What Planck Length Is and It’s Common Misconceptions
The Planck length is an extremely small distance constructed from physical constants. Many misconceptions overstate its physical significance, claiming it is the inherent “pixel size” of the universe. The Planck length does have physical significance in certain contexts; below I explain what it is and what it is not.
Table of Contents
What is the Planck length?
Planck units are defined from physical constants rather than human-scale phenomena. For example, the second was historically defined relative to the day, while the Planck time is based on the speed of light, Newton’s gravitational constant, and the reduced Planck constant. The reduced Planck constant (ħ) equals h/2π and is the quantum of action used throughout quantum theory.
Planck units provide a common, physically based system of units that would be useful if communicating with an extraterrestrial intelligence: they don’t rely on local artifacts. Modern SI units have also shifted toward physical constants (for example, the meter is defined by the speed of light and, since 2019, the kilogram is defined via the Planck constant). That said, choices still remain when forming “natural” units. Convention picks the reduced Planck constant ħ rather than h, and often uses the Coulomb constant (k) for electromagnetic units rather than the dielectric constant or the fundamental charge.
That last choice shows Planck units are not unique fundamental quantities: the Planck charge is about 11.7 times the elementary charge, so the numerical values depend on definitions and conventions.
So what is the Planck length? It is defined as
$$ell_{p}=sqrt{frac{hbar,G}{c^3}}$$
Physically, the Planck length is the distance light travels in one Planck time. In SI units it is on the order of 10-35 meters. By comparison, one of the smallest lengths probed experimentally is the upper bound on an electron’s radius (if the electron has a radius, experiments show it must be smaller than about 10-22 m), which is roughly 1013 Planck lengths. The Planck length is therefore extremely small. But by itself it is a unit of length — useful for scale but not, by established physics, an absolute limit on smaller distances.
Why the Planck length matters
Derivation: when gravity matches interaction energy
The Planck length is the characteristic length scale where quantum gravity effects become relevant — roughly the scale at which gravitational effects of quantum interaction energies are comparable to the interaction energies themselves. The following hand-wavy derivation is the main motivation for that statement.
Consider the electromagnetic interaction energy between two charges (for example, two electrons) separated by a distance r:
$$E=frac{e^2}{4piepsilon,r}$$
Using the fine-structure constant α (α ≈ 1/137), which satisfies
$$alpha=frac{e^2}{4piepsilon}frac{1}{hbar,c},$$
we can rewrite the Coulomb energy as
$$E=frac{alphahbar,c}{r}.$$
If that interaction energy is localized within the distance r, it contributes an effective mass m = E/c^2. Using Newtonian gravitational self-energy as an order-of-magnitude estimate, the gravitational energy associated with that mass is
$$E_{g}=Gfrac{M^2}{r}=Gfrac{left(frac{alphahbar,c}{rc^{2}}right)^{2}}{r}=frac{Galpha^{2}hbar^{2}}{c^{2}r^{3}}.$$
Setting the electromagnetic interaction energy equal to its own gravitational energy and solving for r gives
$$r=sqrt{frac{alpha,Ghbar}{c^3}}=sqrt{alpha},ell_{p}.$$
Because √α ≈ 1/√137 ≈ 1/11.7, this radius is of order ℓp / 11.7. The takeaway: when interactions are localized at distances comparable to the Planck length, gravitational back-reaction of quantum energies can no longer be neglected — quantum gravity becomes relevant.
Black holes and Planck areas
Black holes are among the physical systems where quantum gravity must be considered. When Bekenstein and Hawking calculated black hole entropy, they found it scales with the horizon area in units of the Planck area (ℓp2). Likewise, the Hawking temperature involves ħ, c, and G together, making it a quantum-relativistic-gravitational relation. That connection between horizon area and Planck-scale units is one reason ℓp appears naturally in quantum-gravitational discussions.
How it is not relevant (common misconceptions)
There is a persistent misconception that space is divided into Planck-sized “pixels” — that nothing can be smaller than a Planck length, or that objects move by hopping one Planck length per Planck time. This idea is not supported by established physics (general relativity or quantum mechanics).
One clear argument against Planck-sized pixels comes from special relativity. If a lattice of Planck-sized cells existed in one inertial frame, length contraction would make those cells anisotropic in other frames: in a boosted frame the spacing could be arbitrarily Lorentz-contracted in one direction, so the notion of a universal minimal length that is the same in all inertial frames conflicts with Lorentz symmetry.
Confusion is amplified by popular accounts and sometimes poorly sourced online claims. For example, some online posts have argued that a photon with Planck-scale wavelength must collapse into a black hole — but such arguments typically ignore Lorentz symmetry or misuse classical intuition beyond its domain. A readable thread of discussion on the Wikipedia Talk page documents attempts to insert nonstandard claims into the Planck length article.
There was also an observational study of gamma-ray burst arrival times that discussed whether a discretized spacetime could induce an energy-dependent photon speed. That work concluded that any putative discretization length must be substantially smaller than the Planck length to be consistent with observations; opinions in the field vary on how seriously to take that specific analysis, but it illustrates that observational constraints can test some exotic proposals.
How it might be relevant beyond current physics
Lorentz symmetry explains why the naive “Planck-pixel” idea doesn’t fit with current physics. But current physics is incomplete when it comes to quantum gravity, so there are speculative frameworks in which Planck-scale phenomena are meaningful.
In loop quantum gravity, area and volume operators have discrete spectra: surfaces and volumes come in quantized units. Those quanta are of order the Planck area/volume, but not simply exact integer multiples of ℓp, and the precise numerical factors depend on choices in the theory (so the fundamental “chunk” is of the Planck order but not exactly ℓp2 or ℓp3 in a naive pixel sense).
String theory also introduces a fundamental length scale associated with string dynamics; to recover gravity, this scale is typically of order the Planck length, but again the theory does not imply a rigid lattice of Planck-sized pixels filling space.
Summary: the Planck length is an important order of magnitude for quantum gravity, but it is not proven or required by established physics to be the universe’s fundamental pixel size.
Thanks to John Baez and Nima Lashkari for answering questions about quantum gravity.
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Ph.D. McGill University, 2015
My research is at the interface of biological physics and soft condensed matter. I am interested in using tools provided from biology to answer questions about the physics of soft materials. In the past I have investigated how DNA partitions itself into small spaces and how knots in DNA molecules move and untie. 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.
Energy and Information as a Foundation in Relation to the Planck Constants
As a new starting point, reality is approached from energy and information as fundamental quantities. What can exist manifests itself through energetic interaction and as informational structure. In this perspective, physical existence is not primarily defined by geometric properties, but by dynamic processes and the relations they establish.
Spatial quantities such as length, distance, and volume are therefore not regarded as fundamental building blocks of reality. Instead, they are understood as derived representations that arise when energetic processes are described within a geometric framework. Space is not taken as a pre-existing container, but as an effective description emerging from underlying energetic and informational structures.
Within this framework, the Planck constants acquire a specific and well-defined role. They represent characteristic scale parameters formed from combinations of fundamental physical constants. These scales do not describe a literal microstructure of reality, nor do they imply the existence of minimal geometric elements. In particular, the Planck length is not interpreted as a physically minimal unit of space, but as a limit of applicability of geometric descriptions in regimes where quantum mechanics and gravitation are simultaneously relevant.
When reality is described primarily in spectral terms, emphasis naturally shifts from length to frequency, energy, and informational content. Energy is directly associated with frequency, while wavelength serves only as a spatial projection of that frequency. From this viewpoint, length is not a fundamental physical quantity, but a secondary construct that gains meaning only within a chosen representational framework.
Accordingly, the significance of the Planck constants is repositioned. They do not mark an ontological boundary of reality itself, but rather indicate a theoretical transition beyond which existing models lose their validity. What is fundamentally constrained is not space as such, but the energetic and informational structures that can physically manifest.
By taking energy and information as foundational, a coherent and conceptually consistent framework emerges in which reality is understood as dynamic and emergent. Space and time appear as effective descriptions, while the Planck constants function as guiding scale parameters rather than as indicators of an absolute, geometrically minimal structure of reality.
Наличие второго паспорта за границей становится всё более популярным среди граждан РФ.
Такой вариант предоставляет широкие горизонты для работы и бизнеса.
Гражданство другой страны помогает беспрепятственно путешествовать и избегать визовых ограничений.
Также подобное решение может укрепить финансовую стабильность.
Гражданство Гренады
Большинство граждан рассматривают ПМЖ как способ расширения возможностей.
Оформляя ВНЖ или второй паспорт, человек расширить свои связи за рубежом.
Многие государства предлагают свои программы получения вида на жительство.
Именно поэтому вопрос оформления становится особенно актуальной для тех, кто планирует развитие.
That’s a fascinating topic! The Planck length is considered the smallest meaningful unit of length in physics — about
1.6
×
10
−
35
1.6×10
−35
meters. It represents the scale at which classical ideas of gravity and space-time break down, and quantum gravitational effects become significant.
A common misconception is that the Planck length is a “smallest possible distance” or that space is made of discrete chunks that size. In reality, it’s more of a theoretical boundary — below it, our current physical laws (like relativity and quantum mechanics) can’t reliably describe what happens. It doesn’t mean space is literally quantized at that length.
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, we appreciate how precision and understanding of scale matter whether you’re measuring subatomic distances or crafting the perfect fit for equine comfort.
So, in short, the Planck length isn’t a physical “brick size” of the universe it’s a limit to what our current theories can explain.
Здесь собрана увлекательная и ценная данные по разным вопросам.
Пользователи могут открыть ответы на популярные темы.
Контент размещаются часто, чтобы вы могли получать актуальную подборку.
Простая навигация сайта облегчает быстро выбрать нужные страницы.
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Таким образом, данный сайт — это интересный помощник актуальной информации для каждого пользователей.
“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. What I don’t 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, …). 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.
As for myself I’m taking serious the idea, that all our established physical theories (including GR and QM) are effective theories in the sense, that they don’t express anything fundamental about the ultimate nature of reality, but instead are approximations to the inner workings of reality in the discrete paradigm. Any thoughts?”
Hi, I am a complete physics idiot, but I read your posting. Are you saying that the equations the author of this article uses break down/or do not apply in this situation? I would be interested in hearing more about this. Thank you.
”
As for myself I’m taking serious the idea, that all our established physical theories (including GR and QM) are effective theories in the sense, that they don’t express anything fundamental about the ultimate nature of reality, but instead are approximations to the inner workings of reality in the discrete paradigm. Any thoughts?”
Could be… There’s no way of disproving the possibility. But absent a candidate theory based on this discrete paradigm, there’s also nothing to discuss under the Physics Forums rules.
This thread is closed. As always, PM me or another mentor if you have more to add and want it reopened.
If there is anything that the history of physics has shown us, it is that we don’t shoot with high percentage when we try to anticipate the behavior in fundamentally new regimes. So I think what we really need are experiments that are capable of looking for evidence of discreteness. Until we have that, any theory will be pretty much guessing, in my opinion. 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!
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. What I don’t 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, …). 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.
As for myself I’m taking serious the idea, that all our established physical theories (including GR and QM) are effective theories in the sense, that they don’t express anything fundamental about the ultimate nature of reality, but instead are approximations to the inner workings of reality in the discrete paradigm. Any thoughts?
“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.
I believe the problem is with the premise than an object’s mass increases as it approaches the speed of light. An object’s MOMENTUM increases as [tex]p = frac{m}{sqrt{1 – (frac v c)^2}}v[/tex]; I feel that has been pretty well reasoned out. But the claim that an object’s actual mass has increased (and hence it’s capacitiy to pull other objects toward it by gravity) is NOT well supported by any reasoning I’m familiar with. I’m pretty sure I’ve seen this point made explicitly in some texts, but at 43, I’m well into my fifth decade of memory failure.”
I (a complete physics idiot) actually posted a question that made the assumption that objects gained mass as they approached the speed of light. I was soon set right. 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.
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. A transformed planck volume with a shorter distance but a longer time loses this property.
“I’m not a fan of this theory, but there is an idea that spacetime is divided into pre-existing irregular grains of 1 Planck volume. This is called spacetime “glass” quantization, as opposed to “crystal” quantization should the grains be regular. The glassy properties of the quantization help it escape the usual problems with Lorentz invariance.”
Thank you for that insight. 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. This is hardly unprecedented– the same thing is done to “coarse grain” phase space for statistical mechanical calculations, since there is no need to use a cubic tiling of “equal lengths” of distance and momentum when deciding how to count states. I don’t mean to be unresponsive to the comment
[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]
I simply didn’t understand it. It was my impression that volumes in spacetime would be Lorentz invariant, but perhaps there is something I am missing.
“On the topic of the “Planck pixel,” perhaps this overall idea is being rejected too sweepingly. Presumably, the “pixels” would be in 4-D spacetime, not 3-D space, and volumes in 4-D spacetime are invariant, are they not? 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 they’d still tile the spacetime in the same way. Yes that means objects don’t “move one Planck length every Planck time”, but that’s obvious– any such object would be perceived as moving at 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.
Also, if we think of the “Planck pixels” as being in spacetime, their 1-D version also takes on some kind of meaning. If we choose c=1, it is often said that all objects seem to “move through” spacetime at a rate of 1 unit of spacetime displacement per unit of coordinate time. 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. It seems to me that could all be formulated in an invariant way, though its usefulness and/or ramifications I could not say. Most likely it would be some kind of “ultraviolet cutoff” to doing path integrals in spacetime, or some such thing.”
I’m not a fan of this theory, but there is an idea that spacetime is divided into pre-existing irregular grains of 1 Planck volume. This is called spacetime “glass” quantization, as opposed to “crystal” quantization should the grains be regular. 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]
[RIGHT]Last edited by a moderator: Yesterday at 1:24 PM[/RIGHT]
”
“[URL]http://math.ucr.edu/home/baez/lengths.html#planck_length[/URL]
Fixed that for you…[COLOR=black]..[/COLOR] :oldsmile:”
Aww, gee… thanks for the help…[COLOR=black].:oldeyes:..[/COLOR]
“Last edited by a moderator: Yesterday at 1:24 PM”
[COLOR=black]”..”…[/COLOR]
“Hint: compare the user name with the url.
[SIZE=2]Sorry, could not resist.[/SIZE]”
Hahahaha! Observation OP!
“That’s not how I interpreted that link. It seems to me what the author is saying […]”Hint: compare the user name with the url.
[size=2]Sorry, could not resist.[/size]
” ..it takes approximately enough energy to create a black hole whose Schwarzschild radius is… the Planck length!… ”
That’s not how I interpreted that link. 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)
“Nice post! 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! So, one can argue that it’s impossible to measure distances shorter than this – though the argument is a bit hand-wavy.
To see how the calculation works, go here:
[URL]http://math.ucr.edu/home/baez/lengths.html#planck_length[/URL]”
Hand-wavy is the name of the game here! Thanks for the link, and for the advice.
“To see how the calculation works, go here:”
[URL]http://math.ucr.edu/home/baez/lengths.html#planck_length[/URL]
Fixed that for you…[COLOR=black]..[/COLOR] :oldsmile:
BTW, I’ve been there many, many times…[COLOR=black]…:oldwink:…[/COLOR]
“Eisberg?”
Indeed it is.
“[USER=268035]@JDoolin[/USER]: That neutrino would need an incredible energy. 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.”
I’m not sure if I’m doing this right, but I just googled “energy of a neutrino collision” and found mention of an apparent 5000-10,000 TeV neutrino.
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. (3) [itex]gamma approx frac{10 times 10^{12} }{1times 10^{-3}}=10^{16}[/itex]
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.
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. So yes, as you say, “an incredible energy”
Eisberg?
I’m not going to argue within the last 30 years. I thinknthe book was ’56 or there abouts. Fundamentals of modern physics, and it was by a german author, I’ll try to dig it up here sometime soon.
“Mass increasing is definitely included in some texts, so you’re not losing that memory just yet! 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.”Try to find any publication of the last 30 years using that concept.
“and volumes in 4-D spacetime are invariant, are they not?”You would still get different pixels in each frame. 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.
On the topic of the “Planck pixel,” perhaps this overall idea is being rejected too sweepingly. Presumably, the “pixels” would be in 4-D spacetime, not 3-D space, and volumes in 4-D spacetime are invariant, are they not? 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 they’d still tile the spacetime in the same way. Yes that means objects don’t “move one Planck length every Planck time”, but that’s obvious– any such object would be perceived as moving at 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.
Also, if we think of the “Planck pixels” as being in spacetime, their 1-D version also takes on some kind of meaning. If we choose c=1, it is often said that all objects seem to “move through” spacetime at a rate of 1 unit of spacetime displacement per unit of coordinate time. 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. It seems to me that could all be formulated in an invariant way, though its usefulness and/or ramifications I could not say. Most likely it would be some kind of “ultraviolet cutoff” to doing path integrals in spacetime, or some such thing.
Mass increasing is definitely included in some texts, so you’re not losing that memory just yet! 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.
The use of relativistic mass is purely historic (and in bad popular science).
General relativity predicts that objects can collapse under certain conditions, usually described as sufficient energy density in their rest-frame. 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.
[USER=268035]@JDoolin[/USER]: That neutrino would need an incredible energy. 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.
“I can’t remember what it’s called, even enough to search it via google, but there is actually a solution to this problem. The example provided on the wiki page that I remember used larger masses, as opposed to photons. 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. I really wish I could remember what it was called.
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 you’re observing. Now, this doesn’t necessarily apply when we’re talking photons. Darn my memory, and I’m only 23! I guess it’s all downhill from here =/”
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.
I believe the problem is with the premise than an object’s mass increases as it approaches the speed of light. An object’s MOMENTUM increases as [tex]p = frac{m}{sqrt{1 – (frac v c)^2}}v[/tex]; I feel that has been pretty well reasoned out. But the claim that an object’s actual mass has increased (and hence it’s capacitiy to pull other objects toward it by gravity) is NOT well supported by any reasoning I’m familiar with. I’m pretty sure I’ve seen this point made explicitly in some texts, but at 43, I’m well into my fifth decade of memory failure.
Have you considered the idea of extremely high blueshift reference frames?
I have a common ordinary lightbulb producing wavelengths of light between 400 to 700 nanometers. However, from the point-of-view of a passing neutrino; with it’s velocity negligibly below the speed of light, that same light bulb could be producing light with wavelengths less than the Planck Length.
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’m highlighting the issue with a rather extreme case–the observer on the neutrino. Some people may argue that neutrino observers are not valid, because they have no ears, no eyes, and no souls, and that their reference frame doesn’t exist. 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. The observer flying toward it would find that the wavelength of the photon was smaller than the Schwarzschild radius of the photon’s energy. But the observer flying away would find that the wavelength of the same photon was larger than the Schwarzschild radius of the photon’s energy.
Well, I guess my point is that radiant energy– E = hf = hc/lambda, is simply not the same as mass energy E=mc^2.
The mass has its own reference frame independent of everything else in the universe–mass is an intrinsic property. Also, being a black hole, or NOT being a black hole is an intrinsic feature of matter. The light only has a reference frame in reference to its source and its observer, and frequency and wavelength of light are extrinsic features–observer 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.
[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. 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]
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]
I’m glad to have a good article now to point people to, when it comes up again. Thanks! :biggrin:
Nice post! 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! So, one can argue that it's impossible to measure distances shorter than this – though the argument is a bit hand-wavy. 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. The example provided on the wiki page that I remember used larger masses, as opposed to photons. 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. I really wish I could remember what it was called. 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 you're observing. Now, this doesn't necessarily apply when we're talking photons. Darn my memory, and I'm only 23! I guess it's all downhill from here =/
Ah, upon rereading the article, I see that you really pretty much hit on my issues in my last post.
Nice work!