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Aharanov-Bohm effect and dark energy

  1. Jun 4, 2004 #1
    In the Aharanov -Bohm effect, a magnetic field isolated inside a solenoid,
    changes the phase of an electron interference pattern.The magnetic field does not exert a force on the electrons - it has been shown that the electromagnetic
    vector potential can account for the phase shift.But is it possible to explain the Aharanov-Bohm effect in another way?
    I think the answer to this question is yes and can be given by the force the magnetic field of the solenoid exerts on dark energy particles passing through the solenoid and into the "isolated" magnetic field. If the dark energy particles carry an electric charge they will be deflected by the magnetic field into the path of electrons passing through the slits in the interference experiment and will exert a force on the electrons which will change their trajectories slightly and change the phase of the interference pattern.

    Let’s assume the dark energy particles are moving at close to the speed of light – 10^8 m / s . The magnetic field strength of the solenoids used in experiments of this kind are typically abouts 1 Tesla,the superconducting solenoid is about 10^ - 2 metres wide, and so a dark energy particle moving at about 10^8 m / s would take about
    10^ - 10 seconds to pass through the solenoid.

    The force exerted by the magnetic field in the solenoid on the dark energy particles is:

    Force = q v B
    Force = q x 10 ^ 8 x 1
    Force = 10 ^ 8 q

    A maximum force of 10 ^ 8 q is transferred to an electron by the dark energy particle.

    The acceleration of the electron is given by Force / mass of electron

    This is 10 ^ 8 q / 10 ^ -31 m / s ^ 2 = 10 ^ 39 q metres / s ^ 2

    But the force only acts for 10 ^ - 9 seconds ( the time the electron takes to cross the path of the solenoid and the region in which the dark energy particles are interacting with the magnetic field of the solenoid – assuming the electron has a speed close to 10 ^ 7 m / s ) so after this time the electron could have a maximum speed displacing it from its main direction of motion of
    10^ 39 q x 10 ^ -9 m / s = 10 ^ 30 q m / s.

    In the time the electron takes to cross the path of the solenoid and the region in which the dark energy particles are interacting with the magnetic field of the solenoid,
    the electron will be displaced a maximum of 10 ^ 30 q x 10 ^ -9 = 10 ^ 21 q metres.

    It is known from experiment that the interference pattern shows a phase shift of
    10 ^ -6 metres.
    Therefore 10 ^ 21 q = 10 ^ -6
    But there is more than one dark energy particle so if N is the total number of dark energy particles acting on the electron over a distance of 10 ^ -2 metres then

    10 ^ 21 q x N = 10 ^ -6
    The minimum uncertainty in energy of a dark energy particle is given by the maximum time over which it could change its energy state ( assuming dark energy particles can change their energy state).This maximum time is given by the age of the universe which is 10 ^ 18 seconds.

    using E x t = h bar

    E x 10 ^ 18 = 10 ^ - 34
    E = 10 ^ -52 joules

    Since a dark energy particle must have at least this energy then this means
    the minimum rest mass associated with a dark energy particle is ( by E = m c^ 2 )
    10 ^ -69 kg.
    If we assume that dark energy particles have the same charge / mass ratio as a proton
    ( they have approximately the same mass density per cubic metre – about 10 ^ -27 kg / m ^ 3) then they have an electric charge of 10 ^ -61 Coulombs.

    Using 10 ^ 21 q x N = 10 ^ -6 and q = 10 ^ -61

    we get N the number of dark energy particles in 10 ^ -6 m ^ 3
    ( the width of the solenoid cubed) is 10 ^ 34

    So in one cubic metre there would be 10 ^ 34 x 10 ^ 6 = 10 ^ 40 dark energy particles.

    Earlier on I said the mass of a dark energy particles was 10 ^ - 69 kg.

    In one cubic metre this amounts to a mass of 10 ^ 40 x 10 ^ -69 =10 ^ - 29 kg.

    About one hundreth of the mass of a proton.
     
  2. jcsd
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