A Few Questions About Radioactive Decay

[Techne]

I would greatly appreciate the opinions of people who have studied some physics (third year level and beyond preferably) at university with regards to radioactive decay (anybody is of course welcome to contribute ).

Would you agree that the following representation of Silicon-32 changing to Phosphorus-32 via radioactive beta decay is correct (albeit incomplete, i.e. not fully described in full detail):

1) A neutron (n) in nucleus of Si-32 decomposes to a proton (p), electron (e-) and an antineutrino of the electron type (anti-nu(e)) via a W- boson. When Si-32 changes to Ph-32, a down quark in one of the neutrons of Silicon-32 spontaneously decomposes to an up quark (releasing an e- and anti-nu(e)), which in turn then changes the neutron (udd) to a proton (uud), which in turn changes Si-32 into Ph-32. The picture below explains it pretty well (from here).

2) The process of beta decay (AFAIU) depends on the stability of the nucleus. A neutron in a nucleus will only decompose when the nucleus of an atom is unstable, meaning it has too much energy. This typically happens in atoms with a higher "neutron : proton" ratio. The reason for this is the interaction between the nuclear force and electrostatic forces. The nuclear force is especially attractive when nucleons (both protons and neutrons) are close to each other while the electrostatic force causes protons to be pushed apart. With too many neutrons, the nuclear force becomes too strong, causing the nucleus to become unstable with the position of the particles playing a role in the reaction (i.e. playing a role in mediating the weak interaction.

3) The cause of the transmutation of n -> p is the weak interaction through Fermi coupling.

4) The cause of the weak interaction can be described via weak isospin and weak fields. Weak isospoin is also a property of all particles according to the standard model. My understanding is as follows:
a) The weak isospin of a quark generates a weak field.
b) Weak fields interact with each other.
c) This interaction generates a weak force.
d) This weak force results in the weak interaction that mediates neutron decay.

5) Statistically, the process occurs in a predictable manner. However it is in principle impossible to know the positions of all the particles (measurement of the particles will interfere with either position or momentum i.e. measurement problem) and thus not possible to know the exact moment each and every nucleon will decompose. So it is impossible to predict with 100% certainty when it will happen since we don’t know the location of all the nucleons before the event. Still, it can be statistically predicted with a certain amount of certainty. So, the process is indeterminate and spontaneous, but depends on these causal factors (weak isospin, weak interaction, instability of the nucleus etc.).

 

[azbob]

Want someone to check your homework?

 

[Techne]

Lol .

 

[Techne]

Another question. Given the facts that the process of radioactive decay is:
A) A statistically predictable process.
B) A fully causal process.

Why do some people think or claim that the process is a random process?

 

[copacetic]

This is so far over my head, it's in outer space.

 

[Jehosefat]

Another question. Given the facts that the process of radioactive decay is:
A) A statistically predictable process.
B) A fully causal process.

Why do some people think or claim that the process is a random process?

Statistically predictable is not the same as deterministic. It is much the same as flipping a coin or rolling dice. Sure you know exactly the distribution of possible outcomes but you still don't know exactly what the outcome will be. Hence it is a random process.

 

[Techne]

I understand where you are coming from and agree that the process is not determinate. It is, as far as I can see, an indeterminate process. I just disagree that this implies that it is a random process. I also suspect that this is perhaps to our differing definitions or understanding of the concept of randomness.

So, to clarify my point of view, consider the fact that there is no agreed definition of randomness. However, one can perhaps make sense of the concept as an absence of ALL order or ALL predictability or the opposite of ANY order.

Suppose there is something that behaved in a way that could only be described as random, something that changes in a totally unpredictable manner and acausal amnner. Let’s take an electron with spin Sz=+½ as an example. One moment it is an electron with Sz=+½ around the nucleus of hydrogen in laboratory on earth, the next moment it is moving towards the sun and randomly changes to a proton of carbon and then inexplicably moves back, the next moment it is some gold nugget on its way towards Mars. Suppose you want to measure Sz, you could never in principle know or predict whether it would suddenly change into a gold nugget or a proton or fly to the sun or Mars and back or just be Sx=+½ or Sx=-½ or not change at all etc. One can argue that such an electron behaves in a random manner as there is no way to predict any kind of behaviour.

Contrast this with an electron that behaves in an indeterminate manner. Let’s take the electron with spin Sz=+½ again as an example. From experiments we know that Sx is indeterminate and that the electron is free to be either Sx=+½ or Sx=-½ upon measurement of Sx. We are able to predict that it will be either Sx=+½ or Sx=-½ even though it is indeterminate before measurement. The freedom is determined by something that is part of the electron, some property of the electron. One can say that the electron has certain dispositions, there is order (either Sx=+½ or Sx=-½, not pure radmoness) in the freedom of an electron. The freedom is not random, it is merely indeterminate. So while randomness entails indeterminism, indeterminism does not entail randmoness. One can have indeterminism and order and one can have indeterminism and randomness but one cannot intelligibly argue to have pure randomness and order or orderly randomness.

I would argue that atomic decay. from this point of view, is not random, but merely indeterminate.

 

[Jehosefat]

I see your point although I disagree with the proposition that random implies no order at all. By your definition, if you roll dice, the outcome is not random. Just because it is possible to quantify the randomness does not mean that it is not random.

I would argue that in the 2 examples you give, the behaviour of the electron in both is random (granted, far more random in the first one as the probability space is effectively infinite). Although I guess that if we disagree on the actual definition of random we're wasting our time arguing

 

[Techne]

I see your point although I disagree with the proposition that random implies no order at all. By your definition, if you roll dice, the outcome is not random. Just because it is possible to quantify the randomness does not mean that it is not random.

I would argue that in the 2 examples you give, the behaviour of the electron in both is random (granted, far more random in the first one as the probability space is effectively infinite). Although I guess that if we disagree on the actual definition of random we're wasting our time arguing

I think our disagreement is merely definitional. The results of rolling dice, to me, is also just indeterminate, not random (given my view randomness). I wouldn't say it is a waste of time because I think we understand each other's view better now .

 

[Jehosefat]

Up to this point its good I meant if we carried on arguing after agreeing to disagree on the definition.

 

[Swa]

2) The process of beta decay (AFAIU) depends on the stability of the nucleus. A neutron in a nucleus will only decompose when the nucleus of an atom is unstable, meaning it has too much energy. This typically happens in atoms with a higher "neutron : proton" ratio. The reason for this is the interaction between the nuclear force and electrostatic forces. The nuclear force is especially attractive when nucleons (both protons and neutrons) are close to each other while the electrostatic force causes protons to be pushed apart. With too many neutrons, the nuclear force becomes too strong, causing the nucleus to become unstable with the position of the particles playing a role in the reaction (i.e. playing a role in mediating the weak interaction.

Don't you have it the other way around? The protons push each other apart and the neutrons instead of causing the instability actually mitigates it by both adding to the nuclear force and adding distance between the protons. Atoms with more protons need more neutrons to make them stable. A higher neutron/proton ratio is thus actually more stable. The neutron may decay because of the energy working on it but not because it's making the atom unstable.

Another question. Given the facts that the process of radioactive decay is:
A) A statistically predictable process.
B) A fully causal process.

Why do some people think or claim that the process is a random process?

It's unpredictable on an individual level but many dispute that it's random. If unpredictable was a measure for randomness the weather would be random. You are right that it's a matter of definition but if some are disputing that it fits randomness they should rather use unpredictable instead.

An atom isn't in a constant arrangement all the time but rather in a state of flux. Just like atoms in a substance are constantly bumping "against" each other protons and neutrons in an atom are vibrating back and forth and probably even changing positions. When they are in a position where the force pushing 2 protons with 2 neutrons apart is larger than the force keeping them together for instance we get alpha decay. It's thus not random and just undeterminable with our technology but isn't undeterminable on the fundamental level as the particles have their determinate position, we are just not aware of what those positions are.

Let's take a roulette wheel. From spinning the wheel and releasing the ball at any position at any speed we can't determine the outcome but it isn't random. Some people do actually have the tendency to roll predictable numbers or you can get a biased wheel, but apart from that if you knew the spin of the wheel and the position and speed of the ball you can accurately predict it.

 

[HavocXphere]

10 internet points says this thread is heading for an evolution/religion angle...

 

[Techne]

Don't you have it the other way around? The protons push each other apart and the neutrons instead of causing the instability actually mitigates it by both adding to the nuclear force and adding distance between the protons. Atoms with more protons need more neutrons to make them stable. A higher neutron/proton ratio is thus actually more stable. The neutron may decay because of the energy working on it but not because it's making the atom unstable.

There appears to be a zone of stability.

Neutron rich nuclei tend to favour beta decay while proton rich nuclei tend to decay via positron emission.

It's unpredictable on an individual level but many dispute that it's random. If unpredictable was a measure for randomness the weather would be random. You are right that it's a matter of definition but if some are disputing that it fits randomness they should rather use unpredictable instead.

An atom isn't in a constant arrangement all the time but rather in a state of flux. Just like atoms in a substance are constantly bumping "against" each other protons and neutrons in an atom are vibrating back and forth and probably even changing positions. When they are in a position where the force pushing 2 protons with 2 neutrons apart is larger than the force keeping them together for instance we get alpha decay. It's thus not random and just undeterminable with our technology but isn't undeterminable on the fundamental level as the particles have their determinate position, we are just not aware of what those positions are.

Let's take a roulette wheel. From spinning the wheel and releasing the ball at any position at any speed we can't determine the outcome but it isn't random. Some people do actually have the tendency to roll predictable numbers or you can get a biased wheel, but apart from that if you knew the spin of the wheel and the position and speed of the ball you can accurately predict it.

It does not appear to be random given the view that randomness implies the absence of ALL order or ALL predictability or the opposite of ANY order. Sure, it appears to be an indeterminate process which is of course interesting. It certainly does not appear to be uncaused as the cause (of beta decay) is the weak interaction via Fermi coupling. I.e radioactive decay does not violate the Principle of Causality. Simple as that.

 

[Garson007]

Back to randomness. A quantum particle like the electron is neither spin up or spin down until it is measured, measuring it collapses the wave function and gives you a random result based on some statistical distribution - in this case it's just a 50/50 uniform distribution. There is truly no true random, like the measurement of quantum particles. It's the basis of why some people figure that quantum mechanics proves free will (I disagree, but that's another discussion).

Secondly, something like decay is similarly distributed. Anybody that's done any statistics knows that if a certain experiment has a uniform distribution the sum of those distributions will lead to a Gaussian (or a normal distribution), an infinite sum of those (for simplicity sake it's assumed there are an infinite amount of atoms) will lead to delta functions. These delta functions can then give you accurate half-lives. The only reason why you have order is because of statistics. But at an individual particle level you cannot predict anything and is completely random, according to some distribution and depending on what you're measuring.

All the order you achieve is because of how entropy works. The less information you have (Shannon entropy) the more things seem to be in order.

As for your diagram, I have absolutely no clue. I'm more into statistical physics and quantum mechanics than nuclear physics.

 

[Techne]

Back to randomness. A quantum particle like the electron is neither spin up or spin down until it is measured, measuring it collapses the wave function and gives you a random result based on some statistical distribution - in this case it's just a 50/50 uniform distribution. There is truly no true random, like the measurement of quantum particles. It's the basis of why some people figure that quantum mechanics proves free will (I disagree, but that's another discussion).

Secondly, something like decay is similarly distributed. Anybody that's done any statistics knows that if a certain experiment has a uniform distribution the sum of those distributions will lead to a Gaussian (or a normal distribution), an infinite sum of those (for simplicity sake it's assumed there are an infinite amount of atoms) will lead to delta functions. These delta functions can then give you accurate half-lives. The only reason why you have order is because of statistics. But at an individual particle level you cannot predict anything and is completely random, according to some distribution and depending on what you're measuring.

All the order you achieve is because of how entropy works. The less information you have (Shannon entropy) the more things seem to be in order.

As for your diagram, I have absolutely no clue. I'm more into statistical physics and quantum mechanics than nuclear physics.

I agree with you that "there is truly no true random". I would argue that there are just varying degrees of order and that the wave function collapse (given the Copenhagen Interpretation for arguments sake) is merely indeterminate (see above post for the view I support).

I disagree with the assertion that "The only reason why you have order is because of statistics" and would argue that the only reason why you have statistics is because of order .

 

[Garson007]

I agree with you that "there is truly no true random".

Hah. I think I didn't phrase that very well. I was saying that there is nothing as random as quantum physics.

I disagree with the assertion that "The only reason why you have order is because of statistics" and would argue that the only reason why you have statistics is because of order .

The mathematics is more fundamental than the result, imho.

 

[Techne]

Hah. I think I didn't phrase that very well. I was saying that there is nothing as random as quantum physics.

Fair enough. I am not entirely sure what exactly you mean by "random". For me it is an absence of ALL order or ALL predictability or the opposite of ANY order. Quantum physics does not appear to satisfy this so I would say that "there is nothing as indeterminate as quantum physics".

The mathematics is more fundamental than the result, imho.

Sure, mathematics is important to generate a formal understanding of physical phenomena and the results of experiments. However, I think order in the physical world (even if it is indeterminate) is more fundamental than mathematical formalisms.