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askscience
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Cardinality is one notion of size, and a convenient one for a variety of reasons. It is not, however, the only one.
In terms of cardinality, the whole numbers and just the even numbers have exactly the same size. Its unintuitive, but so is infinity. Keep in mind that "same size" means "for every unique natural you present me, I can provide you exactly one, unique, even natural to pair it with" and that _is_ true.
Having said that, "measure" is also a way to ... Well, measure size. The open interval (0,1) has the same cardinality as the reals, but has measure 1, and so is in that sense smaller than them.
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askscience
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Why should it? Not everything is a two-way consequence. For example, let's say any person who has his brains splattered over a wall is most probably dead, and that this is always true. The opposite won't necessarily be true.
There's different symbols to write it too. A => B means if A happens, B must happen. But this does not imply that B => A.
If B happening means A happens, and the reverse is true, then you write it A<=>B.
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askscience
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Fun thing to think about in relation to zeno's paradox, the atoms and molecules that make us up can never actually touch anything. They can get close, but due to the magnetic field, they cannot touch. So, in line with Zeno's paradox, if you define "reaching a point" as touching that point, you actually never will.
On an atomic scale, the closest you can ever get to touching someone else is when your DNA intertwines with someone elses when you have a child.
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askscience
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Sure! Don't worry if you didn't get it, it's fairly advanced math, which is why it is used as a nice "in-joke"...
Let's begin with a simple example: consider the series:
1 + (1/2^2 ) + (1/3^2 ) + (1/4^2 ) + ... = 1 + 1/4 + 1/9 + 1/16 + ...
If you know a little math, you will recognize this series. The result if adding up all the infinite terms is exactly equal to (pi^2 )/6, which is just a beautiful result.
Now, imagine replacing the exponent in the denominator of each term. In the series we just saw, the exponent was 2. Let's ask the question -- what is the sum of the series, as a function of this exponent (call it s)? Clearly at s = 2, the sum is (pi^2 )/6 -- what is it at other values of s? This is called the Riemann zeta function. For s > 1, it is defined this way:
zeta(s) = 1 + (1/2^s ) + (1/3^s ) + (1/4^s ) + ...
At all values s > 1, the sum "converges" -- that is, it has a well-defined, finite value. Successive terms grow smaller and smaller. If you are patient enough you can get the answer to whatever precision you want by just punching in enough numbers on a calculator.
At s < 1, the sum **doesn't** "converge" -- it has no well-defined finite value. Even if you are infinitely patient, adding successive terms of the series will keep on making the sum larger and larger and there is no upper bound. This is easiest to see for negative s : imagine s = (-2), for example. Then the sum becomes 1 + 4 + 9 + 16 + ... which clearly keeps on growing larger and larger as you add more values.
However, there is a piece of wizardry in mathematics called ["analytical continuation"](https://en.wikipedia.org/wiki/Analytic_continuation). Briefly the idea is this -- we know the value of the zeta function for several values of s (for example s = 2). We can then extend this "backward" to obtain a **unique, well-defined** value for the zeta function at s < 1.
Then, even though the sum 1 + 4 + 9 + 16 + ... is not well-defined, we can abuse the symbol "=". We claim that this sum "is equal to" the value of the Riemann zeta function at s = (-2) -- and, voila, where you first had an infinity, you have a useful number!
And, using exactly the same trick, you can magically make the sum "1 + 2 + 3 + ..." well-defined -- by calculating the zeta function at s = (-1) ! Do you see how?
As it happens, the value of the zeta function at (-1) is (-1/12), which explains why it is meaningful to write (1 + 2 + 3 + ...) "=" (-1/12), explaining the joke :-) Note that this needs to be used in the correct context, which is why I included the scare quotes around the equal to sign, otherwise people can misinterpret this.
You could be forgiven for asking what value all this abstraction has in actual applications. You may be surprised to know that it actually appears in several theories in physics -- such as the explanation for the experimentally observed [Casimir effect](https://en.wikipedia.org/wiki/Casimir_effect), and more speculative models like string theory. In fact, the magical number (-1/12) is actually related to why many string theory models work only in exactly 26 dimensions -- not in 25 or 27 or any other number.
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askscience
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Mathematically, “0.000...1” would be the limit of
(1 / (10^x))
As x goes to infinity. This limit is 0, and it’s possible to prove that analytically in a general way, but that doesn’t really explain much.
Another way to think about it is that two values A and B can be considered equal if there is no number C that can “fit between them” (`A < C < B` or `B < C < A`). Because there is no fixed value larger than 0 and smaller than `(1 / (10^x))` for an arbitrarily large x, they *must* be equal.
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askscience
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Yeah that's what I had issue with, guy above me is the one that suggested there's no distinction between an infinite set of discrete actions and a single action being broken down into infinite sub-actions. I was just trying to point out the flaw in his logic. His statement leads to the idea that there's not really such a thing as infinity and its use is simply a less-than-accurate description of a single action every time, which obviously isn't the case.
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askscience
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I was scared of 2k or 2k+1, integer k answers due to the possibility that you could define odd as 'not even'.
But I think that's actually a different, just as solid approach -- if even numbers are 2k and odd numbers are 2k+1, you're going to have to find an integer k s.t. 2k = infinity or 2k+1 = infinity. Integers are closed under multiplication and addition, so there is no such k. Therefore, infinity is neither even nor odd.
(To anyone arguing about the physicality of the light bulb and light switch, you're dodging the actual question.)
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askscience
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I think you're mistaken in saying that relativity is wrong. Relativity is limited in that it does not describe quantum behavior in the sub-atomic realm. It is, however, very useful, tested and "proven" in the realm in which it was intended to be applied. Just because the theory is not a universal field theory doesn't make it wrong. More generally, our current understanding of physics is not wrong; it is limited. And, spoiler alert: it always will be. As our understanding deepens, we'll be able to see further, to smaller/bigger scales. It's turtles all the way down!
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askscience
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The very short version is, there is a sense in which 1+2+3+... corresponds to -1/12. It's not equal to it under most reasonable definitions of what this summation means but if you wanted to give it any sort of finite value then -1/12th would be the most reasonable. There's a lot of problematic "proofs" of this however. Mathologer made a good (but long) video on it [here](https://youtu.be/YuIIjLr6vUA). It's long but not difficult, there's just a lot to be said.
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askscience
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Great explanation of how infinitesimally small, infinite steps, and a finite distance are one lens through which to see the situation Something to consider: if the traveler (the one traveling one meter) is oblivious to the way you are dividing their travel, they can simply see: first half: ½ second. second half: ½ second. A constant travel rate holds in each lens. and this helps see, in detail, the "other perspective."
&#x200B;
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askscience
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It's entirely possible to have sequences like (0,0,0,...,1) with an infinitely long string of 0s before the 1. These transfinite sequences are used all the time in set theory as a natural extension of the usual natural-number-indexed sequences. The reason these are not used in decimal expansions of real numbers is because, well, there's no convincing reason to use them. The real numbers as a system are useful and mathematically interesting; any number system where 0.000...1 represented a well-defined value not equal to 0 would not be the real numbers, and would probably not be as useful or interesting.
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askscience
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You can find a function that maps elements, so you absolutely can compare cardinalities.
In fact, the proofs I'm familiar with that prove the irrationals have the CoC do so by demonstrating that there are fewer rationals than irrationals.
Additionally to that, the point of cantors theorem is the relationship between countable and uncountable infinities: that the CoC has the cardinality of the powerset of a countably infinite set and that powersets are always larger.
The fact that one is larger than the other, and specifically has more elements, is embedded in their definition.
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askscience
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Cardinality is really the same concept as the normal, intuitive definition of the size of finite sets. Whenever you say a finite set A has size n you are implicitly saying that there exists a bijection A-->n, where n is the nth ordinal. Cardinality of infinite sets is the same thing; it's not a different concept, you just stop restricting your domain of discourse to finite sets alone. So when you say that some infinite set A is larger than some other infinite set B then that makes complete sense even if you haven't defined cardinality, because there is really no other natural way to define size.
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askscience
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Only if you could have fractional times. But that would imply that there were real world times smaller than the unit you chose to divide. If there weren’t, then your physical distance must not be the smallest physical distance.
Dunno. I’m just an accountant. It seems to me that Zeno’s
Paradox allows one to arrive through intuition st the idea that time and space are inextricably linked. That’s the coolest thing I’ve discovered on my own.
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askscience
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It depends a lot on what you mean. In the standard interpretation of the definition of real numbers it's not clear what question you're even asking.
However, there are non-standard reals which allow for things like infinitesimals. I'm reasonably certain that in that non-standard model one can make sense of your idea. Levi-Civita fields look a lot like what you are discribing. Though I'm a lot more comfortable with the ([https://en.wikipedia.org/wiki/Hyperreal\_number](https://en.wikipedia.org/wiki/Hyperreal_number))\[hyperreals\] as they allow for ease of doing calculus with them.
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askscience
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Yeah. Here's a good way of looking at it.
Picture all the natural numbers: 1, 2, 3, 54656, ...
Now flip them all around, so you get 0.1, 0.2, 0.3, 0.54656, ...
Seems like that's all the numbers between 0 and 1, right? Nope. See, there are also *irrational numbers*, things like the square root of two, which is actually impossible to represent as a finite decimal. √2 = 1.41421356237..., and it just goes on forever, never repeating or forming a pattern of any kind. There's no equivalent natural number that can flip around to replace something like (1-√2). That's where all the "extra numbers" come from.
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askscience
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Are you moving the goalposts on purpose, and misquoting Wikipedia to win an internet argument?
What’s being debated here is whether Zeno thought it was a paradox. Not whether it is, in fact, a paradox (which it clearly isn’t). And the resounding answer is yes - he thought it was a paradox because he lacked the mathematical tools to resolve it.
It’s hilarious that you cite Wikipedia and apparently haven’t read through the first paragraph:
> Zeno's paradoxes are a set of philosophical problems generally thought to have been devised by Greek philosopher Zeno of Elea to support Parmenides' doctrine that contrary to the evidence of one's senses, the belief in plurality and change is mistaken, and in particular that motion is nothing but an illusion.
But hey, Wikipedia, right? Let’s turn to another [source](https://plato.stanford.edu/entries/paradox-zeno/):
> Zeno sought to defend Parmenides by attacking his critics. Parmenides rejected pluralism and the reality of any kind of change: for him all was one indivisible, unchanging reality, and any appearances to the contrary were illusions, to be dispelled by reason and revelation. Not surprisingly, this philosophy found many critics, who ridiculed the suggestion; after all it flies in the face of some of our most basic beliefs about the world. [...]
> In response to this criticism Zeno did something that may sound obvious, but which had a profound impact on Greek philosophy that is felt to this day: he attempted to show that equal absurdities followed logically from the denial of Parmenides’ views. You think that there are many things? Then you must conclude that everything is both infinitely small and infinitely big! You think that motion is infinitely divisible? Then it follows that nothing moves! (This is what a ‘paradox’ is: a demonstration that a contradiction or absurd consequence follows from apparently reasonable assumptions.)
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askscience
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No, I wouldn't quite put it that way, because that makes it sound as if mathematics itself gives you different answers depending on "circumstance". That's not correct.
Here's how I would put it: the sum of an infinite series is a subtle thing. It is always well-defined for convergent series and has nice reasonable properties -- for example you can shuffle around any of the terms. But the sum of a divergent series can be defined in a few different ways that may lack these nice properties.
Taking one approach, it is clear that the sum of all integers diverges -- I can always take enough integers for the sum to be greater than whatever finite number you give me. In that sense the sum is "equal to" infinity.
Another way of defining that sum is to take the analytic continuation of a function where it is defined, and then pretend that the functional form holds even where the function is not defined. Using this approach the sum of all the integers is "equal to" (-1/12).
It's the definition of "sum", not the definition of "equal to", that changes. I glossed over that in my original explanation.
The amazing thing is that this other definition of sum turns out to be not only physically meaningful, it can be measured experimentally.
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askscience
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This is similar to the solution to the Painter's Paradox of [Gabriel's Horn](https://en.wikipedia.org/wiki/Gabriel%27s_Horn).
> Since the horn has finite volume but infinite surface area, there is an apparent paradox that the horn could be filled with a finite quantity of paint, and yet that paint would not be sufficient to coat its inner surface. The "paradox" is resolved by realizing that a finite amount of paint can in fact coat an infinite surface area — it simply needs to get thinner at a fast enough rate. (Much like the series 1/2N gets smaller fast enough that its sum is finite.) In the case where the horn is filled with paint, this thinning is accomplished by the increasing reduction in diameter of the throat of the horn.
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askscience
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Reminds me of the Mathematician vs Engineer joke:
A mathematician and an engineer are sitting at a table drinking when a very beautiful woman walks in and sits down at the bar.
The mathematician sighs. "I'd like to talk to her, but first I have to cover half the distance between where we are and where she is, then half of the distance that remains, then half of that distance, and so on. The series is infinite. There'll always be some finite distance between us."
The engineer gets up and starts walking. "Ah, well, I figure I can get close enough for all practical purposes."
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askscience
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This reminds me of [Cantor's Diagonalization Argument](https://en.wikipedia.org/wiki/Cantor%27s_diagonal_argument), which inadvertently demonstrates that there is no such number by trying to enumerate all the real numbers. Every real number can be seen as having an infinite number of digits after the decimal, even if all the digits past a certain point are 0. Therefore, no real number has a "last" digit, and therefore we cannot set the "last" digit to any particular value (1 or otherwise).
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askscience
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There are different proofs for showing that the halting problem is undecidable. A proof I know uses reduction of the diagonal language to the halting problem. For that language, you can show it's undecidable via set cardinality.
Another great use of set cardinality in that field is to show that undecidable problems must exist. It's quite simple: You show that the number of problems (which are each represented by a language) is not countable while the number of Turing machines (problem solvers) is. As each solver solves exactly one problem, there are more problems than we can solve using our computing methods.
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askscience
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Not just 1 and 2, but also 2 and 3, and 3 and 4 and so on... till the known infinity of whole numbers. Each of the individual sets has as its size the same "number", and you just added that number to itself infinitely many times, BUT SOMEHOW ENDED UP WITH THE SAME NUMBER! The math of infinities is very crazy and runs incredibly counter-intuitive to the way we learn to count as children :).
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askscience
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My question was about physics, and your answer was about math, so you didn't really answer the question. Nevermind though, it was actually a lot simpler than I thought. Even if you have an ideal switch that can flip on and off instantly, a wire with zero impedance, and an ideal lightbulb that can handle an infinite amount of voltage, you are still limited by the speed of light. Once the switching reaches a certain frequency the electromagnetic field propagation will not be fast enough to reach the bulb and the bulb will remain off.
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askscience
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Thanks, I was about to write something similar, I was perplexed that no one mentioned it earlier.
There were two opposing opinions amongst Greek philosophers. One exemplified by Zeno, Parmenides and the other Eleatic philosophers that change was impossible, that there existed no void. And another exemplified by Heraclitus that change was constantly happened, "that a man does not step in the same river twice" and such.
It is unfortunate that we are not educated in thinking like the old philosophers where physics and maths were married with philosophy.
Many of the paradoxes we know come are in some ways polemical thought experiments meant to deny the wisdom of rival schools of philosophy.
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askscience
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Except that the words we use for size all refer to a thing's finite extent. If I add an element to a finite set, I can say that the new set is larger than the old set. You can't do that with infinite sets. The set of positive integers is the same cardinality as the set of positive and negatives. The problem is that you can't treat infinity like a number, because it isn't one. Cardinality is the natural extension of our concept of size, but infinities don't play by the same rules as finite numbers.
>Cardinality is really the same concept as the normal, intuitive definition of the size of finite sets. Whenever you say a finite set A has size n you are implicitly saying that there exists a bijection A-->n, where n is the nth ordinal.
No you aren't. That's a far more general understanding size than most people commonly use.
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askscience
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I'm not making a mathematical point, I'm making a linguistic conceptual one. The English words relating to magnitude are most commonly associated with ideas relating to finite amounts. You can't treat infinity or infinite sets with the same rules as you do finite sets, so the common understanding of these terms doesn't map directly onto infinite sets.
If mathematicians choose to use common English words for magnitude to describe infinite sets, that's fine, but it's a technical usage that diverges from the common one.
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askscience
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[Infinitesimals are indeed valid!](https://en.m.wikipedia.org/wiki/Hyperreal_number)!
Keep a few things in mind though:
An infinitely small number is not necessarily the smallest number. If we say some number x is infinitesimal, x/2 is another infinitesimal, and so is x/3, and so one. You could also have a number be infinitesimally small compared to an infinitesimal, and so on. Hyperreal numbers have this branching hierarchy all the way down, and up into infinite values as well.
Another thing is that numbers, from the conventional views of most mathematicians and scientists, have no real world meaning in and if themselves. Some people believe numbers exist out there, such as mathematical Platonists. But most view math very differently. Maths some would say is a language, a way of talking about things that happens to have rigor built in. Some say maths is more of just an extended and particular sort of logic, we are drawing conclusions from axioms after all, but maths has special assumptions logic does not. Some also argue maths is like a story or a game, where we are defining different rules and playing by them to see what happens. And you can have entirely different rules to found maths, so there isn't one superior game so to speak. Mathematical truth is not contingent on physical reality in most conceptions, nor visa versa.
So, there are hyperreals which contain infinitesimals, but no really interesting and consistent systems that extend the integers or the reals contain a "smallest number" (to my knowledge). Also it's maths so none of it has an intrinsic physical meaning according to most.
Make of that what you will.
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askscience
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That is a very good, and reasonable, question to pose to someone who is not a mathematical Platonists. I think it depends on what you mean by "no tie", and what you are calling "pure math".
First of all, if anything is predicted by pure maths, it is already true by that formal system, and experiment is unnecessary. What will happen, however, is that scientists will develop an intuition of physical phenomenon from working with and trying to conceptualize and understand them, and then will take a leap based off a simple assumption or assumptions and develop the math based of those assumptions (like in Special Relaitvity, Einstein could tell from experiment and his intuition that the relativity of velocity and the constancy of the speed of light were simultaneously true, so he worked forwards from those assumptions and found the math that described that sort of system).
For the Euler's formula example, you're asking more about the unreasonable effectiveness of maths in the field of science I think, which is an interesting and ongoing area of debate. Why does maths best phenomenon, and not some other system or language or whatever you call it? Why when we take what we know and extend with mathematics do we get often very reliable new info? Perhaps it is because math is strongly related to logic, and we are more or less just logically extending from simple assumptions. If you moreso meant how do mathematical structures invented a hundred or more years ago not find their real use until much later, yet still do eventually find use, remember that there are a lot of maths that doesn't one day connect, and we have being toying with stuff for millennia. Look at many of the abstract algebra systems which exist and find no particular use value, they are just pretty. Maybe one day they will all find use, but it is no guarantee, and if we keep inventing maths, and maths is formal systems, sometimes those systems will describe things that actually happen by sheer numbers alone. Though maybe resorting to probability to explain the effectiveness of maths is circular hehe
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askscience
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That's why math seems like magic to me. Maybe we are just "extending our logic", but it appears to me that the only reason our logic can be applied to understanding the laws of the universe is because the universe is built off of the same logic, and we can comprehend logic because we are part of the universe. I like thinking of the development of math as a journey to discover how the universe was created, because it makes it way more interesting and it actually makes more sense than explaining it as "oh it just happens to work out that way because we can use logic".
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askscience
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Mathematics proposes systems that may or may not exist in the real world. When physicists discover things from math, it’s because they picked a mathematical system (model), tested how closely it adheres to the real world system, and decided it was a good model. Sometimes they are right on the mark, and everything that’s true in the model is true in the real world. Sometimes they are wrong about the model, and at some point realize they need to pick a different one.
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askscience
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This is something that has been discussed quite a lot. Some see it as miraculous.
https://en.wikipedia.org/wiki/The_Unreasonable_Effectiveness_of_Mathematics_in_the_Natural_Sciences
Some, like Quine, see math as being justified just that extent that it underpins physics.
https://www.jstor.org/stable/25171232
In general though, ask yourself how you would describe the universe if not mathematically. Say you had some other system that conforms well to how reality works. Wouldn't that just be another way to do math?
Still another way to think about it is that we can only reason about the universe in ways that we can reason about the universe. If the universe required some descriptive method that is wholly inaccessible to the human mind, we wouldn't be able to describe it (not entirely impossible). We can describe math though, so if there are some parts of the universe that an be described by math, math seems to the reasonable tool we should use to describe it.
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askscience
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> If math has no real tie to physical world, how is it that physicists discover things based on pure math, then end is proving it true with experimentation?
Saying it has no tie is not correct. The more correct way to say it would be a 'loose tie'. For instance, the Ideal Gas Law is PV=nRT. But, gases aren't always ideal, so to speak. But many times it's close enough.
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askscience
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It does mean that there are or at least could be other ways to describe the universe. I mean, language has described the universe without formal maths for years, unless you are being as vague as all counting is maths, in which case then I would say that that has more to do with how our brains are hardwired.
Also, I don't understand what you mean with your 1+1=2. If you define what 1, 1, and 2 are, then it is by rote definition that 1+1=2. It is similar to the fact that "All bachelors are unmarried" is true. Sure, but it is a tautology, a bachelor is by definition an unmarried person. 2 is by definition the successor to 1, and +1 is by definition that act of applying the successor operation ones. I agree that the universe behaves consistently even outside of our observation, but as soon as you apply mathematical description to it, that is tantamount to acting as if it is observed.
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askscience
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> surely the problem is finite rare minerals, expensive production and expensive maintenance of those solar panels.
1. Silicon solar panels contain no rare minerals. Older thin-film cadmium telluride (flexible solar) panels relied on a heavy metal *and* a rare earth element; this type of panel is nearing obsolescence. Silicon solar panels are 100% recyclable and more material goes into making the glass than the cells themselves. The chemicals used in production are overwhelmingly mundane and are literally the most used chemicals in the world. Things like sulfuric/hydrochloric/phosphoric acids, lye, etc. Literally *everything* involved one of those at one point.
2. [Solar is the cheapest energy source](https://upload.wikimedia.org/wikipedia/commons/8/87/Levelized_cost_of_electricity_Germany_2018_ISE.png).
3. Solar panels need no maintenance. You can wash them off every once in a while but other than that they run 30+ years without even being looked at, so I have no idea where you got the idea that maintenance is expensive. The whole point of solar is that the ongoing costs like fuel or maintenance are so close to zero as to be ignored completely.
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askscience
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Because part of the state of the particle is its spatial wavefunction.
Particles in quantum mechanics don't generally have well-defined position, so when we say that two particles are "in the same position", we mean that they have the same spatial wavefunction. Two identical fermions can only be in the same position if they have different spin projections, or another difference in some additional quantum number that they may have (isospin projection, color charge, etc.).
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askscience
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The Pauli principle only prevents identical fermions from occupying *exactly* the same state, but the antisymmetry of fermion states also creates an energy cost for them to occupy *similar* states. In this case, similar means that they have strongly overlapping wavefunction, or they’re “close together” (as well as all other quantum numbers being the same).
This is referred to as “degeneracy pressure”. It’s a quantum effect that is basically the resistance of identical fermions to occupying similar states. The PEP doesn’t fundamentally prevent them from occupying similar states, only the *exact* same state. But it costs energy to increase the “similarity” of their states.
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askscience
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One thing I always wondered is how does Pauli's exclusion principle apply to composite vs atomic particles.
Take Helium-4. As a whole, it's a boson. But bosons can occupy the same quantum state. Doesn't that imply that one could compress an arbitrary amount of Helium-4 matter to the diameter of a single proton or neutron? Clearly that's not the case. So does Helium-4 behave as a boson at certain distances between protons, but as they get closer together, they start behaving like fermions due to the individual prons and neutrons being fermions?
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askscience
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> Doesn't that imply that one could compress an arbitrary amount of Helium-4 matter to the diameter of a single proton or neutron?
This is called a Bose-Einstein Condensate. They exist.
> Clearly that's not the case.
You probably think this because you believe the 'diameter' you alluded to to be a fixed quantity. However, in the process of making BECs the 'diameter' (extent of the spacial wavefunction of the atom) of the atoms increase and overlap.
All in all, remember the uncertainty principle. The more you try and trap an atom by reducing its speed to zero, the larger its 'diameter' becomes.
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askscience
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You would be right in free space. But if an electron is confined to a star, it's wave function is bounded, and this boundary creates a discrete spectrum of possible states, that are occupied from the lowest energy up.
The conductive electrons in a metal behave like this, too. They are not confined at any one place, but are smeared out over the whole metal. This is described by their electronic band structure:
[https://en.wikipedia.org/wiki/Electronic\_band\_structure](https://en.wikipedia.org/wiki/Electronic_band_structure)
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askscience
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This is the right answer, and it's a great example of the concept of how different physics can emerge at different energy or length scales. If one works purely in the high-energy particle physics regime, one gets QCD physics (quarks which are fermions), while if one works in the classical regime one gets a classical Maxwell-Boltzmann distribution (distinguishable bosons). But for low temperatures at normal pressures, you get Bose-Einstein physics (*indistinguishable* bosons!).
The energy-dependence of physics is a very important concept which has not been properly stressed to the general public imo.
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askscience
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One thing that's been getting me, that I can't seem to find a reason for, is how the nuclear shell model is rationalized in addition to Pauli Exclusion.
The justification being that we observe nuclei with a number of protons or neutrons in a similar "magic number" pattern as electrons. From there, you make the assumption that protons and neutrons each have their own orbitals based off of the same spherical harmonics equations that led you to electron orbitals, populate them, and lo and behold, you have some way to predict stable nuclei based on proton/neutron configuration.
What I don't get is how there wouldn't be any proton or neutron orbitals that are shared by the same two nucleons (in terms of quantum numbers) using this model. Especially for the low-energy orbitals where the difference in energy between any two orbitals is at the highest.
Edit: Magic numbers
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askscience
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The nuclear magic numbers are not the same as the atomic magic numbers, because there are some key differences between the nuclear mean field and the atomic mean field, including the opposite sign of the spin-orbit interaction.
But anyway, I’m not exactly sure what you mean about protons and neutrons sharing orbitals. The set of proton and neuron orbitals are approximately copies of each other, except for small differences due to the fact that protons have electric charge.
A proton and a neutron can occupy the same state, because they are not identical to each other.
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askscience
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>But anyway, I’m not exactly sure what you mean about protons and neutrons sharing orbitals.
Sorry if I wasn't clear there. I mean that, in the absense of Pauli Exclusion, why wouldn't we see multiple protons sharing the same proton orbital, or multiple neutrons sharing the same neutron orbital?
Also, is there still an exchange interaction that goes on with protons or neutrons that are in these orbitals, similar to the one in electrons that gives rise to Pauli Excvlusion?
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askscience
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Good catch, there are different limits here, as you might have assumed from reading my comment. If one increases the energy/temperature while keeping things dilute (the spacing between individual helium-4 atoms is large compared to hc/kT) then you get classical physics, or as I said, distinguishable bosons. In contrast, if you ramp up the temperature while keeping the spacing between the bosons close to or under hc/kT, which is what occurs in the LHC for small amounts of time, one gets QCD physics instead.
(For reference: k=Boltzmann's constant, c=speed of light, h=Planck's constant, T = temperature)
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askscience
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I think the best way to answer your question is to take a simpler system that exhibits the same phenomenon of an "emergent boson". The simplest case is two fermions that form a dimer. So you can ask
"How does the fermi-statistics of individual atoms affect the behaviour of a dimers at low energies"
(This is basically the BEC-BCS crossover)
I cannot find a nice discussion of this, unfortunately. I think given a week and some napkins to write on I could sketch something out for you, but it would probably be a bit too mathy for r/askscience.
Does anybody have a nice succinct explanation?
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askscience
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> How can a combination of fermions turn into a boson?
It doesn't literally become a boson. When you have an even number of Fermions and they bind together into some bound state, then there will be some size (and corresponding energy scale) that characterizes, on average, how close to each other those fermions are in this bound state. So, this lets you identify 2 regimes within the physics of how these bound fermions interact with other objects.
The 'low energy' regime is characterized by interacting with objects that are much larger than the average distance between your bound fermions. These larger objects will not have enough energy (per particle) to separate out the individual fermions from one another (to convert length scales to energy scales, think large debroglie wavelength (per particle) -> small average momentum (per particle) -> small average energy (per particle)). They will only be able to excite the *collective* modes of the bound fermions. That is, this larger object can affect basically all of the fermions at the same time, but it can't affect just one of them and leave the others alone. The physics of that will be *effectively* bosonic because the fermions, when considered as a single collection, have integer spin.
However, as you increase the energy of the object that you're interacting with, the dominant length scale of the interacting object decreases such that it becomes small enough to interact with just 1 fermion in the bound collection (or just 3 fermions, whatever) and not all of them at the same time. Now, you can resolve the underlying fermionic structure of the bound state, and the physics at that high energy scale will obey fermi statistics.
As I've portrayed it (and in reality), the crossover is entirely continuous. There is no magic energy at which the system switches from acting like a boson to acting like a fermion. It's just that at very low energies you can describe the system as effectively behaving like a boson, and that description breaks down more and more as the energy scale increases.
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askscience
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neutron stars occur when the gravitational pressure is so great that it causes the electrons to collapse into the protons, creating a neutron in its place. Without the outwards pressure from the Pauli exclusion principle of the electrons, the star can become much more dense than normal matter. However the size of the neutron stars is still limited by the Pauli's exclusion principle for the neutrons.
As for a black hole, we don't really know what is going on. This is where the whole question of making quantum mechanics mesh with general relativity comes up.
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askscience
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For stars, only two-body orbits are stable. Small objects can work in a three-body system (e.g. the Trojan and Greek asteroids), but stars are too massive for that to work.
However, you can *nest* two-body orbits to get more stars in a system. If you have two stars orbiting around each other, then the third star could be so far away from the system that those two stars effectively feel like one body, and you get a stable orbit. Alternately, the third star could be so close to one of the stars that they feel like one gravitating body to the other star. You can keep on going like that to add more and more stars to the system. Similarly, planets will have stable orbits if they are either so close to one star that they can stick to the star and follow it around, or so far from the whole star system that it all just feels like a single big messy star that they can orbit around.
[Nu Scorpii](https://en.wikipedia.org/wiki/Nu_Scorpii) is a *septuple* star system. It consists of a 3-star system and a 4-star system orbiting around each other. The 3-star system consists of a 2-star binary and third star. The 4-star system consists of a 3-star system orbiting with a fourth star, and that 3-star system consists of a binary star and a third star. So that's the sort of hierarchy you have with multiple star systems.
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askscience
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from u/ctothel :
>The two groups are 150 times further apart than the sun to Pluto
You'd get minimal heat radiation from the far group. As longs as you got appropriate solar energy to be a habitable system from the near group you'd be fine. they'd need to be tightly enough grouped that the orbit treated them as one gravity well to inhabit with a stable orbital path. I don't think they'd likely be uniform visibly though.
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askscience
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> Nu Scorpii is a septuple star system.
1 of only 2 known. The other being AR Cassiopeiae; which is a bit more complicated than Nu Scorpii with 3 main sets instead of 2; consisting of a triple system (AB) with two binaries orbiting each other in a matter of days and a third star orbiting once every half millenia; then there's two stars (C & D) that orbit each other every few millenia, and orbit AB like every half a million years. And two other stars (F & G) that orbit AB ever 400,000 years or so.
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askscience
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The minimum stable orbit radius for a small circumbinary (orbits a binary pair) object is about 6x the orbit radius of the binary it orbits. I'm not sure how it changes for large objects but I expect it is fairly similar or a little higher. So assume that each heirarchical layer has to be 10x bigger than the one below. That ratio is small enough to fit 4 stars inside the orbit of Mercury with a total mass the same as the Sun without destabilizing Mercury's orbit
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askscience
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It could get quite interesting. To be stable, your planet's orbit needs to be dominated by one star or one group of stars. *But* the brightness of a star is extremely sensitive to its mass - if a star is twice as massive, it's a *lot* more than twice as bright. So even if your orbit may be pretty straightforward, a massive distant star can create a lot of light and make an interesting day/night pattern.
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askscience
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This is explaining how your body is able to cool even if the temperature is higher than your body temperature. However OP was asking why we feel colder specifically when it's windy.
Gases are very bad at conducting heat, because of their low density - air molecules interact at a low rate and because of that, temperature spreads (or dissipates) more slowly compared to solids or liquids. Your body on the other hand will very quickly heat the layer of air directly covering your skin. Without wind you are basically sitting in your own bubble of warmth. When that layer of air gets constantly replaced by wind, a steeper temperature gradient is maintained.
With warm wind, a related effect gets important: when sweating, the air layer around your skin is quickly saturated with water, thus exchanging that layer helps your sweating. Similar to how it is harder to sweat in a tropical climate with high humidity which will generally feel worse than dry heat.
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askscience
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It's more the movement of air over your skin making it easier for the sweat to evaporate.
https://en.m.wikipedia.org/wiki/Vapor_pressure
If you look at the red dots, you can sort of think of the phase change as diffusion, except there's an equilibrium where there's a lot less water in the gas phase than the liquid. If there's a breeze, you get a local drop in vapor pressure (less dots in the gas phase) so more water needs to enter the gas phase to restore equilibrium. The phase change still requires energy, though, and it takes that energy from your skin.
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askscience
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Yeah, water transfers heat something like 20x more efficiently than air.
But even without water, the effect is still noticeable with enough wind, as long as it's cooler than your body. I have a motorcycle, and without a windproof jacket, anything below 75F (24C) is uncomfortable.
Conversely, when it's more than 95 or so out (35C), it doesn't matter how fast you go. At 100+mph, it's still like riding in a furnace.
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askscience
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To add to this, air is a pretty good insulator. That's why double pane windows work to keep cold from seeping in through glass windows (or actually the heat inside escaping). There is a layer of air between the glass working to insulate your house.
And so your body warms up the air around you, and it can't get far. But then the wind blows it away and there is new air to warm up.
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askscience
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if you want the science words to google:
* forced convection (what it's called when you're cooling/heating something with a moving fluid, especially look at what a *heat transfer coefficent (HTC)* is)
* hydraulic/thermal boundary layer (BL) (the region in which the heat transfer effect occurs. The *Dittus-Boetler* correlation is a famous correlation between BLs and HTCs)
* Laminar vs Turbulent BLs
If you _really_ want to learn more, any intro to/fundamentals of heat transfer textbook worth its salt will have at least a chapter on forced convection. You can usually find free PDFs of good textbooks around the interwebs if you know where to look.
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askscience
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True, but that doesn't *seem* like it would be a huge contributor. But apparently I'm a huge nerd, so....
I used the calculator [here (WARNING: Excel DL)](http://minerva.union.edu/hollochk/c_geochemistry/other_programs/black_body_radiation.xls) and plugged in 400 K, which is 127 degrees C. VERY hot coffee. It gives a total radiant power of 1450 Watts per square meter, which is actually a lot higher than I thought it would be. I have a moderately big bottle of Gatorade on my desk and a tape measure in my pocket, and I ballparked the area at about .06 square meters (30 cm circumference, 20 cm height, I assume the slant of the bottle cancels out the bottom. Talking about orders of magnitude anyway so....¯\\\_(ツ)_/¯). .06\*1450 = 87, so we're looking at about 87 watts of heat put out by our lawsuit-worthy coffee.
Going further, my bottle says it holds 946 mL, which I'mma call 1L. Specific heat of water is about 4 J/mL/deg, so to drop 1 degree, we gotta drop 4000 J. Let's say we're only radiating at 80W; that would mean that it only takes 50 seconds to radiate away 1 degree! That's a LOT faster than I would have thought, a whopping 72 degrees in an hour!
Now obviously there's a lot of napkins involved here; it's hard to even know what the biggest handwave is. The inner chamber surface area could probably be off from what I calculated; who has a 1L thermos, anyway? I didn't even look at radiant heat from the environment, which will be considerable, given that room temperature is 3/4 our coffee's temperature. And of course as it cools, the rate of radiation falls. Well, one of these can be handled easily; 300 K in the spreadsheet gives 459 W/m^(2), meaning that we should just go ahead and use 1000 W/m^2 in the calculations above. A drop of 1/3 in radiation translates to a 1/3 drop in the temperature loss, so we're down to 48 degrees per hour. Still a lot, but not quite as insane.
So yeah, I guess the moral of the story is that if you try to keep something piping hot for much longer than it takes to drink, you're gonna have a bad time.
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askscience
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These heat transfer comment chains always go this way.
Let’s take a double metal walled coffee cup that has styrofoam between the walls. That’s going to be pretty good insulation. And your coffee is going to stay pretty warm.
An improvement is just an air gap. Why? Because you are eliminating conductive heat transfer through the styrofoam. With an air gap you have only convective heat transfer and radiation.
Now, Argon is better than air, because it’s less dense (making convection harder). And a vacuum is better than Argon. Because no gas at all means no convection.
EDIT: The two paragraphs above aren’t quite right. Convection IS the word that describes transfer from a solid to a fluid. But it has been correctly pointed out that in still fluids and small gaps, they behave like conductors. So in the two walled coffee cup example, we are governed mostly by conduction. The gist of the points still stand: styrofoam worse than air which is worse than Argon, however.
But here’s the thing - the jump from styrofoam to an air gap is a BIG improvement. The change to Argon or a vacuum is only a slight improvement over still air. If you put coffee in any of these three (still air, Argon, or vacuum) it’s going to be hours before your coffee is cool enough to drink. AND Argon and vacuum are both extra manufacturing steps. So you pay more for these but don’t GET much in return.
And of course someone says radiation. While technically correct, the mass and temperature of your morning joe isn’t so much that you should worry, or even mention, radiation at all. You’re morning joe isn’t close to the temperature of the sun, folks.
So while Reddit has this love affair with technically correct is the best kind of correct, it can also be misleading when SCALE is ignored.
Rant over. Go find a cheap, double metal walled coffee tumbler and don’t worry about Argon and vacuums. That’s marketing. (I’m looking at you, Yeti and Starbucks).
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askscience
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Well remember, I'm actually also being a bit facetious; 127C is literally above boiling, and by a significant amount, in the realm of refreshing drinks, so yes, the radiation and so cooling rate will be much higher than you might expect for typical real world. A more reasonable 350K = 77C gives a net heat radiation of only 400 W/m^2, which translates to 20 degrees per hour. The big thing that's being glossed over at this point is the exponential slowing of cooling rate, which would take a little more than just algebra to deal with.
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askscience
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It will not. It certainly always happens, to be sure. I don’t want to give the impression it doesn’t. But the amount of heat lost due to radiation is a drop in the bucket compared to conduction (coffee to container to table it is sitting on) and convection (coffee to container to the air around it).
Things are also misnamed. Your car has a “radiator” that cools your engine. But it’s not giving up heat (much) via radiation. It’s giving up heat through convection (a gas or liquid being the transfer component). When your car is sitting still, it is free convection. This means the gas or liquid is doing what it wants. When your car is moving or the radiator fan is running, it is forced convection.
Now - let’s really blow your mind..... you’re about to eat a most awesome grilled cheese sandwich with a bowl of tomato soup. Your soups too hot, but if you don’t eat it soon, you’re cheese will get cold. Should you stir your soup?
The answer is maybe. See, stirring the soup will add kinetic energy to the soup. Which should heat it. But .... stirring it will ALSO aid the convection to the air from the surface of the soup being exchanged by stirring. Your bringing hotter soup to the top, and that temperature difference also plays into how much heat transfers.
So .... slowly stirring your soup will add kinetic energy, raising the temperature BUT will aid convection at the surface, lowering the temperature. And the heat loss via the stirring through convection will exceed the heat gain by the kinetic energy of stirring.
Now, if you observe this and decide your REALLY hungry and want your soup RIGHT NOW and your really want your soup cold and you realize stirring it cools it off, you may decide to go all in and stir with an outboard motor. You may find that you make your soup HOTTER. Because the kinetic energy of stirring via outboard exceeds the heat lost due to convection.
Heat transfer class makes a lot of mechanical engineers rethink their career choice. It’s not the easiest subject. :-)
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askscience
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I apologize, I’m not near my heat transfer book where I can look up the actual coefficients. But I googled a few sites. The problem is the convective coefficient depends on a few things such as pressure of gas, any flow, and even the actual temperature difference. So it’s not one number, but a range.
Given this, I’m going to simplify ....
If we call the heat lost through a pane of glass 100%, then the heat lost through a double pane window with air is roughly 2.5% of glass alone. And were we to use Argon it would be 1.3%
Argon is clearly better. Half that of air. But, if I put all three next to each other and had you feel them, you’d probably say plain glass was bad and could not tell the difference between Argon and air.
Again, my heat transfer background isn’t in gases, it’s been a while. But I do know a good bit about manufacturing. I could see (given Argon and air being so close) a window maker TELLING you it was Argon when it was just air. How would you even check? Both would feel MUCH better than what you are used to.
But ... your air window would get that internal condensate (I have observed this myself in Windows).
The thing I’m curious about - I could be an above board window maker and put Argon in there. How would I KEEP it in there? It’s a glass window with a plastic frame which is going to have different expansion rates (glass to plastic) with just day/night temperature changes. That’s seems like a hell of a seal to maintain ....
We need us a dude in the trade. You all have exhausted my knowledge on the topic at this point .... ;-)
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askscience
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No, you should run with that. In addition to forced (aided by a fan, say) and free (just sitting there doing what it do) there is open (like a bowl or a river) and closed (like a pipe, or the AC in your home) systems.
So we have now introduced you to four combinations.
You take your plane turbine in closed pipe system and you could just pump your soup into your stomach. At that point, I’m not so sure the temperature would matter. It would get by your mouth so fast it wouldn’t burn it. (You can quickly tap a hot iron to see if it is on without getting burned).
We’d need a biologist in here now to comment if we would “feel” boiling tomato soup in our stomachs. Not sure if there are nerve endings in there.
Or, you could try it. :-) And report back.
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askscience
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The coffee cup itself is also radiating heat, which is absorbed by the coffee (and the other parts of the cup). And not all the heat lost via radiation from either is truly "lost" unless the container is 100% transparent to infrared as the heat radiates off in the infrared spectrum. So it's not as simple as "this is how much is lost per unit time" even assuming a linear rate of cooling. All the factors I've mentioned would slow the rate of energy loss from the coffee, so it'll be quite a bit slower than 20K/hour from just radiation.
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askscience
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And another thought. ...
If you lose the seal on an Argon window, I can see it exchanging with regular atmospheric air. Especially if the window was at a lower pressure. Which would pull in whatever the current humidity was and condense on the inside.
But what if you used dry air? (You’d dry it at the factory with a dryer). If that seal broke, would it exchange like Argon? Seeing as how air is air ... that may fair better long term than Argon.
Again, I don’t know gases at all. We need a dude/dudette in the trade who knows the warranty data.
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askscience
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Small but important note: Heat isn't energy. Heat and work make up the total change in energy of a system in contact with another. This can be seen in the basic formulation of the first law of thermodynamics,
ΔE = q + w
which states that the change of energy in a system is the sum of the energies transferred through heating and work. (What's implied there is that the energy of a closed system is always conserved, which is the big takeaway from the first law). The delta in front of the E term (delta meaning the change in something) implies that energy is changing due to q (heat) and w (work). You cannot define a change without like terms (i.e. final - initial values of the same variable) OR something that is itself defined as the change in something (which both heat and work are). The fact that heat does not require initial and final values to denote a change should tell you that heat is not an energy.
So, to wrap up, the kinetic energy of the photon (which is just energy in a specific context, there is only energy, no different forms apart from human distinction) is absorbed by an atom/molecule and that atom/molecule then begins to move (vibrate). Those vibrations are what we feel as warmth. It is incorrect to say the kinetic energy is converted to heat, but it's correct to say that the energy from the sun is transferred to the object via heating, which in turn raises the object's kinetic energy, causing it to increase in temperature.
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askscience
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Many insulated glass units (IGUs) have a material called desiccant within the void space to absorb potential moisture, regardless of which gas is used as filler. For brand new windows this is mostly a non-issue, but as windows age and the seals start failing, water vapour inevitably enters this space and the desiccant mitigates the vapour from condensing on either of the glass panes, effectively extending the service life. Ideally there would be a vacuum in that void space, but unfortunately the pressure difference would likely cause one of the glass panes to crack/break.
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askscience
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True. Our common sense is also skewed by the fact that we’re typically walking around in environments that are colder than us (unless it’s >98° F). As warm blooded mammals, we need to dissipate excess heat to a heat sink. My understanding is that moving that fluid (air or water) will increase the heat exchange rate (ignoring evaporative cooling effects), trying to bring our bodies and the environment into equilibrium. This is good in sub-body temp environments, but is very problematic as soon as temps approach 100° F. It basically pivots from walking around in a nice cool heat sink to us becoming the heat sink in a convection oven.
[edit: a word]
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askscience
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Good info. My question still stands - how long does the Argon last? I’d imagine pretty long. I can’t keep track of all the responses - but the Reddit Borg Collective intelligence is now certain that with any leak, it will eventually get replaced with air. That should depend on the size of the leak.
Somewhere else, someone pointed out that they include desiccant to help with the moisture.
Given all of this, while vacuum would be better than Argon, I don’t think I’d want vacuum long term. If that seal deteriorated, it would actively suck in air that could be moist.
I’d be curious as to the finished cost of Argon vs dry air. I think the insulation difference would be negligible.
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askscience
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An important reason that many other replies have missed is that moving air has lower pressure than still air. With low air pressure it is easier for liquid to evaporate. it is the same reason why water boils at a lower temperature at high altitudes. There is less air pressure on the surface of the water therefore it takes less energy to transform it from liquid to gas. After that transformation the energy is removed from the surface of the body and you feel a decrease in temperature
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askscience
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You're almost always sweating, even if it's not literal drops of water coming out of your skin, small secretions are always happening for something known as homeostasis, where the body keeps internal temperature (among other factors) inside a very narrow range. So the body is always actively cooling the body if the external temperature is more than the body temperature (sweating etc), and if it gets too cool, it slightly warms it, which overshoots the temperature (delay is response to stop warming) and it cools it again in the cyclical pattern around the mean temperature which is characteristic of these homeostatic mechanisms in our body. Of course this is what I know, and my knowledge is limited.
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askscience
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I’d also argue it’s kind of similar to the fact that if you’re cooling your home with air conditioning during the summer and you open the door on a hot day, you’re letting hot air in, not cold air out. On the other hand, if you’re heating your home in the winter and you open the door, you’re letting the hot air out and not the cold air in. The same goes for your body. The laws of thermodynamics.
Edit: Also want to add that in terms of the human body, this feeling of change in temperature is just your body’s method of working to maintain homeostasis. Or in other words, it’s thermoregulation. Our bodies and the cells in it are constantly working to adapt to our external environment.
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askscience
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Radiation r/vandweller sub guy chiming in here.
Question about radiant barriers such as reflectix.
They all state that an air gap must be present, but how small can that air gap be? Reflectix states that it has to be a 1/4" gap.
Why 1/4"? Does it have to do with anything related to the IR spectrum and the wavelength that IR energy is transmitted at, or is it a 'round number' that people can understand and adhere to?
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askscience
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Woah, hey, misinformation... You still get conduction through fluids like air. Convection only occurs if the fluid is moving, which is a possibility for the thermos because of buoyancy, but not a given. In fact, for tall and narrow enclosures, the heat transfer rate with natural convection is considered to be very well approximated by conduction. (Bejan, *Convection Heat Transfer*)
Now, looking at conduction only: If the entrapped air is at, say, 25degC, the thermal conductivity is roughly 0.026 W/m.K, vs. polystyrene (styrofoam), which is 0.033 W/m.K. So moving to just air from styrofoam is a 20% decrease in thermal conductivity (which is linear with heat transfer rate).
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askscience
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Humidity is directly related to temperature, so unless there is an odd temperature drop during the day, you are correct. Humidity starts high in the morning and drops as the day warms up. As the day cools, humidity will rise again. This is also why you get dew on the grass only in the evening/night. The surface of the grass has to cool down to the "dew point" which is essentially the temperature where humidity reaches 100%. The dew point, or vapor pressure, does not change as temperature rises, but it will decrease when temperature falls below dew point--because water is now condensing out of the air.
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askscience
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From my recollection of building Science courses, the third pane actually provides fairly negligible increase in insulating performance, especially when considering the added cost. It would be far more efficient to provide a second low-E coating on the second pane of a double pane window. Triple panes are more beneficial for noise reduction in particular, and I feel like I remember it being something to do with stronger pane in large windows
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askscience
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Yes, though it is more useful to think about a minimum mass rather than a minimum radius. "Brown dwarfs" are the intermediate between large gas giants and the smallest red dwarf stars. There is some fuzziness about where the boundaries lie, but ~80 Jupiter masses marks the point where hydrogen fusion occurs in the core.
Brown dwarfs (and some gas giants) are able to sustain lithium fusion for a bit but the available lithium runs out real quick so it isn't a long-term power source.
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askscience
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The brown dwarfs form the same way stars do: a cloud of gas collapsing due to gravity. The gas comes from the original Big Bang or from previous generations of stars that blew off some/all of their mass. The majority of the original Big Bang gas was just hydrogen and helium with smaller amounts of some of the heavier elements including lithium. Some of that primordial lithium has stuck around.
While the lithium is burning, the brown dwarf has an extra source of internal energy supporting it against gravity, so its going to be a little hotter and maybe larger in size. Fuel runs out, stuff cools down and maybe contracts.
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askscience
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Thank you! I've always wondered about the opposite end of the star size chart! I appreciate the response.
The scale is always tricky when it comes to visualizing (much less fathoming!) the sizes and masses of things like stars, especially from a teeny tiny human perspective.
So, if I may (for example), offer a "primer/starter scale" —something I can (more or less) wrap my brain around: If ≈1M Earths (my turn to fuzz!) could fit inside our local star (Sol). How many Jupiters would fit in our local star?
These might help me better comprehend the scale of "~80 Jupiter masses" as the [admittedly, fuzzy] size of a red dwarf.
Thank you!
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askscience
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Lithium is generated via fusion, so that's how it gets there. The difference between these stars and others is the pressure/energy(?) In the brown dwarfs are not great enough to fuse to higher elements.
When the energy of lithium fusion runs out it will probably look something like a white dwarf.
I don't really know this too well, but I also think that the time for the brown dwarf to run out of fuel would be ridiculously long, even compared to normal stars, because Fusion run slower the smaller the star.
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askscience
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Just to expand on this answer, its the water availability, rather than the total water content that is important. Water with a high salt or sugar content has a lower water availability, and is harder for cells to grow in. Its not that different to how we can't survive from drinking salt water. This is why, for example, pickles in brine will last longer than a cucumber sitting in a jar, despite the higher water content in the former. Its also why jams last much longer than the fruit they are made from, because the sugar concentration is much higher.
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askscience
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A little late to chime in here, but I agree with u/antiquemule in that salt does not lower the evaporation temperature of water (addition of a solute to a pure solvent raises the boiling point, known as a "boiling point elevation").
In terms of evaporation, this could also be described by considering the vapor pressure of the solvent, and the effect of adding salt to pure water would also be the same as above--salt in your water leads to a lower vapor pressure, i.e. fewer water molecules are coming out of solution and entering the gas phase (link with a cute little animation to describe this: [https://www.chem.purdue.edu/gchelp/solutions/colligv.html](https://www.chem.purdue.edu/gchelp/solutions/colligv.html)).
But, I think u/MarvAlice had a valid point about the salt helping the water to evaporate. The mechanism might be more related to changing the osmotic balance of the system and drawing water out of the meat/fruit. Bringing this water to the surface of the food, outside of the intact cells, would help the water inside the food evaporate faster. So, both parties are making good points. :)
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askscience
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So it's thought it came from the same area that Ebola came from in Kenya although they are not really sure. As humans continue to expand and occupy new territory which was formerly jungle and wilderness we put ourselves at risk for contact with animals that may carry new diseases. Add globalization and a new virus in the jungles of Africa continent could easily spread worldwide very quickly. I just read a book called The Hot Zone by Richard Preston. In it he follows the beginnings of Marburgs virus and Ebola as well as touching on HIV aids. It's thought that human contact of blood form an infected animal. Possibly monkey. FYI. That book is horrifying. Makes you realize how fragile we are and how close we are to another global epidemic.
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askscience
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Expanding human population into an area where no humans lived before. Ebola and Marburgs and HIV /AIDs have similiar traits. So it's probably that they all came from a parent strain and that evolved to different virus through mutations. Remember that the virus is a living organism and it wants to survive. It can only do that through a host. As its primary host starts to have a lower population it's looking for a new host with a greater population (as animals get crowded out and their population shrinks human populations are expanding) making humans a perfect home for the virus to live in. Hence they mutate to find new hosts. It's only a matter of time before one of these mutates into something easily transmittable and knocks out half the human population. Scary thought yet probable.
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askscience
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Thats kind of a complicated question. SIV is many different strains of a virus type that actually infect like 40 or 50 known simian species. There is actually some evidence that cross over events to humans has happened multiple times in history, with only the two that we know as HIV 1 and 2 causing the current epidemic. From what i understand there are similar (and possibly related?) immunodeficiency viruses in other mammals.
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askscience
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Most diseases are more easily transferred between similar species (ignoring oddballs like leprosy), and Africa is home to chimps and binobos, which are the primates most closely related to humans. Throw in gorillas and the rest of the primates in tropical Africa, and that's a lot of possible diseases to catch.
Also, proximity to the other species and ease of transmitting the disease to other populations are also important components. The combination of bushmeat being a thing in Africa at the same time that a person can get to pretty much any part of the world in a day or two increases the chance of a disease catching on. For all we know, the Han did come across a disease like ebola or HIV and it wiped everyone out before it could spread very far.
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askscience
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You might want to actually read the article before making an outlandish claim. From the BBC article itself:
>"Public health campaigns to treat people for various infectious diseases with injections seem a plausible route [for spreading the virus].
It would have to be something with a very high risk factor, like sharing needles, to cause a large scale outbreak. That chances of men contracting it from women are so infinitesimally small, that this route of transmission would be virtually impossible to cause an initial outbreak.
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askscience
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Goddamn dude, I studied Viral Pathology in college. Maybe you should actually try reading some of the aforementioned books and maybe actually read the articles yourself.
" AIDS spread quickly, as carriers of the disease travelled along its length on board cars and trucks, from populated areas to more isolated rural areas. Prostitutes at truck stops helped spread the disease even faster, and it is also referred to as the 'AIDS Highway'"
https://en.wikipedia.org/wiki/Kinshasa_Highway
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askscience
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Sex is not the only thing common to an area where prostitution is high. Drug use is extremely prevalent, as well. Linking the spread to prostitute activity doesn't necessarily link sex as the greatest spreader of the virus in that particular scenario. One could speculate that males passed it to the women prostitutes more readily through sex and they in turn spread it through the sharing of infected needles. There could be other factors at work. Correlations do not always give clear causation.
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askscience
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Where did I say that "sex" was the causative factor? I made a simple statement of fact. The origins of the original HIV pandemic have been traced to the Kinshasa Highway region of the Congo. An area rife with prostitution which helped fuel it's spread.
It seems like there's some kind of strange mental gymnastics going on in the thread where some people are bending over backwards to deny that female heterosexuals are incapable of transmitting HIV to hetero male partners. IS this some kind of weird red pill thing on Reddit?
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askscience
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It does require a preferred frame, which means there is only one foliation into spacelike hypersurfaces over which the particle trajectories are actually classically deterministic (which is the essential promise of the interpretation). Working in other frames, the Bohmian trajectories zig and zag in random, unpredictable ways. In particular, this can be understood via working out the pilot wave trajectories in EPR experiments. If one could observe these trajectories, one could use these random zigs to figure out (by process of elimination) which frame was preferred. But it is also a requirement of the interpretation that one can't ever access these trajectories at the level of granularity required to achieve this. So strictly speaking it is not consistent with SR, but the problem can be kept under the rug for practical purposes. Whether this is philosophically acceptable is up to you. And pilot wave adherents tend to be willing to abandon exact Lorentz symmetry as a guiding principle.
But preferred frame aside, remember that the pilot wave interpretation is also presented in terms of fundamental particle-like entities, while the union of quantum mechanics and special relativity produces quantum field theory, where particles are not really fundamental in this sense. To the extent particles exist at all in QFT, they instead are more like structured patterns in the fields. There is no broadly accepted or worked out pilot wave interpretation of quantum fields, and the idea is not particularly promising. The basic problem is that in QFT there is no analogue of QM's position operator. In QM, particle position can make sense as the defining hidden variable in all cases. In QFT, there is nothing that can perform this role.
Additionally, there is no known way to do particle creation and annihilation in a classically deterministic way, even in a pilot wave interpretation. So when we demand this other important feature of QFT, the whole endeavor to save classical determinism fails anyway.
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askscience
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> If one could observe these trajectories, one could use these random zigs to figure out (by process of elimination) which frame was preferred. But it is also a requirement of the interpretation that one can't ever access these trajectories at the level of granularity required to achieve this.
Thanks! That is very informative. How does pilot wave theory require that we cannot detect the zigs and zags with enough precision to find the preferred frame?
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askscience
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If you have absolute Newtonian time anyway, absolute simultaneity is ok. The issue here is really with violations of relativity of simultaneity, with how nonlocal HVs bring back a secret sort of absolute simultaneity in SR. With access to the HVs of spacelike EPR pairs, you can figure out *the* hypersurface foliation, the unique definition of simultaneity in which the laws of physics are classically deterministic.
But maybe you're thinking of an application of Galilean relativity outside the Newtonian context which I'm not considering?
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askscience
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I think what I'm asking is just whether the laws of physics in a pilot-wave formulation of a QM system depend on the frame of reference even if you have Newtonian time. Are these "random zigs" only necessary to mesh with the relativity of simultaneity in a Lorentz-invariant theory, or are they present to introduce a preferred frame even if you're just working with a Galilei-invariant Hamiltonian with definite particle number?
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askscience
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The zigs are not due to Lorentzian relativity, they are due to how we try to preserve classical determinism in light of entanglement and Bell's theorem. So I would say the zigs still occur in Newtownian spacetime, but they don't represent problems there, due to the preexisting absolute simultaneity.
But let me flesh out the argument in more detail and you can decide for yourself.
Consider the Bell state |UD> + |DU> where we are being good Bohmians and only thinking about position observables, so U (D) = **exits** the upper (lower) port of the SG device. Remember our goal is *classical determinism* for the HVs. So knowing the state of our HVs at t1 must be sufficient to predict the HVs at t2. This means a real Bohmian Bell state looks like
|xUyD> + |xDyU> where x and y represent the pre-existing HVs (u or d) for each particle. Essentially u (d) = **enters** the upper (lower) port of the SG because in BM, this is how spin measurements are actually cashed out.
If we have the state |uUdD> + |dDuU> there is no issue, and everything is classically deterministic in all frames. u always determines U, d always determines D. But Bell's theorem requires that we cannot always have it like this, or else we would have a local HV theory. Sometimes, the preselected state has to be, eg:
|uUuD> + |uDuU>
In this case, if we can "see" the HVs, we see one particle go through the SG normally, but the other one gets kicked off its trajectory so it exits the unexpected side. Again, remember we are after classical determinism, so we have to decide once and for all which particle gets kicked. The solution is to say the first one we measure goes through normally, the second gets kicked. This is a nonlocal deterministic solution, but also an absolute order of spacelike events. Whenever we would locally "see" a kick, we would know that this measurement happened absolutely after the partner's measurement. Alternatively, we need to pre-declare a preferred foliation to simulate deterministic Bohmian time evolution of EPR pairs.
In a Newtonian spacetime though, I think this is fine because there is already supposed to be absolute time, so we just use that foliation. I believe this only jeopardizes our expectations of Lorentzian spacetime.
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askscience
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Yes, where did all the antimatter go? It's a good question and the answer is both disappointing and interesting: We don't know. In (astro)physics, this question is referred to as the "Baryon Asymmetry Problem" because of the apparent asymmetry between baryonic matter (everyday matter composed of quarks) and antibaryonic matter (antimatter composed of anti-quarks).
It's natural to assume that matter and antimatter would be created in equal amounts in the big bang. Yet all we see around is regular matter. One of the possible explanations for this is that matter and antimatter don't behave exactly the same way. That is, that the symmetry between matter and antimatter is broken. Physicists refer to this symmetry as charge/parity-symmetry (CP), which expresses that the laws of physics are the same when you replace a particle with its antiparticle and flip the spatial coordinates.
We know from experiments that CP-symmetry is violated in some cases. The rules apply slightly differently for matter than for antimatter in those cases. However, these CP violations are relatively small and the ones discovered thus far are insufficient to properly explain the matter/antimatter asymmetry. It is, however, the most promising research direction as particle physicists search for more interactions that violate CP-symmetry.
An alternative explanation could be that there are regions in the universe that are antimatter dominated in the same way that our neighborhood is matter dominated. From a long distance, matter and antimatter appear the same, so it would be hard to directly detect large concentrations of antimatter. However, if there are antimatter dominated regions, then there are also border areas where the transition from matter to antimatter takes place. These areas should have a mixture of both and therefore should see plenty of annihilation effects. Matter/antimatter-annihilation produces light that we would be able to detect. Despite searches, no regions have been found that look like these border areas, so if they exist, they most likely only exist outside the observable universe.
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askscience
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Yes, it's possible. Extraordinarily unlikely to happen, but possible. The problem is that the probability we happened to end up in one of those by chance pockets is so, so incredibly tiny that physicists really don't like it as an explanation. It would be sort of like flipping a coin a million times\* and getting heads every single time. Sure, it *can*, technically, happen, but after the first hundred thousand heads you'd probably start wondering if maybe the coin isn't fair, or maybe it's a double-headed coin, or something besides attributing it to pure chance.
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askscience
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I guess I'm not imagining it as a small unlikely pocket, but rather enormous bubbles (Trillions?) of lightyears across so that most observable universe-sized volumes are contained within a homogenous form of matter, and it's actually an unlikely possibility to be near one of the boundaries. I'm picturing something like the next scale up from a galaxy filament; incomprehensibly enormous structures of either matter or anti-matter. Pure speculation and I don't know how we could ever test such a hypothesis, but if the universe is truly infinite and flat, it would seem a potential explanation.
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askscience
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> However, if there are antimatter dominated regions, then there are also border areas where the transition from matter to antimatter takes place. These areas should have a mixture of both and therefore should see plenty of annihilation effects. Matter/antimatter-annihilation produces light that we would be able to detect. Despite searches, no regions have been found that look like these border areas, so if they exist, they most likely only exist outside the observable universe.
This is an interesting idea but I have to wonder, is this really a necessary result of there being pockets of both? As I understand it, just from this solar system to the next is light years. So if we then imagine from this galaxy to the next, or from this supercluster to the next etc could it not be simply possible that the distances are great enough that this can't be noticed? Doesn't empty space in our solar system have an extremely low amount of matter in it, like a few hydrogen atoms per square meter or something? Is there even less outside of the solar system? Would that even be enough to notice the transitional zones really far out?
Also from what I understand, collisions of larger objects isn't something that is happening very quickly, most objects that were going to collide quickly already have by this point right? Clearly the earth and sun are not colliding anytime soon, and we have no reason to think anything else is colliding with us soon. Nothing substantial in mass anyway. So for these even larger systems, collisions are probably even more rare perhaps? Right? Or wrong?
I think it important to consider that maybe the universe is infinite in size as well. There seems to be no reason to think it couldn't be. That's an interesting idea because if the universe is infinitely large, we could expect that everything that can possibly happen by it's laws not only has already happened, but will happen again, an infinite number of times. Such is the nature of infinity.
Even if the "big bang" theory is correct, it could just be that this "primordial singularity" or whatever it's called was only one such event among many others separated by distance, more than there are atoms in our observable universe. Or even if there was only one, it could have happened in a cyclic fashion an infinite number of times before.
One other weird thought, if matter can become energy from the two colliding, matter and antimatter, is there some way energy can turn back into matter?
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