I've retrieved a video in which Dan Fleisch explains Tensors. It's short and there's no complicated mathematics!
To paraphrase Dan, the power of Tensors lies in the fact that they allow observers in different frames of reference to agree on the facts of the universe.
To paraphrase Dan, the power of Tensors lies in the fact that they allow observers in different frames of reference to agree on the facts of the universe.
In Newton's theory of gravity, the gravitational force only affects objects with inertial mass. Inertial mass is the resistance to acceleration given by the m in F = ma.
In Einstein's general relativity, the curvature of spacetime also affects photons which have have no inertial mass. Photons have no resistance to acceleration, always travelling at the fastest possible speed through space.
Einstein's theory permits that which Newton's theory would forbid!
https://sciencing.com/wave-particle-duality-an-overview-13725853.html
"Einstein's theory permits that which Newton's theory would forbid!":
Permits untestable nonsense;-?-: # 730, # 738
Permits untestable nonsense;-?-: # 730, # 738
Attachments
A singularity, ie a divide by zero kinda thing, is very hard to wrap your head around.
dave
Yes it is, but remember it can sometimes still be defined if we take the differential of the expression per L'Hopital's Rule.
We have to accept that there is a lot of nonsense going on in "mathematics" that is not consistent with logic or observation;-)
... such as the bending of illusions, reveries;-)
Perhaps black holes enclose vacuum energy.
"Vacuum energy" is decribed as a "material that results from squeezing matter as much as possible without breaking Einstein’s equations, thus avoiding a singularity."
Not so much a stretch of the imagination as a squeeze of the imagination! 😀
Quote from A Briefer History of Time by S. Hawking with L. Mlodinow:
"General relativity must be altered. By predicting points of infinite density - singularities - general relativity predicts its own downfall."
The reason that all experiments thus far have supported general relativity is because all the gravitational fields we normally experience are weak.
In the presence of the strong fields associated with black holes the effects of quantum theory should be important.
A quantum theory of gravity would open up the possibility that there are no singularities at which the laws of physics break down.
"General relativity must be altered. By predicting points of infinite density - singularities - general relativity predicts its own downfall."
The reason that all experiments thus far have supported general relativity is because all the gravitational fields we normally experience are weak.
In the presence of the strong fields associated with black holes the effects of quantum theory should be important.
A quantum theory of gravity would open up the possibility that there are no singularities at which the laws of physics break down.
That's the very study!
The claim is that there is no need to add anything new to the universe as a source for dark energy - black holes are the dark energy!
If you are talking about the Cosmological Coupling (*) in Cumbb's link, then the hypothesis (and it is just a hypothesis!) further suggests that "cosmological coupling" applies to all material objects in the universe, even we human beings!
In our case, however, the coupling is so weak that we cannot see its effects. So, if you've put on a few pounds recently, you can't blame it on "cosmological coupling". 😀
(*) According to the study, black holes don't only get more massive by merging with each other, but their masses are somehow "cosmologically coupled" to the expansion of the universe i.e. the more the universe expands, the more massive black holes become!
There is junk science (e.g. Astrology), speculative science (e.g. Magazine stuff) and solid science (e.g. Solidly written and Peer reviewed by experts). However it is the nature of science that all of it is unproven.
But, IMO, it is usually best to focus on the good stuff, the stuff that seems to work.
Consider the Kerr Black Hole, which was a major discovery in 1963 for the few people interested in Black Holes at the time:
https://www.cantorsparadise.com/the-genesis-of-kerr-solution-dd778e6be598
You can visualise this solution, which seems to represent the majority of Black Holes:
Naturally I simplify and deconstruct it to glimpse an underlying mathematical pattern, and to guess what will happen next:
I was wanting to talk about the Euclid Space Telescope, but generally find that mentioning 2 topics in one post confuses people.
But, IMO, it is usually best to focus on the good stuff, the stuff that seems to work.
Consider the Kerr Black Hole, which was a major discovery in 1963 for the few people interested in Black Holes at the time:
https://www.cantorsparadise.com/the-genesis-of-kerr-solution-dd778e6be598
You can visualise this solution, which seems to represent the majority of Black Holes:
Naturally I simplify and deconstruct it to glimpse an underlying mathematical pattern, and to guess what will happen next:
I was wanting to talk about the Euclid Space Telescope, but generally find that mentioning 2 topics in one post confuses people.