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The reason for initiating this thread is to have read another, initiated by Serra Nova here in the forum, accessible at the following address.
https://www.physicsforums.com/threads/fundamental-physical-constants.938267/
The starting note of this thread refers to knowing if those terms called fundamental constants are really constant. The attempt to reflect that, led me to the question that titles this thread: why do the fundamental constants have the values we know and not others? I want to expose how little and imprecise I managed to reason, hoping to receive help to filter my ideas, discard what should be discarded and correct what needs to be corrected. Is the next.
The task of looking for an answer always refers to a context. We have learned that quantum electrodynamics is the most reliable theory to date. So the advisable thing is to base ourselves on something that comes from that theory. It is also advisable to start with a mathematically simple expression.
There is a mathematically simple expression that comes from QED. Corresponds to the fine structure ##\alpha## constant.
[tex]\displaystyle \alpha=\dfrac{e^2}{2 \ \varepsilon_o \ C \ h} [/tex]
The method of reduction to the absurd is mathematically valid to demonstrate something. The way to apply it in this case is to treat as variables the four terms of the right member that we normally accept as fundamental constants. That implies treating ##\alpha## as a function of 4 variables, which are ##e##, ##\varepsilon_o##, ##C##, ##h##.
1. The term ##\alpha## is dimensionless. So we can not exclude the possibility that ##\alpha## is a numerical factor proper to the electrodynamic laws. In case that happens, the numeric value of ##\alpha## should appear as a result of a theorem deduced from the electrodynamic laws, in a purely theoretical way and independent of all experimental data. Pure theory, which with a theorem gives the value of ##\alpha##. In that case the term ##\alpha## could not be treated as a variable in the absurdity method and, for that reason, the 4 variables would be forced to adopt a value tetrad according to the value of ##\alpha## imposed by the electrodynamic laws. The absurd method would have a legal framework of application. Nobody has published until today a theorem that expresses the value of ##\alpha## determined by the electrodynamic laws. What will we do then? Will we treat ##\alpha## as a constant or as a variable? Many physicists trust the possibility of formulating this theorem and dedicate a great effort to that. Let's trust them and decide to treat ##\alpha## as a constant in the absurdity method.
2. We know that ##\varepsilon_o## and ##C## are interdependent, because ##\varepsilon_o## appears in the electrodynamic expression of ##C##.
[tex]\displaystyle C=\dfrac{1}{\sqrt{ \mu_o \ \varepsilon_o} }[/tex]
Now we are facing two really fundamental issues.
Is there or not complete interdependence, that is to say that each variable depends on the other 3 ? The electric field and the magnetic field are interdependent. Then the corresponding variables too. The reasonable thing is to assume that there is complete interdependence between the 4 variables. In that case there is only one tetrad of values according to the value of ##\alpha##. The method of varying the short list and demonstrating that the variation is absurd leads to a univocal response, that is, a unique and unambiguous response.
The previously expressed does not answer the initial question of this thread. It simply shows that there is hope of reaching the answer based on the laws of electrodynamics.
https://www.physicsforums.com/threads/fundamental-physical-constants.938267/
The starting note of this thread refers to knowing if those terms called fundamental constants are really constant. The attempt to reflect that, led me to the question that titles this thread: why do the fundamental constants have the values we know and not others? I want to expose how little and imprecise I managed to reason, hoping to receive help to filter my ideas, discard what should be discarded and correct what needs to be corrected. Is the next.
The task of looking for an answer always refers to a context. We have learned that quantum electrodynamics is the most reliable theory to date. So the advisable thing is to base ourselves on something that comes from that theory. It is also advisable to start with a mathematically simple expression.
There is a mathematically simple expression that comes from QED. Corresponds to the fine structure ##\alpha## constant.
[tex]\displaystyle \alpha=\dfrac{e^2}{2 \ \varepsilon_o \ C \ h} [/tex]
The method of reduction to the absurd is mathematically valid to demonstrate something. The way to apply it in this case is to treat as variables the four terms of the right member that we normally accept as fundamental constants. That implies treating ##\alpha## as a function of 4 variables, which are ##e##, ##\varepsilon_o##, ##C##, ##h##.
1. The term ##\alpha## is dimensionless. So we can not exclude the possibility that ##\alpha## is a numerical factor proper to the electrodynamic laws. In case that happens, the numeric value of ##\alpha## should appear as a result of a theorem deduced from the electrodynamic laws, in a purely theoretical way and independent of all experimental data. Pure theory, which with a theorem gives the value of ##\alpha##. In that case the term ##\alpha## could not be treated as a variable in the absurdity method and, for that reason, the 4 variables would be forced to adopt a value tetrad according to the value of ##\alpha## imposed by the electrodynamic laws. The absurd method would have a legal framework of application. Nobody has published until today a theorem that expresses the value of ##\alpha## determined by the electrodynamic laws. What will we do then? Will we treat ##\alpha## as a constant or as a variable? Many physicists trust the possibility of formulating this theorem and dedicate a great effort to that. Let's trust them and decide to treat ##\alpha## as a constant in the absurdity method.
2. We know that ##\varepsilon_o## and ##C## are interdependent, because ##\varepsilon_o## appears in the electrodynamic expression of ##C##.
[tex]\displaystyle C=\dfrac{1}{\sqrt{ \mu_o \ \varepsilon_o} }[/tex]
Now we are facing two really fundamental issues.
Is there or not complete interdependence, that is to say that each variable depends on the other 3 ? The electric field and the magnetic field are interdependent. Then the corresponding variables too. The reasonable thing is to assume that there is complete interdependence between the 4 variables. In that case there is only one tetrad of values according to the value of ##\alpha##. The method of varying the short list and demonstrating that the variation is absurd leads to a univocal response, that is, a unique and unambiguous response.
The previously expressed does not answer the initial question of this thread. It simply shows that there is hope of reaching the answer based on the laws of electrodynamics.
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