There is an incredibly, unmeasurably small chance you are sitting in my chair while reading this. I really wish I could remember what it was called. A slightly more technical explanation can be found here. Heisenberg uncertainty principle involves Planck's constant (h) which is so small that the uncertainties in position and momentum of even quiet small (not microscopic) objects are far too small to be experimentally observed. 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. For example, think about moving faster than the speed of light. View solution > Specific heat of hydrogen at constant pressure, C p = 2 9 joule k e l v i n 1 m o l 1 (a) Find dimensions of C p . What is a zeptosecond? Hi, I am a complete physics idiot, but I read your posting. 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. A planck length because it was small. [USER=268035]@JDoolin[/USER]: That neutrino would need an incredible energy. 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 . Lets go 1000 times smaller than this. Thanks to John Baez and Nima Lashkari for answering some questions about quantum gravity. Body length and sexual maturity status were recorded in . Most likely it would be some kind of ultraviolet cutoff to doing path integrals in spacetime, or some such thing. Max Planck Institute for Evolutionary Biology Pln D24302 Germany . Planck length. Since our understanding of subatomic gravity is incomplete, we know that the statement that the Planck length is the smallest possible length is on shaky ground. 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. [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. 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. The Planck time is said to be the smallest time possible and Planck length the smallest length (If I'm not mistaken). ELI5: Why do pidgeons appear to peck the ground even when ELI5: Why is it considered unhealthy if someone is ELI5: if procreating with close relatives causes ELI5: What prevents people in a coma from waking up? Don't Panic! 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. The Planck length is the distance at which quantum fluctuations lead to tiny black holes. 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. 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. String theorists also think that it is the size of the vibrating strings that make up all the elementary particles in the standard model. In some cases, a Planck unit may suggest a limit to a range of a physical quantity where present-day theories of physics apply. The Planck length is just the smallest we think is measurable. The gravitational constant G, which signifies the magnitude of gravitational force between two massive objects. 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 . 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. 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. 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. How do we know this? 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. Why is it significant?It is the smallest length at which gravity would have an effect. But absent a candidate theory based on this discrete paradigm, theres also nothing to discuss under the Physics Forums rules. 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. The proton is about 100 million trillion times larger than the Planck length. * By taking different combinations of these variables, one can find Planck units, which are truly universal. We received an email from Bill G., an inquisitive reader: "It is said that the Planck length is the smallest length possible. Why the Heisenberg uncertainty principle is negligible and not applicable to macroscopic scale? Scientists are big on observability. Planck Length: Smallest Thing in the Universe.This video gets to the Planck at around 4:00, it's a good common language introduction. 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. To put this into perspective, if we scaled the proton up to the size of the observable universe, the Planck length would be a mere trip from Tokyo to Chicago. It is also smaller than you can imagine. [/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. But what does this length mean? 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]. 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? The reason is that to measure a length you must have something with a wave length no larger than the object. Here, youll find things like a grain of sand or dust mites.Lets go 1000 times smaller than this scale. So, one can argue that its impossible to measure distances shorter than this though the argument is a bit hand-wavy. The glassy properties of the quantization help it escape the usual problems with Lorentz invariance. Fundamentals of modern physics, and it was by a german author, Ill try to dig it up here sometime soon. 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. This is 1X 10^-15 or one quadrillionth of a meter. The more accurate you measure something, the more energy/mass you need to counter inaccuracies. So you know about blackholes, right? [QUOTE=john baez, post: 5227634, member: 8778]To see how the calculation works, go here: In this sense we need new physics to go beyond the planck scale. It is really small. It is brand new, only opened to see the random photo card. 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. 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. Two important constants come into playPlanck's constant and the speed of light (the "speed limit of our universe" 5 ). Another potential model of quantum gravity is string theory, based on the dynamics of really small strings. [/QUOTE]You would still get different pixels in each frame. It seems to me that could all be formulated in an invariant way, though its usefulness and/or ramifications I could not say. Examples of such ecotypic specialization include . For example, think about moving faster than the speed of light. 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. To get an idea of why this is important, think about the difficulties associated with expressing lengths in meters versus feet. 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. Still, until a better theory of quantum gravity is devised, the Planck length is the best estimate we have for a minimum length. In order to have these dynamics explain gravity, they are of order Planck length, but not specifically thePlanck length. While the two were interacting, however, our measuring particle's gravitational pull gave some acceleration to our test particle. 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. 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, ). It seems to me what the author is saying is that if you try to measure a black hole of the plank scale within the accuracy of a radius, then there is enough uncertainty in the momentum that there [i]could exist[/i] another black hole due to the corresponding energy uncertainty of the system (differing by a factor of v/2, classically). The measuring thing influences what is being measured more and more, the more detailed the measurement is, and there is a limit to this. So why is the Planck length thought to be the smallest possible length? $$\alpha=\frac{e^2}{4\pi\epsilon}\frac{1}{\hbar\,c}$$. The Planck scale: relativity meets quantum mechanics meets gravity. By similar mathematical manipulation, you can also get planck time and planck energy. 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. Is that right? x px / 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. It would be even worse if we were talking to some Martian scientists and trying to compare our lengths to theirs. Nothing. See our. 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. Well, I guess my point is that radiant energy E = hf = hc/lambda, is simply not the same as mass energy E=mc^2. Now, this doesn't necessarily apply when we're talking photons. . [QUOTE=BiGyElLoWhAt, post: 5224854, member: 496972]Eisberg? Press question mark to learn the rest of the keyboard shortcuts. [QUOTE=john baez, post: 5227634, member: 8778]To see how the calculation works, go here:[/QUOTE], [URL]http://math.ucr.edu/home/baez/lengths.html#planck_length[/URL]. Instead, what we have is one particle moving into the area another particle is in, the two interacting, and then them separating again. In fact, Planck's constant changes over time, since it is associated with the electromagnetic field through which interactions in the atom take place. Using the slide bar on the bottom, zoom in until you find a hydrogen atom. Still, until a better theory of quantum gravity is devised, the Planck length is the best estimate we have for a minimum length. 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). Or a big beachball, which can be found near oceans and beaches all across America. 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. Thanks! . Remember the gravitational force is M1 * M2 * G / r2. The Planck length is also the quantum of length, meaning that it is the smallest length that can be measured. 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. 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. Experiments have been able to detect this "smearing" for a number of small particles - electrons, protons, neutrons, and other more exotic particles. http://math.ucr.edu/home/baez/lengths.html#planck_length. The smallest lenth theorized to be possible, the Planck length is about 4 X 10^-35 meters. 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. I think. 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 . But What exactly is a Planck length and why is it the smallest length? 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. 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]. 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. Students also viewed. You actually aren't sitting in your chair reading this. So, how does a tiny number such as this tie into physics? Lets go 1000 times smaller than this. 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. I guess its all downhill from here =/[/QUOTE]. E-mail today@fnal.gov. 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. This is the 'quantum of length', the smallest measurement of length with any meaning. [QUOTE=kalimaa, post: 5318776, member: 580335] [QUOTE=mfb, post: 5224410, member: 405866][USER=268035]@JDoolin[/USER]: That neutrino would need an incredible energy. The meter is a useful unit for measuring length, but theres nothing inherently special about it. please mark me brain mark list Advertisement Advertisement [QUOTE=mfb, post: 5229117, member: 405866]Hint: compare the user name with the url. 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. 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. I have an idea as to where the misconception might arise, that I cant really back up but I will state anyway. Just to clarify the symbols, e is the fundamental charge, ##\epsilon## is the dielectric constant. I've never understood this so I took a stab at the related Wikipedia articles to try to digest it. A photon has no mass so by definition it has no gravitational attraction to the test particle. 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. Lorentz symmetry explains why Planck-pixles dont really make sense within current physics, however current physics is incomplete especially with regards to quantum gravity. :biggrin: Nice post! [quote=mfb] 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. [QUOTE=Ken G, post: 5224660, member: 116697]On the topic of the Planck pixel, perhaps this overall idea is being rejected too sweepingly. However, this is an occasion where physics doesnt allow something that mathematics does. 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. Also, if we think of the Planck pixels as being in spacetime, their 1-D version also takes on some kind of meaning. I (a complete physics idiot) actually posted a question that made the assumption that objects gained mass as they approached the speed of light. 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. Heads up, this will take a while because it's going to require covering a lot of background concepts. This thread is closed. Theoretically, this is the shortest time measurement that is possible . 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 . The size of a typical atom is however is 100,000 times bigger than its nucleus. Disclaimer: I'm just interested in particle field theories from an amateur point of view. I believe the problem is with the premise than an objects mass increases as it approaches the speed of light. is 10-22 meters, about ten-trillion Planck lengths. 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. So to completely oversimplify things, it's the closest you can get to a particle with a quantum energy of "1" without being sucked into its own little black hole, and becoming indistinguishable from it. We are neglecting the rest masses of the charges, but those are much smaller than the interaction energy. Exam 2015, questions; 3C25allindexp - Contents; Exam May 2013, answers; Exam May 2013, questions; Lecture 04s; Lecture 16s; Other related documents. So why is the Planck length thought to be the smallest possible length? false false Insertion sort: Split the input into item 1 (which might not be the smallest) and all the rest of the list. 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. Note that I said known laws. There are a lot of misconceptions that generally overstate its physical significance, for example, stating that its the inherent pixel size of the universe. /u/atatassault describes this in more detail. However, this is an occasion where physics doesnt allow something that mathematics does. 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. The measuring particle is usually a photon (but not always). 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. [/COLOR] [COLOR=black][/QUOTE]..[/QUOTE][/COLOR]. This is the highest energy electromagnetic radiation, consisting of the most energetic photons. 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. Cards are in perfect condition. Why Does C Have a Particular Value, and Can It Change? However, the mass of a black hole can be continuous so the number of Planck areas in its surface need not be an integer. On paper you could apply a force to a mass and accelerate it up and past the speed of light, but we know that in nature that just is not physically possible because the mass of the object (and thus, the energy needed to speed it up). This is called spacetime glass quantization, as opposed to crystal quantization should the grains be regular. However, the Planck units appear to give absolute scales of length and time. One of the only physical systems where quantum gravity is relevant is the black hole. A chip-scale broadband light source in silicon carbide Optical frequency combs have changed science and technology as we know it. On any computer screen you can't have anything smaller than a pixel, same applies for the universe with 1 Planck length. By taking different mathematical combinations of these constants, and reducing their units, you can get a length. 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. Or that relativity fails. Pay attention to that repeated word "known." "The Planck length is the scale at which classical ideas about gravity and space-time cease to be valid, and quantum effects dominate. Pay attention to that repeated word "known." Planck mass is about the mass of one eyebrow hair (5 answers) Closed 4 years ago. G/c3, one gets a length. Become Premium to read the whole document. It is the scale and size of the strings in string theory. So what we can do on paper, we can't do in reality. 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. Judging by the ultimate source, a cursory search of reddit questions, the misconception is fairly common. Well to measure things, we have to bounce light, or other particles off of the thing we want to measure. 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 does have physical significance, and I'll talk about what it is, and what it isn't. There is a push towards making our human units based on physical constants, like defining the meter in terms of the speed of light, but at this time the kilogram is still the mass of a brick in France. *Speed of light c. Units: (length)/(time) 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. 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. Have you considered the idea of extremely high blueshift reference frames? The glassy properties of the quantization help it escape the usual problems with Lorentz invariance. To see how the calculation works, go here: [URL]http://math.ucr.edu/home/baez/lengths.html#planck_length[/URL][/QUOTE]. 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. It seems to me that could all be formulated in an invariant way, though its usefulness and/or ramifications I could not say. From Newtonian gravity, we can calculate the gravitational energy associated with our charges. Planck units are defined based on physical constants rather than human-scale phenomena. 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. 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]. These are things like the shrew, or a chicken egg.Now lets go a thousand times smaller than the scale of a human being, on the order of 1 millimeter or one thousand of a meter. [/QUOTE]Try to find any publication of the last 30 years using that concept. [QUOTE=BiGyElLoWhAt, post: 5229000, member: 496972]Thats not how I interpreted that link. Im highlighting the issue with a rather extreme casethe observer on the neutrino. The observer flying toward it would find that the wavelength of the photon was smaller than the Schwarzschild radius of the photons energy. The smallest possible size for anything in the universe is the Planck Length, which is 1.6 x10-35 m across. 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. So suppose we send one particle shooting at another particle we want to know the location of. Reports True iff the second item (a number) is equal to the number of letters in the first item (a word). [/QUOTE] [QUOTE]Last edited by a moderator: Yesterday at 1:24 PM[/QUOTE] and we find that the radius at which the gravitation of the interaction energy is as important as the interaction energy itself is roughly the Planck length (divided by the 11.7, the square root of 137, but well hand-wave that away for now). Planck's constant has the dimensions (unit) of. How was Planck time determined? 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. 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. There is an asymmetry between the mass of the electric charges, for example proton and electron, can understood by the asymmetrical Planck Distribution Law. Then you would be at the plank length. 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. [size=2]Sorry, could not resist. 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. The Planck length is always the same regardless of the unit used to measure it, because it is the smallest unit that can be measured using the fundamental units of the universe. (b) Unit of length is changed to 5 0 c m, . Readers should be warned that this article is a little more complicated than usual. [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. 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). New comments cannot be posted and votes cannot be cast. So, at the Planck scale, we can't actually say that anything is there at all to measure? 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). For instance, by taking [SIZE=2]Sorry, could not resist. If two particles were separated by the Planck length, or anything less, then it is impossible to actually tell their positions apart. There is nothing in established physics that says this is the case, nothing in general relativity or quantum mechanics pointing to it. In 1899, German physicist Max Planck proposed a universal set of units for length, time, mass, temperature and other physical qualities. ELI5: Why does milk pair so well with cake, cookies, etc? Want a phrase defined? This black hole will evaporate immediately, belching out the photon you tried to measure it with, but in a random direction. The Planck constant has shifted downward by 15 parts per billion from its earlier value, due to new data collected since 2014. 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). 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. 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. 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. Phys. Subscribe to our daily newsletter to keep in touch with the subjects shaping our future. A zeptosecond is a trillionth of a billionth of a second. The smallest lenth theorized to be possible, the Planck length is about 4 X 10^-35 meters. 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