Good one, I like it..... both the following formulas are dishonest, so says OnlyMe.. Please Register or Log in to view the hidden image! Please Register or Log in to view the hidden image! Only Honest formula in Physics is.... Relativistic Mass = Momentum. Agains says OnlyMe only.
What is this nonsense ?? This is not my interpretation, something funny in your head. What do you think will be the 'gamma' for 0.99c, it will be just numeral 7.08...yes 7.08 only. Now multiply this 7.08 to proton's mass and see if it can do anything to you or not. I ignored your previous reference to these thinking that you will come around, but you are continuing with your funny understanding of the subject.... Stop...Think...Educate yourself.
Are you serious? Unlikely any such measurement has been attempted and for what should be obvious reasons. But we know from e.g. particle accelerator experiments that inertial mass of particles rises with KE as per the usual SR formula gamma factor (longitudinal vs transverse accelerations are a separate issue). The GR equivalence principle then demands the same for gravitational mass. The more complicated general expression given by e.g. Lev Okun in an article earlier linked to in no way undermines that. Throwing this back - you evidently are seriously suggesting one should doubt application to the case of KE of gas molecules! Please just confirm that. And that you doubt application of equivalence principle. And? Newtonian F = mg = mMG/r^2 can of course have any combination of M or r. Such is irrelevant here. Absurd examples like '90% of infinite' are without proper meaning and anywise no argument against what I have said already. You and a number of other posters have flatly and wrongly and repeatedly claimed gravitational influence of matter is a function of it's rest mass only. Such basic error needs correcting. So I 'dropped in' following an enforced 2+ weeks break while PC was off for repairs, and happened on this thread. I have done wrong somehow? [Edit: for the worshippers of Authority Figures - chew on this: http://arxiv.org/abs/gr-qc/9909014v1]
Rajesh, why can you not conduct a discussion without turning it into a fight and gloating when you think you have scored a point? Science is meant to be about discovery and models of the world, not egos, whether yours or anyone else's.
Q-reeus, the 90% of infinity was obviously an exaggeration, intended to make a point!.. and even then it was intended in the context of the OP's question and the definition of just what Relativistic Mass, is or was.., and Rajesh's claims... The initial point of discussion in this and your earlier post, is one that is debatable and potentially a good discussion, but I believe that though there is some crossover, between the main points you raise and the current thread, it would be best if it were given its own thread. A quote of the OP follows the quote of your post below. Little Bang's question was answered in the negative several times with Rajesh the only descenter. The only massive objects we can refer to are protons and a few heavy nuclei. None of which even when accelerated to near c, in a lab, produce a detectable gravitational field. This was the question of the OP. And the context that all of my responses to Rajesh's unsupported claims that his understanding of relativistic mass, is settled science (in my words not his). There is a related discussion of the issue you raised, but to intermingle the two would not be constructive... I my opinion.
It gives the same result as the relativistic energy equation for total energy. Sloppy physics. For the relativistic energy equation derived from the metric and the principle of extremal aging mass is an invariant while momentum and energy are constants of motion over the geodesic path. Beautiful physics. In GR the momentum energy tensor defines the components associated with local spacetime curvature which is gravity. Stuff like energy, momentum, angular momentum, pressure, mass, torsion, etc..... All contribute to the local spacetime curvature. One of the more egregious interpretations of the relativistic mass equation is that it's the relativistic energy equation. I think it can be a distraction from learning the actual physics. In the link is a revealing derivation for the relativistic energy equation. As you said it's momentum which increases [without limit] as an object speed increases. The link is easy to read. The way the derivation is laid out makes it possible to understand without calculus. LOL. Just remembering the first time I went over this. Choose Chapter 1 Speeding. http://www.eftaylor.com/download.html They start with deriving the SR metric, define the principle of extremal aging [principle of least action] and use both to derive the relativistic energy equation.
This is blatantly faulse and an inflammatory misrepresentation of what I have been saying! There is nothing wrong with the above. Where p is momentum = rest mass times velocity (classically), and the Lorentz transformation modifies the total momentum under relativistic conditions. Notice that mass in the above is always rest mass! The above is misleading and is where I have asked several times now for a reference or proof that your conclusion is an accurate example of our modern understanding of mass and momentum! And yes Rajesh, historically the term relativistic mass, within the context of special relativity served a purpose. A purpose which has become misleading and inaccurate when discussing gravitation, in a lay oriented environment where not all parties understand the historical context and potential for misunderstanding. The point is that relativistic mass, even historically.., is not as you seem to have implied, just an object's rest mass modified by gamma (a Lorentz transformation).., which means nothing at all until you consider some velocity! The transform is applied to the product of mass times velocity, to arrive at the momentum of a mass, with a relativistic velocity....., relative to an observer.... You do understand that the v in the formula is relative to an observer and will be different, for different observers. Such that were, relativistic mass (which should be thought of as the momentum of a mass with a relativistic velocity) gravitationally significant, it would mean that the gravitational field of any moving object would be different for different observers... While velocity relative to any gravitational field will impact interact with that field, it will not change the field! And Other than as affected by time of light propagation delays, any velocity of a mass will not change its gravitational field.
Agreed but as yet our friend lacks any moral or intestinal fortitude to admit he has been in gross error. And of course the following statement has hit the nail on the head.
Both of you should put that knucklehead on ignore. All he's doing is trolling both of you. He's the main problem between both of you. If he disappears maybe the disagreement over how to respond to his trolling will disappear. Rajesh puts being right before intellectual honesty so he's a bad candidate for intellectual discourse. This forum isn't designed to resolve intellectual honesty digressions. Hence the ignore function.
It's status quo for the intellectually dishonest trolls. We could run an experiment and all put Rajesh on ignore. After an appropriate time passage we could take him off ignore and do an analysis of Rajesh posts 'over' the ignore spacetime event.
Suppose you are right. It's such a waste, though. I was very intrigued by the thing about momentum of photons in a medium which he indirectly put me onto.
See that's a good argument for not using the ignore button. What is the idea about the momentum of the photon passing through a medium? I'm intrigued.
No. It is the energy divided by c^2. No. The source of gravity is the energy-momentum tensor, and the energy in this tensor is relativistic mass (with factor c^2).
http://scitation.aip.org/content/aapt/journal/tpt/47/6/10.1119/1.3204111 Einstein Never Approved of Relativistic Mass: During much of the 20th century it was widely believed that one of the significant insights of special relativity was “relativistic mass.” Today there are two schools on that issue: the traditional view that embraces speed-dependent “relativistic mass,” and the more modern position that rejects it, maintaining that there is only one mass and it's speed-independent. This paper explores the history of “relativistic mass,” emphasizing Einstein's public role and private thoughts. We show how the concept of speed-dependent mass mistakenly evolved out of a tangle of ideas despite Einstein's prescient reluctance. Along the way there will be previously unrevealed surprises (e.g., Einstein never derived the expression for “relativistic mass,” and privately disapproved of it).
http://profmattstrassler.com/2013/07/11/mass-ive-source-of-confusion/ Conversations About Science with Theoretical Physicist Matt Strassler extract: Here are the two possible interpretations of this equation. Modern particle physicists (including me) only use the first interpretation. The purpose of this post is to alert you to this fact, and to point you to an article where I explain more carefully why we do it this way. Interpretation 1.E = mc² is true only for an object that isn’t moving. For an object that is moving, E is greater than mc². Energy and mass are not at all the same thing; an object’s energy can change when its motion changes, but its mass never changes. This notion of mass is sometimes called “rest mass” (since it’s related to the energy stored in the object when it is “at rest”) or “invariant mass” (since it doesn’t change when it is moving.) Interpretation 2.E = mc² is always true, for both stationary and moving objects. This can be viewed as saying energy and mass are essentially the same thing. [Recall that in interpretation 1, they are not at all the same thing.] Since the energy of a moving object is larger than when it is stationary, that means, similarly, that its mass is larger when it is moving than when it is stationary. This notion of mass is sometimes called “relativistic mass”, in honor of Einstein’s revolutionary notions of relativity. To sum up — relativistic mass depends on how fast an object is moving, butinvariant mass/rest mass is the same whether an object is moving or not; you can see this in the figure below. Which one of these should we call “mass”, with no modifier? Unfortunately, that’s up to the user. Please Register or Log in to view the hidden image! The two interpretations of what “mass” means. The first (in green) is that mass is something that does not change with speed — often called “invariant mass” or “rest mass”, it is used by particle physicists. The other, “relativistic mass”, is just energy divided by c-squared, and grows with speed. Note the two are almost identical at small velocities, and so are usually equal in daily life. Fortunately, in daily life, these two concepts are almost identical, because most objects we observe in daily life much more slowly than c, in which case their rest mass and relativistic mass are nearly identical, as you can see in the figure. But particle physicists and nuclear physicists and astronomers, among others, often have to be more precise. And when you’re reading an article or book about particles or nuclei or astronomy in which “mass” plays an important role, you will often need to know which of these two interpretations is being used by the author! Einstein, in his early years, contributed to the second interpretation, perhaps inadvertently. But later he made clear statements (most notably in a letter to Lincoln Barnett, which I can’t find in full on the web, but which is quoted widely) in favor of the first interpretation. Not that Einstein’s opinion particularly matters; in science we respect our elders, but we do not slavishly follow them, the way people used to follow Aristotle. We come to a conclusion based on what we know, and often we know things that weren’t known to the previous generations. So why do particle physicists today choose interpretation 1? I’ll give you a couple of quick hints as to why, and if you want to learn more, you can read my article on the matter.
http://profmattstrassler.com/articl...o-definitions-of-mass-and-why-i-use-only-one/ The Two Definitions of “Mass”, And Why I Use Only One Matt Strassler [July 10, 2013]
This much is true. However you seem to have lost sight of just where the components, nicely described by Bruce, ... that contribute to that energy-momentum tensor, come from..., most easily seen in any vacuum solution to EFE (because in a vacuum solution there is nothing but...), a central mass! Without the mass there is no energy or momentum from which a gravitational field can emerge... At least that we can see/observe with any certainty, at present. If any of the rest of your comments are nonsense. At least without a great deal of additional information, defining exactly what springs forth from your imagination. Since the earth, moon and sun have no relative velocity even approaching relativistic speeds, no one needs to deal with relativistic adjustments.
This is how the observer is effected by the components of the stress energy tensor. The relativistic mass is just a sloppy way to express the total relativistic energy. So it definitely effects the local spacetime curvature at the observer coordinates. The way it effects the observer is the local spacetime curvature determines the geodesic path of objects in freefall over the natural path. The natural path is an inertial path through curved spacetime [gravity]. The path of least action. IE no force acting upon the object over it's path. The geodesic path.
Looks like Matt would probably support russ_waters comments in the thread on natural philosophy. "... But we don't slavishly follow them, the way people used to follow Aristotle." Or Newton, or the concept of an ether, etc. as Russ points out. I realize this is part of the human condition. Being clueless without firsthand knowledge of it. Me included. To frequently.
