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How accurate are physical laws?

  1. Jul 17, 2013 #1
    Newton's laws, coulomb's law are all very neat but are they totally accurate? According to modern instruments which can measure up-to remarkable precision, do these laws behave perfectly?
    I haven't studied quantum mechanics yet but as far as I have heard it's all about probabilities ... we can't predict anything, all we can say is about the probability of a certain event happening. So how come there exists such precise relations among physical things when underneath there is so much randomness? I can only think that these laws are only an approximation and don't behave perfectly.

    Further how do we even test these laws? There are so many variables to consider but I suppose that's a different question.
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  3. Jul 17, 2013 #2


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    If physical laws were not accurate they would not be called laws, they would called approximations.

    I can't quote you a source, but I'm sure General Relatively has been found accurate to beyond our ability to make measurements.

    As much as 30 years ago, Richard Feynman was fond of telling folks that quantum mechanics had been found accurate to the equivalent of measuring the width of the United States and getting an answer that fit to within the width of a human hair (and I doubt we could make measurements any more refined than that at the time).
  4. Jul 17, 2013 #3
    Okay, wow! But how does this happen if underneath all the particles are behaving randomly? How does that translate to laws? (I have never studied quantum mechanics before so I might be wrong about the whole random thing)
  5. Jul 17, 2013 #4


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    Newton's 2nd law is approximate; it is really only valid in the non-relativistic domain and non-quantum mechanical domain so you are correct. AFAIK the most scientifically accurate theory we have (with regards to experimental prediction power) is quantum electrodynamics.
  6. Jul 17, 2013 #5
    It's "random" in the technical sense of the word, which essentially means it's impossible to know the outcome of a measurement regardless of how much information you know before you make it.

    However, "random" doesn't mean anything can happen. The laws govern what a particle can do, and what the probability of that happening is. This can include a zero probabability, in which case it's impossible for the particle to behave in such a way.

    For example, in a piece of metal there are an enormous number of "free" electrons moving about inside it, and quantum mechanics tells us that the probability of any two of these electrons occupying the same state is zero. When we do measurements on metals, this prediction is in perfect agreement with the experiment, as far as anyone can tell.
  7. Jul 17, 2013 #6
    Because that random behavior that is present in our theory is present in nature itself.
  8. Jul 17, 2013 #7
    But there might be some modified version of newton's second law given by QED theory or some other, right?
  9. Jul 17, 2013 #8
    I didn't get that.
    EDIT: Are you saying that theories are approximate because of the randomness in nature?
    Last edited: Jul 17, 2013
  10. Jul 17, 2013 #9


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    No, Newton's law is a very deterministic, fixed, classical physics "law" that happens to have been (and still is) a VERY good predictor of mechanics at small scales ("small" = measured in miles, not millions of miles). It is "wrong" in that it is a localized approximation of what General Relatively predicts. It isn't going to be "updated" by anything (other than GR, by which it has already BEEN updated).

    This whole "random" thing is at a sub-atomic level. If you measure something in feet or more, the error produced is trivial besides, this is below our ability to measure.
  11. Jul 17, 2013 #10
    Like the value of PIE = 22/7 is just a certain approximation but used everywhere.
    These laws are the best yet approached approximations.

    So, if we take Newton Law of Gravitation it was more clarified by Einstein in his general relativity. (Describing Gravitation as curvature of Space-Time). I read somewhere that when some people did an experiment with newton's law by applying it on moon's path.. They found a difference in the current position of moon and what it was predicted by using Newton's law.
  12. Jul 17, 2013 #11


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    Newton's laws and Coulomb's law are both approximations which are measurably incorrect in certain regimes. Specifically, Newton's laws are incorrect as v approaches c, and Coulomb's law is incorrect any time charges are moving.

    No, but there are other laws which are accurate to the best precision we can reach experimentally.

    The laws give very precise predictions for the expected probability distributions, so you perform thousands or millions of experiments and use those to set very precise limitations on the actual probability distribution.

    Laws are generally tested using a test theory which is more general than the actual theory in question. The test theory has some unknown parameters and, for certain values of the parameters, it reduces to the actual theory. Then you use the test theory to make an experiment to measure the parameter and put constraints on the possible deviations from the actual theory.
  13. Jul 17, 2013 #12
    This is what I usually hear too. I went to a talk by Freeman Dyson and he claimed that GR is more accurate because it has more digits/significant figures of predictive power.
  14. Jul 17, 2013 #13
    Right, I agree. I think that the use of the word "law" in science is usually a misnomer. Its an old school way of thinking of science from before we developed our modern philosophy of science. In the past they viewed science as though they were looking for "truth" or "reality". With this way of thinking, unfalsified conclusions naturally seem like laws. But now we have a modern way of looking at science where we construct models (mathematical or otherwise) that describe and predict our observations. All conclusions are considered tentative with respect to new observations and evidence. These days new theories are not called laws for this reason.

    You might also consider the mathematical equation the law. If you consider the equation alone as the law then it makes no difference what experimental evidence you have, coulombs equation is coulombs law. The theory is then that the law describes and predicts our observations. I see this as a ad-hoc way of defending sloppy language, but its an interpretation.
  15. Jul 17, 2013 #14


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    Ah that's quite interesting to hear. At least we can appreciate that both theories are both theoretically beautiful and experimentally powerful :smile:
  16. Jul 17, 2013 #15


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    Uh ... "used everywhere"? Really? I don't think so. I take it you don't do any calculations that require more than a couple of significant digits.
  17. Jul 17, 2013 #16


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    Strange. It takes just one fewer keystrokes to type 22/7 than it does to type the number 3.142, which the near f that simple fraction equivalent - but its rounded value is 3.143 - so you can only rely on 3.14 - same number of keystrokes. I wonder why it ever caught on.
  18. Jul 17, 2013 #17
    No, what I mean is that, say, our theories predict that we'll get result X 50% of the time and result Y 50% of the time, but we cant be more certain than that. But this is a reflection of nature where, upon conducting a large number of experiments we find the result of the experiments match that distribution.
  19. Jul 17, 2013 #18


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    The approximation is older than computers.

    It is expected that general relativity is not exact, as it does not include quantum mechanics.
    It is expected that quantum field theory is not exact, as it does not include gravity.

    Therefore, our current "laws of physics" are probably just very good approximations. That is not a fundamental problem - if the universe follows some laws (and it looks like it does), it should be (in theory) possible to discover those laws. Those laws would be exact.
  20. Jul 17, 2013 #19


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    If you're doing it the hard way, using pencil and paper while you're dodging the velociraptors.... You can multiply by 22 in your head (double and add ten percent) and then you just have to do a long division by seven. That's way less work than multiplying by a four-digit number.
  21. Jul 18, 2013 #20
    "Three point one four" is 4 syllables when you say it out loud. "Twenty-two sevenths" is 5, "twenty-two over seven" is even worse at 7 syllables. In addition, if you learn pi as 3.14 then it is easy to add more digits later if they are needed. If you want to upgrade 22/7 to something more precise your next good option is 311/99. If you likewise add 2 digits to 3.14 you have 3.1416 which is ≈24 time more accurate then 311/99.
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