crowman

On 5/16/2023 at 10:09 PM, Genady said:

I think that the equality between Einstein tensor and stress-energy tensor dictates the spacetime geometry, i.e., the spacetime geometry is dictated by the equation rather than by its parts. IOW, the spacetime geometry is such that it makes these two parts equal.

Thanks Genady, I think that’s makes it a bit more clearer for me. IOW, It’s not a leap-frog situation with one part then the other part and so on.

On 5/17/2023 at 5:53 AM, Markus Hanke said:

 To fix a unique spacetime, you need to also supply the right number and kind of initial and boundary conditions; physically these conditions usually describe the distribution of distant sources (as opposed to local ones given by the energy-momentum tensor), as well as overall symmetries of the spacetime.

 

Thank you Markus. So, that would be like ending up with the spacetime geometry around a central symmetrical mass (sphere) Schwarzschild model.

On 5/12/2023 at 5:29 AM, Markus Hanke said:

It's not that GR modifies the background, it's that it does not have any background. It's a fully background-independent theory - in contrast to the other interactions.

Would a roundabout way of saying that be, there is no absolute spacetime and so no frame is special?

Hence, no background dependency when it comes to spacetime.

That’s how I’m making sense of it.

Something to do with the field equations being in two parts, the movements of mass / energy dictates the spacetime geometry and vice versa?

2 hours ago, Genady said:

You mean, non-Minkowskian rather than non-Euclidean. The latter could apply only to space.

Yes, you're right, thanks.

2 hours ago, Genady said:

Alternatively, it would be fair to say that space-time is Minkowskian but gravity affects all rulers and clocks in such a way that measured distances and times are distorted. Einstein field equation describes these distortions. 

On Earth, a thrown stone will naturally take a path that results in maximum ageing between launch and impact. The stone didn't read a clock or use a ruler.

I only say this because your  "gravity affects all rulers and clocks" leaves the backdoor open to calls of "it only affects the instruments of measurement."

Would it be fair to say that 'reality' certainly acts like space-time is a non-euclidean curved manifold, and that physics can't show that it's not? I don't know if that's a catch 22 or not?

10 hours ago, Markus Hanke said:

They fall “down” due to a principle called the principle of extremal ageing. This principle, in simple terms, implies that geodesics in spacetime tend to be the longest (in geometric terms) they can be, given all initial and boundary conditions. Since in an environment such as planet Earth the length of a free-fall geodesic is generally dominated by the time-term within the metric, this implies that such geodesics will tend to be oriented towards regions with higher time dilation, relative to some reference point far away. In other words - closer to the central body. This is why the apple falls down, rather than up - because this is what maximises the geometric length of its world line, given its initial and boundary conditions.

 

In my first post on this site, I was puzzled as to why an apple seeking to accumulate the greatest proper time on its wristwatch, would head ''down'' to where time is slower and hence slowing its accumulating of proper time. In other words, the apple is stopping its ageing by going ''down''.

Compounding my puzzlement, is that time dilation in the schwarzschild coordinates is only between stationary observers, that is, a stationary far away observer and a stationary ''shell'' observer near a black hole.

So, for the falling apple there is no time dilation to travel down to, so to speak.

If there was a slowing of time for the apple it would never reach the event horizon. help someone.

I'm muddled in my thinking and know it's down to my incorrect understanding of things.🙂

I hope you chaps don't mind me not saying anything in replies, but I'm reading your replies and learning new things.

All best

Howdy all.

Hello all.
The principle of Maximum ageing says a stone (with wristwatch) in free fall takes the path which accumulates the greatest proper time on the stone's wristwatch.
Time runs slower at at sea level than at the summit of Mt Everest.
When an apple falls from a tree, its path is down to the ground. Yet, this free fall path would slow the accumulation of the apple's proper time. What am I misunderstanding?