I see. TY. Let's assume AE was aware of what you write after he developed SR. That is, assume he knew that the laws of physics are NOT invariant when one or more frames are non-inertial. What prompted him to developed a theory, GR, based on tensors where the laws of physics* are *invariant under coordinate transformations? Based on your comments, it would seem that a theory which* is* invariant for non-inertial frames, namely GR, is impossible.AG
On Friday, November 18, 2022 at 11:03:17 PM UTC-7 jessem wrote: > If both frames are inertial, any relativistic laws will have the same form > under the coordinate transformation. If either is non-inertial, then there > is no reason to expect the laws to have the same form. What allows us to > say that SR still applies is that all predictions about physical, > coordinate-independent facts, like the proper time elapsed on a given > worldline between two events on that worldline, will be exactly the same as > the predictions made by inertial observers. > > As an analogy, we could use some non-Cartesian coordinate system on a > Euclidean plane, like one with curved coordinate axes, but shapes on the > plane would still be said to obey the rules of Euclidean geometry even if > some of the formulas that work in Cartesian coordinate systems don't work > in this non-Cartesian coordinate system. For example, in a Cartesian > coordinate system, if you have a straight line segment whose ends are at > coordinates (x1, y1) and (x2, y2), then the length of the line segment will > be given by (x2 - x1)^2 + (y2 - y1)^2, but this formula won't work if you > describe the selfsame line segment in a non-Cartesian coordinate system. > > On Sat, Nov 19, 2022 at 12:11 AM Alan Grayson <[email protected]> wrote: > >> Are you claiming that we can have two coordinate systems, one or both >> non-inertial, and a transformation from one to another such that the laws >> of physics will have the same form under this transformation? Is so, what >> allows us to say "SR can be applied to non-inertial frames"? What has SR to >> do with this result? AG >> >> On Friday, November 18, 2022 at 4:26:20 PM UTC-7 jessem wrote: >> >>> If you have two coordinate systems A and B, and you know the coordinates >>> of some physical event in system A, then the coordinate transformation can >>> give you the coordinates of the same event in system B--the transformation >>> is just a mapping from one system to the other. But from what I understand >>> you can use the same coordinate transformation not just for individual >>> events, but for dynamical laws expressed in system A (as differential >>> equations, perhaps), giving equations for the same physical laws expressed >>> in system B. So if someone has the coordinates of some initial >>> configuration of matter in system A, along with the dynamical laws >>> governing that matter in system A, then we can use the transformation to >>> get the equivalent initial configuration in system B, and the equivalent >>> dynamical laws in B. And then if someone uses the initial conditions and >>> laws in A to predict later events, and someone else uses the initial >>> conditions and laws in B to predict later events, all their predictions >>> will correctly map to one another using the same coordinate transformation. >>> >>> To say some laws of physics are "Lorentz invariant" means if you write >>> down the laws in one inertial frame A and then apply the Lorentz >>> transformation to see the equivalent laws in a different inertial frame B, >>> the equations will have exactly the same form in both frames. If you >>> transform the dynamical laws into a non-inertial frame C, the equations >>> won't generally have the same form, but they are still the same >>> relativistic laws and will yield predictions about later events that map >>> correctly back to what the inertial observer predicts, for example if the >>> inertial observer predicts two physical clocks will cross paths when one >>> shows a proper time of 15 seconds and the other shows a proper time of 40 >>> seconds, then the non-inertial observer will get the same prediction. >>> >>> On Fri, Nov 18, 2022 at 5:16 AM Alan Grayson <[email protected]> >>> wrote: >>> >>>> Thanks for that! You seem to know the subject well. What exactly does >>>> it *mean* to say SR can be used for non-inertial frames? Or, do you >>>> deny the claim that SR *can* be used for non-inertial frames? AG >>>> >>>> On Thursday, November 17, 2022 at 8:25:41 AM UTC-7 jessem wrote: >>>> >>>>> The Lorentz transformation is specifically meant for transforming >>>>> between inertial frames, it can't generally be used to transform between >>>>> non-inertial frames (you could construct a pair of non-inertial >>>>> coordinate >>>>> systems that were related by the Lorentz transformation if you wanted, >>>>> just >>>>> like you could construct a pair of non-inertial frames related by the >>>>> Galilei transformation or whatever transformation you wish--as I said to >>>>> John Clark, there's no 'canonical' way to construct a non-inertial >>>>> coordinate system in relativity, you can define one basically however you >>>>> like). However, all the physical consequences of the postulate that the >>>>> laws of physics are Lorentz-invariant can be specified in terms of >>>>> different equations that would apply in a non-inertial frame, and these >>>>> equations can be derived by using whatever coordinate transformation was >>>>> used to define the non-inertial frame's coordinates relative to an >>>>> inertial >>>>> coordinate system. >>>>> >>>>> On Thu, Nov 17, 2022 at 8:07 AM Alan Grayson <[email protected]> >>>>> wrote: >>>>> >>>>>> Jessem: I was wondering if the LT can be used to determine how the >>>>>> laws of physics change between two accelerating frames, accelerating at >>>>>> the >>>>>> same rate but moving in opposite directions. AG >>>>>> >>>>>> On Wednesday, November 16, 2022 at 7:58:31 AM UTC-7 jessem wrote: >>>>>> >>>>>>> That doesn't address my specific question about whether you define >>>>>>> the "predictions of SR" in terms of the same specific equations that >>>>>>> work >>>>>>> in inertial frames, like the time dilation equation delta-tau = delta-t >>>>>>> * >>>>>>> sqrt(1 - v^2/c^2), or whether you would define the predictions of SR in >>>>>>> terms of new equations for the non-inertial frame (which could be >>>>>>> obtained >>>>>>> by applying a coordinate transformation that maps the coordinates of an >>>>>>> inertial frame to those of the non-inertial frame). >>>>>>> >>>>>>> On Wed, Nov 16, 2022 at 5:18 AM Alan Grayson <[email protected]> >>>>>>> wrote: >>>>>>> >>>>>>>> And when I used the word "true", I just meant that no observations >>>>>>>> exist which contradict the predictions of SR. AG >>>>>>>> >>>>>>>> On Tuesday, November 15, 2022 at 11:09:25 PM UTC-7 Alan Grayson >>>>>>>> wrote: >>>>>>>> >>>>>>>>> >>>>>>>>> I just mean, if both frames are accelerating at the same rate, >>>>>>>>> will the v in the LT, be the instantaneous relative velocity? AG >>>>>>>>> On Tuesday, November 15, 2022 at 11:05:42 PM UTC-7 Alan Grayson >>>>>>>>> wrote: >>>>>>>>> >>>>>>>>>> Specifically, will the time dilation of a clock in an >>>>>>>>>> accelerating frame, be the same as a clock as measured for a clock >>>>>>>>>> in a the >>>>>>>>>> observer's accelerating frame, where v in the LT is the >>>>>>>>>> instantaneous >>>>>>>>>> velocity of the clock in the observer's frame at every time t in the >>>>>>>>>> observer's frame? >>>>>>>>> >>>>>>>>> >>>>>>>>>> >>>>>>>>>> On Tuesday, November 15, 2022 at 10:54:06 PM UTC-7 Alan Grayson >>>>>>>>>> wrote: >>>>>>>>>> >>>>>>>>>>> By "valid", I mean "true". IOW, is SR limited to >>>>>>>>>>> non-accelerating frames? If the frames are accelerating, will the >>>>>>>>>>> LT still >>>>>>>>>>> hold for relating the laws of physics between those frames? AG >>>>>>>>>>> On Tuesday, November 15, 2022 at 9:58:27 PM UTC-7 jessem wrote: >>>>>>>>>>> >>>>>>>>>>>> It depends what you mean by "valid". Certainly all the physical >>>>>>>>>>>> laws of relativity such as time dilation can be expressed in a >>>>>>>>>>>> non-inertial >>>>>>>>>>>> coordinate system, like Rindler coordinates. But the equations >>>>>>>>>>>> expressing >>>>>>>>>>>> these laws will not be the same in non-inertial coordinate >>>>>>>>>>>> systems, for >>>>>>>>>>>> example you can no longer assume that a clock moving at constant >>>>>>>>>>>> coordinate >>>>>>>>>>>> velocity for a coordinate time interval of delta-t will elapse a >>>>>>>>>>>> proper >>>>>>>>>>>> time of delta-tau = delta-t * sqrt(1 - v^2/c^2). >>>>>>>>>>>> >>>>>>>>>>>> On Tue, Nov 15, 2022 at 9:50 PM Alan Grayson < >>>>>>>>>>>> [email protected]> wrote: >>>>>>>>>>>> >>>>>>>>>>>>> Wormholes have nothing to do with my question. Please answer >>>>>>>>>>>>> the question defining this thread. TY. >>>>>>>>>>>>> >>>>>>>>>>>>> On Tuesday, November 15, 2022 at 1:00:50 PM UTC-7 >>>>>>>>>>>>> [email protected] wrote: >>>>>>>>>>>>> >>>>>>>>>>>>>> A stable wormhole requires threading by negative energy >>>>>>>>>>>>>> density. Since no such negative energy field is know and it's >>>>>>>>>>>>>> existence >>>>>>>>>>>>>> would imperil the stability of matter, its existence seems >>>>>>>>>>>>>> highly unlikely. >>>>>>>>>>>>>> >>>>>>>>>>>>>> Brent >>>>>>>>>>>>>> >>>>>>>>>>>>>> >>>>>>>>>>>>>> On 11/15/2022 11:17 AM, spudboy100 via Everything List wrote: >>>>>>>>>>>>>> >>>>>>>>>>>>>> Me: Forget acronyms, or even Einstein's gravitic Reference >>>>>>>>>>>>>> Frame dragging (His movie reel analogy), Instead ask yourselves >>>>>>>>>>>>>> are these >>>>>>>>>>>>>> physicists correct in proposing that some black holes are >>>>>>>>>>>>>> wormholes? >>>>>>>>>>>>>> >>>>>>>>>>>>>> Objects We Thought Were Black Holes May Actually Be >>>>>>>>>>>>>> Wormholes, Scientists Say (futurism.com) >>>>>>>>>>>>>> <https://futurism.com/objects-black-holes-wormholes> >>>>>>>>>>>>>> >>>>>>>>>>>>>> For this science fiction boy, I say interesting and maybe, >>>>>>>>>>>>>> hopeful? Let the hard science Bohr flavor of quantum mechanics >>>>>>>>>>>>>> and >>>>>>>>>>>>>> relativity yield for in objection, how this is fictional, >>>>>>>>>>>>>> improbable, and >>>>>>>>>>>>>> crapola? For reference frames, I know Einstein locked this in >>>>>>>>>>>>>> with time, >>>>>>>>>>>>>> which he discussed with Michele Besso (remember the letter to >>>>>>>>>>>>>> Beso's >>>>>>>>>>>>>> family?) but otherwise, how valuable to astronomers and >>>>>>>>>>>>>> physicists is ref >>>>>>>>>>>>>> frame dragging and all that? Does it predict do you think? >>>>>>>>>>>>>> >>>>>>>>>>>>>> The validity of a science is its ability to predict-Vanevar >>>>>>>>>>>>>> Bush. >>>>>>>>>>>>>> >>>>>>>>>>>>>> >>>>>>>>>>>>>> -----Original Message----- >>>>>>>>>>>>>> From: Alan Grayson <[email protected]> >>>>>>>>>>>>>> To: Everything List <[email protected]> >>>>>>>>>>>>>> Sent: Tue, Nov 15, 2022 1:30 pm >>>>>>>>>>>>>> Subject: Re: Is Special Relativity valid for accelerating >>>>>>>>>>>>>> frames of reference? TY. >>>>>>>>>>>>>> >>>>>>>>>>>>>> RA. >>>>>>>>>>>>>> >>>>>>>>>>>>>> On Tuesday, November 15, 2022 at 6:19:02 AM UTC-7 >>>>>>>>>>>>>> [email protected] wrote: >>>>>>>>>>>>>> >>>>>>>>>>>>>> On Tue, Nov 15, 2022 at 6:38 AM Alan Grayson < >>>>>>>>>>>>>> [email protected]> wrote: >>>>>>>>>>>>>> >>>>>>>>>>>>>> >>>>>>>>>>>>>> *> IHA = ?* >>>>>>>>>>>>>> >>>>>>>>>>>>>> >>>>>>>>>>>>>> I Hate Acronyms. >>>>>>>>>>>>>> >>>>>>>>>>>>>> John K Clark See what's on my new list at Extropolis >>>>>>>>>>>>>> <https://groups.google.com/g/extropolis> >>>>>>>>>>>>>> 8gfk >>>>>>>>>>>>>> >>>>>>>>>>>>>> >>>>>>>>>>>>>> -- >>>>>>>>>>>>>> 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/a67cbbac-69e0-40a9-8ee2-8e0caeb344d5n%40googlegroups.com >>>>>>>>>>>>>> >>>>>>>>>>>>>> <https://groups.google.com/d/msgid/everything-list/a67cbbac-69e0-40a9-8ee2-8e0caeb344d5n%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/2142008288.338975.1668539879975%40mail.yahoo.com >>>>>>>>>>>>>> >>>>>>>>>>>>>> <https://groups.google.com/d/msgid/everything-list/2142008288.338975.1668539879975%40mail.yahoo.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/527ac7d6-ada8-422f-b93f-df5b974da65fn%40googlegroups.com >>>>>>>>>>>>> >>>>>>>>>>>>> <https://groups.google.com/d/msgid/everything-list/527ac7d6-ada8-422f-b93f-df5b974da65fn%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/e1136ae4-4886-4cdb-aaa3-ca1e47a1b08fn%40googlegroups.com >>>>>>>> >>>>>>>> <https://groups.google.com/d/msgid/everything-list/e1136ae4-4886-4cdb-aaa3-ca1e47a1b08fn%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/d32ead9c-ef89-4ac3-9518-27b53350c7fdn%40googlegroups.com >>>>>> >>>>>> <https://groups.google.com/d/msgid/everything-list/d32ead9c-ef89-4ac3-9518-27b53350c7fdn%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/84db6bd9-1d24-4d74-a25d-6f18199788fbn%40googlegroups.com >>>> >>>> <https://groups.google.com/d/msgid/everything-list/84db6bd9-1d24-4d74-a25d-6f18199788fbn%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/bc6034d9-70cd-45d3-ad15-e6575f6bd662n%40googlegroups.com >> >> <https://groups.google.com/d/msgid/everything-list/bc6034d9-70cd-45d3-ad15-e6575f6bd662n%40googlegroups.com?utm_medium=email&utm_source=footer> >> . >> > -- You received this message because you are subscribed to the Google Groups "Everything List" group. 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