Monday, November 10, 2008
Musing about Radioactive Decay, Probability, etc.
The rate of decay of a radioactive substance follows an exponential law:
Decay rate at time t = C Exp(-t/T)
where C is the initial decay rate (at time t = 0) and T is the mean lifetime of the substance. Exp is the exponential function.
What I've just written is something that is very well-known. What I muse about is this: how does an individual atom know when its time to decay has arrived? Radioactive materials such as uranium, thorium, and potassium are created in stars, particularly when they explode. Every radioactive atom has a moment in time when it decays. The probability that an atom will decay during a time interval t is Exp(-t/T). If t is very much less than T, the atom has little probability of decaying. However, some atoms decay almost immediately after they are formed. Others decay a bit later. Some stay as formed for billions of years before they decay.
You can see where I'm going. I imagine that the time of death of each atom is specified in some manner at the moment it is formed in the stellar explosion. The formation process is, in my imagination, analogous to an automobile factory in which seemingly identical automobiles are made in large numbers. These automobiles have a design flaw that leads them to break down at some time after manufacture. In use, the automobiles fail according to an exponential law.
What is the design flaw in an atom of uranium that leads to its eventual demise?
I should know better than to waste my time musing on such questions. When I studied quantum mechanics I was taught that one can not know enough about the workings of an atom or a nucleus to predict when it will decay. In order to learn such information would require one to destroy it. The mathematics we use to describe such processes, such as the simple law of radioactive decay, simply provide the probability of a certain event, or the frequency of such events in a large population. The flaw, if there is one, that causes one uranium atom to decay after one hour, another to decay after a day, and another to decay after five billion years can not be known to us.
Decay rate at time t = C Exp(-t/T)
where C is the initial decay rate (at time t = 0) and T is the mean lifetime of the substance. Exp is the exponential function.
What I've just written is something that is very well-known. What I muse about is this: how does an individual atom know when its time to decay has arrived? Radioactive materials such as uranium, thorium, and potassium are created in stars, particularly when they explode. Every radioactive atom has a moment in time when it decays. The probability that an atom will decay during a time interval t is Exp(-t/T). If t is very much less than T, the atom has little probability of decaying. However, some atoms decay almost immediately after they are formed. Others decay a bit later. Some stay as formed for billions of years before they decay.
You can see where I'm going. I imagine that the time of death of each atom is specified in some manner at the moment it is formed in the stellar explosion. The formation process is, in my imagination, analogous to an automobile factory in which seemingly identical automobiles are made in large numbers. These automobiles have a design flaw that leads them to break down at some time after manufacture. In use, the automobiles fail according to an exponential law.
What is the design flaw in an atom of uranium that leads to its eventual demise?
I should know better than to waste my time musing on such questions. When I studied quantum mechanics I was taught that one can not know enough about the workings of an atom or a nucleus to predict when it will decay. In order to learn such information would require one to destroy it. The mathematics we use to describe such processes, such as the simple law of radioactive decay, simply provide the probability of a certain event, or the frequency of such events in a large population. The flaw, if there is one, that causes one uranium atom to decay after one hour, another to decay after a day, and another to decay after five billion years can not be known to us.
Labels: exponential function, Quantum Mechanics, radioactive decay
Sunday, September 28, 2008
An Amateur's Comments about Theology
I read something about the life and work of Martin Luther recently in the New Yorker magazine. Brother Martin (he was a Dominican monk, later defrocked) asserted that faith was essential for salvation. Good Works aren't enough. I don't know what present-day Lutherans believe, but some "born-again" Christians seem to believe that faith is the necessary and sufficient condition for salvation.
I mused, where did such an idea come from? What is the practical use of a religion if it does not teach that good works are necessary and that criminal acts will result in divine punishment, if not in this world then in the next? Perhaps it is a consequence of thinking about the assertion of another religious leader, Calvin. Calvin was a Swiss. He asserted that God is all-knowing and all-powerful. God knows the future as well as the past. Hence, He knows everything that we have done in our lives and everything that we are going to do. He knows if I am going to rob a bank or assault a helpless old woman next week. These things are all pre-determined.
One can use Calvin's idea about an omnipotent and omniscient God to conclude that we poor humans don't have free will. Our Good Works and our Sins are not a result of any conscious decisions we make but they are preordained. When God created the universe, he created the future behavior of all of us.
Now, loss of free will poses a dilemma for religious teachers and pastors. It appears that our salvation or damnation was already determined at the moment the universe was created. Why should we try to be good? Why try to be saved? Why become a supporter of a religious organization?
A way out of the dilemma that reestablishes free will is faith or belief. Those of us who have faith and believe in God and his messages and trust his representatives (i.e., priests and pastors) will be saved. God has predetermined our actions but he has left us free to believe in Him or not. If we believe, we will be rewarded. If not, we will be punished or perhaps just exterminated.
This dilemma does not exist for me. I believe that God created the universe that we can all observe, including Quantum Mechanics. To a physicist, Quantum Mechanics guarantees a certain randomness or uncertainty to the universe. The future can not be foretold precisely. Even God does not override Quantum Theory, because it is one of the most beautiful things in the universe that He created. Hence, He can not know exactly what I am going to do. Predestination is nonsense. The efficacy of good works in earning bonus points toward salvation is restored.
I have rushed into an ancient theological argument that more learned people fear to enter. Obviously I am no angel. Be merciful in your condemnation.
I mused, where did such an idea come from? What is the practical use of a religion if it does not teach that good works are necessary and that criminal acts will result in divine punishment, if not in this world then in the next? Perhaps it is a consequence of thinking about the assertion of another religious leader, Calvin. Calvin was a Swiss. He asserted that God is all-knowing and all-powerful. God knows the future as well as the past. Hence, He knows everything that we have done in our lives and everything that we are going to do. He knows if I am going to rob a bank or assault a helpless old woman next week. These things are all pre-determined.
One can use Calvin's idea about an omnipotent and omniscient God to conclude that we poor humans don't have free will. Our Good Works and our Sins are not a result of any conscious decisions we make but they are preordained. When God created the universe, he created the future behavior of all of us.
Now, loss of free will poses a dilemma for religious teachers and pastors. It appears that our salvation or damnation was already determined at the moment the universe was created. Why should we try to be good? Why try to be saved? Why become a supporter of a religious organization?
A way out of the dilemma that reestablishes free will is faith or belief. Those of us who have faith and believe in God and his messages and trust his representatives (i.e., priests and pastors) will be saved. God has predetermined our actions but he has left us free to believe in Him or not. If we believe, we will be rewarded. If not, we will be punished or perhaps just exterminated.
This dilemma does not exist for me. I believe that God created the universe that we can all observe, including Quantum Mechanics. To a physicist, Quantum Mechanics guarantees a certain randomness or uncertainty to the universe. The future can not be foretold precisely. Even God does not override Quantum Theory, because it is one of the most beautiful things in the universe that He created. Hence, He can not know exactly what I am going to do. Predestination is nonsense. The efficacy of good works in earning bonus points toward salvation is restored.
I have rushed into an ancient theological argument that more learned people fear to enter. Obviously I am no angel. Be merciful in your condemnation.
Labels: Calvin, Free Will, Martin Luther, Predestination, Quantum Mechanics
