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Why can't energy change abruptly?

  1. Sep 27, 2013 #1
    Hi,
    I want to ask your help about energy.
    Why can't energy change abruptly?
    If energy E changes abruptly then power P = dE/dt = ∞. I would like to know why this is impossible?
    I know that energy has to be conserved and they can only change from one form to the other. But why this process (transformation) can't change immediately?
     
  2. jcsd
  3. Sep 27, 2013 #2

    mfb

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    2016 Award

    Staff: Mentor

    Do you know any physical quantity changing abruptly in a real setup?

    Can you imagine any setup where energy could change like that, without particles changing their position abruptly (which cannot happen)?
     
  4. Sep 27, 2013 #3
    Now, I can't find out anything but I can't generalise it.
    Yes, but in my mind :)
     
  5. Sep 27, 2013 #4

    Dale

    Staff: Mentor

    There is an uncertainty relationship between a change in energy of a quantum system and the time required for the transition. Perhaps that is of interest.
     
  6. May 7, 2014 #5
    Now, I just read that the voltage across an ideal inductor and the current through an ideal capacitor can change abruptly.
     
  7. May 7, 2014 #6

    Drakkith

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    Ideal components do not exist in real life.
     
  8. May 8, 2014 #7

    UltrafastPED

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    Gold Member

    I work with very interesting lasers: average energy is quite low, about 1 watt, and the laser is pulsed: 1,000 pulses per second. Thus each pulse has about 1 millijoule of energy.

    Not much, eh?

    But this is an ultrafast laser, meaning that the individual pulses are very short - less than a picosecond in duration. In my case about 30 femtoseconds, or 3*10^-14 seconds.

    Energy is delivered over an area; with adaptive optics this laser can be focused to a spot size of about one wavelength: 800 nanometers; round it up to 10^-4 centimeters (1 micron).

    Putting this all together gives an energy flux of 10^-3 joules/pi*(10^-4 centimeters)^2 =
    10^5 joules/cm^2/pi = 3*10^4 joules/cm^2.

    Apply this energy flux over the very brief pulse duration and the power per unit of area is:
    3*10^4 joules/cm^2/3*10^-14 seconds = 10^18 watts/cm^2. Actually we can do a bit better, and the actual output is slightly over 10^19 watts/cm^2.

    This power flux is sufficient to generate electron-positron pairs when striking a metal target in vacuum - and has done so.

    So you see that it is possible to increase power by quite a bit - but at each step the equipment becomes more specialized and expensive!

    But like so many things, the scaling laws give less and less as you put in more and more - so unlimited power flux is beyond reach.
     
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