Fixing the Constants of Equations to Unity

[ian_dsouza]

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.

 

[tiny-tim]

hi ian!

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.

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

similarly, we ought really to define µ_o (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

 

[Meir Achuz]

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.

 

[Dale]

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.

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

http://en.wikipedia.org/wiki/Lorent...ns_and_comparison_with_other_systems_of_units

 

[pmacias]

I would caution against arbitrarily setting constants in equations to unity. While it may seem simpler and more convenient, it could potentially lead to major errors in our calculations and understanding of the physical world.

Firstly, constants in equations are not arbitrary. They are determined through experimental data and represent fundamental physical quantities. Changing them to unity without proper justification could lead to incorrect results.

Secondly, setting all constants to unity would limit our ability to make accurate predictions and perform precise measurements. Different physical phenomena have different levels of complexity and require different constants to accurately describe them. By setting all constants to unity, we would be oversimplifying these phenomena and potentially missing important details.

Furthermore, constants play a crucial role in connecting different branches of physics. For example, the gravitational constant G is used in equations describing both classical mechanics and general relativity. If we were to set it to unity, we would lose the connection between these two theories and hinder our understanding of the universe.

In addition, constants provide a way to compare and validate theories. By keeping them as they are, we can test the validity of a theory by comparing its predicted value for a constant with the experimentally determined value. If we were to set all constants to unity, this important aspect of scientific inquiry would be lost.

In conclusion, while setting constants to unity may seem like a convenient solution, it is not a scientifically sound approach. It is important to respect the fundamental nature of constants and use them as they are determined through experimental data. This allows for accurate predictions, precise measurements, and a deeper understanding of the physical world.