To be precise, it wasn't 't' (a measure of time, as time) in that, but T (a measure of time, as spacetime) in formulae. [...] One way you can do this is to use "-t^2", another way is to use "+T^2" where T=i.t. And, besides, it was dT.
So, what about =0 not being time-like, but light-like?
Error in my terminology, I think.
Surely there must be some sort of reference out there in the Worldwide Web?
I'm sure, but my Google-Fu fails me on searching when the only known information (that doesn't send you onto mostly unrelated Wiki pages) is bare equations. I learnt it from blackboards[1] and word of mouth and perhaps the occasional reference to the appropriate text books, that I've long since forgotten the author of, but used to roll off my tongue like "Kernighan And Ritchie" did.
[1] For the younger people out there, these are like white-boards, only black, and made of wood, not plastic. And don't worry about it being hard to see black pen on a black board, because they thought of that, and used white chalk which both sticks to wood (in an erasable way similar to white-board pen does for white-boards)
and shows up against the black background. Whoda thunk it! They were ingenious people, in the old days.
Are we talking about the event horizon or the singularity, please?
I have discussed the singularity (mostly in the context of it not existing, because space curves asymptotically, but here I was discussing the EH.
What? I don't believe in FTL either.
Sorry, that was understood, I was just making sure you knew I didn't, either (under 'known universe' conditions, at least... what's shrouded behind an EH might well be another matter).
You don't actually plug in the escape velocity into any formulas, because in that case there is nothing that actually has that velocity.
I was going to say "except for orbital calculations", but as v
e is "gets to infinity" (or 'out of your gravity well and into an adjacent one in a sufficiently short amount of time') and attaining different orbits needs only sub-v
e velocity (or, more usually with actual rockets, a near-continuous impulse of thrust that only need get the craft continuously gaining altitude and eventually to the orbit velocity required, while not running our of fuel), I suppose I better take that back.
I'm actually very interested in 'special case' border situations, though. For example, the universe is expanding and (at one time, and still is in some camps) it was very much a question of whether it had enough outward expansion to continue forever, or if it didn't and it would Big Crunch[2]. But I always wondered about a universe which had the precise quanta of energy that lay between the two extremes. One less, and it would Crunch, one more and it was a definite infinitely expanding and heat-death-fated universe... Of course, it's like rolling a perfectly round ball up a crazy-golf hillock in a frictionless and resistanceless environment. You could
never get it to sit precisely at the top, because if it was still moving enough to move
onto the point of equilibreum, it would move over that point and down the other side. It could take a long time if it had been slowed to a near infinitesimal speed as it reached an point infinitesimally before the 'flat' top, but it would still continue when it got onto there. Regardless, a certain value ultimately dictates the inattainable borderline between rolling over or rolling back, and the EH has that
sort of quality. Depending on its precise movement qualities, an item on this side of an EH may or may not be destined to 'roll over' (be dragged within black hole), but assuming there's no bigger 'hill' waiting on the other side to slow and return the item, another route back that it can take or a windmill-blade/someone using a putter able to give it the energy to return, one that has passed over the top is most definitely going to stay on the other side of the hump. (With those caveats allowed, you can clearly label items that will pass across that boundary and those that won't, but might not be able to say why that boundary was more special than any random boundary in space, so maybe the answer is in the concept of Hawking Radiation and that items don't get lost at all, so it
is barely less arbitrary than any other boundary you could suggest. More like merely the entryway to a region where one-way travel[3] is enforced, along with all points beyond the EH until any 'exit' into more normal, 'bi-directional' space.)
I know this doesn't relate precisely to the limit of 'c', but it relates to the limit of the EH, which has a
gradient of 'c' for all intents and purposes. Nor does it ascribe any special properties to the 'beyond the hillock' territory, I'll readily admit. It is of course a 'classic' physical example. The complications of Dark Energy make things interesting for the Universe, also (though it still wouldn't site
[2] My favoured theory at the time was that we had a universe consisting of a number of Big-Bang/Big-Crunch cycles, and the final conditions of the BC would dictate the starting conditions of the next BB. I think I favour the "n-dimensional bubble sat in n+1 dimensions" idea now, static and timeless within the n+1 dimensional meta-verse, as with any other bubble also sat there, but 'our' time dimension(s) represented in the surface dimensionality of the bubble, i.e. by me "latitude = time" idea, already mentioned previously in this thread. But that's all hypothetical (it's certainly beyond our capability to test) and probably a transient opinion that I'll supercede in a few years' time when I learn something interesting and new about current theories which answers gives a few more answers, or possibly pose a few more interesting questions.
[3] Again, I'll mention the similarity of 'unidirectional space' in this zone and 'uni-directional time' in the universe we can observe, but I don't think you have much truck with that, so please feel free to ignore that reiteration.
Yes, but it's a bad analogy. It's not a case of just some equations missing. According to current physics, going faster than c is impossible. Not just un-described.
Just like the square root of a negative number is impossible and undescribed... until you work with a number system that allows complex numbers with imaginary components? I'm just thinking 'further out'. I may be wrong. And I'm not advocating v>c as a casual thing, merely as response to the severe slope of spacetime beyond the EH.