On Sunday, July 12, 2020 at 12:35:32 PM UTC-6, Brent wrote: > > > > On 7/12/2020 12:37 AM, Alan Grayson wrote: > > > > On Saturday, July 11, 2020 at 10:30:21 PM UTC-6, Alan Grayson wrote: >> >> >> >> On Saturday, July 11, 2020 at 10:20:54 PM UTC-6, Brent wrote: >>> >>> >>> >>> On 7/11/2020 9:00 PM, Alan Grayson wrote: >>> >>> >>> >>> On Saturday, July 11, 2020 at 9:49:31 PM UTC-6, Brent wrote: >>>> >>>> >>>> >>>> On 7/11/2020 8:07 PM, Alan Grayson wrote: >>>> >>>> >>>> >>>> On Saturday, July 11, 2020 at 8:41:21 PM UTC-6, Brent wrote: >>>>> >>>>> >>>>> >>>>> On 7/11/2020 4:29 PM, Alan Grayson wrote: >>>>> >>>>> >>>>> >>>>> On Saturday, July 11, 2020 at 5:05:02 PM UTC-6, Brent wrote: >>>>>> >>>>>> >>>>>> >>>>>> On 7/11/2020 12:54 AM, Alan Grayson wrote: >>>>>> >>>>>> >>>>>> >>>>>> On Tuesday, July 7, 2020 at 10:06:44 PM UTC-6, Alan Grayson wrote: >>>>>>> >>>>>>> >>>>>>> >>>>>>> On Tuesday, July 7, 2020 at 8:50:50 PM UTC-6, Alan Grayson wrote: >>>>>>>> >>>>>>>> >>>>>>>> >>>>>>>> On Tuesday, July 7, 2020 at 8:05:28 PM UTC-6, Bruce wrote: >>>>>>>>> >>>>>>>>> On Wed, Jul 1, 2020 at 4:18 PM Alan Grayson <[email protected]> >>>>>>>>> wrote: >>>>>>>>> >>>>>>>>>> How, exactly, is the Principle of Equivalence used by Einstein to >>>>>>>>>> develop GR? TIA, AG >>>>>>>>>> >>>>>>>>> >>>>>>>>> >>>>>>>>> This lecture by Sean Carroll should answer all your questions: >>>>>>>>> >>>>>>>>> URL: https://wp.me/p2WMeM-3vl >>>>>>>>> >>>>>>>>> Bruce >>>>>>>>> >>>>>>>> >>>>>>>> I'll watch it tonight, but I think I've figured it out; >>>>>>>> specifically, the EP implies space-time is curved by the presence of >>>>>>>> mass/energy (and this is independent of the need to express the laws >>>>>>>> of >>>>>>>> physics in a coordinate independent way via tensors). AG >>>>>>>> >>>>>>> >>>>>>> Here's my reasoning regarding the EP; if an observer is in a box >>>>>>> subject to uniform acceleration, a beam of light starting on the >>>>>>> extreme >>>>>>> left side (moving transverse or perpendicular to the acceleration >>>>>>> vector), >>>>>>> will hit a lower point on the right side, showing that uniform >>>>>>> acceleration >>>>>>> results in curved paths in space-time. But if this result is identical >>>>>>> to >>>>>>> gravity, locally, it means that curved paths in space-time are produced >>>>>>> by, >>>>>>> or are equivalent to gravity. >>>>>>> >>>>>> >>>>>> That makes no sense. You're saying that because curved paths can be >>>>>> produced two different ways then they must always be produced the second >>>>>> way. >>>>>> >>>>>> >>>>>> BUT gravity is only observed in the presence of mass/energy. ERGO, >>>>>>> the EP implies mass/energy curves space-time. AG >>>>>>> >>>>>> >>>>>> And that's not even true. Gravitational waves can propagate thru the >>>>>> vacuum. The Schwarzschild solution is for empty space. De Sitter space >>>>>> is >>>>>> an empty cosmos. >>>>>> >>>>> >>>>> Light can propagate through empty space, but it can't arise from >>>>> nothing. Same presumably for gravitational waves. AG >>>>> >>>>> >>>>> Are you going to say the same thing about matter? electric charge? >>>>> >>>>> Brent >>>>> >>>> >>>> I'm not sure what your point is. All I was saying above is that >>>> mass/energy causes curvature of space-time as per the EP. A gravitational >>>> wave moving through empty space seems no different in principle than light >>>> moving through empty space. In both cases there is a mathematical solution >>>> for the wave motion, with the source of the wave left undefined. But every >>>> wave motion must has a source. AG >>>> >>>> >>>> And every source must have an origin? There is nothing in the >>>> equations that says there must be a source. >>>> >>>> Brent >>>> >>> >>> Can EM waves exist if there are no charges and currents? If you affirm, >>> has this ever been observed? This result, if it is a result, is likely an >>> artifact of the mathematics which has no basis in physical reality. Anyway, >>> are you claiming that spacetime curvature can exist in the absence of >>> matter/energy? Is this what the EP says? AG >>> >>> >>> It's what the equations say. So if waves only exist due to matter >>> sources that's a separate fact, not part of the theory. It seems just as >>> plausible to me that fields existed first and "stuff" appeared as quantized >>> waves in the fields. >>> >>> Brent >>> >> >> What do you find erroneous in my interpretation of the EP? I never heard >> it interpreted to mean that curvature of space-time is NOT caused by >> gravity. AG >> > > Are you claiming that because there are gravitational wave solutions to GR > in the absence of matter/energy, curvature of space-time isn't caused by, > or is equivalent to gravity? But how can there be curvature of space-time > in the absence of matter/energy > > > There can be because it's consistent with the equations. A black hole > doesn't include any matter. General relativity is non-linear, that's why > there can be non-flat cosmologies that contain no matter. Of course there > may be some different, better theory in which spacetime can't be curved > without matter...but it seems unlikely since we have good evidence that > gravitational waves exist. > > Brent >
Yes, good evidence that gravitational waves exist, but as far I know they're always associated with material interactions such as collisions of black holes. In the case of EM waves, I'd be more receptive of your claim that they can exist independent of charges and/or currents, but as far as I know there's no evidence of that. AG > > since, in this case, we're dealing with SR, wherein space-time has no > curvature? AG > >> >>> >>> >>> -- >>> 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 [email protected]. >>> To view this discussion on the web visit >>> https://groups.google.com/d/msgid/everything-list/3372804f-6bf6-44d4-9506-f73bf607e6e6o%40googlegroups.com >>> >>> <https://groups.google.com/d/msgid/everything-list/3372804f-6bf6-44d4-9506-f73bf607e6e6o%40googlegroups.com?utm_medium=email&utm_source=footer> >>> . >>> >>> >>> -- > 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 [email protected] <javascript:>. > To view this discussion on the web visit > https://groups.google.com/d/msgid/everything-list/728ae500-7bf1-4574-bbd6-3a8dae1c1606o%40googlegroups.com > > <https://groups.google.com/d/msgid/everything-list/728ae500-7bf1-4574-bbd6-3a8dae1c1606o%40googlegroups.com?utm_medium=email&utm_source=footer> > . > > > -- 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 [email protected]. To view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/e6336c1e-8e6f-475c-953d-bb80049e2a67o%40googlegroups.com.
