4-vectors

[luc]

Ok, i'm trying to figure out how many different 4-vectors exist in SR

 

-4-velocity

-4-acceleration

-4-force

-energy-momentum 4-vector

-displacement 4-vector

-4-potential

 

 

Is there some other? How many different 4-vectors exist in Special Relativity?

[ydoaPs]

isn't potential a scalar?

[Dave]

Indeed it is.

 

I think. It's been a loooong time

[luc]

I mean the 4-potential where the components are (@,Bx,By,Bz), where @ is the scalar magnetic potential, and the Bs are the components of the vector magnetic potential

[Meir Achuz]

There are a large number of four vectors in SR. You list some of them,

but also some that are not four vectors.

1. The velocity four-vector is (g,g v), where g is the SR gamma and v is the usual three-vector velocity we would measure as dx/dt.

2. Acceleration is not a four vector in SR.

3. Force (and acceleration) are not useful variables in SR.

A four-vector force, the so called "Minkowski force" can be defined by

F=(g dW/dt,g dp/dt} where W is the energy and p the three-vector momentum of a particle.

4. The energy-momentum four-vector is (W,p).

5. The displacement four-vector is (t,x,y,z).

6. The four-potential is usually written as (phi,A), where phi was the NR scalar potential and A the NR vector potential. A is no longer referred to as "magnetic" because it also affects the electric field.

7. The current four-vector is (rho,j).

8. There is a four-divergence, which is a four-vector.

9. Taking the four-divergence of tensors lead to other four-vectors.

10. ... and so on.

[luc]

There are a large number of four vectors in SR. You list some of them' date='

but also some that are not four vectors.

1. The velocity four-vector is (g,g v), where g is the SR gamma and v is the usual three-vector velocity we would measure as dx/dt.

2. Acceleration is not a four vector in SR.

3. Force (and acceleration) are not useful variables in SR.

A four-vector force, the so called "Minkowski force" can be defined by

F=(g dW/dt,g dp/dt} where W is the energy and p the three-vector momentum of a particle.

4. The energy-momentum four-vector is (W,p).

5. The displacement four-vector is (t,x,y,z).

6. The four-potential is usually written as (phi,A), where phi was the NR scalar potential and A the NR vector potential. A is no longer referred to as "magnetic" because it also affects the electric field.

7. The current four-vector is (rho,j).

8. There is a four-divergence, which is a four-vector.

9. Taking the four-divergence of tensors lead to other four-vectors.

10. ... and so on.[/quote']

 

Do you mean that there're an infinite number of different kind of 4-vectors? Or a finite number? If is a finite number what number is it?

[Meir Achuz]

You could ask the same quesiton in NR physics: How many three-vectors are there?