The Smallest Length: Why Everything Breaks At The Planck Length
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- เผยแพร่เมื่อ 5 ต.ค. 2024
- Quantum Gravity, Episode 1
Is there a smallest possible length? Is spacetime continuous like a smooth fabric, or is it made up of "atoms"?
The Planck Length is the smallest length at which our current laws of physics still work. How do we know this? Watch the video to find out why quantum mechanics and general relativity predict that any lengths smaller than the Planck Length are hidden behind black holes.
Thanks for watching, and I hope you enjoyed! Please like and subscribe for more videos on amazing ideas in physics.
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Wow. Two of the most complicated concepts in physics, combined, and explained in very real world terms, in under 10 minutes. VERY well done!
Love the explanation, but there’s a slight issue. E=pc only applies to objects with a very low rest mass compared to their momentum, while E=mc^2 only applies to objects with a very low momentum compared to their rest mass. You can’t use both equations in the same derivation, since that implies m
I agree completely (except that it is a slight issue, your point is correct and makes this a meaningless derivation)
Agree
Thanks for this clarification! But did you really kill a narwhal?
Real ones wanna know @@epicepidemic7131
One of th most underrated vid on yt.
Explaining 2 complex concepts in less than 20 min and without jargon or mathematical barriers...
Sometimes internet is worth it after all.
Man this was amazing. I think this guy taught us something that a professor at MIT cannot do in a whole year. Excellent video. Keep it up
I'm convinced this dude is an advanced life form from another planet. I can't even fathom what it would be like to be this smart.
It's gotta be frustrating for sure. I graduated cum laude at age 35 and I can't stand my fellow Americans.
@@adamwalcott_official As a mathematics honours student, I can confirm that Americans are extremely annoying.
I'm sure the presenter is smart, but anyone sufficiently curious could read the books and learn the constants and basic mathematics shown here and figure this equation out for themselves - it's the fact that the Planck length can be defined in such simple mathematics, when described on top of the mountain of work that produced the theories of Quantum mechanics and general relativity, that I am in awe of.
Also, as they point out, it's not that the Planck length "exists", it's that it describes a limit of the theories and models themselves - within certain constraints the theories work, outside of those constraints we just don't know.
It’s not necessarily about being smart, it’s about having a genuine interest in a subject and studying it for years. Anyone can be this smart if they just put the time into it.
@@RestitutorEuropaYou need to talk to more people. Not everyone can be this smart. Intelligence =/= knowledge.
Matt, I don't really comprehend all the math, but how you explain it leaves me speechless.
You have a gift for teaching.
I kinda got it, & I subbed too!
Thank you, wonderful video. If I understand correctly, the Planck Length doesn't say it is the smallest possible space for sure but from this point most of our physics laws, formulas and theory don't work anymore
and at any smaller than that "length" any particle would be reduced to a black hole, which we then would not be able to observe it.
He kind of glossed it over in this video, but you would need the maximum frequency high gamma to see that small, and that would require so much energy that it would -turn itself- into a black hole. So there can be smaller low energy particals under the plank leght, but as mentioned in the video, only a better theory of quantum gravity could let us glimps its secrets. For now. @@LupusUmbra995
I find the wording a bit strange. I don't know if this is considered synonymous but I wouldn't see it as the smallest length. It's the highest accuracy you can achieve when trying to place a particle in an exact position. The energy required to bring the uncertainty any lower will break everything.
Yes, I’d say this is the main message of the story. Thanks!
But I think his “L” refers to the actual size of the object, not its position (x) or accuracy in measuring its position.
There must be an assumption that possibilities for its position x are proportional to its size L, and that one must be smaller than the other, since he subs L for x.
So the concept here is about size (L), not about Heisenberg limits or accuracy of measuring its position (x).
I couldn't follow the math at all, but the explanation of Planck Length being related to the Schwarzchild Radius was very enlightening. We can't see things smaller than that because they would be a singularity. Wild.
ikr Schwarzchild radius explained a lot
He said event horizon.
Nothing about singularity.
Very deliberately.
FINALLY a video that actually explains the planck length properly and concisely
Even more interesting when you include Frank Znidarsic's equation to derive plank's constant
thank you and finally after thousands of videos somebody made a simple straightforward description apply Planck length has the limit.
Glad you liked it!
4:10 it would have been clearer if you used the full relativistic energy formula and explain that the m^2 c^4 part can be ignored since we are looking for the lowest allowed energy.
Also this channel has a lot of potential. Good luck!
Thanks for watching, and for your comment! Indeed that’s where the expression comes from. I hadn’t really considered introducing it that way, I thought it would be easier not to go into it, but the explanation may well have been more complete with that addition.
Thanks for your support, I hope you enjoy my future videos :)
@@shotsinthequark As you wrote down "E = pc" I was thinking " ok,we are only talkiing about massless particles now". Then you wrote down "E = mc^2" and I was thinking "wait, I thought we are only considering massless particles"...
Everything you say is correct, but Planck published his work on the Planck length in 1899. He didn't have Einstein, Heisenberg, quantum theory, black holes or anything you mentioned to do his work.
Planck used only fundamental constants to derive this. Based solely on the units of the constants he had, he was able to derive distance (length). The later work shows why this works out, but it is truly impressive to think of the idea that there must be a smallest length and then derive it out of nothing but known constants.
I see where several commenters wanted to know the value of the Planck length. If I recall correctly, the universal gravitational constant, G = 6.67 E-11 N m^2 kg^-2, Planck's constant, h = 6.626E-34 Js, h-bar = h/(2*pi), the speed of light, c = 3E8 m s^-1. Thus, the Planck length is 1.61E-35 m.
This number is so small, but sooooo small, that it's in the range of the 10e-5 part of the lowest SI prefix of quectounit, which in turn corresponds to anything multiplied by 10e-35.
Really great video, you explained it really easily. I subscribed, keep the good work!
Thanks so much for subscribing! Glad you enjoyed, stay tuned for more!
Very informative! Before this, I didn't know how the Planck Length was derived, so I learned something new!
The thing you forgot to mention is, the Lp only matters, if an object (particle) is considered. For "empty space" this does not apply, at least when if we don't think about vacuum fluctuations at this point.
I never understood this before, but it was explained so clearly that around halfway through the video I was already predicting the end of it.
Thank you!
Glad to hear it!
Holy crumb, I sorta understood that. I'm serious, this gives me a bit of hope to continue to understand. Thank you/
This is a perfect video! Short and sweet, and genuinely enlightening. As soon as you explained the relationship between mass and measurement it clicked. Thank you
Thanks so much! Glad you enjoyed 😁
just waw, I'm no physicist, but I hear of planck length regularely for 20 years now, and it's the first time I see the math behind it. Astonishing.
A real big tahnk you
Thanks for this. I'm not a scientist or mathematician, and I pick up only what I think is the gist of the argument. Nonetheless I very much enjoy listening and learning, and thinking about how some of these ideas come together in the most fascinating ways.
Best and simplest explanation I ever heard. This guy must be the best teacher to have
Had this realization as a 6 yr old kid with my grandpa at a car auction. Was trying to tear paper as small as I could and realized my fingers were to big to keep tearing, but eventually the fabric of reality would have to invert upon itself if I had was able to keep going.
I feel like I owe you tuition. That was a very easy to understand and intuitive way of explaining this concept. This made me look forward to advanced physics classes I will be taking over the next few years. Thank you!
OMG! This video is the BEST explanation I've ever seen on why the Planck length "may" be the smallest meaningful distance in our universe. The math you used wasn't super-difficult to follow. In this one video, in just a few minutes, you not only explained "why" Planck length is the lower limit on size, you also explained why the Uncertainty Principle doesn't allow us to know both the position and momentum of a particle to the same level of precision, and why quantum physics and General Relativity have not yet been unified in a way that can explain both the very smallest and very largest phenomena in the universe. I just had basic physics and chemistry classes in high school in the 1970's, and my own readings of science-related material since then, so I am 100% a layman, yet everything you said made perfect sense and it was easy to follow your logic and make the connections in my mind that you are trying to teach here. Your students are the luckiest on earth to have you as their instructor.
Thank you for your video, I’m no longer insecure over my little planck!
Planck length makes me feel like we're living in a simulation and the Planck length is the resolution of the system it's running on the same way video games have a finite resolution or accuracy in their engine.
Thank you. I didn't understand theoretical molecular physics before, but after this 9 minute video, I'm pretty sure I got it.
In signal processing we talk about the Nyquist rate. This is the minimum rate where we can perfectly reconstruct a band limited signal. I’ve always wondered if this could be applied to spatial sampling and solve Xenos paradox.
Great video. I wish people would not say "physics break down" about this sorta stuff, though. It misled me for a long time in relation to black holes/singularities.
It's not technically wrong. Physics- the science, what we know about how the universe works, yes that "breaks down" in these extreme situations.
But many people think, like I did, that this is saying the universe breaks and stops working and returns a blue screen of death. There's very little reason to believe that's the case. It's more likely that something predictable happens and it's governed by laws of physics, just ones we don't and possibly cant know.
To me, this difference was a rather profound one, and avoiding the language "physics breaks down" or at least explaining your use of the phrase would probably help others like me with this misconception.
This is incredibly dope and do well explained for how complicated the subject could probably be.
Finally somebody not afraid to present the general public with the math to understand higher concepts. Thank you!
I'm glad you ended with acknowledging that we need a unifying theory to know if the Planck length is actually the smallest area OR if it is just our understanding of physics and the math that is breaking down.
Very interesting and explains the Planck length in a way I hadn’t heard before.
Bro did an excellent job. The elegancy can tell he'll be a great physicist.
Fantastic video! Great pace, had to rewind multiple times to fully understand but a lot of information packed into a short video
Best explanation I have EVER heard!!!!! - Please make more videos!
I love discussing Planck's constants! I'm happy to have found your channel.
Thanks for explaining this deliberately in a manner that's easy to process, mate. Cheers...☀
Oh man this channel is gonna be huge someday. You have a gift
This is the first time i have had my questioned answers...which is. "Why could you not have a half planc length?"
Thank You.
So what you are saying is that on a small enough scale, space is actually pixelated, and time -actually ticks...
Michael cera is killin it in physics
Plank length is the smallest theoretical length you could measure, however you can always divide it down to smaller lengths, they just would not be measurable. In short if you tried to "look" at a plank length you form a plank length black hole that would be at the plank temperature for a plank time and then evaporate.
wow those presentation skills are stellar! not a single um or pause. and explained in simple terms. you really know what you’re talking about!
Great video man and well put
Question: if Lp, the Planck length, is the smallest something can be, is it also the smallest difference between two lengths? I.e. I can have two particles be 100 Lp apart, but can I have them 100.1 Lp apart?
no , i dont think so
Never knew that. Appreciate the education on why it is important.
Now this is a video I've needed for a long time
This is an extremely elegant and to the point explanation of Planck length.
Thanks for this explanation. I could understand the big parts. Thank you
Ok just found this video. ... Actually the best explanation I've ever heard for plank scale
That was a really good physical and mathematical derivation of the existance of the Planck length for me whon doesn't have a background in quantum physics.
That was a very concise explanation, thank you; hope your channel grows 😊
Thanks a lot! Glad you enjoyed 🙂
Well explained for such a complex subject, like I understood any of it lol But you almost made me feel like I understood something there, I more or less got an idea of what you were explaining. I would only suggest a slightly higher audio next time, it was ok but somewhat a little bit low, but really, great video. Keep it up !
Thank you! I never understood why you couldn't have a length smaller (or rather, know anything about a length smaller) than the Plank Length. Now I do (as much as I can!)
Wow. Let me be one more person who chimes in here and says how well-explained and clear this was.
Very well-articulated, thank you.
good job young man! and all explained in a short time!
Now I can measure my Paenus, thank you science man
Excellent presentation. Although physics is not my chosen field, I am a scientist, and I've studied physics as a hobby for decades. My observation is that the two areas that will push physics to the next level are: 1. A better theory of quantum gravity that can be verified, and 2. A much deeper understanding of what is actually going on with quantum entanglement. The absurd weakness of gravity, and the apparent violation of special relativity by quantum entanglement, are the biggest clues that something important lies just underneath the space-time-matter-energy canvas that all of modern physics is painted on. But whatever theory is suggested to better explain these two phenomena - it has to be testable - that is, if we really want to get to that next level. In my opinion, it is time for a renaissance in physics where we take a hard look at known problems that are today, for whatever reason, largely ignored by the physics community.
Thank you! Thank you for the math too! I think I understood that if not enough that I could reexplain it yet; at least enough that I understand concepts an limitations.
That was beautifully explained! Natural born teacher.
Very fantastic explanation ! Many Thanks!
Finally, an explanation of the Plank length that I can understand! Well done. Subscribed
I asked ChatGPT what would happen if we squash an object smaller than Plank's Length. It went bananas.
This is such a wonderfully well explained video. I actually had this question for a long time and thank god for the TH-cam algorithm to suggest this video to me because it answers just that. Thank you.
Thankyou gerard way for teaching me quantum physics
Clean explaination. Thanks for this.
This is a great video. It really did clear a lot up for me, turns out I’ve been staring at this length my whole life!
Love the microphone. Thanks for sharing
Fascinating dance around the limits our comprehension. Keep asking questions!
Best explanation even without any fancy visuals. Thank you!
Excellent description! Thank you!
Professor Donald Hoffman, in studying consciousness and what its source is, describes our perceived reality of 3D SpaceTime as a "trivial and shallow data structure" nested within our consciousness. Sub-atomic particles - quarks, bosons, etc aren't "physical" but are irreducible representations of a group of mathematically described symmetries in SpaceTime. He asks, "Why only 10 -33 cm as the limit? What about 10 -33 trillion?" in describing our reality as "shallow".
Perhaps our view of our 3D realities as incomplete as looking at someone's skin and believing that is the entire person, as opposed to an insubstantial sheen hiding what's really going on.
He describes the work of High Energy Theoretic physicists uncovering "Positive Geometries" which are structures outside of 3D TimeSpace. Which raises the question: are the friendly and loving geometric shapes regularly described by people having psychedelic experiences these same Positive Geometries, now perceivable because of the energetic changes in the neurons as a result of ingesting psychedelic compounds?
I postulate that below the Planck Limit the "Quantum realm" is infinite energy/mass that does not become a black hole but obeys more fundamental "laws" of existence we don't understand - gravity, consciousness, love.
I suspect the next couple of decades will see amazing breakthroughs in our understanding of consciousness as a fundamental aspect of existence. Fascinating!
Excellent, simple, thanks!
Nice explanation!
Great story telling, THX
I've seen many explanations of the Planck length, and yours is the 1st I've grokked. Your use of word atom is very appropriate, as in Greek it means indivisible.
But the atom has been divided.
thank you, this has been very nicely explained
I just found your channel. I look forward to what you do in the future as I’ll be back at university in the spring finishing my physics degree. Good luck!
Nice. Simplified and not overly complicated explanation. I'd never really seen the basics of it before. Might even be able to explain the idea when out drinking with friends ;-)Thanks!
Thanks for this.
Here's how to try to picture the size of a Planck Length.
Take a Hydrogen atom (529 × 10^-10 metres!) and magnify it until it is the size of our galaxy (100,000 LY across) then if we zoom right down to our own scale, a Planch length is about the size of a paramecium, and is almost visible!
If that doesn't make your head hurt, then think about this:
We use the speed of light to define time. And we use time to define the speed of light.
Sometimes you don't seem to be as smart as you would like. For me, this video did it. This young man is absolutely beyond my ability to understand all but the basics. I hope he is able to use his gift to its maximum.
you're a natural born teacher🙂very well explained, keep it up
Thanks for great explanation! We need now one about Plank Energy.
Hi!😊
I love physics but I have always been not good at math, but it never stops me to be interested and it's awesome!!❤🧠 Thanx for your video.👍👍👍👍
That was lovely- incredible to see such fundamental equations combined- it all seems so easy when you know
I like this explanation, and I think it should give those of us not fully immersed in modern physics some confidence that the Planck length is a real limitation. Maybe it is just a limiyof our models, but the photoelectric effect seems a solid indication of quantum energy, and quantum mass and quantum length come right from that. This really made it easy to understand the connection.
Shout out to Max Planck who discovered this constant by accident, using a mathematical hack to solve the "ultraviolet catastrophe". He basically said "let's pretend that energy comes in quanta" and suddenly all the problems with our understanding of blackbody radiation disappeared. He expected his Planck value to be precisely zero, and that the problem was measurement, but it wasn't zero, it was very slightly above zero, so what he actually did was to discover quantum mechanics.
The "let's pretend" method of discovery is wonderful. Euler did a similar thing when discovering complex numbers. He basically said "let's pretend there's a solution to the square root of -1, and we'll call that number i" and in doing so, previously unsolvable equations were now solvable.
Thankyou for great explanation, my understanding has moved forward by at least L-squared. When I was young, I heard of Planck Length and I wondered what would happen if you pushed an object of Planck Length... Or tried to 'bend' it. Presumably if you push it, the effect of the push has to move the other end immediately, breaking the light speed rule. Or if you somehow bend it, then it must be made of something smaller. Thus began a very challenging task of trying to understand things beyond my education!
There is an intuitively simpler concept without the delta P and x maths stuff. 1) At very small scales below protons, there is no solid matter..it is all packets of energy 2) As the frequency of a photon (energy packet) rises, so does its energy, but the wavelength gets correspondingly shorter 3) You must reach a point where the high energy - mass equivalence fitted into the small wavelength reaches the Schwarzschild radius….Bingo! Blackhole and the photon drops out of existence. This gives a minimum wave length of Planck size…An over simplification of course and doesn’t account for Quantum effects..or Hawking Radiation…But it provides an imaginable mechanism. This is how I understood and calculated the minimum length back in my college days thirty years ago! I went in to realised crossing the smallest length (Planck) at the highest possible speed … C … provided a minimum length of possible time (10e-43s) or the Planck time interval. I was quite proud of these workings using pretty basic physics formulae since my maths algebra ability is poor and stuff like calculus is beyond me. This means the space around us is seething foam of holes. Like the safety net below a trapeze artist…anything bigger than the holes rolls around through space, but anything smaller pops through the holes and is gone. What happens to that missing energy is unclear…maybe it Hawking radiates immediately out as a new radiation? Or a quantum effect ‘deals’ with it…Beyond my knowledge cache.
Nice drive with the equations. I bet most of the uncertainty of the equations from not knowing how much > means.
The other explanation of this I heard was that to understand what's happening below planck length, we need to probe with a quantum particle whose wavelength is smaller. Such a particle has such high energy that its mass equivalent is so dense it forms a black hole with a event horizon that is slightly bigger than Planck length. If we tune things a bit, the point where event horizon size and wavelength of the quantum particle actually meet is exactly the planck length.
An analogy: If you think about your phone screen, the pixel count - and therefore pixel size - is the maximum screen resolution. Smaller pixels same screen size means higher resolution.
The planck length represents the maximum resolution of our universe.
Question: We can’t observe beyond a black hole’s event horizon because time is no longer present?
@@yon5925 We can't observe beyond an event horizon because the escape velocity exceeds the speed of light. Arguably from an outside observer's view time stops at the event horizon as well - so you're right in stating the effect.
@@anthonylittle2396 Ah I see, thank you
Excellent explanation and presentation. Thank you very much.
@5:21 Skipped a step, but otherwise, this is the best explanation of anything quantum that I've ever seen. Great job!
It was a pretty obvious step though, just plug the value of E into the equation and do algebra. Not really worth the whiteboard space considering he's already running out of it.
I love this stuff. You are doing an excellent job of explaining things, even this armchair mathematician gets something useful from your presentation.
Wow, I would have never suspected there would be black holes involved! Thanks a lot, it is indeed fascinating! 🎉
That determination sounded like an assumption that gravity is a cause for the "vanishing", when we may just be talking about falling down a "drain grate" which has only to due with surface area rather than density
brilliantly explained
Fascinating stuff; thank you!