D'Alembertian question again (sorry)

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Discussion Overview

The discussion revolves around the transition between equations 32 and 33 in a PDF related to relativistic transformations, specifically focusing on the formulation of the 4-vector potential and the inclusion of the term i*psi/c. Participants are exploring the implications of combining electric and magnetic potentials within the context of 4-vectors.

Discussion Character

  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant expresses confusion about the transition from equation 32 to 33, particularly regarding the term i*psi/c in the new 4-vector potential.
  • Another participant clarifies that φ represents the electric potential and A represents the magnetic potential, suggesting that the two are being combined.
  • A participant questions the absence of A_4 in equation 29 and seeks clarification on how the equations relate.
  • It is noted that equation 33 incorporates both equations 29 and 30, with the 4-vector j_μ defined in equation 27.
  • One participant attempts to relate the square operator applied to the combined vector and scalar potential 4-vector a to the resulting expressions, expressing uncertainty about the relationship to equations 29 and 30.
  • Another participant mentions that equations 29 and 30 are combined to form a 4-vector and discusses the need to factor out μ₀ from equation 30 to align with the formulation seen in equation 27.

Areas of Agreement / Disagreement

Participants exhibit varying levels of understanding regarding the formulation of the 4-vector potential and its components. There is no consensus on the clarity of the transition between the equations, and multiple interpretations of the equations and their implications are present.

Contextual Notes

Participants express uncertainty about the definitions and relationships between the terms involved, particularly regarding the mathematical steps leading to the formulation of the 4-vector potential.

neu
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Sorry to cluter forum with previous thread. I cannot work out the letex code

http://www.cmmp.ucl.ac.uk/~drb/Teaching/PHAS3201_RelativisticTransformationsFull.pdf

in above pdf i do not understand the transition from eq 32 to 33.

That is, I don't understand the presence of the last i*psi/c term in the new 4-vector potential. SHouldn't it just be a= (A1,A2,A3,A4) to get eq29?
 
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You understand 4 vectors? [itex]\phi[/itex] is the electric potential & A is the magnetic potential. They're trying to combine the two.
 
neu said:
Sorry to cluter forum with previous thread. I cannot work out the letex code

http://www.cmmp.ucl.ac.uk/~drb/Teaching/PHAS3201_RelativisticTransformationsFull.pdf

in above pdf i do not understand the transition from eq 32 to 33.

That is, I don't understand the presence of the last i*psi/c term in the new 4-vector potential. SHouldn't it just be a= (A1,A2,A3,A4) to get eq29?

But there is no "A_4" in equation 29 so what do you mean?

No, their equation 33 contains both eqs 29 AND 30! (with the four-vector [itex]j_\mu[/itex] defined in eq 27)
 
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Thrice said:
You understand 4 vectors? [itex]\phi[/itex] is the electric potential & A is the magnetic potential. They're trying to combine the two.


I understand the intention not the method. so I guess I don't understand 4-vectors!

my problem is this:

if square=(d2/dx1,d2/dx2,d2/dx3,-1/c^2 d2/dx4) (eqn 31)

& the combined vector & scalar potential 4-vector a:

a=(A1,A2,A3,i*psi/c) (eqn 32)

Then surely:

square*a=laplacian A - i/c^3 d^2 (scalar)/dt^2

but instead they have (correctly) square*a = mu*j = mu(J1,J2,J3,icp)

why? I can't see how that relates to eq 29 & 30?
 
As nrqed said, you're combining eqs 29 & 30 to form a 4 vector. J and A in eq 29 range as {1,2,3} & eq 30 becomes {4}.

Compare 29 and 30 with 33. Factor out [itex]\mu_0[/itex] from 30 & you have [itex]-\rho c^2[/itex] .. which is why you need to divide by c in 32 to make the 4D [itex]j_\mu[/itex] that you see in 27.
 
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