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    If two waves meet in antiphase they interfere destructively... what exactly does this mean. The energy cant disappear, it must still be there, which means we must still be able to detect it...?

    On youngs double slits for example, what has happened to the photons in the dark patches? (I realise this can be explained by quantum theory, so it's not really a very good example...)

    Basically there must be some idea of negative energy... when you're listening to the radio and get some interference which reduces the amplitude of the radio waves arriving what has happened to the original energy emitted from the radio station? I cant link this with the quantum theory as with youngs double slits because if i do then it means that everything if destined to happen before it happens.

    Basically, is there such a thing as negative energy?
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    (Original post by Drummy)
    no
    Want to expand on that? :p:
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    (Original post by LearningMath)
    If two waves meet in antiphase they interfere destructively... what exactly does this mean. The energy cant disappear, it must still be there, which means we must still be able to detect it...?
    Basically, if you consider the waves in antiphase as two forces of equal size acting in opposite direction,the resultant of those two forces is zero. That doesn't mean those two forces aren't there, they are, they just cancel each other out. Same principle with the two waves in antiphase, but this time if you add the phasors of thos two waves together, the resultant is no phasor and therefore no wave. Both waves are there, but there is no negative energy, just a negative direction.
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    (Original post by Banburyhammer)
    Basically, if you consider the waves in antiphase as two forces of equal size acting in opposite direction,the resultant of those two forces is zero. That doesn't mean those two forces aren't there, they are, they just cancel each other out. Same principle with the two waves in antiphase, but this time if you add the phasors of thos two waves together, the resultant is no phasor and therefore no wave. Both waves are there, but there is no negative energy, just a negative direction.
    Ok, what happens to the energy then..? If it's still there, then it must have some kind of detectable effect, and must end up somewhere.
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    Well in your Young's slits example you have dark patches (loss of energy) and brighter patches (a gain in energy, constructive interference), so there is your energy balance

    In EM waves the energy is normally stored in either electric or magnetic fields, and as one decreases the other increases, etc


    (Oh and negative energy sort of exists in Dirac's theory of antiparticles and stuff, but not in the sense you are describing)
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    (Original post by LearningMath)
    Ok, what happens to the energy then..? If it's still there, then it must have some kind of detectable effect, and must end up somewhere.
    The energy simply dissipates into whatever medium it happens to be surrounded by.

    Imagine a box with two forces acting on it in opposite directions. There is no movement, but the forces are still there. The energy from these forces is absorbed by whatever is causing them in the first place.
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    it is very interesting that two waves meet at a certain point, interfere then carry on as if nothing had happened so I'm not so sure about energy disipating etc..

    If you imagine sending two pulses to meet from either end of a slinky. When they meeet the amplitude is zero if they are in antiphase but then the pulses carry on. In this case the energy is momentarily stored as elastic p.e. in the slinky itself so doesn't manifest itself as amplitude.

    MC REN's answer is about the same.
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    Energy isn't a real quantity anyway, so it's not too counter-intuitive to suggest that it could take negative values. I think there have been some speculations about the possibility of negative energy in QM. Dirac said something like

    \psi(t)=e^{i\alpha Et}=e^{-i\alpha(-E)t}, i.e. you can get a solution of the time dependence function in QM with negative energy values (or, equally, with negative time values).

    Also, I'm sure it's been suggested that potential energy is in some sense negative - that way the total energy in the universe is close to zero, which makes life easier for some Cosmologists.
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    (Original post by shamrock92)
    Energy isn't a real quantity anyway, so it's not too counter-intuitive to suggest that it could take negative values.
    It is in the sense that it's a measurable, conserved quantity. You might want to expand on that statement.

    (Original post by shamrock92)
    I think there have been some speculations about the possibility of negative energy in QM. Dirac said something like

    \psi(t)=e^{i\alpha Et}=e^{-i\alpha(-E)t}, i.e. you can get a solution of the time dependence function in QM with negative energy values (or, equally, with negative time values).
    Well Dirac was a bit wrong about negative energy particles, he did develop a theory of holes to predict existence of antiparticles, but that had problems and has since been super-seeded by Quantum Field Theory.

    (Original post by shamrock92)
    Also, I'm sure it's been suggested that potential energy is in some sense negative - that way the total energy in the universe is close to zero, which makes life easier for some Cosmologists.
    Well that's just about where you define your zero, it's nothing physical.
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    (Original post by TableChair)
    It is in the sense that it's a measurable, conserved quantity. You might want to expand on that statement.
    It's not real in that it's not Lorentz-Invariant. As different observers in different reference frames can correctly measure the same object as having different energies, it's not a real quantity - unlike mass. In any case, we know that energy is just a manifestation of mass. So the idea of "negative energy" isn't that scary.
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    (Original post by TableChair)
    Well that's just about where you define your zero, it's nothing physical.
    People used to say temperature was just arbitrarily "about where you define your zero", but now we know it's not. You could interpret the potential energy as the energy of the field (which seems to make more physical sense); and, in that case, you could perhaps measure its gravitational effects due to mass (though I'm not sure if that's been verified). So I wouldn't just dismiss potential energy as a big fake.
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    (Original post by shamrock92)
    It's not real in that it's not Lorentz-Invariant. As different observers in different reference frames can correctly measure the same object as having different energies, it's not a real quantity - unlike mass. In any case, we know that energy is just a manifestation of mass. So the idea of "negative energy" isn't that scary.
    All observers agree on the conservation of energy. But transforming frames is effectively equivalent to redefining your zero.

    Or, mass is a manifestation of energy.
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    (Original post by shamrock92)
    People used to say temperature was just arbitrarily "about where you define your zero", but now we know it's not. You could interpret the potential energy as the energy of the field (which seems to make more physical sense); and, in that case, you could perhaps measure its gravitational effects due to mass (though I'm not sure if that's been verified). So I wouldn't just dismiss potential energy as a big fake.
    At no point did I say potential energy is a 'fake'. It's simply the scalar field which, by taking the gradient, gives you the 'physical' field. As such you can add any arbitrary constant and not affect the physics, hence you can define it to be negative.


    Your temperature example is simply not relevant.
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    (Original post by TableChair)
    All observers agree on the conservation of energy. But transforming frames is effectively equivalent to redefining your zero.
    Sure; but now energy as a whole concept, and not just potential energy, becomes an arbitrary/unreal concept.

    (Original post by TableChair)
    Or, mass is a manifestation of energy.
    In light of the above, the converse would seem more appropriate. (Also, if the speculation about the Higgs field is correct, that would surely bear out energy being subordinate to mass.)
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    (Original post by TableChair)
    At no point did I say potential energy is a 'fake'. It's simply the scalar field which, by taking the gradient, gives you the 'physical' field. As such you can add any arbitrary constant and not affect the physics, hence you can define it to be negative.
    Nevertheless, if energy is in fact not just about where you define your zero (which is probably sensible to believe, for other reasons), and is about energy possessed by the field, this would fit nicely with Cosmology.
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    (Original post by shamrock92)
    Sure; but now energy as a whole concept, and not just potential energy, becomes an arbitrary/unreal concept.



    In light of the above, the converse would seem more appropriate. (Also, if the speculation about the Higgs field is correct, that would surely bear out energy being subordinate to mass.)
    It's not arbitrary, it's one of the few conserved quantities.

    Well no really no, what it would say is that they are the same thing just interacting in different ways. It's probably more convenient to talk about energy though since it's more general.
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    (Original post by shamrock92)
    Nevertheless, if energy is in fact not just about where you define your zero (which is probably sensible to believe, for other reasons), and is about energy possessed by the field, this would fit nicely with Cosmology.
    No. You're missing the point. The only physical things are really the differences in energy, so your 'energy of the field' is simply the difference in energy of having the field and not having the field.

    Anyways, I think we're straying off topic.
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    It depends on the wave and the medium- water waves are fundementally different from waves on a string, sound waves or EM waves. Take waves on a string- these waves have known energy associated with kinetic and potential energy (sin^2 and cos^2 terms which sum to a constant energy per unit length in the abstract case of a continuous wave rather than this example of a wave envelope). When two bits of wave meet, one peak and one trough, travelling in opposite directions, they momentarily completely cancel to leave no displacement from equilibrium.

    However this does not mean the energy has disappeared- the potential energy (associated with distance from equilibrium due to the elastic restoring nature of the string) is zero, but the string is technically still moving- all the energy is kinetic.

    Furthermore, after the waves pass, the superposition does not apply and they continue as before on their way away from each other. The energy of the system is unchanged.

    I am not certain because it's an intriguing question but I'd guess that the answer you are looking for has something to do with the form of waves in nature as "wave packets" with phase and group velocities and exactly known energies per envelope. If two photons meet, they might just pass each other by instantly with a momentary cancellation of the EM field (perhaps this is more complicated as the EM field manifests in different ways depending on the frame of the observer- also this is complicated by the fact that two photons directly incident of sufficient energy will probably interact).
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    (Original post by TableChair)
    It's not arbitrary, it's one of the few conserved quantities.

    Well no really no, what it would say is that they are the same thing just interacting in different ways. It's probably more convenient to talk about energy though since it's more general.
    (Original post by TableChair)
    No. You're missing the point. The only physical things are really the differences in energy, so your 'energy of the field' is simply the difference in energy of having the field and not having the field.

    Anyways, I think we're straying off topic.
    The fact remains that, since energy is not invariant, and invariant stuff can't be really physical, it can't be physical. Mass is a real, invariant quantity. So energy is just a manifestation of mass, just like magnetic forces are a manifestation of electromagnetism. (More relevantly: it means negative energy isn't so counter-intuitive.)
 
 
 
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