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About LinkBacksDoes modern Quantum Theory make sense?
That depends on what "make sense" means, so there should be plenty of room to comment.
Does modern Quantum Theory make sense?
That depends on what "make sense" means, so there should be plenty of room to comment.
Of course modern Quantum Theory makes sense. QED is part of Quantum Theory and it has the highest agreement with experimental data of any physical theory. Its only problem is that some people don't like what it tells us about the nature of the world.
"makes sense" is up to the individual. Also it is not a precise term.
What does it tell us about the nature of the world?Originally Posted by mvb
It tells me that it is a density function over the domain of a configuration space. This seems to me to be the logical step in going from either quantum mechanics or a classical field theory to a quantum field theory.
It tells us that the world is inherently probablistic, so that we can never be entirely sure what the future will be. This fact has given people more philosophical problems than any other characteristic of nature.
In particular, quantum field theory tells us that we can really build up the macroscopic world using inherently probabilistic quantum mechanical pieces. In practice, that makes little difference to us, since the uncertainties implied for large bodies are small compared to our ability to see positions or infer velocities. However, in principle it is an uncomfortable fact for most people [witness Schrodinger's cat], and we make up some really weird constructions [for example, the many-worlds hypothesis] to try to deal with it.
And further, the probabilities are of a strange sort that can interfere, unlike classical probabilities. That's the really weird part.
The problem is that without something like the many-worlds interpretation, one is left with the unanswered question of how an inherently probabilistic process can occur, or even why the quantum world is inherently probabilistic to begin with.
Indeed. Why does an unstable particle decay at a particular time for example?
Question didn't make any sense.
Well as KJW said there is no process that would explain why it would happen when it does as it is random. If it hasn't decayed at a time t1 but later does as a time t2 what has changed between t1 and t2? Is there anything different about the particle at t2 that would account for it decaying then?
At each instant in time, the particle would have an intrinsic probability of decaying within some period of time, and time symmetry demands that this probability is the same at all times. However, if the particle is not measured, then the particle state and its decayed state remain in quantum superposition. It is only when the quantum state is measured that the quantum superposition becomes one or the other. As time progresses, without measurement, contribution of the decayed state in the quantum superposition increases, thus making it more likely that a measurement will produce the decayed state. But if the measurement produces the undecayed particle state, then the contribution of the decayed state in the quantum superposition is reset to zero. Therefore, if a measurement is performed very shortly after the previous measurement, it is almost certain that the result will be the undecayed particle state. This leads to a decrease in the rate of decay as the frequency of measurement increases. This is the quantum Zeno effect.
I don't think there is any requirement for it to "make sense" at all. It just needs to match empirical data, which it does rather well. I find the expectation that the universe must work according to what makes sense to us humans rather...misplaced.Does modern Quantum Theory make sense?
I take the somewhat different view that the universe ultimate does make sense, and that it simply requires the development of one's knowledge so as to have an expanded notion of what does make sense.I don't think there is any requirement for it to "make sense" at all. It just needs to match empirical data, which it does rather well. I find the expectation that the universe must work according to what makes sense to us humans rather...misplaced.
I would tend to agree - "making sense" is very much a relative notion. The human mind is not that different to the human body in that it can be exercised and developed.
I understand how it works on paper, but it really doesn't make much sense. How can something that happened in the past (a recent measurement) effect the present decay rate? I thought a key aspect of probability was that the past is irrelevant.
It's more a case that the measurement erases the past. The intrinsic decay rate remains the same, but the measured decay rate depends on the rate of measurement.
So you erase the past and the clock starts ticking again from zero. But what clock?
Bear in mind that for a classically behaving particle, the probability of decay within a certain period of time is the same at all times, thus satisfying the Markov property. But if we consider the probability that the particle has not yet decayed after an extended period of time, then this will be somewhat lower due to the requirement that the particle didn't decay during all of the previous intervals of time. Similarly, for a quantum particle, the contribution of the decayed state in the superposition increases over time even though the intrinsic rate of decay is the same at all times (satisfying the Markov property).
That would suggest that if you were constantly measuring it it would never decay. Might it be possible to hold particles in an undecayed state until we wanted them to decay, using this method?
Theoretically, it would seem possible, but I don't know what the practical issues are.That would suggest that if you were constantly measuring it it would never decay. Might it be possible to hold particles in an undecayed state until we wanted them to decay, using this method?
Nope. Only the probability is removed this way, we would just know when particle decayed exactly and immediately.That would suggest that if you were constantly measuring it it would never decay. Might it be possible to hold particles in an undecayed state until we wanted them to decay, using this method?
Measurement is based upon probability, but what is it?
A probability function is not a true function, but a relation; a map from one to many.
Time symmetry would dictate that an probability densities using an inverse one to many map is also a valid proper of quantum mechanics: many past states were the function of a current state, for instance.
Last edited by Useful Idiot; 03-16-2014 at 03:47 AM.
Like multiverses that converge? Is there a theory based on this as I have struggled to find one in the past.
Oh dear, you better not tell all the migrating birds that as they seem to rely on this effect for their magnetic compass sensory mechanism.
Quantum Zeno effect - Wikipedia, the free encyclopedia
I guess that isn't gonna shock them as much as what you say.
Magnetoreception - Wikipedia
If, in "constantly measuring", by "constantly" you mean "with no intervals whatsoever" and by "measuring" you mean "returning to the same state", then "returning particle to the same state with no intervals whatsoever" is equivalent to "keeping in the same state" or "frozen". If it is possible to keep the particle in the same state, it is indeed possible to freeze it. Whether one can actually do that still depends on whether both "no intervals" and "same state" are achievable.
I could imagine that the "no intervals" might be the limiting factor, but for practical purposes it may not matter too much.
Apparently, the "no intervals", is limited by theuncertainty principle. As for "same state", the measurement takes the form of obtaining a "yes" or "no" answer to the question: Has the state transitioned? "Same state" corresponds to the "no" eigenstate, which is almost guaranteed by frequent measurement. It isn't so much a case of forcing the state into the "no" eigenstate, but that of not providing the opportunity of a significant likelihood of the "yes" eigenstate. The quantum state still decides if it has or hasn't transitioned (in the case of interpretations involving wavefunction collapse).
And with h being such a small number.....it may not matter for practical purposes?
Still struggling. I don't quite get that we have the path integral formulation of QM, but I can find nothing about convergent histories. Perhaps I am using the wrong terminology. Any ideas?
I have no idea. Penrose may have mentioned it one time, or maybe it was Alan Cramer looking for evidence. But it shouldn't be that obscure; it's just sticking two ideas together.
Try searching on "premeasurement." This would be about experimental findings without any requisite interpretational baggage.
After some bit, I think what you need for a search involves the keyword phrase "pre- and post selected ensembles."
The path integral formulation includes time-ordering and therefore accounts for causality. Even though the objective reality may be time-reversible, the observer only observes futures that are consistent with the observed past. That is, unobserved alternative pasts do not contribute to the future of the observer. In other words, the probability in quantum theory is a conditional probability.
When you say "unobserved" we should take that to mean we didn't see them when they were measured, rather than they were not measured, right?
Thanks Useful!
In this case, I meant the alternative possible results of a measurement that were not observed. (Good question, btw, because the distinction you asked about is an important one.)When you say "unobserved" we should take that to mean we didn't see them when they were measured, rather than they were not measured, right?
I've been reading about conditional probabilities and wondered if that is why we require the Born rule.
If
<y|x> is the amplitude of y given x and <x|y> is the amplitude of x given y then the joint amplitude is <y|x><x|y> or <y|x><y|x>*
Or perhaps I am barking up the wrong tree here?
The probabilities are conditional in the sense that if I toss a coin and want to know the probability of obtaining heads, the probability will only take into account that the only other possibility is tails and that I don't need to know the probability of the formation of the solar system (the probability that the big bang led to me tossing heads would be quite small indeed).
The Born rule is about determining the contribution of each orthogonal eigenvector associated with a measurement within the quantum state vector. Given that the quantum state vector is a unit vector, Pythagoras' theorem ensures that it is the "square" of the contribution from each orthogonal eigenvector that corresponds to the probability of that contribution.
By the way, the correct key words I was looking for were "pre selected and post selected ensembes." Whatever became of this investigation?
I didn't find anything about converging histories using your suggestion but I found this which was interesting
Brazilian Journal of Physics - Quantum probabilities versus event frequencies
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