3 ms·

With the idea that different theories hold at different scales, I've always wondered what happens as you transition between the scales? Saying "Oh, this theory

by eridius 11y ago

With the idea that different theories hold at different scales, I've always wondered what happens as you transition between the scales? Saying "Oh, this theory holds at macro scales, and that one at micro scales" doesn't explain what happens as you slowly build up the micro. At which point does it become macro? What happens on the boundary?

abdullahkhalids 11y ago
There doesn't have to be clear boundary. You can continue using the micro theory at the cost of computational resources and (often) loss of analytical analysibility. Or you can use a mix of both theories. Remember the map is not the territory; the theory/ies not the actual system. This is typically apparent to people working in numerical simulations of systems that don't fall cleanly in one bucket. For example, someone in my department does simulations of biological molecules. They simulate only the part of the system they are interested in (a few atoms) using quantum mechanics. For the rest they use classical physics. The accuracy is much better than what experiment can achieve.
- eridius 11y ago
  So you can keep using the micro theory? That's good to know. Especially given the claims of this article that different scales will always want different theories, I got the impression that micro theories simply don't work anymore at macro scales. I can quite readily believe that the computational resources necessary to evaluate a micro theory at macro levels may be completely infeasible, but as long as the theory still actually holds true (even if you can't compute it), that makes a lot more sense. So I guess the real claim here about the nonexistence of a Theory Of Everything is really about there not being a computable theory that holds true at all scales? It also seems like there's a bit of a confusion going on here between a theory that describes all forces, and a theory that works at all scales. The article here is making the argument that there won't be a Theory Of Everything because you really do want to use different theories at all scales, rather than finding one grand theory that works everywhere. But previous discussion of a "Theory of Everything" (or "Grand Unifying Theory") that I've seen were concerned with finding a theory that describes all the forces, not one that works at all scales. The article did talk a bit about that, and mentioned string theory and superstring theory, but it seemed like more of an aside. My impression is that if we do find a Grand Unifying Theory that describes all the forces at the smallest scale we know of, that still wouldn't be a Theory Of Everything according to this article because it wouldn't be usable at macro levels.
  - amelius 11y ago
    I'm also confused by the premise that "scale" is a concept that is meaningful at any micro/macro level of a theory-of-everything. I mean, at some point, the whole idea of space and "scale" may not even exist anymore.
  - abdullahkhalids 11y ago
    You are essentially correct in the third paragraph. Let me elucidate and be more correct. Bear with me. We have found four field theories (electromagnetism, weak theory, strong theory, gravitation)[1]. Each of theories have a domain of applicability in which, in principle, all the results of all experiments can be predicted using that one theory. Domain of applicability includes length scale, time scale, energies involved etc. This is not a satisfying situation because it is extremely common for systems to not respect this human-imposed domain. Therefore, we want a single theory whose domain is the union of the domains of all of these theories. Call this goal the goal of unification. This has been partly been achieved (electroweak theory), and work continues. Then there is another goal. To find a theory that has a even larger domain of applicability than before. This is the problem of scale. The article claims that the problem of scale is never ending because finite experimental data (and philosophical claims not discussed in the article). String theory is an attempt at the unification goal but it comes with a larger domain of applicability as a bonus. I think this makes the two separate issues discussed in the article clear. I make a third point that you asked about. I make the following observations. General relativity under reasonable restrictions reduces to Newton's law of gravity. The correspondence principle claims that quantum mechanics (typically) reduces to classical mechanics if your system has a large number of particles. Special relativity reduces to classical mechanics for low speeds. These are three pairs of micro-macro theories. In all of these cases the micro theory also works at the scale of the macro theory if you choose to use it: In other words the domain of applicability of the macro theory is a strict subset of the domain of applicability of the micro theory. This subset business does not work so nicely for field theories. Or when looking at general relativity and quantum theories at the same time. There are overlapping domains but no nice strict subset. In that case there is not simple notion of micro-macro theory. However, returning to your original question you can sometimes use multiple theories at the same time to make predictions. Eg. particle physics experiments at CERN do this (multiple field theories), or that blackhole physics that keeps making headlines (quantum and gravity). This situation is of course far from satisfactory and work towards the goal of unification continues. [1] All of these theories of fields assume quantum mechanics which is a theory of particles. Our universe is made up of particles and fields, as far as we know.
n0us 11y ago
I don't know about physics specifically but there is a significant amount of discussion in the Philosophy world about the class of problems that you are describing. http://plato.stanford.edu/entries/vagueness/ http://plato.stanford.edu/entries/vagueness/ http://plato.stanford.edu/entries/sorites-paradox/ http://plato.stanford.edu/entries/sorites-paradox/
lisa_henderson 11y ago
At any scale, you use what is convenient to your goals. Think about maps. If you want to hike a mountain in Colorado, you might go with a topological map where 1 centimeter equals 2 meters. If you'd like to hike the Appalachian Trail, you might want a map where 1 centimeter equals 50 meters. If you want to drive around New York, you might want a good street map where 1 centimeter equals 200 meters. If you are teaching the history of World War II, and you are focused on the Normandy invasion, you might want a map where 1 centimeter equals 500 meters. If you are teaching world history and you want 1 map of the world, you might want a map where 1 centimeter equals 100 kilometers. What details you leave off the map, at each scale, is always a hotly contested issue. You could create a world map with the same level of detail as your topological map of the Colorado mountain: 1 centimeter equals 2 meters. However, the map would be too huge to work with, and it would contain too much detail. You remove detail to keep the map convenient to work with, but it must always be convenient to the task that you are working on. You will get yourself into trouble if you work with too large or too small a scale. I remember when I was young, I was often frustrated with the high-level maps we used in history classes, as the scale was often too high for me to understand what was actually going on. I recall seeing the map of the 30 Year War, a bunch of big red and yellow and blue arrows invading different parts of Europe, and it really told me nothing at all about what happened during the war.
gaze 11y ago
I dunno what these other people are going off about but if you apply quantum mechanics to gravity, you can't renormalize it. If you look too deep at the standard model you run against cutoffs that you yourself have to impose to make things work. So honestly, you take a limit and things blow up. There should be finer structure but instead the theory gives you nonsense.

by eridius 11y ago

abdullahkhalids 11y ago

There doesn't have to be clear boundary. You can continue using the micro theory at the cost of computational resources and (often) loss of analytical analysibility. Or you can use a mix of both theories. Remember the map is not the territory; the theory/ies not the actual system. This is typically apparent to people working in numerical simulations of systems that don't fall cleanly in one bucket. For example, someone in my department does simulations of biological molecules. They simulate only the part of the system they are interested in (a few atoms) using quantum mechanics. For the rest they use classical physics. The accuracy is much better than what experiment can achieve.

eridius 11y ago
So you can keep using the micro theory? That's good to know. Especially given the claims of this article that different scales will always want different theories, I got the impression that micro theories simply don't work anymore at macro scales. I can quite readily believe that the computational resources necessary to evaluate a micro theory at macro levels may be completely infeasible, but as long as the theory still actually holds true (even if you can't compute it), that makes a lot more sense. So I guess the real claim here about the nonexistence of a Theory Of Everything is really about there not being a computable theory that holds true at all scales? It also seems like there's a bit of a confusion going on here between a theory that describes all forces, and a theory that works at all scales. The article here is making the argument that there won't be a Theory Of Everything because you really do want to use different theories at all scales, rather than finding one grand theory that works everywhere. But previous discussion of a "Theory of Everything" (or "Grand Unifying Theory") that I've seen were concerned with finding a theory that describes all the forces, not one that works at all scales. The article did talk a bit about that, and mentioned string theory and superstring theory, but it seemed like more of an aside. My impression is that if we do find a Grand Unifying Theory that describes all the forces at the smallest scale we know of, that still wouldn't be a Theory Of Everything according to this article because it wouldn't be usable at macro levels.
- amelius 11y ago
  I'm also confused by the premise that "scale" is a concept that is meaningful at any micro/macro level of a theory-of-everything. I mean, at some point, the whole idea of space and "scale" may not even exist anymore.
- abdullahkhalids 11y ago
  You are essentially correct in the third paragraph. Let me elucidate and be more correct. Bear with me. We have found four field theories (electromagnetism, weak theory, strong theory, gravitation)[1]. Each of theories have a domain of applicability in which, in principle, all the results of all experiments can be predicted using that one theory. Domain of applicability includes length scale, time scale, energies involved etc. This is not a satisfying situation because it is extremely common for systems to not respect this human-imposed domain. Therefore, we want a single theory whose domain is the union of the domains of all of these theories. Call this goal the goal of unification. This has been partly been achieved (electroweak theory), and work continues. Then there is another goal. To find a theory that has a even larger domain of applicability than before. This is the problem of scale. The article claims that the problem of scale is never ending because finite experimental data (and philosophical claims not discussed in the article). String theory is an attempt at the unification goal but it comes with a larger domain of applicability as a bonus. I think this makes the two separate issues discussed in the article clear. I make a third point that you asked about. I make the following observations. General relativity under reasonable restrictions reduces to Newton's law of gravity. The correspondence principle claims that quantum mechanics (typically) reduces to classical mechanics if your system has a large number of particles. Special relativity reduces to classical mechanics for low speeds. These are three pairs of micro-macro theories. In all of these cases the micro theory also works at the scale of the macro theory if you choose to use it: In other words the domain of applicability of the macro theory is a strict subset of the domain of applicability of the micro theory. This subset business does not work so nicely for field theories. Or when looking at general relativity and quantum theories at the same time. There are overlapping domains but no nice strict subset. In that case there is not simple notion of micro-macro theory. However, returning to your original question you can sometimes use multiple theories at the same time to make predictions. Eg. particle physics experiments at CERN do this (multiple field theories), or that blackhole physics that keeps making headlines (quantum and gravity). This situation is of course far from satisfactory and work towards the goal of unification continues. [1] All of these theories of fields assume quantum mechanics which is a theory of particles. Our universe is made up of particles and fields, as far as we know.

n0us 11y ago

I don't know about physics specifically but there is a significant amount of discussion in the Philosophy world about the class of problems that you are describing. http://plato.stanford.edu/entries/vagueness/ http://plato.stanford.edu/entries/vagueness/ http://plato.stanford.edu/entries/sorites-paradox/ http://plato.stanford.edu/entries/sorites-paradox/

lisa_henderson 11y ago

At any scale, you use what is convenient to your goals. Think about maps. If you want to hike a mountain in Colorado, you might go with a topological map where 1 centimeter equals 2 meters. If you'd like to hike the Appalachian Trail, you might want a map where 1 centimeter equals 50 meters. If you want to drive around New York, you might want a good street map where 1 centimeter equals 200 meters. If you are teaching the history of World War II, and you are focused on the Normandy invasion, you might want a map where 1 centimeter equals 500 meters. If you are teaching world history and you want 1 map of the world, you might want a map where 1 centimeter equals 100 kilometers. What details you leave off the map, at each scale, is always a hotly contested issue. You could create a world map with the same level of detail as your topological map of the Colorado mountain: 1 centimeter equals 2 meters. However, the map would be too huge to work with, and it would contain too much detail. You remove detail to keep the map convenient to work with, but it must always be convenient to the task that you are working on. You will get yourself into trouble if you work with too large or too small a scale. I remember when I was young, I was often frustrated with the high-level maps we used in history classes, as the scale was often too high for me to understand what was actually going on. I recall seeing the map of the 30 Year War, a bunch of big red and yellow and blue arrows invading different parts of Europe, and it really told me nothing at all about what happened during the war.

gaze 11y ago

I dunno what these other people are going off about but if you apply quantum mechanics to gravity, you can't renormalize it. If you look too deep at the standard model you run against cutoffs that you yourself have to impose to make things work. So honestly, you take a limit and things blow up. There should be finer structure but instead the theory gives you nonsense.