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Site last modified: 2021-Aug

Welcome to Relativistic Quantum Reality: Virtual worlds of imaginary particles: The dreams stuff is made of: Life, the eternal ghost in the machine...
This site is dedicated to the quest for knowledge and wisdom, through science, mathematics, philosophy, invention, and technology. 
May the treasures buried herein spark the fires of imagination like the twinkling jewels of celestial light crowning the midnight sky...

Quantum Mechanics is derivable from Special Relativity
See SRQM - QM from SR - Simple RoadMap (.html)
See SRQM - QM from SR - Simple RoadMap (.pdf)
See SRQM - QM from SR - Summary (.pdf)
See SRQM - Fundamental Constants (.pdf)
See SRQM - Online SR 4-Vector & Tensor Calculator
See Online Complex-capable RPN Scientific Calculator

***Learn, Discover, Explore***

See also these Math/Physics Javascript programs:

Physics+Math: Minkowski Diagram - WorldLines - Poincaré Invariance - Lorentz Transformations


Poincaré Invariance is the idea that the tensor mathematics describing our universe have linear relationships.
i.e. An SR 4-Vector V'μ = V' = (v0,v1,v2,v3)' in one frame
is linearly related to Vμ = V = (v0,v1,v2,v3) in another frame.
V'μ = Λμν Vν + ΔVμ
V'= Λμν V + ΔV

This is exactly like the standard linear equation.
x' = A x + B

This leads to Poincaré Invariance, that there exists an invariant magnitude V'·V' = V·V = (v0)2-(v1)2-(v2)2-(v3)2 = Invariant.
All inertial observers will measure the same invariant magnitude, independent of any coordinate system used.

A physics example of this is the 4-Displacement ΔRμ = ΔR = (cΔt,Δx,Δy,Δz)
The invariant interval is ΔR·ΔR = (cΔt)2-(Δx)2-(Δy)2-(Δz)2 = (cΔτ)2

The Lorentz Transformation Tensor is Λμν : The SpaceTime Translation Tensor is ΔVμ
The combination of the two is a Poincaré Transformation, aka. an Inhomogeneous Lorentz Transformation.

The Lorentz Transform takes several forms:
Continuous:
==============
4D Boost: Λμν → Bμν : transforms between a temporal and spatial axis as function of velocity parameter β
= [ γ -γβj ]
[-γβi (γ-1)βiβj/β·β+δij]

4D Rotation: Λμν → Rμν : transforms between two spatial axes as function of spatial angle θ about axis n̂
= [ +1 0j ]
[0i (δij-ninj)cos[θ]-(εijknk)sin[θ]+ninj]

Discrete:
==============
4D Identity: Λμν → Iμν = Diag[+1,+1,+1,+1]: Leaves a system unchanged
4D TimeReverse: Λμν → Tμν = Diag[-1,+1,+1,+1] : Reverses the time coordinate
4D SpaceReverse: Λμν → Pμν = Diag[+1,-1,-1,-1] : Reverses the space coordinates
4D ChargeReverse: Λμν → Cμν = Diag[-1,-1,-1,-1] : Reverses the time & space coordinates
This leads to CPT Invariance.

Some properties of Lorentz Transformations:
Determinant[Λμν] = { +1 for Proper : -1 for Improper }
Trace[Λμν] = specifies some types: Rotations={0..4}, Identity={4}, Boosts={4..Infinity}


PhD Systems


coords


Event R1 = (t1,x1,y1,z1):





Event R2 = (t2,x2,y2,z2):
























fA(t)= for
fA(t)= for
fA(t)= for


fB(t)= for
fB(t)= for
fB(t)= for


fC(t)= for
fC(t)= for
fC(t)= for


fD(t)= for
fD(t)= for
fD(t)= for

Conditions: {x = = #, x!=#, x<#, x>#, x<=#, x>=#, true, false}

PhD Systems












SiteMap of SciRealm | About John | Send email to John
John's Science,Math,Philosophy Stuff:
The Science Realm: John's Virtual Sci-Tech Universe | 4-Vectors | Ambigrams | Antipodes | Covert Ops Fragments | Cyrillic Projector | Forced Induction (Sums Of Powers Of Integers) | Frontiers | IFS Fractals | JavaScript Graphics | JavaScript Graphics Using Table | Kid Science | Kryptos | Philosophy | Photography | Prime Sieve | QM from SR | QM from SR-Simple RoadMap | QM from SR-Simple RoadMap (PDF) | SR 4-Vector &Tensor Calculator |Quantum Phase | Quotes | RuneQuest Cipher Challenge | Secret Codes &Ciphers | Scientific Calculator (complex capable) | Science+Math | Sci-Pan Pantheist Poems | Stereograms | SuperMagicSqr4x4 |Turkish Grammar |Melike Wilson Art

Welcome to Relativistic Quantum Reality: Virtual worlds of imaginary particles: The dreams stuff is made of: Life,the eternal ghost in the machine...
This site is dedicated to the quest for knowledge and wisdom,through science,mathematics,philosophy,invention,and technology. 
May the treasures buried herein spark the fires of imagination like the twinkling jewels of celestial light crowning the midnight sky...

Quantum Mechanics is derivable from Special Relativity
See SRQM-QM from SR-Simple RoadMap (.html)
See SRQM-QM from SR-Simple RoadMap (.pdf)
See SRQM-Online SR 4-Vector &Tensor Calculator
See Online Complex-capable RPN Scientific Calculator

***Learn,Discover,Explore***