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There is an even simpler thought experiment you can do to reach this conclusion: consider what the result of measuring anything to an infinite precision could p
by lisper 2y ago
There is an even simpler thought experiment you can do to reach this conclusion: consider what the result of measuring anything to an infinite precision could possibly look like. It would require somehow recording an infinite amount of information. How would you do that, particularly when you take into account that everything you can interact with to make an information storage device is subject to the Heisenberg uncertainty principle?
- oniony 2y agoIt would simply be written down on an infinitely long strip of paper.
- tonetegeatinst 2y agoMöbius strip for double surface area....I can practically see the cheese TV comercial
- __MatrixMan__ 2y agoYou could use a Turing machine tape for the job. I'm told they're stored in the parentheses mines beneath MIT, somewhere near the point masses.
- thfuran 2y agoThe shelving down there is frictionless, so they're often not so nearby.
- enkid 2y agoJust because you can't record something doesn't mean it doesn't exist.
- lisper 2y agoWho said anything about recording? What would the subjective experience of measuring something with infinite precision possibly be like?
- JumpCrisscross 2y ago> would require somehow recording an infinite amount of information... >> Just because you can't record something... >>> Who said anything about recording?
- lisper 2y agoSorry, my mistake, I was distracted when I wrote that reply. Yes, I did write that, but it's not actually essential to the point I was trying to make, which was: what could the result of measuring anything to an infinite precision possibly look like?
- JumpCrisscross 2y ago> what could the result of measuring anything to an infinite precision possibly look like? Depends on what you're measuring. To illustrate why that isn't a facetious response, consider the difference between 'measuring' pi, 'measuring' a meter and 'measuring' the mass of a proton. (Or, for that matter, the relative mass of three of something to one of it.)
- lisper 2y agoHow do you measure pi?
- JumpCrisscross 2y ago> How do you measure pi? Pick your method. It’s the ratio of a circle’s circumference to its diameter.
- winwang 2y agoConsidering that we don't know the value of pi (not that we could write it out nor read it), I'm not sure your definition of "measure" is the same as mine or most people's.
- asdasdsddd 2y agoSure but i can invent infinitely many unfalsifiable claims that mean nothing
- mannykannot 2y agoThis brings to mind one of my favorite quotes: The Schrödinger wave-function is expressed in a unit which is the square root of an inverse cubic meter. This fact alone makes clear that the wave-function is an abstraction, forever hidden from our view. Nobody will ever measure directly the square root of an inverse cubic meter. Freeman Dyson, Why is Maxwell’s Theory so hard to understand? https://www.clerkmaxwellfoundation.org/DysonFreemanArticle.pdf https://www.clerkmaxwellfoundation.org/DysonFreemanArticle.p...
- JumpCrisscross 2y ago> consider what the result of measuring anything to an infinite precision could possibly look like. It would require somehow recording an infinite amount of information This is Zeno's dichotomy paradox [1]. Finitely-defined infinitely-complex systems (e.g. fractals and anything chaos theory) are the escape. [1] https://en.wikipedia.org/wiki/Zeno%27s_paradoxes#Dichotomy_paradox https://en.wikipedia.org/wiki/Zeno%27s_paradoxes#Dichotomy_p...
- A_D_E_P_T 2y agoThere's a much simpler escape: That space is ultimately discrete (i.e. that there's an elementary length) rather than infinitely continuous.
- JumpCrisscross 2y ago> a much simpler escape: That space is ultimately discrete (i.e. that there's an elementary length) rather than infinitely continuous Sure. The point is the gedankenexperiment proves nothing. We don't need to "[record] an infinite amount of information" to encapsulate the infinity between any pair of real numbers.
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- tomrod 2y agoIs there? Planck length isn't a pixel.[0] [0] https://www.physicsforums.com/insights/hand-wavy-discussion-planck-length/ https://www.physicsforums.com/insights/hand-wavy-discussion-...
- astrange 2y agoIf space is discretized, we should see "upscaling artifacts" in the CMB, but we don't.
- defrost 2y agoMaybe we would .. but Musk has to turn off his leaky Starlink over the Murchison (not so) Quiet (anymore) Zone first.
- A_D_E_P_T 2y agoThe Planck Length is a practical limit to the precision you can possibly attain in space. The electron might be smaller. Its diameter is known to be smaller than 10^-22m, but could be much smaller than that. Further below the Planck Length, there are strong indications that the universe isn't continuous -- it's discrete. That there's an absolute limit to precision, something really quite analogous to a pixel. This elementary length could be somewhere around 10^-93m.
- JumpCrisscross 2y ago> there are strong indications that the universe isn't continuous -- it's discrete There are indications discrete space is plausible. It's actively debated. There are also strong indications space is continous, e.g. Lorentz symmetry. (This was recently the death knell for a branch of LQG.)
- euroderf 2y agoIm my murky conception of reality, the existence of Planck limits indicates that reality is discrete, and that therefore quantum uncertainty must exist. For example, I pound the picnic table. Presumably this is somehow transmitted thru the entirety of the Earth, or at least thru a tiny portion of it. But is there a cutoff ? Where is the cutoff ? Where is the effect simply too small to "register" in any conception of reality ?
- adrian_b 2y agoThe attainable precision is limited to much lower values by much simpler causes. The theory that the Planck length has any significance is just a speculation. Nobody knows how interactions would behave at distances so small and there are no known methods that could compress anything into volumes so small. There is no basis to believe that extrapolating the behavior from normal distances and sizes to the scale of the Planck length is valid. There are pure speculations that are interesting, but in my opinion any speculation about the Planck length is not interesting, because nobody has been able to formulate any prediction based on such a speculation that can be verified in any way. Most speculations about the Planck length are made by people who obviously know very little about the meaning of the so-called fundamental constants or of about the significance of the useful natural units for physical quantities, to which the Planck length does not belong. The Planck length is just one way to express the intensity of the gravitational interaction, i.e. an alternative to Newton's constant of gravitation. Its numeric value does not say anything about any other physical phenomena. The numeric smallness of Planck's length is just an expression of how weak the gravitational interaction is in comparison with the other interactions. It does not have any other significance.
- pazimzadeh 2y agoI have similar reasons for not believing that the world that we experience is a computer simulation.
- ur-whale 2y ago> It would require somehow recording an infinite amount of information You're assuming spacetime behaves like the set of reals (something with cardinal ℵ1, if you accept the continuity hypothesis), an object that even if you stay confined within the bounds of pure mathematics, behaves in very, very weird ways. It may be that spacetime at small scales maps better to a different kind of mathematical object and not even a grid-like one.
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- woopsn 2y agoHow does this not break the foundations of quantum theory? For example the Heisenberg uncertainty principle itself implies that the conjugate of a discrete variable must have a continuous spectrum. Thus if there are no continuous variables, there can be no discrete ones either. Either this or we need to throw out one of the variables and call it non-physical/observable -- and yet it very much seems like both position and momentum are things.
- lisper 2y ago> it very much seems like both position and momentum are things. The operative word being "seems". Position and momentum (and indeed real numbers in general) are mathematical models that predict observations. But the observations themselves are the results of physical interactions that transfer energy, and those can only ever be discrete because energy is quantized.
- krastanov 2y agoEnergy levels in simple finite systems are indeed quantized, but this does not mean we can not make the energy quanta be continuously parameterized. For instance, if your system is two mirrors facing each other and you are using the quantum description of the light trapped between these mirrors, you can pick any real value for the energy separation between levels of this system simply by continuously varying the distance between the mirrors. Maybe one can make the argument that position itself is quantized (thus the position of the mirrors can not be varied continuously), but we do not have experimental reasons to believe space is discrete (and quantum mechanics does not require it to be discrete). And while it is pleasing to imagine it discrete (it is more "mathematically elegant"), we do not have any significant rigorous reasons to believe it is. Edit: Moreover, if you want to describe (in quantum mechanics) the interaction between a finite system and the open environment around it, the only way to get a mathematical description that matches real-world experiments is to have continously parameterized energy levels for the systems making up the open environment. If you assume that only discrete values are possible, you will simply get the wrong result. Most quantum optics textbooks have reasonably good discussion of this. E.g.: Quantum Optics by Walls and Milburn Quantum Optics by Scully and Zubairy Methods in Theoretical Quantum Optics by Barnett and Radmore
- _cs2017_ 2y agoThe article made the wrong statement. The thought experiment isn't that you can't measure length with infinite precision. It's that you can't measure length with precision better than the Planck length. No infinities are involved here.
- BLKNSLVR 2y agohttps://en.wikipedia.org/wiki/On_Exactitude_in_Science https://en.wikipedia.org/wiki/On_Exactitude_in_Science Jorge Borges' way of telling a story as analogy is beautiful and simple. It takes the resources of the universe to simulate the universe.
- Joker_vD 2y agoI think the Pythagoreans had the same silly crisis about square root of two that you have about the real-valued measurements. And the solution, I believe, would be the same: there simply are two physical things with lengths that relate to each other exactly as sqrt(2) to 1. So, how would result of measuring e.g. length of something to an infinite precision look like? It would look like two particles that are kept at rest relative to each other; the distance between them is the measured distance. Whether this distance has to be commeasurable with the Planck scale or not is an interesting question but it really can go either way.
- lisper 2y ago> two particles that are kept at rest relative to each other And how do you do that in the face of Heisenberg uncertainty?
- Joker_vD 2y agoAnd how do you measure the length of a burning rod (that's moving past by you at a considerate speed) in the face of relativity of simultaneity? I guess it's impossible, and so the very concept of length must be meaningless. To actually try to answer your question: I don't know. But that's just me; and ain't there some interesting experimental setups with super-cooled crystals? In any case, inability to imagine something is hardly a convincing proof of anything.
- lisper 2y agoIn some cases it is. Do you think perpetual motion machines are impossible, or is that just a matter of our inability to come up with a sufficiently clever design?
- s1artibartfast 2y agoIntegers have perfect precision, but finite storage. For example, pi is infinite information and digits in float, but finite when represented as a single symbol