Do all objects really fall at the same velocity to the ground in vacuum?

Discussion in 'Physics & Math' started by pluto2, Sep 23, 2012.

  1. Farsight

    Messages:
    3,492
    Huh? Electrons don't travel at speed = c. Ah, I presume that was a typo rpenner.

    Hansda: mass is a measure of energy content. See Einstein's 1905 paper. A radiating body loses mass, and the emitted photon is massless. However there's a sliding scale to all this. If you slow down a photon to less than c in say a crystal, it then has an "effective mass". If you slowed it down further, this effective mass would increase. If you could contrive a way to make a photon speed up and slow down in free space, you'd have something similar to neutrino oscillation. The effective mass depends on the amount of energy present and how much less than c it's going. It's wrong to presume that the energy depends on the rest mass and how fast it's going, because we've never seen a neutrino at rest.
     
  2. Google AdSense Guest Advertisement



    to hide all adverts.
  3. OnlyMe Valued Senior Member

    Messages:
    3,914
    Rpenner, doesn't the data from the SN 1987a (super nova) at least suggest that, (in vacuum) neutrinos travel at c? Even a very small variation over the time and distance involved, should have been detectable.

    Or am I just making another error in scales? It seems I read something, likely around the time of the initial OPERA paper in late 2011, that suggests a velocity of c, in that case.
     
  4. Google AdSense Guest Advertisement



    to hide all adverts.
  5. RJBeery Natural Philosopher Valued Senior Member

    Messages:
    4,222
    Farsight, I don't think you're quite on track here. If you say mass is a measure of energy content then you immediately have a problem if you admit that emitted photons, of varying energy, are all massless. Also, I don't think Einstein would appreciate claiming that "effective mass" increases as we slow energy down. I believe a more proper characterization would be that it is the curvature of a photon's travel which exhibits mass; this could even allow for the idea of the electron being a "bosonic soliton"; literally a ball of light, orbiting through its own self-enforcing EM fields. (Oh boy, that should rile up the stodgy ones...

    Please Register or Log in to view the hidden image!

    )
     
  6. Google AdSense Guest Advertisement



    to hide all adverts.
  7. rpenner Fully Wired Valued Senior Member

    Messages:
    4,833
    Fixed in original.
    The rest is better summarized as \(E^2 = (mc^2)^2 + (p c)^2\) and \(\vec{v} = \frac{\vec{p} c^2}{E}\). Photons don't slow down in crystals -- light slows down in crystals due to momentum and energy being passed between photons which travel at the speed of light and electrons that don't.
    In 1987, 24 neutrino events in detectors over a 13 second time frame were associated with core events in a super nova 170,000 light years away with the visible light from the surface of the star peaking hours later.

    http://adsabs.harvard.edu/full/1989ARA&A..27..629A (see p. 661 for neutrino mass estimate, page 662 for limits on neutrino velocity to be between \((1-10^{-8})c\) and \(c\). That these are lower energy neutrinos than CERN-OPERA neutrinos, the limits on neutrino mass are much tighter than OPERA can establish.)

    A. Burrows, "Supernova neutrinos" Astrophysical Journal 334: 891-908 (1988)
    D.N. Spergel, J.N. Bahcall "Mass of the Electron Neutrino: Monte Carlo Studies of SN 1987A Observations" Physics Letters B 200: 366-372 (1988)
    L. Stodolsky. "The speed of light and the speed of neutrinos" Physics Letters B 201: 353-354 (1988)

    OPERA was (see the three previous drafts of the arXiv pre-print) announcing a speed experimentally distinguished as faster than light in their original results. They eventually found a loose timing cable and fixed their results accordingly.
     
  8. OnlyMe Valued Senior Member

    Messages:
    3,914
    That is in agreement with what I remember, noting that, that is as close the velocity of light as the velocity of light is known. What I remembered from earlier was that had the neutrino velocity varied from those figures either faster or slower, due to the distance they had traveled there would have been an exagerates change in the arrival times between the neutrinos and light.

    An interesting reference, I had not seen before.

    I only mentioned OPERA as passive recall placed the last I read about SN 1987a, at about that same timeframe.
     
  9. eram Sciengineer Valued Senior Member

    Messages:
    1,877
    actually, newton's law comes from Galileo's law of falling bodies.
     
  10. Farsight

    Messages:
    3,492
    That's what Einstein said, RJ. See Does the Inertia of a Body Depend on its Energy content? His actual words were "The mass of a body is a measure of its energy-content". He also said "If a body gives off the energy L in the form of radiation, its mass diminishes by L/c²". Photons are massless in that you can't ordinarily slow down a photon or speed it up, rest mass doesn't apply. The word mass is a bit of a problem here, because it's a bit ambiguous. For example, whilst a photon has no rest mass, it does have an active gravitational mass.

    I think he would actually. I confess I've never read Einstein talking about effective mass, but note that this isn't something I'm making up. Google on photon effective mass for information on the subject.

    I don't think curvature is quite the thing, RJ. If you trap light in a mirror-box it bounces back and forth inside and increases the mass of the system. It does this because in aggregate it's now not moving with respect to you. I think it's important to look at Compton scattering for this. Imagine you're the electron, and the photon bumps into you and makes you move. That's because it has its momentum. It's better to say energy-momentum, but nevermind, the thing is that you decelerate the photon in the vector sense by changing its direction, and it accelerates you. You altered its state of motion and it altered yours. Now imagine that the photon wasn't barrelling along at c, but instead was rattling back and forth between two mirrors at c. Make them gedanken mirrors that have no mass and don't get in the way. Now run at that photon and give it a bump. You still change its state of motion and it changes yours. The photon-mirror contraption will now move at some speed. You accelerated it and it decelerated you. Only now you talk of inertia rather than momentum.
     
  11. Farsight

    Messages:
    3,492
    Yes, sorry, my mistake. One analogy that is sometimes used is walking at 4mph on an empty pavement and then walking at 4mph through a crowd. You still walk at 4mph but overall your progress is less than 4mph. I'm not fond of E² = (mc²)² + (p c)² as it happens. Or perhaps I should say I'm not fond of is that nobody ever seems to talk about the flip-flop that occurs between the (mc²) and (p c) terms in pair production and annihilation. One for another day perhaps.
     
  12. hansda Valued Senior Member

    Messages:
    2,424
    As per the paper you linked.

    At such a high velocity of particle neutrino, does it follow Lorentz transformation of mass within its kinetic energy?
     
  13. rpenner Fully Wired Valued Senior Member

    Messages:
    4,833
    Using algebra, we can eliminate momentum from these equations as \(p^2 c^2 = E^2 - m^2 c^4 = c^{-2} v^2 E^2\) thus \(v^2 = c^2 \left( 1 - \frac{m^2 c^4}{E^2} \right)\) or when \( E \gt \gt mc^2\), \( \left| v \right| \approx \left( 1 - \frac{(m c^2)^2}{2 E^2} \right) c\).
    Thus given \(E = 17\, \textrm{GeV}\) and \(0 \lt m \lt 5 \, \textrm{eV} / c^2\) theory says the speed of the neutrinos at OPERA is between \(\left( 1 - \frac{25 \, \textrm{eV}^2}{5.78 \times 10^{20} \, \textrm{eV}^2} \right) c = ( 1 - 4.3\times 10^{-20} ) c\) and \(c\).

    Alternately, \(m^2 = \left( \frac{E}{c^2} \right)^2 \left( 1 - \frac{v^2}{c^2} \right)\) If \(v = (1-x)c\) and \( x \lt\lt 1\) then \(m \approx \sqrt{2 x} \frac{E}{c^2}\).
    So if \(E = 17 \, \textrm{GeV}\) and \(0 \lt x \lt 1.8 \times 10^{-6}\) then \( 0 < m < \sqrt{3.6 \times 10^{-6}} \times 17 \, \textrm{GeV} / c^2 \approx 32 \, \textrm{MeV}/c^2\) so the OPERA experiment wasn't precise enough to tell us something new about the speed or mass of neutrinos.


    Pair-production/annihilation: \(\gamma_1 \; + \; \gamma_2 \quad \longleftrightarrow \quad e^{+} \; + \; e^{-}\)

    In any inertial frame:
    \(\vec{p}_{1} + \vec{p}_{2} = \vec{p}_{e^{+}} + \vec{p}_{e^{-}} \\ E_{1} + E_{2} = E_{e^{+}} + E_{e^{-}} \\ E_{1} = \left| \vec{p}_{1} \right| c \\ E_{2} = \left| \vec{p}_{2} \right| c \\ E_{e^{+}}^2 = \vec{p}_{e^{+}}^2 c^2 + m_e^2 c^4 \\ E_{e^{-}}^2 = \vec{p}_{e^{-}}^2 c^2 + m_e^2 c^4\)

    But if \(E_{\Sigma} = E_{1} + E_{2} \) and \(\vec{p}_{\Sigma} = \vec{p}_{1} + \vec{p}_{2}\) there is a unique velocity associated with this system. \(\vec{v}_{\Sigma} = \frac{\vec{p}_{\Sigma} c^2}{E_{\Sigma}}\). When \(\vec{p}_{1}\) and \(\vec{p}_{2}\) are not pointed in the same direction, \( \left| \vec{v}_{\Sigma} \right| < c\), so we can Lorentz-transform to the center-of-momentum frame.

    In the center of momentum frame, \(E'_{1} = E'_{2} = E'_{e^{+}} = E'_{e^{-}} , \; \vec{p}'_{1} + \vec{p}'_{2} = \vec{p}'_{e^{+}} + \vec{p}'_{e^{-}} = 0\). Also, \(\vec{v}'_{\Sigma} = 0\).

    So simple conservation of energy, conservation of momentum and relativistic kinematics force these experimentally verified relationships to hold true. While you never bothered to explain what you "dislike" about it, the relationship is forced by the definition of photon as massless particles, and the definition of electrons as massive particles. The fuller standard model quantum field theory bit is much the same. Electromagnetism couples a massless photon field with a massive electron/positron (or another electromagnetically charged) field in a way that respects conservation of energy, conservation of momentum and relativistic kinematics.

    All evidence says yes.
     
  14. Tach Banned Banned

    Messages:
    5,265
    Nice post.
     
  15. Farsight

    Messages:
    3,492
    No problem with the algebra, rpenner. Can I say though that definition is inadequate here. A photon has no rest mass because you cannot make it go slower than c. An electron however does have rest mass because you can make it go faster or slower as you wish, using for example Compton scattering. It resists your efforts to change its speed.

    In a way a "photon field" couples with an "electron field" in Compton scattering. With respect to E² = (mc²)² + (pc)² and my unhappiness that nobody ever seems to talk about the flip-flop that occurs between the (mc²) and (p c) terms in pair production and annihilation, I can find no explanation of how a "photon field" interacts with another "photon field" to produce two "electron/positron fields", no explanation of how an "electron field" interacts with a "positron field" to produce (usually) two "photon fields", and no explanation of the difference between a "photon field" and an "electron field". They seem to be treated as two distinct things instead of two very common electromagnetic-field/wave phenomena. There seems to be no explanation of exactly how two electromagnetic field variations propagating at c are transformed into two standing electromagnetic fields and vice versa. It feels like a hole in the heart of physics. Also see two-photon physics on wikipedia, where we can read this:

    "From quantum electrodynamics it can be found that photons cannot couple directly to each other, since they carry no charge, but they can interact through higher-order processes. A photon can, within the bounds of the uncertainty principle, fluctuate into a charged fermion-antifermion pair, to either of which the other photon can couple."

    But photons definitely do interact, we have hard scientific evidence of that. What we do not actually observe is one photon fluctuating into a charged fermion-antifermion pair. This article is essentially saying pair production occurs because pair production has occurred. I find that most unsatisfactory.
     
  16. Farsight

    Messages:
    3,492
    I should add: not so much mass as charge. Maxwell didn't call it curl for nothing. Note though that charge is associated with mass. There are no massless charged particles. But what about the neutron? I hear you say. The neutron has its magnetic moment, see wiki:

    "The neutron magnetic moment is the magnetic moment of the neutron. It is of particular interest, as magnetic moments are created by the movement of electric charges. Since the neutron is a neutral particle, the magnetic moment is an indication of substructure..."

    There's charge in there, but there's no net charge.
     
  17. Tach Banned Banned

    Messages:
    5,265
    The neutron? What does the neutron have to do with the notion of mass-less? LOL.
     
  18. rpenner Fully Wired Valued Senior Member

    Messages:
    4,833
    The Higgs boson, Z boson, and all neutrinos are a massive particles with no electromagnetic charge.
    The photon and gluon are massless particles with no electromagnetic charge.
    The gluon is massless, yet has a chromodynamic charge.
     
  19. hansda Valued Senior Member

    Messages:
    2,424
    Is the speed of particle neutrino constant or variable?


    As per wiki speed of neutrino is same as speed of light. They give reference for http://arxiv.org/pdf/1203.3433v3.pdf .
     
  20. Guest254 Valued Senior Member

    Messages:
    1,056
    Now I always try to look for the best in people, Farsight, but I'm finding this one a little trying. I've told you in the past about this, but either you're willfully ignoring facts or you didn't understand them when they were presented to you. You cannot equate the differential operator of curl (or rot) with curling, or rotating. I know you're fairly open about your lack of technical ability, but that doesn't give you a right to be willfully ignorant of basic results that have been explained to you. Because I'm a true believer in educating people for the better, I have knocked up this little picture:

    Please Register or Log in to view the hidden image!


    I hope this illustrates the point. If you want to talk about mathematics (i.e. the language in which Maxwell wrote his theory of Eletromagnetism), then you must understand it first.
     
    Last edited: Oct 1, 2012
  21. rpenner Fully Wired Valued Senior Member

    Messages:
    4,833
    Variable depending on momentum.

    \(\vec{v} = \frac{\vec{p} c^2}{\sqrt{(m c^2)^2 + (\vec{p} c)^2}}\).


    That reference does not show same speed. It shows a speed where the precision of the experiment is insufficient to distinguish it from the speed of light.
    This is usually the case in neutrino experiments because most neutrino detections require the neutrino to have a momentum of over 100,000 times \(mc\) before the neutrino is detected, so \(\frac{c - \left| \vec{v} \right|}{c} < 1 - \frac{10^{5}}{\sqrt{1 + 10^{10}}} \approx 5 \times 10^{-11}\) which is significantly smaller than the precision of the experiment described.
     
    Last edited: Oct 1, 2012
  22. Farsight

    Messages:
    3,492
    The neutron is a massive particle with no electromagnetic charge too. The association is the other way round. If it's got charge, it's got mass.

    No problem with the photon.

    The gluon is a virtual particle. It's akin to the virtual photon which is described as the messenger particle of QED. See wikipedia which says:

    Gluons ( /ˈɡluːɒnz/; from English glue) are elementary particles that act as the exchange particles (or gauge bosons) for the strong force between quarks, analogous to the exchange of photons in the electromagnetic force between two charged particles..

    It's important to remember that there are no flashes of light flitting back and forth between the electron and the positron in the hydrogen atom. It isn't a photon exchange, it's said to be a virtual photon exchange. We've never actually seen a virtual photon, and in similar vein we've never actually seen a gluon.
     
  23. Farsight

    Messages:
    3,492
    Sadly it doesn't, Guest. You've got the wrong illustration I'm afraid. See the one here. Scroll down and you can see a picture of Maxwell and "For a fluid flow the non zero curl is the regions where a 'whirlpool' or a 'vortex' appears." I can only presume you're never read the original Maxwell. Here, take a look at On physical lines of force. Note the page heading is "the theory of molecular vortices". Sadly Maxwell got the particles and vortices back to front and died in 1879 before JJ Thomson discovered the electron in 1897.

    Please Register or Log in to view the hidden image!



    Image by Fibonnacci, see http://commons.wikimedia.org/wiki/File:Vector_field.svg
     

Share This Page