Julian asked:

I'm studying necessity and modal logic, and thinking about whether the world could have been
different than it is. I'm not sure if this is really a philosophy or a physics question, but here goes.

Imagine I have a process depending on random, quantum-mechanical effects: e.g. a radioactive
decay. I set up a Geiger counter and I measure the number of decays per minute for 60 minutes, and
record the numbers.

Now I do a thought experiment. I go back in time and repeat the experiment. Nothing is different, both
the equipment and I are the same as before, in the same states. Will I get the same numbers?

I know that radioactive decay is random. It is not predictable, but follows probabilistic laws. To
Einstein's dismay, there is no internal mechanism we can observe which is behind the probabilities
and which explains them. Yet I find it hard to believe that I will not get the same numbers. Why
shouldn't I?

More specifically

— Does it mean anything to say that the equipment is in the same state as before, if there is nothing
"inside" which could be called a state?

— Although this though experiment is impossible, are there any real experiments which shed light on
the question?

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The experiment you've just described is known in the "business" as Schrodinger's Cat. Practically
every introductory text on quantum physics talks about it (Stephen Hawking once said, "every time I
hear about Schrodinger's Cat, I feel like reaching for my revolver!"). There is also a book by Jonathan
Gribbin called *In Search of Schrodinger's Cat", worth reading. Most of these books also discuss
further experiments, from EPR to Bells inequalities, to improve your perspective on the matter. I
append a couple of remarks to point you in another direction of fascinating research.

But first, I don't quite understand your worry over not having a repeatable experiment on your hands.
To say that equipment is in a particular state is probably the issue on which you've cut your teeth in
vain. The equipment is not in any state whatever. It is the observer who is in a state, and identifies his
own and the equipment's state as one quasi-symbiotic setup. In that combined state, you cannot, by
any normal criterion of the meaning of "repeatable" repeat your experiment. The initial conditions
defeat you. Radioactive decay is a random phenomenon precisely because the exactinitial conditions
of even a captive atom would be incalculable.

You must understand that the language being used in physics is the same language you speak every
day in your neighbourhood, so that a special mental effort is usually required to rid yourself of the
shackles of common usage to comprehend the changes of meaning. Asking for "the same numbers"
in any such experiment performed twice or many times in a row is therefore asking for numbers with
billions of digits after the decimal point matching each other one for one. In a word, whatever you may
mean by "state", it is an intrinsically unique constellation of numbers I am tempted to say, impossible
to unravel even for God.

One interesting and often pursued branching line of inquiry is the "possible worlds" scenario. It is
arguable that each unique experiment, in failing to register the identical "state" of previous
experiments, gives evidence of divergencies in the (sub)atomic texture of events. Again, this is an
issue puzzled over in many introductory physics books; but be warned that many are close enough to
science fiction to make you wonder on how much science they rely. At any rate, I suggest you pick up
any basic physics text in your library and check the index for "possible worlds" and carry on from
there.

One of the great philosophers, Leibniz, was knee-deep into such theories, which have recently been
reinterred with a lot of fanfare by a number of physicists, e.g. Smolin, Barbour, as well as some fiction
writers, e.g. Borges. All are worth chasing up for what they've written on the subject. (And, for what its
worth, Pathways to Philosophyhas a program of study devoted to "Possible Worlds", if you find
yourself developing a taste for the philosophy of "possible worlds").

This is where I might leave it, before I start writing a treatise. Meanwhile: bon voyage!

Jürgen Lawrenz

But think about it... what assumptions are you making when you say you'll "go back in time"? First,
you can'tgo back in time. Second, if you couldin some way, say, observewhat was in the past, you
couldn't alterit. You are assuming that "going back in time" implies that you can literally do so and
changethings when you do. But there's nothing at all in physics to support that assumption. So if you
"go back in time" the way you cando it, i.e., by rememberingthe situation, then of course everything
will be identical and the exact decay pattern will "repeat" itself in your memory. So yes, you'll get the
same numbers.

But also, there's a lot of fiddling right now with the whole conception of "hidden variables" and that
sort of thing. Bell's Inequality, for example, has been shown (as far as I know) to apply to only a
limited subset of physical situations. Further, there has been some work which seems to show that
we can look at processes "below" the quantum limits, in a kind of indirect way. And there's always
Boehm. As for nothing "inside"... what does that mean? Again, you're making the assumption that
some sort of functional epistemologicalviewpoint is reflected in ontology, a very bad mistake, in my
opinion, which people have made over and over. Take a look at this, for example:

Hess, K., and W. Philipp. 2001. "A possible loophole in the theorem of Bell". Proceedings of the
National Academy of SciencesUSA 98 (25):14224-14227.

Steven Ravett Brown

Whilst not a physicist, my own take on your "thought experiment":

If radioactive decay is random then it is not predictable but if it follows "probabilistic laws" then it must
be probably predictable. Otherwise what is the point of these "laws".

If radioactive decay is random and probably predictable then, when using the random generator, we
can reliably predict that we will probably generate a random number. So I would say that in your
experiment you will have a high probability of getting a different set of numbers generated but you
might not, although I would bet my dog on it!

My question to you is "What is it you find "hard to believe" when considering the case where you do
not get the same numbers"? or "What is it that makes you think you should get the same numbers?"

My own difficulty is in thinking of a case where you would get the same numbers as, even if we ignore
all the problems inherent with the idea of "going back in time", I find it difficult to conceive of a way to
restart the experiment and it still not produce different numbers.

The only way I can see to get the result of generating the same numbers is to abandon the idea of
"probabilistic laws" and look for something else that lets you explain whatever it is these "laws"
explain and allows you to show how the"random-number" generator is not really random but
deterministic in some sense. Then when you go back in time you can restart the experiment but with
the tweak that you set the deterministic rules to work on the experimental state in just such a way as
to produce the numbers you want.

Pretty thin but best I can do.

Kim Boley

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