Pete

Meaningful in what sense? Even if there is no "intrinsic" meaning there is a physical meaning. I.e. we know that time intervals and spatial intervals are not inot intrinsic yet they are physically very meaningful. One needs to be careful about this too. For instance I can define the term mass of particle as measured by observer by mobs = P*Uobs/c2 where Uobs is the observer's 4-velocity and P is the 4-momentum of the particle and mobs is the relativistic mass of the particle as measured by the observer. This is a geometric quantity and is invariant in the sense that it remains unchanged by an arbitrary Lorentz transformation. Different observers measure different masses. A similar idea holds for the electric and magnetic field. I.e. there are quantities known as electric field as measured by observer/I] and magnetic field as measured by observer which are both (observer dependant) 4-vectors. They mean the exact same thing. I use the more appropriate term stress-energy-momentum tensor because it more fully decribes this tensor, i.e. the components are energy, momentum and stress, not just energy and momentum. Different [math]X[/math] gives different [math]\rho[/math]'s. Normally the time-like vector is the 4-velocity of an observer and in that sense is a scalar. If the [math]X[/math] is intrepreted to be a unit vector which defines a coordinate system then the quantity becomes coordinate dependant and non-invariant in that sense. The [math]\rho[/math] as you have defined it will equal the energy density and not the mass density. Mass density is defined as the ratio of momentum density to velocity. Even if you let v -> 0 it will be different than energy density. Remember that E = mc2 does not always hold. What is the purpose of [math] \sqrt{-g}[/math] in that definition? I seem to have gotten off track of the purpose of this thread, i.e. inertia. Sorry. A word on invariance here - The components of a tensor quanity are defined as the scalars which result by inputing unit 4-vectors/1-forms which define the coordinate system. Although this is still a map of 4-vectors/1-forms to numbers they are still scalars in that sense. However they are not invariants in the sense that a change in coordinate system requires a change in unit vectors. Pete

Why do you think it should be invariant? Is this related to your preferance to speak only in terms of proper mass? I was speaking in terms of the stress-energy-momentum tensor in the first place because mass densities cannot be be defined with anything other than a second rank tensor. Pete

I don't follow. Why should mass need to have an intrinsic meaning in order for mass density to be defined? Pete

You're thinking purely in terms of special relativity. Within general relativity there are ways to get around this by "cheating". One way has been devised and is known as the Alcubierre Warp Drive. That and other examples of faster than light travel are on a NASA web site at http://www.nasa.gov/lb/centers/glenn/research/warp/ideachev.html#alcub Pete

I'd wager that most physicists don't look into it past physics 101 In this thread I'm sticking within special relativity. The mechanics of contniuos media is addressed in special relativity. That's where it can get tricky. That works for a photon. So I guess you're saying that a photon has inertia due to its energy? How do you think you'd define mass density if you wanted/needed to? Oooo! Good question. Could a graviton interact with other kinds of particles, e.g. can they scatter off other particles? Pete

I recommend that you seek out someone who is doing this kind of work and ask them for advice. Pete

In such a case all charged particle's will have an infinite electromagnetic mass. If a particle has no charge then one has to accelerate it by other means, e.g. by scattering other particles off of it or, if it has a magnetic moment, by placing it an an inhomogenous magnetic field and delfect it using the neutron's magnetic moment. I take it that you never consider things other than particles, would that be correct? In relativity it is know that stress has inertia (its the purpose of this thread to investigate what that means). I question that interpretation, hence the purpose of this thread. E.g. French defines inertial mass as m = p/v and as such it must have inertia, yet it is unable to accelerate. I believe that this is the case in any place in which one defines the mass of a tardyon. Always nice to test the boundaries of one's basic concepts, yes? Geodesics deviation applies to locally inertial frames too and one doesn't assign inertia to such frames. Pete

I assume that you mean "point object" since a photon is considered a particle and I imagine that you'd say that it has no mass at all, correct? What do you mean by "point" mass/object? Do you mean an object whose size is zero? The term particle has also been defined as an indivisible unit of matter. The two are not neccesarily the same. In classical mechanics the term particle applies to objects which can be considered small with respect to the system being considered (e.g. see Newtonian Mechanics, A.P. French, pages 1-4). E.g. an atom will behave like a particle under various circumstanecs. But if one looks closely it can't be considered a particle. A planet can be considered a particle if one is only concerned with celestial motion. I don't think that it has ever been proven that an elementary particle such as an electron has zero size. I doubt that one can locate an electron with infinite precision and thus speaking of it as being a "point" is not quite clear. String theory actually supposes that objects like electons are not pointlike, that they are like strings and thus have dimensions. In classical mecanics it is troublesome to think of point charged particles due to its infinite self energy. So one may argue that true point particles are those which have zero size this becomes a serious problem in classical mechanics. And the subject I wish to addess here is classical mechanics, not quantum mechanics. Question: Would you consider a photon or an EM wave to have inertia? Pete

A friend of mine pointed out an error in the interpretation that I started with. He explains I guess its best to think of inertia as that quantity that defines momentum for a given velocity. That depends on how the term particle is defined. If it is possible for an object to have internal stesses, regardless of its size, then a 4-descrition can't work in general. Pete

Of course. That's basic SR and you need to explain the basics to me. To be precise that is not true. What is true is that proper mass is the "proportionality constant" between change of 4-momentum and 4-acceleration. After all 4-velocity is not the time rate of change of 4-position. Its the rate of change of 4-position per unit proper time' date=' not [i']time[/i]. The 4-vector approach cannot work in all possible cases. It only works in special cases. The quantity that fully describes mass is the stress-energy-momentum tensor. Thanks' date=' but I was overly aware of that 23 years ago. Note: Needless to say, I'm trying to avoid discussions which have to deal with [i']mass[/i] for obvious reasons and am thus I'm only interested in inertia. Using 4-velocity one can't even speak of an object at rest so I'm avoiding 4-vectors, escpecially since they have only a limited usage. Thanks. Pete

The reason I posted this in the relativity forum is because [math]m a(x(t)) = m \frac{d^{2} x(t)}{dt^{2}}[/math] doesn't hold. If it did then the two interpretations would be the same. Seems to me that if this was an example of a "motion" then it would have to correspond to something physical. If not then such a Lagrangian cannot exist. In my opinion, a Lagrangian that has such a form but does not lead to an equation of motion which describes something physical is not a valid Lagrangian. Pete

The term inertia is a term which describes what mass is a measure of. But one doesn't say that "The inertial of a body is 12 grams". Some people like to say that inertia is a measure of a body's resistance to changes in velocity. Hard to say. At http://scienceworld.wolfram.com/physics/Inertia.html the definition is inerrtia: The resistance to change in state of motion which all matter exhibits. But at http://www.merriam-webster.com/dictionary/inertia the definition is inertia - a property of matter by which it remains at rest or in uniform motion in the same straight line unless acted upon by some external force At http://www.neutron.anl.gov/hyper-physics/inertia.html inertia - inertia (în-ûr¹she)' date=' in physics, the resistance of a body to any alteration in its state of motion, i.e., the resistance of a body at rest to being set in motion or of a body in motion to any change of speed or of direction of motion. What kind of motion is that? Can you give me an example? Newton used the term "quantity of motion" to refer to momentum. So in that sense I'm the above definition is what I'm thinking of (even though the author of that definition probably meant otherwise). Pete

Request for opinion - Do you think there are any logical problems in defining the the term "inertia" to refer to the resistance of body to a change in mometum? The fact that inertial mass is defined as m = |p|/|v| seems to suggest this definition. Pete

No. A photon consists of a single frequency/energy. What you have described is a sum of states having different frequencies/energies. Pete

The term annihilate as it is used in physics refers to the process that occurs when a subatomic particle collides with its respective antiparticle. The term megaton is used to refer to the energy released in an explosion. E.g. 1 megaton is the amount of energy released when a process releases the same amount of energy released when 1million tons of TNT is detonated. So I guess you could say that the explosive energy released when 1 million tons of TNT is detonated is 1 megaton. When two particles annihilate matter doesn't just disappear. It changes from particles with non-zero proper mass to photons, each of which has zero proper mass. Pete

The USNET FAQ discusses this. You can read all about it at http://math.ucr.edu/home/baez/physics/Relativity/SR/experiments.html The FAQ states It only mentions moving sources. But it seems to me that it must apply to the Michelson-Morely Experiment (MMX). If not then would anyone care to explain why it doesn't apply to MMX? Pete

Yes in that the average speed through a medium is less than that in a vacuum due to the process of absorption and reemission. The quantity labeled c is called the speed of light in a vacuum and which applies locally in a gravitational field too. Pete

In general relativity it seems possible to have a negative inertial mass. Since stress contributes to mass then it follows that when the tension of a body is greater in magnitude that the energy density of the body then the inertial mass will become negative. E.g. if you had a long very strong rod which has two charges on the ends and it is placed in a very strong electric field then, when the stress in the rod is great enough, its inertial mass will become negative. The meaning of a negative inertial mass is that the momentum is in a direction opposite to that of velocity. Pete

Does the same thing hold true if one does not assume the mass shell condition, since that is a postulate that is abandoned for Tachyons. Are you sure that QFT theory can't handle this since it seems that the author would have said something about this. How long has perturbative quantum field theory been around? Pete

Classically this would be described as a particle subjected to an relusive gravitational force but the inertial mass is negative and thus the force is in the opposite direction of the particle's acceleration. There is an interesting article on this subject that you might enjoy readind. The article I speak of is Negative Mass in General Relativity, Herman Bondi, Rev. Mod. Phys, 29(3), July 1957 I have a copy if you'd like to read it.

I see. I was doing something different though. I will solve the exact problem that you described and post the results later today. Inertial mass (akak relativistic mass) is not a scalar either. The transverse mass as the exact same value as the relativistic mass. However the longitudinal mass is different and has the value [math]m_t = \gamma^3 m_0[/math]. That's why one has to assign different names to them. The term transverse mass comes from the fact that when the motion is transverse to the force then the force is given by F = mta. The math is shown in one of my web pages at http://www.geocities.com/physics_world/sr/long_trans_mass.htm Pete

Not necessary anyway since I already know basics physics. I have to say that this is wrong. Its not like I haven't studied this before. Okay. Let us define some terms and solve the problem. Let m1 = -M where M is the absolute value of the active gravitational mass of body 1 (e.g. a planet). Let m2 = m where m is the passive gravitational mass of body 2 which we will assume equals the inertial mass of body 2. Then [math]F = - G\frac{ Mm}{r^{2}} = ma[/math] Therefore [math]a = G\frac{M}{r^{2}}[/math] Which shows that this results in gravitational repulsion. I don't understand why you disagree with this result, can you elaborate more please? Thank you. There are more ways to do this when you keep in mind that there are three kinds of mass (1) active gravitational mass (i.e. the source of gravity) (2) passive gravitational mass (what gravity acts on) and (3) inertial mass (i.e. the quantity defined by m = p/v). The equivalence principle only requires that these quantities be proportional, not equal. Pete

I know. Sometimes things come out different than one wanted them to. I understand that. Pete

Why are they at rest with respect to each other? I was addressing the specific problem of an observer at rest in a gravitational field (i.e. at rest with respect to the source of gravity, e.g. at rest in a uniform gravitational field) in which the scale is at rest but for which the body is moving with respect to this frame, i.e. the planent's frame of reference. I don't see that mass, as defined in this sense, is a vector quantity. A vector being functionally dependant on another vector (acceleration) doesn't make a lot of sense. I wouldn't define mass in that way myself. However it is very useful in certain kinds of problems, of which this is one. Pete

So you say. But that is no way true. To describe physics that is true. But not to define some of the elementary terms. Just because I disagree with you it in no way means that I don't understand something. Again, please define the terms time and physical space (as opposed to a mathematical space) mathematically or either state that it can't be done or that you know how to. Pete