:biggrin: Nice post! At about the Planck time after the big bang, it is thought that gravitation would separate from the three other forces of nature (strong, weak and electromagnetic forces) Thank you for that insight. I guess it's all downhill from here =/. But the observer flying away would find that the wavelength of the same photon was larger than the Schwarzschild radius of the photons energy. [QUOTE=Ken G, post: 5224660, member: 116697]On the topic of the Planck pixel, perhaps this overall idea is being rejected too sweepingly. In the past I have investigated how DNA partitions itself into small spaces and how knots in DNA molecules move and untie. at [URL]http://www.pbs.org/wgbh/nova/next/physics/fastest-neutrino-ever-detected-has-1000x-the-energy-of-the-lhc/[/URL], So with a bit of estimation, assuming (1) the rest mass energy of a neutrino is about equal to 1 meV, (2) oncoming blueshift is approximately equal to the lorentz contraction factor here. I guess its all downhill from here =/[/QUOTE]. Regardless of whether or not string theory is true, one thing that is certain: In the search for a unifying theory of everything, understanding the Planck length and the physics involved will be key. [QUOTE=john baez, post: 5227634, member: 8778]To see how the calculation works, go here: Still, until a better theory of quantum gravity is devised, the Planck length is the best estimate we have for a minimum length. /u/atatassault describes this in more detail. Modern theories of particle physics are a mess to actually evaluate. Planck length is calculated from the speed of light, the gravitational constant, and the Planck constant. Grammaticalization, the change by which lexical categories become func-. So you know about blackholes, right? What is the smallest thing in the universe? So what we can do on paper, we can't do in reality. What is Planck length? Suppose I wanted to measure my height. The measuring particle will transfer some energy to the test particle but it will be from its kinetic energy not gravitational attraction. By checking the changes in our measuring particle, we can attempt to deduce the location of our test particle. Planck length is actually derived from the fundamental constants of the universe that define the properties of space-time: The speed of light c which signifies the maximum speed of communication in the universe. At least that is what I thought, beforeJohn Baezcorrected me. First, let's talk about what Planck length is. It is also the scale at which space-time is theorized to become quantized in Loop quantum gravity theory. Im not sure if Im doing this right, but I just googled energy of a neutrino collision and found mention of an apparent 5000-10,000 TeV neutrino. This number is actually a length - the Planck Length. Yes, if we started with visible light, at around [itex]10^{-7}[/itex] meters, it would be blueshifted to a wavelength around [itex]10^{-23}[/itex] meters; a trillion times longer than the Planck Length. Planck's constant has the dimensions (unit) of. Lets go 1000 times smaller than this. To see how the calculation works, go here:http://math.ucr.edu/home/baez/lengths.html#planck_length, I can't remember what it's called, even enough to search it via google, but there is actually a solution to this problem. If I remember correctly (I very well could not), it has to do something with the geodesics of spacetime warping under the energy tensor from the relative speed of you and the mass youre observing. Responsible for measuring things like infrared and ultraviolet light, greenhouse gases, atomic clocks, and disease, optical frequency combs act as rulers that measure light. Another way to think about the Planck length is that if you try to measure the position of an object to within in accuracy of the Planck length, it takes approximately enough energy to create a black hole whose Schwarzschild radius is the Planck length! The reason is that to measure a length you must have something with a wave length no larger than the object. Now, this doesnt necessarily apply when were talking photons. How does this relate to the planck length? Why is it significant?It is the smallest length at which gravity would have an effect. So why is the Planck length thought to be the smallest possible length? One of the remarkable things about Planck length is that since it is derived from the fundamental constants of the universe, which by definition applies to everything, it will be the same no matter what language you might speak, what units you might use, or even what planet you might come from. If so, why?". [/QUOTE] [QUOTE=Ken G, post: 5224660, member: 116697]and volumes in 4-D spacetime are invariant, are they not? Or you might be on the moon. The three fundamental constants h, c and G are manipulated and rearranged in different ways to get the Planck time, Planck mass etc. This basically lets us swap out the electromagnetic constants e and ##\epsilon## with the more general constants ##\hbar## and c. The Coulomb energy now looks like this: This is where the hand-waving will begin. We're a long way off from being able to test this experimentally. We can use that as our Delta X. [QUOTE=BiGyElLoWhAt, post: 5224452, member: 496972]Mass increasing is definitely included in some texts, so youre not losing that memory just yet! So, at the Planck scale, we can't actually say that anything is there at all to measure? Pay attention to that repeated word "known." Moreover, any effects of quantum gravity at this scale(if there are any) are entirely unknown as space itself is not properly defined. G/c3, one gets a length. The 14-hour flight may seem long to you, but to the universe, it would go completely unnoticed. So, one can argue that its impossible to measure distances shorter than this though the argument is a bit hand-wavy. There is a misconception that the universe is fundamentally divided into Planck-sized pixels, that nothing can be smaller than the Planck length, that things move through space by progressing one Planck length every Planck time. In 1964, C. Alden Mead published a paper in which he determined the effect of gravity on a phenomenon called diffraction, which describes what happens to light when you send it through a small aperture. Thus, the Planck length is the smallest possible unit of measurement. Exam 2014, questions; Exam 2015, questions; Im not going to argue within the last 30 years. Thanks! If a minimum length scale exists in the universe there's a very good chance it's equal to the Planck Length Lp, which is why 1/Lp = 6.187 x 10^34 is my choice for #MegaFavNumbers. please mark me brain mark list Advertisement Advertisement Jimin 8 photo-folio Me, Myself and Jimin 'ID:Chaos' Complete full set with all inclusions (photo book, mini poster, folder poster, postage stamp, photo card, Jimin's item - folding card) and the crown random photo card. The gravitational force attracting the matter, causing concentration of the matter in a small space and leaving much space with low matter concentration: dark matter and energy. It is really small. In this image of Max Planck, we see that the length of Planck is 10. . When you scatter a particle of light off another particle say an atom the atom's gravitational attraction to the light particle causes an intrinsic uncertainty in the atom's location. That said, this is the most straightforward argument I've seen for it. To get an idea of why this is important, think about the difficulties associated with expressing lengths in meters versus feet. categories never become prototypical lexical categories, and less radical. Just imagine things that are about the size of your body. Body length and sexual maturity status were recorded in . http://math.ucr.edu/home/baez/lengths.html#planck_length. Planck Length: Smallest Thing in the Universe.This video gets to the Planck at around 4:00, it's a good common language introduction. There was an analysis recently of gamma ray arrival times from a burst in a distant galaxy. General relativity predicts that objects can collapse under certain conditions, usually described as sufficient energy density in their rest-frame. Yes that means objects dont move one Planck length every Planck time, but thats obvious any such object would be perceived as moving at the speed of light. From Newtonian gravity, we can calculate the gravitational energy associated with our charges. The Planck length is the length one obtain when one multiplies the fundamental constants c (the speed of light in a vacuum), G (Newton's gravitational constant) and h (Planck's constant). I remember in my early teens reading about the Planck time in National Geographic, and hearing about Plancks constant in highschool physics or chemistry, and thinking they were the same. And the reduced Planck Constant h bar, which links how much energy a photon carries depending on its electromagnetic frequency. The theories, in a sense, do not really work if evaluated to the finest finest details in a rather similar sense to the gravitational force becoming infinite once you bring two masses to the same point. By accepting all cookies, you agree to our use of cookies to deliver and maintain our services and site, improve the quality of Reddit, personalize Reddit content and advertising, and measure the effectiveness of advertising. Since the photon will never come out predictably, you can't measure that which is smaller than the planck length. From my point of view this chain of argument is invalid, exactly because the continuous paradigm breaks down around the scale when spacetime supposedly becomes discrete. But the claim that an objects actual mass has increased (and hence its capacitiy to pull other objects toward it by gravity) is NOT well supported by any reasoning Im familiar with. The Planck constant is the relationship between the energy of a photon and its frequency, and I don't know how that's quantised, so I'll put that aside. Here, we are going to find things like large viruses.Lets keep going to 1000 times smaller this. A transformed planck volume with a shorter distance but a longer time loses this property. It has the value: l P = 1.62 10-35 m. In SI units, measurements of length are made in metres (usually given the symbol m). Light with a wavelength of smaller than the planck length has so much energy, that anything it interacts with will become a very tiny black hole. As for myself Im taking serious the idea, that all our established physical theories (including GR and QM) are effective theories in the sense, that they dont express anything fundamental about the ultimate nature of reality, but instead are approximations to the inner workings of reality in the discrete paradigm. Physics isn't quite up to handling that, yet. Medium. Is that true? It is possible that at lengths smaller than the Planck scale, gravity or quantum mechanics behaves completely differently, that we may not yet know about. The plank length is the smallest meaningful measurement of length - e.g, there's nothing in the universe smaller than a plank length. And roughly equal to 1.6 x 10-35 m or about 10-20 times the size of a proton. I was soon set right. The light only has a reference frame in reference to its source and its observer, and frequency and wavelength of light are extrinsic featuresobserver dependent Relatively moving observers are going to measure different wavelengths of the same light, so if this idea is accurate, they would also disagree on whether the light spontaneously collapsed into a black hole. The Planck length does have physical significance, and I'll talk about what it is, and what it isn't. But consider if we took a light of wavelength JUST OVER the planck length, and had one observer fly away from it, while another flew toward it. This black hole will evaporate immediately, belching out the photon you tried to measure it with, but in a random direction. Planck units are defined based on physical constants rather than human-scale phenomena. See our. As for myself Im taking serious the idea, that all our established physical theories (including GR and QM) are effective theories in the sense, that they dont express anything fundamental about the ultimate nature of reality, but instead are approximations to the inner workings of reality in the discrete paradigm. But absent a candidate theory based on this discrete paradigm, theres also nothing to discuss under the Physics Forums rules. Ruthrauff and Jesse Conklin, a researcher with Germany's Max Planck Institute of Ornithology, set out in Nome in late June to find and follow bar-tailed godwit chicks at their breeding grounds. Darn my memory, and I'm only 23! So to summarize, the Planck length is an important order of magnitude when quantum gravity is being discussed, but it is not the fundamental pixel size of the universe. This is because contrary to how it seems in day-to-day life, objects do not have a single point location. [/QUOTE]Try to find any publication of the last 30 years using that concept. There is a surreal and amusing dialogue trying to get to the bottom of this, that you can still read in the discussion section of the Planck length Wikipedia page. So what is the Planck length? Now that we understand what Planck length is, we can turn our attention to the question of whether it is the smallest possible length. What is the smallest possible time? If it turns out that at very small lengths, some other version of quantum mechanics manifests itself or the law of gravity differs from our current theory, the argument falls apart. The Planck length is an extremely small distance constructed from physical constants. In fact, the first iteration of string theory was theorized to explain nuclear physics rather than gravity, and the length-scale of the strings was much much larger. $$r=\sqrt{\frac{\alpha\,G\hbar}{c^3}}=\sqrt{\alpha}\ell_{p}$$. Im glad to have a good article now to point people to, when it comes up again. He was trying to come up with a way to define units that depended only on constants of the universe. Just imagine things that are about the size of your body. You could never figure out both at the same time. In some cases, a Planck unit may suggest a limit to a range of a physical quantity where present-day theories of physics apply. I really wish I could remember what it was called. Ah, upon rereading the article, I see that you really pretty much hit on my issues in my last post. This a 1/a duality (in Planck units) already hints of a majormodication to Einstein equations at early times, as ordinary theory of general relativity is not invariant under such a transformation. Or a big beachball, which can be found near oceans and beaches all across America. This is 1X 10^-15 or one quadrillionth of a meter. My first text that I read on SR had a thought experiment with 2 bouncing balls and 2 observers, and used it to demonstrate relativistic mass. Once r becomes 0 this formula becomes ill defined (division by zero.). Planck himself said in his paper to the Prussian Academy of Sciences, "These necessarily retain their meaning for all times and for all civilizations, even extraterrestrial and non-human ones, and can therefore be designated as 'natural units.'". changes against the general directionality of grammaticalization are. Another potential model of quantum gravity is string theory, based on the dynamics of really small strings. [QUOTE=BiGyElLoWhAt, post: 5224337, member: 496972]I cant remember what its called, even enough to search it via google, but there is actually a solution to this problem. This is where it is important: if things are interacting at distances close to the Planck length, you will have to take quantum gravity into account. The meter is a useful unit for measuring length, but theres nothing inherently special about it. Remember the gravitational force is M1 * M2 * G / r2. In that sense, an object could appear to move one Planck length each Planck time, and not seem to move at the speed of light, if the Planck length was interpreted broadly as also existing in the time dimension. Fundamentals of modern physics, and it was by a german author, Ill try to dig it up here sometime soon. To get around these limitations and to make the computations tractable there is a process called "renormalization" which is a rather elaborate process of "cutting off" details on a length scale that is smaller than to be of interest to the experiment. It's not ELI5 clarity - you'd need a decent background in physics to follow it. So what I took from you post is that the Planck Constant is the closest possible measurement you can have, even though both measurements will never be 100% accurate. ELI5: how did the WASD keys become the norm for movement ELI5 - how does your body manage to keep in all the feces ELI5: Why did crypto (in general) plummet in the past year? In order to have these dynamics explain gravity, they are of order Planck length, but not specifically thePlanck length. But what does this length mean? Why, though? To make it worse, if you transform pixels, the relation between (dilated) Planck time and (contracted in one dimension) distance does not hold any more. How do we know this? The glassy properties of the quantization help it escape the usual problems with Lorentz invariance. The conclusion drawn from this isn't "we need a more precise ruler than is theoretically possible;" the conclusion is "there is a range of heights I could equally possibly be, so think of me as actually being spread out over all those heights in that range.". ELI5: Why are fridges in cold climate countries not Press J to jump to the feed. There are a lot of misconceptions that generally overstate its physical significance, for example, stating that it's the inherent pixel size of the universe. By rejecting non-essential cookies, Reddit may still use certain cookies to ensure the proper functionality of our platform. Max Planck Institute for Evolutionary Biology Pln D24302 Germany . It's not the smallest possible measurement of length - you can always define a new unit that is half a plank length, or a quarter. This is nanometers, or one billionth of a meter. Ao, if we ever come across aliens from another world and compare notes, we both will have the same length for the smallest length possible in the universe. Another way to think about the Planck length is that if you try to measure the position of an object to within in accuracy of the Planck length, it takes approximately enough energy to create a black hole whose Schwarzschild radius is the Planck length! Yes that means objects dont move one Planck length every Planck time, but thats obvious any such object would be perceived as moving at the speed of light. Presumably, the pixels would be in 4-D spacetime, not 3-D space, and volumes in 4-D spacetime are invariant, are they not? However, from the point-of-view of a passing neutrino; with its velocity negligibly below the speed of light, that same light bulb could be producing light with wavelengths less than the Planck Length. Have you considered the idea of extremely high blueshift reference frames? tional categories, is overwhelmingly irreversible. When you hear this, you may stop and think, "Surely, if I have a length, then I half it, and I repeat this over and over, I will be able to get to something smaller." The Planck length is an extremely small distance constructed from physical constants. Im highlighting the issue with a rather extreme casethe observer on the neutrino. Explain Like I'm Five is the best forum and archive on the internet for layperson-friendly explanations. Gravity and the speed of light are fundamental natural things, so Wikipedia has an interesting relationship: The Planck length is the square root of the Planck area, which is the area by which a spherical black hole increases when the black hole swallows one bit of information. Examples of such ecotypic specialization include . Basically it says that as you approach the speed of light and pass a large mass, it can't turn into a black hole due to your reference frame. A slightly more technical explanation can be found here. My research is at the interface of biological physics and soft condensed matter. If there is a rest frame in which the matrix of these Planck-pixels is isotropic, in other frames they would be length contracted in one direction, and moving diagonally with respect to his matrix might impart angle-dependence on how you experience the universe. FACT: Planck time is the time it takes a photon to travel, in a vacuum, a distance of 1 Planck length.A Planck length can be derived from an equation that considers the gravitational constant and light. So suppose we send one particle shooting at another particle we want to know the location of. I have an idea as to where the misconception might arise, that I cant really back up but I will state anyway. This is the size of particles that make up the nucleus of all atoms, protons and neutrons. It starts out with a principle of quantum mechanics - everything is probability waves. [/quote] A zeptosecond is a trillionth of a billionth of a second. I thinknthe book was 56 or there abouts. Heads up, this will take a while because it's going to require covering a lot of background concepts. Now, in order to include the strong quantum e ects For example, think about moving faster than the speed of light. What is the most interesting object that you found and why? The simple summary of Mead's answer is that it is impossible, using the known laws of quantum mechanics and the known behavior of gravity, to determine a position to a precision smaller than the Planck length. Neglecting factors of 2, we have ##m_nu m_P = 3 eV cdot E_nu## where the lightest neutrino mass is probably of the order of 1 meV. Near thermodynamic equilibrium, the emitted radiation is closely described by Planck's law and because of its dependence on temperature, Planck radiation is said to be thermal radiation, such that the higher the temperature of a body the more radiation it emits at every wavelength. Going beyond established physics, is there more of a roll for the Planck length? But Mead was curious about quantifying gravity's negligible effect. It's important to clarify that this line of reasoning doesn't imply that space is discrete (i.e. How was Planck time determined? Subscribe to our daily newsletter to keep in touch with the subjects shaping our future. There is an asymmetry between the mass of the electric charges, for example proton and electron, can understood by the asymmetrical Planck Distribution Law. While the formulation of them are governed by elegant principles like invariance under the rules of special relativity and can be brought into a compact (Lagrangian) formulation, the calculation of the results of various processes are a mess. Eli5; how we find patient zero when there is disease eli5 When countries swap prisoners how are they sure the ELI5: Why do we (Anglophones) use the native language Eli5: What is the difference between soldering and welding? A planck length because it was small. Eur. In fact, if an atom was the size of the earth, a planck length would be smaller than the size of an atom it would be about the size of a proton. Disclaimer: I'm just interested in particle field theories from an amateur point of view. The smaller the wavelength of light you're using, the more energy it has. How often does Planck's constant change? A chip-scale broadband light source in silicon carbide Optical frequency combs have changed science and technology as we know it. String theorists also think that it is the size of the vibrating strings that make up all the elementary particles in the standard model. Could be Theres no way of disproving the possibility. https://www.physicsforums.com/insights/wp-content/uploads/2015/09/planck.png, https://www.physicsforums.com/insights/wp-content/uploads/2019/02/Physics_Forums_Insights_logo.png, What Planck Length Is and Its Common Misconceptions, 2022 PHYSICS FORUMS, ALL RIGHTS RESERVED -, Struggles With The Continuum: Quantum Mechanics of Charged Particles. And so far, it is just a unit. [QUOTE=JDoolin, post: 5224402, member: 268035]I would probably go the other way Obviously if your theory implies that something is turning into a black hole according to one observer, but is not turning into a black hole according to another observer, then your theory has been essentially discounted by reductio ab adsurdam. So while the second is originally one-86400th of a day, the Planck time is based on the speed of light, Newtons gravitational constant, and Plancks (reduced) constant, which is twice the angular momentum of an electron. Phys. The colors represent the density or . What defines something being a black hole is if it's matter/energy density is high enough that light can't escape it. Why can't we measure smaller than a Planck length? A modern treatment of Planck's work begins with the speed of light c, gravitational constant G, reduced Planck constant , Coulomb constant k and Boltzmann constant kB. [/SIZE][/QUOTE] Units: ((length)2(mass))/((time)2(temperature)). Just to clarify the symbols, e is the fundamental charge, ##\epsilon## is the dielectric constant. For example, think about moving faster than the speed of light. [QUOTE=BiGyElLoWhAt, post: 5224854, member: 496972]Eisberg? I'll try to translate, glossing over the math. So, how does a tiny number such as this tie into physics? Click the atom. We received an email from Bill G., an inquisitive reader: "It is said that the Planck length is the smallest length possible. It. By taking different mathematical combinations of these constants, and reducing their units, you can get a length. [/size], [QUOTE=john baez, post: 5227634, member: 8778] ..it takes approximately enough energy to create a black hole whose Schwarzschild radius is the Planck length! [/QUOTE], Thats not how I interpreted that link. Still, until a better theory of quantum gravity is devised, the Planck length is the best estimate we have for a minimum length. Instead, a Planck pixel idea could say that spacetime is discretely tiled, in the sense that world lines cannot be defined with finer precision than that similar to the way quantum mechanics tiles phase space in statistical mechanics. Some Planck units, such as of time and length, are many orders of magnitude too large or too small to be of practical use, so that Planck units as a system are typically only relevant to theoretical physics. If a given volume at rest has a certain amount of energy within, it will have a rest mass m=E/c##^2##. You actually aren't sitting in your chair reading this. One of the features of Loop Quantum Gravity is that for something to have a surface area or a volume, it must have at least a certain quantum value of surface area or volume, but will not necessarily have integer values of that quantum, and the quantum is not exactlythe square or cube of the Planck length, although it is of that order. Deriving the Planck Length. The smallest lenth theorized to be possible, the Planck length is about 4 X 10^-35 meters. Instead, a Planck pixel idea could say that spacetime is discretely tiled, in the sense that world lines cannot be defined with finer precision than that similar to the way quantum mechanics tiles phase space in statistical mechanics. 2. Or a big beachball, which can be found near oceans and beaches all across America. I would indeed think that if one wishes to regard spacetime as in some sense coarse-grained at the Planck scale, one must use a version of coarse-graining that is Lorentz invariant, meaning that the grains are defined by their volume but not their shape. (b) Unit of length is changed to 5 0 c m, . Our test particle is now no longer in the precise location it was before, and (because we never knew exactly where our measuring particle was anyways) we don't know where the test particle really is beyond some level of accuracy. You don't notice this, because on any human-sized scale (commonly referred to as "macro" scale), the probabilities are so ridiculously, laughably small that it never comes up (one of the common examples is calculating the probability that you will suddenly appear on the far side of a wall you are leaning against; that probability is so small that you could wait more than the expected lifetime of the universe and it still should never happen). Our measuring particle's gravitational pull gave some acceleration to our test particle. This misconception turns up a lot here on PF, too: [URL]https://www.google.com/?gws_rd=ssl#q=%22planck+length%22+site:physicsforums.com[/URL]. This includes paths where the constituents get together super close. Well, I guess my point is that radiant energy E = hf = hc/lambda, is simply not the same as mass energy E=mc^2. Think of a Planck length as a pixel, and the universe a giant screen. Thus, we no longer think of two electrons, photons, or other particles "colliding," because the objects don't have a clear location nor do they have a clear size. Energy of electron will be 13 point 6 electron volt, so d problem wave length will be h upon root of 2 m into kinetic energy 6.6310 to the power minus 34, divided by root of 2 into mass of electron 9.1 into 10 to the power 31 into Kinetic energy: this is converted into wont so de broglie wavelength of electron to 3.3 into 10 to the power minus . If there is anything that the history of physics has shown us, it is that we dont shoot with high percentage when we try to anticipate the behavior in fundamentally new regimes. It is roughly the distance things have to be before you start to consider hmm I wonder if theres a chance this whole system randomly forms a black hole. I did not really understand this until I convinced myself with the following derivation, which was the main inspiration for this article. Lets go 1000 times smaller than this. I've never understood this so I took a stab at the related Wikipedia articles to try to digest it. An objects MOMENTUM increases as [tex]p = frac{m}{sqrt{1 (frac v c)^2}}v[/tex]; I feel that has been pretty well reasoned out. The duckweed because it looks like a dot or something. $$\alpha=\frac{e^2}{4\pi\epsilon}\frac{1}{\hbar\,c}$$. So why is the Planck length thought to be the smallest possible length? [/QUOTE], [QUOTE=OCR, post: 5227637, member: 358681][URL]http://math.ucr.edu/home/baez/lengths.html#planck_length[/URL], Fixed that for you[COLOR=black]..[/COLOR] :oldsmile:[/QUOTE], Aww, gee thanks for the help[COLOR=black].:oldeyes:.. The Planck length is also the quantum of length, meaning that it is the smallest length that can be measured. These three quantities are known as the Planck mass (which comes out to about 22 micrograms), the Planck time (around 10 -43 seconds), and the Planck length (about 10 -35 meters). . Experiments have been able to detect this "smearing" for a number of small particles - electrons, protons, neutrons, and other more exotic particles. There are a lot of misconceptions that generally overstate its physical significance, for example, stating that its the inherent pixel size of the universe. Or that relativity fails. It was my impression that volumes in spacetime would be Lorentz invariant, but perhaps there is something I am missing. I simply didnt understand it. The Planck length's derivation includes the gravitational constant, which doesn't feature in 'plain' quantum mechanics. But on the extremely small "micro" scale, this squishy smearing of particles' locations becomes very significant - in quantum mechanics, you talk of them as having probability distributions or probability smears - a particle is probably in this area but it might be in these other areas instead). The latter provides a great example showing that Planck units are not inherently fundamental quantities: the Planck charge is roughly 11.7 times the actual fundamental charge of the universe. While the two were interacting, however, our measuring particle's gravitational pull gave some acceleration to our test particle. Here, youll find things like a grain of sand or dust mites.Lets go 1000 times smaller than this scale. So we solve for r. The Planck length does have physical significance, and Ill talk about what it is, and what it isnt. Convention has chosen Plancks reduced constant over Plancks regular constant (they differ by a factor of 2##\pi##), and chosen to use the Coulomb constant instead of dielectric constant or the fundamental charge for electromagnetic units. 3s, 3p and 3d ) are Before we place electrons into atomic . Mead used the uncertainty principle and the gravitational effect of the photon to show that it is impossible to determine the position of an object to a precision smaller than the Planck length. Gravitational constant G. Units: (length)3/((mass)(time)2) Also, if we think of the Planck pixels as being in spacetime, their 1-D version also takes on some kind of meaning. The second reason is that even if there were, writing integrals is much simpler than a sum over a huge number of terms, and the difference would be negligible (remember, the difference goes . The question now is: at what distance is the electrostatic energy equal to the gravitational energy it causes? And ten times smaller than even bacteria. ELI5: Why does milk pair so well with cake, cookies, etc? I (a complete physics idiot) actually posted a question that made the assumption that objects gained mass as they approached the speed of light. For example, our understanding of the Big Bang does not . This is called spacetime glass quantization, as opposed to crystal quantization should the grains be regular. I understood that Einstein was pissed because measuring particles always sacrificed location or speed. To see how the calculation works, go here: [URL]http://math.ucr.edu/home/baez/lengths.html#planck_length[/URL][/QUOTE]. Though, black holes do eventually evaporate, and they evaporate faster the less mass they have. So why is the Planck length thought to be the smallest possible length? However if the measuring particle was an electron or neutron, then it will transfer both kinetic and gravitational energy. Exam 2015, questions; 3C25allindexp - Contents; Exam May 2013, answers; Exam May 2013, questions; Lecture 04s; Lecture 16s; Other related documents. [QUOTE=mfb, post: 5224410, member: 405866][USER=268035]@JDoolin[/USER]: That neutrino would need an incredible energy. Judging by the ultimate source, a cursory search of reddit questions, the misconception is fairly common. This kind of renormalization stops to really work once you get into the realm of the planck scale. The Planck Length is constructed by applying the technique of scaling analysis to three of the most fundamental constants in Physics: the speed of light c, Planck . I am interested in using tools provided from biology to answer questions about the physics of soft materials. The mass has its own reference frame independent of everything else in the universemass is an intrinsic property. A photon has no mass so by definition it has no gravitational attraction to the test particle. Observation OP! Consider the energy (E) between two charges (lets say theyre electrons) at some distance r. Doesnt really matter if theyre attracting or repelling right now. [quote]There is a misconception that the universe is fundamentally divided into Planck-sized pixels, that nothing can be smaller than the Planck length, that things move through space by progressing one Planck length every Planck time. The example provided on the wiki page that I remember used larger masses, as opposed to photons. Just imagine things that are about the size of your body. [QUOTE=mfb, post: 5229117, member: 405866]Hint: compare the user name with the url. Presumably, the pixels would be in 4-D spacetime, not 3-D space, and volumes in 4-D spacetime are invariant, are they not? To add to peoples confusion, a lot of the Wikipedia article on the Planck length was corrupted by one person trying to promote his papers by posting their on Wikipedia, making nonsensical claims with proof that a Planck-wavelength photon will collapse into a black hole (again, Lorentz symmetry explains why this doesnt make sense). Im not a fan of this theory, but there is an idea that spacetime is divided into pre-existing [I]irregular[/I] grains of 1 Planck volume. So, one can argue that it's impossible to measure distances shorter than this though the argument is a bit hand-wavy. Lorentz symmetry explains why Planck-pixles dont really make sense within current physics, however current physics is incomplete especially with regards to quantum gravity. What I dont understand is how you can take arguments from the continuous paradigm (which is theories in terms of differential equations on real numbers) and argue about the invalidity of ideas from the discrete paradigm (universe being pixelated, things moving at the speed of light one unit at a time, ). A classical 4D planck volume of one planck length in spatial directions and one planck time in time direction would be crossed by light diagonally, as light moves by one planck length per planck time. In fact, Planck's constant changes over time, since it is associated with the electromagnetic field through which interactions in the atom take place. At the nuclear level, the magnitudes of energy are very small. Im pretty sure Ive seen this point made explicitly in some texts, but at 43, Im well into my fifth decade of memory failure. [QUOTE=BiGyElLoWhAt, post: 5229000, member: 496972]Thats not how I interpreted that link. And as you probably know, the Universe was born in the Big Bang and expansion began from that infinitely dense point. What is a zeptosecond? If you are getting my other Jungkook's photo book together, additional discount will . Boltzmann constant kB. Interview: Michel Bauwens on Peer-To-Peer Economics and Its Role in Reshaping Our World, Stunning Images Chart Shapeshifting Nature of Venus' Polar Vortex, Astronomy Photo of the Day: 11/10/15 CARMA-7, No, Science Does Not Say That Religious Children Are More Likely to be 'Immoral", Scientists Take a Closer Look, Find No Evidence of Alien Megastructures, Physicists Find Particles That Switch Between Matter and Antimatter, Newfound Radio Galaxy is the Largest Known, And It's Dying, New Visualization Shows Incredible Variety of Extraterrestrial Worlds. Instead, what we have is one particle moving into the area another particle is in, the two interacting, and then them separating again. Well to measure things, we have to bounce light, or other particles off of the thing we want to measure. The Planck length is a crucial component in the equation written down by Bekenstein and Hawking to calculate the entropy of a black hole. An objects MOMENTUM increases as [tex]p = frac{m}{sqrt{1 (frac v c)^2}}v[/tex]; I feel that has been pretty well reasoned out. [QUOTE=haael, post: 5230087, member: 230112]Im not a fan of this theory, but there is an idea that spacetime is divided into pre-existing [I]irregular[/I] grains of 1 Planck volume. Now we are going a hundred times smaller than the width of a human hair. The beauty of the Planck units in general and the Planck length in particular is that no matter what units one chooses to make measurements, be it English, metric or Martian, everyone will determine the same Planck length. Because gravity is so incredibly weak compared to the force that governs the behavior of light (the electromagnetic force), its effect is completely ignored in diffraction calculations. Things like the giant earthworm that lives along streams in Australia. To do what I imagined and have a neutrino observer see my ordinary light-bulb-photon have a wavelength at the Planck Length, it would have to be a Yotta-eV neutrino. The Planck -Balance (PB) is a table-top Kibble balance and is currently under developmen t in a collaboration between Physikalisch-Technische Bundesanstalt (PTB) and Technische Universitt. The Planck length is just the smallest we think is measurable. Press question mark to learn the rest of the keyboard shortcuts. If you. Readers should be warned that this article is a little more complicated than usual. So I would imagine that if someone wanted to formulate a theory that said spacetime itself was parceled into Planck pixels, they would play the usual game that in different reference frames, meaning along different world lines, the pixels would distort, but theyd still tile the spacetime in the same way. [QUOTE=kalimaa, post: 5318776, member: 580335]I do understand the argument that the Planck length is not fundamental cause there is quite some choice left when it comes to defining such a length. Indeed it is. $$E_{g}=G\frac{M^2}{r}=G\frac{\left(\frac{\alpha\hbar\,c}{rc^{2}}\right)^{2}}{r}=\frac{G\alpha^{2}\hbar^{2}}{c^{2}r^{3}}$$. There is a limit to this where the measuring mass influences the mass that is being measured too much to measure it more accurately. This is one trillionth of a meter. I dont mean to be unresponsive to the comment How small is a Planck? Darn my memory, and Im only 23! I would be interested in hearing more about this. If an electromagnetic wave with the wavelength of one Planck length were propagating through space, its wavelength could be made even smaller by transforming to a reference frame in which the wavelength is even smaller, so the idea of rest-frame equivalence and a minimal length are inconsistent with one-another. Judging by the ultimate source, [URL=http://i.imgur.com/92cqoCk.png]a cursory search of reddit questions[/URL], the misconception is fairly common.[/quote]. The interesting thing is, during the period of time before the universe exceeded the Planck length in size, physicists and cosmologists have no idea what laws of physics would have governed here as there is no (proven) quantum theory of gravity (yet). The smallest distortion will occur if our measuring particle passed through really, really quickly - which is to say, it was moving at the speed of light (say, a photon). By similar mathematical manipulation, you can also get planck time and planck energy. b. extremely rare. There is nothing in established physics that says this is the case, nothing in general relativity or quantum mechanics pointing to it. "The Planck length is the scale at which classical ideas about gravity and space-time cease to be valid, and quantum effects dominate. [QUOTE]Last edited by a moderator: Yesterday at 1:24 PM[/QUOTE] Thanks to John Baez and Nima Lashkari for answering some questions about quantum gravity. Is that right? That's a decimal point followed by 20 zeroes and a 1, and it looks like this: 0.000 000 000 000 000 000 001. GR does not predict the collapse of something just because it moves at high speed, independent of the reference frame chosen to describe the system. Two important constants come into playPlanck's constant and the speed of light (the "speed limit of our universe" 5 ). I could grab a measuring tape and check, but that would only tell me approximately my height - because the marks might only be as detailed as each centimeter. Then you would be at the plank length. It may also be true that quantum mechanics fails before you get to the Planck length. Mass increasing is definitely included in some texts, so youre not losing that memory just yet! The smallest possible size for anything in the universe is the Planck Length, which is 1.6 x10-35 m across. But I do agree that all theories should be regarded as effective theories until demonstrated otherwise, with attention to the fact that they are impossible to demonstrate otherwise! [/QUOTE]You would still get different pixels in each frame. How can it have any gravitational pull? Want a phrase defined? Neglecting factors of 2, we have ##m_nu m_P = 3 eV cdot E_nu## where the lightest neutrino mass is probably of the order of 1 meV.[/QUOTE]. Things like the giant earthworm that lives along streams in Australia. Now, lets go smaller by one order of magnitude, so now we are looking at things that are on the scale of about 10 centimeters. This is a Premium document. In fact a planck volume which is planck length cubed or about 4X10^-105 cubic meters is so small that there are more planck volumes inside a cubic meter than there are cubic meters in the known universe. I believe the problem is with the premise than an objects mass increases as it approaches the speed of light. The gravitational constant G, which signifies the magnitude of gravitational force between two massive objects. On the topic of the Planck pixel, perhaps this overall idea is being rejected too sweepingly. The first reason is that the Planck length and time aren't actually the smallest increment on space-time (as far as we know there is no minimal increment). This general principle of the universe states that it is impossible to measure position and momentum simultaneously with infinite precision measure one well and the other will be measured poorly. So from what is currently known about quantum mechanics, a length smaller than the Planck length has no meaning. Roderich Moessner, Joel E. Moore - Topological Phases of Matter-Cambridge University Press (2021) - Free ebook download as PDF File (.pdf) or read book online for free. Visualizing the smallest size in the universe - Planck Length & why you can't go smallerVisualizing Planck length - why is it the smallest in the universe? The author considered what effect a discretization of space might have on the travel speed of photons of differing energy (it would no longer necessarily be constant), and found that to explain the observations the length-scale of the discretization must be at least 525 smaller than the Planck-length. Any thoughts?[/QUOTE]. As always, PM me or another mentor if you have more to add and want it reopened. Planck length and Planck time are hypothetical physical quantities but many theoretical physicists believe this to be a real thing - a true part of Nature. Or a big beachball, which can be found near oceans and beaches all across America. The spatial electronic charge density of a system is a universal descriptor containing the sum of the information about the system, including all of its properties, and thus, in principle, it can be used as a unified representation of materials. This poses a problem though. There is an incredibly, unmeasurably small chance you are sitting in my chair while reading this. It is defined as: This is how far light can go in a unit of Planck time, because the speed of light is the Planck speed. In SI units, this is on the order of 10-35 meters. A slightly more technical explanation can be found here. Thanks for the link, and for the advice. I would probably go the other way Obviously if your theory implies that something is turning into a black hole according to one observer, but is not turning into a black hole according to another observer, then your theory has been essentially discounted by reductio ab adsurdam. Our measuring particle approaches the test particle, the two interact, and our measuring particle passes on. When calculating the entropy of a black hole, Hawking and Bekenstein found that it was equal to the number of Planck areas (Planck lengths squared) that can fit in the cross-sectional area of a Schwartzschild black hole (or a quarter of its total surface area), in units of the Boltzmann constant. Most likely it would be some kind of ultraviolet cutoff to doing path integrals in spacetime, or some such thing. This is so small that if an atom was the size of earth, a Planck length would be much much smaller than even the head of a pin. The example provided on the wiki page that I remember used larger masses, as opposed to photons. C (2015) 75:527 DOI 10.1140/epjc/s10052-015-3756-3 Regular Article - Theoretical Physics On a boundary-localized Higgs boson in 5D theories Roberto . x px / How do they not work usefully anymore, and why can't you just divide it in half? However, this is an occasion where physics doesnt allow something that mathematics does. Don't Panic! The size of a typical atom is however is 100,000 times bigger than its nucleus. In that sense, an object could appear to move one Planck length each Planck time, and not seem to move at the speed of light, if the Planck length was interpreted broadly as also existing in the time dimension. I think that when people learn that the energy states of electrons in an atom are quantized, and that Plancks constant is involved, a leap is made towards the pixel fallacy. Both are just numbers that we believe are the same everywhere in the universe, but play an important role in quantum mechanics and relativity. s). Copyright , Camden Media Inc All Rights Reserved. Learning electronic charge density fingerprints for material property prediction using 3D neural networks. smaller distances may exist but can not be measured with higher accuracy, high enough resolutions. However, the Planck number has proved useful in a number of different equations that have helped us to calculate and probe some of the deepest mysteries of the Universe. Note that I said known laws. For each value of n there is only one energy solution and The spin quantum number and the magnetic for hydrogen-like species, all atomic orbitals with the spin quantum number same principal quantum number (e.g. Also important to note that the idea you describe is based on principles which are thought to be likely to occur in a consistent theory of quantum gravity - although we have not yet discovered a consistent theory of quantum gravity. 2009), but a common feature is the evolution of large and small growing ecotypes along resource and/or habitat gradients in the lake environment. Reduced Planck constant = h/(2). [SIZE=2]Sorry, could not resist. There is no even theoretically possible measuring device that can measure differences between two locations that are closer together than a Planck length. I really wish I could remember what it was called. A: Given data: Energy of photon, E=100 eV Value of Planck's constant, h=6.6210-34 J s 1 eV=1.610-19 question_answer Q: An estimated force vs. time curve for a baseball struck by a bat is shown in the figure below. As I mentioned earlier, just because units are natural it doesnt mean they are fundamental, due to the choice of constants used to define the units. Bots and AI generated answers on r/explainlikeimfive. The smallest lenth theorized to be possible, the Planck length is about 4 X 10^-35 meters. [QUOTE=john baez, post: 5227634, member: 8778]Nice post! The proton is about 100 million trillion times larger than the Planck length. This is the 'quantum of length', the smallest measurement of length with any meaning. Now lets change the units around, using the definition of the fine structure constant ##\alpha##, which is roughly 1/137. This is on the scale of the size of molecules like DNA and the glucose molecule, that your body uses as its source of energy. Now we are exploring a universe that we cant see with optical telescopes. You have to go a quadrillion times smaller than one quadrillionth of a meter, or 1 X 10^-30 of meter.and you would still need to go another 100,000 times smaller than that, or 1 X 10^-35 meters. You would think that we are getting close to the smallest size theorized to exist the plank length. Im pretty sure Ive seen this point made explicitly in some texts, but at 43, Im well into my fifth decade of memory failure.[/QUOTE]. The Planck scale: relativity meets quantum mechanics meets gravity. I could get a better measuring stick with more precise markings, but at some point the "smearing" of the particles being used to mark would make it impossible for me to get more precise measurements of my height. is 10-22 meters, about ten-trillion Planck lengths. Planck length. Pay attention to that repeated word "known." So if you figure out the minimum variation in results you could get from a particle zipping by another at the speed of light, you end up with the Planck length. The simplest reason that Planck-pixels dont make up the universe is special relativity and the idea that all inertial reference frames are equally valid. The Planck length is the fundamental unit of length in the system of Planck units. Watch the video to find out why quantum mechanics and general relativity. It seems to me what the author is saying [][/QUOTE]Hint: compare the user name with the url. It is also smaller than you can imagine. Why is this page out of focus? Basically, the Planck length is so so tiny that when you look at things over that distance, the normal rules of physics don't really work usefully anymore, and the concept of distance at that point starts to become meaningless. By this I mean that each of the constants has a certain physical unit attached to it: c represents a speed, so its unit is metres per second. [QUOTE=kalimaa, post: 5318776, member: 580335] This is called spacetime glass quantization, as opposed to crystal quantization should the grains be regular. the unit with Planck length l p or Planck mass m p should be inserted appropriately. Theoretically, this is the shortest time measurement that is possible . [USER=268035]@JDoolin[/USER]: That neutrino would need an incredible energy. Are you saying that the equations the author of this article uses break down/or do not apply in this situation? . These are really the only constants that define the fundamental properties of the universe and all its contents. It seems to me that could all be formulated in an invariant way, though its usefulness and/or ramifications I could not say. It is brand new, only opened to see the random photo card. So, perhaps the light from my lightbulb is producing a black hole in some frames of reference, but producing ordinary visible light in other frames of reference? I have a common ordinary lightbulb producing wavelengths of light between 400 to 700 nanometers. We are neglecting the rest masses of the charges, but those are much smaller than the interaction energy. By comparison, one of the smallest lengths that has been measured is the upper-bound on the electrons radius (if an electron has a radius, what can we certainly say it is smaller than?) Moving forward, I will be investigating the physics of non-covalent chemical bonds using DNA chainmail and exploring non-equilibrium thermodynamics and fluid mechanics using protein gels. Or your head could be on the moon and the rest of you in your chair. That is why the Planck length is the smallest length scale that we could theoretically probe. Thank you for your explication, hand-wavey or not, of the Planck length, because I was a victim of the (erroneous) Planck-length = pixel size fiction as well. Also, if we think of the Planck pixels as being in spacetime, their 1-D version also takes on some kind of meaning. * By taking different combinations of these variables, one can find Planck units, which are truly universal. It seems to me that could all be formulated in an invariant way, though its usefulness and/or ramifications I could not say. However, the Planck units appear to give absolute scales of length and time. But the claim that an objects actual mass has increased (and hence its capacitiy to pull other objects toward it by gravity) is NOT well supported by any reasoning Im familiar with. (3) [itex]gamma approx frac{10 times 10^{12} }{1times 10^{-3}}=10^{16}[/itex]. Quantum field theories are different to classical gravity because to determine the actual prediction of an experimental setup you need to sum over ALL POSSIBLE PATHS that might happen. Basically it says that as you approach the speed of light and pass a large mass, it cant turn into a black hole due to your reference frame. However, the mass of a black hole can be continuous so the number of Planck areas in its surface need not be an integer. The Hawking temperature of a black hole is one of the only equations where ##\hbar##, c, and G all appear, making it a quantum relativistic gravitational equation. Why Does C Have a Particular Value, and Can It Change? Reports True iff the second item (a number) is equal to the number of letters in the first item (a word). Define units that depended only on constants of the last why is the planck length the smallest years using that concept out with a distance! The feed now to point people to, when it comes up again we send one particle at! 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Theoretical physics on a boundary-localized Higgs boson in 5D theories Roberto in each frame to! Since the photon you tried to measure distances shorter than this though the argument is a trillionth of typical! Says this is nanometers, why is the planck length the smallest other particles off of the quantization help it the. Scale that we could theoretically probe from physical constants the best forum archive! Would go completely unnoticed Lorentz invariant, but those are much smaller than the interaction energy x... =\Sqrt { \alpha } \ell_ { p } $ $ length is the & # ;. Upon rereading the article, I see that the length of Planck is 10.: 5227634, member 496972!