# 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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Claudio Costa19 days agoSeems interesting!

BakonKingMonth agoAssume nonzero curvature and go faster than light.

Laggy AcerMonth 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 sinhaMonth agoHow Momentum is mass times velocity and light has no mass

Brendan HaMonth agoI had to make this video go at .75x speed because it’s going pretty fast

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

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

Mark SusskindMonth 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 SusskindMonth 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 !2 months agoBut if the objects is massless then momentum is also 0 .-.

0bada2 months agoYou've said in another video that light has mass.

In the video "Misconceptions in physics"

Prateek Panwar2 months agoWhy that bulb is cracked

Admit it, You didn't rechecked the video

Huzaifa Nihal3 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???

pibroch2 months agoLight has measurable momentum, so for light, p is not given by the cross product of mass and velocity. Simple.

SimonDaBug3 months ago1:08 that makes so much sense because electrons have almost no mass, and they move in waves!

Nirvana One3 months agoI guess the ancient Egyptians worked this out with their pyramids lol

Seriously this answers heaps of questions 😎

Jerico Reyes4 months agoAfter six years I finally understood this

KatanaX4 months agoE=mc2=deconstruction. Mc2=e=construction.

KatanaX4 months agoMc2=E

Abhirup Chattopadhyay4 months agoIf mass is zero then p is also zero then how is a photons energy measured

Jamie Anderson4 months ago^{+1}by measuring photon's wavelength which is inversely proportional to its energy

Eric Steele4 months agoi love this channel

Kshitij Desai4 months agoIsn't momentum mass times velocity

jimmy alderson4 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 shrivastav5 months agoIf mass is zero the momentum will also zero

Jamie Anderson4 months agoObviously not as all photons have energy.

Krushna Thakare5 months agoWhat is time ?

Osu! Autoplays5 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 ,5 months agodrive.google.com/file/d/1B0T7wRDzdbaZKn5HjmmzVuh87Z7kVSLD/view?usp=drivesdk

Ken Behrendt5 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 Stalin5 months agoPc Master race confirmed

ketsuu thebest6 months agowhat is momentiup

Matheus Barreto6 months agoCan someone explain me why V = c (pc/E)?

ErnestoStaccolanana6 months agoI needed a momentum to understand this

Andrew ramirez6 months agoIm confused, if mass is 0 then shouldn't momentum be zero?

Cqsi5 months ago^{+1}Andrew ramirez waves like light, does not have any mass, but momentum ;)

Matthew Palmore6 months ago@minutephysics but for momentum, don't you need mass (p=m*V)? So wouldn't the energy=0 if mass=0?

Marek Basovník6 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 #breakthrough6 months agobut is p in the triangle = mc or gamma. mc ????

Junhan6 months ago^{+1}He is also speaking with the speed of light

Earth Man7 months ago^{+1}I had been missing the momentum P variable. You helped me shape my understanding of relativity SO MUCH.

Mathew Farry7 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.

pibroch4 months agoYou haven't watched the video.

Maldo Gabriel7 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 Voloshin7 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 :)

kormannn17 months agoknew something was wrong with this equation!

Bennett Austin7 months agoYou’re a god

Baring Fan Account8 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?

pibroch4 months agoCorrect. But the momentum of something without mass is not dependent on mass.

Aethin8 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.

pibroch4 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 Clarke8 months agoHow does light have momentum if it had no mass? Me confused

UltimateGaming 90008 months agoCan't it be E=γmc²?

pibroch4 months agoThat is 100% correct!

'Eternal Optimism...8 months 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 DOOM9 months agoYou know Einstein explained this in his relativity theory

Prashun Raj Dhital9 months agoHahaha! You’re funny.

Raina Gautami9 months agoAwesome

iamcsxii9 months ago^{+1}Sorry,I’m only ten years old lol

iamcsxii9 months 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 Anderson9 months agoE=mc2 is NOT Einstein's equation. He used Eo = mc2 where the subzero denotes rest energy. So the video is incomplete.

iamcsxii9 months ago^{+2}E=mc^2 is about how much energy is in an object,not how much energy it can produce by moving

kingp9 months 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 ΦΖΞ9 months agoWhat is the practical application of

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

E = γmc² ???

Jamie Anderson9 months agoThe second equation does not work for objects with no mass - it is incomplete.

Artur Zagraienko9 months agoMath once lead to wrong conclusions about nature.(ultraviolet catastroph) It seems we done mistake again.

Mehul Manian9 months 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 Dziewierz9 months agoE²=(m[c²])²+(pc)²

A²+b²=[c²]

C²umanati confirmed

Andron Schultz10 months agoMy fellow Illuminatirs where are your presence?

Rasmus Suonio10 months 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 Suonio10 months ago^{+1}Or p≠0 but negative momentum doesn't exist.

Rasmus Suonio10 months ago^{+1}*if p>0

Rasmus Suonio10 months agoYes and of p>0

pibroch10 months 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 Suonio10 months 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.

Zogurtool10 months ago0:12 everything is squared.

Kapitan Benon10 months ago.

AstoundingJB10 months 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

pibroch10 months 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 Eagle10 months agoI am not sure about geometry analogy

pibroch10 months agoIt's not a physical analogy, it's just a graphical way of looking at how the mathematics works.

Prajyot Singh10 months agoIf it's a massless particle, wouldn't it's momentum be zero hence making it's energy zero

pibroch10 months 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 Pavit10 months agoI hate triangles and especially Pythagoras for this!!!!!!😠😠😠😠😠😠😡😤

Raju Maharjan10 months agoGalaxies travel faster than speed of light and you don't compare E,mc^2 and pc to a right angled triangle.

Rot10 months agoOmg this is so impressive

Hawk Eye10 months agoBro if mass is 0

Then how it has momentum

Hanif Shakiba10 months 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 Agrawal10 months agobut when m= 0 then how could be P ...coz it's to zero

João Vítor Costa10 months agoYeah, but isn't p = m • v?

Sazzad Hussain10 months agoDamn....now i will my whole class with this equation

Aaron Wang11 months agoNegative Mass

DUB VERSE11 months agoHow you make these type of video?

Matt Bruce11 months agoThis one is one of your best videos! Great work! :)

Medi König11 months agoWow, brilliant !

Triple A City11 months agoThat is not the case with light and spacetime, but yes if we talk about mass energy

Harsh kumar11 months agoCan anyone explain that how can v=C.pc/E

PureLSD11 months agoReally good visual explanation of why something with mass cannot go at the speed of light.

Simply Curious11 months 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 delivered11 months agoOHD

Peter Parker11 months ago^{+1}illuminati confirm

Triple A City11 months agoOh...No, that triange represents that a hypotenuse can never be equal to base until the perpencular side is zero. But until an object has mass, the mass-energy (mc²) will never be zero so momentum can never be directly converted to energy without mass-energy unless we are talking about photons

pibroch11 months agoIf an object has no mass its mass energy will always be zero, won't it?

Jagjit Singh11 months agoIf photon doesn't have mass how can it have momentum as p=mv

pibroch11 months agop does not equal mv for a photon so it is not used for a photon.

Space noodles11 months agobecause its v is huge

Full ActivityYear ago^{+1}Which means that as long as we have a mass, we can never reach the speed of light. But does that indicate that if you have a negative mass you could go faster than speed of light? Maybe theoretical but the equations tell that negative mass square still ends up as positive, therefore not faster than c.

Sagar JainYear agoFor those who think p=mc. This is not true.

Here p=h/lambda

Chandrakant KushwahaYear agoBut when you put e=mc^2 as an equation in a right triangle and reduce the value of m to 0,the 'p' also gets reduce to 0 and you are only left with 'E' and don't get 'pc', also, you shouldn't get energy as you took m=0 so no mass is being converted into energy

Nirav JhaveriYear agoVery nice

bigseba123Year agowow

Aaron WangYear ago^{+1}Can't that be written as E = mc^2 + pc?

Max BuskirkYear agoSo the area of the triangle is 0.5mpc^3.... what could this mean?

Firal RallyYear agoSounds relatively simple

Shane GaryYear agoPrepare the Way for the Messiah, He will Pray to the Father for Us to have the Spirit of God, for a Teacher, and Comforter Forever, in the Bible book of John, chapter 14, verse 26... John chapters 14, 15, and 16, are Spiritual Rebirth Chapters... Peace

Shane GaryYear agoE=mc squared+John 14:26= infinity Forever...

Call_me_kevYear agoE=mc2 MAYBE the most important equation in the world

PedroYear agoWait, but isn’t the linear momentum of a particle proporcional to its mass? So if the particle has no mass it has no Kinect energy?

Rajani DasYear agoYou said something about mass less objects. But isn't P= mv?

Thus if the object has no mass then it has no momentum and thus it has no energy.

As E= pc

=> E=0*c=0

George CookiesYear agotriangles... are every where. doritos fidget spinners doges cats dogs memes and now science.

ILLUMINATI CONFIRMED

Suby125Year agoThis was quite the eye-opener. Excellent explanation

Wizard PerryYear agoHow can momentum exist without mass?

Тенелбай МакытовYear ago+minutephysics

Corrclty

(E^2)=(((m*(c^2))^2)+((c)^2))

For small mass about,for big mass wrong

E=c

For big mass about,for small mass wrong

E=m*(c^2)

If get energy(E)-total energy,first energy-mass energy(m*(c^2)) and second energy-light speed(c).

Can not total energy less than first or second energy.Second energy light speed have,then total energy less than energy light speed this is a wrong.

E

Manav GoelYear agoThat was unreal , amazing GGG !!!!