# E=mc² is Incomplete

Embed

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

translate.minutephysics.com

MinutePhysics is on Google+ - bit.ly/qzEwc6

And facebook - facebook.com/minutephysics

And twitter - @minutephysics

Minute Physics provides an energetic and entertaining view of old and new problems in physics -- all in a minute!

Music by Nathaniel Schroeder - www.soundcloud.com/drschroeder

Thanks to Nima Doroud and Bruno LeFloch for contributions and to Perimeter Institute for support.

www.perimeterinstitute.ca Created by Henry Reich - Science & Technology

Stuka !2 days agoBut if the objects is massless then momentum is also 0 .-.

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

In the video "Misconceptions in physics"

Prateek Panwar10 days agoWhy that bulb is cracked

Admit it, You didn't rechecked the video

Huzaifa NihalMonth 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???

pibroch13 days agoLight has measurable momentum, so for light, p is not given by the cross product of mass and velocity. Simple.

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

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

Seriously this answers heaps of questions 😎

Jerico Reyes2 months agoAfter six years I finally understood this

KatanaX2 months agoE=mc2=deconstruction. Mc2=e=construction.

KatanaX2 months agoMc2=E

Abhirup Chattopadhyay2 months agoIf mass is zero then p is also zero then how is a photons energy measured

Jamie Anderson2 months ago^{+1}by measuring photon's wavelength which is inversely proportional to its energy

Eric Steele2 months agoi love this channel

Kshitij Desai2 months agoIsn't momentum mass times velocity

jimmy alderson2 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 shrivastav3 months agoIf mass is zero the momentum will also zero

Jamie Anderson2 months agoObviously not as all photons have energy.

Krushna Thakare3 months agoWhat is time ?

Osu! Autoplays3 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 ,3 months agodrive.google.com/file/d/1B0T7wRDzdbaZKn5HjmmzVuh87Z7kVSLD/view?usp=drivesdk

Ken Behrendt3 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 Stalin3 months agoPc Master race confirmed

ketsuu thebest4 months agowhat is momentiup

Matheus Barreto4 months agoCan someone explain me why V = c (pc/E)?

ErnestoStaccolanana4 months agoI needed a momentum to understand this

Andrew ramirez4 months agoIm confused, if mass is 0 then shouldn't momentum be zero?

Cqsi3 months ago^{+1}Andrew ramirez waves like light, does not have any mass, but momentum ;)

Matthew Palmore4 months ago@minutephysics but for momentum, don't you need mass (p=m*V)? So wouldn't the energy=0 if mass=0?

Marek Basovník4 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 #breakthrough4 months agobut is p in the triangle = mc or gamma. mc ????

Junhan4 months ago^{+1}He is also speaking with the speed of light

Earth Man5 months ago^{+1}I had been missing the momentum P variable. You helped me shape my understanding of relativity SO MUCH.

Mathew Farry5 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.

pibroch2 months agoYou haven't watched the video.

Maldo Gabriel5 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 Voloshin5 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 :)

kormannn15 months agoknew something was wrong with this equation!

Bennett Austin5 months agoYou’re a god

Anonymous Unknown6 months agoWhat you did is ..... What u were doing gone over my brains. Dammit. How did u got dat mind

Snikerx Loraina6 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?

pibroch2 months agoCorrect. But the momentum of something without mass is not dependent on mass.

Aethin6 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.

pibroch2 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 Clarke6 months agoHow does light have momentum if it had no mass? Me confused

UltimateGaming 90006 months agoCan't it be E=γmc²?

pibroch2 months agoThat is 100% correct!

'Eternal Optimism...6 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 DOOM7 months agoYou know Einstein explained this in his relativity theory

Prashun Raj Dhital7 months agoHahaha! You’re funny.

Raina Gautami7 months agoAwesome

iamcsxii7 months ago^{+1}Sorry,I’m only ten years old lol

iamcsxii7 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 Anderson7 months agoE=mc2 is NOT Einstein's equation. He used Eo = mc2 where the subzero denotes rest energy. So the video is incomplete.

iamcsxii7 months ago^{+2}E=mc^2 is about how much energy is in an object,not how much energy it can produce by moving

kingp7 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 ΦΖΞ7 months agoWhat is the practical application of

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

E = γmc² ???

Jamie Anderson7 months agoThe second equation does not work for objects with no mass - it is incomplete.

Artur Zagraienko7 months agoMath once lead to wrong conclusions about nature.(ultraviolet catastroph) It seems we done mistake again.

Mehul Manian7 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 Dziewierz7 months agoE²=(m[c²])²+(pc)²

A²+b²=[c²]

C²umanati confirmed

Andron Schultz8 months agoMy fellow Illuminatirs where are your presence?

Rasmus Suonio8 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 Suonio8 months ago^{+1}Or p≠0 but negative momentum doesn't exist.

Rasmus Suonio8 months ago^{+1}*if p>0

Rasmus Suonio8 months agoYes and of p>0

pibroch8 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 Suonio8 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.

Zogurtool8 months ago0:12 everything is squared.

Kapitan Benon8 months ago.

AstoundingJB8 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

pibroch8 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 Eagle8 months agoI am not sure about geometry analogy

pibroch8 months agoIt's not a physical analogy, it's just a graphical way of looking at how the mathematics works.

Prajyot Singh8 months agoIf it's a massless particle, wouldn't it's momentum be zero hence making it's energy zero

pibroch8 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 Pavit8 months agoI hate triangles and especially Pythagoras for this!!!!!!😠😠😠😠😠😠😡😤

Raju Maharjan8 months agoGalaxies travel faster than speed of light and you don't compare E,mc^2 and pc to a right angled triangle.

Rot8 months agoOmg this is so impressive

Hawk Eye8 months agoBro if mass is 0

Then how it has momentum

Hanif Shakiba8 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 Agrawal8 months agobut when m= 0 then how could be P ...coz it's to zero

João Vítor Costa8 months agoYeah, but isn't p = m • v?

Sazzad Hussain8 months agoDamn....now i will my whole class with this equation

Aaron Wang9 months agoNegative Mass

DUB VERSE9 months agoHow you make these type of video?

Matt Bruce9 months agoThis one is one of your best videos! Great work! :)

Medi König9 months agoWow, brilliant !

Triple A City9 months agoThat is not the case with light and spacetime, but yes if we talk about mass energy

Harsh kumar9 months agoCan anyone explain that how can v=C.pc/E

PureLSD9 months agoReally good visual explanation of why something with mass cannot go at the speed of light.

Simply Curious9 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).

top movie clips delivered9 months agoOHD

God Slave9 months ago^{+1}illuminati confirm

Triple A City9 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

pibroch9 months agoIf an object has no mass its mass energy will always be zero, won't it?

Riddhiman Dutta9 months agoit shouldn't have been incomplete but its what einstein described in imaginary case ... but we need to modify that formula for real case...

pibroch9 months agoNot so. The equation is Einstein's formula for the energy of a stationary body at rest, but missing the subzero next to the "E" to indicate rest energy. It is a misquote of Einstein's equation. It is only incomplete if E represents total energy.

Jagjit Singh9 months agoIf photon doesn't have mass how can it have momentum as p=mv

pibroch9 months agop does not equal mv for a photon so it is not used for a photon.

Space noodles9 months agobecause its v is huge

Full Activity10 months 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 Jain10 months agoFor those who think p=mc. This is not true.

Here p=h/lambda

Chandrakant Kushwaha10 months 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 Jhaveri10 months agoVery nice

bigseba12310 months agowow

Aaron Wang10 months ago^{+1}Can't that be written as E = mc^2 + pc?

Max Buskirk10 months agoSo the area of the triangle is 0.5mpc^3.... what could this mean?

Firal Rally10 months agoSounds relatively simple

Shane Gary10 months 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 Gary10 months agoE=mc squared+John 14:26= infinity Forever...

Call_me_kev10 months agoE=mc2 MAYBE the most important equation in the world

Pedro10 months 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 Das10 months 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 Cookies10 months agotriangles... are every where. doritos fidget spinners doges cats dogs memes and now science.

ILLUMINATI CONFIRMED

Suby12510 months agoThis was quite the eye-opener. Excellent explanation

Wizard Perry11 months agoHow can momentum exist without mass?

Тенелбай Макытов11 months 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

CJR2916 #7466-02811 months agoThat was unreal , amazing GGG !!!!

Brilliant academy11 months agoIf in case of light E=PC and P=mv then E=0 if m=0

how is this possible?

Jamie Anderson10 months agoIt's not possible. For a photon P = h/λ (not mv).

Adarsh Vinesh Karan11 months agoHow is v=c x( pc/E)

Zogurtool11 months agoAmazing explaintion

Nicolas Cacace11 months agoWhy is Energy = Mass x Speed of Light squared?

I understand that the Units and Magnitude work BUT Why c^2 (c x c)? What does it mean in relation to time space?

Titanic11 months agoE = BORING