pmb, Acceptable answer. Note: Lethe had already raised the issue of gravitomagnetics. Here I think some qualification could be helpful. In Lethe's posts he favored the gravitomagnetic process but holds that GR is flawed. You seem to accept GR. Curious how each could support GM and not both agree on GR. Well that gives you much more credability. But as indicated even among academics there is much debate on many issues. Actually, No. I have had a lot of physics, including nuclear engineering. But I am unbelievably handicapped in higher mathematics. Had some calculus over 40 years ago but have never used it. Please Register or Log in to view the hidden image! Why did I expect that answer. As the others have said "Welcome" to SF.
Really? Hmmm ... that's odd. Why does he reject GR? Oh yes! I'm acutely aware of this fact when it comes to mass that's for sure. Please Register or Log in to view the hidden image! lethe and I have discssed this mass thing on another forum at length. I reallty dislike such debates since it gives the false impression that I want to force people to think like me. The truth is that this is not what I desire. I merely have an opinion - I've made a choice on definition - and I back up my position. For some reason that comes across as me forcing he issue. Thanks! Pete
the situation is complicated for a moving mass. it has the same inertia for transverse forces as if it weighed the same as its rest mass. likewise, the gravitational field due to a moving source is not isotropic. so for one thing, you cannot describe the weight of a moving body with a scalar. there is an inertia tensor, but this also doesn't directly give you the gravitational source. but in the appropriate direction, the weight of a moving body is more, yes this is only reasonable if you don't mind replacing mass that is a Lorentz scalar with a couple of weird tensors. in other words, i disagree with you.
i don't "reject" GR. i don't think GR is correct at all scales. indeed, it is known that GR is not compatible with quantum mechanics, and we know that quantum mechanics is correct on some scales. this is a reasonable viewpoint. i know many who share it.
I'm not sure what you mean by this. Let me be more specific on what I was refering to: For the moment consider the simple example of a single particle with no internal structure. Let the field be a uniform gravitational field aligned in the z direction pointing in the -z direction. Such a field is defined my the metric ds^2 = c^2(1+gz/c^2)^2 dt^2 - dx^2 - dy^2 - dz^2 where g is the gravitational acceleration as measured at z = 0. Let the particle move with speed v in the xy-plane. The magnitude of the weight is defined as the magntitude of the force exerted by whatever is constraining the particle to move in the xy-plane. The weight W is related to the relativistic mass "m" by W = mg = m_o*g/sqrt[1-v^2/c^2] For the details of the derivation see -- http://www.geocities.com/physics_world/gr/weight_move.htm For force required to restrain it is transverse to the motion. However this force is not the rest mass times the acceleration if that is what you meant I never mentioned the weight of a moving body. That is more complex. I spoke only of the moving of a moving particle. The relation m = m_o/sqrt[1-v^2/c^2] is derived for a particle and it does not apply to anything which cannot be considered a particle. For example: Suppose you have a rod that is lying on the x-axis in the inertial frame S. On the +x end there is a force F directed in the -x direction. On the -x end there is a force F directed in the +x direction. Since the forces are equal and opposite the rod will not accelerate and it therefore remains at rest. Let the proper mass of the rod be m_o. Transform to frame S' which is in standard configuration with S. The momentum of the rod in S' is not given by mv and thus the relativistic mass of the rod is not m. If you're refering to transverse and longitudinal mass then that is not a tensor quantity in that the long-mass and trans-mass are not components of a tensor. As with energy, the complete description of relativistic mass is with a second rank 4-tensor if that's what you meant. The same tensor which defines the source of gravity is identical to the tensor which defines the gravitational field. The weight the a moving particle in any direction is a function of speed. But weight is defined as the force required to support an object in a gravitational field. That means there is no vertical motion of the particle, only horizonal motion. Therefore the weight is always transverse to the velocity and the weight is also a function of speed. that's a given
"For the moment consider the simple example of a single particle with no internal structure." Do such particles exist?
An object is often considered a particle when the size of the object is so small as to be taken as a point. In that sense the term "point" does not mean there is no internal structure. An electron and a positiron are two obvious examples of particles with no internal structure. I was speaking about a point particle so as not to complicate the point I was making. Otherwise the structure of a body must be known to determine the weight of the body. I know of at least one case that while the size could be neglected the structure would not. This is similar to refering to a point charge in an electric field. Place a charged particle in an electric field E. The force on the charged particle is given by F = qE. This is not valid in general if the object is not a point particle. To determine the force on a charged body one must know the shape of the body. If the body is small enough to be considered a point then charge distribution may still be a factor in some cases - I can't think of an example off hand
It modifies the potential, in that instead of it being the integral of something like 1/(r-r')dr', it is p(r)p(r')/(r-r')dr'. Where p(r) and p(r') are the density at r and r' respectively. In Hartree-Fock theory in atomic physics, this is the potential due to the fact that an electrons position is not delta(r-r') but rather, some distribution p(r').
the tensor which defines the inertia, transverse and longitudinal, is different from the tensor which describes the mass a source of the gravitational field
Sorry. That was a mistake. I meant to say that I only mentioned the weight of a moving particle and not the weight of a moving body. I consider these to be very different things. Especially when it comes to weight. re - "the tensor which defines the inertia, transverse and longitudinal," There is no such tensor. You're trying to assign the property of inertia to ratio of force to acceleration and then call it "inertial mass." That is an incorrect definition of inertial mass. Force is defined as F = dp/dt where p = mv. Force is not defined as F = ma. The quantities of which you speak do not form a tensor quantity, at least not a tensor according to the strict definition of the term as found in physics. It is neither a Cartesian tensor, a Lorentz 4-tensor nor a general 4-tensor. As mentioned above - Force is defined as F = dp/dt where p = mv. Therefore mass is defined as the ratio of the magnitude of momentum to the magnitude of speed. To be more precise: mass, "m", is defined such that mv is a conserved quantity. I.e. mass is that quantity which is a measure of a particle's resistance to changes in momentum. Even Newton didn't define force as F = ma. That was Euler's definition. F = ma is merely an equality when mass is constant. Both Adler and Okun made this mistake in their articles on this subject. Sandind correct that error in his article on the subject.
Your answers here are great, thanks. It seems intuitively obvious that the strength of the gravitational field increases with speed, and it likewise seems obvious that the Sun will not become a black hole with my speed relative to it. What I still don't grasp is, if the strength of the gravitational field can approach infinity with speed, beyond the point where reference frames (that is, space itself including the objects within the space) are drawn to the moving object at >= c, why is that not technically a black hole? Also, is it true that if a grain of sand grazed the Sun at close enough to c, then it could wreck the Sun given its large relativistic mass, which could be millions of times the mass of the Sun?
You're welcome zanket Good question. Not sure of a good answer. Consider the following though. The simplest event horizon I can think of is the so-called "Rindler Horizon" in an accelerating frame of reference. This corresponds to a locus of points in spacetime which delineates two regions of spacetime. One region corresponds to events above the event horizon and ther other region cooresponds to events below the event. photons from the region below cannot get to the region above. The reason for this is that photons below the event horizon cannot catch up to observers above it even though the observers are always moving more slowly. There is a diagram here on this point. See Fig. 1 at http://www.geocities.com/physics_world/sr/uniform_accel.htm The red line corresponds to an accelerating particle. The dashed line corresonds to the wordline of photons. Look at the top right section. The dashed line is a photon trying to cathc up to the particle which is represented by the red line. Therefore nothing to the left of of the diagram can send a photon to that particle and all particles in the region between the dashed lines (there are two of them one with slope +1 slope and the other with slope -1) Sounds right. Even a single photon can have a supermassive g-field given the right frame of referance
pmb, One question I have raised on this MSB before and didn't get an answer was if relative velocity does infact cause change in gravity of an object, what evidence, or lack of it, is there for high recession velocity galaxies. Some are in excess of 90%c. I think I know your answer but I will await your response.
I'm sorry but I don't understand the question. The evidence of such galaxies would be through spectroscopic data, i.e. redshift/doppler etc. I don't see how this pertains to gravity.
pmb, It would seem logical that should relative velocity alter mass, that we should see a trend of more massive galaxies as one moves further out into higher recession velocity galaxies. More mass would also mean more gravity.
Relative veclocity alters *inertial* mass. Not proper mass. When you speak of more massive galaxies what are you refering to as a measure of the mass? What does that have to do with redshift other than the further away the higher the redshift?
pmb, I have never seen anyone seperate mass into inertial and "proper". NOt saying you are wrong, just that I have never seen it done. It would seem to mean that you are claiming an object becomes harder to accelerate but doesn't display greater gravity. Is that correct, since I had thought you had said gravity also increased. Do you or do you not accept tha accelerating expansion of the universe? Do you not agree the more remote galaxies have higher recession velocities, upto and including some over 90 % c? At such high relative velocity do we or do we not observe a trend increase in galatic masses?
