ƒ(x) said:
I don't know enough physics to answer these questions myselfs. For all I know, they might be foolish.
Is there a branch of physics that takes perspective into account. I use that word in its most basic sense. To an observer on the quantum level, might everything appear to work according to the rules of normal physics? Similarly, to another observer on a macro level, might the planets and galaxies behave according to the rules of quantum physics?
According to everything we know, the answer no -- scale is absolute. Atoms are not small solar systems; galaxies are not large molecules. I can see the attraction of a theory where the universe is "turtles all the way down" but to my mind the real world is much more beautiful. The fact that the same theory can describe the world accurately over a giant range of scales, but also tell us why specific systems behave differently on different scales is, to me, nothing short of breathtaking. A few examples,
1. Warm-blooded animals on Earth cannot be smaller than a certain size. This is because warm-blooded animals must keep their body temperatures above the ambient temperature to live, and most of the time the environment is colder than the inside of the animal. The amount of heat energy contained in an animal at a certain temperature is roughly proportional to its volume, which goes roughly as its (length)
3. The rate at which body heat radiates away is proportional to its surface area, which goes roughly as its (length)
2. So as an animal shrinks, the amount of heat contained inside it goes down much more quickly than the rate at which which it radiates heat to the environment; a mouse looses a larger fraction of its body heat per second than an elephant. To keep its body temperature up, then, a small animal must eat much more food than a large animal relative to its size. A mouse eats its body weight every day, and that's about the limit for warm-blooded animals. Animals like insects are much smaller than mice, but they are all cold-blooded. (If you've ever seen the movie
Honey, I shrunk the kids, all this implies that the kids would actually freeze to death!)
2. There is a similar argument for upper limits on animals' size. Bone strength is proportional to the cross-sectional area of the bones, which goes roughly as (length)
2, and again, volume goes as (length)
3. So if you keep an animal the same but simply scale it up, its bones get weaker relative to its body mass. Elephants aren't the biggest animals possible; some dinosaurs got a lot bigger, and some animals bigger than elephants existed in more recent times before early humans killed them off, as hunting technology advanced faster than evolution. But fantasy animals like Godzilla and King Kong would just collapse under their own weight. At the other end of the scale, insects are much stronger relative to their mass than large animals. You may have heard than ants can lift fifty times their own weight, and if you could do the same you could life a schoolbus or something. But it's exactly because they are so small that ants have such large relative strength. If you scaled them up, they would be as weak as larger animals.
3. Now to more basic physics. The atom with the smallest nucleus is Hydrogen-1, which is just a proton. The proton is the smallest nuclear particle; you can't make a nucleus smaller than a proton. Now protons and neutrons are attracted to each other by the strong nuclear force, so larger elements are readily created by fusion in stars. But the nuclear force is mediated by a massive particle called a pion. A proton or neutron in one part of the nucleus emits a pion, which is absorbed by another proton or neutron, and this interaction communicates an attractive force. But pions are massive particles, which according to the rules of quantum field theory means that they only live for a short amount of time. Pions are so massive that most of the time they decay in the time it takes to cross a large atomic nucleus, which means that the nuclear attraction gets very weak with distance. Meanwhile, protons also repel electrically because they are all positively charged. The particle that carries the electric force, the photon, is massless, so it can travel forever, unlike the pion. All this means that, for small nuclei, the strong nuclear attraction wins over the electrical repulsion, but at larger distances electrical repulsion wins. And so atomic nuclei have a certain size range, which is unavoidable -- you cannot make a bigger nucleus by putting more nuclei together, because that large nucleus would immediately decay.
4. Speaking of stars, there is a reason they are the size they are. Stars are powered by fusion, which cannot occur unless atoms are squeezed very close together. The force that squeezes the atoms together in stars is gravity. So you need a lot of mass in order to generate the forces necessary. The sun is large enough to sustain fusion, but a smaller clump of gas, like planet Jupiter, isn't. So the sun shines and Jupiter doesn't, purely because the sun is bigger. You might ask if there is an upper limit, and it seems that the upper limit is just how much gas is available. In the early universe, stars were much more massive, but massive stars burn hotter and faster, and so die quicker. In the modern universe, the surviving stars are much smaller because there is not as much available hydrogen left to burn anymore. In fact, the rate of star formation in the universe has already peaked -- today on average, more stars are dying than are being created.
There are countless more examples. I have only talked about size scales, but of course there is scale-dependent behavior in energy, speed, mass, time, temperature, and any other measurement we can think of. It is remarkable that the more we discover laws that apply to all scales, the more we can see that the actual behavior at different scales varies widely, precisely because the laws are universal.
I hope that wasn't too verbose. I've had the above essay bouncing around in my head for a while, and it seemed like a good answer to your question. I may not have understood your question though -- is that what you were asking?
