Your Daily Equation #15: The Planck Length - Why String Theory is Hard to Test

Episode 15 #YourDailyEquation: The Planck scale is often described as the arena in which both quantum mechanical and gravitational effects come into play. The Planck length is tiny (compared to the sizes of everyday things) and the Planck mass is huge (compared to the mass/energy of elementary particles). In this episode of Your Daily Equation, join Brian Greene to understand where the Planck values come from.

Even if your math is a bit rusty, join Brian Greene for brief and breezy discussions of pivotal equations and exciting stories of nature and numbers that will allow you to see the universe in a new way.

The World Science Festival (WSF) is an innovative multi-media organization that produces original live and digital content straddling the arenas of science, technology, the arts, media, performance and education. With the goal of radically transforming public perceptions of science, WSF creates world-class programming, both live on stage and televised, featuring inspired collaborations, outstanding talent and novel production techniques that bring scientific discovery, insight and perspective to a broad general audience.

[philochristos]

I had heard that the Planck units came from dimensional analysis, but this is the first time I've seen it demonstrated. Thank you.

[TheTwick]

Thanks much, doc. When this world gets “back” to some semblance of order (‘normalcy”), we will all be a little smarter because of you.

[elizabethjohnson]

I appreciate how you leverage digital, social and old time media to put science in the daily dust. Never stop!

[luisfelipe]

thank you so much once againg professor, you are a true inspiration for to dive in the numbers and learn through mathmatics, columbia sure has an excelent teacher.

[onderozenc]

Thank you for this inspiring lecture.
By the same token,
I wonder if we can get a reasonable quantity for Planck temperature corresponding to vacuum decays with the help of the Planck constant, Boltzmann constant and the speed of light ?
I attempted to get
one and I got something at the order of 10^31 Kelvin.

[BitwiseMobile]

I'm getting flashbacks of differential equations! I actually loved that course - many people complained. What killed my career as an astrophysicist was linear algebra :P. What I loved about differential equations was the fact that algebra was all you really needed. I guess you need to know how to evaluate a definite integral, but that's super simple and could be taught to any algebra student - it's just evaluating the equation at the two points and taking the difference really.

[sunshine]

I feel fortunate to be born in this era, when great scientists like Dr. Greene, riding on technology, can teach fundamentals to millions of novices like me.

[jasongibbs]

One of the best explanations of natural units I have ever encountered! I have long struggled intuitively with the concept of natural units, and this video brought it into focus for me. The proverbial light bulb just clicked on; Thank you Dr. Greene!

[johnjobs]

I feel much better now, after my daily mental pushup with Dr Greene.
Best of wishes for you and the family in the coming year from a big fan. 🎆🇨🇦

[kevinblackandwhite]

Seriously Dr. Green, I rarely comment on youtube content but I have to tell you that you are a legend!! The WSF is literally the most interesting academic content on the platform.. delivered with humour and proffesionalism. One couldn't expect any better 'education type' presentations. Untill you start teaching the world, at no charge, the nitty gritty mathematical side of all the concepts already discussed on your panels. Thank you. There is other great content put out by the Royal Institute, the cyber security guys like DefCon and BlackHat, the philosophy lectures by Harvard, Google Talks etc.. But the WSF takes the cake due to the diversity of subject matter actually discussed on the panels, and the quality, in-depth analysis of the subjects. So again, thank you sir! You are a legend!

[gregparrott]

Thanks for describing how Planck length, mass and time were computed and the reason for doing so.

[rayxu]

Hi sir I really appreciate the series so far. I just wonder if deeper into the series we can get slightly more complicated calculations and mathematics. Most videos you can find on youtube are either too general or straight up lectures. Hope to see more from you sir!

[dominiqueschlogl]

Dear Prof. Greene,

great series!
I had expected things going more into that direction when you explain planck length (lp), sorry for the crude notation:

E = hv = hc/£   Photoel. Effect
E = Mc2   GTR
E = pc   GTR
c = £×v

hv = pc   deBroglie
hc/£ = pc
h/p = £
p = h/£
dp = h/d£

dx×dp >= 0.5hbar   Uncertainity principle
dx/d£ >= 0.5/2TT = 1/4TT,
£min for Emax:
£min = 4TTx

rs = 2GM/c2   GTR-Schwarzschild
= 2GMc2/c4   GTR+deBroglie, Emax
= 2Ghc/£/c4 = 2Gh/£/c3   Uncert. Pr.
= 2Gh/4TT/x/c3   rs = x:
x = (Gh/2TT/c3)^0.5 = (Ghbar/c3)^0.5 = lp

Planck length more or less describes that energy with a shorter wavelength -> higher energy -> stronger gravitation ... will ultimatively create a black hole. Beyond its event horizon everything is unknown, until now. So there is a limit.

Would you agree?
Best regards

[mikevaldez]

Fascinating conclusion tying in the difficulties of testing string theory due to the super large quantities that emerge out of the theory which the large hadron collider can not reproduce & therefore can not be

[ozdergekko]

I love to watch the podium discussions of the WSF.
But this is like having a privatissimum with one of the best physicists and best teachers available. Thank you so much!

[SkinnyCow.]

So String Theory could be much like Communism? In "theory" Communism works but in practice it fails. String Theory could be much the same?

[ineskucharz]

No more comments on this wonderful series since 2021? I discovered it about a week ago and am doing my 2 daily equations every morning! as a layperson with very limited notions of maths, I truly enjoy the series. I wonder how many episodes there are? when I watched them all, I´ll start watching them all over again. Thank you so much, Brian Greene, for making us a little smarter!

[Henrikbuitenhuis]

Thanks so much. I Hope you Will do this FOREVER AND EVERY DAY.

[fabiocaetanofigueiredo]

I am taking 101 classes with one of my Physics/Science idols... how cool is that?!? Professor Greene, I consider you and Professor Al-Khalili the absolute champions of transmitting complex scientific concepts with perfect didactics, in a way that any human on the street will understand. Thank you much for your work, Sir!

[ranapratap]

Planck mass, time and length are so small but Planck temperature is so big!