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Natural Science Forum / Physics / General Physics / June 2007What am I missing?
If all mass can theoretically be converted into energy and vice versa (E=mc^2) and light has no mass, then wouldn't it be contradictory if you could convert mass to energy (light energy for this example) on an object that exerts gravity and then you "beam" this light energy to a place away from the object, then convert it back to mass and let it fall to the object? I see an easy way that this could be resolved: light could be slightly susceptible to gravity, but much less than its mass counterpart. But I seem this to also contradict that gravity only attracts mass to mass. Can anyone clear up my confusion/ show me a flaw in my reasoning? > If all mass can theoretically be converted into energy and vice versa.. I disagree. The amount of mass in a closed system is a conserved quantity since the mass of a system is the magnitude of the total 4-momentum of that system. If the system is closed then the energy of the system remains constant. This energy is called rest energy of the system. Therefore since rest energy remains constant in that frame then so it does in all inertial frames and thus the rest mass remains constant as measured from any other inertial frame. > (E=mc^2) and light has no mass, then wouldn't it be contradictory if > you could convert mass to energy (light energy for this example) on an > object that exerts gravity and then you "beam" this light energy to a > place away from the object, then convert it back to mass and let it > fall to the object? No, because you're refering to the proper mass of light. If all the energy of the light is headed in one single direction then the proper mass of the system is zero. However the passive gravitational mass of light is not zero and that is why it is attracted by gravity. Einstein demonstrated this in 1911 as I recall. > I see an easy way that this could be resolved: light could be slightly > susceptible to gravity, but much less than its mass counterpart. But I > seem this to also contradict that gravity only attracts mass to mass. > Can anyone clear up my confusion/ show me a flaw in my reasoning? Yes. First provide a rigorous definition of what you mean when you write "mass". The m in E = mc^2 refers to relativistic mass. If was proper mass then it should read E_0 = mc^2. Best regards Pete : If all mass can theoretically be converted into energy Ok... and vice versa Ah... That's a problem and could be what you are missing. When did you show that can happen? On Jun 28, 11:00 pm, "wiiwiillw...@gmail.com" <wiiwiillw...@gmail.com> wrote: > If all mass can theoretically be converted into energy and vice versa > (E=mc^2) and light has no mass, then wouldn't it be contradictory if > you could convert mass to energy (light energy for this example) on an > object that exerts gravity and then you "beam" this light energy to a > place away from the object, then convert it back to mass and let it > fall to the object? What's the contradiction? Are you seeing a problem in that it seems like you've achieved free propulsion? (a) Convert mass to energy at surface, (b) Send energy far away (c) Convert energy back to mass, which is now far out of the original gravity well at (apparently) no cost. I think if you work out the details of such a scenario you'll find that momentum and energy are conserved. For one thing, mass energy conversion preserves momentum. > I see an easy way that this could be resolved: light could be slightly > susceptible to gravity, but much less than its mass counterpart. But I > seem this to also contradict that gravity only attracts mass to mass. Light is affected by gravity in general relativity (e.g. gravitational lensing). > Can anyone clear up my confusion/ show me a flaw in my reasoning? I need to understand more about what paradox you're worried about. - Randy On Jun 28, 11:00 pm, "wiiwiillw...@gmail.com" <wiiwiillw...@gmail.com> wrote: > If all mass can theoretically be converted into energy and vice versa > (E=mc^2) and light has no mass, then wouldn't it be contradictory if [quoted text clipped - 7 lines] > seem this to also contradict that gravity only attracts mass to mass. > Can anyone clear up my confusion/ show me a flaw in my reasoning? No real contradiction here, since GR says that energy, independent of matter, can produce gravitational fields and will also respond to them. |
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