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Thread: Paradox

  1. #1 Paradox 
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    They say photons have momentum, but momentum has dimension kgm/s. Isn't it paradoxial to heve something with no mass having a property with dimension where kg occurs in?


    It also matters what isn't there - Tao Te Ching interpreted.
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    Not at all. Consider the more general definition of momentum in the context of 4-vectors



    Now calculate the magnitude of this 4-vector



    This is equivalent to



    For a photon ( m=0 ) this just becomes



    as expected. The momentum in this case has dimension of N*s, and is not defined in terms of kg.


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    N is still defined as kgm/s^2 and replacement is valid, so logically you still sit with "kg" in the definition.
    It also matters what isn't there - Tao Te Ching interpreted.
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    Quote Originally Posted by talanum1 View Post
    N is still defined as kgm/s^2 and replacement is valid, so logically you still sit with "kg" in the definition.
    As you point out, momentum has dimensions of mass*length/time. Why are you selectively perturbed only by a photon's lack of mass, but not by its lack of time?
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    Quote Originally Posted by tk421 View Post
    Quote Originally Posted by talanum1 View Post
    N is still defined as kgm/s^2 and replacement is valid, so logically you still sit with "kg" in the definition.
    As you point out, momentum has dimensions of mass*length/time. Why are you selectively perturbed only by a photon's lack of mass, but not by its lack of time?
    Or, more specifically its lack of "inverse time" (whatever that is). [Edit: I suppose inverse time is frequency and so ....]

    This would appear to be the physics equivalent of the etymological fallacy; just because something appears in the dimensional analysis, doesn't mean it exists.
    Last edited by Strange; October 17th, 2012 at 04:37 AM.
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  7. #6  
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    Quote Originally Posted by Strange View Post
    Quote Originally Posted by tk421 View Post
    Quote Originally Posted by talanum1 View Post
    N is still defined as kgm/s^2 and replacement is valid, so logically you still sit with "kg" in the definition.
    As you point out, momentum has dimensions of mass*length/time. Why are you selectively perturbed only by a photon's lack of mass, but not by its lack of time?
    Or, more specifically its lack of "inverse time" (whatever that is). [Edit: I suppose inverse time is frequency and so ....]

    This would appear to be the physics equivalent of the etymological fallacy; just because something appears in the dimensional analysis, doesn't mean it exists.
    Good "paradox"!
    For me is a good signal that something could be wrong in the current concept/model of a photon...
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    See wikipedia re Proposed future definitions of the kilogram:

    "Such a definition would theoretically permit any apparatus that was capable of delineating the kilogram in terms of the Planck constant to be used as long as it possessed sufficient precision, accuracy and stability. The watt balance (discussed below) may be able to do this...
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  9. #8  
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    Quote Originally Posted by talanum1 View Post
    N is still defined as kgm/s^2 and replacement is valid, so logically you still sit with "kg" in the definition.
    So ? Momentum is a general feature of all particles, regardless of whether they have mass or not. Momentum is just a form of energy, and photons do carry energy. Remember that all forms of energy are equivalent. I don't understand where the issue, let alone the paradox, is ?
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  10. #9  
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    Quote Originally Posted by Markus Hanke View Post
    Quote Originally Posted by talanum1 View Post
    N is still defined as kgm/s^2 and replacement is valid, so logically you still sit with "kg" in the definition.
    So ? Momentum is a general feature of all particles, regardless of whether they have mass or not. Momentum is just a form of energy, and photons do carry energy. Remember that all forms of energy are equivalent. I don't understand where the issue, let alone the paradox, is ?
    Momentum is not "a form of energy". They are different things with different dimensions.
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  11. #10  
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    Quote Originally Posted by martillo View Post
    Momentum is not "a form of energy". They are different things with different dimensions.
    Not as different as you seem to think. Look up "energy-momentum relation."
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  12. #11  
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    Quote Originally Posted by tk421 View Post
    Quote Originally Posted by martillo View Post
    Momentum is not "a form of energy". They are different things with different dimensions.
    Not as different as you seem to think. Look up "energy-momentum relation."
    Googling "energy-momentum relation" easily comes at wikipedia the relativistic formula:
    E^2 = m^2.c^4 + p^2.c^2
    and for an assumed massless photon (m=0):
    E = p.c

    Don't you see momentum and energy are very different things?
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  13. #12  
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    Quote Originally Posted by martillo View Post
    Momentum is not "a form of energy". They are different things with different dimensions.
    Not at all. Did you not follow my maths in post 2 ? The momentum of a photon is just



    which is simply a measure of the photon's energy. In fact energy, momentum and stress are all manifestations of the same thing, which is why they can all be unified into just one object, the stress-energy-momentum tensor :

    Stress

    Even more generally, momentum can be defined via the Lagrangian of a given system through



    All of this is applicable to massive as well as massless particles - there are no paradoxes anywhere.
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    Quote Originally Posted by martillo View Post
    Googling "energy-momentum relation" easily comes at wikipedia the relativistic formula:
    E^2 = m^2.c^4 + p^2.c^2
    and for an assumed massless photon (m=0):
    E = p.c

    Don't you see momentum and energy are very different things?
    No, E=pc, so the momentum p is just a measure of energy. This is exactly as shown in post 2.
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    Quote Originally Posted by martillo View Post
    and for an assumed massless photon (m=0):
    E = p.c

    Don't you see momentum and energy are very different things?
    Study the equations and see what they are saying. Re-read what Markus has told you several times, now. If you open your mind, you will see that they are not at all "very different things." As one hint, notice that the last equation you copied, above, has an equals sign; on the left is energy, on the right is momentum, with a scaling factor of c. Think about what that means. Are energy and momentum truly such different things?
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  16. #15  
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    Quote Originally Posted by Markus Hanke View Post
    Quote Originally Posted by martillo View Post
    Googling "energy-momentum relation" easily comes at wikipedia the relativistic formula:
    E^2 = m^2.c^4 + p^2.c^2
    and for an assumed massless photon (m=0):
    E = p.c

    Don't you see momentum and energy are very different things?
    No, E=pc, so the momentum p is just a measure of energy. This is exactly as shown in post 2.
    Well, I guess the same way it is sustained that energy and mass are equivalent as a consequence of the E=m.c^2 formula, isn't it?
    This way energy, mass, momentum and who knows what else are all the same thing.
    I prefer to think they are different things and that's why I agree in that the problem of dimensions for a photon could be seen as a "paradox"...
    At the end in all those formulas appear the c factor wich is a velocity (even if with constant value) so it has sense for me to consider them as different things.
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  17. #16  
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    Quote Originally Posted by martillo View Post
    Well, I guess the same way it is sustained that energy and mass are equivalent as a consequence of the E=m.c^2 formula, isn't it?
    Yes, of course. That is the result of the same energy-momentum relation, only for particles at rest ( p=0 ).

    I prefer to think they are different things
    Your personal preferences are just that - personal preferences.
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    Light is a waves, and when waves hit something: it transfer momentum. Just like a collision. Waves on a rope and waves at sea can collide and transfer momentum.

    Imagine this:
    when an emitter produce magnetic & electric component (of light wave) some internal force will be created* and this changes the momentum of the emitter, and when the light wave hit a reciever then the receiver receive the opposite momentum (caused by the same magnetic & electric interaction) and the total momentum (of both emitter & receiver) is Zero (0). Momentum is conserved & a 'collision' happened.

    *force created due to electron's interaction with magnetism. ie: Only conductor with free electrons could create & reflect lightwave.
    Last edited by msafwan; October 18th, 2012 at 12:28 AM.
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    The way I picture photon momentum is like this. Picture yourself as operating in Planck time, that is everything operates from one moment to the next. A photon flies toward an electron at close to the speed of light, but still, within your frame of reference, it looks like a low frame rate movie. Upon collision with this electron there is a moment where the velocity of the photon begins to change, and thus there is a moment it is "at rest." For this incredibly short period of time, it is possible to measure the photon's mass, and therefore view it as "containing momentum."
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    The photon will disappear (absorbed by electrons) and then re-appear (re-emitted back by electron) in the opposite direction. So you can't see any acceleration and it certainly doesn't have acceleration. -Electron-photon interaction explain alot of things, from how lightwave is produced to how lightwave could exert momentum.

    Photon is a carrier of force. It doesn't have acceleration, mass or momentum, and it only 'carry' force*.http://en.wikipedia.org/wiki/Force_carrier

    *It is a WAVE. All wave behave like this.
    Last edited by msafwan; October 18th, 2012 at 12:33 AM.
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  21. #20  
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    Quote Originally Posted by msafwan View Post
    The photon will disappear (absorbed by electrons) and then re-appear (re-emitted back by electron) in the opposite direction. So you can't see any acceleration and it certainly doesn't have acceleration. -Electron-photon interaction explain alot of things, from how lightwave is produced to how lightwave could exert momentum.

    Photon is a carrier of force. It doesn't have acceleration, mass or momentum, and it only 'carry' force*.Force carrier - Wikipedia, the free encyclopedia

    *It is a WAVE. All wave behave like this.
    Thank you for explaining this.
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  22. #21  
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    Quote Originally Posted by talanum1 View Post
    They say photons have momentum, but momentum has dimension kgm/s. Isn't it paradoxial to heve something with no mass having a property with dimension where kg occurs in?
    Photons have relativistic mass which gives them relativistic momentum, however the technical term for this is 'momenergy'.

    Mass and energy are equivlanet therefore they have a relative 'kilograms' I wonder what the weight of a photon would be as it falls from the photon sphere to the singularity. A relative energy weight?
    "If you wish to make an apple pie from scratch, you must first invent the universe". - Carl Sagan
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    Quote Originally Posted by Quantime View Post
    Quote Originally Posted by talanum1 View Post
    They say photons have momentum, but momentum has dimension kgm/s. Isn't it paradoxial to heve something with no mass having a property with dimension where kg occurs in?
    Photons have relativistic mass which gives them relativistic momentum, however the technical term for this is 'momenergy'.

    Mass and energy are equivlanet therefore they have a relative 'kilograms' I wonder what the weight of a photon would be as it falls from the photon sphere to the singularity. A relative energy weight?
    Modern Relativity finds "relativistic mass" inappropiated and recommended to not be used to avoid misinterpretations. Mass is considered an invariant (constant) in the four-vector formulation of the theory.
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  24. #23  
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    Quote Originally Posted by martillo View Post
    Modern Relativity finds "relativistic mass" inappropiated and recommended to not be used to avoid misinterpretations. Mass is considered an invariant (constant) in the four-vector formulation of the theory.
    That is precisely why Quantime explained to you the term "momenergy", which is an invariant 4-vector, as already shown in post 2.
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    I have a solution to the problem under the following interpretation:

    The photon can cause momentum onto an electron it collides with, and it can cause this momentum because it carries energy. Note I use the word "cause" and not "transfer". In this view the photon does not carry momentum.

    In this view the photon must carry a direction (as we see with laser light) and energy (since p is a vector).

    Isn't collision with a particle the only way to measure a photon's "momentum"?
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    Quote Originally Posted by talanum1 View Post
    The photon can cause momentum onto an electron it collides with, and it can cause this momentum because it carries energy. Note I use the word "cause" and not "transfer". In this view the photon does not carry momentum.
    I absolutely 100% agree. The energy from incoming photons can create a momentum on the target electrons. -Magnetic and electric field of photon will definitely (100% sure will) cause motion on any electron(s), no doubt.

    This don't violate law of momentum conservation because both the emitter & the absorbing electrons experience the exact opposite motion. Everything involving photon-electron 'collision' is absolutely 100% basic physic (can't possibly be wrong).
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    Quote Originally Posted by msafwan View Post
    This don't violate law of momentum conservation because both the emitter & the absorbing electrons experience the exact opposite motion.
    I'm afraid that's not correct. The conservation of momentum does not just apply to the end result of an interaction, but to all intermediate stages as well. You cannot have one electron where momentum suddenly vanishes, then a photon which does not carry momentum, and then another electron where momentum suddenly re-appears. This would constitute a clear violation of the momentum conservation law, both under classical mechanics and under quantum physics.

    If there are still doubts whether a photon actually carries momentum, please refer here :

    Photon - Wikipedia, the free encyclopedia
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    That doesn't make semi-classical explaination wrong. In fact, semi-classical photon can explain all alot of phenomenon like diffraction, dispersion, scattering, light in gravity potential, heinsenberg uncertainty, and everything else.

    While more advanced interpretation of photon seems to loose all resemblance to observable world, like interpreting creation of photon from pertubation of quantum field and interaction with virtual photon of arbitrary property (like possibility of having mass or being able to manifest gravitational field). In such case, then "momentum" doesn't make sense anymore because it might as well be a derivative propery (like how "mass" is not really a 'mass' but derivative of somesort of force field).

    There's no wrong thing here.
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    Well Energy has the dimensions of kg*m^2/s^2 And I don't see any meters in energy either!

    Your paradox isn't a paradox. Momentum is the cumulation of force over time. In the case of light, this was a quantum jump, hence a quantum of energy. Yet still a change in force. It feels intuitively wrong. Just like it feels as if air has no weight. yet, a filled balloon is heavier then an empty one. If I'd have a perfectly reflective surface on my hand. And a strong laserpulse shining on it. You can still feel the light press with twice the momentum it has. (also it will actually feel a little colder)
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  30. #29  
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    Quote Originally Posted by msafwan View Post
    That doesn't make semi-classical explaination wrong.
    Not wrong, just incomplete. It is a good approximation for certain scenarios.
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    Quote Originally Posted by Markus Hanke View Post
    Quote Originally Posted by msafwan View Post
    That doesn't make semi-classical explaination wrong.
    Not wrong, just incomplete. It is a good approximation for certain scenarios.
    Its not an approximation. Photon is a real wave and is created by real field (electric & magnetic field), and it exhibit wave property like all wave would do.

    Quantum property is NOT a property photon alone. Everything will exhibit wave & particle property in quantum level and they all became indistinguishable from each other at this level.

    Semi-classical explaination for photon is accurate. Not an approximation
    Last edited by msafwan; October 26th, 2012 at 03:00 AM.
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    Quote Originally Posted by Markus Hanke View Post
    The conservation of momentum does not just apply to the end result of an interaction, but to all intermediate stages as well. You cannot have one electron where momentum suddenly vanishes, then a photon which does not carry momentum, and then another electron where momentum suddenly re-appears. This would constitute a clear violation of the momentum conservation law, both under classical mechanics and under quantum physics.
    Intermediate steps doesn't violate the natural world. See here: Lenz's law - Wikipedia, the free encyclopedia .It happen.
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    Quote Originally Posted by msafwan View Post
    Intermediate steps doesn't violate the natural world. See here: Lenz's law - Wikipedia, the free encyclopedia .It happen.
    How does Lenz's law imply that the photon involved in electron-electron interactions does not carry momentum

    Semi-classical explaination for photon is accurate. Not an approximation
    Can you clarify what you understand "semi-classical" to mean.
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    Quote Originally Posted by Markus Hanke View Post
    How does Lenz's law imply that the photon involved in electron-electron interactions does not carry momentum
    No it doesn't. It just says that such dilemma has occured before, and the suggestion is to give momentum to the field.

    Quote Originally Posted by Markus Hanke View Post
    Can you clarify what you understand "semi-classical" to mean.
    A photon is a wave and is subjected to quantization.
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    Quote Originally Posted by msafwan View Post
    No it doesn't. It just says that such dilemma has occured before, and the suggestion is to give momentum to the field.
    Yes, that's right.

    A photon is a wave and is subjected to quantization.
    Yes, that is right.

    Semi-classical means that part of a system is treated quantum mechanically, and part of it classically. Mathematically this is achieved by developing the governing relations in power series, usually in terms of Planck's constant. By considering higher and higher powers you can achieve an arbitrary degree of accuracy, but it does remain an approximation until all powers are accounted for, in which case it becomes full quantum mechanics. If only the first power is taken into account you get a classical description. See also here :

    Semiclassical physics - Wikipedia, the free encyclopedia
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    Im a layman mathematically...but would this not perhaps fall into the realm of isotropy and could even be cashed out in Euclid? If not just ignore.
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    Quote Originally Posted by Kerling View Post
    Well Energy has the dimensions of kg*m^2/s^2 And I don't see any meters in energy either!
    This is different: Energy is a concept and a photon is a real particle.

    I do not think it has relativistic mass due to E = mc^2 because this is the equation of conversion of energy to mass.
    It also matters what isn't there - Tao Te Ching interpreted.
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    Quote Originally Posted by talanum1 View Post
    This is different: Energy is a concept and a photon is a real particle.
    I do not think it has relativistic mass due to E = mc^2 because this is the equation of conversion of energy to mass.
    Quote Originally Posted by talanum1 View Post
    They say photons have momentum, but momentum has dimension kgm/s. Isn't it paradoxial to heve something with no mass having a property with dimension where kg occurs in?
    No it is exactly the same. In fact it is safe to say that Energy is more real then a photon. A Photon is a quantization of the electromagnetic field. And the ideal photon (a point particle) would have an infinitetly broad fourier spectrum, meaning a completely undefinded energy.

    Energy however is measurable, and electromagnetic waves are quantized in energy.
    Also a photon isn't a particle. As it cannot interact with its own kind. It can only cause interference. There is no scattering of photons on photons.

    Also, considering that everyone is fucking up this energy business lets solve it once and for all; E=mc^2 is for particles in rest. Considering light is, well, light. It must therefore travel at the speed of light. And this means that it isn't 'in rest' . In that case we need to use the Klein Gordon equation: E^2 = m^2*c^4 + p^2*c^2.
    Since a photon doesn't have mass; E^2 = p^2*c^2. Or more simple p=E/C since E is the energy the momentum of a continous wave would be hf/c or p= h/labda where labda is the wavelength.

    However, we are speaking of a photon. Which is a summation of several different kinds of modes from the spectrum. Since it scales linearly with the spectrum of energy, it inherits is Gaussian nature. In other words, Photon's have Gaussian momentum distribution. Either way. They have momentum. And, it can be seen. In fact I have one of those mirror fans in my window. It turns fast when it is sunny, slow when it is dark.
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    Quote Originally Posted by Kerling View Post

    No it is exactly the same. In fact it is safe to say that Energy is more real then a photon. A Photon is a quantization of the electromagnetic field. And the ideal photon (a point particle) would have an infinitetly broad fourier spectrum, meaning a completely undefinded energy.

    Energy however is measurable, and electromagnetic waves are quantized in energy.
    Also a photon isn't a particle. As it cannot interact with its own kind. It can only cause interference. There is no scattering of photons on photons.

    Also, considering that everyone is fucking up this energy business lets solve it once and for all; E=mc^2 is for particles in rest. Considering light is, well, light. It must therefore travel at the speed of light. And this means that it isn't 'in rest' . In that case we need to use the Klein Gordon equation: E^2 = m^2*c^4 + p^2*c^2.
    Since a photon doesn't have mass; E^2 = p^2*c^2. Or more simple p=E/C since E is the energy the momentum of a continous wave would be hf/c or p= h/labda where labda is the wavelength.

    However, we are speaking of a photon. Which is a summation of several different kinds of modes from the spectrum. Since it scales linearly with the spectrum of energy, it inherits is Gaussian nature. In other words, Photon's have Gaussian momentum distribution. Either way. They have momentum. And, it can be seen. In fact I have one of those mirror fans in my window. It turns fast when it is sunny, slow when it is dark.
    Precisely. I had that shown already in post 2, but unfortunately talanum1 chose to pretty much ignore my post.
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    Quote Originally Posted by Markus Hanke View Post

    Precisely. I had that shown already in post 2, but unfortunately talanum1 chose to pretty much ignore my post.
    Great minds are ignored (think) alike :P
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