Being too far or too fast isn't the same as being infinite. Beyond spacetime, nothing exists; not space or time. We can't be sure of the size of the universe beyond that which can be observed, but that is only because we don't know the rate of expansion through the history of existence. But spacetime is finite in size.
Science progresses with one new discovery trumping the previous one, e,g. Relativity supersedes Newton's Laws but doesn't make the latter wrong. If I correctly recall the issues, the gulf between relativity and quantum mechanics has not been resolved. Hence we don't have a unified theory of everything.
Newtonian mechanics is an approximation of General Relativity where any relative motion is far less than the speed of light, and gravity fields are weak. So you can take equations from General Relativity, plug in small velocities and weak fields, and then you can take approximations of those equations and produce Newtonian mechanics. Yes. QM for small scale [microscopic and smaller], and Relativity for large scale. But no consistent theory connecting the two.
This all goes back to the Einstein-Podolsky-Rosen [EPR] paradox where Einstein describe entanglement as spooky action at a distance. https://plato.stanford.edu/entries/qt-epr/ One key difference between this and speed of light limitations is that you cannot send useful information faster than light even using entanglement. This eliminates apparent conflicts between Relativity and QM. ie, entanglement does not violate Relativity.
It may surprise many to learn that Einstein did not receive his Nobel Prize for his work in Relativity. He received the Nobel for his work on a core concept in Quantum Mechanics - The Photoelectric Effect; also the key to how a solar cells works. https://www.aps.org/publications/apsnews/200501/history.cfm#:~:text=Light, Einstein said, is a,collision produces the photoelectric effect.
This is how the equation for the relativistic energy of motion of a mass reduces to the Newtonian equation for the energy of motion. It can be shown mathematically that the following approximation is true where x is very small (1 + x)^n ~ 1 + nx where x is << 1 This reads as: the value of 1 + x raised to the nth power is approximately equal to 1 + nx, where x is much much less than 1. For our purposes, this means the velocity u must be much much less than the speed of light C. Using this approximation, the derivation shown below starts with the Relativistic equation for energy and arrives at the Newtonian equation.
In a similar manner, the equations from Quantum Mechanics reduce to the equations from classical physics as we go from submicroscopic [or a single "particle"] to large scale and many billions of particles.
That postulate does not actually mathematically bear out. There are far too many different combinations, which exponentially grow the more variables you add. The universe may seem to last for a near infinite period of time, but the level of possible combinations is a different order of infinity.
Explain to me the different orders of infinity. And how many are there? May seem to last a near infinite period? Firstly, near infinite isn't infinite. Secondly, to whom does it seem like infinity? Is somebody sitting around and waiting the whole time?
which is actually just a label like any other number. It stands for a concept. Infinity is a concept. Not a size, distance or time.
The postulate rises or falls on whether the premise that infinity is true. It is true in the abstract, however. For me, it is more logical that the physical realm is infinite, than it is logical that it is finite. Since we can't prove it, conclusively, all we have at our disposal is logic. But, I'm not master of logic, so I defer to your infinite wisdom .
So did Felix Hausdorff roughly 100 years ago. Infinity has no end. That is the definition. If it has an end it isn't infinity. It really is that simple. You can't "prove" language.
Oh boy. There are big infinities, and small infinities. That was 40 years ago, I have no doubt they've added to the menagerie since. I think the problem here is that you can create a lot of different situations in math. Think of it as being like math mdoelling, it doesn't have to reflect back to the real world. Physicists will occasionally take a bit of math, and see if they can get it to work in something like the real world. Math has rules, but within those rules you can create a wide array of theorems, and usually without regard to how it would play out in the real world.
"Near infinity" is an oxymoron, right? I mean, there can be no such thing, because in order for something to be near something, that something would have to be finite.
Big infinities or large infinities, they are oxymorons. In order to have size, it must be measurable, and in order to be measurable, it must be finite. Right?
Correct. However there are different "cardinalities" of infinity - ie not all infinities are the same. Countable infinity, or Aleph Naught, is the lowest cardinality. It is called countable because it maps 1 to 1 with counting numbers. ie for every element in a set of countable infinity, there is a unique number, ie 1,2,3,4...
Unless math guys have changed their minds, nope. Math can get mind bendingly weird. Really glad I didn't take the advanced geometry class..
It turns out there are an infinite number of infinities [I remember doing that proof too!]. For a long time we didn't know which cardinality of infinity maps 1 to 1 with the set of all infinities - which infinity is the number different infinities? We learned only recently - the last couple of decades - that the set of all infinities maps 1 to 1 with Aleph Naught.
Infinity is endless so has no describable limits. As a student many years ago I found a dark silent place and began to imagine infinity. Since all we have ever known has edges, it is really difficult to imagine. I got close and then couldn't hold onto the idea anymore.
Yeah, comparing infinite sets has to do with showing that for every element in one set, there exists a unique element in the other set, IIRC. But set theory gets tricky, esp for infinite sets. It was always difficult and it has been a long time so my statements about specifics of set theory may not be exactly correct. But they are approximately correct.
