v_SRPD² / (1 + v_SRPD²/c²)

     v_noSRPD = v_SRPD / (1 + v_SRPD²/c²)^.5                                    Equation 2 

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

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 (v_noSRPD /v_SRPD) is identical for all Relativistic equations:

      v_SRPD = v_noSRPD /(1 - v_noSRPD²/c²)^.5
    v_SRPD/v_noSRPD = 1/(1 - v_noSRPD²/c²)^.5
    v_noSRPD/v_SRPD = (1 - v_noSRPD²/c²)^.5

And

     v_noSRPD = v_SRPD /(1 + v_SRPD²/c²)^.5
    v_noSRPD/v_SRPD = 1/(1 + v_SRPD²/c²)^.5
    v_SRPD/v_noSRPD = (1 + v_noSRPD²/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:

     Time_SRPD = Time_noSRPD * (1 - v_noSRPD²/c²)^.5                        Equation 3

     Time_SRPD = Time_noSRPD /(v_noSRPD/v_SRPD)

     Time_SRPD = Time_noSRPD * (v_SRPD/v_noSRPD)

So

     Time_noSRPD = Time_SRPD * (1 + v_noSRPD²/c²)^.5                        Equation 4

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

     Time’ = Time / (1 - v_noSRPD²/c²)^.5                                   Equation 5

And

     Time = Time’/ (1 + v_SRPD²/c²)^.5                                       Equation 6

SRPD velocity was confirmed determined using the Special Relativistic Perspective time equations, dividing the Time_noSRPD value into the Time_SRPD. That proportion is used to calculate the Relativistic 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.  Velocity_Real/_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 more specific definitions.  |Mass_SRPD| would be the mass of a body in kilograms from an SRPD viewpoint under Special Relativistic Distortion;  Mass_noSRPD – the mass of the body from an SRPD perspective under no Special Relativistic distortion

              Mass_SRPD = Mass_noSRPD /(1–v_noSRPD²/c²)^.5                      Equation 7
              Mass_SRPD = Mass_noSRPD /(v_noSRPD/v_SRPD)
              Mass_SRPD = Mass_noSRPD * (v_SRPD/v_noSRPD)

              Mass_noSRPD = Mass_SRPD / (1 + v_SRPD²/c²)^.5

                    Equation 8

And the length equations.

          Length_SRPD – the length of a body in meters under Special Relativistic Distortion from an
           SRPD Velocity viewpoint

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

                             Length_SRPD = Length_noSRPD * (1–v_noSRPD²/c²)^.5                      Equation 8

              Length_SRPD = Length_noSRPD * (v_noSRPD/v_SRPD)
              Length_SRPD = Length_noSRPD * (v_SRPD/v_noSRPD)

                              Length_noSRPD = Length_SRPD / (1 + v_noSRPD²/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 + v_SRPD²/c²)^½| for a moving perspective 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 calculate an exact v_Real||noSRPD value.  Theoretically, it always will be.

Relativity equations are more appropriate for low speeds.  The motion is always relative to the observation point. 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 contracts 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 high 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. It can be used to calculate your Relativistic velocity.  Then used as a check on the velocity 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 still be estimated and be set as well.  There is an exciting supposition to be made on any of the objects we observe: what would they look like if they were really going at a relativistic velocity. Even if they were not exclusively moving directly away from us.  If we were dead center in the Universe, it is 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 an unreasonable supposition, even if you accept the spatial expansion business.  If anything, the spatial expansion hogwash supposition would impose 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.  They do not contradict General Relativity. They are equations from a General Relativistic viewpoint.  The value of Real velocities and Relativistic velocities (Special or General) has precisely the same validity.

* ALL of the equations in this paper have been confirmed in a table of velocities. They are checked to 2000 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 logic of this paper would work just as well for a Universe with a different light-speed.

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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NGC 6888 - The Crescent Nebula