Hi 1.61803.
1.61803 writes:
A singularity is a point not an object. Sorry but that is just the way it is.
Heh, no need to apologize. I don't mean to give the impression that I disagree with anything that's been said. I'm just trying to understand
why that's the way it is. Any time you see me write "I have a problem with [insert counter-intuitive scientific reality here]" please feel free to read it as "I have a problem
understanding [insert counter-intuitive scientific reality here]."
1.61803 writes:
But trying to understand how space can be bent to that extreme by infinte density is difficult to conceive.
The infinite curvature of space I actually don't have as much of a problem with. I am comfortable visualizing that using the old analogy of a two-dimensional rubber sheet with, in this case, infinite warpage such that the curvature has no "bottom" or is curved back on itself. I realize this isn't the way it actually works in reality, but I have a love of dimensional concepts so I understand how the analogy applies.
The problem I have with (understanding) point-like concepts, be they particles, singularities or whatever, is that I can't picture a more intuitive "equivalent" to help me comprehend the reality.
Indeed, the concept of a volumeless singularity even seems to defeat the purpose of the "rubber sheet" analogy, as the curvature (at least from an intuitive perspective) would require a non-zero diameter to be truly bottomless. Otherwise you could say that its bottom is at the singularity.
Then I recall that this is where the laws of physics, as we know them, break down. But then I think...well...
where? At that point? But it has no size! No matter how far "down" you go, it will never have
any extension whatsoever in any direction. There is no space there within which our current physics break down.
Where, then, is it happening?
Again, this is probably a limitation of using intuitive analogies to "understand" concepts that simply aren't intuitive. They can only ever get so close to describing the
reality of such things. If the analogies were perfect descriptions we could do away with them and understand the realities themselves.
1.61803 writes:
I still have trouble understanding time dilation and quantum entanglement, quantum tunneling.
Kind of off-topic, but I think the best explanation I've ever read of time dilation was by Brian Greene who describes it with the analogy of racing cars across a set distance out on a large, flat desert plane.
He shows how, assuming a constant speed for each trip, you will measure one time when travelling in only one dimension, say, north/south, between the start and finish line, but
another time when travelling simultaneously in two dimensions, say, north/south and east/west, between the start and finish line. The time measures differently because, in the first scenario, your speed is dedicated to travel in one dimension, while in the second scenario, it is shared between travel in two dimensions.
In this way, he showed how our travel through space and time can be seen as both drawing on the same unchanging "reserve" of velocity, which works out to the speed of light. He said that this shows how our travel through space affects our travel through time and is another reason we can never travel faster than light through space. To do so would require a greater overall velocity than we have at our disposal.
Again, as an analogy, this description is inherently imperfect. But I must say, it is easily the most satisfying explanation of time dilation that I've ever read. I've known for a long time
what happens, but not until I read that did I finally get a handle on
how it happens. I don't know how closely this analogy reflects the reality, but it gave me a great mechanism by which to visualize the process.
1.61803 writes:
Thinking in terms of size suggest it is an object. That is not the case. Matter itself when you get down to it is just probabilities.
Now
this, I think, is one of my biggest hurdles. The only way to
really show how many of these concepts work is mathematically. Popular science books can give you some reasonable "compromises" in the form of intuitive analogies, but if you want to understand their reality,
really understand it, you need to understand the math.
Well, this is how it seems from my perspective anyway. I don't know how many times I've heard "Here are the equations describing..." but then, when asking what they actually mean, heard "Well, try thinking of it like this..." It can be so frustrating not understanding the math. These things can be shown with such precision on paper, yet we are cursed with these "intuitive" minds that recoil at the consequences of the math because it seems to contradict our familiar everyday surroundings.
1.61803 writes:
I think it was Heisenburg who said:" If you think you understand quantum mechanics then you dont."
Indeed. And if you think you
don't understand it...you don't.
Thanks for the link, 1.61803. I'm
curious about the math. I'll take a look but I can't guarantee I'll understand it. If it's anything like some of the other advanced math that I've seen I'll be lucky if I can recognize half of the symbols.