There are ways to work with infinitesimal numbers just as with real numbers, but that does not really do the trick, as physics is not based on that. To my understanding (not an expert in cosmology or that deep into physics) the energies/fields of back then can cause infinite densities.

> If the universe as a whole(including outside of the observable universe) then it wasn't a single point, infinite was always infinite and will always be infinite.

This misconception is weirdly common and contradicts basic topology:

If every bubble of, say, 10^10 ly, was once a single point, then the entire universe was once a single point.

Proof: assume x,y are any two points. Connect them by a path of finite (but potentially extremely large, even by universe standards) length. Overlay that path with finitely many of those 10^10 ly bubbles, such that they overlap, forming a "chain". Let A, B be two neighboring overlapping bubbles. Then once all points of A were the same point a, and all of B were once the same point b. But now look at any point p in their intersection: p was once both a and b, thus a=b! Doing this iteratively with the chain of bubbles, we arrive at the conclusion that any two points were once the same! [ ]

And indeed, the infinite(!) 3D (or 4D) space is contractible, it can be contracted into a single point in finite time. Even at locally finite & bounded speed.

Anyway, there are quite a few models of the Big Bang where the universe was always infinite, just with also infinite density at the beginning. The Big Bang needs not necessarily be a single point in the usual sense.

Be careful, technically a torus is not flat at most points when drawn as a donut. One needs to use the "flat torus" which can only be properly embedded ("drawn") in 4 dimensions.

I have no idea why people down-voted you, this is a perfectly legitimate and pretty good question; some here are just jerks...

Yes, but rarely. And mostly at the end when the star is at its hottest in the center. I don't have numbers on how often it actually happens, but it definitely does.

At the most extreme end in particular, when a star goes supernova (not all do) it collapses so hard to its center that this creates extreme pressure and releases absurd amounts of energy. This fuses iron and all the other stuff beyond all limits; the energy is almost irrelevant, we are talking about hundreds of Earth masses(!!!) as pure energy. This is one of the two processes that creates the elements beyond iron in the amounts we find them (the other option are collisions of neutron stars).

There could be. But all our physics* implies that any such thing would be unable too interact with us slower-than-light beings. Like, at all, not even in the weakest sense. Then it boils down to the question of what "exists" means; can things "exist" that we cannot, will never, nor could ever in any way detect?

The material/scientific version says no, because either Occam's razor or it not being testable makes it pointless for it. Quite a few religions allow such concepts, though. Same with Science-Fantasy, with parallel universes and all.

*: Which could be completely wrong, we have just found it to be accurate to a very high degree and probability.

But it does not really answer the question: why can light not be even faster? Why are there not other massless things that are faster than light?

No, the 1 is to represent 1 and nothing else. It comes from the definition of sin and cos in the unit circle.

But you still do not have -5 sheep, just a debt of 5. That is conceptually not exactly the same. Sure, you can now define(!) negative numbers as debts, and that's okay. This would be one formal way to extend the natural numbers to the integers. Similarly one can extend further and further if careful.*

But exact numbers, irrational ones in particular, are already esoteric in real life. No fence ever will have exactly length pi. No diagonal of a square with side 1 truly has length sqrt(2), however precise you drew it. And maybe that third of a pizza was actually slightly less or more (but that one can be done, if we get down to counting atoms).

So what we do is to accept that those numbers mostly exist conceptually and abstractly. But if pi and sqrt(2) are fine, why not i? We artificially added the circumference of a circle and a solution of x² = 2, why not also x² = -1? And as mathematicians realized this is maybe where we can stop: every (non-constant) polynomial equation has already a solution in the complex numbers (they are algebraically closed), and every limit (such as pi as an infinite sum) that should exist actually exists (they are complete).

It also has applications in real life, and you don't need to go to quantum mechanics for that: The laws of electricity for DC extend neatly into those of AC. But only if you treat capacitors and coils as resistors of imaginary(!) "resistance". Hence like pi being the best way to deal with a fence of arbitrary precision, i works really well to deal with currents.

There are more abstract reasons in mathematics as well. As a simple example (as going into the true applications would go way beyond ELI5 or ELI18):

What is sin(0°) + sin(1°) + sin(2°) + sin(3°) + ... + sin(179°) + sin(180°) ?

Complex arithmetic tells you that sin(x) = ( e^ix - e^-ix ) / 2i, with x in radians. Using that and the geometric series

1 + a + a² + a³ + ... + a^n = ( 1-a^n+1 ) / (1-a)

will lead to the result; details are left to the reader ;-) .

tl;dr: they just work and make life easier, so why not use them?

*: The more common one is to work with pairs (a,b) of naturals, which we treat as if it were the number a-b: we consider (a,b) equal to (c,d) if and only if a+d = b+c (note how this only involves natural numbers now), similar to how "a/b" and "c/d" are the same if and only if a·d = b·c. And so on...

Aren't all but maybe the natural numbers "impossible"? You cannot have -5 sheep. You can even less have 5/3 trees, even less so -pi hamsters. Why is imaginary numbers suddenly the issue?

Well, it simply isn't. All those extension of the numbers made sense, do not cause contradictions, and most importantly, turn out to be useful in everyday life, engineering (electricians, for example use them) and physics (all over the place). Notwithstanding the immense effect on mathematics itself.

Fruit flies, not normal flies. Normal flies are large enough to die. The heating of an object significantly below the wavelength (centimeters) is proportional to the size, due to the electric potential created by the microwaves. The fruit flies also have the added bonus of much surface area per volume.

It is also not just the sweet spots, the flies survive even if they move around randomly. Anyway, here is a video by Cody.

Alternating current starts electrolysis just as well, only that now all products are created equally at both ends.

It's probably not the vibrations but the ultrasound cavitation. It forms little bubbles at enormous forces, ripping stuff apart.

Fun fact: this is also the reason why you cannot microwave fruit flies (in case you ever tried... for... reasons...).

We could. It would be horribly inefficient, taking way more than other methods, and most importantly, the current methods of power generation would produce way more CO2 than this destroys. And to make it work at all you would need to remove the CO2 from air to get a tank full of it; at which point you could just sequester it, store it underground, or whatever else works and takes much less energy.

Both carbon and oxygen are way easier to get differently, even if energy were free it would not be worth it.

Pure water electrolyses if you try hard enough. It's just silly inefficient.

Table salt is normally not used by people doing electrolysis. Other salts such as sodium/potassium hydroxide, or if nothing better is at hand, sodium (bi)carbonate, are safer, similarly cheap, and also do the job better.

From your poop, duh!

It's not like they have any control over it...

Both? It is slightly basic, just pretty weak. Sodium bicarbonate mixed with water also has the typical "soapy" feel to it.

Yeah, a lot of people see the terminology and shut down despite it only being place-holders for "the thing I explain to you". Duodenum sounds alien, but replacing it with "that thing right after your stomach" in every sentence gets tedious and unreadable pretty fast.

I fully agree that instead of all those "omg! that is not ELI5!" posts people throw around (some ignorant of the actual meaning, some not), they should just ask for clarifications. I really wish that was a rule, as in, telling people that something is not ELI5 instead of asking for clarification is forbidden. I've only very rarely seen such responses where I would consider it justified.

I had several instances where OP asked for an explanation that technically does break the rules. Something like "As an engineer, I learnt this and that math. But how does [complex mathematical theory] fit into my work?", where the only serious option is to explain based on OP's knowledge, not a layperson's.

As an example of how that can end see the Goiânia accident. There the same stuff, caesium-137 inside a secured box, was just thrown away in a trash dump. Then someone found the box, wondered what valuables are inside such a closely locked thing, broke it open and... played around with and spread the glowing magic powder to the neighbourhood. A lot of people got severe radiation doses, it needed very serious clean-up, and people died.

> And how is it lost off a truck if it’s so dangerous?

The honest answer is: because people are sometimes idiots and don't follow adequate safety measures. Somebody screwed up. In the above incident, that wouldn't be the guy who found it (you can't expect random people to know about caesum-137 and its use), but whoever carelessly threw it away.

But the bow shock is a result of the magnetic field, not atmospheric density or effects. Ultimately the question is "who cares?"; it doesn't matter at all if one is technically inside the atmosphere or not.

Even in English, it's paedophile in BE. Only Americans f***ed it up.

More like a foot fetishist :-p

> I’m not sure how the tardigrade could be entangled. From my (limited) understanding, entangled particles don’t remain entangled if they are far apart or if something else “touches” one of them, which is not at all how it is explained in the article.

There is no known or conjectured limit on the distance of entangled particles. We have created and maintained entanglement over kilometers (newest result between two atoms on Earth was 50km; photons in space was 1200km). You can also perfectly well "touch" them; if A, B are entangled, you can entangle B with C without it loosing the entanglement with A. It is unknown what the limit for the amount of entangled atoms is, or if there even is one.

Hence it is potentially possible to entangle a tardigrade. The issue here is the question if that actually happened and many disagree. But the discussion is still up and should be left to those that actually work on such things on a daily basis.

Oops! Edited.