About effective (relativistic) mass of photon

Discussion in 'Physics & Math' started by Ultron, Jun 14, 2016.

  1. Ultron Registered Senior Member

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    If you dont believe us, just let me google it for you

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    http://lmgtfy.com/?q=relativistic mass of the photon wavelength

    Just select the most reliable sources, spend some hours studying it and then come back to report what have you found out.
     
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  3. Layman Totally Internally Reflected Valued Senior Member

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    Then if I found out who discovered the relativistic mass of a photon, wouldn't I know more about it than you two?
     
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  5. Layman Totally Internally Reflected Valued Senior Member

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  7. Ultron Registered Senior Member

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    At the end of the thread you have linked is link to FAQ posted by science advisor:
    https://www.physicsforums.com/insights/do-photons-have-mass/

    Do photons have mass?
    The quick answer: NO. However, this is where it gets a bit confusing for most people. This is because in physics, there are several ways to define and measure a quantity that we call “mass”. Now, it doesn’t create any confusion among physicists because we tend to know in what context such a quantity is defined. However, for the general public trying to decipher scientific papers and presentation, this is a trap that many fall into and can be the source of many confusion. In physics, the most important definition of a bare mass (we are not going to deal with effective mass that is a part of solid state/condensed matter physics) is what is known as the invariant mass. Invariant mass ([itex]m_0[/itex]) (aka rest mass, proper mass or intrinsic mass) is independent of reference frame. In other words, an object’s invariant mass has the same value no matter who is observing the object and no matter what their velocity is relative to the object. The invariant mass of a particle is defined as the total energy of the particle measured in the particle’s rest frame divided by the speed of light squared. More generally, the invariant mass is defined via the general relationship \(E^2 = (m_0 c^2)^2 + (pc)^2\) which leads to \(m_0 = \sqrt{\frac{E^2}{c^4} – \frac{p^2}{c^2}}\) Now for a photon, this is zero since [itex]E = pc[/itex]. In many aspect, this is all that we need to know. In physics, something that is invariant after some operation is very desirable.
    But photons have energy. By [itex]E = mc^2[/itex], doesn’t this mean that they have A mass? A photon can still have zero invariant mass ([itex]m_0[/itex]), and can still have energy. There’s nothing inconsistent here. All of the photon’s energy is in the term [itex]pc[/itex]. Some people would say that this is the photon’s “inertial mass”, since it is similar to the inertia that one feels when trying to stop a moving mass. This may or may not be useful to consider. However, it certainly should not be confused with the concept of the ordinary mass that most people are familiar with. There are, of course, other definitions of mass. Most commonly used terminology is something called “relativistic mass”. This mass is defined as \(m = \gamma m_0\) where \(\gamma = \frac{1}{\sqrt{1-\beta^2}}\\ \beta = \frac{v}{c}\) This “relativistic mass” is what most people attribute to the “gain in mass” of particle moving at relativistic speeds. However, one needs to be aware that in professional circles, such concept is very seldom used. One very seldom hears this when one attends a high energy physics seminar, for example, or read a particle collider experiment paper. This is because in citing a relativistic mass, one must also cite the speed of the particle with respect to what reference frame. This is cumbersome and unnecessary especially when the invariant mass would have been clearer (that’s why we love invariant anything).
     
  8. exchemist Valued Senior Member

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    Ah OK, so you are OK with applying E=mc²+pc to photons now, are you?

    And the connection with Planck's and de Broglie's relations?

    Turning to the concept of relativistic mass, which none of the above invokes, I've already pointed out, either here on the other thread, I forget which, that the concept of relativistic mass is simply the ratio of momentum to velocity. That's how it is defined and that all it is. It is not a question of "discovering" anything. Mass is always (I think?) measured indirectly, as the ratio of two quantities, conventionally force and acceleration, but momentum and velocity will do equally well. So there's nothing to "discover".

    Because you seem so hung up on this, I've had another quick look on the internet and come across the following link, which may describe what you are thinking of in treating the concept as suspect: http://sasuke.econ.hc.keio.ac.jp/~ken/physics-faq/mass.html

    It strikes me as a nice discussion of the history of the concept, its limitations, current usage and the care one needs to take not to use the unqualified term "mass" when relativistic mass is what is meant.

    But note that nowhere in this does it say the concept is wrong.
     
    Last edited: Jun 15, 2016
  9. exchemist Valued Senior Member

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  10. Layman Totally Internally Reflected Valued Senior Member

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    In this equation, a particle traveling the speed of light with a rest mass of zero would then have a relativistic mass of 0/0 in this equation...
     
  11. Layman Totally Internally Reflected Valued Senior Member

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    I looked into de Broglie's work, and he discovered how to find the relativistic mass of electrons. I would have no problem applying to electrons which had a nonzero rest mass.
     
  12. exchemist Valued Senior Member

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    This is starting to try my patience. Do you now accept that E=mc² +pc can be applied to photons, given the natural connection I have demonstrated between it and Planck's and de Broglie's relations?
     
  13. origin Heading towards oblivion Valued Senior Member

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    It seems this has discussion degenerated into an area that is simply semantics. Layman how would you feel if the term was not relativistic mass but effective mass? So while a photon has no mass it can have an effective mass based on it's momentum.
     
  14. Layman Totally Internally Reflected Valued Senior Member

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  15. Layman Totally Internally Reflected Valued Senior Member

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    I would also like to add that the equation λ=h/mv is the same equation you claim that is the relativistic mass of the photon. Just by dividing both sides by the wavelength and multiplying both sides by mass and changing v back to c. I don't see how removing mc^2 could result in the same equation for a photon as it does for an electron, in which it is assumed that it has mass.
     
  16. exchemist Valued Senior Member

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    It states no such thing. It merely states that, because particles of matter, which is what interested de Broglie in this exercise, cannot travel at c, he substituted v, the velocity of the particle of matter in question, instead.

    Obviously with mv in the denominator, it can only apply to QM entities with (rest) mass. But if you write p in the denominator it works for photons as well - obviously, since he got the whole idea by seeing what would happen if he treated particles of matter as the same as light. That in fact is the whole point behind de Broglie's insight: light and matter behave analogously, as far as the relationship between energy, momentum and wavelength are concerned.
     
  17. Layman Totally Internally Reflected Valued Senior Member

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    So you think that the de Broglie wavelength equation is equally valid on electrons and photons, since the velocity of a photon is the speed of light? It is the same exact equation. One derived by assuming that mc^2 equals zero and the other derived assuming that it was a value greater than zero.
     
  18. Layman Totally Internally Reflected Valued Senior Member

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    I have never really known the mass of the photon to be effective at doing anything...
     
  19. exchemist Valued Senior Member

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    De Broglie's relation, λ=h/p is true for both light and matter.

    In the case of matter, p =mv.

    In the case of light, p = E/c, as per Einstein's formula E²=(mc²)² +(pc)².

    This is what you will find in any 1st year undergraduate textbook or course notes. As the references I have already provided you with confirm.

    Now can we stop derailing poor Ultron's thread?

    P.S. You can easily check this for light as follows: -
    Substituting E/c for p, you get λ=hc/E. Rearranging, you get E=hc/λ.

    But wait, the standard relation between the wavelength, frequency and velocity of any wave is c/λ = ν.

    So you have E = hν. Voila! Planck's relation!
     
    Last edited: Jun 15, 2016
  20. origin Heading towards oblivion Valued Senior Member

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    Oops, I mistakenly thought you were serious and not just being obstinate. Carry on.
     
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  21. Layman Totally Internally Reflected Valued Senior Member

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    I think there is a much better way to derive the same equation that would make a lot more sense. If you say E = hc/λ and replace that with E in E = mc^2, then you get mc^2=hc/λ. Then there is no need to assume that particles and waves act the same way or that you can replace c with v in mc^2. If you solve mc^2 = hc/λ for λ, then you just get the same equation of λ = h/mc, but then since the mass of light is zero, the answer would then be undefined for a photon. That is most likely why De Broglie didn't make an equation for photons, like he did for electrons...
     
  22. Layman Totally Internally Reflected Valued Senior Member

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    I was being serious... I have never actually ever known the photons mass to ever be very effective at anything...
     
  23. exchemist Valued Senior Member

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    You have just read, a few minutes ago, in the link you yourself posted, that de Broglie got his insight by seeing if he could apply what had been discovered about light to matter. He was extrapolating from light to matter. He thus made an equation that worked identically for both. As I have now explained several times.

    For some reason of your own, which I cannot fathom, it seems important to you to pretend that de Broglie's relation cannot be applied to light. But that is cock: it can.
     

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