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Mark Says:

June 6th, 2007 at 7:27 pm

I’ve just read this discussion and I am impressed by angryphysicist’s and John’s perseverance with Pioneer.

I was thinking that the troublesome idea of “constant of nature” might be pinned down easier by moving away from G and focusing on something simpler like the density of water.

Pioneer, take some quantity of water. Measure its volume using any units you choose. Measure its mass using any units you choose. Using the same units, repeat this for different quantities of water. You will notice that the mass of the water is always some constant times its volume. That constant is water’s density with respect to the units you have chosen. It is a constant of nature because if you explain how you measure mass and volume another scientist will come up with exactly the same constant.

You will now probably argue that “that value can’t be a constant because its defined in terms of my units. If I change my units the density of water will change!”. There are two responses to this.

Firstly, suppose you initally chose metres cubed for volume and kilograms for mass. The density of water you observe will be in kilograms per metres cubed. If someone else decided to repeat your experiments using inches cubed and pounds they would arrive at a different value for the density of water. However, there is a purely mathematical transformation from kgs/m^3 to lbs/in^3. If you know the relationship between kgs and lbs as well as ms and ins you can compute the density of water in either system without doing any further experiments. Something is invariant here under a change of units. That thing that is invariant is what people call a “constant of nature”, not any particular measurement of that constant.

If that doesn’t convince you, we can extend the experiment slightly. This time, choose your units and experimentally come up with a value for the density of water AND the density of lead. Divide the latter by the former and you will get some number which tells you how much more dense lead is than water. You can repeat this experiment with ANY units you choose and you will arrive at exactly the same number. This number is also a constant of nature. It just so happens that it is dimensionless - i.e., independent of the units you choose to measure it with.

In both these cases there was some fact about the universe that we were measuring. In the first case it was the density of water. In the second it was the relative density of lead to water. In the case of the constant G it is the relationship between the masses of two objects, the distance between them and the force of attraction between them.

For me and other scientists these experimentally observed constants of proportionality are what are known as “constants of nature”. How does your understanding of the term differ from this? If you disagree with this definition could you please try to explain your difficultly with respect to the examples I have just given?