luc Posted March 30, 2005 Share Posted March 30, 2005 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? Link to comment Share on other sites More sharing options...
ydoaPs Posted March 30, 2005 Share Posted March 30, 2005 isn't potential a scalar? Link to comment Share on other sites More sharing options...
Dave Posted March 30, 2005 Share Posted March 30, 2005 Indeed it is. I think. It's been a loooong time Link to comment Share on other sites More sharing options...
luc Posted March 30, 2005 Author Share Posted March 30, 2005 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 Link to comment Share on other sites More sharing options...
Meir Achuz Posted March 31, 2005 Share Posted March 31, 2005 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. Link to comment Share on other sites More sharing options...
luc Posted April 2, 2005 Author Share Posted April 2, 2005 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? Link to comment Share on other sites More sharing options...
Meir Achuz Posted April 2, 2005 Share Posted April 2, 2005 You could ask the same quesiton in NR physics: How many three-vectors are there? Link to comment Share on other sites More sharing options...
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