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We expect religious fundamentalists to fight over a word. Scientists should be a bit more tolerant and understanding.
We expect religious fundamentalists to fight over a word. Scientists should be a bit more tolerant and understanding. Confusion over the term "mass" and it's various symbols and abbreviations results from a lack of consensus and authority. Until all leading international governing bodies pass a resolution, binding on their members, to adhere strictly to an accepted nomenclature, the controversy will continue. Authors will be free to use their own favorite nomenclature. We can only hope that each author will make it clear what he means by "mass" and the letter "m", or whatever letter he uses. I've gotten into the bad habit of using the terms "mass" and "m" without distinguishing which kind of mass I'm talking about. I've been doing it since my first intro to physics as a college freshman, before I learned about relativity. It's a hard habit to break, but I shall make an effort to do so. I won't attack those who disagree with me, but I will argue in favor of my preference. I prefer to define "inertial mass", mi, as a measure of how much momentum changes per unit change in velocity in a given reference frame; mi = dp/dv. By that definition, the mass of a particle depends on the reference frame. The opposite camp in this controversy defines mass as the momentum change for the first small increment of velocity change beginning at rest. By that definition, the mass of a particle is the same in all inertial reference frames. Since "m" has been used in the literature to represent both kinds of mass, perhaps the best solution is to abandon "m" altogether (except where relativity is clearly not an issue) and use only symbols that, historically, have been used only to mean one kind of mass or the other. I like the term "m0" for rest, invariant or proper mass, and I like the term "mi" for relativistic inertial mass. PMB likes to use "μ" instead of "m0" and "m" instead of "mi". I guess Lightarrow prefers "m" instead of "m0" and "γm" instead of "mi". I will be happy with any nomenclature that is unambiguous until such time as the international governing bodies make a unanimous ruling on the matter. [Edited to change "mr" to "mi".]
Since "m" has been used in the literature to represent both kinds of mass, perhaps the best solution is to abandon "m" altogether (except where relativity is clearly not an issue) and use only symbols that, historically, have been used only to mean one kind of mass or the other. I like the term "m0" for rest, invariant or proper mass, and I like the term "mi" for relativistic inertial mass.
Maybe, the fact people used the term "relativistic mass" and a symbol "m" for it, is because a lot of physicists still believe there is a difference between that mass and energy. Some still make confusion about mass and energy and talks about "converting mass into energy", for example when they talk about the energy freed in a nuclear reaction. I also talked in that terms, in the past, but it's incorrect. I have to thank a professor of physics for having (with difficulty) understood it. Actually, it's quite easy to understand; the difficult part is to accept it...
Edit: Let's make a simple example: a nucleus of rest mass m = 10-25 kg undergoes nuclear fission and two equal fragments are shoot away in opposite directions. Let's say the total kinetic energy of the fragments is 1/1000 the energy of the initial nucleus: 0.0001*m*c2 = 0.001*10-25*(3*108)2 Joule Question: compute the *Rest* mass of the system before and after the nuclear reaction. Rest mass of the system before reaction: 10-25 kg Rest mass of the system after reaction: 10-25 kg There are no mistakes. Now I ask again: why using a different concept of mass different from rest mass? -- lightarrow
I totally agree that rest mass (or proper mass) is captive energy.
Any energy that is bound within a system, by any attractive force, is captive energy; it contributes to the rest mass of the system.
Any energy has both gravitational and inertial mass, whether it is bound within a system or not. Both kinetic energy and photons have mass.
Quote from: lightarrow on 14/05/2012 14:32:27Edit: Let's make a simple example: a nucleus of rest mass m = 10-25 kg undergoes nuclear fission and two equal fragments are shoot away in opposite directions. Let's say the total kinetic energy of the fragments is 1/1000 the energy of the initial nucleus: 0.0001*m*c2 = 0.001*10-25*(3*108)2 Joule Question: compute the *Rest* mass of the system before and after the nuclear reaction. Rest mass of the system before reaction: 10-25 kg Rest mass of the system after reaction: 10-25 kg There are no mistakes. Now I ask again: why using a different concept of mass different from rest mass? -- lightarrow Assuming that the split was spontaneous and not triggered by any external particle, the sum of rest masses of the two halves after the split must equal the original rest mass MINUS the kinetic energy of the fragments. Kinetic energy is the difference between relativistic mass and rest mass. The key word in your argument is "system". If the two halves are bound by opposite electric charges, they are a system. Then, you are correct about the rest mass of that system. The rest mass of the system is the sum of rest masses of the two halves PLUS their kinetic energy. The kinetic energy of the halves is 10-27 kg
; the kinetic energy of the system is zero. Kinetic energy of the two halves is captive within the system; captive energy is mass. If their kinetic energy is too great to be bound by electrostatic attraction, then I would consider the halves to be two independent systems. The sum of rest masses of the two systems would be 9.999 * 10-24 kg. [/font]
"A photon can accelerate by the way. It does so by scattering off, say, an electron as in Compton Scattering. The magnitude of the photon's velocity remains constant. It's the change in direction that changes, which means that velocity changes, i.e. the photon accelerates."
And what about those rotating black holes 'frame dragging'?That should create a mass too, shouldn't it?
Quote from: yor_on on 14/05/2012 21:29:37And what about those rotating black holes 'frame dragging'?That should create a mass too, shouldn't it?In GR the concept of mass becomes infinitely more smooth and vague:http://en.wikipedia.org/wiki/Mass_in_general_relativity(they say "more complex" but it's euphemistic )As long as we stay in SR, I can talk about something; in GR, mass or energy is still...science fiction for me.
If you want to get technical about it, mass doesn't belong in special relativity, at all. Mass has no meaning apart from gravity and acceleration, and the absence of gravity and acceleration is what makes SR "special".
Einstein was bending the rules when he gave us a formula for relativistic mass. When you talk about chemical processes (at the molecular level) and oscillating springs, you're talking about accelerations. At the atomic level, time can be reckoned in terms of electrons accelerating around a nucleus. The only sort of clock that doesn't involve acceleration is the theoretical light clock, in which light reflects back and forth between ends of a vacuum tube. When we discuss mass in the context of SR, we also must bend the rules to include minimal gravity and acceleration within a bound system which has relativistic motion in the observer's reference frame. That's how I am able to talk about time dilation of a planetary system. The bodies accelerate toward one another, due to their mutual gravitational attraction. As long as motion within the planetary system is not a significant fraction of the speed of light, the formulas of SR can be applied to the planetary system which has relativistic speed in the observer's reference frame. If the barycenter of a planetary system is moving at gamma = 10 in Frame A, time dilation slows the orbital period to 1/10th of what it is to an observer in Frame B, moving with the barycenter. So in Frame A, the acceleration is 10th normal. If both the gravitational mass and the inertial mass were 10 times normal, the attractive force would be 100 times greater, and the acceleration and orbital period would be 10 times faster, not 10 times slower. (The problem is simple if the orbital plane is perpendicular to the line of relative motion of the barycenter in Frame A. For other orientations of the orbital plane, you have to take length contraction into account.)
"the idea of accelerating a photon gives me "cold sweat""Yep, somehow the universe seems to steered by equivalences, symmetries and?That we find 'rules and regulations' is a very strong indication of there being real 'constants' to me. The question is what those constants are. I find 'c' to be the one relativity is built on, and 'c' is defined through SR.It discuss a two way (mirror) experiment of reflected light in a vacuum, ignoring 'gravity' bending 'space', instead assuming a 'flat space'. And it seems to be correct? 'c' I mean, we've found all sorts of evidence for it, from frame dragging to ... Because what GR does is to add gravity 'distorting/bending/reshaping the 'space' that light 'propagates' in.And that reshaping is equivalent both to a acceleration, and a 'weight'. But the spinning disk?? How does it create a mass? And why?
PMB likes to use "μ" instead of "m0" and "m" instead of "mi".
Pete, perhaps you could clear up a question I've had.
I've done some work in quantum mechanics and a little in (special) relativistic quantum mechanics.
Could you comment on where relativistic mass sees use in physics? Where do calculations get simplified by its use?
Although I argue for the usage of relativistic mass I do not argue that proper mass is not an important tool in relativistic dynamics.
Measuring the active gravitational mass of a moving object, D.W. Olson and R.C. Guarino, Am. J. Phys. 53(7), July 1985 If a heavy object with rest mass M moves past you with a velocity comparable to the speed of light, you will be attracted gravitationally towards its path as though it had an increased mass. If the relativistic in active gravitational mass is measured by the transverse (and longitudinal) velocities which such a moving mass induces in test particles initially at rest near its path, then we find, with this definition, that M_rel = \gamma(1 + \beta)M. Therefore, in the ultrarelativistic limit, the active gravitational mass of a moving body, measured in this way, is not \gammaM but is 2\gammaM
Never make a calculation until you know the answer. Make an estimate before every calculation, try a simple physical argument (symmetry! invariance! conservation!) before every derivation, guess the answer to every paradox and puzzle. Courage: No one else needs to know what the guess is. Therefore make it quickly, by instinct. A wrong guess brings refreshment of suprise. In either case life as a spacetime expert, however long, is more fun!
My general take on the subject was along the line of what Lightarrow said: that relativistic mass is just renaming energy, and we can use energy to do all the computations required without introducing a new name for it. Is this true?
It's amazing! No matter where you go on the internet there's always someone trying to force their views down your throat. It never ends!
Thanks for the information, Pete. It'll probably take me a while to wade through the links.
You're right that I haven't done much work with general relativity/cosmology, which is where it sounds like relativistic mass finds use.
I'm much more familiar with quantum mechanics, where invariant mass is useful, and quantum optics, where invariant mass of single photons is zero.
My other general impression is that arguing over what should be called "mass" actually obscures a more important point: that when you transition from Newtonian physics to general relativity, there is no single quantity that has all the properties of Newtonian mass, so of course you can argue over the proper generalization of mass!
Quote from: Pmb on 29/05/2012 00:00:50It's amazing! No matter where you go on the internet there's always someone trying to force their views down your throat. It never ends!I'm dibled and can't get around much. I can only take so miuch TV. If I don't use my mind then I'll forget alot about the physics I know. I won't be challenged. The alternate is worse, hence my staying where the nuts are.Simple solution - stay off the internet, but what does that have to do with this thread?
. . . One way of thinking of it may be to leave the concept of mass and instead consider tension and pressure . . .
Thinking of the original question. "If E =mc^2, and the photon transfers energy, how can it have no mass even if the mass is minuscule?"One way of thinking of it may be to leave the concept of mass and instead consider tension and pressure. Then invariant proper mass and the photon share that ability. They both influence other particles, as well as get influenced by them.The problem here being one of experience. We all differ between bosons and what we call matter, but as Pete pointed out, Einstein didn't. He called both EM and invariant proper mass 'matter'. And EM is defined through photons.
Quote from: JP on 25/05/2012 15:12:32My general take on the subject was along the line of what Lightarrow said: that relativistic mass is just renaming energy, and we can use energy to do all the computations required without introducing a new name for it. Is this true? No. It's not true. First off they are not the same thing. They're equivalent, not identical. And even then only in a limited use of the relationship. That use is the limitation to particle physics or any physics which is not a closed system. E.g. a drop of water in an electric field like, for example, an electrical storm. The electric field polarizes the drop of water. This leaves the drop in a state in which there is stress in the drop. This stress contributes to the inertia of the drop. In this case the relation E = mc2 is wrong.
That relation can't be wrong, if you consider the right system ....
Quote from: lightarrow on 02/06/2012 19:52:58That relation can't be wrong, if you consider the right system ....That's what it means when it is said that E = mc2only works under certain circumstances.
So your ojection that relativistic mass and energy are not the same, means that we have to specify which is the system and which is the energy?It's a poor argument...
I finally found that paper on this topic I was referring to. There is an earlier paper than this by the same author but I'll have to start searching for that tomorrow. The article is On the Inertial Mass Concept in Special Relativity by Mendel Sachs, Foundations of Physics Lectures, Vol. 1, No. 2, 1988------------------In this regard I have re-examined in an earlier paper the meaning of Einstein's energy-mass relation in special relativityE = m0c2 (proper frame)E = m0c2/[1 - (v/c)2 ]1/2 (moving frame)demonstrating that, in the frame of the free particle with inertial mass m0, this equation does not signify that "energy is equivalent to mass", as it is usually asserted. What was pointed out earlier in this regard is that the concept of “energy” per se and the concept of “inertial mass” per se are, firstly, the same as they are in classical physics, and secondly, that they are logically different concepts: “energy is defined as the capacity of matter to do work and “inertial mass” is defined as a quantification of the inertial property of matter, i.e. a measure of its resistance to a change of state of constant speed (or rest) with respect to any observer.. Since these are entirely different concepts, energy cannot be said to be “equivalent to mass”.------------------which is exactly what I've been saying for years of course.
We were discussing if your relativistic mass is the same concept of total energy or not.
A straw man is a type of argument and is an informal fallacy based on misrepresentation of an opponent's position. To "attack a straw man" is to create the illusion of having refuted a proposition by replacing it with a superficially similar yet unequivalent proposition (the "straw man"), and refuting it, without ever having actually refuted the original position.
I already showed you a counter example which proved you wrong. Why are you making no attempt to show that the physics is wrong?