# E=mc² is Incomplete

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**Published on Oct 28, 2012**- You've heard of E=mc²... but you probably haven't heard the whole story.

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froop2 days agoright to the point 👏

Barry Bunt2 days agowait but for when its massless and E=pc, how does that work since momentum is mv, and there is mass needed. If it was massless it would be 0 times c

Simon Suman4 days agoNice

An Keyri11 days agoHahaha "all because the hypotenuse of a right triangle is longer than its legs". Yeah, that's the thing to blame 😂

movies now Naik15 days agoWhat happens if both the mass and Momentum is zero

jr2013 junior17 days agoThe way you explained it means that if you do reach equal the same speed of light the math equals what albert said. I think that is what his math was saying, that it is not incomplete but a whole.

Ummer Farooq26 days agoWhere's the lambda?

STILL NOT CLICKEDMonth ago^{+1}The most famous formula is a plagiarised form of the Pythagoras Theorem

You learn something new everyday

Why didn't Teachers teach this?

alexssandro menesesMonth agoDamn you Pitágoras and trigonometrie!!!😅

Matthew LuiMonth agoTrigonometry is everywhere

Jerry YuanMonth agoIsn't momentum mass times velocity? Which means that if a particle is massless it still won't have energy?

Wait Beat DropsMonth agoI love da bass

Prabhu AkashMonth agoDon't consider a triangle

Gaming ChampMonth agoYou can accelerate to the speed of light! All you need is some exotic matter and you can warp through space and time!!!

Zach Petch2 months agoHoly balls.

guy rubin2 months agoit explains SOOOO MUUUUUCH

supercombo 20x 68hit lựu đạn nổ2 months agoAn object moving at the speed of light produces heat and a decrease in mass

David Wilson2 months agoI'm trying to figure the energy of two different types of Mass but both being the same quantity of Mass. The first mass being uranium 235 and the other being peanut butter, which figure do I use for C²? Is it meters per second, MPH , miles per second or a different number?

Mortonator2 months agowait. But isn't P=MC?

wouldn't that make

E²=(mc²)²+(pc)²

equal to

E²=(mc²)²+(mc•c)²

which is

E²=(mc²)²+(mc²)²

simplified to

E²=2(mc²)²

Is that right?

I'm assuming I've got something wrong somewhere, smarter people would have already figured it out if it was true

Apo Giov2 months agoA particle with no mass (a photon) has energy E=pc=0 because with no mass p^2=(mu)/(1-u^2/c^2)=0 . Am I wrong ?

Claudio Costa3 months agoSeems interesting!

BakonKing4 months agoAssume nonzero curvature and go faster than light.

Laggy Acer4 months ago^{+1}But if e=mc2 shows us this then shouldnt light have a little bit of mass? Meaning it not really the max speed limit????

Bhavesh sinha4 months agoHow Momentum is mass times velocity and light has no mass

Ordinary Knife4 months agoI had to make this video go at .75x speed because it’s going pretty fast

William Harvey4 months agoBut isn't momentum mass times speed ? Because in French we call it quantity of movement and it is mass times speed ?

Mark Susskind4 months agoNow that mass will be measured in terms the Planck constant, would the products mc^2 and pc be the same value?

Mark Susskind4 months agoIf m=0, then everything is the same, except that gamma is not calculated, but declared 1, since gamma assumes an object can be at rest, and there's no sense of a massless particle being at rest-- just one speed at all times.

Mark Susskind4 months agoOK I figured it out: if m>0, then E = gamma * h * nu, where gamma = (1-(v/c)^2)**(-0.5), m is the mass of the object, v is the speed of the object, E is the energy of the object, c is the speed of light in a vacuum, h is Planck's constant, and nu = (c**2/h)*m

Stuka !5 months agoBut if the objects is massless then momentum is also 0 .-.

0bada5 months agoYou've said in another video that light has mass.

In the video "Misconceptions in physics"

Prateek Panwar5 months agoWhy that bulb is cracked

Admit it, You didn't rechecked the video

Huzaifa Nihal6 months ago^{+1}You said that in case of massless objects E=pc,but p is given by the cross product of mass and velocity than how can light have momentum if it's massless???

pibroch5 months agoLight has measurable momentum, so for light, p is not given by the cross product of mass and velocity. Simple.

SimonDaBug6 months ago1:08 that makes so much sense because electrons have almost no mass, and they move in waves!

Nirvana One6 months agoI guess the ancient Egyptians worked this out with their pyramids lol

Seriously this answers heaps of questions 😎

J7 months agoAfter six years I finally understood this

KatanaX7 months agoE=mc2=deconstruction. Mc2=e=construction.

KatanaX7 months agoMc2=E

Miachel De santa7 months agoIf mass is zero then p is also zero then how is a photons energy measured

Jamie Anderson7 months ago^{+1}by measuring photon's wavelength which is inversely proportional to its energy

Eric Steele7 months agoi love this channel

Kshitij Desai7 months agoIsn't momentum mass times velocity

jimmy alderson8 months agoWhat does 'momentum' mean on the sub atomic level?

Because photons are massless so it's not like p = mv anymore, so what is the definition of momentum at this scale?

Obviously you can rearrange the e = pc to get p = e/c and for a photon that should be the same as p = e/v but that's hard,y a definition.

Also does this equation (e = pv) work for anything other than light? I believe it doesn't but i don't understand why it shouldn't

Varun shrivastav8 months agoIf mass is zero the momentum will also zero

Jamie Anderson7 months agoObviously not as all photons have energy.

Krushna Thakare8 months agoWhat is time ?

ItzJake Roblox8 months agoWait guys, what if all operations were in reverse? What if got all math wrong, I know if that would happen The full e=mc^2 would like this instead: √e=√(√m/c) - √(p/c) but what else would change

sauronfupoc ,8 months agodrive.google.com/file/d/1B0T7wRDzdbaZKn5HjmmzVuh87Z7kVSLD/view?usp=drivesdk

Ken Behrendt9 months agoActually, adding the pc term for photons of light because they are supposed to be "massless" still introduces mass because p = mv. This implies that there is a mass associated with the energy of a photon that can not ignored. That mass should also create a gravity field which would explain how, for example, the Sun's gravity field can be see to be deflecting the trajectories of incoming photons from distant stars and the move past the rim of the Sun during a total eclipse. That deflection is due to simple gravitational attraction between two masses and has nothing to do with photons moving through warped "space-time" surrounding a massive object like the Sun.

Joseph Stalin9 months agoPc Master race confirmed

ketsuu thebest9 months agowhat is momentiup

Matheus Barreto9 months agoCan someone explain me why V = c (pc/E)?

ErnestoStaccolanana9 months agoI needed a momentum to understand this

Andrew ramirez9 months agoIm confused, if mass is 0 then shouldn't momentum be zero?

Cqsi9 months ago^{+1}Andrew ramirez waves like light, does not have any mass, but momentum ;)

Matthew Palmore9 months ago@minutephysics but for momentum, don't you need mass (p=m*V)? So wouldn't the energy=0 if mass=0?

Marek Basovník9 months agoThe introduction of this video is completely missleading! Equations "E = mc^2" and "E^2 = (mc^2)^2 + (pc)^2" are absolutely the same. The point is that the "m" in equations are not the same. At first eq. E = mc^2, the "m" is a relative mass. Varying due to movement. On the other hand the "m" in second equation is invariant mass. That is the reason why it is commonly written as m_0 anyway. And there is an equation at all: E^2 = (m c^2)^2 = (m_0 c^2)^2 + (p c)^2.

Atharva #breakthrough10 months agobut is p in the triangle = mc or gamma. mc ????

Junhan10 months ago^{+1}He is also speaking with the speed of light

Earth Man10 months ago^{+1}I had been missing the momentum P variable. You helped me shape my understanding of relativity SO MUCH.

Mathew Farry10 months agoThe fundamental parts of the equation are based on the ASSUMPTION that light is the fastest thing possible. If you replace the speed of light with say the speed of sound the equation will try to tell you it's impossible to travel faster than the speed of sound, because your mass will increase exponentially, before you reach it. But that's not right, because we've already traveled faster than the speed of sound. If you assume that the max speed in the universe is 5x the speed of light, the equation will tell you, you can't go faster than 5x the speed of light.... So don't worry if you don't understand it, It's just theory after all.

pibroch7 months agoYou haven't watched the video.

Maldo Gabriel10 months ago^{+1}Science will never be 100% accurate. Don't get me wrong it's useful ofcourse but being 100% with a 100% equation of accuracy is obscurity and with a 15 centimeter average brain size is vanity. Ecclesiastes Chapter 3:11 He hath made everything beautiful in his TIME: also he hath set the world in their heart,so that no man can find out the work that God maketh from the beginning to the end.

Konstantin Voloshin10 months ago1:16 Where does this come from? I don't believe this equation for speed is a common knowledge or somehow else obvious. And it's not cool to explain a physics phenomenon through an equation that came out of nowhere :)

kormannn111 months agoknew something was wrong with this equation!

Bennett Austin11 months agoYou’re a god

Baring Fan Account11 months agoI'm confused, correct me if I'm wrong, but if momentum is dependent on both velocity and mass, then won't no mass result in no energy?

pibroch7 months agoCorrect. But the momentum of something without mass is not dependent on mass.

Aethin11 months agoE=mc^2 wasn’t incomplete when it was first written!

In older notation, “m_0” is rest mass, while just “m” is the so-called relativistic mass (which is gamma*rest mass). That meant that really and truly, E=mc^2 to Einstein, since his m was not our m.

We don’t teach relativistic mass anymore, since it turned out not to be a useful interpretation of the equations. Instead, we’ve thrown the factors of gamma back in explicitly and just gone back to using “m” for the rest mass.

pibroch7 months ago^{+1}E=mc2 is NOT Einstein's equation. He used Eo = mc2 where the subzero denotes rest energy. So the video is incomplete. Einstein's m is our m, and the great man was at pains to warn people not to use relativistic mass, which he quoted as M. You can read about this here:www.hysafe.org/science/KareemChin/PhysicsToday_v42_p31to36.pdf

Joe Clarke11 months agoHow does light have momentum if it had no mass? Me confused

PanosGaming YTTV11 months agoCan't it be E=γmc²?

pibroch7 months agoThat is 100% correct!

'Eternal Optimism...Year agoWhat state of being is "nothing" (made of)?

Simple logic of three apples on an object represent the sum existence of the visible/empirical total. In order to make the object have zero apples on it, (In actuality) any form of reduction cannot cause the apple's existence to no longer be. The form of reduction may re-move the apples from its place, and even reduce its form (when eaten etc.), but cannot invalidate the apple's existence of its new form despite measure of visibility.

Selflessly,

Ps. A basic global fundamental of the number zero (0) as merely a place holder, truly describes the actuality of something as only reduced (in whatever form) from its existing place. What is the all encompassing 1st Cause for all things in existence, but proven with empirical validity of an oxymoron "perfectly infinite" character trait? (before religion or science)

facebook.com/notes/selfless-inc/what-is-nothing-made-of-illogical-contradictions/761347933922592

MF DOOMYear agoYou know Einstein explained this in his relativity theory

꧁Prasoon ꧂Year agoHahaha! You’re funny.

Raina GautamiYear agoAwesome

iamcsxiiYear ago^{+1}Sorry,I’m only ten years old lol

iamcsxiiYear ago^{+1}And C^2 is just the constant of the speed of light,the object doesn’t have to be moving,so in conclusion Albert Einstein’s Equation is correct

Jamie AndersonYear agoE=mc2 is NOT Einstein's equation. He used Eo = mc2 where the subzero denotes rest energy. So the video is incomplete.

iamcsxiiYear ago^{+2}E=mc^2 is about how much energy is in an object,not how much energy it can produce by moving

kingpYear agoOhhhh that's why we have light's energy E=hc/λ

E^2 = (pc)^2+(mc^2)^2

for light it's E=pc and since p = h/λ that's why we have the equation E=hc/λ that we learned in high school

Dj Savic ΦΖΞYear agoWhat is the practical application of

E² = (mc²)² + (pc)² if we already have

E = γmc² ???

Jamie AndersonYear agoThe second equation does not work for objects with no mass - it is incomplete.

Artur ZagraienkoYear agoMath once lead to wrong conclusions about nature.(ultraviolet catastroph) It seems we done mistake again.

Mehul ManianYear agoBut I mean were the ones who made E pc and mc in that triangle so why should it definitively tell us that nothing can go faster than light. This is like assuming Einstein’s equation was a given fact not something we derived and could be false

Mateusz DziewierzYear agoE²=(m[c²])²+(pc)²

A²+b²=[c²]

C²umanati confirmed

Andron SchultzYear agoMy fellow Illuminatirs where are your presence?

Rasmus SuonioYear agoIf side pc gets "crushed that leaves us E²=(mc²)² like mc²=E both of them squared is all right but If m=0 E=0 so pc=0

Rasmus SuonioYear ago^{+1}Or p≠0 but negative momentum doesn't exist.

Rasmus SuonioYear ago^{+1}*if p>0

Rasmus SuonioYear agoYes and of p>0

pibrochYear agoThe video gives E² = (pc)² + (mc²)².

So for objects with no mass like photons, m = 0, then E² = (pc)² or E = pc or E/p = c.

So you are correct. And E/p = c ONLY if an object has no mass.

If an object has mass then you use the full equation E² = (pc)² + (mc²)².

If an object has mass and is not moving then p=0 and E² = (pc)² + (mc²)² becomes E² = (mc²)², or E=mc².

You were wrong when you said "If object's mass is 0 it's momentum is 0!" Something can not have zero mass and zero momentum: then there would be no object. Every object has mass or energy. (Momentum is a type of energy.) If that's what you were trying to say then you are of course correct and you are a very advanced 5th grader! And your English is quite good too for 5th grade , but not good enough yet for me to make sense out of what you are saying about the physics here. Or you are confused about the physics. I don't know which :-)

Rasmus SuonioYear agoI ment at my first comment that the ones with mass doesn't have momentum and E=mc² so E²=(mc²)² and ones without mass are like gravitons or photons so E=pc and E/c=p i ask now from you does E/p=c? in any cases.

ZogurtoolYear ago0:12 everything is squared.

Kapitan BenonYear ago.

AstoundingJBYear agoNice video! Just to improve a bit on the discussion, what you said is the "modern interpretation" of the relativistic energy equation. Now m is the proper mass and is considered an invariant (the mass of the object as measured in its rest reference frame). In this sense, and as you showed, the equation E = mc^2 is not complete in the case of a moving object. Anyway, previously, some textbooks ago, m was the "relativistic mass" equals to gamma*rest_mass, where gamma is the Lorentz factor, depending on the velocity of the particle. Form that the idea that the (relativistic) mass of an object is bigger if it is moving at a certain speed.See here for further details: en.wikipedia.org/wiki/Mass_in_special_relativity#Relativistic_mass

pibrochYear ago^{+1}You make a very interesting point. But relativistic mass isn't a type of mass: it's an energy term, as you no doubt know. Putting brackets around "relativistic" followed by "mass" , like you just did, is incorrect, but I guess you did that just to make your point.

Desert EagleYear agoI am not sure about geometry analogy

pibrochYear agoIt's not a physical analogy, it's just a graphical way of looking at how the mathematics works.

Prajyot SinghYear agoIf it's a massless particle, wouldn't it's momentum be zero hence making it's energy zero

pibrochYear agoNo - p = mv does not define momentum - it is just used as a way of calculating it for slow moving objects which do have mass. The faster the object with mass is moving the less accurate the result.

Tech Master PavitYear agoI hate triangles and especially Pythagoras for this!!!!!!😠😠😠😠😠😠😡😤

Raju MaharjanYear agoGalaxies travel faster than speed of light and you don't compare E,mc^2 and pc to a right angled triangle.

RotYear agoOmg this is so impressive

Hawk EyeYear agoBro if mass is 0

Then how it has momentum

Hanif ShakibaYear agoHawk Eye actually light does have momentum despite its massless, this is calculated by dividing the Planck constant (6.63x10^-34) by the lights wavelength. So p=h/lambda. (Lambda is wavelength) so the momentum of a photon of red light would be (6.63x10^-34)/(7x10^-7)= 9.47x10^-28

Harshit AgrawalYear agobut when m= 0 then how could be P ...coz it's to zero

João Vítor MarcenesYear agoYeah, but isn't p = m • v?

Sazzad HussainYear agoDamn....now i will my whole class with this equation

Aaron WangYear agoNegative Mass

DUB VERSEYear agoHow you make these type of video?

Matt BruceYear agoThis one is one of your best videos! Great work! :)

Medi KönigYear agoWow, brilliant !

Triple A CityYear agoThat is not the case with light and spacetime, but yes if we talk about mass energy

Harsh kumarYear agoCan anyone explain that how can v=C.pc/E

PureLSDYear agoReally good visual explanation of why something with mass cannot go at the speed of light.

Simply CuriousYear agoTo readers browsing the comments, the kinetic energy of an object is (L-1)mc^2 and potential is mc^2, where m is rest mass, and L is the lorentz factor, and when object is at speed v, will give mass n=mL, so the kinetic energy and potential give E=nc^2, so the equation is complete, if one understands m in the equation is the relative mass. The equation E^2=(mc^2)^2 + (pc)^2 is found from finding the momentum four vector,(Pc,iE), dot producting it by itself, giving (P^2)c^2 -E^2, which must be invariant, so at P=0, have -E^2=-(mc^2)^2, which due to invariance(due to the lorentz transformations) means E^2=(mc^2)^2+(pc)^2. So both are right given the context of the variables(or constants).

ahmad faeaz khan deliveredYear agoOHD

Peter ParkerYear ago^{+1}illuminati confirm