Why haven't you read Einstein's E=mc² proof?

[@WWTormentor]

My 14 year old daughter and I accidentally stumbled onto your channel. We have been watching other channels about science in general including biology, chemistry, physics, and astronomy. We have to say that we are surprised that you don’t have more followers as rich, entertaining, and informative as your channel is. Thank you for the great job and looking forward to more videos. PS. She says she wants to be the next Stephen Hawkins!

[@spirit5923]

Heck yea. Wishing her the best!

[@neilbrucker5985]

Also watch Dr Becky smothers i think her name is. She is a astrophysics specialist in supermassive black holes from the UK. Sooooo good

[@mattb6646]

She's almost over a million, she doin alright

[@duudsuufd]

Because this is a science channel for smarter people than the average science-interested people. I watch different science channels on YT too. But when there are too many equations in it, I can't follow. No problem with Tibee's channel for me, because people have different degrees of smartness.

[@andrehenkel9121]

Sabine Hossenfelder is even right good!

[@henrycadman5564]

Even though I am a musician and struggled greatly with math in school, I have always found physics and its equations/representations very beautiful for some reason. Your videos are amazing and I really appreciate them. Thank you.

[@WoefulMinion]

Music and math are closely related.

[@henrycadman5564]

@@WoefulMinion Absolutely! Unfortunately, my math teachers wouldn't accept any sheet music in place of my homework. lol I would love for Tibees to do a video on the mathematics of acoustics and maybe even Pythagoras' "Music of the Spheres" though!

[@omp199]

I wonder if you might have an appreciation for mathematics that remained dormant at school because you had bad teachers. You might want to consider seeking out a better teacher and trying again.

[@tricky778]

We should be suspicious of beauty in physics. It is unlikely that physics was made to be beautiful to us, and unlikely that we evolved to find it beautiful given that we so recently learned its details. That means we probably _permit_ ourselves to report only beautiful facts. In a sense, like how a photographer frames only a beautiful scene, a painter paints only a beautiful muse, and a composer composes only beautiful music, science is an art.

[@markpmar0356]

You wouldn't be the first to notice the sheer elegance of the equations of physics. That is, right up until you see how crabbed and inelegant the equations of general relativity turn out to be. Special relativity and the Schrodinger equation as well as Maxwell's equations are distinguished by the apparent simplicity and economy of expression.

[@ryan-cole]

Could you make this a series going through some other original papers? There is surprisingly almost no videos on KZbin that does this.

[@holliswilliams8426]

I could do this, I have read a lot of Einstein's original papers and understand them well (I'm a physicist with publications in respected journals).

[@rxltv_]

I agree

[@dickybannister5192]

my personal favourite, not by Einstein, but the story is great, is the 2 page note Bose sent to Einstein after getting it rejected in England. Bose certainly didnt get the recognition for the simple leap he made in deducing that it makes no sense to consider "identical" particles as phsyically distinct. Einstein translated it to German and got it published. IDK but I think no copy of the original exists, but it has been translated BACK to English when he died and was re-printed. a copy of that in PDF form is linked to on his wikipedia page.

[@whyplaypiano2844]

@@holliswilliams8426 Do you teach at Montgomery College?

[@jacobpeters5458]

a book said when an assistant showed Einstein his proof he said he could've written it way more simplified

[@scopaf1662]

This is some high quality ASMR.

[@smasha3143]

came here to say this ... physics lecture AND AMSR .... gawd help me.

[@eduardomelo4340]

literally my first tought when i opened the video

[@starbase51shiptestingfacility]

Einstein was at least good at math, but not so good at physics or astronomy. Proofs: Matter is not interchangeable with energy. You can not create matter with energy. Go ahead and try to prove this wrong. He wasn't good at astronomy. He failed to understand that the Sun orbits around the Milkyway galaxy's center. This can be proven by his failure to account for Mercury's imperfect circle orbit around the Sun. E = mc^2 can also be proven wrong. Energy = mass x speed of light square. Energy = 5 grams x 300,000 kilometers squared Energy = 5 grams x (300,000 x 300,000) Energy = 5 grams x 90,000,000,000 450,000,000,000 = 5 grams x 90,000,000,000 Light speed squared has no bases for unit of measurement. All it produces is a large number and no bases for unit of measurement. The end product correlates to nothing. He is still hyped by people who learned science from science fiction shows and movies, like Doctor Who.

[@fghsgh]

@@starbase51shiptestingfacility Let me present you with: particle accelerators. Which pump huge amounts of (kinetic) energy into particles to create more particles. Also the fact that summing up the mass of all the quarks and leptons in regular matter gives you only 10% of the expected mass. The rest comes from energy, mostly in the strong force. Oh, and if you pull apart two quarks that are being held together by the strong force, the energy you put into it will actually _create a new quark pair in the middle._ I have no idea about what you're saying about him not acknowledging the sun orbiting the Milky Way, but you didn't provide any evidence anyway. The sun is orbiting it so slowly that the effect would likely be negligible anyway. Oh, and, according to Newtonian mechanics, joules (the unit for energy) is just newtons (force) times meters (distance). Newtons are kilograms (mass) times m/s^2 (acceleration). Putting this all together, J=N*m=kg*m/s^2*m=kg*m^2/s^2=kg*(m/s)^2. Which is mass times velocity squared. The units match up.

[@sharpnova2]

@@starbase51shiptestingfacility holy hell you're not kidding. you are a top tier crackpot.

[@qwel5981]

I dont think anyone here has read the original paper

[@chinesecabbagefarmer]

I can't read

[@josephkarl2061]

It's one of those bizarre things where everyone talks about the equation and thinks they know all about what he wrote, but when you actually ask "Have you read the paper?", it's like um -

[@bhuvanraj9276]

Especially the German version

[@ergodeus]

I'm studying german, maybe after 5 more years of German and 10 years of maths and physics I can read it. And only half of it will fly over my head.

[@Xplodinggiraffes]

Club penguin

[@jansagichnicht3500]

Your calm way of talking is so unique all over KZbin. This is the first video I have seen on this channel and liked this style of talking since the first second. Thanks a lot!

[@divyanshidubey7382]

I started getting interested in papers and thesis because of your precise and simple analysis of them. I tried reading papers before, but with no guidance and proper skills I felt like I didn't gain anything significant from them. Thanks you for igniting my spark again! And do make these videos more. I personally enjoy these more than examination analysis (maybe because I have extreme exam anxiety). But I love the sheer raw knowledge you gain from academic papers ( and other sources as well).

[@abyssaljam441]

Ibe found nothing more staisfing than reading and rereading technical books from before computers and trying to work out what exactly they mean. Im a master's naval architect student and I feel there is always something lacking from textbooks written after computers became mainstream for design. they just don't seem to have the same mathematical logic written into them that the older books do.

[@divyanshidubey7382]

@@abyssaljam441 Exactly! They try to simplify and level down things to the point that the whole essence just dies. And in the end, everything boils down to just learning for passing an exam.

[@veramae4098]

Dr. John Campbell, YT channel, PhD in nursing education. Almost every episode is devoted to Covid research papers.

[@GeertDelmulle]

At 1:36 the sentence actually says: delta mass = delta energy over c squared. It’s a difference statement. Following from that we can discuss the ground state of things and the granularity of those differences. As it turns out those differences are multiples of a finite quantity related to Planck’s constant. Heisenberg’s inequality didn’t simplify things, either, imposing some more constraints on the matter (make of the pun what you will).

[@The_Green_Man_OAP]

There is no "rest mass" as such, but I think people later misinterpreted what Einstein was saying, which was not that the mass is variable as you go faster, but that when an object emits light, mass is 'diminished' (consumed or transferred?) to generate that light. Einstein said: γ.∆E(rest)/½v² - ∆E(rest)/½v²= ∆m and that: L=∆E(rest), ~~~> L=½∆mc²(1/γ+1/γ²) =∆mc²(½√(1-β²)+½(1-β²)) If β≈0, then L≈∆mc²(½+½)=∆mc². ...QED 😊

[@aydin74]

Great video, but there is a mistake, I think, at 7:33. The kinetic energy of the electron Einstein refers to is not ½mv², but rather the relativistic kinetic energy he had derived in his previous paper, which is mc²(γ-1) and only in the 1st approximation is ½mv². Hence, this formula has to be used for the equation on the left hand side. This mistake seems to have happened quite often, so that some physicists until today believe that Einstein‘s derivation is not correct. This might have been caused by the english translation, because reading the paper in German, it is more obvious.

[@eliteteamkiller319]

Hi. What do you mean "reading the paper in German, it is more obvious?" That the "mistake" is more obvious or that the "mistake" was created by the English translation? . . Anyway, for me personally, an approximation is an approximation. It's good enough for me. Let the mathematicians worry about mathematical rigor. I mean they already did back in what, 1910 with Minkowski?

[@ichangedmyself4362]

@@eliteteamkiller319 EXCELLENT REJOINER

[@Ironman1234-D]

The things is here written that magnitude of forth and higher orders are neglected hence the equation got modified from relativistic form to classical form of kinetic energy I.e. 1/2mv^2.The equation is also for classical prosoective I.e. when speed of certain object is less than speed of light,then realistic kinetic energy dimishes so cant used in expression. For eg in case of photoelectric effect also the speed of electron ejected is very less as compare to speed of light so classical form is kinetic energy is used there.There are maximum eg even in this world general eg we cant achieve the speed comparable to velocity of light except microscopic level ,electron in certain cases have speed comparable with that,but generally classical form is mostly used ,so here is not mistake in video or english research paper.

[@marcelmolenaar5684]

No it is half.

[@MrDrociuk]

E=mc^2 appeared in Poincare's paper in 1904, in the form Einstein wrote it.

[@hyperduality2838]

Energy is dual to mass -- Einstein. Dark energy is dual to dark matter. Time dilation is dual to length contraction -- Einstein, special relativity. "Always two there are" -- Yoda.

[@earthling9891]

i always admire your talent for wording as well as your talent for science, unique combination I find- although I know many scientists who are very eloquent as well … still I always notice this

[@iamtheusualguy2611]

One of the coolest things being a German speaker is the ability to read all of these papers in the original language :D With all the English language dominance these days, it's not that usual to read anything of significance in science that isn't in English. It also is a reminder that the German speaking world once housed the best and brightest in the world of science and the inevitable decline of the language as a language of science shortly after Einstein.

[@dnickaroo3574]

Yes, in German there are two words for mass: 1) Mass as defined by a body’s resistance to acceleration, or inertial mass - expressed in the equation F = ma. 2) Then there is Gravitational Mass. The Gravitational Force of attraction which is proportional to the product of two masses (and inversely proportional to the square of their distance apart), in Newton’s Theory. So it was perhaps more natural for Einstein to wonder why these two masses should be exactly equal.

[@MarionTIA]

@@dnickaroo3574 In English, those would be "mass" and "weight". Mass is the raw mass it has, weight is gravitational force expressed as a unit of mass.

[@mikemondano3624]

@@dnickaroo3574 Name them.

[@starbase51shiptestingfacility]

Einstein was at least good at math, but not so good at physics or astronomy. Proofs: Matter is not interchangeable with energy. You can not create matter with energy. Go ahead and try to prove this wrong. He wasn't good at astronomy. He failed to understand that the Sun orbits around the Milkyway galaxy's center. This can be proven by his failure to account for Mercury's imperfect circle orbit around the Sun. E = mc^2 can also be proven wrong. Energy = mass x speed of light square. Energy = 5 grams x 300,000 kilometers squared Energy = 5 grams x (300,000 x 300,000) Energy = 5 grams x 90,000,000,000 450,000,000,000 = 5 grams x 90,000,000,000 Light speed squared has no bases for unit of measurement. All it produces is a large number and no bases for unit of measurement. The end product correlates to nothing. He is still hyped by people who learned science from science fiction shows and movies, like Doctor Who.

[@mikemondano3624]

@@starbase51shiptestingfacility Actually, Einstein always struggled with math, even failing some tests. He commented that he could no longer understand his own theories due to the math. His strong points were physics and astronomy. Mass and energy are interchanged all the time. Even burning coal shows a mass loss equivalent to the energy produced.

[@hasanimason]

Brilliant Tibees , outstanding super good content as always.

[@Gurseerat_Singh]

Why is her voice sooooo low,polite and just really calming in general

[@Keaza.]

I listen to your videos whilst I work. It helps me feel less anxious and stressed, plus I learn a lot too!

[@SiqueScarface]

I actually read Albert Einstein's proof. And I read it it in the Annalen der Physik in German, as I am German ;) PS: Isaac Newtons famous quote of the dwarfs on the shoulders of giants is itself a quote from Bertrand of Chartres, as quoted by John of Salisbury. Even the quotes are standing on the shoulders of giants.

[@moegreen3870]

hmmm it seems its giants all the way down! and at the bottom of the giants, perhaps a turtle! :p

[@lawrencedoliveiro9104]

So here’s a question: since E ≠ 0 for a photon, doesn’t that mean a photon has mass? There seem to be some people who are now insisting that photons are massless.

[@SiqueScarface]

@@lawrencedoliveiro9104 The mass of a moving photon is hf/c². A theoretical non-moving photon would have the mass zero, e.g. photons have no rest mass. That means that photons have no inertia and are always moving at the speed of light.

[@lawrencedoliveiro9104]

@@SiqueScarface You said “rest mass”. And I would, too. But the physicists are now saying photons have no “mass”.

[@SiqueScarface]

@@lawrencedoliveiro9104 Photons carry energy, thus they have a mass as soon as they travel at light speed. But as photons have no rest mass, they can't move slower than light speed.

[@goonrick]

Thank you , Toby! Your approach to science is calming.

[@garymartin9777]

There was a derivation in my freshman physics textbook which was quite simple and elegant. All it used, as I recall, was a right triangle, formula for inertia of a pendulum and the speed of light, I was astonished how it just dropped out with some expression manipulation.

[@RichardAlsenz]

No irrational number has ever dropped out of anything, for irrational numbers do not exist as numbers.

[@MohamedSalah-gb5tc]

You always giving me passion to study more, toby.

[@CuriousCyclist]

You have created a fantastic and unique brand with the way you speak and teach physics via KZbin. Keep it up.

[@florinfiltervac1415]

I'm a Mechanical Engineer, and studied some math and physics, but never went too deep in that. I read some /a lot of books that popularize science. The thing is that science is the most interesting thing to live for, at least for me. Understanding ideas make you feel like having an absolute power. But you need a good teacher to help. Please try to explain a bit more all the things in those equations, because many details we don't know, things that people who studied find it obvious.

[@tombufford136]

I am glad you have sponsorship Toby. You clearly go to some effort making these videos with Captions ,pictures and narratives. You also present yourself with very nice looks and pleasant Voice.

[@III-zy5jf]

My community college professor taught in an insanely tiny classroom all the math leading to E=mc^2, and twenty years later I still think about that moment and the shock and excitement. I retook that class at another college, and those equations weren't taught. He was a black professor who read a Chinese newspaper everyday, too.

[@spiralsun1]

Who are you? Are you for real? I loved your story about that guy thanks!!!! ❤️‍🔥👍🏻

[@myxail0]

in chinese?

[@RetNemmoc555]

On the first day of my first chemistry class (also at a community college) the professor walked us through a mathematical proof of the equation, but did not tell us until she concluded what her point was, and that we did not have to remember the math. I've forgotten the lecture, but will never forget the room full of terrified students frantically taking notes, while I sat there worrying that I had gotten in over my head.

[@ToriKo_]

@@spiralsun1 recognize u from Curt’s channel!

[@christophergroesbeck1436]

@@RetNemmoc555 why would a professor go over this in a gen chem class is beyond me lol

[@andrewmorton7482]

An overhead projector! That is properly old-school and I love it!

[@kevincurrie2052]

My thoughts exactly! I remember at primary school when overhead projectors were cutting edge , so I guess I am old school 😂

[@frede1905]

I took a while to get through the full context of this equation by not only reading through this paper, but also getting through the context of it (by reading through large parts of the electrodynamics of moving bodies paper). This largely meant reading his derivation of the relativistic Doppler shift formula. His derivation of this equation is a lot more satisfying than all other sources I've seen on the topic, which typically find it by using Planck's law to relate the energy of the EM wave to frequency, whose Doppler shift formula is well known. Einstein, however, used classical electromagnetism to derive the formula, solely using the formula for electromagnetic energy density. This not only makes the derivation more satisfying, as Planck's equation came later, but it also helps to justify Planck's equation in the first place, as it shows that frequency and electromagnetic energy have the same Doppler shift (PS. in response to the controversy part, I've found a slightly modified version of Einstein's derivation that invokes momentum conservation in addition to energy conservation. This result is particularly powerful, as you can generalize it to obtain the relativistic equations for momentum/energy (E=mc^2 of course only applying when the mass is at rest)).

[@luker.6967]

Yes that derivation at the end you mention is what I was fortunate enough to be shown in a first year physics course in Uni (I dropped out). It was quite mind blowing.

[@frede1905]

@@luker.6967 It is indeed. Despite knowing the thought experiment and the mathematics behind the derivation, I am still somehow blown away that simply applying Einstein's postulates and simple considerations of electromagnetism can somehow lead to the equivalence of mass and energy. That conclusion seems so vastly different from what relativity is all about, namely how various quantities change as you go from one reference frame to another.

[@notabirdorabeaver]

Thank you for explaining this! I like that you added a section about the controversy of the original proof, that was especially enlightening.

[@78anurag]

I found this proof especially delightful due to its apparent simplicity, it's amazing.

[@GregoryJByrne]

Try reworking the formula using algebra. "Energy is neither created nor destroyed." Einstein. On this planet. In this solar system. All electromagnetic gravitational energy either comes from & or returns to the Galaxies Fermie bubbles magnetosphere via the Sun's Oort cloud magnetosphere to power the Earth's double torus magnetosphere. Jesus warned us about the AntiGoylumites & these the climate change END TIMES with the book of REVELATION & the cause with the 7 north stars of the PRECESSION of the Earth's orbit equinoxes when Earth's orbit ellipses the Sun's magnetic equator at the Alpha & or Omega equinoxes every 12,000 years for a 1,000 years causing these the cliamte change END TIMES Jesus warned us to watch & prepare for. These are just the birthing pains of the climate change END TIMES. Noah's floods won't be pulled OUT & around the planet east to west until the conjunction of Mercury-Venus-Moon-Earth in 2033 & every 40 years thereafter for the millennium it takes to eclipse the magnetic plane of the Sun's fermie Bubbles Oort cloud magnetosphere. You are not God's. You can no more change the climate of this or any planet than you can change your gender.

[@munaq-jp]

As a child I was fascinated at the amount of energy every particle holds hidden inside and I had a very difficult time trying to understand why protons would keep themselves together like that without exploding and causing a planetary chain reaction. Learning about the strong force was a great relief.

[@31337flamer]

I did actually read it :) .. i have a few more of his papers printed and bound to a nice book :D. Im from germany so i have all the original papers in german :D "Erzeugung und Verwandlung des Lichts", "Ist die Trägheit eines Körpers von seinem Energieinhalt abhängig", .. and also "Annalen der Physik - Die Grundlage der Allgemeinen Relativitätstheorie" Thumbs up!

[@pepaxxxsvinka3379]

Ich mag Deutsch sehr sehr. Ein mal wenn ich besser mit Deutsch bin, werde ich das auf Deutsch lesen!

[@31337flamer]

@@pepaxxxsvinka3379 Ich mag Peppa Pig. :D Es gibt viele lange Wörter in den Texten über Physik. Das lesen ist manchmal schwer. Viel Erfolg! Dein deutsch ist schon sehr gut. :)

[@pepaxxxsvinka3379]

@@31337flamer Das ist sehr lieb von dir! Die langen Wörter sind ja schwierig, aber interessant. Physik in dem Artikel ist nicht weniger zu verstehen! Haha ja! ich heiße Pepa Pig ohne Grund hier :)

[@ShaneOsborne]

That must be intensely interesting!

[@pepaxxxsvinka3379]

@@ShaneOsborne auf jeden Fall

[@nikosneely1558]

Thank you so much for not having auto generated captions !!!!

[@shhhhdigital]

Great to see you again Tibees. Read it when I was 14 (I'm now 54 years old). Thank you so much for producing this video as this is a topic that deserves as much attention as Quantum Physics, because the two are intrinsically related despite their mutual effort to deny any such relationship. You're getting us closer to a Quantum theory of gravity, if not, a theory of gravity that accounts for why people are so attracted to watch your videos ;-)

[@hyperduality2838]

Energy is dual to mass -- Einstein. Dark energy is dual to dark matter. Time dilation is dual to length contraction -- Einstein, special relativity. "Always two there are" -- Yoda.

[@misterlau5246]

@@hyperduality2838 not quite. The idea you said and quoted Yoda is right but not that simple. We basically know that symmetry, like "always two... " exists, non locally, meaning not necessarily in the immediate environment around, it could be a little far to say it someway... 🤔 And not just in pairs, take in account, atomic nucleus, it has 8 for symmetry stuff, and gives us a 9D matrix to work with. More than two at quantum level but your idea is well oriented.

[@hughbarton5743]

A lovely and clear explanation of an equation that we can literally observe all around us every day ( once, of course, we are made aware of it....), but which is never discussed! Thank you. I just subscribed.

[@fraktaalimuoto]

As a physicist I really appreciate the elegance of presentation.

[@brazenzebra]

Excellent! Thank you Toby. Your video reminded me of a conversation I had at lunch many years ago about nuclear weapons. My co-worker, a PhD in nuclear physics, asked me, "You know how they do it?!" I gave him a blank stare. "With mirrors!", he said, grinning like the Chesire Cat. We were talking about the hydrogen bomb. It turns out that for a fusion bomb, a fission bomb is exploded first (the primary), and then before the bomb container can rupture, the extremely high-energy radiation from the fission bomb is focused by mirrors onto a pod of material that then undergoes fusion and releases even more energy (the secondary). It's like Kaboom! ... BOOM!! All because of Einstein's equation and Einstein's letter.

[@hyperduality2838]

Energy is dual to mass -- Einstein. Dark energy is dual to dark matter. Time dilation is dual to length contraction -- Einstein, special relativity. "Always two there are" -- Yoda.

[@bdnugget]

Really awesome Dall-E images, they fit so well :)

[@geowar20]

There’s an excellent book “Why e=mc^2… and why it matters.” that goes into the detail of how he derived it.

[@smoorej]

I never believed in AMSR until I started listening to you. I love physics, I love Australian accents, and I love your voice. Absolutely brilliant.

[@guitarista666]

Close, she is from New Zealand.

[@hyperduality2838]

Energy is dual to mass -- Einstein. Dark energy is dual to dark matter. Time dilation is dual to length contraction -- Einstein, special relativity. "Always two there are" -- Yoda.

[@The_Green_Man_OAP]

0:53 5:25 ∆E=L in rest frame? So.... ∆m≈L/c²=(∆Erest)/c² I think there is no "rest mass" as such, but I think people later misinterpreted what Einstein was saying, which was not that the mass is variable as you go faster, but that when an object emits light, mass is 'diminished' (consumed or transferred?) to generate that light. Einstein said: γ.∆E(rest)/½v² - ∆E(rest)/½v²= ∆m and that: L=∆E(rest), So, (γ-1).L/½v² = ∆m => L= ½∆mv²/(γ-1) 1/(γ-1) can be written as a fuction of β² & γ with β=v/c, and lots of algebra later we have: L=½∆mc²(1/γ+1/γ²) =∆mc²(½√(1-β²)+½(1-β²)) So, if β≈0, then L≈∆mc²(½+½)=∆mc². ...QED 😊

[@markholm7050]

Your overhead projector takes me back to Jr High School Algebra 1 in 1968.

[@dielaughing73]

Still in use in the late 80s at least. One maths teacher had the transparency on a roll so she could write the whole lesson without changing pages

[@Pengochan]

To summarize: Einstein considers the change of energy of a particle emmitting light in two systems, one in which the particle is at rest, and one in which it is moving (I.e. the system is moving relative to the particle). He does that by simply applying the principle of conservation of energy: The energy emitted as radiation is lost to the particle. He then finds that there is a difference between the change of energies he calculated for the different reference frames. Now in the system where the particle is at rest the change between before and after sending out the two photons each with energy L/2 is L, and can be considered as the change in the inner energy of the particle. In the other system, where the particle moves the change is slightly larger. The change in inner energy should be the same, since it's the same particle, so where does the difference come from? Since in that system the total energy of the particle is inner energy + kinetic energy he concludes, that the change must be attributed to a change in kinetic energy. But the velocity of the particle can't have changed, because due to the nice symmetric arrangement in the system with the particle at rest (with photons of energy L/2 in opposite directions) it should be at rest before and after the emission. Another way to look at it is, that a third observer moving in the exact *opposite* direction as the second observer in his moving reference frame would get the exact same results. Einstein already knew, how the "classic" kinetic energy resulted from the relativistic kinetic energy as the first nonzero term of the Taylor series. Now since the velocity of the particle didn't change, the kinetic energy of the particle can only change if it's mass has changed, and it lost a mass of m_delta=L/c^2, where L is the combined energy of the emitted photons. Of course the Taylor series term being of the same form as the classic kinetic energy is very suggestive. That Einstein compared like terms of the Taylor series is IMO not a problem, it just means that this first conclusion holds only to an order of magnitude of v^2. It's important to note that Einstein used the emission of *two* photons in a symmetrical fashion. If e.g. the particle emmits only one photon the difference in the change of energy depends on the direction of the emitted photon relative to the direction of the moving system, and may even change sign. That is due to momentum conservation: The momentum of the emitted photon would have led to a change in velocity of the emitting particle, another contribution to its kinetic energy (even when that particle is held by some larger apparatus there would be a momentum transfer to the whole system, and it could just be considered as a "particle" of larger mass). Einstein saw that he could avoid that (i.e. the difference depending on the direction of the emission) by creating his thought experiment in a symmetric fashion. I'm not sure if he was already aware of the momentum of photons, he theorized that later in a 1909 and 1916 paper, or if he just saw a way to make his result independent of the direction of the emitted photon, but that he needed that symmetry, and that otherwise the direction of the emission resulted in another contribution to the difference of the change in energy (consistent with a change of kinetic energy of a moving particle due to momentum transfer) might have set him on that path.

[@misterlau5246]

Well yes. Relativity was refined for some years. Einstein did what you said, but basically, let's take this like changing the way the gravity model was. Using the space geometry change instead of forces, similar to electrical field. Things like neutrons were discovered after relativity. No wonder Einstein didn't believe something like a nuclear bomb would exist. With those N, of course it was done and... It's a very destructive weapon.....

[@josephkarl2061]

Tibees and Einstein is the combo we've all needed right now 👍

[@hyperduality2838]

Energy is dual to mass -- Einstein. Dark energy is dual to dark matter. Time dilation is dual to length contraction -- Einstein, special relativity. "Always two there are" -- Yoda.

[@screenoholic]

Great video. I got flashbacks of my Physics classes in undergrad where we were showed the proof (not the Einstein one, but the Energy-momentum relation).

[@PetraKann]

E=mc^2 is not the original and full equation. It is a special case for the rest mass. It should be written as E=m0 c^2. The actual equation is: E2=p2c2+m2c4 For a body at rest the velocity and therefore the momentum, p is equal to zero, so E2 = m2c4 Therefore E = +/- mc2 The +/- is important

[@hyperduality2838]

Energy is dual to mass -- Einstein. Dark energy is dual to dark matter. Time dilation is dual to length contraction -- Einstein, special relativity. "Always two there are" -- Yoda.

[@lawrencedoliveiro9104]

Is that to try to argue that photons have no mass? But a photon (actually I think a pair of photons) can be produced from the meeting of an electron and a positron, both of which have mass. So if they produce a massless result, where does the mass go?

[@PetraKann]

@@lawrencedoliveiro9104 No. And it's mass AND energy that is conserved. I don't know of any violations of the conservation of mass AND energy Law. Do you Leonardo DiCaprio?

[@PetraKann]

@@hyperduality2838 Dark energy and Dark matter are distinctly different phenomena Mr Hydraulic. Scientists infer the existence of both through indirect observation and measurement. The only similarity between the two is that they are both currently "invisible". Dark matter pulls galaxies together, while dark energy pushes them apart. You should apologise my friend.

[@hyperduality2838]

@@PetraKann Convex is dual to concave -- lenses, mirrors. Convergent (syntropy) is dual to divergent (entropy) -- the 4th law of thermodynamics! Decreasing the number of dimensions or states is a syntropic process -- homology. Increasing the number of dimensions or states is an entropic process -- co-homology. Homology (syntropy, convergence) is dual to co-homology (entropy, divergence). The 4th law of thermodynamics is hardwired into mathematics. "Always two there are" -- Yoda. From a convergent, convex (lens) or syntropic perspective everything looks divergent, concave or entropic -- the 2nd law of thermodynamics. All observers have a syntropic perspective according to the 2nd law of thermodynamics! My syntropy is your entropy and your syntropy is my entropy -- duality. Duality creates reality! Teleological physics (syntropy) is dual to non teleological physics (entropy). Syntropy (prediction) is dual to increasing entropy -- the 4th law of thermodynamics! "Entropy is a measure of randomness" -- Roger Penrose. Syntropy is a measure of order. Randomness (entropy) is dual to order (syntropy). Uncertainty (unpredictability) is dual to certainty (predictability) -- the Heisenberg certainty/uncertainty principle. Dark energy is repulsive gravity, negative curvature or hyperbolic geometry. Positive curvature is dual to negative curvature -- Gauss, Riemann geometry. Curvature or gravitation is dual -- gravitational energy is dual. Potential energy is dual to kinetic energy. Gravitation is equivalent or dual (isomorphic) to acceleration -- Einstein's happiest thought, the principle of equivalence (duality).

[@vibackup]

You don't have to switch to the english version; you can see the meaning in the original (0:57 in your video one row below the equation). The problm may be that V instead of c is used for the speed here.

[@stabbrzmcgee825]

That paragraph defining the relationship of mass to energy was a very big "Oh" moment for me. For many years, I have wondered why E=mc^2 has no 0.5 (1/2) in it; why it is not of the same form as the equation for kinetic energy.

[@mbulelodaliwe3597]

Love you Tibees 🤞🏽❤️

[@bknesheim]

Read through "Relativity: the Special and General Theory" a few times many years ago after buying it as a part of books that was forgotten/left on the trains. 🙂 Used some time on it, but Einstein do a very good job in the book explaining his theory in a way that can be understood without PhD in math and physics.

[@tawny-scott]

Been 4 years watching your videos. Always something new.

[@DrumsTheWord]

What a wonderful video. Thank you for this!

[@aniketeuler6443]

Was waiting a long time for this thanks for bringing out this beauty

[@allanploth6031]

Hugely enjoyable. Thank you. I don't know what else to add. I enjoy all of your presentations, but perhaps most of all this one.

[@cicad2007]

Tibees, thanks for another great video with your beautiful voice. 🙂 Btw, Patreon did not advise me about this video, I found it by accident on KZbin.

[@campbellmorrison8540]

Really good over view of a ubiquitous equation and its derivation that is now taken as gospel. I have never read this original paper either but I have seen the others who might be associated with this equation. I'm no physicist and have only degree level maths but I enjoy your fair and reasoned explanations of what I would consider deep understanding of principles.

[@Theone-ou2xt]

Tibees you come up with some good stuff

[@math.physics]

Nice timing. I have recently published videos on that article by Einstein, as well as on the electrodynamics of moving bodies. I have Always been more keen on the mathematically "rigorous" approach, but your videos are definitely more interesting and appealing, that's for sure :).

[@limitless4375]

Her voice is a whole other kind of therapy

[@limitless4375]

@Tibees1 okay scammer 🙄🙄🙄

[@mayflowerlash11]

This is brilliant. As students we a simply presented with the end result equations which we take on trust. If we understand the process of thoughts that lead to the concluding equation our understanding is improved enormously. I have often thought that maths, physics, chemistry and biology should be taught as history. They are all related and some of the early ideas (Sumerian and Greek) are surprisingly difficult to understand. By secondary school students should be able to appreciate the subtleties. And the history could be covered at a faster pace. This would result in a deeper understanding by the end of secondary school. I wonder if there is a school in Australia which has the courage to take this approach. Curricula would have to be written, although a lot could be lifted from standard curricula. This truly would be a revolution in education. The added bonus is that people in general would be less skeptical of science and understand it better.

[@ElVerdaderoAbejorro]

Not only in Australia, but the whole world. I agree 100% that not following a timeline and the lack of proofs really undermine understanding. It's absurd we "learn" the electron orbitals (1s2, 2s2, 2p6,...) in Chemistry in high school yet in order to arrive at such result you need to learn quantum physics first. Then teach the bloody quantum physics first (even if that means more math is needed).

[@jaimeduncan6167]

No no, I don't know of any Physics student that has not seen a derivation. I have to do one for homework and another during an exam (using the kinetic Energy equation for the second one). When one studies physics or math a good part of the time is used in proofs, in part because they are trying to teach you to think with rigor and also for understanding. Engineering students see the full derivation of most of the results of classical mechanics, and then see at least partial derivations of Maxuel equations using vector calculus. In applied math courses we also go with the derivation of rigid bodies equations, and some of the fluid mechanics too. We do the derivation of ideal gas equations, and if you are lucky your professor will do the calculation leading to the ultraviolet catastrophe. So if you are wondering if you will get just recipes when you go to University you are for a nice surprise. Sorry for any errors English is not my mother tongue. Best regards.

[@aoeu256]

Note also before Newton the Ancient Greeks believed that fire (plasma/chemical reaction happening) was the primordial substance which like a stream was always moving stuff, and matter was just "frozen fire".

[@mayflowerlash11]

@@aoeu256 Indeed.The ideas of the Greeks and other ancients could be touched on initially and briefly. Students would not be mislead because when the current state of knowledge is taught it becomes obvious where the Greeks were right and where they were wrong.

[@mayflowerlash11]

​@@ElVerdaderoAbejorro You are correct. I remember as a secondary level student being taught that electrons orbit the nucleus. I was also taught that positive and negative charges attract. Sadly the question of why the electrons did not immediately plunge towards the nucleus did not occur to me until much later when I was struggling to understand quantum physics. (still working on that)The clarity of the moment when I associated the wavelength the electron with the circumference of an atom has never been forgotten. Wrap one cycle of the electron's wavelength around the nucleus and you get the smallest radius possible. No smaller radius is possible.

[@jensphiliphohmann1876]

About 05:00 Since the coordinate system moving with respect to the body has Greek letters for the coordinates, I suspect that the letter 'H' is meant to read as 'Eta' rather than 'Age'.

[@DrBrunoRecipes]

Excellent 👌🏻 Greetings from Scotland 😊Have a great day everyone 🌻

[@wernerheisenberg1299]

oh, scotland my favorite country

[@islamadam8502]

Love to Scotland from Egypt ⚘️

[@mainakbiswas2584]

What a great video. Was missing you 😢 ❤️

[@timothycrooks9123]

Love the content. Thanks very much. I teach writing for a living and decided as an adult that I wanted to improve my maths abilities. So, I stumbled across your channel a couple of years ago and have now gone through every video. I am not yet able to call myself competent with maths, but I am certainly more confident to take it on and keep trying. :)

[@l.h.308]

I recommend "Mathematics for the Million" by Lancelot Hogben, a good old book that you can find in PDF (free) on Internet. Excellent!

[@hillaryclinton2415]

3:25 the only fault is the constancy of the speed of light... Light slows as the disturbance passes through mass .. vacuum has minimal mass, so the effect is VERY small... As particles can appear and disappear as they do, and vacuum has energy, and energy is related to light speed (time) they are all intertwined..

[@PatrickSmeaton]

You should narrate audiobooks....seriously.

[@davidreinders6609]

Because I have been waiting for this video

[@larryyonce]

I've been waiting for you to do it for me! 👍

[@bon12121]

7:57 That's amazing. But does that mean the equation is an approximation given that the Taylor series was truncated?

[@gerardcoyle2587]

Thanks

[@zidanidane]

3:40 ooooh i've been thinking of that a lot recently thank you for mentionning it

[@neoultra6528]

*IMPORTANT!!!: Henri Poincaré historical 1900 paper apparently includes the ACTUAL equation in "Sur la dynamique de l'électron" (On the Dynamics of the Electron). That equation is supposedly E=mc^2 in the limit where v approaches 0 (i.e., for a body at rest), although more complex for other cases. Supposedly the current concept of E=mc^2 also ONLY applies when a body is at rest ALSO.*

[@aydin74]

I have found the letter that Einstein wrote to his friend Conrad Habicht, but I could not find the quote (at 9:20). Could it be that these words are an invention from National Geographic from their TV-Series „Genius“?

[@narfwhals7843]

If you're looking at the collections of letters from the swiss years, it is in "document 29 july 1905". The original German is "Die Überlegung ist lustig und bestechend aber ob der Herr- gott nicht darüber lacht und mich an der Nase herumgeführt hat, das kann ich nicht wissen." Another translation reads it as "The consideration is amusing and seductive; but for all I know, God Almighty might be laughing at the whole matter and might have been leading me around by the nose. "

[@aydin74]

@@narfwhals7843 I found it there, thanks, Narf! :-)

[@carnsoaks1]

His findings were that brilliant that he thought he might be losing his sanity.

[@JFBassett2050]

Tibees: You always have something exceptionally good! I hang on as best I can, and it is always very rewarding. Love ya!!!

[@hemlo7494]

Tibees, your channel is a credit to humanity.

[@user-rm2qj2jh4l]

So cool!!! This is a great idea for a video! One question I have related to the video: if the relativistic doppler effect is just a downstream effect of time dilation (which then affects the frequency of a photon, which then affects its energy), does this imply that a photon will be doppler-shifted the same way regardless of whether you are traveling towards or away from it? Because the difference in speed is the same, so then the difference in time dilation is the same? Or am I missing something here?

[@narfwhals7843]

The "traditional" doppler effect still applies. The relativistic term is just added to that.

[@nabanitasaha7941]

Your sound is sooo soothing to the ear that i can't stop watching your voice mainly i am also graduated in physics ..

[@ZedaZ80]

This was so cool! And it's wild that DALL-E made those images, they were so good :0

[@Clover-qz8nl]

Thank youuuu for sharing your great work 🫶 you’re doing a great job explaining it in an honest and professional manner 🍀 keep it up ♾️ my friend

[@JoelVonlanthen]

Can i say, that your Videos brings my stress down. I like your fine Speaking voice and i find your Videos even though i didn't study math or physics, i'm Interested in that kind of Videos because you made it interesting. Greetings from the choice home Country from Einstein, Switzerland.

[@rgudduu]

12:28 'If a charged body moves thru an electromagnetic field, its mass would be affected'. What's that...can someone please help?

[@narfwhals7843]

Accelerating a charged particle through its own electric field takes more force than an uncharrged particle of the same mass. This self-induction gives an increased "effective mass". en.m.wikipedia.org/wiki/Electromagnetic_mass

[@monicapushkin3274]

I like the Far Side explanation for the origin of E=mc2. Einstein is writing on a chalkboard behind his desk .... E=mc3 .... E=mc4 ... etc .... The cleaning lady has just walked in and tidied up Einstein's desk. Satisfied with her job, she says "Everything's squared away, yup, squared away" .... Einstein is looking over his shoulder, bug-eyed with realization of the answer.

[@evlogiy]

Interesting fact that Einstein received his Nobel prize not for this, but for his discovery of the law of the photoelectric effect.

[@jensphiliphohmann1876]

03:56f: > _The relativistic Doppler effect takes into account the time dilatation effects..._ It rather founds it. The time dilatation can be derived from the fact that the optical Doppler effect (ODE) must be symmetric. Let's assume someone within a non-driven spacecraft B who sees an object B' (another non-driven spacecraft) approaching at an unknown speed v. She wants to know v, so she sends a radar signal with a frequency f₀. Since B' and the signal approach at a difference speed c+v, the signal ought hit B' with frequency f₁ = f₀(1 + β), β being v/c. Since the difference speed c−v, it should get a frequency f₂ = f₁/(1 − β) = f₀(1 + β)/(1 − β). Since ODE must be symmetric, an observer in B' must not measure f₁ but f'₁ = √{(1 + β)/(1 − β)} which is more than f₁ by a factor γ := 1/√{1 − β²}.

[@martynewport]

Amazing video. I learned much and also enjoyed watching you.

[@FoieGras]

Wow! Much more intuitive the way Einstein explained it originally!

[@michaelbrodsky]

I was waiting for you to read it to me. Thank you.

[@CosmologDiraEinstformula]

Mass energy equivalence can be deduced from binomial expansion of lorentz factor xE . First term will be kinetic energy and other mc2.

[@Seanbo88]

Tibees has the most informative non-asmr asmr channel.

[@davepullin8572]

Einstein's letter to Roosevelt has exactly the tone of the scientists in "Don't Look Up" trying, unsuccessfully, to tell the president that a meteor was going to wipe out life on earth.

[@MikkoRantalainen]

Great video and I see your production equipment has also improved - SM7B is a great mic for your voice.

[@SteakPerfection]

Thank you, Toby. You once again explained a complex subject in understandable language. Al would be pleased.

[@rohanestrohan]

You have a very calming voice, which helps my anxiety.

[@lilmaxez]

Great video i learned a lot, thanks.

[@karmageddon9136]

Seeing Einstein's original paper was very enlightening. Note that Einstein equated inertia to energy, he did not refer to it as mass. If mass did increase with an increase in velocity, gravitational attraction would increase as well. There is no difference between rest mass and moving mass.

[@niko-laus]

to 7 :11 again be more critical the energie of the electron depends of the speed not velocity In essence, speed is a simpler version of velocity. For objects moving in a straight line at a constant speed, the magnitude of the velocity will be exactly the same as the speed. However, if the object changes direction or has varying speeds, velocity gives a more complete picture of its motion.

[@jgreen2015]

I've actually searched for a video of someone actually explains the derivation. Do glad this was recommended

[@AdelaideBen1]

New viewer - first time commenter (sorry that most probably means I don't have anything to say)... but bravo on actually going back to the source, and a huge triumphant trumpet call for actually using an OHP... it's somehow so emotionally triggering (in a good way) to see someone actually writing something. Now... for more meaningful comments (see below... or above... however YT works)... edit and to show I'm not a neanderthal..... mostly... kudos for also sprinkling in some Dall-E spiciness.

[@YTEdy]

In college I asked a professor if I could do a special project on the math behind E=mc^2, and he talked me out of it. He said it's just calculus and not enough for a project. He told me that general relativity was tensors and that was very advanced, so my idea never came to be. I suppose he would have walked me through E=mc^2, or I could have worked it out myself, but I never did. This video made me think of that. I gather Poincare worked out the precise math to this before Einstein did, but he didn't apply it to the physical world.

[@thstroyur]

Tensors are not an exclusivity of GR, nor is the latter really required to understand E=mc^2 (though I'm aware of Klein's 1918 paper). The mass-shell relation -p^2=(mc)^2 (basically what is shown @11:00) is indeed very straightforward to derive: all you need is some basic Lorentzian geometry, the momentum of a free particle, and the ticking rate of a clock at rest. On the other hand, getting E=mc^2 out of this is, to me, rather dubious; it requires the relation E/c=p^0 - and to the best of my knowledge, _that_ one has never been proven - it's more like assumed true, and then the consequences are explored.

[@voidisyinyangvoidisyinyang885]

Einstein definitely read Poincare so I'm sure that was his original source.

[@louislouis2963]

Hi! This morning I watched your reel about the 4 D Cube, When I was watching it I image my self into this transparent cube at the same time you were outside of it in your own four dimentions, it helpme to imagine the extra dimentions that exist. Thank you

[@iamsandrewsmith]

Interesting moment for me at 10:55 -- Einstein giving a lecture on the stage where I gave my masters piano recital. Not the same year, of course...

[@RalphDratman]

Wonderful video! Thank you, Tibees.