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Conservation of Momentum puzzle

  1. Oct 10, 2011 #1
    One key aspect of Special Relativity is the fact that nothing can travel faster than the speed of light. This concept derives from Maxwell's Equations, which calculate the speed of light (electrodynamics). Since Maxwell's Equations describe the formation of magnetic fields (as a result of moving electric charges), I propose a potential conflict in the creation of magnetic fields and the speed of light limit on the movement of those fields through open space (vacuum). This conflict challenges the Law of Conservation of Momentum. The thought experiment illustrating this conflict is a bit too long to present in a post, so I have presented it in the attachment.
     

    Attached Files:

  2. jcsd
  3. Oct 10, 2011 #2

    Dale

    Staff: Mentor

    This is incorrect, Maxwell's equations are guaranteed to always conserve momentum:
    http://farside.ph.utexas.edu/teaching/em/lectures/node91.html

    See the exchange between Tominator and myself starting with his post 40 where he proposes a device like yours and works through the implications:
    https://www.physicsforums.com/showthread.php?t=287164&page=3
     
    Last edited: Oct 10, 2011
  4. Oct 10, 2011 #3

    jtbell

    User Avatar

    Staff: Mentor

    Like Tominator in the thread that DaleSpam linked to, you are not taking into account the momentum of the electromagnetic field.
     
  5. Oct 10, 2011 #4

    Bill_K

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    Science Advisor

    You are also assuming the device is infinitely rigid, which in special relativity is not possible. You speak of "the velocity of the device" changing immediately due to a force on one end. But in fact a velocity change will require time to propagate from one end to the other.
     
  6. Oct 10, 2011 #5
    Lots of good information here.

    Let me see if I can summarize. The battery sends energy to the coil to create an electromagnetic field. The energy given up by the battery is stored in this field and the field expands away from the coil at the speed of light. If an object or device captures a portion of this energy, the momentum associated with that energy portion is transferred to the object or device.

    Put another way, if the device I described was sitting out in space and the device was made to work as I described, then the device would start moving as I described. The momentum gain of the device is offset by the momentum of the remainder of the field energy that wasn't captured by the device. It would be an engine for a space vehicle.
     
  7. Oct 10, 2011 #6

    Dale

    Staff: Mentor

    I don't know if it would work exactly as you described, I only skimmed the document enough to recognize the parallels with Tominator's proposal. But you could indeed make a (very inefficient) space propulsion system this way. But you would be far better off just shining a flashlight.
     
  8. Oct 11, 2011 #7
    Suppose there is a coil and battery sitting in open space, which will be called Coil Device One. The battery is turned on for a short time, then turned off. Now there is a magnetic field expanding around Coil Device One and this field moves outward. The total momentum of the system is zero because the field is symmetrically distributed and expanding everywhere at the same velocity. Sitting away from Coil Device One is Coil Device Two, directly in line with the North pole of Coil Device One. Just before the magnetic field reaches Coil Device Two, it is switched on. Coil Device Two is oriented so that its North pole is in line with Coil Device One. When the magnetic field reaches Coil Device Two, it is repelled and moves away from Coil Device One.

    A second experiment is just as described for the first experiment above, except this time Coil Device Two is oriented so that the South pole faces the North pole of Coil Device One. In this experiment, when the magnetic field reaches Coil Device Two, it is attracted by this field and moves toward Coil Device One.

    In both experiments, the momentum of the field generated by Coil Device One is exactly the same. But in the first experiment, the momentum of Coil Device Two is directed away from Coil Device One and it the second experiment, the momentum of Coil Device Two is directed toward Coil Device One. How does the momentum of a magnetic field explain these two different outcomes?
     
  9. Oct 11, 2011 #8

    Dale

    Staff: Mentor

    From the first link in post 2, what is the expression for the momentum of an EM field? How does that differ in the two cases?
     
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