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Laws of physics on a page

  1. Aug 2, 2012 #1
    I have two questions. First, Paul Davies stated that the" Great Rule Book of Nature" would fit comfortably onto a single page. Is there a reference for these laws of physics?
    Second, the velocity of light is a fundamental constant. Has anyone analyzed what would change if the value were different, say a thousand times greater? Thanks
     
  2. jcsd
  3. Aug 3, 2012 #2
    This rule book of nature you are referring to, is the future goal of physics. We do not yet have this rule book, as our most fundamental theories of nature today certainly cannot fit on a single page. On top on this, we are far from having a complete understanding of nature. The closest pursue of this goal today is perhaps string theory, claiming to be able to produce the "Great Rule Book of Nature", consisting of just a single page.

    Yes. Nature as we know her is filled with random constants, such as the speed of light, which numerical values does not seem to have any connection to anything we know. Again, string theory is perhaps the best present theory, striving to give an explanation of the values of these constants.
    We know one thing though; if you were to mess with the values of the constants, as you describe, our universe would be a very different place. Change the value of any constant (eg the speed of light) sufficiently (often just by a few percentages), and our universe would not be able to incorporate atoms, much less life of any kind.
    As an example, if the speed of light were to change by a few percentage (up or down), the process that converts helium into more massive atoms inside stars would fail. That means that the universe would be comprised of just two kinds of atoms; hydrogen and helium. This is insufficient to lead to any imaginable form of life. For a list of similar results of changes to the fundamental constants, see
    http://www.rareuniverse.org/evidence_for_creation/finetuned.html
     
  4. Aug 3, 2012 #3

    mfb

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    The Standard Model Lagrangian easily fits on a single page (and even on T-shirts). The calculations based on this can fill several books, but that is not part of the fundamental theory.

    At the moment, string theory is an interesting collection of mathematics, without significant relevance to any measurements of particle physics.


    "Changing the speed of light" is not a well-defined process. The speed of light is exactly 1 (by definition) in natural units, and there is no way to change this. The speed of light is used to define the length of a meter - a different speed of light would simply change the length of a meter, together with all other length scales. You would not see any difference.
    As you can see, the speed of light is not a fundamental parameter. It is just a convenient thing we use to define our everyday units (here: the meter) in a reproducible way.

    The fundamental parameters of nature are dimensionless. In this case, you can measure them independent of all measurement systems. The fine-structure constant (about 1/137) is a famous example of that. If you change this, physics changes.

    Different constants lead to different universes, some of them might produce completely other structures, and other life forms. Is our universe fine-tuned for us? No, we are fine-tuned for our universe, just because we evolved there.
     
  5. Aug 3, 2012 #4
    If any of the components of the Standard Model of particle physics were even a few percent different tha we observe them, we would not be here. The charge of the electron; the mass of the proton, etc,etc,etc.

    Wikipedia explains it this way:
    http://en.wikipedia.org/wiki/Fine-tuned_Universe



    Why our observed constants? Nobody knows, we cannot yet derive them from first principles:

     
  6. Aug 3, 2012 #5
    This may have less to do with physics and more to do with our ability to develop concise mathematical tools and language as we advance along in our knowledge. For example let's consider Newton's universal law of gravitation vs. Einstein's general relativity, specifically how much more space do I need on a page for Einstein?. Newton's equation can be written down using 10 symbols (counting mass subscripts and division bar). Einstein's field equations (EFE) can be written down using only 25 characters, not that much more than Newton. Yet my Gravitation book which *explains* Einstein is the size of a yellow pages, and it assumes a lot of prerequisite knowledge. Even Newton's "simpler" laws require mastery of calculus, algebra, and arithmetic, each of which require more than a page to describe.
     
  7. Aug 5, 2012 #6
    I do not understand natural units where h,c,Ke all equal 1. How is mass or energy calculated in natural units? From the equation E = mc2, if the value of c were different, doesn't mass or energy have to change? Thanks
     
  8. Aug 5, 2012 #7
    Having different set of units is nothing magical. See, the speed of light is 300000 km/s, or 300000000 m/s, or 186000 mi/s, etc. So depending on your choice of units the speed of light is different, therefore energy of a body with mass m is different. But that's not a problem because you measure energy in different units as well (or mass or both). The only important thing is that energy is proportional to mass. That's the physical. In relativity it is very convenient to set c = 1, so that you don't have to write the c's everywhere. So energy becomes E = m. Numerically then the mass is equivalent to the energy (in the rest frame). Physically the mass is proportional to the energy.
     
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