# What Does Up Indice Paired with Up Indice Mean in Relativity Notation?

• Joe D
In summary, this equation is trying to find the four functions that correspond to the values of beta for a given electric field and magnetic field.
Joe D

## Homework Statement

Find t(τ), x(τ), y(τ), z(τ) for constant electric field E=E(sinθx+cosθz) and B=Bz, and constant magnetic field where E,B, and θ are all constants.

I haven't seen this notation before, and I really just want to know what it means specifically. I know and up indice paired with a down indice essentially gives an inner product, but I don't really know what an up indice paired with an up indice gives me. So this is equation 12.32 in Jackson Electrodynamics that I'm trying to understand.

## Homework Equations

m(d2xα/dτ2)=(e/c)(∂αAβ-∂βAα)(dxβ/dτ)

## The Attempt at a Solution

Also, the 4 vector potential that I've already calculated is:

Aα=(-E(xsinθ+zcosθ),-By,0,0) where E, B and θ are all constants.

or Aα=(-E(xsinθ+zcosθ),0,Bx,0) I can't decide which one is more convenient.

I've attached an image of my best guess for what that equation means.

#### Attachments

• IMG_20151215_143708814_HDR.jpg
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Last edited:
I think its best to think of this way:

Since beta is a free index, you get one equation for each value of beta (so you get 4 equations). In each of those equations, alpha is summed over (it is up for A and down for x). So each one of those equations can now be solved for the four functions you need.

By the way for n free indicides in an equation in dimension d, you get d^n equations. In this case, d=4 and n=1

Last edited:
Brian T said:
I think its best to think of this way:

Since beta is a free index, you get one equation for each value of beta (so you get 4 equations). In each of those equations, alpha is summed over (it is up for A and down for x). So each one of those equations can now be solved for the four functions you need.

By the way for n free indicides in an equation in dimension d, you get d^n equations. In this case, d=4 and n=1
Just a small correction (I am sure it is a typo): it is alpha which is a free index and beta is summed over.

nrqed said:
Just a small correction (I am sure it is a typo): it is alpha which is a free index and beta is summed over.

Ohh thanks. Got them flipped xD

## What is relativity mathematical notation?

Relativity mathematical notation is a system of symbols and equations used to represent the concepts and principles of Einstein's theory of relativity. It allows for precise and concise communication of complex ideas in the field of physics.

## What is the difference between special relativity and general relativity?

Special relativity is a theory that describes the laws of physics in non-accelerating frames of reference, while general relativity is a theory that extends these laws to include accelerating frames of reference and the effects of gravity.

## What is the significance of the speed of light in relativity?

The speed of light, denoted by the symbol c, is a fundamental constant in relativity. It is the maximum speed at which all energy, matter, and information can travel. It also plays a crucial role in the equations of special relativity, including the famous equation E=mc^2.

## What is the role of tensors in relativity?

Tensors are mathematical objects used to describe the relationships between different quantities in space and time. In relativity, tensors are used to represent concepts such as energy, momentum, and curvature, and they allow for the precise formulation of Einstein's equations.

## How does relativity mathematical notation differ from classical mechanics notation?

Relativity mathematical notation differs from classical mechanics notation in several ways. For example, it includes the use of four-vectors and tensors to describe quantities in space and time, as well as the incorporation of the speed of light as a fundamental constant. It also differs in terms of the concepts and principles it represents, as relativity introduces new ideas such as time dilation and the curvature of spacetime.

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