The Planck scale: Is there a fundamental limit to space and time?
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- čas přidán 29. 12. 2020
- This video explores the fundamental lower limits of space and time by considering what would happen if two electrons are squeezed closer and closer together. After discussing the ratio of electric and gravitational forces, Heisenberg's uncertainty principle is combined with Einstein's theory of special relativity to show that at very small distance scales the strength of gravity becomes comparable to the electrostatic force. It is shown that when the two electrons are squeezed to a distance equal to the Planck length, a black hole form, placing a fundamental lower limit on the distances that can be meaningfully probed. It is shown that the Planck length, mass and time can all be derived using dimensional analysis and by combining the fundamental constants of quantum mechanics, relativity and gravity.
References:
[1] Nima Arkani-Hamed. Space-time is doomed. Messenger lectures, Cornell, 2010. url: www.cornell.edu/video/nima-ar... spacetime-is-doomed.
[2] Arkani-Hamed, “The future of fundamental physics”, Daedalus, Vol. 141, No. 3, Science in the 21st Century (Summer 2012), pp. 53-66 (14 pages)
[3] Hossenfelder, S. Minimal Length Scale Scenarios for Quantum Gravity. Living Rev. Relativ. 16, 2 (2013). doi.org/10.12942/lrr-2013-2
[4] Mead, C.A., “Possible Connection Between Gravitation and Fundamental Length”, Phys. Rev., 135, B849-B862 (1964).
[5] R. J.Adler, “Six easy roads to the Planck scale” Am. J. Phys.78, 925-932 (2010).
doi.org/10.1119/1.3439650
[6] Edward Witten. “Reflections on the Fate of Spacetime”. In: Physics Today 49.4 (1996), pp. 24-30.
[7] David Gross. “Einstein and the Quest for a Unified Theory”. In: Einstein for the 21st Century: His Legacy in Science, Art, and Modern Culture. Ed. by Galison P. L., Holton G., and Schweber S. S. Princeton University Press, 2008, 287-297. V
[8] Frank Wilczek; Scaling Mount Planck I: A View from the Bottom. Physics Today 1 June 2001; 54 (6): 12-13. doi.org/10.1063/1.1387576
[8] L. J. Garay, “Quantum gravity and minimum length,” Int. J. Mod. Phys. A 10 (Mar, 1994) 145-166, arXiv:9403008Wdqqwd.
[9] Salecker, H. and Wigner, E.P., “Quantum limitations of the measurement of space-time distances”, Phys. Rev., 109, 571-577 (1958).
[10] Ng, Y.J. and van Dam, H., “Limitation to quantum measurements of space-time distances”, Ann. N.Y. Acad. Sci., 755, 579-584 (1995). [arXiv:hep-th/9406110].
[11] Low, A.M., “The Chandrasekhar Limit: A simplified approach, Phys. Educ. 58 045008
[12] M Srednicky, Quantum Field Theory, Cambridge University Press, 2007.
[13] Hobson, M., Efstathiou, G., & Lasenby, A. (2006). Frontmatter. In General Relativity: An Introduction for Physicists (pp. I-Vi). Cambridge: Cambridge University Press.
[14] R. J. Adler, M. Bazin, and M. Schiffer, “Introduction to General Relativity,” (McGraw Hill, N. Y. 1965, second edition 1975)
[15] Gorelik, G.E., “Matvei Bronstein and quantum gravity: 70th anniversary of the unsolved problem”, Phys. Usp., 48, 1039-1053 (2005).
[16] Adler, R.J. and Santiago, D.I., “On gravity and the uncertainty principle”, Mod. Phys. Lett. A, 14, 1371 (1999). [DOI], [arXiv:gr-qc/9904026].
[17] Planck,M.,“Ueber irreversible Strahlungsvorgänge”,Ann.Phys.(Berlin),1,69(1900).
[18] Scardigli, F., “Generalised uncertainty principle in quantum gravity from micro-black hole gedanken experiment”, Physics Letters B, Volume 452, Issues 1-2, 1999
[19] Oriti.D, “Approaches to Quantum Gravity”, 2009, Cambridge University Press, ISBN: 978-0-521-86045-1.
A summary article of the video: iopscience.iop.org/article/10...
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There are a lot of other great physics channels out there that go into the larger and theoretical concepts of physics, but few that go into the math in such a clear and digestible way!
Maths.
100% agree
My goodness, I was looking for a word to express the way that I feel about this topic, "Digested", when explained by him.
Well said, the maths and concepts build on each other. To have one without the other limits understanding
@@ravenmad9225 math*
Deriving the Planck length from the fundamental units blew my mind!
There is a shorter method at arriving at the Planck values:
h = M^1 x L^2 X T^-1
or
h^-1 = M^-1 x L^-2 x T^1
this, with
G = M^-1 x L^3 x T^-2
gives L and T in values of h & G
then c = L x T^-1 is used to form L and T in the 3 values c,h,G
and M is formed from either M = h x L^-2 x T or M = L^3 x T^-2 x G^-1
@EastingAndNorthing
RE: "Deriving the Planck length from the fundamental units blew my mind!"
Here are the derivations of all of the Planck units . . .
G = universal gravitational constant = 6.67419E-11 N∙m²/kg² (m³/kg∙s²)
c = speed of light in a vacuum = 299,792,458 m/s
h = Planck constant = 6.62607004E-34 m²∙kg/s
ħ (h bar) = reduced Planck constant = h / 2π = 1.05457E-34 m²∙kg/s
kB = Boltzmann constant = 1.380649E-23 J/K
ke = Coulomb constant = 1/4πε0 = 8.987552E+09 kg∙m³/s⁴∙A²
ε0 [epsilon sub zero] = vacuum permittivity = 8.854188E-12 F/m
lP = rS = Schwarzschild radius = Δx = √(G∙ħ/c³) = 1.61624E-35 m = PLANCK LENGTH
mP = mass required for black hole formation = √(ħ∙c/G) = 2.17645E-08 kg = PLANCK MASS = mass of a flea's egg
tP = Planck time = √(ħ∙G/c⁵) = 5.39120198E-44 s = PLANCK TIME
TP = Planck temperature = √[ħ∙c⁵/G∙(kB)²] = 1.4168E+32 K = PLANCK TEMPERATURE
qP = Planck charge = √[ħ∙c/ke] = 1.87555E-18 C = PLANCK CHARGE
Yes, that was awesome! He was very clear. I've got to re-watch this over and over again to absorb as much as I can.
@@firstnamelastname4792 you could just be throwing random letters and numbers around and I wouldn't know the difference.
@@firstnamelastname4792 I'm so happy people like you exist.
I'm not the smartest person in the world, but I do understand physics at least. This is the first video that described WHY the planck length is the planck length in a meaningful way that I could understand. It also helps me visualize why planck time is the same way.
So plank time is almost like the smallest possible frame rate of our reality?
@@LiberalsReadmyBio From what I got that's essentially it. To get smaller time values you have to stretch energies in the equation to infinite or near infinite values.
@@Aelov See I dont understand all that , I get the basic premise on most physics stuff but when it comes to the breakdown of specifics like gravity's effects and why this must be that, etc etc, or like how time slows down when traveling fast , my brain just doesnt get it
@@LiberalsReadmyBio the simple answer is just that we don't know. sure, SOMETHING might be going on at that scale, but we cannot make theories about it without the ability to observe..which we are far from having
@@Aelov Physics majors have the highest IQ out of any other college major
A year of college physics in just under 30 minutes. Understanding how these constants are related to each other gives me inner peace.
I graduated with a degree in Electrical Engineering in 1982 and had covered this all as part of my undergraduate coursework. However, it was never explained with this particular flow or objective. It's nice to look back at it after 40 years and see a review of all of the math. Very satisfying to know that I can still easily follow along.
Now just borrow 100,000 from the gov't and not pay it back it will be exactly the same. Well this is more informative with no leftist commy brainwashing.
@@nastybastardatlive Not everyone is going to college; NOBODY reads an entire text book in the first day, you are either outright lying or even more out of touch than you come off as; and it's still admirable to be able to break down this subject in a manner effective and informative enough to be digestible to a layman in under 30 minutes, regardless of this info being accessible elsewhere.
Hop off it, you old fart.
@@ranbymonkeys2384 40 years ago universities didn’t cost $25K/semester. You may think college is “leftist brainwashing” but how many high paying jobs only require a HS diploma?
@@twt1524 Why do you people comment without reading. I said that she should be paying her gov't student loans and not investing that money. Here you are saying WHAT??? I know millionaires with just a GED. If I have 1 paycheck in the bank I probably have more money than you do so keep runnin' it.
every time this man says "big G" I'm forced to imagine a giant gangsta G extorting the other letters.
Big G and Little m
@@JoeWyley oh
G
H
The Suge Knight of equations
OMG, not only is your grasp of physics impressive... but your ability to describe it and paint such a rich picture of the universe is incredible.
Thank you!
Drawing out Plancks constants using 2 different routes was great. This lays them down in the minds more firmly.
Glad it was helpful, thanks for the feedback
One of the rare physics channels that gives us the whole mathematical background while most of them are just random spawnage of fancy words that even the owner fails to understand. Even though I almost knew all of this, it was fun seeing it again and having it sistemized. Also, it made me fully understand what's the task of quantum gravity and what kind of challenges are there for the new generations of scientists and engineers. Great work !
Thanks for the feedback, much appreciated
@@frankdimeglio8216 no u
@@RockBrentwood ThankZ a lot, for time spent ex-pose-ing whatever hidden under-lying mis-tinkering taking place here too, AND for time figure-ing-out, HOW TO explain flaws in tinkering like this. ThankZ
@@RockBrentwood Dude, these constants are experimentally measured values. I've personally measured G in my college physics lab. A ten dimensional compact manifold won't make G have any other measured value.
For real though. One of the most interesting facts is that anything smaller than a Planck Length cannot interact with photons, because photons with such small wavelength are massive enough to collapse into a black hole. There appears to be a limit causing the uncertainty principle. Another interesting fact is that we can at least tell by how much position is uncertain when measuring for velocity and vice versa variations of which reveal frequencies and amplitudes of gravitational waves.
Edited to add:
The equations explain these, but we can break them down further I'm sure. I think the lowest goes to thermodynamics where quantum interactions are considered possible microstates and their entropy is considered.
For example a perfect crystalline solid at absolute zero 0K has static entropy, only one state. You can do the same with time.
19:10 blew my mind. I knew theoretically anything could be squeezed down small enough to create a blackhole. But, showing it through calculations what the lower bound of the mass, equavalent to that a flee egg, squeezed down to 10^-35 meters could create it as well. That is just so facinating!
Please make more videos like this! This was awesome!
It is mind blowing but then it's difficult to conceive the size of a plank length. I recently read that if the Earth was scaled down to the plank length, the entire observable universe would be smaller than an atom. 10^-35 is unimaginable small, so yeah, a flea egg would be unimaginably larger than a square plank size, and a black hole would easily be created.I believe the black hole would be so small though that it would instantaneously disisintegrate, if I'm not mistaken.
@@ray_ray_7112 you aren’t mistaken. Except it wouldn’t necessarily “easily” be made into a black hole. At that point exactly it would be made into a black hole. The if you took more mass than Planck’s mass then it would technically be “easily” made into a black hole.
Hands down the clearest, most vivid description of the subject I’ve ever seen. Well done!
Glad it was helpful!
Me to, but then this is the only time So qudos for the subject.
I only managed to skip through 8 minutes though. Sp i'll never know the conclusion.
I've watched MIT professors explain blackholes, etc with less math.
@@PhysicsExplainedVideos
G = universal gravitational constant = 6.67419E-11 N∙m²/kg² (m³/kg∙s²)
c = speed of light in a vacuum = 299,792,458 m/s
h = Planck constant = 6.62607004E-34 m²∙kg/s
ħ (h bar) = reduced Planck constant = h / 2π = 1.05457E-34 m²∙kg/s
rS = Schwarzschild radius = Δx = √(G∙ħ/c³) = 1.61624E-35 m = PLANCK LENGTH
m = mass required for black hole formation = √(ħ∙c/G) = 2.17645E-08 kg = PLANCK MASS = mass of a flea's egg
Comsider the fundamental Planck units:
Planck length = 1.616255(18)×10^−35 m
Planck mass = 2.176434(24)×10^−8 kg
Planck time = 5.391247(60)×10^−44 s
Planck temperature = 1.416784(16)×10^32 K
Planck charge = 1.875545956(41)×10^−18 C
All of them, except one, are far beyond what humans can experience directly. That exception is the Planck mass, 2.176E-08 kg. This is comparable to things we can experience, such as the mass of a flea's egg, which is 0.0342 mg = 0.0000342 g = 3.42E-08 kg
. That order of magnitude is also comparable to the mass of one eyelash hair (7.00E-08 kg). My point is that it is odd that the Planck mass alone is within human experience. I wonder why that's true?
Actually, however, the short answer is no. There is no concept of spatial distance or temporal distance in Minkowski geometry or curved Lorentzian space-time geometries - not in the usual sense. For instance, though the distance between you and I *at the same time* (in the Earth's center of mass frame) may be thousands of miles, but the distance at a relative time displacement (around 50-10 milliseconds away from each other) is *zero* ! Not figuratively 0, literally 0! Likewise, the time interval for that separation is 0.
Likewise, that "0" is the distance and time interval between here & now versus Andromeda & 2 million some-odd years before now (and also between here & now versus Andromeda & w million some-odd years after now). It's 0 for things even on the other side of the Universe - at appropriate time displacements.
Thus, there is no concept of spatial or temporal smallness in space-time! Not at all. Even the slightest impulse to visualize it that way is totally wrong out of the starting gate and dead on arrival.
Distances and time intervals in Minkowski and Lorentzian geometries do not measure smallness of space or time intervals. They measure *proximity to the light cone* ... how close your separation is to being a *null interval* (i.e. an interval in space-time at 2 point-instants at a sufficient distance and time apart from one another that to span between the two point-instants would be to go at light speed). The so-called "Planck scale" is an increment of the "next speed over" from light speed, not an increment of space or time atoms.
@@timboatfield
RE: "I've watched MIT professors explain blackholes, etc with less math."
The narrator only used a MINIMUM amount of math. Besides, math IS the language of physics.
It's refreshing to learn something that's not political religious or about entertainment this is one channel I would like to support.
This video gave me the chills because it was well put together. Just like when you hear a good song. Math is beautiful.
Glad you enjoyed it!
I stopped the video at 23:45 and solved the same problem that Planck must have solved. And it was surprisingly easy. I feel some affinity with Planck now. It was simple arithmetic. We hold these guys as geniuses and all they did was solve a simple math problem that anyone in grade school should be able to solve. I guess what makes Planck a genius is that he found a question worth asking.
It pays to be first. Most of the Beatles songs are super simple in terms of notes/chords but the genius is in being first to put these things together for the first time. One day someone will have the thought of what happens inside a black hole. The universe ultimately conspires to understand itself.
It seems that emulating something already knowing which steps to follow is easier than make your way through the unknown. Surely, if you stop in front of the equation instead of doing all the previous analysis by yourself then solving it will feel obvious and easy.
@@franciscomunozarias2983 Sure, I agree. But I had no idea that the mechanics of the actual math was so easy.
ah you must be a mathematician, if you understand it, its trivial! If you don't, it's complicated.
@@juannicolaspardomartin8332 Fair argument, in a way. Do you always feel the need to insult people who say that a video successfully educated them?
Find it amazing that, despite super computers, science hasn't advanced a theory beyond general relativity and quantum mechanics, which shows how smart those pioneers were back then
Because quantum mechanics smacked science with the baseball bat of reality....which is that time is non-linear.
This is something they did not predict and cannot comprehend. To progress honestly in this direction means the end of materialism....and science per-se. And of course there are far too many super-rich people invested in materialism....they don't want the party to end see?
@@surfinmuso37 No I don't, how does quantum mechanics imply that time is non linear?
@@Invictus_Mithra At the quantum level, time as we know it doesn't apply. Time is a human made concept-we then applied it to reality. The nature of Quantum mechanics is kind of instantly omni-directional. That is why many laws of physics don't apply at the quantum level, and how a super computer would be able to solve multiple problems all at once. arxiv.org/abs/quant-ph/9801041
@@surfinmuso37 how could a quantum computer do that? Is there a limit to how many at once?
@@surfinmuso37 The paper you linked states:
It has been suggested [8][9][10][11] [12] that under some circumstances the
superposition principle of quantum mechanics might be violated - that is, that
the time evolution of quantum systems might be (slightly) nonlinear. Such non-
linearity is purely hypothetical: all known experiments confirm the linearity of
quantum mechanics to a high degree of accuracy.
So not only has the non-linearity of time at the quantum level not been proven but it also appears to be slight and under specialized circumstances. That sounds very far off from the certainty that you stated things
Always assumed that the Planck constant was experimental, amazed to see it was this elegant and simple. Mad respects for Dr. Planck who I have learned died and was laid to rest a couple dozen kilometres away from where I live which is random but felt weirdly profound.
Oh, jemand aus Göttingen.
It probably surprises you that Planck's constant has irrational units in it:?(
A lot of other physics channels, programs, and documentaries always show how beautiful and connect our world is, but without really explaining how we came to those conclusions, or even proving it, in a more formal manner. However, this video actually shows, very precisely how ACTUALLY all those variables are tied together to their most fundamental level.
Although I only managed to grasp the math on a more surface level, it really inspired me to learn more about math, and maybe understand this at its fullest!
Thanks!
Looking at the comments here, I think something should have to be made clearer in the beggining of the video: This is not a rigorous mathematical explanation nor a modern physics approach to the topic. This is a bridge between pop-science explanations (which are completely wrong but use usefull metaphores) and physics textbook explanations (which are very good but usually lack the pedagogiacl ability to make concepts conect to each other). The education approach of this video is awesome, but yeah, there are many things that are not entirely true. This is what physicists call a "back-of-the-envelope calculation". There is some true in it, but certainly the true explanation is way deeper, and accounts for many many reasonable questions you might have guys. Don't expect a youtube video to adress it all while simultaneusly been a clear and concise revelation. This is a good introduction to the topic, if you have more questions, the simple mix of Newtonian mechanics, Relativity and Quantum Mechanics is not of enought coherence for you, and you should jump to a physics textbook.
You are right, this video presents a 'back of the envelope' approach. As you mention, my aim is to bridge the gap between pop science and rigorous textbook explanations. Thanks for the comment
You talk about uncertanties in energy, distance and momentum as actual values for energy, distance and momentum with no bridge as how you made the jump?
Thank you. This can be all-too-easily
confusing for even the initiated.
Like me. Thanks. 👍
A value of this video is that it shows how the combination of asking *one* simple question and following it through with unflagging curiosity, experimental measurements, the most basic theory and the simplest of mathematics can lead to a progressively deeper understanding of how things work. I was fortunate enough to have Feynman as a teacher,. He taught in precisely the way this video was presented.
The path to bridging an understanding of the macro and micro aspects of reality is often twisted and torturous, but this video has cut through the weeds and straightened the path considerably..
Hopefully the beauty of this video will capture some young students’ imaginations to pursue science as his or her passion and profession.
We are dealing with nothing but symbolism, in any case. Space-time is, by definition, LIMITATION. And physics will only take you so far in understanding it, because we are EXPERIENCING limitation. Physics will only take you so far, but METAPHYSICS will take you to the answers, as some of the best physicists have understood (Including Max Planck.) Here is the best way you can envision our perspective as compared to an absolute view: THE UNIVERSE OF OUR CONSCIOUS PERCEPTIONS IS ACTUALLY INFINITE ETERNITY, AS VIEWED AT A LESS-THAN-INFINITE SAMPLING RATE. When your mind returns to the infinite sampling rate from which it fell you will experience absolute Reality, and you will KNOW it in every way. Give me a "click" and read my book if you want to know more...
Honestly the best physics channel out there - I cannot be more grateful that you have returned!
Thanks for the kind words of encouragement, much appreciated!
Currently studying physics at university, your content is crystal clear and amazing
Glad you are enjoying the content
I never thought such concepts could be explained in such an easy to understand way. This video is astonishing.
This channel is pure gold
Cheers!
I love it, listen and pay attention... hoping one day it sticks. Sheesh. I suck.
You mean Au _laughs in chemistry_
na, not enough mass
Super Nova jokes👍🏻
4.55 " as far as we can tell there is no such thing as negative mass" , another mindboggle
This has given me the quantum jitters
Just discovered your channel. The clarity and depth of your videos is absolutely stunning and unique on CZcams. I've decided to watch them all.
What I find fascinating is that Plank's length and mass through manipulating particles involving QM & SR is exactly equal to the result you get from using dimensional analysis and power rules taught in any middle school. The two techniques seem so unrelated.
So THAT'S how escape velocity makes sense! Amount of energy needed to fly away forever is not infinite!
Jeez, I read about stuff like wormholes, but such a simple thing was always something I just shrugged about.
I would have never guessed to find such a beautiful explaination of the schwarzschild radius in a video about plank lenght, you explained better than my university ever could, just giving you a formula and nothing behind it. I really appreciate the effort you put behind this video. Thank you
You're very welcome! Thank you for taking the time to provide some feedback
Totally the most beautiful presentation of the most fundamental concepts in physics Ive seen, brilliant job!
This is the first video I've watched where the math was way over my head, yet I still understood the explanation. How the hell did he do that. Earned my sub.
This type of verbiage actually makes me sleepy and relaxes me. I don't understand it but ..... for some reason relaxes me to the point of falling asleep. Yes I did have a difficult time staying awake and now I will do that. Enjoyed immensely and use this tonight instead of a sleeping pill. By the way isn't it beautiful how mathematics describes reality.
For me watching this is like wandering into a random classroom seeing hieroglyphs and still understanding the lesson
Absolutely brilliant to listen to even if it'd be unlikely I'd ever use the formulas in question
I am glad you got something out of it!
Brilliant video. I enjoyed how you take the viewer through the older ideas (which are always worth interrogating) and ultimately get them to think about newer ideas like quantum gravity, and what that would necessarily entail.
Cheers for the encouraging feedback, much appreciated
I was drvining home to my students ALWAYS FOLLOW THE UNITS... bravo!!!
This is one of best series I've ever encountered that explained physics so clearly and easy to follow, thank you for this fantastic job!
You are one of the few youtubers who actually delve into these things with some degree of mathematical rigour. It is appreciated by many, now, a series like this with say 10 or 20 one hour+ episodes, would be great. Like Leonard Susskind's lecture series', but with pretty graphics.
Thanks for the feedback, I think that is an excellent idea and certainly something I am looking at for the furture
I've watched 3 of your videos nonstop and now I finally understand why gravity increases when you squeeze matter, thus the Schwarzschild radius and the principle of uncertainty creating black holes.
I really love how detail and clear your videos are despite me not having depth mathematical knowledge
What's even better is the lack of pseudo-scientists attacking your videos claiming bs like flat earth, fake gravity and holographic universe since you demonstrate all claimed points.
God this channel is so good.
Wow! The way you presented the math is so incredibly digestible, even a person as lacking in physics knowledge (let alone quantum mechanics) as me could calculate (and understand) the final result! I was honestly really surprised when I saw 10^-35m as that was the same answer I got after my rough calculations.
Wonderfully put together in a concise and clear way. True understanding is not in the numbers but in the relationships with other concepts. This video lays that out beautifully
Brilliant. The best explanation of the Planck length I've seen anywhere.
This completly blew my mind, everything was just amazing, keep up videos like this, greetings!!!
Glad to hear it! Thanks for the feedback, much appreciated :-)
@@PhysicsExplainedVideos
Comsider the fundamental Planck units:
Planck length = 1.616255(18)×10^−35 m
Planck mass = 2.176434(24)×10^−8 kg
Planck time = 5.391247(60)×10^−44 s
Planck temperature = 1.416784(16)×10^32 K
Planck charge = 1.875545956(41)×10^−18 C
All of them, except one, are far beyond what humans can experience directly. That exception is the Planck mass, 2.176E-08 kg. This is comparable to things we can experience, such as the mass of a flea's egg, which is 0.0342 mg = 0.0000342 g = 3.42E-08 kg
. That order of magnitude is also comparable to the mass of one eyelash hair (7.00E-08 kg). My point is that it is odd that the Planck mass alone is within human experience. I wonder why that's true?
@@spaceman081447 Because its only got one factor of c. I mean that's certainly not a "natural" answer in any sense but if you think about it the real question isn't "why is that one close to human scale" so much as "why is human scale close to that one"?
You could just as easily pick out the Planck temperature as being the only one that's "big" and ask why that is. And if you take a different viewpoint and look at it as if you were some of the earliest life on Earth (eg: bacteria) you might ask why both the Planck mass and the Planck temperature are "big" compared to your scale.
Overall, the answer is likely just "'coincidence". Mostly. There will be some lower limits based on how atoms arrange into molecules and the minimal structure that molecules can combine into to form something capable of reproducing (ie: life). Likewise, there is quite likely an upper limit that things we would consider "alive" can take due to macroscopic effects like structural integrity and the square/cube law. But even when we consider that such limits exist, there's no reason to think the "scale of life" couldn't be a half dozen or so orders of magnitude larger or smaller if it had evolved on a different planet with different size, mass, temperatures, element ratios and other such things that affect biology.
And of course the Planck constants aren't the only constants in nature. They're the ones we use to set our measurement scales but there are also dimensionless constants that span a wide range of values. For example the fine-structure constant which is very very close to.. 1/137. That's a pretty understandable value, now isn't it? But that brings up not only the question of why that's such a "normal" number (no huge positive or negative exponents) but also why its so very close, but not exactly, equal to the inverse of an integer. And why 137? Does it being prime have any meaning? I mean probably not since the value isn't exactly 1/137, but maybe? Anyway, there are 26 of these constants that are (apparently) just randomly splattered along the number line as well.
You get all kinds of weird questions when you try to apply anthropomorphic ideals to fundamental physics. Not that those questions aren't always worth asking - they can sometimes lead to a more intuitive interpretation of what all that math means and having a "correct" intuition can help push new answers and new questions. But its also terribly easy to fall into metaphysics (or just straight up nonsensical quackery) when trying to formulate an anthropomorphic ideal around the questions of physics, and the only real way to avoid that is to make sure you have the math to back up your theory. And the math tends to be very hard. Even after having watch the video, just try to go back to 23:14 and then re-derive the Planck units. By the standards of modern physics, simple dimensional analysis like that would be considered absolutely trivial but I probably would still take a reasonable amount of time on it even having seen the answers.
Ideally we would like to get rid of all these constants by constructing a more fundamental theory where our current list of constants just "falls out" when you calculate the theory rather than having to just measure them and plug them in with no mathematical basis beyond "they're necessary to make it work". The absolute best theory would be one with zero fundamental constants and all of the currently-known constants can be derived from pure equations. That would imply a universe that really could be created from nothing rather than having to posit hyperdimensional brane-verses and other such touching-on-metaphysical constructs for our universe to "live" in / be born from. Whether or not such a theory will ever be found (or indeed, whether its even possible - we can't rule out a hyperdimensional brane-verse at this point either!) is certainly up for grabs, but it certainly would make physicists happy if we did find such a thing. At least until they realize that theoretical physics is done and they all have to start working in applied physics.
this is amazing!! I already knew all these concepts. But never got to understand it in numbers, your baby steps approach makes it so easy to follow. I'm having such a great time. This is so great!!!
This video deserves a super like. Thanks for this video. This is called making someone understand from the fundamentals
This was phenomenal. All the equations I've worked with before but you connected the dots for me. This deserves more views! Wonderful job.
Thanks you very much for your kind comment and encouragement, much appreciated
Thank you for this amazing content, I love these types of videos of explaining things with step by step derived equations, it helps form a cohesive view rather than jumping to the end expression and then expecting to gulp down the somewhat overwhelming amount of information at once. Keep up the amazing work, love your video style!
Glad you enjoyed it! Thanks for the feedback, much appreciated
I have learned so much from your videos and it keeps on coming.This is the best physics channel hands down and I admire your depth and breadth in this field and I have to wonder what else you have in there.I expect you are getting noticed by people who can make a difference..You can’t produce videos of this quality very long and not expect to be noticed.I look forward to everything coming up. Cheers
WOW, This is the best explanation of the Planck scale I have ever seen! So clear and concise that can be understood by a layman. Chapeau Bas to the channel creator!
Nice to see u back👍......and thanks for these interesting informations
My pleasure
Another brilliant video, extremely clear and yet completely respectful of the theories involved.
I'm precisely the kind of amateur physicist who is fond of videos like yours !
So thank you again !
PS : I won't be the one understanding what happens before Planck's time... :) All I can do, and will do, is relaying the knowledge we have after this threshold which you presented in this video.
Thanks for the feedback, I am really glad that you enjoyed the video and that you feel like you learnt something
I too, appreciate this video and intend to go over and over it for an even better understanding... thank you for doing it. I believe it is really good.. and see no reason for it to be criticized by anyone.
@Alexandre Ollé
RE: "I won't be the one understanding what happens before Planck's time... :)"
I assume that by "before," you mean "before the Big Bang." Actually, that question is a non-sequitur. Since, at the Big Bang, both space and TIME were started, there was no "before" and there could not be any "before." It's like asking, "How high is up?" or "How does blue taste?"
@@spaceman081447 No, I did not mean before the Big Bang but indeed before Planck's time. I was referring to the DURATION between the beginning of the Big Bang and Planck's time. This duration EXISTS since it is defined after the Big Bang happened and thus after time was created. And because this duration exactly starts at the moment the Big Bang (and thus time itself) started, it would be equivalent to talk about the Planck's duration here, not just Planck's time (which is too close to the notion of instant and not duration I feel).
What happened during this Planck's duration ? That is what the current theories can not answer and where quantum gravity could bring an answer.
If we were to talk about what happened BEFORE the Big Bang, the irony would indeed be, like you pointed out, that everyone would understand what we are referring to while yet making no sense rigorously speaking because time itself would not exist then (ACCORDING to our current understanding of the concept of time, nowhere is it written that this understanding will never change, maybe again with something like quantum gravity).
@@alexandreolle2340
I'm glad that you made that clear. You're right; physicists have no idea of what could have happened during the first Planck time unit. There are now several theoretical contenders or maybe someone will come up with something entirely new in the future. But how will they test their theory's predictions at those levels of space, time and energy? A super-LHC as large as Earth's orbit maybe?
Man I love your videos. You have inspired me to take on the challenge of finding out what happens "below" the Planck "length". So well explained, you make it easy.
Well, that escalated quickly!
Great video to end the year with. Glad that you're back with the amazing videos!
Happy new year!
I think I've rarely seen a youtube video that had such a great value for me and my understanding of physics. Thank you very much!
Glad it helped! Thanks for the kind words
i was blown away when you solved for the schwartzschild radius without the EFE’s
Sir Roger Penrose got a Nobel for proving that black holes follow from general relativity. You derived the existence of black holes from Newtonian physics, so you deserve also a Nobel price. Great video!
Wow! This is got to be the neatest video I have ever seen! This is the first time I truly understood how the set of Planck constant is derived and what it means. The amazing part is that all this was derived using high school algebra (with a bit of calculus)!
Glad you enjoyed it! Thanks for the feedback
This video is amazing! Most physics on youtube barely delve into maths and stay on the conceptual level. I love this!
Glad you liked it!
With your clear and comprehensive explanations even most complicated physics phenomena seems so simple and straightforward that it makes me wonder why it took decades and centuries for mankind to get to know :)
As a layman, that likes to listen to this lectures from the outside, it always brings me back to my teenage years when I read "The incredible shrinking man " by Richard Matheson's, that part when he is getting smaller and then starts seeing fields of galaxies and stars finally stopping at a planet in a matter of minutes, when he is talking with the locals they tell him they have seen him come for centuries, never forgot that. Thank you for this lecture.
This video inspires me to become a teacher in Physics. Very thorough and simple explanation and at the same time getting viewers to think about advanced ideas like Quantum Gravity. Even High school students may be able to understand if explained in such a way and maybe get inspired!
Wow, thanks!
After spending hours on Khan Academy, Leonard Susskind and 3Blue1Brown, this tutorial is the best presentation I've seen explaining the mathematics behind the most prolific constants used in physics in less than 30 min. I love the fact that you used a simple example of two electrons to build the equations up incorporating QM, classical Newtonian and black holes. Would you be able to do some tutorials on the kind of Tensor calculus used in GR. Spacetime matrices , covariant and contravariant vectors are mindboggling. Great work on all your videos none the less!
Extraordinary post. About as clear and relevant as there has been on Physics. Elevates CZcams to a new level of importance. Mega thanks for your effort.
I have never seen fundamental physics limits explained in such a comprehensive way. The explanation of the black hole and the role of c as escape velocity putting a limit on its size is mindblowing.
Glad you are back. I have been following you since the lockdown times. Wonderful work.
When I saw the title of this video, my expectation was a kind of treatise which would explane the limits of our universe on the largest possible scale. But no, in stead of going large we went super-mini-micro. After seeing it through I saw the sense of this. But... now I have a nagging suspicion that the answeres we find at this super-mini-micro level will explain the how and why of the outer limits at the end of the largest possible scale side of this story. Anyhoo, in both cases not there... yet. But who knows? The year is new and we have the fullest confidence...
Its all about the limits of our mind you see? We cannot conceive/imagine infinity...or even things on a truly immense scale. So we follow the other direction-into smaller and smaller matter.
How do they not realize the end result of both approaches is the same?...that there is always a common limit to these approaches-our mind.
@@surfinmuso37 I don’t think it’s that they don’t realize something, more so that we have a thirst to know everything.
@@upsettingrock1 As an apparent intelligent species we should have the common sense and maturity to know that one person..nor one species can never ever know everything.
Not only that..the major problem is what we do with what we discover. Look around at our dying, toxic and polluted world..this is what we do with it.
We need to come to terms with our own nature and act intelligently from that perspective.
Real maturity means one can no longer lie to oneself. Wilful ignorance must end.
Restraint from destructive and polluting actions....for a start.
We actually have the same compulsion with money/greed as we do with information-we mindlessly seek to accumulate as much as possible....mainly for the aim of using and abusing others to accumulate more money/information.....and around and around we go...till there is nothing left and we all lose.
And please don't say "but we might discover a way to stop our greed/destruction!"-these answers have already been with us for hundreds of years, and we keep ignoring them.
@@surfinmuso37 since certainty is unattainable r u suggesting we should not search for certainty? how is that at all helpful?
One of the very best physics presentations I’ve ever seen. Brilliant.
Your expose on dimensional analysis is cunningly beautiful. Whenever I return to one of your videos, I learn something new and gain a deeper understanding of the subject matter. Thank you, please.
As others have commented below, what an incredibly effective concentration of concepts and their mathematical representation in such a brief video. I was especially impressed by the end. Yes, I am inspired. Thank you very much!
My pleasure, thanks for the kind words
Just this morning I woke up thinking, as one does, "Gee, I wonder how the Planck length was determined."
And then, out of nowhere, this video appears in my recommendations.
Spooky!
You are quantum entangled with this content creator
Spooky action at a distance.
I don't comment kn CZcams videos but this truly deserved one. You discussed all approaches to it really well and now I truly as if I understood the subject. Thanks a ton!
It just opened a new sense of perceiving the limit of space-time in my mind. Thanks a lot ... This video was just amazing!!!
That’s it, black holes are just the simulation’s exception handler. I’m convinced.
There was this friend of mine that had an experience like that our freshman year in college. We had been studying Aeronautical Engineering in a little college town just south of Jackson, Ms. After talking to his old friends from highschool, he decided to take a road trip back to his hometown in Memphis after taking a rather large amount of psychedelics. I remember him saying it had started snowing on the drive and he thought he had some how reached hyperspeed in his old beat up car, the blacktop of the highway disappeared from view as the snowflakes hung in defiance against gravity and became streaks of light around him in his cars headlights. Some how he made it to the party that night, but I remember somehow he had said it struck him odd how it had taken exactly double the amount of time it would have normally taken, despite him speeding the entire way on a completely empty highway at almost midnight.
@@jacobpatterson3737 Of course: arriving at the speed of light, the time referential in the friends party was actually going faster than his ! He simply checked the time before and after the trip. All logical.
Press X to respawn.....
Just, thank you for a wonderful topic to get lost in in such uncertain times. Actually quite calming.
You're very welcome!
Great video, very concise! It is amazing how close we are to understanding this fundamental principle.
I am blown away by your ability to explain and teach. I was going to just tune out your maths and equations and calculus but you kept me hooked. Please do more. I know nothing, but I want to know more about how mass can be created. From you.
Every single video of yours is amazing👍👍
"This doesn't shine much light on the matter"....I see what you did there lol
the comment I was looking for
I laughed really hard when he said that. Intentionally or not (I am sure it was) it is a great pun.
Thanks for creating and sharing this. I would love to see a video about Heisenberg's uncertainty principle and perturbation theory, in a way that further explains what this video touches on with regards to increasing mass as the particle distance approaches the plank distance.
Thank you. I have always felt curious about why physics needed a new theory for quantum gravity, but never could grasp what that meant, since I’m not trained in the math. But this explanation I could follow and now I see the Planck-sized black hole at the limit of classical mass-energy-time mathematics, beyond which information disappears. Fascinating. Truly fascinating. Thank you again.
every 2 minutes of this video i had both less confidence of my knowledge of physics yet more interest, hence this is the perfect physics explanation
Subbed. I do not understand quantum physics at all but I stayed to the end because of the clear explanations. Well structured. Great work
Awesome, thank you!
CZcams is an amazing gift of humanity
Mate, your method of description and explanation, tone, inflection and delivery style is second to none. Some of the more frenetic formulae gets a bit lost on undereducated me, but you make it way easier than all others. Bravo, good sir!
Oh, and buy my next album...a geezer would hafta be bloomin' radio to not shell out couple of Ayrtons....
Great content! Thank you for using some math in attacking these concepts. Makes your channel uniquely valuable compared to many others. Your explanation of black holes got me thinking that it would fun to see similar explanation of why the large hadron collider does not pose much risk of obliterating us. You might have seen some funny media reporting around this.
A good description to questions so fundamental that even babies can ask “how small can something be?” explained clearly! Thank you! Even though it’s not as decisive as I wanted it to be, the immersion was great
Glad you enjoyed it!
This feels like walking in after the last class finished but yours hasn't started yet and listening to a physics student and the professor talking about the mathematical summoning circle they just left on the whiteboard.
YES!!!! I’ve been looking for this video for so long. There’s literally nowhere else that I can find on the internet that explains these concepts and connects them to others
I love your videos & I'm shocked that you don't have more views, though that will change I think if you keep up your fantastic work :)
I have a questions that is only marginally related to this video, but it's been burning in my head for a long time now:
I understand that if the escape velocity of an object with mass is greater or equal to the speed of light, it becomes a black hole. And as we all now, this object then is a singularity. Now my question: It seems to me that the fact that a black hole is automatically a singularity is a huuuge coincidence. Could an object with an escape velocity > SoL not just be a heavy object, without automatically becoming a singularity?
I'd really love to hear your (or anyone's) thoughts on this :)
this is a brilliant explanation of a topic i have always found fascinating but have never quite had the mathematical chops to pursue formally. this channel as a whole is fantastic and i do hope you continue making videos!
a couple of questions that occurred to me while watching this one:
- at 10^-34m, the electrostatic and gravitational forces are equivalent. in this case, would we expect two electrons separated by this (tiny) difference to just... hover there? would they remain in some sort of equilibrium?
- also, if the gravitational force grows stronger as the distance decreases, the net repulsive force (i.e. the electrostatic force minus the gravitational force) will grow weaker, correct? if this is the case, would this mean the amount of energy we have to put into pushing the two electrons together would actually decrease as the distance between them gets smaller?
- and finally, on a more speculative note, 10^-34m is obv far beyond our ability to probe. if the two electrons do remain in equilibrium when gravitational attraction and electrostatic repulsion become equal, could this provide a possible explanation as to why hypothetical prions -- i.e. particles that make up the particles of the standard model -- are bound together, without requiring a new force?
i do hope you read this! i'd love to hear your thoughts on the above.
Wow, keep teaching us this way, and we may all provide the answers that so few are currently searching for! Magnificently excellent and can't wait long enough to see your next video!
Thanks for the feedback, much appreciated
@@PhysicsExplainedVideos It's real. I really really meant it. The more you teach us (crayons style for me) the more people will be abled to provide answers. There's that famous quote about giving a man food and teaching him how to catch a fish. In any case, you are awesome and confident in your knowledge to share it. Congratulations on that one fact alone, but I'm surely positive that there are plenty more... 🙂
Dimensional analysis is half the work. Brilliant way of showing that and then some more.
Thanks!
Very well done! Thanks for creating such nice contents. Waiting for more!
More to come!
Very excited that you have posted a new video!
This is currently the best explanation of connection between fundamentals of nature I have ever encountered
WELL DONE ! That's a completely different approach oh physics than in the other channels, that's perfect, it's a real treasure, Thank you ! Thank You !
I've mostly followed physics videos from PBS Spacetime and Fermilab but I really like how you streamline your explanations and keep the math accessible to most people. I look forward to checking out your other work.
I love how you made the math seem so obvious. This video is perfect.
Holy cow. Three minutes in and i realize how having great enthusiasm for a subject does not inherently grant understanding of said subject.
More please!
I'm from the economics field and I like to research the history of economics and one thing I learned is the influence of newtonian mechanics into economics. In order to understand this, I decided to study how physicists work and I've been watching your channel and I'm impressed how didactic it is, even for someone with introductory knowledge in physics like me. Fun fact: Jan Tibergen, one of the greatest economists of the last century, was advised by Paul Ehrenfest and he actually wondered if he should incorporate the nascent quantuum mechanics to economics and his advisor said it wasn't a good idea because quantuum mechanics was at its infancy. Considering how it turned out, I guess there is a reason, heh, but still it's an open thing.
Superb production values and great narration. I got to the level of Trade School Diploma Electronics Maths and if seems that is sufficient to describe phenomena I was always told was way too complex for an undergraduate to understand. Thank you for your rigour and your respect for your audience. Look forward to your next. If I might request PID and Laplace ? But anything you lend your attention to has always been very enjoyable.
I really appreciate the comment, thank you. I am sure that I will get to Laplace at some stage!
Great video, as always! Physics is such an interesting topic and your videos help me love physics even more! Thank you
Glad you like them!
Well done! The pace and math explanation were perfectly timed. Thank you for the digestable lesson.
Glad it was helpful!
Fantastic work. I am subscribed to many physics/science channels and you are now my favorite!
Thanks! Very much appreciated