That is answered as back as my Post # 8....If you cannot read or comprehend, how can I be of any assistance to you ? Do you have any clue what you are talking about ?
http://math.ucr.edu/home/baez/physics/Relativity/SR/mass.html What is Relativistic Mass? extract: This definition of mass was applied in a straightforward way for almost two centuries. Then Einstein arrived on the scene and, in his theory of motion known as special relativity, the situation became more complicated. The above definition of mass still holds for a body at rest, and so has come to be called the body's rest mass, denoted m0 if we wish to stress that we're dealing with rest mass. But when the body is moving we find that its force–acceleration relationship now depends on two quantities: the body's speed, and the angle between its direction of motion and the applied force. When we relate the force to the resulting acceleration along each of three mutually perpendicular spatial axes, we find that in each of the three expressions a factor of γm0appears, where the gamma factor γ = (1–v2/c2)–1/2 occurs frequently in special relativity. The idea of a speed-dependent mass actually dates back to Lorentz's work. His 1904 paper Electromagnetic Phenomena in a System Moving With Any Velocity Less Than That of Light introduced the "longitudinal" and "transverse" electromagnetic masses of the electron. With these he could write the equations of motion for an electron in an electromagnetic field in the newtonian form, provided the electron's mass was allowed to increase with its speed. Between 1905 and 1909, the relativistic theory of force, momentum, and energy was developed by Planck, Lewis, and Tolman. It turned out that a single mass dependence could be used for any acceleration, thus enabling mass to retain its independence of the body's direction of acceleration, if a speed-dependent "relativistic mass" m was understood as present in Newton's original expression p = mv. So a body moving with speed v and whose momentum has magnitude p has a relativistic mass given by m = p/v, and (it turns out) a total energy of mc2. A body with rest mass m0 turns out to have relativistic mass γm0. But the definition m = p/v now also neatly defines a relativistic mass for a photon: this moves with speed cand has energy E, and electromagnetic theory gives it a momentum of magnitude p = E/c, so it has relativistic mass p/v = E/c2. The expression m = γm0 doesn't apply to a photon, for which γ is infinite. But on the other hand, writing m = γm0 won't lead to any contradictions for a photon if we define the photon's rest mass to be zero. See the FAQ article What is the mass of a photon? for more discussion of this. The quantities that a moving observer measures as scaled by γ in special relativity are not confined to mass. Two others commonly encountered in the subject are a body's length in the direction of motion and its ageing rate, both of which get reduced by a factor of γ when measured by a passing observer. So, a ruler has a rest length, being the length it was given on the production line, and a relativistic or contracted length in the direction of its motion, which is the length we measure it to have as it moves past us. Likewise, a stationary clock ages normally, but when it moves it ages slowly by the gamma factor so that its "factory tick rate" is reduced by γ. Lastly, an object has a rest mass, being the mass it "came off the production line with", and a relativistic mass, being defined as above. When at rest, the object's rest mass equals its relativistic mass. When it moves, its acceleration is determined by both its relativistic mass (or its rest mass, of course) and its velocity. The use of these γ-scaled quantities is governed only by the extent to which they are useful. While contracted length and time intervals are used—or not—insofar as they simplify special relativity analyses, relativistic mass has found itself at the centre of much debate in recent years about whether it is necessary in a physics curriculum. All physicists use rest mass, but not all physicists would have relativistic mass appear in textbooks, preferring instead always to write it in terms of rest mass when it is used (although this can't be done for photons). So, if all physicists agree that rest mass is a very fundamental concept, then why use relativistic mass at all? When particles are moving, relativistic mass provides a very economical description that absorbs the particles' motion naturally. For example, suppose we put an object on a set of scales that are capable of measuring incredibly small increases in weight. Now heat the object. As its temperature rises causing its constituents' thermal motion to increase, the reading on the scales will increase. If we prefer to maintain the usual idea that mass is proportional to weight—assuming we don't step onto an elevator or change our home planet midway through the experiment—then it follows that the object's mass has increased. If we define mass in such a way that the object's mass does not increase as it heats up, then we will have to give up the idea that mass is proportional to weight. Another many-particle example occurs in pre-relativistic physics, in which the centre of mass of an object is calculated by "weighting" the position vector ri of each of its particles by their mass mi: ∑i miri Centre of mass = ———————— ∑i mi The same expression will hold relativistically if each of the above masses is now a particle's relativistic mass. If we prefer to use only rest mass then we must replace the mi in the above expression by γi mi where mi isrest mass, but now the expression has lost a certain economy. Similarly, if two objects with relativisticmasses m1 and m2 collide and stick together in such a way that the resulting object is at rest, then its (relativistic = rest) mass will be m1 + m2. This accords with our intuition, and intuition is mostly what good conventions are about. In contrast, a rest-mass-only analysis describes the interaction by saying that the objects have (rest) masses of M1 and M2, with a combined (rest) mass of γ1M1 + γ2M2. Whether our intuition has anything to gain from this new expression is not clear. Another place where the idea of relativistic mass surfaces is when describing the cyclotron, a device that accelerates charged particles in circles within a constant magnetic field. The cyclotron works by applying a varying electric field to the particles, and the frequency of this variation must be tuned to the natural orbital frequency that the particles acquire as they move in the magnetic field. But in practice we find that as the particles accelerate, they begin to get out of step with the applied electric field and can no longer be accelerated further. This can be described as a consequence of their masses increasing, which changes their orbital frequency in the magnetic field. Lastly, the energy E of an object, whether moving or at rest, is given by Einstein's famous relation E = mc2, where m is its relativistic mass. Because, for example, the photon has no rest mass but does have relativistic mass, the use of relativistic mass makes it much easier to describe the mass changes that happen when light interacts with matter. See the FAQ article What is the mass of a photon?. While relativistic mass is useful in the context of special relativity, it is rest mass that appears most often in the modern language of relativity, which centres on "invariant quantities" to build a geometrical description of relativity. Geometrical objects are useful for unifying scenarios that can be described in different coordinate systems. Because there are multiple ways of describing scenarios in relativity depending on which frame we are in, it is useful to focus on whatever invariances we can find. This is, for example, one reason why vectors (i.e. arrows) are so useful in maths and physics; everyone can use the same arrow to express e.g. a velocity, even though they might each quantify the arrow using different components because each observer is using different coordinates. So the reason rest mass, rest length, and proper time find their way into the tensor language of relativity is that all observers agree on their values. (These invariants then join with other quantities in relativity: thus, for example, the four-force acting on a body equals its rest mass times its four-acceleration.) Some physicists cite this view to maintain that rest mass is the only way in which mass should be understood. As with many things, the use of relativistic mass can be a matter of taste, but it seems that at least some physicists who vehemently oppose the use of relativistic mass believe, mistakenly, that pro-relativistic mass physicists are against the idea of rest mass. It's not clear just why there should be this perennial confusion about preferences, and why some of those who dislike the idea of relativistic mass show such fundamentalist opposition to a choice of formalism that can never produce wrong results. The world of physics and its language is full of useful alternative notations and ways of approaching things, and different choices of notation and language can shed light on the physics involved. Selecting one of the other of relativistic versus rest mass will never lead to problems for practitioners of the subject. more at the link.......
The answer is no, the relativistic mass will not have a gravitational impact. http://www.itep.ru/theor/persons/lab180/okun/em_3.pdf
Relativistic Mass = Gamma * Rest Mass, that I had written in my first couple of posts. Now what do you want to say with this lengthy copy paste........ In fact the last line from the passage, takes you off..
I suggest you read the post/paragarph in total without any convoluted taking words out of context. Rest mass, or the measured mass, does not change with velocity. And that is what contributes to the gravitational field. Relativistic speeds changes the relationship between momentum and energy.
The problem with you Paddoboy, is that you poke your nose everywhere without knowing the nitty gritty of the subject, the irony is that I cannot even tell you to understand GR equations, that is highly mathematical and you will find really really tough to get through them. The question of OP is being reframed by me.... Take Earth as observer 1. If a test particle of very less mass at slow speed passes closer to Earth, will the spacetime around Earth get distorted by this particle........the prevalent answer is no, because we neglect the mass, and speed is also non relativistic. 2. Now if the same particle moves at a very high speed that gamma becomes significant, so that [gamma*rest mass] becomes non negligible as compared to the Earth Mass, then will the spacetime distortion be any different ? Answer to the above, will help you in understanding things in right perspective.
I read and this what I got somewhere in between.. Your copy paste is veering towards what I have been saying since my post # 8...self goal ?
Please Register or Log in to view the hidden image! You'll just have to get used to that now, won't you? Me poking my nose in that is. At least I reference all my links, unlike you, hmmm? Ever heard of plagiarism"?
Cop out? Please Register or Log in to view the hidden image! Pot kettle black again! And like I said, I do reference and link my stuff....all of it. Rest mass, or the measured mass, does not change with velocity. And that is what contributes to the gravitational field. Relativistic speeds changes the relationship between momentum and energy. "Inertial mass equals gravitational mass and is constant"
You get no response from me, till you answer the question in Post # 46, being reproduced.....bye till then Take Earth as observer 1. If a test particle of very less mass at slow speed passes closer to Earth, will the spacetime around Earth get distorted by this particle........the prevalent answer is no, because we neglect the mass, and speed is also non relativistic. 2. Now if the same particle moves at a very high speed that gamma becomes significant, so that [gamma*rest mass] becomes non negligible as compared to the Earth Mass, then will the spacetime distortion be any different ?
When I quoted Lev Okun I did not quote the whole of his paper. I mistakenly expected that you would actually read it, to understand your.., misunderstanding on the issue. That aside.... The OP asks a question about how relativistic mass affects an object's gravitational field.., by asking if an increased gravitational field of a relativistically moving particle would be detectable by a (relatively) stationary observer.... The whole difficulty with the issue in the OP and your misunderstanding, is that the term relativistic mass is an archaic and misleading term. The fact that it contains the word mass, leads the lay person to believe, that the mass of an object changes proportionally to its velocity. This is not true. An object has only one mass, which depending on the discussion may be referred to as inertial mass, gravitational mass or rest mass..., however all three of these are equivalent.., meaning, inertial mass = gravitational mass = rest mass, in all circumstances. So as in the earlier quote from Lev Okun, there is only one mass in physics, and it does not change with velocity. The archaic therminology relativistic mass is better understood as the momentum of a relativistically moving object. If you had really read Okun's paper.., the short one aimed at the interested lay person I linked, you should have understood your misconception. The above portion in bold is the statement I would like you to prove. prove as in provide a credible reference that supports the statement! Why? Because what you believe it means, is not prevailing science.., it is a common lay misunderstanding of historical and misleading terminology... Again, relativistic mass = momentum.., and momentum does not change an object's gravitational mass or gravitational field, in any way other than the gravitational field of an object moves with it.
Paddoboy, leave dead horses in the threads they died in. It is not constructive to keep dragging old arguments and threads into new threads.
Only if you get out of this, can we address the OP meaningfully.....Pl see my post # 22 which counters this very gaffe of yours, I have even given you dimensional analysis, relative mass formula, momentum formula....still you are continuing with this, why and where did you get this form ?
The above sums up your misunderstanding! Is was useful only within the context of special relativity, where the incorporation of the Lorentz transformation, necessitates an inertial observer.., and in the context of GR only applies where gravity can be ignored and SR remains applicable. Even then today for physicists, working with particle accelerators where the math involved is used, the term relativistic mass is replaced by or understood to be momentum. Rajesh, every single day there are relativistic cosmic rays, particles.., protons and even alpha particles that impact our atmosphere, even the earth itself. If what you have been saying, about the mass of those particles were true, they would be gravitationally significant and gravitationally detectable. They are not. We only detect them as they impact and interact with specially designed detectors. They have a great deal of momentum and no greater mass than a similar particle at rest relative to the observer, earth and/or detector! Stop, talking long enough to read the information (references) that have been provided. Educate yourself. If you still disagree, provide some credible reference to support your position. You have been asked several times to proved and/or provide credible reference, supporting your understanding. The rules of the forum require that you do so!...
You have not proven your position and have refused to provide any credible reference supporting your understanding. Again, read Lev Okun's paper, The Concept of Mass, http://www.physics.uoguelph.ca/~des/Phys2320/concept of mass.pdf
Ok, but first please tell me from where you got this, not even Okun claims this, rather none other than you, it appears.. relativistic mass = momentum ........How ? Actually the relationship between the relativistic mass and momentum is as follows...... Please Register or Log in to view the hidden image! PS: In fact you should read Paddoboy copy paste stuff as given in his post # 42, that will give you and idea about the Relativistic Mass is....drop Okun immediately from your library, no need to get into Apendix argument.
All the many foregoing assertions by posters claiming only rest mass = gravitational mass are plain wrong. This is one case where Rajesh has it basically right (I haven't bothered to read all details of every post). To those who disagree, see http://www.sciforums.com/threads/black-holes-a-opposed-to-the-big-bang.145854/page-8#post-3298801 The same would apply if e.g. adding rotational energy to a flywheel - both inertial and gravitational mass will rise in equal measure. The added factor of a 'gravitomagnetic field' in the latter example is irrelevant. As is the mundane fact of an invariant proper mass. While it is fashionable to eschew 'relativistic mass' in favor of 'relativistic energy', that is a matter of current convention, and 'relativistic mass' correctly conveys that gravitational influence of matter very much depends on it's KE which is thus a frame-dependent thing.
I don't believe you have read any of the provided information.., maybe skimmed through for something you believe is saying what you think it should. Most of post #42 is a, historical chronology. It is an attempt to describe how we got to where we are. Your formula is dishonest, because your relative mass term is not itself fundamental. It is derived from the object's rest mass as modified by its relativistic velocity. And you have once more failed to provide any supporting reference, for your position.
OK, so provide a credible reference that demonstrates where an increase in gravitational mass due to heat, has been measured. Mass and weitght are not the same thing.., in modern physics. And the debate you are dropping into this discussion has nothing to do with the OP or even the issue of what the ARCHAIC term relativistic mass means, as defined in modern terms. Do you really believe that a proton moving at near the speed of light has a gravitational field 90% of infinite? Because that is what Rajesh's interpretation of the term relativistic mass, implies. And that is a different discussion than the one you are interjecting, into the discussion. If you want to restart a discussion about heat and mass, start a new thread and see what response you get. Rajesh has enough trouble with the question as it applies to this thread.
