I liked your quote of professor David Morin, and see his point, but probably will continue to speak of "relativistic and rest mass." I was glad to note that he agrees that the "tranverse mass" measured by old Newtonian concept F = ma and in my cyclotron example F = EBV (charge, magnetic field, velocity product) was OK. Recall, in another thread where I think we were exchanging ideas about what mass is (it was you, was it not?) that I had V essentially c and increased the B field to keep the path of the particle gaining mass/energy in the cyclotron of constant radius. Thus we have essentailly constant transverse "a" in F = ma = EBV =~EBc (constant speed around constant radius circle implies this constant radial acceleration.) and only B and m to change, essentially linearly together. That is, I was showing emperically how one could measure the "relativistic increase in mass" (via the magnitude of B required to keep the radius constant.) Thanks to your posted quote, I now understand that relativistic mass {at least when "mass" is defined by its inertia or resistence to acceleration and not by the associated energy m = E/c^2} does have non-scalar characteristics, but I continue to think it is usefull, to speak of "rest mass", and "relativistic mass" (even though two different interpretations of the later are possible and in common use - the total transverse mass as measured above by B and sometimes only the increase in the total mass over the rest mass.) The counter agrument to David's well taken position is that it is nice to have a mass that is unique for each particle (the rest mass, even if it is usually expressed in energy units Please Register or Log in to view the hidden image! I.e. the rest mass of an electron is 0.511Mev) If I were to adopt David's view, I could not say the mass of an electon is 0.511Mev. The important thing is that we can communicate even if we express the same ideas in different ways. I don't think either "language" is correct and the other is wrong. (In passing, I will note that I still think it OK to at least describe the bending of light ray passing near the sun as either the sun's gravity acting on the the relativistic mass of the photon, or in GR terms as curved space time or perhaps even in flat space time with some curved coordinates, as you and Pete have been discussing in another thread, (above my full comprehension). In this post of yours, I am have difficulty understanding something more simple: - What you mean by: Yes, Mass is independent of velocity. Are you also ignoring David's recomendation and stating (less clearly than I would) that rest mass is independent of velocity? or are you saying something I just don't understand?
Interest has as much to do with it as hatred of sources that just make claim with no justification. And math is not a problem for me, I've taken plenty of advanced math courses.
I am just saying, when I say "mass" I mean "rest mass". I will never refer to "relativistic mass" as "mass" in any sense of the word "mass". When I refer to "relativistic mass" as you think of it, I call it "kinetic energy" as is the case with most modern physicists. Please Register or Log in to view the hidden image!
Ok - that is what I thought, but ask that you not be too hard on us old relicks that still speak an archaic version of the physics language.
Hi everyone, I'm new here. My friend PhysMachine told me about the community here so I thought I would come a see what's up. Here goes ... physicist, you're wrong about the black hole thing aer, you're right you mentioned some skill with advanced math so let me recommend Sean Carroll's lecture notes online at http://pancake.uchicago.edu/~carroll/notes/ probably you've already seen this, if so sorry. it is pretty mathematical. see page 29 and 30 for examples of stress energy tensors, though he lacks the formal definition. the black hole discussion later is also excellent the book by A. Zee, QFT in a Nutshell (this book is a bit whimsical so be careful) has in section I.10 a clear definition of the stress energy tensor, that definition is as follows: in general your write down an action S which is a GR scalar, and the functional derivative of the action with respect to the metric is (proportional to) the stress energy tensor. this works best with field theories because with particles the stress energy tensor is singular i.e. particle energy density is a delta function for a particle the action is proportional to the proper time elapsed along the particle's world line. using this you can easily get the stress energy tensor for one particle, but issues arise when trying to treat more than one particle since there is no longer a single global proper time
Welcome. In physicist's defense, let me note that he did not say a very energetic proton could be a black hole, only the it would resemble one. I am suffering under the belief that any very energetic small object would have intense gravity very near it. - I.e. resemble a micro black hole but not being a singularity, not perfectly, but perhaps the field gradient might "swallow" only one of a virtrtual particle pair like a black hole and then make it less massive (a little "evaporative cooling" but not with the terminal flash of a real black hole). (And of course there are some reptuable physicists who believe neither is a black hole a singularity.) I will now let physicist defend himself, but as he may not now be reading I want to comment and solicite comments. If some one starts a black hole thread, I have more questions about them exploring the idea that their may be an upper limit to their mass.
indeed he does not say that a black hole will form, and so he's not too wrong. also, his other comments about the sources of gravity are essentially correct and clear. i think he (she?) is only slightly confused. however, a fast moving particle will never, as I understand things, look like a black hole. let us analyze the situation. the proton's mass is about 10 MeV, now this is so small a mass that it will not produce any detectable curvature. curvature, or the lack of it, is the signature of gravity in GR. in the rest frame of the proton then all we see is Minkowski space, no curvature. the world lines of other test particles will be straight, no trace of black holes or event horizons etc. other interesting effects would certainly be present i.e. think of the radiation that would be emitted when you accelerated the proton (as long as you didn't take infinitely long to do it!), but nothing connected with black holes per se
Does it matter whether the motion is inertial or not? If a particle was moving fast enough on a circular track or any other closed loop, what would happen? Assume an uncharged massive particle. Could it get enough energy density to form an event horizon? Be gentle - I'm learning. Please Register or Log in to view the hidden image!
It seems I was bit confused there, though I was aware that an actual black hole would not form. Since the spacetime is completely flat in the proton's rest frame there can't be any effects from intense curvature (black hole effects) or so it would seem. However, my answer to your original question is correct. Thanks for the correction, Aer.
How about we try to answer the question, Will any of this kinetic energy contribute to the gravitational potential? My intuition would say no. But this leads me to have to accept that thermal energy does not contribute to a gravitational potential either. This is why I started this thread - I want to know exactly what energies do contribute to a gravitational field and why. The why part requires rigorous mathematics - I will not accept flat out "claims". As far as I know, most people claim that thermal energy becomes part of the "rest mass" of an object - but I object to this until I see any proof because it leads to contridictions as I think I've alluded to.
Pete, the simple answer to your question is that yes it does matter rather the motion is accelerated or not. Previously, in order to conclude that the motion of the uncharged small mass could not generate a black hole simply by going very fast in one frame, we considered the problem in the rest frame which was an inertial frame. Now the rest frame is accelerated and we must be more cautious. I am not saying SR does not apply, indeed the standard results of SR are used constantly in particle accelerators to predict very accurately the motion of particles undergoing fantastic accelerations. The message here is that when spacetime is flat, SR is sufficient. Let us now analyze the problem from the rest frame of the mass, an accelerated frame. SR tells us (for details see Chap. 6 of Gravitation by Misner, Wheeler, and Thorne, sorry I don't have an online ref for this) that we can use accelerated reference frames so long as we keep them small. The condition can be expressed mathematically as L << c^2/a where L is the size of my rigid network of rods and a is the acceleration of the frame I am in relative to some inertial frame. What does using this accelerated frame cost us? Three things, first fractional effects of order gL are present. Second, Coriolis type forces as found in Newtonian classical mechanics are present. Third, inertial forces also as found in Newtonian classical mechanics are present. The inertial forces are, according to Einstein and the equivalence principle, equivalent to unifrom gravitational fields which produce no curvature. No balck holes from them. The coriolis forces can be removed by attaching gyroscopes to your frame preventing it from rotating. The frame now moves in circle, but does not spin. No black holes here either. The particle is still at rest. We thus conclude no black hole so long as the fractional effects of order gL can be neglected. Now, where can we go from here? Is there anything gravitational about an oscillating mass? Yes, but as before the gravitational effect is very weak. What can happen is the emission of gravitational radiation. For gravitational waves see Chap. 35 on in Gravitation by MWT. Since a mass moving in a circle has a quadrupole moment it can emit gravitational radiation (note that in GR the quadrupole is the first moment that can generate radiation, there is no dipole or monopole radiation). These waves will be extremely weak because the mass of the particle is so small and frequency is low except in extreme situations. In principle this effect is essentially what Taylor and Hulse observed in their binary system (you simply put another mass on the opposite side of the circle), and the observed decay of the orbit due to energy lost by gravitational radiation agrees beautifully with the GR prediction. To summarize, no black hole, but weak gravitational waves can arise. In fact gravitational waves can arise from any accelerated mass in complete analogy with EM waves provided the system has a non-vanishing quadrupole moment. I emphasize finally that these waves are far to weak to detect for any reasonable mass moving at any accelerations we can achieve. Interesting experimental possibilities due arise from matter falling into black holes. Hope I got all that out without any errors. Hopefully this helps some Pete. I highly recommend Gravitation if you really want to understand GR and can handle the math.
I wouldn't agree on some physical limit on mass but I would agree on some physical limit on gravity produced by mass in that I expect that as objects become as massive as Black Holes the gravity to mass ratio begins to change and therein a limit of gravity (hence no singularities) is the reality. This of course is conjecture based on my own views. Please Register or Log in to view the hidden image! PS: Also Welcome to Physics Monkey.
I doubt that kinetic energy would contribute to gravitional potential. After alpha/beta decay the loss in mass of the remaining nucleus is not equivalent to the emitted particles mass+ kinetic energy. The 'missing energy' is still inside the nucleus and exites the nucleus but emitted as gamma radiation subsequently. It does not add to the mass of the nucleus.
Good idea. That is a point of puzzlement for me as well. I just hope that the community is up to it! What sort of contradictions? Something like an event horizon forming in one frame but not another? Or some real force being applied (a tidal force) in one frame but not another? Or something more devious?
It is a minor point (I can't fully participate at the subtile levels that are being approached here) but I think the accleration in modern accelerators may befar from "fanatastic" when the mass is twice or more times the rest mass. They were probably more "fantastic" in Lawrence's original little cyclotron than in the kilometer diameter machines that achieve orders of magnitude more energy. (Just guessing) After all, the acceleration is essentially zero in the tangential direction and the radial acceleration arround the large circle is lowered by the greatness of the circle with velocity limited by c. As I said: it is a minor point, but we should keep in mind that not everything about high energy physics is "fantastic." If someone wants to do the numbers, it might be interesting to compare the acceleration in an accelerator to that of a high speed bullet when it is one tenth of the way down the gun barrel. Please Register or Log in to view the hidden image!
Billy T, Haha, obviously 'fantastic' depends on what you're comparing to (everything's weak compared to the tidal forces deep in black hole!), but let me try to convince you. Here are some numbers: For the LHC coming online in 2007 (hopefully Please Register or Log in to view the hidden image! ) the beam of protons travels in a tube of circumference 27 km. This gives a radius r of roughly 4.3 km. Now, these protons will be traveling at essentially the speed of light c so the typical accelerations they experience will be of the order v^2 / r = c^2 / r which is roughly 10^13 m/sec^2. This acceleration is roughly twelve orders of magnitude greater than the acceleration due to gravity here on Earth. By contrast, the average acceleration suffered by a bullet in a barrel is typically about 10^6 m/sec^2 (the math is easy to do, here is a ref with other refs: http://hypertextbook.com/facts/2003/MichaelTse.shtml ). You can easily see that there is about 7 orders of magnitude difference between the two. I think that is fairly fantastic, but that's just a matter of opinion Please Register or Log in to view the hidden image! . However, if this isn't fantastic enough for you, then consider the accelerations suffered by a neutron in a nucleus. The neutron is moving fairly close (around a tenth or twentieth maybe) to the speed of light at a radius of about a fermi, put in the numbers again and you get an acceleration of the order of 10^31 cm/sec^2 or 10^28 times the acceleration due to gravity on Earth (10^3 cm/sec^2). This, I think, is a pretty fantastic acceleration, and SR is routinely used in nuclear physics. We can go even higher by considering the accelerations particles undergo in actual high energy scattering events.
Thanks. I agree, fantastic! Let my Poor Guess be a lesson to all who are too lazy to do the numbers. Thanks again, sorry to have troubled you.
I wish my imagination drifted that far.. Anyway, the link is pretty trival really. Thermal energy is nothing but the kinetic energy of atoms. If kinetic energy in general does not contribute to the gravitational field, then neither should thermal energy. It's just that simple.
No, it's not that simple. You can't get rid of thermal energy by going to another reference frame. A brick has the same gravitational effect, whether it is travelling at 100 km/hr or is stationary, because you can eliminate its kinetic energy by going to its rest frame. But a hot brick at 100 degrees Celcius has more energy than a cold brick at 0 degrees. The atoms are jiggling around inside the brick faster. And there's no frame you can go to which will eliminate that "thermal" energy. In relativistic terms, the thermal energy contributes to the energy in the rest frame of the brick, and therefore contributes to the brick's rest mass. The gravitational "field" of the brick depends on the rest mass, and therefore is greater when the brick is hotter.
