SR 4-tensors, enjoy! A powerful, online, Calculator, written in Javascript.

It employs tensor math, and will have hundreds of tensors and tensor functions in proper time. :)

Currently has over 100 SR Tensors and calculates the Invariant (Lorentz Scalar Self-Product) of all 4-Vectors and the Invariant (Trace & Determinant & InnerProduct) of all 4-Tensors.

It lists, but doesn't really calculate, the EigenValues for type (1,1)-Tensors. I am working on Tensor Addition and Tensor Products, Exterior Products, Index Raising and Index Lowering.

It calculates the symmetry of 2-index Tensors.

See also, my Online RPN Complex-capable Scientific Calculator

** Note ** This is still a work in progress... If you notice any errors, please bring them to my attention, I will fix them. Thanks!

I always choose to have the 4-Vector (or 3-vector) refer to the

4-Vector

3-vector

In addition, I like the convention of having the (c) factor in the temporal part for correct dimensional units. {eg. 4-Position

This also allows the SR 4-Vector name to match the classical 3-vector name, which is useful when considering Newtonian limiting-cases.

I use:

UPPER CASE

lower case

Note that the (

Likewise, try to use different index letters than the other variables in an equation.

Many, many other texts do not use different letters. It can be very confusing and ambiguous.

I also adopt Wolfgang Rindler's convention of using:

lower case

lower case

*Note* (

You can get close though...

In a rest frame:

Following the same idea, I am also implementing:

lower case

while retaining the historical (φ) for the Electromagnetic ScalarPotential (temporal component)

Also, I use the "at-rest" notation "naught" (

Thus

v

v

v

v

Based on this, I prefer restmass = m

All SR 4-Vectors have the following properties:

==============================================

A

= (a

with A

One can also use

but once you start doing physics, most of the component values (physical variable names) are lowercase letters,

An exception is that the Energies are usually uppercase E = Energy, U = PotentialEnergy, H = Hamiltonian.

The energy-densities are usually lowercase:

Therefore, I prefer

However, there are a few cases where the Uppercase letters are helpful.

4-Velocity

The relativistic spatial component of 4-Velocity is ( U

This type of thing also occurs in the 4-Acceleration and the 4-Force, and a few others.

The main idea that makes a generic 4-Vector into an SR 4-Vector is that it must transform properly according to a Lorentz Transformation Λ

(A

with both (A

We also have (Tr[Λ

Likewise: { (Λ

If you have a comment about this site, or find a bug, or want more features added, or just want to say 'hi'

Please, send comments to John Wilson

relativity

See SRQM: QM from SR - The 4-Vector RoadMap (.html)

See SRQM: QM from SR - The 4-Vector RoadMap (.pdf)

SRQM 4-Vector : Four-Vector and Lorentz Scalar Diagram

SRQM + EM 4-Vector : Four-Vector and Lorentz Scalar Diagram

SRQM + EM 4-Vector : Four-Vector and Lorentz Scalar Diagram With Tensor Invariants

SRQM 4-Vector : Four-Vector Stress-Energy & Projection Tensors Diagram

SRQM 4-Vector : Four-Vector SR Quantum RoadMap

SRQM + EM 4-Vector : Four-Vector SR Quantum RoadMap

SRQM 4-Vector : Four-Vector New Relativistic Quantum Paradigm

SRQM + EM 4-Vector : Four-Vector New Relativistic Quantum Paradigm (with EM)

SRQM 4-Vector : Four-Vector New Relativistic Quantum Paradigm - Venn Diagram

SRQM 4-Vector : Four-Vector SpaceTime is 4D

SRQM 4-Vector : Four-Vector SpaceTime Orthogonality

SRQM 4-Vector : Four-Vector 4-Position, 4-Velocity, 4-Acceleration Diagram

SRQM 4-Vector : Four-Vector 4-Displacement, 4-Velocity, Relativity of Simultaneity Diagram

SRQM 4-Vector : Four-Vector 4-Velocity, 4-Gradient, Time Dilation Diagram

SRQM 4-Vector : Four-Vector 4-Vector, 4-Velocity, 4-Momentum, E=mc^2 Diagram

SRQM 4-Vector : Four-Vector 4-Velocity, 4-WaveVector, Relativistic Doppler Effect Diagram

SRQM 4-Vector : Four-Vector Wave-Particle Diagram

SRQM 4-Vector : Four-Vector Compton Effect Diagram

SRQM 4-Vector : Four-Vector Aharonov-Bohm Effect Diagram

SRQM 4-Vector : Four-Vector Josephson Junction Effect Diagram

SRQM 4-Vector : Four-Vector Hamilton-Jacobi vs Action, Josephson vs Aharonov-Bohm Diagram

SRQM 4-Vector : Four-Vector Motion of Lorentz Scalar Invariants

SRQM 4-Vector : Four-Vector Motion of Lorentz Scalar Invariants, Conservation Laws & Continuity Equations

SRQM 4-Vector : Four-Vector Speed of Light (c)

SRQM 4-Vector : Four-Vector Minimal Coupling Conservation of 4-TotalMomentum)

SRQM 4-Vector : Four-Vector Relativistic Action (S) Diagram

SRQM 4-Vector : Four-Vector Relativistic Lagrangian Hamiltonian Diagram

SRQM 4-Vector : Four-Vector Relativistic Euler-Lagrange Equation

SRQM 4-Vector : Four-Vector Relativistic EM Equations of Motion

SRQM 4-Vector : Four-Vector Einstein-de Broglie Relation hbar

SRQM 4-Vector : Four-Vector Quantum Canonical Commutation Relation

SRQM 4-Vector : Four-Vector QM Schroedinger Relation

SRQM 4-Vector : Four-Vector Quantum Probability

SRQM 4-Vector : Four-Vector CPT Theorem

SRQM 4-Vector : Four-Vector Lorentz Transforms Connection Map

SRQM 4-Vector : Four-Vector Lorentz Discrete Transforms

SRQM 4-Vector : Four-Vector Lorentz Transforms - Trace Identification

SRQM 4-Vector : Four-Vector Lorentz Lorentz Transforms-Interpretations

CPT Symmetry, Baryon Asymmetry Problem Solution, Matter-Antimatter Symmetry Solution, Arrow-of-Time Problem Solution, Big-Bang!

See SRQM: QM from SR - The 4-Vector RoadMap (.html)

See SRQM: QM from SR - The 4-Vector RoadMap (.pdf)

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