geordief

Yes ,you draw a triangle on the flat water and measure the 3 angles. If they add up to 180 it is flat . Less and it is a positive curvature ;more and it is negative (like a saddle) And ,less obviously you can do the same in 3d(perhaps using a 2d surface embedded in the 3d in the same way) Not sure how you would do it in 4d spacetime.

OK .So can subsets of the physical universe (eg the solar system) be described as "local" or "global"? Does "local" only describe the model and not the physical objects it attempts to model? And are we talking about spacetime curvature or the topology of the physical (subsets of the) universe? I think I was talking about just topology in that last post(even if I used terminology that applies normally to spacetime curvature) ie is there such a thing as local topography versus global topography?

very distant= still local ? That wouldn't be evidence of a global topology, would it? The observable universe is still "local" isn't it? Does the maths you are referring to make any physical predictions or is it entirely " theoretical"? ("theoretical" in layman's speak)

How do we know that a global topology exists at all and that we don't just have a patchwork of local topologies?

Are there any physical models that do that with posited versions of an actual universe? Are there any models that picture such a universe "from a bird 's eye view"? Or is that just an illogical question to ask?(the "bird"/observer being part of the universe could not take a "bird's eye view" of itself as a part of the whole)

Can we populate the surface of that 2d model of a sphere with 3d objects of an imaginary universe which is posited to be edgeless and bounded? How would I see in the model that the objects were 3d if they were embedded in the 2d surface?

Is this a space with no time component? A space that is ready to be populated with objects? I think I am more familiar with a space that is created by objects reconfiguring themselves(in an overall expansionist way as per observations) I think that is the orthodox view even if I am not up to speed with it. It still seems difficult for me to imagine the 3d universe existing on the 2d surface of the sphere There doesn't seem to be room for the 3 dimensions. Is it just an analogy? And the universe is not hollowed out ,is it?)unless the "hollow" is somehow the past history-surely not that)

The difficulty I have is of picturing a topology for a universe that has no edge or boundary. It seems others don't have that problem or perhaps they have enough of a mathematical understanding of the possibilities that they don't need to have a mental picture Would I be right to think that a topology doesn't require any particular shape but it just describes the way parts of the whole connect with each other?

How many different kinds of topology are possible for the universe? Would these topologies depend on more than the spacetime curvature? Are they all expanding ,contacting ,steady state? Any other ways to distinguish between different candidate topologies?

Interesting, though that apparently Laplace and Mitchell (1815?) considered the idea of a Black Hole.They must have thought light had some mass,I suppose.

is the topology not a function of spacetime curvature? (perhaps the "curvature" description of the topology gave me the wrong idea) What might cause different topologies to arise?

Did/does Newtonian physics predict something similar?(light returning to sender) Wasn't there someone before Einstein who also predicted that light would be affected by gravity?

It is understood that the 7th out of every ten gave as a reason that number 6 had told them so. It is not known who was the original source of the information.

Not the Court system,I think. The Secretary of State in this case.

"You can't catch me" Nobody's fool.

Not really.I think I have heard this from time to time but can't remember where I did. Not recently ,anyway.

Especially Thanks.(I hope nobody took the use of the word literally ,as in time travel.I just used it as a turn of phrase) Thanks.It doesn't seem that extraordinary to my untrained ears. Would probability equations in QM normally have a time component?(it comes as a surprise to me that they would but I only aspire to a layman status )

I don't "mean" anything.I am asking a question. You seem to be suggesting that the question is trivial and might as well be considered in macro systems. I have no way of knowing if that is right or wrong as I don't have the expertise.

Is it just that there are some interactions where reversing the time signature in the maths doesn't change the outcome?(I am fairly sure I have heard this more than a few times)

I think I have read that there are circumstances where ,at the quantum level the direction of time does not apply. Is this is true ,is it just for limited circumstances or is it across the board? Do perhaps quantum systems evolve in time generally but some do not?

Can a scenario involving only quantum objects be modeled using spacetime diagrams and their frames of reference? Is it ever done? Would there be a need? I understand that special relativity is used in such scenarios.

Well a frame of reference can have its origin tied to a physical point in space (even though ,I think it applies generally and not to one in particular) If ,though the frame of reference with a spatiotemporal origin coinciding with a quantum object is populated with other physical quantum objects then it seems to me that it is not simple to map their positions onto the frame of reference I did have a look at @MigL video and perhaps I begin to see how some circles can be squared. So perhaps frames of reference can apply to physical scenarios where objects' position and momentum are not separately defined? Might one map objects' combined states into a Minkowski like frame of reference chart? (Eg position and momentum combined) As to the parsing of my phrase ,"Does a frame of reference have to be applicable to a potential physical scenario to be physically valid?” .... I had thought first of writing "Does a frame of reference have to be applicable to a potential physical scenario to be valid?” Maybe the second "physically" made it less comprehensible?

Ok.I am a bit of a literalist myself.If someone greets me in the street with a "How are you?" my reflex is to wonder how I am and to communicate my state of being with the person

There could never be two physical objects at rest wrt each other could there? Does a frame of reference have to be applicable to a potential physical scenario to be physically valid?

Which came first ,religions with a soul or religions without a soul? Is there a connection between the two belief systems? Or do we call them both "religions" out of laziness . Is there a better word that would describe all the world's "religions"?