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Homework Help: Creating new energy by E-m conversion - why can't this work?

  1. Dec 1, 2012 #1
    1. The problem statement, all variables and given/known data
    This isn't a homework problem, but a question my physics teacher asked us in school, more than 25 years ago. I've thought about this from time to time, but I never found anyone to ask whether my explanation is at least plausible.

    Imagine you had a machine that could convert matter into energy and vice-versa. Now you take a mass, say, 1kg of iron, and convert it into energy that you receive as photons. Direct the stream of photons to the ISS, where you use another machine to convert it back to 1kg of iron.

    Obviously, the 1kg in orbit has a greater potential energy that it had back on earth. Where did this energy come from?

    2. Relevant equations

    None. No exact (numerical) answer is expected. Assume no atmosphere between the earth and the ISS, and assume your machines convert mass to energy and back without losing either during the process.

    3. The attempt at a solution

    It's obvious that the mass on the ISS must be less than it was on earth, so it must have decreased somewhere "en route" while it was in the form of light. The number of photons can't have decreased, so it's their frequency that must have. The beam of light must have been red-shifted, but how?

    My only explanation is that this happens every time an electromagnetic wave moves away from a source of gravity. Hence, to exaggerate a bit, if you point a ray of blue light at the moon, an astronaut there would see it as red. And, conversely, if this astronaut shines a red light on us, we'd see it as blue. (That's VERY exaggerated; I don't know whether the change in frequency would be noticeable at all to a human eye.)

    Is this what my teacher was thinking of? Or am I missing something?
  2. jcsd
  3. Dec 1, 2012 #2


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    Light leaving a gravitational well loses energy. This is a consequence of General Relativity.

    1kg of rest mass is the same amount of mass no matter where it is, regardless of its potential energy. To assemble 1kg of mass in a given location requires the same amount of energy, ##E = M c^2##. However, whatever energy is required to do it has to first get to that location in some way, either by transporting it in some material form or, as you suggest, "beaming" it there as photons.

    Since photons lose energy climbing out of a gravitational well you'll have to supply additional energy over and above that which comes directly from converting the 1kg mass to photons on the Earth's surface, so that the total energy made available at the new location is the required amount to "build" 1kg of matter. The additional energy you need to supply will in fact match the potential energy difference between the starting location on the Earth and the orbit at the ISS, plus any kinetic energy difference corresponding to the orbital velocity. The extra energy will be "small change" compared to the amount of energy of 1kg converted to photons!
  4. Dec 1, 2012 #3


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    The only way I can solve this is to actually build a device that does what you are saying.
    First I would start with a half kilogram each of iron and anti-iron atoms. I would bring these together, atom by atom, into a photonic collimating device pointed towards the ISS. The photons, as you mentioned, would lose energy on the trip due to red shifting. At the ISS, the photons would be sent to a pair production module, where the iron and anti-iron atoms would be separated and stored in special containers. Now the atoms on earth will be attracted to each other via the coulomb force and this energy has to be added to the equation. When the photons generate the atom pairs at the ISS, the velocities will indicate a slightly lower energy level, balancing the whole thing out.

    awaiting infraction for creating an overly simplified crackpot fantasy machine in my head in under 60 seconds
  5. Dec 1, 2012 #4


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    Gravitational redshift is right. I recall this being presented to me as a theoretical argument why photons had to be red-shifted when climbing a gravitational gradient. If not, you can construct an energy-generating perpetual motion machine by dropping the brick out of the station and harnessing its kinetic energy before beaming it back up.
  6. Dec 1, 2012 #5
    Thanks a lot for the confirmation. As I thought (and Ibix spelled out), I could perform the experiment my teacher sugegsted, but I'd not end up with 1kg on the ISS, but slightly less. Or (as gneill suggested), I'd have to add some "small change" to make up for what the photons lost on their way up the earth's gravity well.

    So no chance of a perpetuum-mobile device then? I'm saddened, but not at all surprised.
  7. Dec 1, 2012 #6


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    The gravitational redshift has been experimentally verified here on Earth - look up the Pound-Rebka experiment.
  8. Dec 1, 2012 #7
    Thank you, phyzguy. From what I could find about the Pound-Rebka experiment, it seems that for my own thought experiment to work at all, the E-m converter on the ISS would have to be moving upwards by some small speed v relative to the stationary converter on earth, and this speed v would depend on the difference Δh in height between the two machines.

    So if I don't get a perpetuum-modile device from all this effort, at least I'd have a fancy altimeter. :smile:
  9. Dec 1, 2012 #8


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    It's perpetual motion device
  10. Dec 1, 2012 #9


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    I believe "perpetuum mobile" is the latin translation. But I don't speak latin, so I may be wrong.

    Perhaps Michael is a doctor. They speak latin, don't they?
  11. Dec 1, 2012 #10
    I can read and write Latin, but I don't actually speak it. And it's "perpetuum mobile" in Latin. ("modile" was a typo in my earlier post.)
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