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Fixing the Constants of Equations to Unity

  1. Jan 11, 2014 #1
    So I was revising elementary classical physics and Newton's equations of motion.

    When you apply a force on an object in free space, far from gravitational fields, you find that the object accelerates. By conducting experiments where you vary the force or the mass and look at the acceleration, you find that

    Force, F α Mass, m * Acceleration, a
    Introduction the constant k of the equation,
    F = kma

    Now, accelration is well-defined if you know how to define length (through a unit metre stick) and time (through an atomic clock - cesium i believe is used to standardize it).
    You can standardize a unit mass as well. Any other mass is equal to the unit mass if it balances out on a see-saw type of balance.

    Now, we define 'k' as the force required to accelerate a mass of 1 kg by 1m/s^2
    If we choose the units of force such that this particular quantity of force is one unit, the k=1.

    My question is wouldn't we just be better off by setting the constant in all the relations in physics to be 1 in a similar manner.

    My initial guess is that we are allowed to do this only once. Whenever we have any equation even remotely relating to a force, we can't set the constant equal to one. If we attempted to do so, we would first have to modify our unit of force, by making k≠1.

    I would love to hear from the members of the Forum regarding your views on this.
  2. jcsd
  3. Jan 11, 2014 #2


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    hi ian! :smile:
    we can for example put c = G =1 (cosmologists often do this, to make the equations easier)

    unfortunately, that would mean that everyday distances and masses (such as your height
    and weight) would be measured in billionths of light-seconds and light-weights :wink:

    similarly, we ought really to define µo (permeablility of the vacuum) to be 1 (or 4π, for technical reasons), but that would mean everyday current or voltage would be measured in millions of units, so we use 4π*10-7 instead
  4. Jan 11, 2014 #3

    Meir Achuz

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    In gaussian units, used by most physicists in doing their own research,
    E=q/r^2, and F/L=2II'/(c^2 d).
    In natural units, used by most high energy theorists, c and hbar are 1.
    The most important constant is alpha=e^2=1/137, and is dimensionless.
  5. Jan 11, 2014 #4


    Staff: Mentor

    You are definitely allowed to do this. This is the basis behind Gaussian units or Lorentz Heaviside units.

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