What Everyone Gets Wrong About E=mc²

[@ScienceAsylum]

Support us on Patreon: www.patreon.com/ScienceAsylum Support us with a KZbin membership: kzbin.info/door/XgNowiGxwwnLeQ7DXTwXPgjoin Support us on Nebula: go.nebula.tv/scienceasylum where you can watch this video ad-free: nebula.tv/videos/scienceasylum-what-everyone-gets-wrong-about-emc

[@PetraKann]

When we set the momentum term to zero for the "rest mass" case we end up taking the square root. ie E^2 = m^2 c^4 E = +/- mc^2 A square root by definition gives us two solutions, a positive and negative solution. Do we ignore the negative solution for the Energy of an object at rest? Or does it have some other physical significance?

[@ScienceAsylum]

@@PetraKann That's true mathematically, but (as you're suggesting) physics must then interpret what those two cases would mean. Sometimes they mean something and we use them. Sometimes they _kinda_ mean something in certain circumstances. Sometimes they don't mean anything at all and we ignore them. The -mc^2 case is ignored because it's not consistent with the equivalent solution Einstein came up with. Also, while some energy is negative, it wouldn't make sense for mc^2 to specifically be negative.

[@PetraKann]

@ScienceAsylum anti matter perhaps?

[@ScienceAsylum]

@@PetraKann A negative mc² would mean a negative mass. For a while, there was some speculation that antimatter had negative mass. But, if memory serves, CERN recently tested this and found the mass of antimatter to be positive.

[@ChristopherCurtis]

Along these lines, I was thinking "what if we set c = π ?" It seems there may be a lot of opportunities for expansion in that scenario. Also interesting would be to set "c = i", in which case E = m·c² → E = m·i² → E = -m.

[@MelancholicBodhisattva]

Realizing that physics is about making models to predict the information we can get from reality, as opposed to physics being reality, has helped me understand these kind of ideas better. Dont mistake the map for the territory, yall!

[@fuseteam]

Yes this, it removes the woowoo too wave function collapse ❎ Wave model + particle model ✅

[@anonymes2884]

@@fuseteam We don't _know_ collapse is "woo" though. Claiming that is just erring in the _other_ direction (the wave function _may_ be real and it _may_ really collapse). The correct approach is just to accept we have a predictive, useful mathematical formalism but don't know (yet, at least) what it _physically_ means. Doesn't mean we shouldn't _try_ to determine what it means physically.

[@Marinealver]

Know that the Universe is under no obligation to match your mathematical models or any other model you may have.

[@fendobis9033]

@@fuseteam This fear of something being "woo woo" is ironically becoming quite irrational in itself. The universe doesn't care about your aesthetic prefernces.

[@sarnxero2628]

@fendobis9033 "The universe doesn't care about your aesthetic" C R I N G E 😬

[@HalKworasmi]

"Mathematicians generalized it to death!" You really think that we stop at death. You, physicists, are adorable 😂. Great video as usual👍

[@ScienceAsylum]

😆

[@mikel4879]

HalK • Fortunately, you do. Your joke is in the same vein with the difference between REALITY and its theoretical modeling. Theoretically, you don't stop at death, but in REALITY you do.

[@SteelBlueVision]

Mortician: Hold my beer...

[@ahgflyguy]

Is there life after death? Of course! Death isn’t the end, just ask a probate attorney.

[@gabrielgauchez9435]

@@SteelBlueVision when we generalize for all x, its for all! dead, alive, both or neither

[@spitsmuis4772]

7:36 "We've defined energy in such a way that it obeys that rule" Exactly.

[@darrennew8211]

Wonderful. And when we find something in which energy isn't conserved, we make up a new "kind" of energy and say "that's where it went!"

[@narfwhals7843]

@@darrennew8211 And then we check more carefully and find its really just all kinetic and potential. And then we do field theory and things get weird...

[@darrennew8211]

@@narfwhals7843 No, that's my point. It's not kinetic and potential. What does "potential energy" mean except "energy we can't measure until it turns into some other energy"? We can *calculate* potential energy, because we know at different heights how much kinetic energy will be produced by the fall. But energy itself is nothing more than a variable that appears in a bunch of equations and doesn't change due to symmetries in physical systems.

[@mikel4879]

darrenn8 • Energy of any kind theorized in mathematical equations represents only an idealized theoretical model of REALITY. The REALITY is never symmetrical in its fundamentals, therefore in REALITY there's no absolute conservation of any kind of aggregate, either being theoretical conventional representations like "matter" or "light", "particle" or "field", etc..

[@edgeeffect]

Thank you SO much for not having mid-roll ads! And thank you to your supporters for enabling you to not have mid-roll ads. It's one of the things that means I get to the end of your videos and stop early in so many other people's. Which means that I now know... it's OK to be a little crazy!

[@endleontiozae7061]

I'm freaking insane and I love every second of the insanity that is physics

[@michaeljames5936]

That's the littlest crazy thing I've ever read.

[@tommyjones1357]

Back to basics! Love these simple scripted videos! Keep it up, my guy!

[@ScienceAsylum]

Yep. I recently mentioned to Patreon patrons and KZbin members that I needed to get back to what I _loved_ about making videos. I lost myself there for a while.

[@2nd_foundation]

​@@ScienceAsyluma masterclass thanks!!!!

[@surendranmk5306]

Only thing I can do is subscribe, which already done years before and add a like to every vedeos. Can you come once daily atleast?

[@ScienceAsylum]

@@surendranmk5306 Once per week would be amazing, uploaded on the same day every week. Unfortunately, I would die of exhaustion and still probably miss most deadlines.

[@surendranmk5306]

@@ScienceAsylum You are so important for us. Words are insufficient to describe it and how we miss you. Try your best and excuse my English!

[@spitsmuis4772]

We need more people being pedantic sometimes

[@AlleyKatt]

Amen!

[@maynardtrendle820]

@@spitsmuis4772 Maybe not...🤔

[@pancake891]

My friends disagree, im pedantic enough

[@Art_official_in_tellin_gists]

hmm... myes... .. shallow AND pedantic lol

[@protocol6]

Useful thing to note about the Lorentz factor, or rather the inverse Lorentz factor (often denoted 𝜶), is that it's just the circle equation. It's common to use 𝛽 in place of v/c but for this let's just use x for that and y for 𝜶 and write it as y=√(1-x²). Square both sides, y²=1-x², and rearrange to x²+y²=1. We're essentially just talking about a unit constraint on rotation. Acceleration is a pure rotation in space-time.

[@ScienceAsylum]

Yep! That's true. It's something I absolutely love about Minkowski's view of relativity.

[@PR-fk5yb]

@@protocol6 I understand that. But I now loses everything I tought I understood in the video in the first place.😛

[@angeldude101]

Rearrange the E² = m²c⁴ + p²c² into (mc)² = (E/c)² - p² and what you get is the invarient quantity on one side, and the variable quantities on the other side, and if you plot all values of E and p, you get a hyperbola. These are all possible spacetime velocities that a particular object can take (in 1+1D)! It also suggests that energy is really a type of momentum, only it's momentum through time rather than space. Combine momentum through time as just another component of momentum and apply the Minkowski metric, and you essentially just get m = |p⃗|, which has the effect of making the classic equation of p⃗ = mv⃗ true even in special relativity! It just requires p⃗ and v⃗ to be 1+3D spacetime vectors instead of 3D space vectors. If you apply this equation for massless particles like light, you get the null-cone of the hyperbolic space, which exactly corresponds to the light cone of a particular point in physics. It _also_ gives a mathematical description of tachyons as objects with imaginary mass, much like how tachyons themselves are also imaginary.

[@ScienceAsylum]

@@angeldude101 That's such an important aspect of quantum field theory that particles obeying E² = m²c⁴ + p²c² have a name: "on shell." All real particles are on-shell, but virtual particles are allowed to be off-shell.

[@AlleyKatt]

I like this video's lesson and how you've expanded upon what you said about E=MC² in the livestreams. I absolutely love how you present it, though, along with all of the grin-inducing creative gimmicks and call-backs. A professional production indeed.

[@ScienceAsylum]

Thanks! Glad you enjoyed it. I'm trying to get back to what I used to _love_ about making videos and I feel great about this one.

[@Lucky10279]

3:58 OK, Nick, you have _officially_ sent me down a rabbit hole, lol. 🤣 Went to page 204, realized I didn't remember the actual definition of 4-momentum, started scrolling up, and next thing I know, I'm on chapter 6 reading about tensor notation. 🤣

[@ScienceAsylum]

😂 You're welcome 😉

[@trevormugalu3797]

Happy new year nick!

[@ScienceAsylum]

Happy new year!

[@DavionStar]

The difference between matter and energy was something I was always wrong about until I discovered your channel, and I learn more about it every video. The whole "electron/positron annihilation turning into photons" was one of those things, so I'm glad you addressed it directly. I'll have to find some money to donate to your patreon since I do have a couple of questions about light I wanted to ask.

[@dennisconley5068]

I'm studying physics at a university, and this is an extremely helpful video on the differences between light and energy, and mass and matter.

[@GhoshDiptangshu]

The misinterpretation of Einstein's equation is a really massive problem in the science community Thanks for making such a wonderful video on this topic

[@JamesSmith-qu4yf]

"massive problem" I see what you did there

[@anonymes2884]

I mean, not so much "in the science community" because even undergrad physics students know this stuff (or should :). But in what you might call the "science fandom" or among the general public, sure. (I still appreciate the joke though :)

[@mcnugget9999]

Love seeing you guys post something. Thanks for the upload pal

[@craigsimpson9561]

Nick: What's the matter? It's simply a matter of moving your perspective. They're all made-up numbers! Me: [ stares at Earth ] Wait! It's all just abstract numbers? Nick: [ floating behind me ] Always has been.

[@henrikleppa7632]

🌎🧑‍🚀🔫🧑‍🚀

[@danilolabbate]

You gotta be kidding, 30+ years knowing what E=mc2 means, just to find out I didn't.

[@catmate8358]

Always a pleasure to watch your videos Nick. Thank you for spreading knowledge and education rather than chasing easy clicks with nonsense. We need more people like you. All the best!

[@mattfanslow]

Your book behaves differently than mine. Yours slows down. Mine speeds up and goes right over my head.

[@muskyoxes]

I got the classic Misner Thorne Wheeler book because it generates its own gravitational field

[@evilotis01]

happy new year, Nick Lucid! you do really wonderful work

[@ScienceAsylum]

Thanks! and happy new year to you too!

[@jcmo5900]

Thank you for your dedication to science above monetization. You're a legend.

[@bytefu]

Clicked the video fast fast and gave it a massive thumbs up. I just noticed that you channel has >7e4 subscribers, glad to see it gaining momentum while not shortening the content.

[@BattleBunny1979]

Welcome back and happy new year Nick!

[@ScienceAsylum]

Happy new year!

[@ianPedlar]

Good old Al' sitting alone for hours on end in his patent office doing, goodness knows what.

[@underthemoon-p7q]

Oh ok. Him being AI is making more sense to me now.

[@CliffSedge-nu5fv]

Probably composed many principles and postulates tossing paper airplanes around the office.

[@MilesMcCusker]

Eternal thanks for what I thought would be a video clarifying what I already knew, but turned out to be a video that I will need to watch multiple times in order to figure out if my framing of that equation has been a little off all these years, or maybe I'm all good, maybe I never framed it with exactly the right language before! Hmmm... So good!

[@HyenaEmpyema]

Me too. As I heard "Light is not energy" I knew I will be watching it again.

[@spencerwenzel7381]

Wonderful explanation. Great to have you back, keep these ones coming 👍

[@EvilSandwich]

That feeling when you realize that e = mc² is just applied version of the Pythagorean theorem. I swear to God all of math and science is just a big drinking game where you have to take a shot every time you run into the Pythagorean theorem again in another application. Actually don't do that. You'll likely end up in the hospital.

[@entropyachieved750]

Love this channel. Thanks

[@ScienceAsylum]

Thanks for watching!

[@darrellseike3185]

Great video. I love the pedantic nature of your videos. Great stuff.

[@xislomega242]

Most concise. brief. and effective explanation of these topics all in one video. Bravo. I will make sure to share this video.

[@physred]

Finally someone being lucid about this.

[@florinadrian5174]

Minkowski was Einstein's teacher of mathematics in Zürich and at the time had a very low opinion of him.

[@CliffSedge-nu5fv]

Albert was too busy drowning in women to study or go to class. Man was a playa.

[@Lucky10279]

1:06 Oh, I was expecting the E² with momentum version, lol. Kinda blows my mind that that equation is equivalent to E=mc²γ though. I knew it already but it still blows my mind.

[@ScienceAsylum]

I do get to that one later in the video, but you can't derive it without treating time as a dimension (so it had to wait for Minkowski).

[@devluz]

This one hit me right into my misconceptions. Well done :D

[@alfadog67]

Nick, thanks for clearing some of this up!! BTW... you nailed Troll Clone!! 0:58

[@artdonovandesign]

Great video, Nick, I going to watch this sbout 10X Great to see you! Best of the New Year to You and Em 😊

[@ScienceAsylum]

Happy new year to you too!

[@GG-dx6cu]

Hi Nick, what have you smoked over Christmas. Language Physics - this was one of the smartest and thought provoking things you have ever published on this channel

[@mahermagdy4604]

This is probably the first asylum video i fully 100% understand. Thank you Nick

[@luudest]

4:26 What is the difference between the energy of a photon and the momentum of a photon?

[@angeldude101]

One is the photon's spacetime momentum projected onto the time axis, and the other of the spacetime momentum projected onto the space hyperplane. Numerically, the magnitude of the photon's momentum through space is equal to the photon's momentum through time, aka energy, at least up to some number of factors of c. If they were different, then the mass would be the square root of the difference of squares, which, if non zero, means it's no longer a photon. (If the momentum exceeds the energy, making the quantity under the square root negative, you might want to double check you measurements since they're currently saying that you have a tachyon on your hands, which probably isn't actually the case.)

[@threeMetreJim]

@@angeldude101 While this is likely true (and I understand too little to know or not), is there any way to describe it in simpler terms or to depict it in some way to enable it to enter the imagination. I suspect Einstein had a way to do this, and that is why he was a genius and how he could come up with thought experiments.

[@angeldude101]

@@threeMetreJim A one-sentence summary? Energy is momentum through time. This is true for both massive objects and massless ones.

[@threeMetreJim]

@@angeldude101 Is this stating that applying or removing energy changes momentum? If so then why is there any need to make it sound more complicated - there must be some reason.

[@timmowarner]

There are so many interesting and mind expanding videos on this channel. But I think this may be the one that EVERYONE should see.

[@gaelonhays1712]

A lot of comments have mentioned going back to basics, and you've said you're going back to what you loved about videos; as a pretty new viewer, I'm glad. All your videos are good, at least that I've seen, but the old ones have something about them that's similar to Jon Collins at Bible Project: they ask questions all of us had, in a way that makes sense relative to the subject matter, and then the professional nerds (as opposed to us amateurs) can give us an actual answer.

[@AirwavesEnglish]

As a high-schooler, I really didn't "get" a lot of our maths concepts and as such, it wasn't really my favourite subject. Fast-forward to about ten years ago and my love and interest for astronomy kind of "forced" me to learn it all over again. Now, as it stands, I'm totally infatuated with maths, algebra, trigonometry, geometry etc.... I have spent countless hours over the years watching YT videos and learning and trying my own examples. Maths is AMAZING *IF* one can get into the groove of it. (I am struggling with derivations and calculus though I am still trying hard. (It's coming VERY slowly)😅 Your videos are always so informative and each time I watch them, I understand a little bit more about the particular subject, and understand *how* it ties into other concepts. Thanks so much! I feel like YT videos can be such a powerful tool if used correctly.

[@dandurkin9735]

Fantastic! Really nice work, Nick. When I was at Johns Hopkins in the late 1980's, Russian physicist Lev Okun gave a colloquium about this very topic - the misunderstanding of E = m c^2, specifically, the "m" part. Best wishes!

[@clavierwintergreen5574]

I've been saying this for so long, even using the electron-positron example on similar lines! People really do confuse mass and matter as if they are one and the same. Ditto with the word "energy", which so many people use as an umbrella term. On a side note - great job at emphasising the concept of mass as ‘resistance to acceleration’. If I'm not mistaken, one of Einstein's questions while approaching this topic was, "Does the inertia of a body depend upon its energy content?"

[@Dippedinsilver1974]

I’m completely useless when it comes to mathematics. I really appreciate how you explain things in a way that even I can grasp.

[@ScienceAsylum]

I always get nervous when I cover math like this, so it's nice to know it gets through to viewers.

[@AQLK87]

Such a clear explanation. Love it (and your channel).

[@phoule76]

"We're going to get a little pedantic today." - Me every morning

[@wesshepard]

Awesome video Nick!

[@ScienceAsylum]

Thanks!

[@catmate8358]

It looks like Minkowski is the real father of general relativity. It's such a shame that he died young or maybe we'd be talking about Minkowski's theory of relativity.

[@ScienceAsylum]

Yeah, Einstein gets all the publicity but so many other people were involved in making relativity what it is today.

[@red6alert6onesmit-iy5jz]

U sound like Einstein was minor add, Nop, He was only one brave enought to to postulate C speed is consntant in all frames, this why he winner of race.

[@juzoli]

@@catmate8358 Grandfather maybe. None of the scientists were working in vacuum, making up things out of nowhere. Every single one of them were building upon the work of other scientists. I could list like 10 names who contributed a LOT to the theory of relativity. But nevertheless, Einstein was the one who put it together.

[@marianoramirezdeleon1034]

Made it through the end of the video and unfortunately I’m not financially able to support the channel, but I wanted to tell you that this channel has helped me understand physics as someone who is not that smart to be a physicist, but enjoy it as a topic/hobby, the ideas of the understanding of our universe and how tiny we really are amaze beyond thoughts. Thanks.

[@oidbio2565]

very cool, I didn’t realize the Lorentz factor was originally apart of the Equation.

[@vog51]

While I don't have money right now to support you, I will always watch every video and give a thumbs up. Great channel!

[@ScienceAsylum]

Thanks for watching!

[@MasterHigure]

"You use relativistic mass. I integrate the 00-component of the stress-energy tensor over a 3-volume with time-like normal vector. We are not the same."

[@ScienceAsylum]

😂

[@grizzlyb9625]

For the longest of time of my life i can never understand how the universe operates exactly as explained with math. Your video help me realize that its a made up concept that help us understand the universe. So we basically make up things as we go until it makes sense and use that knowledge to keep moving forward and repeat the cycle

[@thedeemon]

en.wikipedia.org/wiki/The_Unreasonable_Effectiveness_of_Mathematics_in_the_Natural_Sciences

[@sr6k795]

I almost forgot how much i love your videos, i'm so glad i came to watch this!

[@thedagit]

I'm enjoying the new format. I guess it's not even that new anymore, but I just wanted to let you know that at least one viewer appreciates how you're doing things.

[@ScienceAsylum]

Thanks! That's good to know. I wasn't sure how people were going to feel about the set change. It was a lot of work and I think it looks/sounds great, so thanks for the validation.

[@Nicoder6884]

3:06 What about gravitational potential? How is that affected by relativity rather than Newtonian gravity?

[@narfwhals7843]

There is energy in gravitational fields. Getting e=mc^2 to work with gravity is one of the reasons Einstein needed to develop general relativity. Since there is energy in gravity, gravity creates gravity. This makes the equations "non-linear" and is one of the reasons they are so notoriously difficult to solve.

[@VuNguyen-mh4oo]

The more I watch Nick, the more I love his style and his mind and his way of explaining things. You are my go to physics guru Nick. ❤

[@petersage5157]

3:30 Bit of a stylistic critique, Nick. I appreciate a flanged reverb effect as much as the next guy, but a vestibular growl (think Tati Shmayluk, Alissa White-Gluz, David Draiman, etc.) might have been more effective there, even without any post processing. It's actually pretty easy to access once you learn how it feels.

[@kingofgoldnessr9364]

This video is amazing, hits every nail necessary that nearly no one talks about. Watching your videos gives me the same feeling I get when I watch an inhumanely good once in a generation athlete do their respective sport, except for science communication.

[@bryanlib137]

What a great explanation! It took me a long time to differentiate these things. Your video makes it much easier.

[@louis-philip]

"He generalized it to DEATH" That was great! haha. Awesome video as usual 😊

[@Marinealver]

I remember using it to calculate the energy output of lasers of certain wavelength. Needless to say quite small but still quite fun. I think I have to go back and find the formula though.

[@Lucky10279]

5:31 Tell that to the mathematical platonists, lol. 😂

[@tolkienfan1972]

Agreed. Lots of mathematicians and physicists would disagree.

[@SyDatNguyen-r4j]

Happy new year 2025 Nick! 🎉 I also like that new background behind you

[@Yes24232b]

Thank you!! This was clarifying! Love it! Thank you!

[@MrAlexFortis]

Great video as always. If anything I would've added the notion that if we measure speed of light in "speeds of light" then c² is indeed one, but the energy is no longer "measured" in Joules. It is obvious, but I had a bit of a feeling I could've jumped onto some weird conclusions (and then figured it out) if I were like in an early school physics level. (no, you don't need to reupload a video, that is not what I am saying)

[@ScienceAsylum]

True. Thanks for the added nuance. The units get even weirder in general relativity where we also make G=1. Almost _everything_ changes units.

[@aniksamiurrahman6365]

Hello Mr. Nick 👋. I got a question. If E=mc2 means, mass is energy, doesn't the Einstein field equation in GR similarly means mass Is the curvature of space-time and not merely the cause of it?

[@foxhound1008]

Just watched on Nebula. Really good explanation, and in line with what I was taught many, many years ago in college. Sean Carroll has a video discussing that “relativistic mass” should be a banned term. However, Dr. Matt Strassler in his new book “Waves in an Impossible Sea” uses relativistic mass routinely, arguing that there are different types of mass. This is frustrating for us “laymen” people, when people with advanced degrees use conflicting terms & definitions. I prefer the explanation that mass is the energy that something has when at rest. Since photons can never be at rest, they have no rest energy. Nick, do you have any comments on how people with advanced degrees use conflicting terms?

[@ScienceAsylum]

TL;DR - Relativistic mass is a useful lie we tell introductory students, but something advanced students have to unlearn. I have _lots_ of thoughts about relativistic mass and I've had debates about it. It's incredibly useful when students are first learning about relativity, especially if your students only want a quick picture of how it works. If they do go deeper into relativity later, relativistic mass is something they'll have to unlearn if they want the _full_ picture because it makes more sense without it. This isn't the only concept that we do this with though. I heard once that "teaching is the art of knowing exactly how much to lie" and that has stuck with me throughout my entire teaching career. In physics, we can't just tell people the complete truth about reality. Students will just reject it. So introductory courses are structured to give students the _impression_ they have a complete picture when they finish, even though they only have a fraction of the complete picture patched together with useful lies ("fibs" might be a better word). If students continue in physics, later courses gradually correct those lies, one by one, and repatch the holes. It might be an outdated technique in the internet age though. I'm open to counterarguments.

[@costa_marco]

@@ScienceAsylum Similar to the "useful but flawed analogy" motif. Perfectly acceptable, as long as the caveat is given clearly.

[@user-sl6gn1ss8p]

@@ScienceAsylum I think it is a perfectly fine technique so long as it is done as transparently as possible given the maturity of the students. Ideally people should be taught this about teaching itself while they're still kids, and deepen this "meta-understanding" as they go, so by the time you reach physics you should expect this to be the case and even be thrilled by it. Culturally, "what they didn't teach you", "how it really works", "what it really means", etc, would then have a predominantly friendlier, supplemental, sneak-peaky connotation as well - so exposition because of the internet wouldn't create as much confusion, possibly the opposite even. Very anecdotal, but I have bounced off hard as small kid in school for having a bit more knowledge about what was being taught but no understanding of teaching. Honestly, I think kids should have pedagogy classes in school - they're there largely to learn yet for some reason we don't teach them about how that is being facilitated and just hope they go along with and eventually get it. (as an aside, this could also facilitate more democratic / student-inclusive management of schools and the learning process in general, richer criticism and feedback and, I bet, better teachers as well. Oh, and possibly make things easier in some cases of neuro-divergence)

[@user-Aaron-]

​@@ScienceAsylum Could you (or someone) please elaborate on why "In physics, we can't just tell people the complete truth about reality. Students will just reject it."? Is it because the foundational knowledge and level of understanding required in order to be able to accept it is beyond their current capability? Or is the reason more existential, like requiring them to accept a counterintuitive and seemingly nonsensical view of reality and learning to treat it as equally valid as the one they've always known and have long been comfortable with? Or, perhaps it's something else? I'd always assumed that the little 'fibs' were mostly due to the difficulty level of the mathematics involved and the degree of abstraction (and sometimes even convolution) required to conceptualize it and gain some intuitive understanding of it (or at least of the mathematics).

[@edit4310]

Nick, unrelated but years ago a video you did on geodesics was one of the best I had seen. It still took me some time, but you explain things so well. I trust you'll do the same here too. Glad you're around Happy New Year and thank you 🫂

[@hacked2123]

This is the first of his videos that I felt comfortable enough to watch at 2x speed, glad to hear I wasn't flawed in my understanding of e=mc², it's derivatives, or it's alternate equations.

[@gurkdoinwork]

I like the new wall decal Nick! Hope your 2025 is off to a good start

[@ScienceAsylum]

Thanks! I'm feeling good about 2025.

[@tommywhite3545]

"They generalised it to death!" Haha. It's weird that the most famous equation is a rather useless equation. And indeed often misunderstood. I awnsered lots of questions about it like "why the Speed of light .. squared?" or "how did Einstein came up with it?" About which you can write an article. I miss the livestreams sometimes by the way, but currently the passion is in an ebb (if that's correct English, but I'm sure you know what I mean, we all have it, ebbs ond flows with .. stuff). Hopefully it'll come back this year, since, well, I still am a patron. Anyway, good work on the video! 👍

[@ScienceAsylum]

I still do the Q&As every month, but I think you've said before that the time zone difference makes it difficult for you to attend.

[@tommywhite3545]

@ScienceAsylum Yes that to. But it's also a matter of .. well, multiple things actually. Very busy, priorities so I'mnot very active with physics atm .. and not to be pedantic or anything, but my questions go beyond which you can explain in a livestream. My knowledge by now, I don't learn very much from any popular science video or article anymore. But still. Every single time I did join the livestream it was very nice. Very friendly and ppl having the same interests communicating in the chat. So I most likely will join again. Just don't know when yet.

[@ScienceAsylum]

*"Not to be pedantic or anything, but my questions go beyond which you can explain in a livestream."* No offense taken. That makes perfect sense.

[@redjr242]

This is a very interesting topic and I hope you can do another on it. But I still feel a little confused. I can get behind energy being arbitrarily defined because that's the impression i got when learning the work energy theorem: potential energy was defined in order for total energy to be conserved. However mass really seems to me to be something fundamental. How could it be any different? We observe two objects accelerate at different rates under the same force. They must have a different property. That property we happen to call mass, but whatever we call it, that property has to exist doesn't it? Thanks for all the insightful videos!

[@darrennew8211]

How do you know the force is the same? Force is like energy. There's no way to measure it. You can measure the acceleration of an object, but you can't measure the force. You can't measure the mass, but only the inertia. You measure the inertia or energy or acceleration in several different ways, and then you calibrate your understanding of force based on those. The force is the thing that the spring and the gravity exert in equal amounts when you hang an object from a spring. The mass is the thing that stays the same in different formulas for energy or force. The "matter" is what's there, and mass is a measurement that is conserved in some ways. Stick a bunch of photons in a completely reflective box, and suddenly the box has mass.

[@mjkluck]

Good stuff, Bubs.

[@001firebrand]

We're glad you're back, our honored sensey Dr. Lucid! 🥰

[@saphcal]

love the spacetime t-shirt! :3

[@thstroyur]

EVERYTHING. Shortest video ever, Nick.

[@nashs.4206]

Could you explain the difference between rest mass energy and internal energy? It can be demonstrated that a hot object is more massive than the equivalent cold object. Likewise, it can be demonstrated that a loaded spring is more massive than the equivalent relaxed spring. But in classical physics, couldn't we attribute this increase in mass due to the fact that the internal kinetic energy of the hot object contributes to the internal energy of the hot object, and that the elastic potential energy of the loaded spring contributes to the internal energy of the spring, and that is what is causing the increase in mass? From this perspective, it seems like there is some sort of connection between internal energy and rest mass energy. Does rest mass energy (i.e. the E in E = mc^2) account for internal energy, or does internal energy account for rest mass energy? Historically speaking, internal energy came first so I would imagine that rest mass energy is the more "generalized" energy that accounts for internal energy rather than the other way around, but I'm having a hard time distinguishing between the two in this context (i.e. for matter). For photons and other point-particles, I guess the notion of internal energy doesn't really make sense.

[@narfwhals7843]

Rest energy is _all_ the energy an object has when it is at rest. That includes all internal energies, like tension, temperature, or excited atoms/molecules and other potentials. You can derive that a compressed spring will have more inertia from newtonian mechanics. E=mc² gives you an easy formula for it. (Though, that formula is actually older than Einstein's derivation. Einstein gave us a derivation in the context of Special Relativity)

[@mlonguin]

I got peace when I realized that mass (rest mass) is just small things giggling in a confined place at speed of light (as Nick said). Then, if c is the only speed that is, when a mass moves, it has to obviously move at speed lower than c, otherwise the giggling things at c cannot be giggling anymore. This is time dilation! I have no idea, though, about how this applies to time dilation near gravity, if anyone knows, please help!!!

[@alexvilonyay8597]

You're awesome! Crazy for life!! Keep up the great work

I always like to say that "words matter." Or more specifically, "language matters." The view of _linguistic philosophy_ holds that most philosophical disagreements, differences, or problems come down to language. And that by examining the limits of language and choosing our words much more deliberately, we could eliminate the vast majority of such problems, which really stem from the fact that each of us uses language just a little bit differently. It's something I find a lot of merit in.

[@IlIlIlIlIlIllIlIlI]

I learnt lot from you. Thanks Nick 👍

[@narfwhals7843]

If we use m=E0/c² as the *definition* of mass, it immediately becomes clear that anything moving at the speed of light can not have mass. E0 is the energy an object has at rest. Since E0 requires the existence of a restframe, which can not exist at the speed of light. It also implies that anything _without_ mass *must* move at the speed of light, because it can never be at rest, or its energy would be zero, so it doesn't exist. I might be making the assumption that c is the _only_ velocity that has no rest frame, but I think that follows from the postulates of SR pretty quickly. Another thing I've taken to is to define newtonian "mass" or inertia as the resistance to acceleration _from rest_ . This forces us to consider the invariant mass, rather than get ideas about relativistic mass. Hawking defines it as just "resistance to acceleration" in an attempt to show there is only rest mass. But just "resistance to acceleration" is exactly what observers see change on objects at high velocities. Don't ask me about the Higgs, though...

[@aresgalamatis7022]

@8:45 another non-math student complaining about math 🤣

[@Paleolithics]

I always learn something from your videos. Math and physics are my favorite subjects and always have been. Thanks for everything you do!!

[@tomersch13]

Knew the topic in general before,but this video still helped me understand it all batter! Maybe just one point in the end, equation are made up sure but if you change one madure of unity (for example C=1) you must change and update the rest of the units of the other parameters... It maybe made up but the realtionship between the parameters are not...

[@legendgames128]

The thumbnail having the Bug Fables font (Bubblegum Sans, for the curious ones) brought me in Your explaining kept me going. =D TIL what E=MC^2 really means: Mass *is* energy.

[@luisfilipe2023]

So essentially mass and energy are the same thing we just use it in different contexts depending on wether the thing in question has matter or contained energy

[@idknemore]

I didn't realize how much I misunderstood this equation until this video

[@michaeljames5936]

I look forward to seeing Matt, wearing a Science Asylum T-Shirt on PBS-Space Time. I do wonder if that particular design is going to be seen as ironic, as we hurtle towards the Big Crunch.

[@lantonovbg]

Expansion is by power series or Taylor-McLauren theorem, not by the binomial theorem

[@Niightblade]

Please do "zero gravity" next!

[@1005corvuscorax]

In all honesty, I truly feel that you and your channel are a FAR superior Science Communicator than Stephen Hawking was with books. This vid cleared up SO much for me, thank you so much.

[@viralsheddingzombie5324]

Nick made it all UP.

[@ShawnRavenfire]

This has been a pet peeve of mine for a while, especially when people think the "m" stands for "matter."

[@mlonguin]

Why don’t we just say m = confined energy to a small space, so we explain inertia properties?

[@ShawnHCorey]

@7:35 Be careful of language. The 1st law of thermodynamics states that in a closed system, the total amount of energy remains constant. It says nothing about open systems.

[@robertroach9157]

@@ShawnHCorey no, it does: "open" systems are always a subset of a larger closed system (or another "open" system)

[@philochristos]

Thank you for that explanation.

[@ScienceAsylum]

You're welcome!

[@nm_97]

Is the "E" in this video a more general kenetic energy? Bc none of this takes into account any potential energy so its not like the E is all energy, right?

[@narfwhals7843]

E=mc^2 takes into account _all_ internal energy of that object. If there are potentials inside the objects affecting its constituent particles, that energy will affect the mass of the object.

[@knuckles1006]

Another great explainer from Nick. When I tell people if all energy in the atoms of a paperclip were to be suddenly be released, that explosion would be greater the energy released by the atomic bomb that exploded over Hiroshima. When they doubt me, I just show them that equation.