tag:blogger.com,1999:blog-9124539381685751273.post8542962228048477580..comments2023-06-19T04:35:06.263-07:00Comments on Skeptic's Play: Quantum superpositionmillerhttp://www.blogger.com/profile/05990852054891771988noreply@blogger.comBlogger14125tag:blogger.com,1999:blog-9124539381685751273.post-85255536953360134852013-09-29T08:47:56.130-07:002013-09-29T08:47:56.130-07:00It is important to talk about superposition if you...It is important to talk about superposition if you want a predictive theory. Whenever you measure the position of an electron, it may appear to have a definite position, but to predict how it behaves between measurements, we need to speak of a wavefunction.millerhttps://www.blogger.com/profile/05990852054891771988noreply@blogger.comtag:blogger.com,1999:blog-9124539381685751273.post-5576739577546598282013-09-29T01:07:05.437-07:002013-09-29T01:07:05.437-07:00As a layperson of physics, I don't understand ...As a layperson of physics, I don't understand why superposition says a particle is everywhere at once, since I don't see any particles. All I see are waves being combined with others. <br /><br />And yes, I understand that a particle isn't there until a wave function collapses. But on the other hand, isn't superposition a more mathematical extrapolation than what may be happening? Especially if one were to think of an electron as a form of standing wave where the particle isn't manifested until it collapses?Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-9124539381685751273.post-88318185712930024302013-02-27T10:49:33.662-08:002013-02-27T10:49:33.662-08:00Statist,
You are correct, and I have misused the t...Statist,<br />You are correct, and I have misused the term. What I refer to as "mixed states" are merely pure states that can be broken up into a superposition of different eigenstates.millerhttps://www.blogger.com/profile/05990852054891771988noreply@blogger.comtag:blogger.com,1999:blog-9124539381685751273.post-1778277325274741182013-01-28T01:43:48.800-08:002013-01-28T01:43:48.800-08:00Your description is incorrect. Superpositions are...Your description is incorrect. Superpositions are not mixed states, they are pure states. A particle that is in "two states at once" (that is, for which a measurement on an observable could produce two results) is nevertheless in a pure state. Each vector in the Hilbert space representing that property in question is a pure state, even if it is a superposition. Mixed states are more akin to classical statistical ensembles of particles, not quantum superpositions. Statistnoreply@blogger.comtag:blogger.com,1999:blog-9124539381685751273.post-29126320578279559302009-08-22T09:00:14.047-07:002009-08-22T09:00:14.047-07:00Vin,
Whenever computing probabilities in quantum m...Vin,<br />Whenever computing probabilities in quantum mechanics, you always calculate the square of the <i>magnitude</i> of the wavefunction (or equivalently, multiply the wavefunction by its own complex conjugate). So even if the wavefunction has an imaginary component, this still results in real, positive probabilities. Does this answer your question?millerhttps://www.blogger.com/profile/05990852054891771988noreply@blogger.comtag:blogger.com,1999:blog-9124539381685751273.post-4617658135552690862009-08-21T21:55:55.713-07:002009-08-21T21:55:55.713-07:00hi guys, i am a bit confused. Geometrical interpre...hi guys, i am a bit confused. Geometrical interpretation of mixed state like (a1 + a2) or (a1-a2) is understandable. but how do I interpret a state like (a1+ i.a2) where i is a complex number.Anonymoushttps://www.blogger.com/profile/11379014791902931053noreply@blogger.comtag:blogger.com,1999:blog-9124539381685751273.post-39096379014725356222009-06-05T15:53:39.874-07:002009-06-05T15:53:39.874-07:00No, I have no plans to convert anything to pdf.No, I have no plans to convert anything to pdf.millerhttps://www.blogger.com/profile/05990852054891771988noreply@blogger.comtag:blogger.com,1999:blog-9124539381685751273.post-59065546860090577332009-06-05T15:00:53.694-07:002009-06-05T15:00:53.694-07:00Nice. This is something I've been wondering ab...Nice. This is something I've been wondering about for a while. There wouldn't by luck be any chance of getting the previous writeup and this one in .pdf format, for archival and future reference?Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-9124539381685751273.post-91178910491578935502009-05-14T20:04:00.000-07:002009-05-14T20:04:00.000-07:00But isn't it strange to say that superposition is ...But isn't it strange to say that superposition is necessarily a consequence of the math and not the physical thing? I mean ideally, the math would perfectly describe the physical thing; or, in other words, the physical thing would be a perfect embodiment of the math. In that case the distinction is pretty meaningless. <br /><br />On the other hand, if you're saying that the physical things aren't perfect embodiments of the math, then you're effectively saying QM is somehow wrong. Aren't you?Scotthttps://www.blogger.com/profile/11332828263550581927noreply@blogger.comtag:blogger.com,1999:blog-9124539381685751273.post-8065459202391598802009-04-14T03:38:00.000-07:002009-04-14T03:38:00.000-07:00actually, quantum superposition isn't a strictly p...actually, quantum superposition isn't a strictly physical thing. it is actually a consequence of the linear algebra upon which QM is based. in maths-speak, it means that a vector can be written as an sum of vectors in a different basis, kind of like when you ask a chinese person to translate a particular character of their alphabet and the give you a bunch of english words, that when taken together mean the same as the original chinese word.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-9124539381685751273.post-91773571159568467922009-03-18T14:15:00.000-07:002009-03-18T14:15:00.000-07:00The principle of superposition states that we can ...The principle of superposition states that we can add and subtract <I>wavefunctions</I>, rather than the probabilities themselves. The square of the wavefunction is interpreted as probability. Thus, the square-root of the probability gives you a wavefunction.<BR/><BR/>There's no particular reason why it should be so, but that's what we see in experiments. For example, we can observe two probability waves interfere destructively (meaning they cancel each other out because one is positive and the other is negative).millerhttps://www.blogger.com/profile/05990852054891771988noreply@blogger.comtag:blogger.com,1999:blog-9124539381685751273.post-44598747911895583102009-03-18T08:10:00.000-07:002009-03-18T08:10:00.000-07:00hello guys,i am little bit unaware of this probabi...hello guys,i am little bit unaware of this probability principles,the doubt arised to me is why should one consider square root o the probability for mixed statesAnonymousnoreply@blogger.comtag:blogger.com,1999:blog-9124539381685751273.post-18166673499463097292008-10-08T10:37:00.000-07:002008-10-08T10:37:00.000-07:00No, there is no way to tell the difference. Theor...No, there is no way to tell the difference. Theoretically, and only under the Many Worlds Interpretation, yes, but for all practical purposes, no. We can tell the difference for small, well-controlled sets of particles, but probably never for anything so large as a virus.millerhttps://www.blogger.com/profile/05990852054891771988noreply@blogger.comtag:blogger.com,1999:blog-9124539381685751273.post-18823858447451344772008-10-08T03:15:00.000-07:002008-10-08T03:15:00.000-07:00If I survive a quantum suicide experiment, is ther...If I survive a quantum suicide experiment, is there a way to tell whether I'm just a partial fragment of my former self in a mixed state or whether I'm just really, really lucky?Anonymousnoreply@blogger.com