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Natural Science Forum / Physics / Relativity / May 2006Speed and mass
Speed and Mass Over in a different science discussion forum: http://www2b.abc.net.au/science/k2/stn/ http://www2b.abc.net.au/science/k2/stn/newposts/2309/topic2309840.shtm there is a long term disagreement over whether the increase of mass with speed is a real or virtual effect. I'd like to know if this disagreement is a real one, or whether it's just a different interpretation of the same mathematical equations. The two views are: A) Mass increases with speed and this increase is given by the equation m=m_0/sqrt(1-v^2/c^2). As an object gets faster its gravitational field gets stronger. Light has energy and therefore mass from E=mc^2 and two photons will gravitationally attract one another. B) Mass doesn't increase with speed but appears to do so. As an object gets faster its gravitational field appears to get stronger. The correct equation is E^2=(mc^2)+(pc)^2 so light does not have mass. I'll withhold judgement on whether two photons will gravitationally attract one another until I see the experimental evidence. > Speed and Mass > [quoted text clipped - 17 lines] > withhold judgement on whether two photons will gravitationally attract > one another until I see the experimental evidence. The answer actually is neither. In modern physics mass is considered to be the invariant rest mass. However consider for example a container of gas. As temperature rises the pressure increases and so does the average velocity of the particles. This will be reflected in a slight increase in mass of the gas ie in the mass of the 'stationary' system. In that sense mass increase is real. Similar considerations apply to light trapped between mirrors etc. Also see http://math.ucr.edu/home/baez/physics/Relativity/SR/mass.html Thanks Bill > Speed and Mass > [quoted text clipped - 17 lines] > withhold judgement on whether two photons will gravitationally attract > one another until I see the experimental evidence. I forgot to add in GR gravity is space-time curvature which means gravity is independent of a particles velocity etc ie the EFE's hold regardless of the coordinates you use. Of course from the EEP we can always find a coordinate system where gravitational forces does not exist locally - just as we can find one where it is any value we like. However gravity being space-time curvature is the same regardless of velocity or coordinate system. That is absolutely fundamental to GR. Thanks Bill > Over in a different science discussion forum: > http://www2b.abc.net.au/science/k2/stn/ > http://www2b.abc.net.au/science/k2/stn/newposts/2309/topic2309840.shtm > there is a long term disagreement over whether the increase of mass > with speed is a real or virtual effect. This argument is primarily a difference in the usage of words. > I'd like to know if this > disagreement is a real one, or whether it's just a different > interpretation of the same mathematical equations. The two views are: > A) Mass increases with speed and this increase is given by the equation > m=m_0/sqrt(1-v^2/c^2). Most physicists today, when they say "mass" without qualifier, mean the invariant mass of an object. So we say the mass of an electron is 511 keV/c^2, and do not need to specify any speed for which it is valid, because this is invariant. This choice for the use of the word "mass" is primarily motivated by connection to its original meaning of "amount of stuff", which _clearly_ must be invariant for a given object (looking at an object from a different reference frame cannot possibly change the object itself). For a massive object this is the same as its rest mass, which you notated as m_0 above (most physicists notate it simply as m). Your m above is normally called "relativistic mass"; it is really an anachronism, and it does not appear explicitly in any modern theory of physics; the invariant mass appears in many places in every modern theory of physics. > As an object gets faster its gravitational field > gets stronger. This is plain and simply not true. BUT -- in GR the source of gravitation is the energy-momentum tensor, not just mass, and relative to a given set of inertial coordinates a moving object has quite different e-m tensor components than an object at rest. There is a _qualitative_ difference in their gravitational fields that cannot be captured by the simple comparison "stronger". What does increase with velocity is an object's inertia, and it increases faster than the classical proportionality. > Light has energy and therefore mass from E=mc^2 and two > photons will gravitationally attract one another. Again, using these words in the standard way physicists use them, light does not have any mass. It does, of course, have both energy and momentum, and it satisfies the relativistic equation E^2 = p^2 + m^2, where E is the energy of an object or light pulse, p is its 3-momentum, and m is its mass (invariant mass); c=1. E=mc^2 is a famous equation of limited applicability, and it does not apply to light. > B) Mass doesn't increase with speed but appears to do so. This depends on what you mean by "appears". > As an object > gets faster its gravitational field appears to get stronger. See above for the error here. > The > correct equation is E^2=(mc^2)+(pc)^2 so light does not have mass. TYPO: Insert ^2 here -----------^ Yes. > I'll > withhold judgement on whether two photons will gravitationally attract > one another until I see the experimental evidence. In GR, two light pulses do gravitationally attract one another; remarkably, however, two infinite and continuous light beams do not attract each other if they are parallel [#]. [#] Technical caveats omitted.... It is highly unlikely that the gravitational interaction between light pulses will ever be measured, much less for individual photons. Tom Roberts Thanks for helping to clear that up Bill and Tom. "EFE" = Einstein's field equations and "EEP" = Einstein's equivalence principle ? > "relativistic mass"; it is really an anachronism OK, got that. > There is a _qualitative_ difference in their gravitational fields that cannot be captured by the simple comparison "stronger". Would "frame dragging" be an example of this? E^2=(mc^2)^2+(pc)^2, Yes, sorry for the typo. > In GR, two light pulses do gravitationally attract one another; remarkably, however, two infinite and continuous light beams do not attract each other if they are parallel ... Technical caveats omitted That's interesting! Please direct me to a technical reference for this. > It is highly unlikely that the gravitational interaction between light pulses will ever be measured, much less for individual photons. My original thought was that this may (or may not) have had a measurable influence on the period of our universe's history that was still light-dominated, before the universe became dominated by matter, and that that may have affected the early evolution of the universe. Any comments? >> In GR, two light pulses do gravitationally attract one another; >> remarkably, however, two infinite and continuous light beams do not >> attract each other if they are parallel ... Technical caveats omitted > > That's interesting! Please direct me to a technical reference for this. I'd never thought about that before, but I imagine it's simply because the light beams are causally disconnected. If you take two parallel light beams on a Minkowski background, something like x(t) = x'(t) = ct y(t) = 0 y'(t) = 1m then it's not hard to see that there's no worldline that intersects both. So I suppose the gravitational influence can't get between them either. > My original thought was that this may (or may not) have had a > measurable influence on the period of our universe's history that was > still light-dominated, before the universe became dominated by matter, > and that that may have affected the early evolution of the universe. It did, and big bang cosmological models take this into account. But there's no alternative version of special relativity with a different mass-speed relation. That debate is just over terminology. -- Ben >>> In GR, two light pulses do gravitationally attract one another; >>> remarkably, however, two infinite and continuous light beams do not [quoted text clipped - 4 lines] > I'd never thought about that before, but I imagine it's simply because > the light beams are causally disconnected. No. I specified continuous beams, and they definitely are "causally connected" (in that there exist timelike and null geodesics that connect regions of the two light beams). The underlying reason is that the energy-momentum tensor for electromagnetism is traceless. Tom Roberts > Thanks for helping to clear that up Bill and Tom. > > "EFE" = Einstein's field equations and "EEP" = Einstein's equivalence > principle ? Yep. >> "relativistic mass"; it is really an anachronism > [quoted text clipped - 4 lines] > > Would "frame dragging" be an example of this? From how you worded the question I would say no. > E^2=(mc^2)^2+(pc)^2, > Yes, sorry for the typo. [quoted text clipped - 4 lines] > > That's interesting! Please direct me to a technical reference for this. Zee - Quantum Field Theory in a Nutshell - page 427 - The Gravity of Light. Thanks Bill >> It is highly unlikely that the gravitational interaction between light > pulses will ever be measured, much less for individual photons. [quoted text clipped - 4 lines] > and that that may have affected the early evolution of the universe. > Any comments? > Most physicists today, when they say "mass" without qualifier, mean the > invariant mass of an object. So we say the mass of an electron is 511 [quoted text clipped - 19 lines] > where E is the energy of an object or light pulse, p is its 3-momentum, > and m is its mass (invariant mass); c=1. The age-old debate of how to interpret mass is subject to how you model the physical world around you with emphasis on observations in which an experimental physics like yourself should have no objections. If I model mass as invariant, I have to fill in my equations describing how this mass interacts with its suroundings with extra terms such as (1 / sqrt(v^2 / c^2)). However, if I model mass as merely an observed quantity dependent on who and where the observer is, the other argument for mass becomes very clear and makes more sense. > E=mc^2 is a famous equation of limited applicability, and it does not > apply to light. You are so narrow minded. This equation makes a lot of sense if you model the mass as an observed quantity dependent on the observer. The question is which interpretation makes more sense. >From the erroneous concept of GR, I can write down the following following equation in accordance with the Schwarzschild metric. E = m c^2 sqrt(1 - 2 U) / sqrt(1 - B^2) Where ** E = observed energy ** m = rest mass at infinite distance ** U = G M / c^2 / r ** B = v / c To make things very, very simple, I can claim the observed mass under the curvature of spacetime as m sqrt(1 - 2 U) / sqrt(1 - B^2) The above equation indicates the rest mass being a function of the curvature of spacetime. > In GR, two light pulses do gravitationally attract one another; > remarkably, however, two infinite and continuous light beams do not [quoted text clipped - 4 lines] > It is highly unlikely that the gravitational interaction between light > pulses will ever be measured, much less for individual photons. And yes we will never know if light pulses do gravitationally attract each other. In the meantime, as we have demonstrated, there are many ways to interpret GR. Since there is always a better solution, GR can never be wrong. Just choose a better interpretation to it. The similarity is when declaring Voodoo being a state religion. It then must be right. Excuse me, being valid. Any interpretation must be correct under the concept of Voodooism. >> Most physicists today, when they say "mass" without qualifier, mean the >> invariant mass of an object. > The age-old debate of how to interpret mass is subject to how you model > the physical world around you Yes. > If I model mass as invariant, I have to fill in my equations describing > how this mass interacts with its suroundings with extra terms such as > (1 / sqrt(v^2 / c^2)). However, if I model mass as merely an observed > quantity dependent on who and where the observer is, the other argument > for mass becomes very clear and makes more sense. Obviously you have never done this. As I said before: >> Your m >> above is normally called "relativistic mass"; it is really an >> anachronism, and it does not appear explicitly in any modern theory >> of physics; the invariant mass appears in many places in every modern >> theory of physics. You are wrong -- invariant mass makes the equations of theoretical physics simpler. At base this is so because the equations themselves must be Lorentz invariant (locally). Tom Roberts > > Over in a different science discussion forum: > > http://www2b.abc.net.au/science/k2/stn/ [quoted text clipped - 18 lines] > an object from a different reference frame cannot possibly change the > object itself). And even this motivating meaning is soon found to be outmoded, because the invariant mass of a *system* of particles is not (surprise!) the sum of the invariant masses of the particles in the system. That is, the invariant mass of a system does not necessarily represent the amount of "stuff" present, which we intuit to be additive. The invariant mass of two colliding electrons, for example, is frequently seen to be several thousand times larger than 2 x 511 keV/c^2. The anachronism "relativistic mass" to which the OP refers is also motivated by a classical meaning of mass: the m that appears in F=ma. To account for the fact that "a" drops lower than proportion with F would indicate, a rise in "m" was suggested, but that is purely based on trying to make the old physics connect with the new. It's in fact interesting, and many physicists have worried about this over the last century, that there is no persistent concept for what mass *is* anymore, other than an operational definition by virtue of invariance. > For a massive object this is the same as its rest mass, which you > notated as m_0 above (most physicists notate it simply as m). Your m > above is normally called "relativistic mass"; it is really an > anachronism, and it does not appear explicitly in any modern theory of > physics; the invariant mass appears in many places in every modern > theory of physics. > Speed and Mass > [quoted text clipped - 17 lines] > withhold judgement on whether two photons will gravitationally attract > one another until I see the experimental evidence. As it turns out, mass might not even be real, see, http://www.calphysics.org/mass.html For a photon, E = f.h / c^0 p = f.h / c^1 For an electron, f = gamma.fC E = f.h / c^0 p = beta.f.h / c^1 m = f.h / c^2 where, f is the frequency, h is Planck's constant, c is the speed of light in a vacuum, E is the energy, p is the momentum, m is the inertia, gamma is 1/sqrt(1-v^2/c^2), fC is the Compton frequency, beta is v/c, v is the velocity of the electron. So it is no longer a question of whether the mass increases, but whether the frequency is shifted, which it certainly is. The other guys explained that the source of gravitation is the energy-momentum tensor, but as you can see above, energy, momentum and mass are all dependent upon frequency, which is the real source of gravitation. > As it turns out, mass might not even be real, see, http://www.calphysics.org/... >From that link. "Tentative outline of a research program on the nature of mass originating in the quantum vacuum", "However an accelerating observer will experience an asymmetry. Acceleration through the quantum vacuum results in the appearance of an electromagnetic effect -- a cousin of the well-known Unruh-Davies radiation -- whose strength is proportional to acceleration". Yes, I've heard of this. Last I heard, though, was that different research papers on the topic contradict one another. The result depends on how the coordinate transformation relating to the acceleration is done. I'm withholding judgement until I hear more. |
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