On Sat, Feb 22, 2014 at 3:37 PM, Edgar L. Owen <edgaro...@att.net> wrote:
> Jesse, > > But from the links you yourself provide: > http://adsabs.harvard.edu/abs/1985AmJPh..53..661O > > To quote from the abstract: > > 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 > increase 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 > Mrel=γ(1+β^2)M. Therefore, in the ultrarelativistic limit, the active > gravitational mass of a moving body, measured in this way, is not γM but is > approximately 2γM. > So this reference from the Harvard physics dept. says that the active > gravitational mass of a relativistically moving particle DOES INCREASE and > has a stronger gravitational attraction to what it is moving relative to. > > So that seems to contradict your own conclusion. > How so? > > Clearly from Harvard, the increased mass (relativistic mass) of a moving > object DOES have an increased gravitational attraction. So since > gravitational attraction is due to curvature of spacetime one can say that > from the POV (the frame) of the stationary observer, the moving object must > be curving spacetime more. > I don't believe there is any rule which says that "gravitational attraction" as they quantify it in the paper is proportional to any simple measure of the "amount" of spacetime curvature, and if there isn't then you can't say that a greater attraction in this sense implies "curving spacetime more". I imagine the the attraction depends on the way in which the curvature tensor varies at different points along the object's path through spacetime. Jesse > > Correct? > > Edgar > > > > > Read more: http://www.physicsforums.com > > On Wednesday, February 19, 2014 10:32:07 AM UTC-5, jessem wrote: >> >> The curvature of spacetime is understood in a coordinate-invariant way, >> in terms of the proper time and proper length along paths through >> spacetime, so it doesn't depend at all on what coordinate system you use to >> describe things. Physicists do sometimes talk about the "curvature of >> space" distinct from the curvature of spacetime, I'm not sure if you meant >> to distinguish the two or were treating them as synonymous. But defining >> the curvature of space depends on picking a simultaneity convention which >> divides 4D spacetime into a series of 3D slices, and then defining the >> curvature of each slice in terms of proper length along spacelike paths >> confined to that slice. So the "curvature of space" is >> coordinate-dependent, since different simultaneity conventions = different >> slices with different curvatures. >> >> I don't know if there's any meaningful sense in which picking a >> coordinate system where an object has a higher velocity means it curves >> space "more"--if there is, it would presumably depend on a choice to >> restrict the analysis to some family of coordinate systems where each >> possible velocity would be associated with a particular choice of >> simultaneity convention, rather than using any of the arbitrary smooth >> coordinate systems (with arbitrary simultaneity conventions) that are >> permitted in general relativity. >> >> I found some discussion of the issue of how velocity relates to curvature >> and gravitational "force" on these pages: >> >> http://physics.stackexchange.com/questions/95023/does-a- >> moving-object-curve-space-time-as-its-velocity-increases >> >> http://www.physicsforums.com/showthread.php?t=602644 >> >> >> On Wed, Feb 19, 2014 at 9:15 AM, Edgar L. Owen <edga...@att.net> wrote: >> >>> Russell, Brent, Jesse, et al, >>> >>> The "increased kinetic energy of the particle" is not due to its >>> acceleration but to its relative velocity to some observer. Mass also >>> increases with relative velocity, but that apparent increase in mass is >>> only with respect to some observer the motion is relative to. In fact all >>> kinetic energy is only with respect to relative velocity with some observer >>> frame. >>> >>> So this means that any increased curvature of space from that increased >>> kinetic energy and increased mass should be only with respect to observers >>> it is in relative motion with respect to. >>> >>> So in this case we seem to have a case in which the curvature of space >>> is relative rather than being absolute. >>> >>> Would you not agree? >>> >>> Edgar >>> >>> >>> >>> On Tuesday, February 18, 2014 4:44:58 PM UTC-5, Russell Standish wrote: >>>> >>>> On Tue, Feb 18, 2014 at 01:28:09PM -0500, John Clark wrote: >>>> > On Sun, Feb 16, 2014 at 12:54 PM, Edgar L. Owen <edga...@att.net> >>>> wrote: >>>> > >>>> > > >>>> > > >> You say that "You can tell if spacetime is curved or not by >>>> observing >>>> > >> if light moves in a straight line or not." and then you say that >>>> light does >>>> > >> NOT travel in a straight line in the accelerating elevator example >>>> you give. >>>> > >> >>>> > > >>>> > > > So, by your terminology, does that mean that the acceleration of >>>> the >>>> > > elevator IS curving space ? >>>> > > >>>> > >>>> > You should stop talking about "space", it's "4D spacetime"; but yes >>>> it's >>>> > curved, although if you were inside that sealed elevator you couldn't >>>> tell >>>> > if the curvature was caused by rockets accelerating the elevator in >>>> deep >>>> > space or if it was caused by the Earth's gravity. Acceleration is >>>> absolute >>>> > in that there is no need to look outside your reference frame to >>>> detect it, >>>> > but according to General Relativity there is no way to tell the >>>> difference >>>> > between it and being in a gravitational field. >>>> > >>>> > >>>> > > > It seems like you might be saying that the acceleration does >>>> curve space >>>> > > >>>> > >>>> > Yes. >>>> > >>>> >>>> In which theory? IIUC, acceleration of an infinitesimal point particle >>>> does not change the curvature of space. And acceleration of a massive >>>> particle only changes the curvature by the amount due to the increased >>>> kinetic energy of the particle. >>>> >>>> >>>> -- >>>> >>>> ---------------------------------------------------------------------------- >>>> >>>> Prof Russell Standish Phone 0425 253119 (mobile) >>>> Principal, High Performance Coders >>>> Visiting Professor of Mathematics hpc...@hpcoders.com.au >>>> University of New South Wales http://www.hpcoders.com.au >>>> ---------------------------------------------------------------------------- >>>> >>>> >>> -- >>> You received this message because you are subscribed to the Google >>> Groups "Everything List" group. >>> To unsubscribe from this group and stop receiving emails from it, send >>> an email to everything-li...@googlegroups.com. >>> To post to this group, send email to everyth...@googlegroups.com. >>> Visit this group at http://groups.google.com/group/everything-list. >>> For more options, visit https://groups.google.com/groups/opt_out. >>> >> >> -- > You received this message because you are subscribed to the Google Groups > "Everything List" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to everything-list+unsubscr...@googlegroups.com. > To post to this group, send email to everything-list@googlegroups.com. > Visit this group at http://groups.google.com/group/everything-list. > For more options, visit https://groups.google.com/groups/opt_out. > -- You received this message because you are subscribed to the Google Groups "Everything List" group. 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