Q&A: Dependence of the Physical Constants on One Another
Dependence of the Physical Constants on One Another
Question
Hi Rabbi,
I saw that someone asked you whether one cannot prove the existence of God from the fine-tuning among the physical constants, because perhaps there are several constants that depend on one another, and when one of them allows life, the second is automatically tuned to a precise value that also allows life.
You answered that even if there are two constants that depend on one another, that merely reduces the count by one constant overall (instead of a fit among 6 constants, there is a fit among 5).
And I, in my humble way, do not understand how this reduces the number of constants from which one can argue, for even if two constants depend on one another, that itself is not necessary; rather, it follows from a very particular mechanism that causes it so that if G equals 6.67, then Planck's constant equals some value x that allows life (just an example). As long as one can conceive of a world in which a life-supporting value of G does not yield a life-supporting value of Planck's constant, the question returns regarding the present mechanism: why is the universe built in such a special way that one life-supporting constant is "enough," and all the other constants are necessarily derived from it and receive a life-permitting value.
As long as you have not shown that there is a *logical* or *mathematical* necessity for a certain value of G to bring about a certain value of Planck's constant, one cannot say that we have "lost" one constant.
Best regards.
Answer
If the dependence between constants is itself a law of nature, then there is no dependence here (because the mechanism creating the dependence would itself contain another constant). What is meant here is logical-mathematical dependence, not scientific dependence. That is exactly what you wrote at the end of your remarks.
Discussion on Answer
If there is a constant X and a constant Y such that for some logical reason X=3Y. I didn't understand the question. You yourself said this, so what exactly is unclear? I didn't say that in practice there are such constants, only what the possible states of affairs could be.
As for our actual world, there is an identity between inertial mass and gravitational mass, and Einstein explained that this is really the same constant (expressing the curvature of space created by mass). That is an apparent example of logical dependence, but not really. A space is formed that curves because of masses, and that is what creates the dependence.
That is exactly what I meant: do we actually know of the existence of such constants in practice? Because atheists claim there are, and in practice I haven't found any such case.
In the end it always turns out that although there is a connection between the constants, the connection itself follows from a non-necessary equation, or from some particular property of mass/space that is itself not necessary.
Do you not know of such a thing in practice?
There are lots of connections, and therefore they defined six independent constants. There is a connection between the speed of light in a vacuum and the speed outside a vacuum (through the dielectric coefficient). There are many other connections too, but as stated, the discussion has no real significance.
*Logical connections*!! Not just any connections.
That is not a well-defined question. Anything that is logically connected is not two constants but one. Therefore if you ask whether there is an example of two constants that are logically connected—the answer is no, by definition. But as stated, that does not mean anything. I think this is the place to end it.
Do you have an example of constants that are dependent on one another logically-mathematically, such that the dependence could not have been otherwise?