Re: (De)coherence
Hello Eric, Just my tuppenceworth... Eric Cavalcanti wrote: I think this discussion might have already took place here, but I would like to take you opinions on this. How do we define (de)coherence? What makes interference happen or be lost? First, these are two separate questions. Decoherence is said to occur when two waves (or wavefunctions) which were initially in phase (or having a constant or well-defined phase difference) are no longer in phase. This can be for a variety of reasons. Typically, this is cited as occurring due to interactions with large numbers of particles (or a single interaction with one particle that goes on to affect a large number of particles). In this case the fact that these particles have a large number of internal states means that it is unlikely that the two waves remain in phase. Another example of decoherence would be in light from a regular light-bulb. The polarization of the light is subject to rapid and random changes in direction (due to emission of individual photons by the bulb), so that while the horizontal and vertical components of the light are instantaneously coherent, they rapidly decohere from each other to give some other value of polarization. The fact that at any particular instant there is a well defined but random value of polarization for regular light is what allows us to do Young's Double Slits with unpolarized light, as at any point on the screen the light arriving from either slit shares the same polarization, even though the value of this polarization is subject to rapid fluctuations. In answer to your second question, the loss of interference (at least in the Copenhagen Interpretation) is due to the collapse of the wavefunction, from a superposition of different possibilities to one actuality. The Copenhagen Interpretation really does not say anything about what causes this collapse (apart from the nebulously defined notion of observation). Decoherence has been invoked as one possible explanation for this loss of interference, specifically that once a large number of particles are involved in the quantum system, it is unlikely that any of them will be in phase enough for us to be able to see interference in practice. In the Many Worlds Interpretation, it is not necessarily decoherence, but the linearity of the Schroedinger Wave Equation that makes interference disappear. Specifically, once an observer (or any other system for that matter) interacts with a superposed wavefunction, that system's wavefunction is also put into a superposition of relative states. The relative states are all separately solutions of the SWE, so linearity prevents them from directly interacting ( = exchanging energy) or subjectively noticing each other through interference, in the same way as ripples on a pond are capable of moving through each other. Decoherence comes into the MWI explanation of (apparent) wavefunction collapse once a second observer (or system) interacts with the superposed system. Let's say our first observer/system has interacted with the particle on its way from the double slits to the screen in such a way that that observer/system knows (or has an unambiguous record of) which slit the particle went through. Now a second observer is going to record the position the photon strikes the screen. Under MWI, the particle is *still* in a superposition of states when it reaches the screen. However, it has also interacted with the first observer system, which for the sake of argument we shall assume consists of a large number of particles. Because of the interaction with the first observer, the second observer is not just interacting with the wavefunction of the particle that went through the slits, but also with the superposed relative state wavefunctions of the first observer(s). These two relative states are highly unlikely to be in phase because of the large number of particles involved. Therefore, the second observer is also highly unlikely to observe an interference pattern at the screen when the experiment is repeated many times. Note that in MWI the second observer's wavefunction is also split into two relative states by watching the screen, and so she may obtain a result indicating that the particle went through either slit regardless of the first observer's result (who is actually in a superposition of having got both results). Linearity of the SWE ensures that the second observer's result will always agree with the first observer's result should they compare notes later in that particular branch of the multiverse. This is also how the MWI preserves locality in the EPR paradox/Aspect experiments, which I think is an important experimental vindication of MWI. Take the a double-slit-like experiment. A particle can take two paths, A and B. We can in principle detect which path the particle went through. Suppose we can make the detecting apparatus
Re: Quantum accident survivor
Hello David, David Barrett-Lennard wrote: Please note that my understanding of QM is rather lame... Doesn't MWI require some interaction between branches in order to explain things like interference patterns in the two slit experiment? What does this mean for the concept of identity? - David There is a technical difference between interference and interaction. Interaction refers to two or more particles influencing each other through the exchange of force. Only particles within the same universe (within the broader multiverse) may interact with each other in this way. These particles are represented by wavefunctions in quantum mechanics, which have wavy properties like amplitude and wavelength, and so can exhibit interference just like waves on a pond. Also just like waves on a pond, particle wavefunctions can pass through each other, even annihilating completely in some places, without interacting (i.e. without exchanging force). Typically in single-particle experiments like Young's double slits, there is no interaction, and the interference arises from the sum of all the different trajectories (or worlds if you like) that the particle may have taken. In experiments involing two or more particles, frequently every possible path of each particle and every possible interaction must be considered as a separate world. Interference then takes place between these possible worlds, and must be taken into account in order to correctly make statistical predictions of how the particle system will behave. So in answer to your question, no, the MWI does not require interaction between branches to explain interference. Indeed interaction (exchange of force) is prohibited by the linearity of the Schroedinger Wave Equation (SWE), which indicates that its different possible solutions (universes) should move through each other as easily as ripples through a pond. We can only see the interference when we're not interacting with the rippling system. Once we do, the rippling system expands to include us within its folds. From that point on, there are multiple versions of us, each experiencing a different ripple, completely unable to interact with the other versions of ourselves moving through us all the time. Hope this helps, Matt. When God plays dice with the Universe, He throws every number at once...
Re: Quantum accident survivor
Hello Hal, Hal Finney wrote: You can indeed choose to believe that as long as any version of yourself continues in any universe, then you will consider yourself to still be alive. You could also choose the contrary, that if the total measure (ie. probability) of your survival is extremely small, that you are dead. How is this different from the current situation? Isn't your measure extremely small compared with the rest of the multiverse already? Wouldn't this mean that mean you're already dead by this definition? If so then I'm not really expecting a reply :-) Matt. When God plays dice with the Universe, He throws every number at once...
Re: Quantum accident survivor
Hi Benjamin, Benjamin Udell wrote: Assume I survive a car/plane crash which we assume could have many different quantum outcomes including me (dead || alive) Since I was the same person (entire life history) up until the crash/quantum 'branch' - then can't I assume that since there was at least one outcome where I survived, that TO ME I will always survive other such life/death branches? Furthermore if I witness a crash where someone dies can I assume that the victim will survive in their own world so far as at least one quantum branch of survivability seems possible? Yes, this is Quantum Immortality in a nutshell. If the MWI is correct, it is impossible to die from a subjective point of view. Hooray! Survive as what, though? And in what condition? I know from personal experience that one does not always experience oneself in that world-branch in which one is in tip-top shape. Reminds me of the ancient Greek myth of the goddess whose mortal lover was granted immortality at her request by Zeus, but not eternal youth, because it didn't occur to the goddess to ask Zeus to grant her lover that too. So the lover never died, but grew ever older, more wrinkled bent, till he became a grasshopper. This is the story of Tithonos and Eos. A similar thing happened to Sibyl, too. Perhaps QI imposes some kind of limit on how physically decrepit one can actually get. Another possibility is that QI does not say that it is impossible to lose consciousness, it says that it is impossible to lose it forever. So perhaps really all it does is guarantee some kind of afterlife (in the most physically likely set of circumstances where that can occur). Matt. When God plays dice with the Universe, He throws every number at once...
Re: a possible paradox
Hi Hal, I agree with everything you wrote about duplication...but I have to take issue with your last point. Hal Finney wrote: Another interesting result of this paper concerned daughter universes. In some models, it may be possible to trigger the formation of new inflating regions which would bud off from our own space time and produce their own infinite-sized level 2 universes. The authors of this paper had proposed in an earlier one that this could be a mechanism for civilizations to survive heat death, that they could create daughter universes and somehow send information into them which could be taken up and incorporated by civilizations evolving in the daughter universes. However, in the context of the multiverse, this won't really work, because any finite number of messages are insignificant in the context of an infinitely-duplicated multiverse. Only a finite number of regions can receive the messages, compared to an infinite number of regions that either don't receive them, or receive spontaneously-generated fake messages (like our discussion earlier today of magical universes). Therefore the messages can have only an infinitesimal impact on the evolution of the daughter universes and cannot be considered a meaningful form of survival. I think that the survival would be meaningful for the civilisation doing the broadcasting so long as at least one daughter universe is able to replicate the civilisation, just as I have meaningfully survived so long as future versions of me exist somewhere in the multiverse, even if I only survive in an infinitessimally small fraction of the universes (Quantum Immortality). Matt. When God plays dice with the Universe, He throws every number at once...
Re: a possible paradox
Hello Stathis and James, In answer to the first question, does the multiverse inlude perfect duplications of entire universes, the answer is yes with a but. Any particular universe in it can be sliced up in any number of ways, just as 1 = (1/n + 1/n + 1/n. n times) for any value of n. This gives rise to a picture of a very large number of universes differentiating from each other as time moves forward, as opposed to the more conventional picture of a single universe splitting as time moves forward. Both pictures seem to be mathematically valid and mutually compatible, IMHO. The fact that at a particular instant any given universe has multiple possible futures means that any given universe can be considered as a sum of however many identical copies of that universe you like. In answer to the second question, in addition to these perfect duplications, there are duplications that differ only by the state of a single photon somewhere in a galaxy on the other side of the universe (i.e. arbitrarily close), as well as 'duplications' that share nothing in common with our universe save the laws of physics, and everything in between. In the plenitude theories of Max Tegmark and others, the requirement that other universes share the same laws of physics and the same big bang is relaxed. Hope this helps, Matt. Stathis Papaioannou wrote: Let me add a postscript to this quicky: does the multiverse include perfect duplications, or only arbitrarily close to perfect - and does it make a difference? Stathis From: James N Rose [EMAIL PROTECTED] To: [EMAIL PROTECTED] Subject: Re: a possible paradox Date: Wed, 29 Oct 2003 15:52:30 -0800 quicky: does the multiverses version of existence include perfect duplications - included redundencies - of universes? James _ Hot chart ringtones and polyphonics. Go to http://ninemsn.com.au/mobilemania/default.asp -- When God plays dice with the Universe, He throws every number at once...
Re: Quantum accident survivor
Hello David, David Kwinter wrote: Another quickie: Assume I survive a car/plane crash which we assume could have many different quantum outcomes including me (dead || alive) Since I was the same person (entire life history) up until the crash/quantum 'branch' - then can't I assume that since there was at least one outcome where I survived, that TO ME I will always survive other such life/death branches? Furthermore if I witness a crash where someone dies can I assume that the victim will survive in their own world so far as at least one quantum branch of survivability seems possible? Yes, this is Quantum Immortality in a nutshell. If the MWI is correct, it is impossible to die from a subjective point of view. Hooray! Matt. When God plays dice with the Universe, He throws every number at once...
Re: a possible paradox
Hello Frederico, I've recently been taking part in a discussion on very similar lines on the Fabric of Reality mailing list (yahoo groups). Federico Marulli wrote: My reasoning is rather simple. Dealing with an infinite level 1 multiuniverse, if an event, even an improbable one, doesn't violate any pshysical laws, it necessarly has to happen infinite times and in infinite different points of the space. So we can try to reason upon some examples which has a meaning from a physical point of view. For instance, we can think about the second principle of thermodynamics, according to which the entropy of a closed system necessarly has to increase. That means that, for instance, a gas put into a container of volume V will tend to spread by occupying all the available volume. This way we get the most possible disorder and the state is the most probable. Anyway the state in which all the gas is firmly in a v V volume is not forbidden by thermodynamics; it is just a rather improbable state. But this event, having some chances to take place, has to happen in infinite places and times in our multiverse. So there will be infinite Hubble spheres in which everything happens exactly as in our own sphere, but in which any time you put a gas into a container, it will never occupy the whole volume. At the same time, there will be infinite spheres in which some day the gas will occupy all the volume and some others not. And so on. Yes, this is predicted to happen (in very rare universes) in the Many Worlds Interpretation (MWI). It's also predicted to happen under the Copenhagen Interpretation (CI), you'd just have to wait a very long time to expect to see such a violation of the 2nd law of thermodynamics. snip From all these examples we should deduce that, if all the infinite observers we have considered took advantage of the same approach we have, they would obtain very different interpretations. So the model seems to admit in itself the chance of being wrong. It is consistent with its foundamental hypotheses the fact that it is inconsistent. So here we have the paradox. But shall we put into discussion our experimental method just because some unlucky observers are not in the condition to understand the universe and the way it works? To answer this question I have tried to go even further with my reflection. I believe we have no reason to think of being privileged observers just because we observe the universe moving according to our physical laws. Moreover, physics has been formunlated just starting from our observations, so it is clear that our models come out to be consistent with them. If these observations were not like that, we would discard them. But the same thing would be valid for all the other infinite observers and any of them could think of being privileged. Besides, from one day to another, we could also realize that all our models are no longer valid. What would happen if we lived in an Hubble sphere in which, by chance, entropy began to lower all of a sudden? We can call these universes where strange things that seem forbidden by our statistical laws of physics (which are not fundamental) happen regularly through shear chance 'magical'. I believe your question could be rewritten, is there any evidence that we are not living in such a 'magical' universe ourselves? You are quite right that any particular physical law you could construct *could* be the result of observing quantum statistics which have been skewed in one way or another. For instance, you could be in a 'magical' universe where gases don't expand in line with the predictions of our statistical mechanics/thermodynamics. Instead, you would draw up your own set of laws to describe this behaviour, assuming that the deviations happen in a systematic way. Or you could be in another 'magical' universe where even fundamental particles obey totally different equations of motion, as a result of skewed sampling on every microscopic observation of the wavefunctions concerned. In order to formulate these laws, the deviations would have to be systematic. Universes admitting such 'magical' laws would be very much rarer than those where the deviations do not permit systematic modelling to occur. The evidence that we are not in such a 'magical' universe is this. Though our laws describing the behaviour of gases etc. were originally derived from observations of large amounts of gases - macroscopic investigation - we have since found that they are 100% bconsistent with our observations of single particles of gas - microscopic investigation. In 'magical' universes, we would not expect this consistency. Observations of large amounts of gas would not be consistent with measurements made on individual particles in the vast majority of these universes. The fact that these two sets of laws of physics are consistent indicates that we are not in a 'magical' universe with very high confidence - because if we were in a
Re: a possible paradox
Hi Hal, Hal Finney wrote: Matt King writes: I should point out that there does remain a vanishingly small possibility that we could be in one of the extremely 'magical' universes where both macroscopic and microscopic laws of physics are skewed in a mutually consistent way, however given the tiny probability of this being the case I think it is quite safe to ignore it. That seems rather extreme, because the probablity that we are in a regular magical universe is already vanishingly small and we would truly be safe in ignoring it. Even the probability of observing a single large scale violation of the laws of probability is vanishingly small. (Magical universes suffer from repeated large-scale violations.) Going beyond that and asking for consistency between the physics of the large and the small is really gilding the lily. I don't see what would motivate you to draw the line there. Oh I quite agree that it is overwhelmingly likely that we're not in a 'magical' universe anyway. My point concerned trying to *demonstrate* that we're not, which is easily done if you assume 'magical' universes with consistent macroscopic and microscopic physics are even rarer than 'magical' universes in general. Matt. -- When God plays dice with the Universe, He throws every number at once...
Re: Is reality unknowable?
Hey all, Nice to see some activity on this list again. I think the filament's blown, but then again I'm a physicist :-) Matt. Norman Samish wrote: Perhaps you've heard of Thompson's Lamp. This is an ideal lamp, capable of infinite switching speed and using electricity that travels at infinite speed. At time zero it is on. After one minute it is turned off. After 1/2 minute it is turned back on. After 1/4 minute it is turned off. And so on, with each interval one-half the preceding interval. Question: What is the status of the lamp at two minutes, on or off? (I know the answer can't be calculated by conventional arithmetic. Yet the clock runs, so there must be an answer.Is there any way of calculating the answer?) I've been greatly intrigued by your responses - thank you. Marcelo Rinesi, after analysis, thinks that the problem has no solution. Bruno Marchal thinks that the Church thesis . . . makes consistent the 'large Pythagorean view, according to which everything emerges from the integers and their relations.' George Levy, after reading Marchal, thinks there may be a solution if there is a new state for the lamp besides ON and OFF, namely ONF. Stathis Papaioannou thinks the lamp is simultaneously on and off at 2 minutes. He thinks the problem is equivalent to asking whether infinity is an odd or an even integer. He shows that there are two sequences at work, one of which culminates in the lamp being on, while the other culminates in the lamp being off. Both sequences can be rigorously shown to be valid. Now Joao Leao paraphrases Hardy to say that 'mathematical reality' is something entirely more precisely known and accessed than 'physical reality' So I'm to understand that mathematical reality is paramount, and physical reality is subservient to it. Yet mathematics is unable to determine the on-or-off state of Thompson's Lamp after 2 minutes. What are the philosophical implications of unsolvable mathematical problems? Does this mean that mathematical reality, hence physical reality, is ultimately unknowable? When God plays dice with the Universe, He throws every number at once...
Reality of i (was Something for Platonists)
Hi James, I don't want to get into the Platonism discussion as I'm not of a philosophical bent, but I would like to start discussion based on something you wrote in one of your posts on the subject: James N Rose wrote: The square root of a negative number has no physical reality (or so it is presumed, because no abject examples have yet been shown/proven) but it has a most definite platonic ideal existence. The whole square root of a negative number question boils down to the reality/unreality of a single number, the square root of minus one, usually called i, as every other negative square root can be expressed as a real multiple of this imaginary number. Now, I'd be the first to accept that you can't have i oranges, so i does not have the same kind of physical reality as the natural numbers, or even the positive real numbers. However, you also cannot have zero oranges, or minus five oranges for that matter. So perhaps it is no less physically real than the negative numbers or zero. I'd also like to say that in a great deal of physics, the imaginary number is indispensible, at least in doing the math - could this be sufficient evidence to declare it physically real? Specifically, if we have used i to predict the result of a particular experiment, and we find that our prediction and the result match, is this evidence for the physical reality of i? I'm reminded of looking out of the window to watch the trees move, and concluding that it is windy, even though I haven't seen or felt the wind... Just a thought, Matt. When God plays dice with the Universe, He throws every number at once...
