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These "laws" of physics can be written as simple mathematical equations only because these equations make various simplifying assumptions. Whenever mathematics

These "laws" of physics can be written as simple mathematical equations only because these equations make various simplifying assumptions. Whenever mathematics is applied to the real world, there are always simplifying assumptions made. Otherwise, the problems become intractable. It does not matter what area that you investigate, you will find that assumptions are made to simplify the mathematics. For our purposes, these "simple" equations work, but they are still limited approximations of what we see around us.

lisper 9y ago
> these equations make various simplifying assumptions Not the fundamental equations. Yes, a lot of complexity emerges from those, just like a lot of complexity emerges in the Mandelbrot set. But as far as experiment has been able to determine, the equations of GR and QM are exactly correct.
- projektir 9y ago
  Isn't the whole problem that current QM equations are not the whole picture, and work on QM scale only?
  - lisper 9y ago
    No, QM works at every scale, it's just that at large scales the math is too hard to carry through and we have to use approximations. It is true that either QM or GR (or both) as currently formulated will break down near the event horizons of black holes, but there is no reason to believe that once we figure that out the result will be significantly different in character than all the other laws of physics that have been worked out up to now.
    - projektir 9y ago
      > QM works at every scale > either QM or GR (or both) as currently formulated will break down near the event horizons of black holes These seem to be in conflict. Black holes is exactly what I was talking about. From what I've understand there's no unified theory or anything close to a unified theory for certain objects in space, which means the landscape is very open for some weird, weird stuff. Physics is already extremely weird. > there is no reason to believe that once we figure that out the result will be significantly different in character than all the other laws of physics that have been worked out up to now I would consider both general relativity and quantum mechanics to be drastically different things compared to what came before, going from "this is reasonable" to "WTF", so I can't agree with this statement at all.
      - lisper 9y ago
        > the landscape is very open for some weird, weird stuff Yes, that's true. > Physics is already extremely weird. Yes, that's true too. It is weird. But it's not complicated (in the strict computational sense). > I would consider both general relativity and quantum mechanics to be drastically different things compared to what came before In one sense yes, but not in the sense that matters for this discussion. GR and QM are conceptually very different from Newtonian mechanics, but they are similar insofar as they can be written down as simple (in the technical sense) mathematical equations. So there's no reason to expect that the next surprise will be different in that regard.
        projektir 9y ago
        > In one sense yes, but not in the sense that matters for this discussion. I'm not really sure when you decided on this, as I don't really evaluate the complexity of something based on whether it follows math. I evaluate it based on the nature of the logic and abstraction that needs to be used to follow it. The fact that you can approximate the location of particles with a math equation doesn't really feel to me that we're doing the same thing, even mathematically, that we were doing in Newtonian mechanics. That seems very much in line with "These "laws" of physics can be written as simple mathematical equations only because these equations make various simplifying assumptions.".
        lisper 9y ago
        > I evaluate it based on the nature of the logic and abstraction that needs to be used to follow it. What do you think math is? > The fact that you can approximate the location of particles with a math equation doesn't really feel to me that we're doing the same thing, even mathematically, that we were doing in Newtonian mechanics. Huh? Are you referring to the fact that QM is probabilistic? That's not a simplifying assumption, that's a reflection of how the world actually is.
- oldandtired 9y ago
  I have had my dinner and a wonderful dinner it was too - my wife is a brilliant cook. She pours love into every meal and it shows in the outcome. So, with that out of the way, The fundamental equations all have simplifying assumptions. Even the equations of GR and QM are based on simplifying assumptions. Otherwise, you wouldn't have various scientists disputing their veracity. I have copies of a certain portion of some work done in the 1960's which look at the assumptions made for the development of QM. The particular author quite clearly demonstrates the various assumptions made in the development of QM. In his case, he removed some of those assumptions and redeveloped the various models. He came up with a different formulation. I have over the years tried to have a good look at the work in question to see if there is things that can be engineered from the work. There is a certain level of mathematics that I am still trying to wrap my mind about. It is used in both models (QM and his). From my perspective, it does away with the strong force as unnecessary by making a modification to electromagnetic theory and it gives what you see in experimental results. Does it have merit, I don't know. But I am happy to put it on the same footing as QM as a possible explanation of what we see. There is a model that also does away with gravity as a separate force. The model in question formulates gravity as a residual effect of electromagnetic theory. Does it have merit. Again, I am putting it on a similar footing. My attempts to use a CAS have only been partially successful as I need to understand a bit more about Maxima first and what I can do with it. For me, these are ongoing interests (among many) which I dabble in when I have time on my hands. I am looking at one paper that does an analysis of SR and as yet I have not finished studying this paper. The author's main conjecture is that SR only works because Einstein made some simplifying assumptions by which SR then gets the measured results. His conjecture is that if those assumptions are not made then SR gives the wrong results. Does it have merit, I can't say at this point. It again hinges on whether or not I can get the work into Maxima. For the same reasons above, I only look at this when I have time on my hands. Many people assume that the E = mc2 is a specific formulation of Einstein's work. Yet in my engineering undergraduate days in the late 1970's, the same formula was developed directing from Classical Electromagnetic Theory with no recourse to anything that Einstein did. But even here, it is not a simple equation that is correct, you have to know what the E represents and what the m represents. It is context sensitive and you have to know what the assumptions are.
  - 9y ago

lisper 9y ago

> these equations make various simplifying assumptions Not the fundamental equations. Yes, a lot of complexity emerges from those, just like a lot of complexity emerges in the Mandelbrot set. But as far as experiment has been able to determine, the equations of GR and QM are exactly correct.

projektir 9y ago
Isn't the whole problem that current QM equations are not the whole picture, and work on QM scale only?
- lisper 9y ago
  No, QM works at every scale, it's just that at large scales the math is too hard to carry through and we have to use approximations. It is true that either QM or GR (or both) as currently formulated will break down near the event horizons of black holes, but there is no reason to believe that once we figure that out the result will be significantly different in character than all the other laws of physics that have been worked out up to now.
  - projektir 9y ago
    > QM works at every scale > either QM or GR (or both) as currently formulated will break down near the event horizons of black holes These seem to be in conflict. Black holes is exactly what I was talking about. From what I've understand there's no unified theory or anything close to a unified theory for certain objects in space, which means the landscape is very open for some weird, weird stuff. Physics is already extremely weird. > there is no reason to believe that once we figure that out the result will be significantly different in character than all the other laws of physics that have been worked out up to now I would consider both general relativity and quantum mechanics to be drastically different things compared to what came before, going from "this is reasonable" to "WTF", so I can't agree with this statement at all.
    - lisper 9y ago
      > the landscape is very open for some weird, weird stuff Yes, that's true. > Physics is already extremely weird. Yes, that's true too. It is weird. But it's not complicated (in the strict computational sense). > I would consider both general relativity and quantum mechanics to be drastically different things compared to what came before In one sense yes, but not in the sense that matters for this discussion. GR and QM are conceptually very different from Newtonian mechanics, but they are similar insofar as they can be written down as simple (in the technical sense) mathematical equations. So there's no reason to expect that the next surprise will be different in that regard.
      - projektir 9y ago
        > In one sense yes, but not in the sense that matters for this discussion. I'm not really sure when you decided on this, as I don't really evaluate the complexity of something based on whether it follows math. I evaluate it based on the nature of the logic and abstraction that needs to be used to follow it. The fact that you can approximate the location of particles with a math equation doesn't really feel to me that we're doing the same thing, even mathematically, that we were doing in Newtonian mechanics. That seems very much in line with "These "laws" of physics can be written as simple mathematical equations only because these equations make various simplifying assumptions.".
        lisper 9y ago
        > I evaluate it based on the nature of the logic and abstraction that needs to be used to follow it. What do you think math is? > The fact that you can approximate the location of particles with a math equation doesn't really feel to me that we're doing the same thing, even mathematically, that we were doing in Newtonian mechanics. Huh? Are you referring to the fact that QM is probabilistic? That's not a simplifying assumption, that's a reflection of how the world actually is.
oldandtired 9y ago
I have had my dinner and a wonderful dinner it was too - my wife is a brilliant cook. She pours love into every meal and it shows in the outcome. So, with that out of the way, The fundamental equations all have simplifying assumptions. Even the equations of GR and QM are based on simplifying assumptions. Otherwise, you wouldn't have various scientists disputing their veracity. I have copies of a certain portion of some work done in the 1960's which look at the assumptions made for the development of QM. The particular author quite clearly demonstrates the various assumptions made in the development of QM. In his case, he removed some of those assumptions and redeveloped the various models. He came up with a different formulation. I have over the years tried to have a good look at the work in question to see if there is things that can be engineered from the work. There is a certain level of mathematics that I am still trying to wrap my mind about. It is used in both models (QM and his). From my perspective, it does away with the strong force as unnecessary by making a modification to electromagnetic theory and it gives what you see in experimental results. Does it have merit, I don't know. But I am happy to put it on the same footing as QM as a possible explanation of what we see. There is a model that also does away with gravity as a separate force. The model in question formulates gravity as a residual effect of electromagnetic theory. Does it have merit. Again, I am putting it on a similar footing. My attempts to use a CAS have only been partially successful as I need to understand a bit more about Maxima first and what I can do with it. For me, these are ongoing interests (among many) which I dabble in when I have time on my hands. I am looking at one paper that does an analysis of SR and as yet I have not finished studying this paper. The author's main conjecture is that SR only works because Einstein made some simplifying assumptions by which SR then gets the measured results. His conjecture is that if those assumptions are not made then SR gives the wrong results. Does it have merit, I can't say at this point. It again hinges on whether or not I can get the work into Maxima. For the same reasons above, I only look at this when I have time on my hands. Many people assume that the E = mc2 is a specific formulation of Einstein's work. Yet in my engineering undergraduate days in the late 1970's, the same formula was developed directing from Classical Electromagnetic Theory with no recourse to anything that Einstein did. But even here, it is not a simple equation that is correct, you have to know what the E represents and what the m represents. It is context sensitive and you have to know what the assumptions are.
- 9y ago