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Is the decaying of radioactive stuff truly random? If 50 pounds of Uranium decay, for instance, and then you go back in time -- would the exact same pounds of Uranium decay? If so, then how can it be said to be random -- it is random until it happens, then it is settled.
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posted
The short answer is that the decay of a particular atom is unpredictable, and the resulting set of data is random.
You're confusing the concepts of randomness and unpredictability. Things that are random are unpredictable before they happen, but things that have happened may still be random. For example, flip a coin 50 times and record the results. Assuming an unbiased coin, you couldn't reliably predict the sequence that resulted before you flipped. But the results, even when recorded and looked at later, are still random.
In computing, a string is random if it can't be compressed. In science, something is random (really, seems random to us) if it's cause can't be determined or it can't be controlled for. In mathematics, randomness of a set of nubers can be formally analyzed in various ways. Aggregate outcomes of random events can be predicted by probability, even though the individual events cannot.
As to the actual question - we don't know if the same atoms would decay, because we don't know the cause. Therefore, we consider it unpredictable and, in the scientific sense, random. Mathematically, I believe the resulting set would be considered random, and I'm guessing the string of which atoms decayed couldn't be compressed (or really, a sample of such strings would have an average compression rate of 0).
posted
To the best of our knowledge, you would get different atoms decaying; this is what quantum mechanics predicts, and it is our best theory to date. Now, there may be a deterministic hidden-variable theory hiding under quantum mechanics, but if so, its properties are seriously weird. I don't have the time to go into this at the moment, but you could google for "EPR paradox" and "Bell inequality".
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Dag -- actually, if our theories are even vaguely correct, we do know that radioactive decay is necessarily nondeterministic.
It is possible to simulate our current observations with a deterministic theory, but this would require several dozen particles that we've just happened to not seen, and that the few particles we have seen happen to be the ones which fall into a beautiful pattern in relationship to each other.
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Random has two distinct meanings -- random data or random event. The data could be random even with determinism, but the event couldn't.
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But the meaning of "random event" is based specifically on our ability to predict. And whether it's deterministic or not, we can't predict it at this point. Therefore it's random.
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No, random event is not based specifically on our ability to predict in quantum mechanical terms.
In quantum mechanics, inability to predict means inability for anyone, anywhere, with any amount of knowledge, to predict.
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Yes, I know that "inability to predict means inability for anyone, anywhere, with any amount of knowledge, to predict." But scientific randomness is based on whether the cause is known or knowable. So if whether it's deterministic or not, radioactive decay of uranium is random at this point in time.
Flipping a coin is random (even if the coin isn't balance), even though theoretically we could predict it knowing all the appropriate forces and masses at work.
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quote:Dag -- actually, if our theories are even vaguely correct, we do know that radioactive decay is necessarily nondeterministic.
It is possible to simulate our current observations with a deterministic theory, but this would require several dozen particles that we've just happened to not seen, and that the few particles we have seen happen to be the ones which fall into a beautiful pattern in relationship to each other.
This is not exactly accurate. It's possible to reproduce the predictions of non-relativistic quantum mechanics with a deterministic theory called Bohmian mechanics, but this theory doesn't entail any additional kinds of particles beyond the ones we observe. In fact, in Bohmian mechanics there's only one kind of particle, and a particle's "type" (electron, photon, or whatever) is determined by how it interacts with the wave-field that surrounds it.
I don't know of any other deterministic theory that can explain quantum predictions.
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I suspect Bohmian theory satisfies Bell's inequality, which is experimentally violated. In other words, I suspect it doesn't account for all modern data.
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Nothing is random, and no one believes it is, at core, since random implies "uncaused." EVERYTHING is caused by something. The most we can say is that, theoretically, events that appear random to us cannot be known because any means by which we could observe the process would disrupt it. Thus Schrodinger's cat. It's about knowing, not about happening.
And I know, there are mathematicians who insist to the contrary, but only because they only know the game, not the underlying suppositions. A truly random universe is, literally, unthinkable.
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Just because the universe may have a cause does not imply that there aren't random elements in it.
I think it's important to separate the macro and micro levels and not read more into the scientific claims than are really there.
Same thing goes on the other end of the argument. If a stochastic model is the best fit for a basic phenomenon, that does not imply that all phenomena can be (or should be) thus explained.
Ultimately, I think a lot of the agument centers on whether or not the principle of parsimony (Occam's Razor, etc.) is a good and cautious way to proceed for scientists, or whether we should seek to have all people adhere to it in their thinking about life, the universe and everything.
Clearly, where the gaps in our knowledge are most profound, the best course is to proceed cautiously in our pronouncements (whether they arise from scant scientific data or long traditions based on scripture), but to open our minds to the maximum extent possible in order to seek the possible.
That is, if we seek a truth that is verifiable through external means (experimentation, corroborating evidence) and not ONLY shared belief (whether it be belief in a religion or belief in some scientific theory).
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OSC, don't bring your theology into physics, it makes you look like an uneducated hick. Look up vacuum diagrams, which are indeed uncaused and random. And if there is a hidden-variable theory, ie causes we don't know about, then it has extremely weird properties such as violating special relativity; which is to say, the effect could come before the cause. Nature is weird; deal with it.
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quote:I suspect Bohmian theory satisfies Bell's inequality, which is experimentally violated. In other words, I suspect it doesn't account for all modern data.
Actually, the distinguishing feature of Bohmian mechanics from other hidden variable theories is that it obeys the Bell results just like normal QM.
There is a price to be paid, of course. Bohm's theory is non-local, though the corresponding theory of measurement makes certain that we can never detect the faster-than-light causal connections.
Interestingly, John Bell himself strongly favored Bohmian mechanics as the solution to his "no hidden variable" results. I would tend to disagree with him, though, since I'd prefer an interpretation of quantum mechanics which obeys every tenet of special relativity.
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KoM, I think it goes without saying that your last post is not appropriate. Please change it. I really don't want to see an interesting thread like this turn into a shouting match.
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I stand by it. Just who is OSC to tell me what I do and do not believe, anyway? Next he'll be telling me that deep down I'm actually a Christian. And until he shows that he at least understands the mathematics of the theory he disparages, I'm inclined to be just a touch contemptuous of his theorising. Easy enough for a science fiction author to add theology to his theories; he doesn't have to account for real-world results.
Destineer, you've got me interested now. Could you explain the theory of measurement you refer to, or link to somewhere? Also, does this theory of Bohm's expand into quantum field theory in a satisfactory way?
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posted
I have never studied this Schrodinger's Cat before. Maybe some of you more familiar with this could answer some questions for me.
I have heard theories that because of this concept of multiple realities at the quantum level, every moment our universe is constantly "splitting" onto different paths according to what "actually happened" in each reality.
So, is it possible therefore that the way we solve the apparent paradox of Schrodinger's Cat that in our universe we experience one outcome--let's say dead cat, while in another splitoff reality there is a live cat? Therefore the two realities diverge at that point?
Or am I completely misunderstanding this situation?
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Also, please someone tell me: why is the cat neither alive nor dead until we look? Isn't there some other more rational explaination? I just don't know enough--see what I don't know is, if subatomic particles can exist in more than one state only until observed, than how can we observe that it happens? And if we can observe it happening (more than one reality for a subatomic particle) why *coudln't* we observe more than one reality for a macroatomic object? Why the difference?
I agree with Schrodinger--it isn't that it is neither (alive nor dead), it's that something is missing in our understanding of reality.
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My understanding is only limited, and I'm sure some physicist might have a better response, but my impression is that without it being possible for there to be a superposition of states (not necessarily with the cat, but at the subatomic level), quantum mechanics leads to violations of relativity -- that is, effect can come before cause.
Superposition of states means sort of that something is in more than one state at the same time, and sort of that its not in any one state at the one time.
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To my untrained ears, it sounds like the things we observe look really, really confusing, and the superposition theory is the lesser of two confusions--basically superposition actually makes more sense to us than effect coming before cause. Am I correct?
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Again, there are others better qualified, but yes, there's a certain amount of cutting with Occam's Razor going on.
Of course, its also scientifically possible that we're all just living in the Matrix and our perceptions are being fed to us, but we reject that one too.
We've got some good info relativity's correct, and we've got some good info quantum mechanics is correct, so the tendency is to accept explanations which allow both to be correct rather then requiring us to toss out one theory, which determinism would involve.
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Now I am an unabashed believer in God. I have often wondered if the bizarreness of quantum mechanics could have plenty of room for "God in the details".
For instance, we observe that particles can be more than one thing at once. What if God can "select" which path he wants this reality to take in subtle ways, therefore influencing all that we see around us? Shaping our very reality? That somehow all the other possible realities are not "viable"?
For instance, God wants the cat to live for His own purposes, so he chooses a reality in which the particle does not decay.
I am not asking anyone to believe this, I am just bouncing ideas out there to help myself figure out the possibilities.
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Given that God is pretty much uniformly given supernatural powers, its perfectly possible for the the natural universe to be nondeterministic and the natural universe + god to be deterministic. That sort of crazy stuff doesn't violate scientific principles because the nature of god is by definition nonscientific.
Lots of scientists have similar beliefs to the one you just sketched, even while thinking quantum mechanical events are "purely random".
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The basic idea of Bohmian mechanics is that particle position is set up as the privileged observable, and the wave exists to "guide" the particles around. This is completely deterministic and, more importantly, position is completely determinate -- the uncertainty principle does just govern our uncertainty in predicting things.
I've become more interested in BM recently, not because I think it's true, but because I'm working on a sci fi story set in a universe governed by Bohm's theory, in which people have learned to harness the FTL signaling for time travel and communication.
quote:Also, does this theory of Bohm's expand into quantum field theory in a satisfactory way?
Not so far, but there is new research going on along those lines. Goldstein and some co-authors have proposed a Bohm-like structure called a "Bell-type quantum field theory" which is supposed to reproduce QFT's predictions. Interestingly, Bell-type QFTs exhibit stochastic behavior (particles can be randomly created and annihilated) and so are not deterministic like non-relativistic Bohmian mechanics.
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quote:For instance, we observe that particles can be more than one thing at once. What if God can "select" which path he wants this reality to take in subtle ways, therefore influencing all that we see around us? Shaping our very reality? That somehow all the other possible realities are not "viable"?
For instance, God wants the cat to live for His own purposes, so he chooses a reality in which the particle does not decay.
The one constraint on this sort of interpretation is that the theory also gives statistical predictions. So for a particular prepared system, it might be the case that three times out of four the cat will die. God would have to act out his will in such a way as to obey these statistics, or else the theory would not be successful.
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I imagine most of the time God's interference would be far too slight to show up in any statistical study. After all, for all scientific purposes it would simply appear that we are one possible outcome of an infinite number. That we exist in this outcome would just be coincidence.
But my little "theory" does provide opportunity for "miracles". Quantum mechanics tells us that the sandwich I am eating right now could suddenly appear in Timbuktu, or on the other side of the solar system. Granted, it is an extreme improbability, but it *could* happen. If God selected a reality in which it *did* happen, some would call it a miracle.
Disclaimer: This is pure speculation on my part. I do not necessarily believe it.
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If I were you, I wouldn't insert my god into gaps in physics. They have a tendency to close, leaving you with rather less god than you had before.
As for Schrödinger's cat, it is not in a superposition of states; the cat itself is a perfectly valid observer. Things only remain in a superposition as long as they aren't interacting with the rest of the universe. Thus objects of reasonably macroscopic mass are never ina a superposition; but the exact process by which quantum systems of indeterminate state make macroscopic systems go into a definite state is not well understood. It has been suggested that a unification of quantum theory with general relativity, thus bringing gravity into the picture, will allow us to understand this.
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Correct me if I'm wrong, but these particular "gaps" weren't there before we started examining reality so closely.
It seems to me the more we study the universe, the more complicated it gets, therefore the more room for God--not less.
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beverly, I heard a physicist on NPR say exactly the same thing today. In his view, science is a source of information that is separate from religion and, if anything, it gives us information that can excite our imagination and intellect to all sorts of things.
if one is inclined to believe that God did it all, then studying nature is really the study of God, no matter what someone else tells you.
If one is inclined to believe that everything is a result of random chance and mechanistic processes, then studying nature is no less rewarding because we still want to understand our place in it.
Everyone seems to want that.
There's a way in which this discussion really transcends the unnecessary rancor or division, as long as people don't get too worked up over the particular details.
We are still, and will be for a long time, dealing with speculations that go far beyond the data and our ability to conduct relevant experiments. We can't create a new universe of our own as a laboratory, for example.
So, the ultimate questions are still the ultimate questions. Same as always. Science is a great source of information regardless of whether one believes in God or not. Why? Because as far as human intellect goes, it is the only source of empirically verifiable truth. That's one version of truth. It has one advantage over all other known varieties and that is that the facts are as solid as we can make them. Nobody who understands the science can say "well, that's what you believe, but I believe different" when referring to repeatable results from scientifically produced observations.
We can, of course, argue about interpretation of facts.
But we can always do that, and will always be able to do that.
It's not a religion versus science thing. It's all about trying to put meaning to the facts.
Anyway, science is a tool of human understanding. Anyone who rejects it is putting themselves outside of the discussion entirely. That's their choice, but they render themselves irrelevant to most of the ensuing debate.
But anyone who thinks science has all the answers is just as guilty of misunderstanding its uses and its purpose.
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That is a beautiful sentiment, Bob. I do think that the religious and non-religious alike may experience the same awe at the magnificence of the universe.
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Yep, and I think the more one knows about it, the more awe-inspiring it becomes.
I don't know that many scientists who are atheists. I know a vast number of them who don't have what anyone would call an "orthodox" faith, however.
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quote:Originally posted by beverly: Correct me if I'm wrong, but these particular "gaps" weren't there before we started examining reality so closely.
Granted, but then, we've closed a lot of other gaps over the years, from conservation of momentum to the requirement for intelligent design. This is just the latest in a long list.
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Certainly our understanding of science has changed over the years, and many of the assumptions we have made about God based on our then current understanding of science has changed.
But whether or not you see a evidences of God being eradicated or the picture simply becoming more clear with God still very much in it depends on your perspective. As someone so eloquently put it, it is a big Rorshauch Test.
Certainly the religious tend to be slower to accept science than the non-religious. Creationism is a fine example of that. But that just makes me sad. I like Bob's sentiment that in studying science we are in fact learning about God, not disproving his existance because we find that something we earlier believed just isn't true. I truly wish that the religious of the world did not fear science and its ability to observe.
But I also wish that people would not treat scientific theory as "gospel truth", since it has quite a history of being disproved again and again.
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The problem is known as the "God of the gaps" -- there has been a tendency throughout history for some people to ascribe to the action of God anything currently unexplained by science. This of course leads to problems when science explains those things.
There's nothing wrong with believing God is behind physical phenomena; its perfectly in line with science (though not supported in a scientific sense either). Believing, however, that God is not merely behind but the direct agency of unknown behaviors does have the God of the gaps problem.
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For whatever reason, I find the concept of a God that works through the natural laws of the universe far more satisfying than a God that breaks those laws.
If God can go "Shazam!" and make something instantly happen, I find it comforting that there is a scientific explaination for how the "Shazam" happened.
Any "technology" seems like magic to those who do not understand.
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that there's a scientific explanation for that shazam doesn't mean the action of God isn't supernatural -- I mean, science doesn't even begin to tackle the fundamental "whys" of the universe. Also, the addition of true randomness actually gives "room" for God to act in a sense.
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quote:Things only remain in a superposition as long as they aren't interacting with the rest of the universe.
KoM, do other subatomic particles count as "observers" or the "rest of the universe" for purposes of determining if something is in a superposition? The detector in the two-slit experiment is what causes the wavelike behavior to disappear, not whether something "reads" the detector, right?
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"Nothing is random, and no one believes it is, at core, since random implies "uncaused." EVERYTHING is caused by something. The most we can say is that, theoretically, events that appear random to us cannot be known because any means by which we could observe the process would disrupt it. Thus Schrodinger's cat. It's about knowing, not about happening.
And I know, there are mathematicians who insist to the contrary, but only because they only know the game, not the underlying suppositions. A truly random universe is, literally, unthinkable."
Said just like a happy fat cat.
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quote:KoM, do other subatomic particles count as "observers" or the "rest of the universe" for purposes of determining if something is in a superposition? The detector in the two-slit experiment is what causes the wavelike behavior to disappear, not whether something "reads" the detector, right?
Again, note that this is not well understood, so I am giving you my best guesses rather than well-supported experimental finding, here. That said, any particle can be an 'observer'. This gives us something of a puzzle, since all particles are interacting with all others at all times through gravity, according to the usual general-relativity picture. The resolution is to note that we do not yet understand how gravity operates on scales below a few microns.
You are more-or-less correct about the two-slit experiment; the wave behaviour is caused by the slits, right enough, but it doesn't make sense to ask whether it exists without an observer. This is a bit like the old tree falling in a forest with nobody to hear; the proper answer is "your question is meaningless", or as the Buddhists very succinctly put it, "Mu!" Again, though, the term 'observer' is a little misleading, since it seems to imply consciousness. Anything capable of interacting with the photon coming out of the slit is a perfectly valid observer.
Does that answer your question?
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quote:Again, note that this is not well understood, so I am giving you my best guesses rather than well-supported experimental finding, here. That said, any particle can be an 'observer'.
This can't be right. One of the assumptions of scattering theory is that a lone particle can interact with a single other particle without collapse. The idea that any interaction is a measurement is patently false. After all, electrons are constantly interacting with the atoms they orbit even though they have to be in a superposition of position states in order to occupy energy levels.
There has to be some further criterion for observation besides interaction. This, as you've pointed out, is the ill-understood "measurement problem."
As for a future quantum gravity theory solving the measurement problem, this is something you hear sometimes. I'm skeptical. Neither string theory nor loop quantum gravity (the two best prospective QG theories) even attempts to offer a theory of wavefunction collapse.
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Would someone explain to me what is meant by "collapse of wave function"? We never discussed this particular thing in any of my college classes, and I have never heard of it elsewhere. The uncertainty principle and the concept of subatomic particles existing in more than one place at the same time according to a pattern of probability I understand.
It almost sounds like it's this illusion, this movement on the edge of vision that disappears if you ever look directly at it--a rainbow that if you try to get closer to it it always looks further away.
I thought the uncertainty principle and the fact that we cannot know the speed *and* velocity of a particle simply had to do with the fact that in order to observe it we have to change it. That we basically have to interact with it in order to observe it.
Please help fill in the gaps for me here.
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