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Results from a new A-Theory

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  • davidj95650
    In their rebuttal to the critics of their original paper, Further Considerations on Electromagnetic Potentials in the Quantum Theory , Physical Review, August
    Message 1 of 5 , Nov 3, 2003
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      In their rebuttal to the critics of their original paper, "Further
      Considerations on Electromagnetic Potentials in the Quantum Theory",
      Physical Review, August 15, 1961, Aharonov and Bohm state that a
      moving electron will have a back-reaction on to a source of A
      (magnetic vector potential). Unfortunately they did not further
      explain this back-reaction. After posting my message (MEG_builders
      message #1204, Sep 11, 2003) about the convective derivative, how
      the velocity of charge is affected by it's motion through a gradient
      of A, I wanted to observe some change in the magnetic field of an
      output coil which may be caused by such a condition. I built a
      transformer on a nanocrystalline core with small "sense" coils at
      the base of the output coil. Two sense coils are on the outside of
      the leg of the core, two others are in the interior space of the
      core.

      See the bitmap image, "ACoreTst1.bmp".
      Go to "Files" then go to the folder "MESSAGE ATTACHMENTS", go
      to the folder "Results from a new A-Theory", and open
      "AcoreTst1.bmp".

      The basic core is a Honeywell AMCC-320, cut core (The core has
      been cleanly cut into two halves. Uncut cores can be purchased
      also, and will have lower reluctance because there is no gap from
      the cut). Honeywell cores can be purchased from Eastern Components,
      www.eastern-components.com.

      Spaced from the core by 0.02-inch-thick tape, the ferrite sense
      coils are placed at the side and the center of the leg of the main
      core. This was to provide an indication of any differences between
      the outside edge of the output coil and its center. Above the
      sense coils is a sheet of 0.002-inch thick brass which acts as a
      shield to any electrical field between the output coil and the sense
      coils. (Typically the output coil operates at several hundred volts
      peak, and coupling of that voltage into the sense coils could mask
      measurements of the magnetic field.) The ends of this shield layer
      are insulated from one-another to prevent it from becoming a
      shorted turn which of course would kill the transformer action.

      There is another layer of 0.02-inch tape over the brass shield
      to reduce the capacitance between it and the output coil. The
      output coil is a bifilar (two wires in parallel) winding of #23
      enamel-coated magnet wire, of 23 bifilar turns per layer, with
      a 0.006-inch layer of teflon tape between the winding layers.
      There are a total of 13 layers for a total of 299 bifilar turns.
      Then end of one bifilar wire is connected to the start of the
      other wire to provide an effective total of 598 turns. At the
      junction of the two wires, a capacitor can be placed to adjust
      the series-resonant frequency so that different operating
      frequencies can be tested (This series resonance is between the
      transformed capacitance of the output coil and the leakage
      inductance of the drive coil).

      In the illustration, a permanent magnet is shown. Tests
      were made with and without a stack of Neodymium magnets to note
      any differences.

      The outside sense coils are in a region where there is only
      one contribution to the A-field, from the leg of the core. The
      other sense coils are in the interior space of the core where
      there are contributions from the top, bottom, and the leg of
      the core. The magnetic-vector-potentials are additive, in
      accordance with the usual vector addition (direction and
      amplitude are equally important).

      See the bitmap image, "AgradCor1.bmp".
      Go to "Files" then go to the folder "MESSAGE ATTACHMENTS", go
      to the folder "Results from a new A-Theory", and open
      "AgradCor1.bmp".

      The image illustrates the A-potential vectors as I visualize
      them around the nanocrystalline core. This drawing was to
      illustrate the static A from a permanent magnet, but it also is
      true for the dA/dt when the core is used as a transformer. In the
      case of the dA/dt, there are only three contributions to the A in
      the interior of the core space, A from the magnet is ignored.

      I had anticipated that where the A-potential was greatest, there
      would be the greatest B-field reaction from the electrons moving
      in the coil. Instead what I find is that the volume where the
      A-potential is weakest (outside the core leg), has the greatest
      B-field from the output coil. I'm cetain I'm observing the
      B-field, and it is solely from the current in the output coil.
      This was verified by driving the core at low frequencies where the
      drive coil would magnetize the core significantly, but little
      resonant current and only load current would occur in the output
      coil. The jpeg, "AllSigsLowFreq.jpg", illustrates this. This
      image is in the folder "Results from a new A-Theory".

      Channel 1 of the oscilloscope is connected to the side-mounted
      sense coil on the outside of the core leg, channel 2 is connected to
      the side-mounted sense coil on the interior side of the core leg,
      channel 3 is the timing clock from the drive-coil logic, and channel
      4 is connected to the output coil through a 200:1 voltage divider.
      There is a simple R-C filter on the sense coil outputs to linearize
      their response with frequency so that the voltage indications at
      different frequencies will be proportional to the magnetic field,
      and not the frequency. The top trace is the clock for the drive-
      coil controller and its leading-edge indicates the beginning of a
      cycle. Digital logic makes each phase of the drive signal about 49%
      of the period, which provides a square wave to the drive coil.
      Channel 1's trace is just below the square-wave of the driver-
      controller signal, and ranges from about 3.3 divisions above the
      bottom of the screen to about 6.7 divisions. Thus the peak-to-peak
      signal is about 3.4 divisions at 50 mV/division for an amplitude of
      170 mV. Channel 2's trace ranges from just about 0.3 division above
      the bottom to about 3.9 divisions at 20 mV/division for an amplitude
      of 78 mV. The output voltage ranges from 2.8 divisions to 5.1
      divisions at 200 volts/division for an amplitude of 460 volts. Thus
      the ratio of voltages between the two sense coils is 170/78 which is
      2.2 to 1. NOTE: the notation at the bottom of the screen says
      800VP-P and was for a different measurement and is in error for this
      measurement. The load on the output coil was 15k ohms. Also, only
      one wind of the bifilar coil was used, so that resonance of the
      output coil would be at a frequency much higher than the operating
      frequency for this test. I didn't want resonance effects to
      interfere with the transformer action.

      The image, "AllSigsHiFreq.jpg", in the folder "Results from a new
      A-Theory", illustrates the output coil operating in series resonance
      with the drive-coil. A 500 pF capacitor and 2.2 mH inductor are in
      series between the end of one bifilar wire and the start of the
      other. The 2.2 mH inductor was placed to allow higher frequency
      effects such as the Lenz pulse to occur more easily (less capacitive
      loading of the core). Note that the channel 1 and 2 sensitivities
      have been changed significantly. Channel 1's signal now ranges from
      3.5 divisions to 6.5 divisions at 200 mV/division for a total
      amplitude of 600 mV peak-to-peak. Channel 2's signal ranges from 0.8
      divisions to 3.2 divisions for an amplitude of 240 mV. The ratio of
      the two sense coils is 2.5 to 1. The output coil amplitude is now
      6 divisions at 200 volts/division for a total amplitude of 1,200 volts
      peak-to-peak. As noted on the screen, there is a 60k ohm load
      connected to the output coil.

      NOTE: the sense-coil signals are shifted (delayed) about 90
      degrees (1/4 cycle) due to the R-C filters. Without the R-C filters,
      the signals from the sense-coils are in phase with the output voltage,
      as they should be, but then high-frequency artifacts appear stronger
      than they are in reality.

      The image "CoreBuildUp.jpg", in the folder "Results from a new A-
      Theory", shows the built-up core. There are two drive coils in place
      to try different resonance frequencies because the leakage inductance
      will change based on the length of the magnetic path from the drive
      coil to the output coil. The output coil being tested is on the
      right-hand side of the image, where the coaxial-cable connections to
      two of the sense coils can be seen. The output coil on the left has
      the connections to each layer brought out so that experiments can be
      performed with different total turns in its circuit.

      A note about the drive circuit: it is composed of four MOSFETs in
      a bridge configuration so that the full supply voltage can be applied
      across the drive coil for each phase of the drive. For this test,
      it's only function is to provide a variable-frequency square wave to
      the drive coil to provide large values of dB/dt in the core, and
      consequent large values of dA/dt outside the core. A simplified
      circuit diagram can be seen in the image "TestCir1.bmp", in the
      folder "Results from a new A-Theory".

      The ratio of measured B-field inside the output coil is close to
      the 3:1 value of the A strength ratios in my idealization. Why they
      are not precisely 3:1 is probably due to the fact that I have
      approximated the A values, and because A is not blocked by the core
      (or any other physical matter) there are some vectorial subtractions
      occurring due to vectors interfering around the output coil which
      results in less than a 3:1 ratio occurring.

      By the way, the addition of the permanent magnet to the core
      did not change the ratio significantly and I have not made precise
      measurements of its impact at this time. The difference in ratio
      may have been 10%, not a lot compared to the basic ratio. The
      images in this report are those with the magnet in place.

      Also, there was no significant difference in signal level
      between the sense-coils on the outside of the leg versus
      those at the center.

      To help eliminate experimental error, I built an entirely
      different configuration, on an AMCC-1000 uncut core, which is
      dramatically different in size from the AMCC-320. The sense-
      coils are also very different in size. The effect is
      repeatable as the measured ratio between outside and interior
      of the core is 3.2:1 which is close to that reported here.

      A symmetrically wound coil will have a reasonably uniform
      magnetic field at points that are symmetrically similar. (The
      field distribution in a rectangular shape is not uniform, although
      at symmetric points around the center of the shape the field will
      be the same.) This experiment indicates to me that the magnetic
      vector potential is real, as theorized by Aharonov and Bohm, and
      that we have not fully exploited it as yet.

      David J.

      Files:
      ACoreTst1.bmp
      AgradCor1.bmp
      AllSigsLowFreq.jpg
      AllSigsHiFreq.jpg
      CoreBuildUp.jpg
      TestCir1.bmp
    • jonfli
      David, Nice test report. Will take some time to digest your findings. Keep up the good work! Jon ... From: davidj95650 To:
      Message 2 of 5 , Nov 3, 2003
      • 0 Attachment
        David,

        Nice test report. Will take some time to digest your findings. Keep up the
        good work!

        Jon

        ----- Original Message -----
        From: "davidj95650" <djenkins@...>
        To: <MEG_builders@yahoogroups.com>
        Sent: Monday, November 03, 2003 10:44 AM
        Subject: [MEG_builders] Results from a new A-Theory


        > In their rebuttal to the critics of their original paper, "Further
        > Considerations on Electromagnetic Potentials in the Quantum Theory",
        > Physical Review, August 15, 1961, Aharonov and Bohm state that a
        > moving electron will have a back-reaction on to a source of A
        > (magnetic vector potential). Unfortunately they did not further
        > explain this back-reaction. After posting my message (MEG_builders
        > message #1204, Sep 11, 2003) about the convective derivative, how
        > the velocity of charge is affected by it's motion through a gradient
        > of A, I wanted to observe some change in the magnetic field of an
        > output coil which may be caused by such a condition. I built a
        > transformer on a nanocrystalline core with small "sense" coils at
        > the base of the output coil. Two sense coils are on the outside of
        > the leg of the core, two others are in the interior space of the
        > core.
        >
        > See the bitmap image, "ACoreTst1.bmp".
        > Go to "Files" then go to the folder "MESSAGE ATTACHMENTS", go
        > to the folder "Results from a new A-Theory", and open
        > "AcoreTst1.bmp".
        >
        > The basic core is a Honeywell AMCC-320, cut core (The core has
        > been cleanly cut into two halves. Uncut cores can be purchased
        > also, and will have lower reluctance because there is no gap from
        > the cut). Honeywell cores can be purchased from Eastern Components,
        > www.eastern-components.com.
        >
        > Spaced from the core by 0.02-inch-thick tape, the ferrite sense
        > coils are placed at the side and the center of the leg of the main
        > core. This was to provide an indication of any differences between
        > the outside edge of the output coil and its center. Above the
        > sense coils is a sheet of 0.002-inch thick brass which acts as a
        > shield to any electrical field between the output coil and the sense
        > coils. (Typically the output coil operates at several hundred volts
        > peak, and coupling of that voltage into the sense coils could mask
        > measurements of the magnetic field.) The ends of this shield layer
        > are insulated from one-another to prevent it from becoming a
        > shorted turn which of course would kill the transformer action.
        >
        > There is another layer of 0.02-inch tape over the brass shield
        > to reduce the capacitance between it and the output coil. The
        > output coil is a bifilar (two wires in parallel) winding of #23
        > enamel-coated magnet wire, of 23 bifilar turns per layer, with
        > a 0.006-inch layer of teflon tape between the winding layers.
        > There are a total of 13 layers for a total of 299 bifilar turns.
        > Then end of one bifilar wire is connected to the start of the
        > other wire to provide an effective total of 598 turns. At the
        > junction of the two wires, a capacitor can be placed to adjust
        > the series-resonant frequency so that different operating
        > frequencies can be tested (This series resonance is between the
        > transformed capacitance of the output coil and the leakage
        > inductance of the drive coil).
        >
        > In the illustration, a permanent magnet is shown. Tests
        > were made with and without a stack of Neodymium magnets to note
        > any differences.
        >
        > The outside sense coils are in a region where there is only
        > one contribution to the A-field, from the leg of the core. The
        > other sense coils are in the interior space of the core where
        > there are contributions from the top, bottom, and the leg of
        > the core. The magnetic-vector-potentials are additive, in
        > accordance with the usual vector addition (direction and
        > amplitude are equally important).
        >
        > See the bitmap image, "AgradCor1.bmp".
        > Go to "Files" then go to the folder "MESSAGE ATTACHMENTS", go
        > to the folder "Results from a new A-Theory", and open
        > "AgradCor1.bmp".
        >
        > The image illustrates the A-potential vectors as I visualize
        > them around the nanocrystalline core. This drawing was to
        > illustrate the static A from a permanent magnet, but it also is
        > true for the dA/dt when the core is used as a transformer. In the
        > case of the dA/dt, there are only three contributions to the A in
        > the interior of the core space, A from the magnet is ignored.
        >
        > I had anticipated that where the A-potential was greatest, there
        > would be the greatest B-field reaction from the electrons moving
        > in the coil. Instead what I find is that the volume where the
        > A-potential is weakest (outside the core leg), has the greatest
        > B-field from the output coil. I'm cetain I'm observing the
        > B-field, and it is solely from the current in the output coil.
        > This was verified by driving the core at low frequencies where the
        > drive coil would magnetize the core significantly, but little
        > resonant current and only load current would occur in the output
        > coil. The jpeg, "AllSigsLowFreq.jpg", illustrates this. This
        > image is in the folder "Results from a new A-Theory".
        >
        > Channel 1 of the oscilloscope is connected to the side-mounted
        > sense coil on the outside of the core leg, channel 2 is connected to
        > the side-mounted sense coil on the interior side of the core leg,
        > channel 3 is the timing clock from the drive-coil logic, and channel
        > 4 is connected to the output coil through a 200:1 voltage divider.
        > There is a simple R-C filter on the sense coil outputs to linearize
        > their response with frequency so that the voltage indications at
        > different frequencies will be proportional to the magnetic field,
        > and not the frequency. The top trace is the clock for the drive-
        > coil controller and its leading-edge indicates the beginning of a
        > cycle. Digital logic makes each phase of the drive signal about 49%
        > of the period, which provides a square wave to the drive coil.
        > Channel 1's trace is just below the square-wave of the driver-
        > controller signal, and ranges from about 3.3 divisions above the
        > bottom of the screen to about 6.7 divisions. Thus the peak-to-peak
        > signal is about 3.4 divisions at 50 mV/division for an amplitude of
        > 170 mV. Channel 2's trace ranges from just about 0.3 division above
        > the bottom to about 3.9 divisions at 20 mV/division for an amplitude
        > of 78 mV. The output voltage ranges from 2.8 divisions to 5.1
        > divisions at 200 volts/division for an amplitude of 460 volts. Thus
        > the ratio of voltages between the two sense coils is 170/78 which is
        > 2.2 to 1. NOTE: the notation at the bottom of the screen says
        > 800VP-P and was for a different measurement and is in error for this
        > measurement. The load on the output coil was 15k ohms. Also, only
        > one wind of the bifilar coil was used, so that resonance of the
        > output coil would be at a frequency much higher than the operating
        > frequency for this test. I didn't want resonance effects to
        > interfere with the transformer action.
        >
        > The image, "AllSigsHiFreq.jpg", in the folder "Results from a new
        > A-Theory", illustrates the output coil operating in series resonance
        > with the drive-coil. A 500 pF capacitor and 2.2 mH inductor are in
        > series between the end of one bifilar wire and the start of the
        > other. The 2.2 mH inductor was placed to allow higher frequency
        > effects such as the Lenz pulse to occur more easily (less capacitive
        > loading of the core). Note that the channel 1 and 2 sensitivities
        > have been changed significantly. Channel 1's signal now ranges from
        > 3.5 divisions to 6.5 divisions at 200 mV/division for a total
        > amplitude of 600 mV peak-to-peak. Channel 2's signal ranges from 0.8
        > divisions to 3.2 divisions for an amplitude of 240 mV. The ratio of
        > the two sense coils is 2.5 to 1. The output coil amplitude is now
        > 6 divisions at 200 volts/division for a total amplitude of 1,200 volts
        > peak-to-peak. As noted on the screen, there is a 60k ohm load
        > connected to the output coil.
        >
        > NOTE: the sense-coil signals are shifted (delayed) about 90
        > degrees (1/4 cycle) due to the R-C filters. Without the R-C filters,
        > the signals from the sense-coils are in phase with the output voltage,
        > as they should be, but then high-frequency artifacts appear stronger
        > than they are in reality.
        >
        > The image "CoreBuildUp.jpg", in the folder "Results from a new A-
        > Theory", shows the built-up core. There are two drive coils in place
        > to try different resonance frequencies because the leakage inductance
        > will change based on the length of the magnetic path from the drive
        > coil to the output coil. The output coil being tested is on the
        > right-hand side of the image, where the coaxial-cable connections to
        > two of the sense coils can be seen. The output coil on the left has
        > the connections to each layer brought out so that experiments can be
        > performed with different total turns in its circuit.
        >
        > A note about the drive circuit: it is composed of four MOSFETs in
        > a bridge configuration so that the full supply voltage can be applied
        > across the drive coil for each phase of the drive. For this test,
        > it's only function is to provide a variable-frequency square wave to
        > the drive coil to provide large values of dB/dt in the core, and
        > consequent large values of dA/dt outside the core. A simplified
        > circuit diagram can be seen in the image "TestCir1.bmp", in the
        > folder "Results from a new A-Theory".
        >
        > The ratio of measured B-field inside the output coil is close to
        > the 3:1 value of the A strength ratios in my idealization. Why they
        > are not precisely 3:1 is probably due to the fact that I have
        > approximated the A values, and because A is not blocked by the core
        > (or any other physical matter) there are some vectorial subtractions
        > occurring due to vectors interfering around the output coil which
        > results in less than a 3:1 ratio occurring.
        >
        > By the way, the addition of the permanent magnet to the core
        > did not change the ratio significantly and I have not made precise
        > measurements of its impact at this time. The difference in ratio
        > may have been 10%, not a lot compared to the basic ratio. The
        > images in this report are those with the magnet in place.
        >
        > Also, there was no significant difference in signal level
        > between the sense-coils on the outside of the leg versus
        > those at the center.
        >
        > To help eliminate experimental error, I built an entirely
        > different configuration, on an AMCC-1000 uncut core, which is
        > dramatically different in size from the AMCC-320. The sense-
        > coils are also very different in size. The effect is
        > repeatable as the measured ratio between outside and interior
        > of the core is 3.2:1 which is close to that reported here.
        >
        > A symmetrically wound coil will have a reasonably uniform
        > magnetic field at points that are symmetrically similar. (The
        > field distribution in a rectangular shape is not uniform, although
        > at symmetric points around the center of the shape the field will
        > be the same.) This experiment indicates to me that the magnetic
        > vector potential is real, as theorized by Aharonov and Bohm, and
        > that we have not fully exploited it as yet.
        >
        > David J.
        >
        > Files:
        > ACoreTst1.bmp
        > AgradCor1.bmp
        > AllSigsLowFreq.jpg
        > AllSigsHiFreq.jpg
        > CoreBuildUp.jpg
        > TestCir1.bmp
      • carbonprobe
        The possible mechanism on how the Meg actually works, I believe, is described in this 1998 patent WO9840960: http://l2.espacenet.com/espacenet/bnsviewer?
        Message 3 of 5 , Nov 4, 2003
        • 0 Attachment
          The possible mechanism on how the Meg actually works, I believe, is
          described in this 1998 patent WO9840960:

          http://l2.espacenet.com/espacenet/bnsviewer?
          CY=ep&LG=en&DB=EPD&PN=WO9840960&ID=WO+++9840960A1+I+

          "The electromagnetic device of the present invention exploits a
          practically unlimited source of energy and it is thus vey
          cheap.....The pulses applied to the windings 110 and 115 perturb the
          magnetic field generated by the magnet 105 and produce a total
          magnetic field having an amplitude which is extremely higher than the
          amplitude of the magnetic field generated by the magnet 105.
          Experimental tests have shown that the resulting magnetic field has
          an amplitude far higher (e.g. several thousand times) than the field
          produced by the magnet 105 and that the energy generated by the
          electromagnetic device 100 is extremely higher than the energy
          absorbed by the unit 120 for generating the pulse sequences."

          Ken
        • carbonprobe
          David, In the photo of your MEG there are flat pieces of metal in between your magnets to make the stack fit inside the core. This causes fringing B-fields
          Message 4 of 5 , Nov 5, 2003
          • 0 Attachment
            David, In the photo of your MEG there are flat pieces of metal in
            between your magnets to make the stack fit inside the core. This
            causes fringing B-fields around the core and the Aharonov-Bohm effect
            will not happen as Bearden explains.

            Ken
          • davidj95650
            Hi Ken, On a third build-up of this type of test set-up, I measured the leakage flux around the magnet stack and especially near the transformer-laminations
            Message 5 of 5 , Nov 7, 2003
            • 0 Attachment
              Hi Ken,

              On a third build-up of this type of test set-up,
              I measured the leakage flux around the magnet stack and
              especially near the transformer-laminations used to make
              the magnet stack fit tightly inside the AMCC core. Placing
              a gaussmeter probe against the edge of the transformer
              laminations, I measured up to 350 gauss. At the junction
              of the magnet stack and the AMCC core I measured up to
              145 gauss. At the surface of the output core, adjacent to
              the transformer laminations I measured up to 48 gauss.
              Away from that location the measured field decreased to
              about 10 gauss, then increased to about 25 gauss near the
              locations at top and bottom where the magnet stack contacts
              the AMCC core. Outside the AMCC core, there is no
              measurable magnetic field (gaussmeter resolution = 1 gauss).

              I am assuming that with the low-reluctance path provided
              by the nanocrystalline core, the NIB magnet stack will reach
              a field strength of about 10,000 gauss (a single magnet in
              air measures 4,000 gauss at its surface). Thus these
              measurements are a small percentage of the total field.
              The dA/dt still holds even if the A is not entirely curl-
              free (B = del x A). In the event of curled A (B), there
              is a transverse force by the familiar relationship of qV x B.
              I am assuming that Dr. Bearden means that if there is a B
              field present, the surface electrons will be driven
              transverse to their propagation along the wire, thus
              increasing their collisions with atoms at the surface and
              reducing their velocity.

              Because of your question, I conducted an experiment on
              this third build-up of this configuration (yes, the
              relationship of outside/interior sense coil voltage still
              holds, although enhanced in this build-up because I used a
              larger block of ferrite on the outside sense coil). I
              placed an NIB magnet, 1/2-inch x 1-inch x 1/2-inch thick,
              4,100 gauss at its surface, near the interior sense coil.
              For "N" polarity of the magnet face the sense voltage of
              only the interior coil decreases about two per-cent. For
              the "S" polarity, the outside sense coil voltage decreases
              about one per-cent and the voltage from the interior sense
              coil does not change. The polarities of this magnet react
              oppositely depending on which side of the output coil it
              is placed. Placing either face near the outside of the
              output coil and in the vicinity of the outside sense coil,
              there is no discernable effect on the sense voltages.
              This by itself is an interesting effect, and needs further investigation. I repeated these tests about ten times to
              be sure the effects were real and not something as simple
              as a changing resonant frequency of the output coil. (N
              of the magnet stack inside the AMCC core is at its top).

              An e-mailer asked if this set-up isn't measuring the CEMF
              of the output coil, and I replied that yes that is exactly
              what is being measured. The fact that it is different for
              locations on opposite sides of a core leg is the point that
              is important. By classical E-M it shouldn't be. "A" is
              real.

              David J.

              --- In MEG_builders@yahoogroups.com, "carbonprobe" <carbonprobe@y...> wrote:
              > David, In the photo of your MEG there are flat pieces of metal in
              > between your magnets to make the stack fit inside the core. This
              > causes fringing B-fields around the core and the Aharonov-Bohm effect
              > will not happen as Bearden explains.
              >
              > Ken
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