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Oct 24, 2020, 3:02:47 AM10/24/20

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Sidney Coleman wrote a report in 1961 that derived the LAD equation for a classical electron using what was then 'modern theory':

https://www.rand.org/pubs/research_memoranda/RM2820.html

I've tried to copy his diagram below which formats OK using classic Google groups but not in the newer, current version. On page 35 he writes:

"-----"

If we remember that in Maxwellian dynamics, the radiation field is given by the difference of the advanced and retarded fields, it is easy to see that the electron radiates.

\ |t /*

\ | /*

\ | /.

\ | /

\ | / *

\ \ | / /

_______________\__\ /__* ___/__________x

\ / \ * /

/ | \ /

/ \| \ */

/ | \/.

/ |\ /\

/ | \/ \*

/ | /\P \*

|/ \

/ \

/| \

/ | \

The figure shows the world line of an electron undergoing hyperbolic acceleration. The past light cone from the point P does not interact with the electron worldline, so the retarded potential vanishes; the future light cone intersects it once, so the advanced potential doesn't. Thus there is a radiation field at P."

"-----"

I don't agree with this. The past light cone of the observation point P not intersecting with the electron's world line means the retarded field at P is undefined rather than being zero, and hence the radiation field there is also undefined.

Thanks in advance for any comments.

J McA

https://www.rand.org/pubs/research_memoranda/RM2820.html

I've tried to copy his diagram below which formats OK using classic Google groups but not in the newer, current version. On page 35 he writes:

"-----"

If we remember that in Maxwellian dynamics, the radiation field is given by the difference of the advanced and retarded fields, it is easy to see that the electron radiates.

\ |t /*

\ | /*

\ | /.

\ | /

\ | / *

\ \ | / /

_______________\__\ /__* ___/__________x

\ / \ * /

/ | \ /

/ \| \ */

/ | \/.

/ |\ /\

/ | \/ \*

/ | /\P \*

|/ \

/ \

/| \

/ | \

The figure shows the world line of an electron undergoing hyperbolic acceleration. The past light cone from the point P does not interact with the electron worldline, so the retarded potential vanishes; the future light cone intersects it once, so the advanced potential doesn't. Thus there is a radiation field at P."

"-----"

I don't agree with this. The past light cone of the observation point P not intersecting with the electron's world line means the retarded field at P is undefined rather than being zero, and hence the radiation field there is also undefined.

Thanks in advance for any comments.

J McA

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