We’re as quiet as possible, so we don’t disturb her; if you like, we can imagine that we’ve placed spy cameras or laser sensors. And what precisely happened when we did make our observation? When you dig deeply into what those “things” are, and what it means to “happen,” you find that nothing really bad is going on–nothing has actually moved faster than light, and no real information can be conveyed outside anyone’s light cone. Again, we do the experiment enough times that we can figure out the probabilities. What we now find is that it didn’t matter whether she stopped at the scratching post, or at her food bowl; in both cases, we observe her ending up on the sofa exactly half the time, and under the table exactly half the time, completely independently of whether she first visited the bowl or the scratching post. Artist's impression of entangled particles, from YouTube/stargazer via Business Insider. The problem of the arrow of time was there for Boltzmann and his collaborators, before quantum mechanics was ever invented; we can go very far talking about entropy and cosmology without worrying about the details of quantum mechanics. Apparently the intermediate step along the way didn’t matter very much; no matter which alternative we observed along the way, the final wave function assigns equal probability to the sofa and the table. And vice versa: If the wave function is concentrated on a single momentum, it is spread out widely over all possible positions. In classical mechanics, that’s no problem; if the state of one object is described by its position and its momentum, the state of two objects is just the state of both objects individually–two positions and two momenta. — Democritus[i]. Wave functions in quantum mechanics work the same way. Others, especially those who think carefully about the foundations of quantum mechanics, are convinced that we need to do better. The information about our entanglement with the messy external environment is analogous to the information about the position and momentum of every molecule in a box of gas–we don’t need it, and in practice can’t keep track of it, so we create a phenomenological description based solely on macroscopic variables. But let’s say we also know that she has two possible routes to take from the upstairs bed to whatever downstairs resting place she chooses: She will either stop by the food dish to eat, or stop by the scratching post to sharpen her claws. There are great hopes–although little consensus–that decoherence can help us understand why wave functions appear to collapse, even if the many-worlds interpretation holds that such collapse is only apparent. We don’t know exactly where this journey is taking us, but we’re savvy enough to anticipate that certain tools will prove useful along the way. [ix] (If we only measure the position approximately, rather than exactly, we can retain some knowledge of the momentum; this is what actually happens in real-world macroscopic measurements.). Classical mechanics isn’t a particular theory; it’s a paradigm, a way of conceptualizing what a physical theory is, and one that has demonstrated an astonishing range of empirical success. For non-senior undergraduates, the exam will be available at noon on Tues 6/13, due at noon on Thurs 6/15. A completely generic state would feature all kinds of entanglements between our small system and the external environment, right from the start. Probably not. As before, we imagine that when we look for Miss Kitty, there are only two places we can find her: on the sofa or under the table. Surely we don’t want to suggest that the phenomenon of consciousness is somehow playing a crucial role in the fundamental laws of physics? “Many worlds” is a scary and misleading name for what is really a very straightforward idea. According to quantum mechanics, the wave function of the universe assigns every one of these four possibilities a distinct amplitude, which we would square to get the probability of observing that alternative. Despite its advantages, the many-worlds interpretation of quantum mechanics isn’t really a finished product. In other words, why can’t we take a cat with an arbitrary wave function, observe its position so that it collapses to one definite value, and then observe its momentum so that it also collapses to a definite value? For large enough systems, the uncertainty is relatively small enough that we don’t notice at all. In that case, our simple picture in which the state of our perceptions becomes entangled with the state of Miss Kitty’s location is an oversimplification. “Space-time” is simply the physical universe inside which we and everything else exists. Now you observe where she is. The only acceptable answer is: no. On the other hand, quantum mechanics is very likely to play some sort of role in the ultimate explanation, even if the intrinsic irreversibility of wave function collapse doesn’t directly solve the problem all by itself. It simply can’t be done, in general. Remember, it’s not hard to understand why entropy increases; what’s hard to understand is why it was ever low to begin with. Something Deeply Hidden: Quantum Worlds and the Emergence of Spacetime Sean Carroll Dutton, September 10, 2019 Of all the weird ideas that quantum mechanics has to offer, the existence of parallel universes is the weirdest. Extensions are generally not encouraged, but if you really need one, make sure one of the TAs knows by 24 hours before the set is due. The leading contender for an alternative to the Copenhagen view of quantum mechanics is the so-called many-worlds interpretation. It is the idea that space-time emerges from a weird property of the quantum world that means particles and fields, those fundamental constituents of nature, can be connected even if they are at opposite ends of the universe. You will have to trust me that this extra apparatus is extremely important to the workings of quantum mechanics–either that, or start learning some of the mathematical details of the theory. (I once heard a lecture claming that the basic ideas of primordial nucleosynthesis were prefigured in the Torah; if you stretch your definitions enough, eerie similarities are everywhere.) [iii] More recently, dogs have also been recruited for the cause. [vi] At a workshop attended by expert researchers in quantum mechanics in 1997, Max Tegmark took an admittedly highly-unscientific poll of the participants’ favored interpretation of quantum mechanics (Tegmark, 1998). The Copenhagen interpretation of quantum mechanics is as easy to state as it is hard to swallow: when a quantum system is subjected to a measurement, its wave function collapses. But the amplitudes for ending up under the table were opposite for the two intermediate cases–so when we add them together, they precisely cancel. Tentative Outline (realistically, probably a subset of this). Now let’s ask: What do we expect to see if we only look for Miss Kitty? (Yes, it would.) And that’s a mystery. This isn’t so obvious in our simple example where there are only two possible observational outcomes–“on sofa” or “under table”–but becomes more clear when we consider observations with continuous possible outcomes, like the position of a real cat in a real room. Schematically, that means the state of the system must be of the form. where the last piece describes the (unknown) configuration of the external world, which will be different in the two cases. Your email address will not be published. In quantum mechanics, there is no fact of the matter about where Miss Kitty (or anything else) is located. In either case, there was nothing left to interfere with, and her wave function evolved into a state that gave her equal probabilities to end up on the sofa or under the table.[vii]. In the Copenhagen interpretation, we would say, “The camera is a classical measuring device whose influence collapses the wave function.” In the many-worlds interpretation, as we’ll see, the explanation is “the wave function of the camera becomes entangled with the wave function of the cat, so the alternative histories decohere.”. The problem is that interference–the phenomenon that convinced us we needed to take quantum amplitudes seriously in the first place–can no longer happen. Classical mechanics is a way of thinking about the deep structure of the world. Individually, Miss Kitty’s two possible intermediate paths left us with a nonzero probability that she would end up under the table; but when both paths were allowed (because we didn’t observe which one she took), the two amplitudes interfered. We might think that the answer is a superposition of the form (table)+(sofa), like we had before we had ever introduced the canine complication into the picture. Entanglement between two far-apart subsystems seems mysterious to us, because it violates our intuitive notions of “locality”–things should only be able to directly affect nearby things, not things arbitrarily far away. When Billy unexpectedly sees Mr. Dog bounding out of the spaceship on Mars, he makes an observation and collapses the wave function. Physics 125c is the third quarter of the upper-level undergraduate/graduate quantum mechanics sequence. On the other hand, we shouldn’t expect that even this weaker notion of locality is truly a sacred principle. Rather, “you” are either one of those alternatives, or the other. After we observe Miss Kitty’s location, the wave function evolves into something of the form. Most modern physicists deal with the problems of interpreting quantum mechanics through the age-old strategy of “denial.” They know how the rules operate in cases of interest, they can put quantum mechanics to work in specific circumstances and achieve amazing agreement with experiment, and they don’t want to be bothered with pesky questions about what it all means or whether the theory is perfectly well-defined. General relativity provides an extremely successful description of gravity as we see it operate in the world, but the theory is built on a thoroughly classical foundation.