Matt Strassler [December 14, 2012]
Now here’s a remarkable fact, with enormous implications for biology. Take any isotope of any chemical element with atomic number Z. If you take a collection of atoms that are from that isotope — a bunch of atoms that all have Z electrons, Z protons, and N neutrons — you will discover they are literally identical. [A bit more precisely: they are identical when, after being left alone for a brief moment, each atom settles down into its preferred configuration, called the ``ground state.''] You cannot tell two such atoms apart. They all have exactly the same mass, the same chemical properties, the same behavior in the presence of electric and magnetic fields; they emit and absorb exactly the same wavelengths of light waves. This a consequence of the identity of their electrons, of their protons and of their neutrons, which will be discussed later.
That all atoms of the same isotope are identical, and that different isotopes of the same element have nearly identical chemistry, is a profound fact of nature! Among other things, it explains how our bodies can breathe oxygen and drink water and process salt and sugar without having to select which oxygen or water or salt or sugar molecules to consume. Contrast this with what a construction company has to do when building a house out of bricks, or out of concrete blocks. Bricks and concrete blocks vary, and are sometimes defective, and so a builder must exercise quality control, to make sure that cracked or over-sized or misshapen bricks and blocks aren’t used in the walls of the house. No such quality control is generally needed for our bodies when we breathe; any oxygen atom will do as well as any other, because we only need the oxygen to make molecules inside our bodies, and chemically all oxygen atoms are essentially the same. (This is all the more true since, for most elements, one isotope is much more common than the rest; for example, most hydrogen atoms [one electron and one proton] have no neutrons, and most oxygen atoms [eight electrons and eight protons] have eight neutrons.)
Would a radioactive atom (Say K-40) be a defective building block?
If any two given atoms of the same isotope of an element are completely identical, how does this sit with the Pauli exclusion principle? Surely something must differentiate them, or do they obey the maths of bosons?
I’m probably stepping on the professor’s toes here, but atoms aren’t single particles. In 2 atoms of the same element, each electron is in each atom in its proper orbital that obeys the principle, but the two atoms aren’t linked (unless they are a molecule, in which case each electron is in its orbital and the valence electrons are in their hybrid bonding orbital, all of which obey the exclusion principle).
You are correct in that atoms are composite particles, but so are things like protons. An atom can behave like a single fundamental particle in that I can perform experiments like the double slit experiment on it. (I beleive the largest aggregation this has successfully been performed on is C60 fullerene molecules.) I also know that atomic nuclei can be fermions (Odd number of nucleons) or bosons (even number of nucleons) and that this is directly responsible for say, Helium-4′s ability to become a superfluid at higher temperatures than that of helium-3.
Kudzu is correct, andy; your objection isn’t accurate. Because of quantum mechanics, composite objects in their ground states can still be exactly identical, just as Kudzu describes.
Kudzu, your point about radioactivity is a good one. Not sure how to bring it in though. Our biology is designed with error-correction mechanisms, to handle the damage from the small amounts of radioactivity that we’re likely to encounter in daily life.
As for Pauli’s exclusion principle for identical fermions — I am confused about your point. Electrons are identical, in that you can swap one for another and nothing changes. They are indistinguishable. But that doesn’t mean they are *doing* the same thing; one of them could be here on earth and another on the moon, or one could be in the inner shell of a carbon atom with another in the outer shell. (Think about identical twins; you can’t tell them apart, but they don’t have to do the same thing at the same time.) Since electrons are fermions, and identical, they can’t be in the same location, doing exactly the same thing; that’s Pauli exclusion. Exactly the same logic holds for atoms of the same isotope in their ground state. The statement that they are identical isn’t the statement that they are doing identical things; it is the statement that if you swapped two of them, making the first do what the second was doing and vice versa, you wouldn’t be able to tell you’d made a swap. And if they are fermions, they can’t be doing exactly the same thing (since, for experts, the swap would produce a relative minus sign in the wave function, which would be impossible if they were behaving identically.)
Right. I guess I should have been more specific, and on further thought this question may be better worded not relating primarily to the exclusion principle at all.
As you know you cannot force an arbitrary number of identical fermions into the same space, I cannot make a ‘laser’ beam out of fermions. Given that some atoms are fermions, I assume that you cannot place two of them in the same space in their ground state. Does this affect interatomic forces? I have always assumed the primary force keeping atoms from packing closer together than they do was electromagnetic repulsion between electrons in the orbitals of neighboring atoms, though I have recently seen it argued with some force that it is in fact the exclusion principle not allowing an atom’s electrons to occupy the same space. I am very doubtful of this, but would like to know if the exclusion principle has any affect on atoms, does a gas of helium 4 atoms have a higher density than one of helium-3 (In terms of atoms of course) since He-4 atoms are bosons?
I’m not sure that sugar is the best example because of the possibility of chirality — the difference between D-glucose and L-glucose is very important for biology!
You point out that the chemical activity of different isotopes of the same element is just about identical and so one’s body does not have to pick and choose. However, your choice not to mention basic molecules of an element, oxygen for example, leaves out the possibility of an interesting contrast between different isotopes, which can be processed without problem, versus different allotropes: O3 (ozone) versus O2, which do not affect the body in the same way at all. I realize that this would require a much longer article, but somehow I felt it was missing.
Hmmm. I haven’t thought about where that would fit in my presentation. I’m trying to get to particle physics as quickly as possible and not do too much with molecules. Maybe at some point I’ll be able to add that in.
check for a typo in the caption to figure 3
Sorry, I meant Fig 3 in the nucleus article
So are these authors just completely on drugs? http://arxiv.org/abs/1302.6012 “Nonidentical protons” T. Mart, A. Sulaksono (Submitted on 25 Feb 2013) We have calculated the proton charge radius by assuming that the real proton radius is not unique and the radii are randomly distributed in a certain range.
Let’s do this mind experiment. We have two radioactive atoms of the same isotope, A and B. Let’s say that A is in your hand and B is in mine (assume that all external forces are exactly the same for each atom). Now, yours (A) decays after 10 seconds and mine (B) does not. Imagine us going back in time 10 seconds and swapping atoms so that A is in my hand and B is in yours. Which one will decay in 10 seconds? I will suggest that the one in my hand will, because the internal workings (arrangements of subparticles in the atom) would result in decay in that particular atom.
Recall however that radioactive decay is a quantum process. Atoms do not have little ‘internal clocks’ that count down to their decay time. As such if we reversed time and swapped the atoms there’s no guarantee that either of them would decay in ten seconds.
How do we know that? Atoms of the same isotope may APPEAR identical from an external perspective, and the process of decay may APPEAR random. Nevertheless, is it possible that there are subatomic processes in an unstable nucleus that we are unaware of from our limited view. Historically, processes that appear to be random turn out not to be once we have developed more precise instrumentation.
Someone on this thread posted a comment linking to research saying that protons themselves may not be exactly identical, as previously thought, which may suggest that the nuclei of unstable atoms may not be identical, not to mention that gluon cloud configurations in quarks may differ just as electron shell configurations may differ from one atom to another.
Perhaps inserting randomness in our models in order to predict decay is useful for large numbers of atoms, but to assume it is “random” for each single nuclei may be taking the concept too far.
The problem is the assumption of randomness works so *well* The half life of an isotope can be related to the difference in energy levels between the parent and daughter product plus the mechanism of decay. The standard model predicts the structure we see and fails to predict (as far as I am aware) any mechanism for radioactive decay that would be ‘non-random.’
We have evidence that particles in a nucleus are highly identical; nuclei have specific energy levels that in several cases have been measured quite exactly and any variation would show up as ‘broadening of the bands’ in these measurements. Likewise with hadrons themselves we have measured excitations on things like the proton. The evidence that protons may not be identical is tentative and the effect is hardly a major one..
Then of course there is the question of whether or not simply not being identical would have a measurable or predictable effect on decay. (The chemical environment of electron-capture nuclei affects their decay rate, but not that of other decay modes.) And if the difference itself is random…
Certainly if we find even that protons are not identical it will be a monumental discovery most certainly requiring extensive new physics.
It works “well” in the sense that there is a predictable “average” for decay rates when looking at a large quantity of atoms. It does not work well when looking at an individual one.
Kudzu wrote <<>>
We can speed up decay rates for certain isotopes under certain conditions (like in a nuclear reactor). Solar flares of the sun tend to speed up decay rates for many radioactive isotopes so that even the average mentioned above is not actually constant (as previously thought). These ideas suggest that decay is not entirely “random”.
The weakness when dealing with individual atoms is an inherent weakness of all random processes. It is what we *expect* if the process were indeed random. This is the problem with postulating a non-random process. All the facts so far are consistent with a random process.
A big problem is that, as you note, radioactive decay isn’t entirely random in that in order for it to occur various conditions have to be met. A fully ionized K40 nucleus is stable, it needs an electron in the vicinity of the nucleus to decay. (This is usually a 1s electron that spends some time there, hence the dependence of the decay rate on chemical environment.) Likewise changing conditions WILL change the decay rates of various isotopes as conditions are made more or less conductive to decay.
But this does not eliminate the ‘core randomness’ of the process. You can double the rate of decay of an isotope, but all that means is that any given atom in it has twice the probability of decaying in any time. What you propose would be some mechanism where we could, in theory, measure a single atom and know exactly when it would decay, eliminating *all* randomness from the process. This is something that would be relatively easy to prove but very hard to disprove. It is one of those things like the ‘shadow biosphere’ where you can never be totally sure it isn’t there, but we have no good reason to assume it is.
Some scientists have suggested that the solar flares are producing increased particles (perhaps neutrinos) which when reacting with an unstable nucleus in a certain way, which may cause the decay. Granted, this is speculative at this time, but there is some evidence:
http://www.purdue.edu/newsroom/releases/2012/Q3/new-system-could-predict-solar-flares,-give-advance-warning.html
Just because we have a hard time measuring when a reaction from one of these particles will trigger decay in an unstable nucleus, does not mean that there is ‘core randomness’. Instead, as previous posters have suggested, it just means that our methods/instruments are not sophisticated enough in order to predict it.
“It is random” does not seem like a scientific statement, and I do not even think it is possible to measure a process and establish for a fact that it is “random”. You can only establish that the process obeys a given statistical model.
Quantum mechanics yields statistical distributions, which are backed up by experiment. In other words, we insert “randomness” into our models and our equations, and sometimes we may even claim there’s “randomness” yielding the distribution, but that’s only for reasons of convenience; i.e. in order to have practical use for the phenomenon. That is not grounds to claim that there is ultimately no cause for radioactive decay whatsoever.
“It is random” is as much a scientific statement as “It is not random” , it can be tested and disproved. What is unscientific is dogmatically sticking to an explanation in the face of good evidence.
Part of the problem here is I believe the different uses of the word ‘random’ Radioactivity has definite ’causes’ that aren’t random, but the process does not currently appear deterministic.Solar neutrinos would just be another non-random factor. To eliminate randomness entirely we would need to observe a perfectly predictable situation where a particle such as a neutrino caused a decay.
If I read your posts right you are suggesting that the universe is a ‘clockwork’ one; where there is no inherent randomness in QM. I myself rather liked this idea in my youth but things like Bells theorem http://en.wikipedia.org/wiki/Bell%27s_theorem have led me to the view that randomness is an inherent part of our universe. I might be wrong but I do not currently see any compelling evidence.
Incidentally the solar neutrino mechanism you link to would cause your original atom switching problem not to work, the atom in your hand will never decay because it will never be in the right location to be hit by a solar particle in ten seconds.