Recent content by gnnmartin

Thanks.

Thanks. I was aware of the M T &W's figure, but it is rather a 'third person' view annd not very quotable. The description I thought I remember reading talks about a first person view: someone in curved space visualising the coordinates. I thought I remembered a rather snappy quotable...

In curved space, geodesics are curved relative to lines which are straight in the coordinate system. I remember seeing a text book that illustrated the corollary, the coordinate lines 'swooping' through physical space. I wish to reference it. I thought it was in 'Gravitation' by Milner Thorn...

Thanks, very helpful.

Many thanks to all for your replies. I'm disappointed that nobody seems to have any sympathy with what I am trying to ask/say, but that in itself is useful to know. I'll continue to monitor this thread, and will respond to any post that adds something I find useful, but will otherwise retire...

You might assert here that 'local' means flat, but the person asking the question doubtless just uses 'local' in the everyday sense given in an English/American dictionary. We detect gravitational waves 'locally'. What you think of as flat becomes not-flat as your ability to measure improves...

It is my assumption when asked 'what is the local effect of the expansion of the universe' is that the enquirer seeks to find some difference in local physics, due to (to use your words) the deviation from 'flat' of space time in our neighbourhood consistent with an expanding universe. My...

Indeed, so you are giving the same answer as I am, but in different words. My answer was the difference is negligible. Your answer is because the expansion has a negligible effect on the local curvature. Both answers fail to acknowledge the underlying problem.

Can you show how, please? Choose different coordinates (T,X,YZ) parallel to the first (t,x,y,z), and let dX/dT=a.dx/dt, then the value of Sqrt(-g(X,X)/g(T,T) is the same as the value of Sqrt(-g(x,x)/g(t,t) so the ratio that I am calling 'the speed of light' remains unchanged.

No, I'm definitely interested in the physical speed, so not (dx/dt), but Sqrt(-g(x,x)/g(t,t), where the coordinates are locally orthogonal and isotropic.

Where does 'local' end? We notice locally the expansion of the universe by noting the red shift of distant stars, isn't that incompatible with 'The correct answer is "none"'?

Thank you. I am only interested in the effect of any such variation on the metric. I set out my argument in 7 steps. It would help me if you can say which step is illogical or meaningless. Or even if you think it nonsense. I agree with all your other comments, and apologise if I am careless...

Bill comes closest to my concern. I note that Wikipedia https://en.wikipedia.org/wiki/Variable_speed_of_light describes a number of papers exploring the possibility that the speed of light is not constant. I am not so interested in these theories per se, but rather in the implication for...

Many thanks for all your replies. I'm struggling to decide whether I just expressed myself badly, or am simply confusing myself. If I decide after all that I do have something I wish to clarify, I will post again.

I am interested in making an observation that involves the speed of light. It is widely stated that the speed of light is constant, but without saying what that means. I need to be precise, and would like a reference to an acknowledgement of the problem. When people talk about the speed of...