• Which constrained motions of a system of charges are time reversal by o

    From john mcandrew@21:1/5 to All on Wed Aug 5 17:51:45 2020
    Say I have a system of charges interacting with one another, but constrained by additional local forces: what are the necessary conditions for finding a valid solution to Maxwell's equations by only reversing the velocity of the charges? I can think of
    two cases:

    1. Each charge is constrained to travel at an arbitrary constant velocity generally different to one another. The system doesn't radiate from Lamor's formula.

    2. Each charge is constrained to accelerate at a constant acceleration such that each charge maintains a constant proper distance from one another. The system radiates via Lamor's formula, but this radiation is reversible and given the name "acceleration
    energy/momentum", "Schott energy/momentum" etc.

    Are there any other examples?

    Thanks in advance,

    JMcA

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  • From Jos Bergervoet@21:1/5 to john mcandrew on Thu Aug 6 13:41:39 2020
    On 20/08/06 2:51 AM, john mcandrew wrote:

    Say I have a system of charges interacting with one another, but constrained by additional local forces: what are the necessary conditions for finding a valid solution to Maxwell's equations by only reversing the velocity of the charges?

    If you just use time reversal your velocities will be reversed.
    In classical physics time reversal is a symmetry so your solution
    with the reversed velocities will be a "valid solution" as required,
    without the need to impose any "necessary conditions".

    In the non-classical (QFT standard model) case, you would not
    have time reversal symmetry for all possible forces (there you
    only have CPT-invariance). So there you would have to impose
    extra conditions, for instance that the forces are only from
    the strong interaction and the electromagnetic interaction, but
    not coming from the weak interaction. (This of course would make
    it a bit unphysical, because the existing particles we know of
    actually do feel the weak interaction..)

    --
    Jos

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  • From john mcandrew@21:1/5 to Jos Bergervoet on Thu Aug 6 16:47:44 2020
    On Thursday, August 6, 2020 at 12:41:41 PM UTC+1, Jos Bergervoet wrote:
    On 20/08/06 2:51 AM, john mcandrew wrote:

    Say I have a system of charges interacting with one another, but constrained by additional local forces: what are the necessary conditions for finding a valid solution to Maxwell's equations by only reversing the velocity of the charges?
    If you just use time reversal your velocities will be reversed.
    In classical physics time reversal is a symmetry so your solution
    with the reversed velocities will be a "valid solution" as required,
    without the need to impose any "necessary conditions".

    In the non-classical (QFT standard model) case, you would not
    have time reversal symmetry for all possible forces (there you
    only have CPT-invariance). So there you would have to impose
    extra conditions, for instance that the forces are only from
    the strong interaction and the electromagnetic interaction, but
    not coming from the weak interaction. (This of course would make
    it a bit unphysical, because the existing particles we know of
    actually do feel the weak interaction..)

    --
    Jos

    Yes, here I'm interested in the special case where the fields at any point in the time-reversed case can still be traced back to a time-reversed source that generated it. More generally, the forward case creates "irreversible radiation" that can still be
    traced back to the sources, but not so when time reversed where this sourceless field has to be added in. I think what I'm after is the non-radiation condition:
    https://en.wikipedia.org/wiki/Nonradiation_condition#:~:text=Classical%20nonradiation%20conditions%20define%20the,will%20not%20emit%20electromagnetic%20radiation.&text=In%20some%20classical%20electron%20models,that%20no%20radiation%20is%20emitted.

    This gives a few other examples of accelerated systems of charges that don't radiate and, I'm guessing, is therefore time-reversible via the sources alone. Or put another way: retarded-field - advanced-field = 0 everywhere.

    JMcA

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  • From Jos Bergervoet@21:1/5 to john mcandrew on Wed Aug 12 19:26:17 2020
    On 20/08/07 1:47 AM, john mcandrew wrote:
    On Thursday, August 6, 2020 at 12:41:41 PM UTC+1, Jos Bergervoet wrote:
    On 20/08/06 2:51 AM, john mcandrew wrote:

    Say I have a system of charges interacting with one another, but constrained by additional local forces: what are the necessary conditions for finding a valid solution to Maxwell's equations by only reversing the velocity of the charges?
    If you just use time reversal your velocities will be reversed.
    In classical physics time reversal is a symmetry so your solution
    with the reversed velocities will be a "valid solution" as required,
    without the need to impose any "necessary conditions".

    In the non-classical (QFT standard model) case, you would not
    have time reversal symmetry for all possible forces (there you
    only have CPT-invariance). So there you would have to impose
    extra conditions, for instance that the forces are only from
    the strong interaction and the electromagnetic interaction, but
    not coming from the weak interaction. (This of course would make
    it a bit unphysical, because the existing particles we know of
    actually do feel the weak interaction..)

    Yes, here I'm interested in the special case where the fields at any point in the time-reversed case can still be traced back to a time-reversed source that generated it. More generally, the forward case creates "irreversible radiation" that can still
    be traced back to the sources, but not so when time reversed where this sourceless field has to be added in. I think what I'm after is the non-radiation condition:
    https://en.wikipedia.org/wiki/Nonradiation_condition#:~:text=Classical%20nonradiation%20conditions%20define%20the,will%20not%20emit%20electromagnetic%20radiation.&text=In%20some%20classical%20electron%20models,that%20no%20radiation%20is%20emitted.

    You will then still not get time reversal "by only reversing the
    velocity of the charges" as you write in the title. You also have
    to change the sign of the magnetic field if you do that (and other
    things as well perhaps..)

    To have only reversed velocities and nothing else changed in the
    time reversed solution you would need a case where the magnetic
    field is zero everywhere, it seems..

    One possibility is of course a pure electrostatic case, but then
    all velocities are zero and you don't have to change anything to
    get the time-reversed solution!

    Another case would be a current distribution (ignoring individual
    particles, only looking at bulk currents) where the current is
    such that it has no magnetic field. For instance a purely radial
    current. To avoid the need for an infinite charge reservoir at
    the center, you could take a "breathing mode" time-dependence
    for the radial current. An AC current flowing radially in some
    medium between two concentric spheres. It will create an ac E-
    field, also radial, and 90 degrees out of phase, but no B-field.
    For time reversal you now *only* have to reverse the current, i.e.
    reverse the velocities of the carriers.

    But if you actually do look at the microscopic fields between the
    individual charge carriers, you will see that the B-field is not
    really zero and the E-field also not really invariant under time-
    reversal, I'm afraid..

    But in any case, non-radiation is insufficient. A coil with ac
    current in a perfect Faraday cage is a non-radiating system, but
    for time-reversal it needs more than velocity-reversal, also the
    B-fields inside the cage will need a sign flip!

    --
    Jos

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  • From john mcandrew@21:1/5 to Jos Bergervoet on Thu Aug 13 00:02:37 2020
    On Wednesday, August 12, 2020 at 6:26:23 PM UTC+1, Jos Bergervoet wrote:
    On 20/08/07 1:47 AM, john mcandrew wrote:
    On Thursday, August 6, 2020 at 12:41:41 PM UTC+1, Jos Bergervoet wrote:
    On 20/08/06 2:51 AM, john mcandrew wrote:

    Say I have a system of charges interacting with one another, but constrained by additional local forces: what are the necessary conditions for finding a valid solution to Maxwell's equations by only reversing the velocity of the charges?
    If you just use time reversal your velocities will be reversed.
    In classical physics time reversal is a symmetry so your solution
    with the reversed velocities will be a "valid solution" as required,
    without the need to impose any "necessary conditions".

    In the non-classical (QFT standard model) case, you would not
    have time reversal symmetry for all possible forces (there you
    only have CPT-invariance). So there you would have to impose
    extra conditions, for instance that the forces are only from
    the strong interaction and the electromagnetic interaction, but
    not coming from the weak interaction. (This of course would make
    it a bit unphysical, because the existing particles we know of
    actually do feel the weak interaction..)

    Yes, here I'm interested in the special case where the fields at any point in the time-reversed case can still be traced back to a time-reversed source that generated it. More generally, the forward case creates "irreversible radiation" that can
    still be traced back to the sources, but not so when time reversed where this sourceless field has to be added in. I think what I'm after is the non-radiation condition:
    https://en.wikipedia.org/wiki/Nonradiation_condition#:~:text=Classical%20nonradiation%20conditions%20define%20the,will%20not%20emit%20electromagnetic%20radiation.&text=In%20some%20classical%20electron%20models,that%20no%20radiation%20is%20emitted.

    You will then still not get time reversal "by only reversing the
    velocity of the charges" as you write in the title. You also have
    to change the sign of the magnetic field if you do that (and other
    things as well perhaps..)


    I'm under the impression that for a charge travelling at a constant velocity, say: when its velocity is reversed, the E field it creates is the same as before but the sign of the B field flips compared to the forwards direction the charge was travelling
    at. Feynman has a section on this for anyone else interested: https://www.feynmanlectures.caltech.edu/II_26.html

    B = v x E (26.9) in the above link.

    Likewise for two charges travelling at constrained constant velocities wrt one another, the B fields they create will flip sign, hence cancelling the sign change in v in the Lorentz force equation, giving the same EM force on the charges as in the
    forward case.

    [snipped]

    JMcA

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  • From Jos Bergervoet@21:1/5 to john mcandrew on Thu Aug 13 11:38:18 2020
    On 20/08/13 9:02 AM, john mcandrew wrote:
    On Wednesday, August 12, 2020 at 6:26:23 PM UTC+1, Jos Bergervoet wrote:
    On 20/08/07 1:47 AM, john mcandrew wrote:
    ...
    You will then still not get time reversal "by only reversing the
    velocity of the charges" as you write in the title. You also have
    to change the sign of the magnetic field if you do that (and other
    things as well perhaps..)

    I'm under the impression that for a charge travelling at a constant velocity, say: when its velocity is reversed, the E field it creates is the same as before but the sign of the B field flips

    Exactly, so "only reversing the velocity" in your title is
    incorrect. Both the B-field and the velocities flip sign.

    You can argue that change of B is somehow "implicit" in what
    you write, but it is the opposite: what you write simply is
    not possible. You cannot "only" change the velocity without
    changing something else.

    Or else you could also argue that the change is correctly
    phrased as: "by only reversing the sign of the B-field" and
    that the necessary change in velocity is then implicit. It
    always follows from the fields which source there must be
    present, like it follows from the sources which fields there
    must be (if incoming fields are excluded).

    What you mean is not "by only reversing the velocities" but
    "by only specifying that the velocities are reversed" (which
    leaves room for other changes.)

    --
    Jos

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