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6 years ago
If I understood your post correctly, it wasn't the second law that relied on the universe existing, it was the idea that the second law indicates that time is finite. You were saying energy has a max amount per moles of matter, but if we have infinite moles of matter, that doesn't mean anything. The ratio can't change if it's always infinity over infinity, meaning the ratio will not change with time, at least as far as the universe is concerned. As for energy flowing from place, I don't think we can understand an infinite universe well enough to make that judgment. If the universe is infinite, does the conservation of energy still apply, or is that only for a system smaller than the universe? And how fast does the energy travel to a place with less energy when we're talking about a distance that's infinitely large? Can an infinite distance be crossed in an infinite amount of time?
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6 years ago
The questions you asked are indeed interesting, and please keep in mind that all I can do is to
to answer them.
You were saying energy has a max amount per moles of matter
I apologise if I accidentally wrote that; I didn't mean to. I meant that
has a maximum amount, not energy.
it was the idea that the second law indicates that time is finite
Yes. And, I believe, it would still be true if the universe was infinite. Why do I think that?
Just think about it. I could phrase the second law in another way: that
, all of the potential energy will be converted to kinetic energy.
Now comes a bit more difficult part, but after thinking a bit, it is easy to cope with.
In thought, divide the infinite universe to an infinite number of finite systems which contain both potential and kinetic energy.
It is easy to see that
of them will have their potential energy converted to kinetic energy - and what's even more important,
. And as we divided the universe to infinitely many finite systems, it is easy to see that this conversion will take a finite amount of time.
I think you can see the point now. It does not matter, how much energy the universe has; because
the more energy it has, the faster it will convert
There may be flaws with this thought, but such surprising phenomena are known about infinity, mostly in mathematics, of course. There are improper integrals, for example, which are similar in one of their aspects. Here is one example that surprised me immensely: take the function f(x)=1/x^2.
Let's examine the curve from 1 to infinity. Of course, the curve stretches into infinity; yet the area under it is a round 1. Which is at least as surprising as what I've said above.
I apologise for this one, which might seem off-topic; it is not. I simply attempted to highlight the often unexpected and astounding properties of infinity and its relation with finite numbers.
The ratio can't change if it's always infinity over infinity
Without the intention to sound dogmatic or certain: I believe it indeed can.
'Infinity per infinity' (the marks are there due to the simple fact that infinity is not a number) can yield different results.
I can come with mathematical example again. For first, there is limes calculation.
An example that might seem a bit complex:
Let us take the function: f(x)=(4x^2-9)/(x^2-4)
Let's see its limes if x keeps to infinity. It appears to be an 'infinity per infinity' limes.
Either we can use the l'Hôpital-rule and see that the 'infinity per infinity' is, in this case, four; or we can divide both the numerator and the denominator with (x^2) to gain the same result.
Or an example that looks simpler, but is, I think, much more difficult to grasp:
Let's see the ratio of integers to natural numbers. It is infinite per infinite.
Now let's take the ratio of real numbers to natural numbers. Also infinite per infinite.
Yet, the latter is
, despite the fact that there are infinitely many integers and real numbers, there are still
real numbers. It is a fact, and similarly to the 'time problem' we had above, this is easy to see via breaking the 'system' down to infinitely much finite 'systems'.
Let's see the numbers between one and five. There are five integers - one, two, three, four and five. And there are inifnitely many real numbers.
This will be the case with all intervals we can divide the numbers to; therefore, it's a simple induction.
Even though these were mathematical examples, and more abstract ones than I wanted them to be, I think - or rather hope - that they can highlight the rather weird nature of infinity.
If the universe is infinite, does the conservation of energy still apply, or is that only for a system smaller than the universe? And how fast does the energy travel to a place with less energy when we're talking about a distance that's infinitely large? Can an infinite distance be crossed in an infinite amount of time?
A brilliant question, I must say; but I think that energy will never have to travel an infinite distance - if it will have to travel at all.
This is also easy to grasp, and can be demonstrated without abstract mathematical analogies.
Potential energy will eventually transform into kinetic energy. And what is the most generic form of kinetic energy, which has the highest entropy of them all?
And any little amount of matter can have any amount of thermal energy, the converted energy will not have to travel any distance; it will be stored in the material as thermal energy, right there.
I hope they were clear. Thanks for reading and replying!