Differences between GR & SR are frame-dependent

[pixchips]

Hi All - can't follow all this, but maybe I can pick up some terminology. To wit: 'massless test particle"? You called it non-physical ... so it's a mathematical construct to test something? What exactly is it testing? (My guess - massive particles don't follow the Hubble flow because of their inertia, so a massless particle would just 'go with the flow' - can't be a real massless particle since it would have to tool around at c all the time.) Also: "peculiar velocity" seems to be the velocity relative to the 'Hubble Flow', which seems to be the 'average' motion of space due to expansion. But you seem to say that in some coordinate systems there is no expansion ... is the coordinate system expanding?? Okay, that's enough for now ... sorry to intrude, but sometimes the kids listen in when the adults are talking, and they have questions.

 

[jonmtkisco]

Hi pixchips, good questions:

Hi All - can't follow all this, but maybe I can pick up some terminology. To wit: 'massless test particle"? You called it non-physical ... so it's a mathematical construct to test something? What exactly is it testing?

The only reason to refer to the test particle as "massless" is to make it clear that for the purposes of this exercise we're ignoring any effects caused by the active gravity of the test particle itself. It is not intended to imply that the test particle does not feel the effect of gravity from other objects. Nor is intended to imply that the test particle is relativistic, such as a photon.

Also: "peculiar velocity" seems to be the velocity relative to the 'Hubble Flow', which seems to be the 'average' motion of space due to expansion.

Correct.

But you seem to say that in some coordinate systems there is no expansion ... is the coordinate system expanding??

A "proper distance" coordinate system does not expand, so observers moving apart in the Hubble flow measure each other as moving apart in these coordinates. On the other hand a "comoving" coordinate system can be thought of as expanding exactly in synch with the Hubble flow. So all comoving observers are considered to be "at rest" with respect to each other, even though the proper distance between observers increases over time due to the Hubble flow.

Hope that helps.

Jon

 

[pixchips]

Yes, thanks. The co-moving coordinate system is a new concept for me. It would perhaps be like drawing a cross hatched x-y coordinate (latitude/longitude) system on a balloon and then blowing up the balloon? Things stuck to the balloon, at rest relative to its surface, separate as the balloon expands relative to a proper distance frame but don't move relative to the cross hatch pattern I drew on the balloon. The cross hatch is the comoving coordinate system? So this is a mathematical convenience to help talk about things relative to the Hubble Flow? In this coordinate system geometric relations are fixed, but scale is constantly changing? Hmmm ... I need to grok this ...

Simple example: two comoving charges would have a force between them that goes as 1/'proper distance'^2. To change to the comoving coordinate system, I would need to change Maxwell's equations ... but how can I do that? If they are comoving (I don't know what's got them glued in place, but for sake of argument ...), then in the comoving coordinate system the distance doesn't change. So my law for attraction of charges would then be dependent on distance and time ... I do not grok this ...

 

[jonmtkisco]

Hi pixchips,

Your description of comoving coordinates is basically right. The "dots on a balloon" model is one of the standard analogies used to describe this concept, although it's explanatory power is subject to some important limitations. If you haven't, check out Wikipedia on http://en.wikipedia.org/wiki/Metric_expansion_of_space" .

I'm not the best one to give a technical answer to your questions about Maxwell's equations. But I think that conceptually, Maxwell's equations will need to be recalculated at each instant in time, to address the fact that two massive objects are moving apart from each other. In everyday terms, the Hubble flow is so tiny at the distances over which electromagnetism is significant that it makes no significant difference. And if two charged objects are close enough to be electromagnetically (or gravitationally) bound together, they don't move apart.

Jon

 

[pixchips]

Thanks ... yeah, I knew about the balloon, but nobody drew a coordinate system on it and called it the comoving coordinate system.. Anyway, just hooked into a couple much deeper references (for me anyway) and I'm working through those. Thanks for your attention.