How do half-lives allow full decay?
My understanding is that in time t, half of the radioactive sample decays. I don’t understand how the full sample can decay if it is a half of the sample at a time. Eventually, there will be one radioactive atom left. There cannot be half of the atom, and I know it doesn’t just stay there (then we’d have Oganesson), so what happens to the final atom?
Individual atoms have no way to know what the other atoms are doing. The half-life we see is just a practical result of statistics. The half-life is the period in which there’s a 50% chance that an atom of that type will spontaneously decay. When you have trillions of atoms, those statistics pretty much smooth out, and we see what looks like some kind of uniform “half has decayed in this time” effect. But it’s still entirely random.
When you get down to the point where there’s only a few atoms left, you run into the problem of using statistics on small numbers. The 50% chance of decay is still there, but like flipping a coin, you might hit a run of several heads in a row. Eventually, even that last atoms will finally flip a tail, even if there are no other atoms of that type left.
That makes a lot of sense. Thanks!
What I’ve never understood is the quantum physics assertion that a nucleus can be in a superposition of being decayed and undecayed. It seems to me that that’s the point at which Schrödinger’s Cat is now definitely either alive or dead.
My understanding is that the superposition is only when the nucleus or cat is unobserved.
That’s the part I don’t understand; how could one not observe it when suddenly decay particles slam into their surrounding environment? In the case of gamma rays, at the speed of light so no previous causal influence could have preceded it. How could an unstable nucleus be sufficiently isolated from the rest of the universe to maintain that superposition?
That is the point of the experiment. Schrödinger’s Cat was made to show the ridiculousness of the Copenhagen interpretation (I don’t know enough to argue for or against it). It is a thought experiment, not something that scientists are actually going to test.
And yet I’ve read people argue that superposition of a decayed/undecayed nucleus is a real state.
It’s above my pay grade too, but quantum computing depends on superpositions. It may be nascent tech, but it’s not fraudulent tech.
Superposition is as real as gravity. Schrödinger and his misbegotten menagerie notwithstanding. What constitutes “observation” is a textbook in itself.
Another point to be made is the fact that the second you observe the cat/nucleus, it is no longer alive/dead or decayed/undecayed. It may be a real state, but the second it is observed, the cat is dead. (Or alive, the nucleus is decayed, etc.)
While I agree that what counts as an observation is a very broad, semantical idea, I assume that looking at a cat counts as observing. No one can see the cat in the thought experiment, so then it is definitely not being observed (unless you count the cat itself as an observer, which is not the point I am trying to make, especially considering that, from the perspective the cat, it wouldn’t be a superposition) at all. When you open the box and look inside, the cat is either alive or dead, and it is being observed. For the cat, I don’t think there’s a lot of gray area about the semantics of observing. For the nucleus, there definitely is gray area, simply because we cannot see atoms or nuclei. However, considering it is the same experiment in a way, I believe we can conclude that we are observing the nucleus with our technology to the point in which it is not a superposition.
In practice, such a superposition would have an immeasurably short coherence time due to the surrounding environment, which aligns with the intuition you expressed upthread.
The observation part is rarely discussed in the simplistic summaries most of us have access to. Be it direct observation by the five senses, or through sensors or electron microscopes, it smacks of some degree of necessary sentience, if not sapience. It would seem that we hopped-up apes (or other alien species) are making ourselves the center of our respective universe[s].
Not really.
Essentially QM “observation” amounts to “the QM object in question interacts with the rest of the universe in any way”. IOW, the thing can remain superposed until anything else bumps into it in any way. While it’s sitting there in splendid isolation it can remain superposed theoretically indefinitely.
The problem is the universe is full of matter and energy and fields an’ shit all jostling everything else around themselves. So very quickly, like instantly, any macroscopic object will be jostled somewhere by something somehow, and the house of cards that is superposition promptly collapses into the static single-valued state we’re used to dealing with in our daily lives. Artificially holding even a handful of QM objects in a superposed state for even computer-meaningful time intervals is a very difficult problem at the edge of human tech today.
How that connects back to humans is that there is no way for us to collect information about a QM object of interest except to actively prod it and measure how our probe is changed by the experience, or to passively observe it and see what the universe happens to bounce off our object and how that experience changed the object and the inbound vs. outbound stuff.
It’s not that our observation causes decoherence. It’s that there’s nothing to observe until after something else triggers decoherence. We can see the balloon only after it pops.
ETA: Welcome back. 12 years is a long time..
Simple; at that point the decay has already happened, and what is being observed is the results.
An atom that is continually observed however will not decay.
In quantum mechanics, the theory of the microscopic world, there is
a paradox which is similar in spirit to Zeno’s paradox. In 1977, B. Misra
and George Sudarshan of the University of Texas showed theoretically that
the decay of an unstable particle – for example, a radioactive nucleus –
is suppressed by the act of observation. The more times it is observed,
the greater is the suppression. When it is observed continuously, the decay
simply does not happen.
Nah, it’s possible to see atoms. Some scientist years ago came up with a method of doing so because he was told it was impossible to see atoms. The method involves trapping it in a magnetic field, shining a laser on it and a lens, the result being you can see the atom as a dot of light.
You can say that a system is observed whenever it interacts with anything… but you can also say that, when it interacts with anything, now the thing it interacted with is also in a superposition of states. Take this to the logical extreme, and that’s how you get the Many Worlds interpretation of quantum mechanics.
I’d heard of that, and it makes sense. What I have a problem with is that it seems to me that radioactive decay is an example of spontaneous decoherence: the unstable nucleus self-observes and then forces the rest of the universe to acknowledge that a decay took place.
Cat: All of my positions are super positions, watch! >sits in 16 different ways, all comfortable<
That’s because cats are liquid quantum fluids.
It’s still environmental at the heart of it. Consider a different scenario involving two laser-trapped atoms isolated from the rest of the universe and initialized in a superposed, entangled way such that Atom 1 is in state A and Atom 2 is in state B or Atom 1 is in state B and Atom 2 is in state A.
Upon measuring Atom 1’s state, there is a 50% chance (say) of measuring A and, immediately after that, Atom 2 would be measured as B with a 100% chance.
But the environment interferes. In practice, Atom 1’s state might not be 50%/50% A/B, and Atom 2’s state won’t be 100% determinable from the measurement outcome for Atom 1. Coherence is lost with time, and it’s hard to fight even in extremely controlled settings.
For the nucleus example: the state “The nucleus has decayed” is much much less isolatable from the environment – so much so that one would never even think about the superposition of the pre- and post-decayed states in any practical situation. After all, stuff comes shooting out into the environment immediately, and there’s also no way to practically set up an experiment that could reveal a superposition without also measuring a specific state for the nucleus in the process.