E=mc² is Incomplete

  • Published on Oct 28, 2012
  • You've heard of E=mc²... but you probably haven't heard the whole story.
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    www.perimeterinstitute.ca Created by Henry Reich
  • Science & TechnologyScience & Technology

Comments • 8 922

  • froop
    froop 2 days ago

    right to the point 👏

  • Barry Bunt
    Barry Bunt 2 days ago

    wait 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 Suman
    Simon Suman 4 days ago


  • An Keyri
    An Keyri 11 days ago

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

  • movies now Naik
    movies now Naik 15 days ago

    What happens if both the mass and Momentum is zero

  • jr2013 junior
    jr2013 junior 17 days ago

    The 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 Farooq
    Ummer Farooq 26 days ago

    Where's the lambda?

    STILL NOT CLICKED Month 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 meneses

    Damn you Pitágoras and trigonometrie!!!😅

  • Matthew Lui
    Matthew Lui Month ago

    Trigonometry is everywhere

  • Jerry Yuan
    Jerry Yuan Month ago

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

  • Wait Beat Drops
    Wait Beat Drops Month ago

    I love da bass

  • Prabhu Akash
    Prabhu Akash Month ago

    Don't consider a triangle

  • Gaming Champ
    Gaming Champ Month ago

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

  • Zach Petch
    Zach Petch 2 months ago

    Holy balls.

  • guy rubin
    guy rubin 2 months ago

    it explains SOOOO MUUUUUCH

  • supercombo 20x 68hit lựu đạn nổ

    An object moving at the speed of light produces heat and a decrease in mass

  • David Wilson
    David Wilson 2 months ago

    I'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?

  • Mortonator
    Mortonator 2 months ago

    wait. But isn't P=MC?
    wouldn't that make
    equal to
    which is
    simplified to
    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 Giov
    Apo Giov 2 months ago

    A 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 Costa
    Claudio Costa 3 months ago

    Seems interesting!

  • BakonKing
    BakonKing 4 months ago

    Assume nonzero curvature and go faster than light.

  • Laggy Acer
    Laggy Acer 4 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 sinha
    Bhavesh sinha 4 months ago

    How Momentum is mass times velocity and light has no mass

  • Ordinary Knife
    Ordinary Knife 4 months ago

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

  • William Harvey
    William Harvey 4 months ago

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

  • Mark Susskind
    Mark Susskind 4 months ago

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

    • Mark Susskind
      Mark Susskind 4 months ago

      If 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 Susskind
      Mark Susskind 4 months ago

      OK 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 !
    Stuka ! 5 months ago

    But if the objects is massless then momentum is also 0 .-.

  • 0bada
    0bada 5 months ago

    You've said in another video that light has mass.
    In the video "Misconceptions in physics"

  • Prateek Panwar
    Prateek Panwar 5 months ago

    Why that bulb is cracked

    Admit it, You didn't rechecked the video

  • Huzaifa Nihal
    Huzaifa Nihal 6 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???

    • pibroch
      pibroch 5 months ago

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

  • SimonDaBug
    SimonDaBug 6 months ago

    1:08 that makes so much sense because electrons have almost no mass, and they move in waves!

  • Nirvana One
    Nirvana One 6 months ago

    I guess the ancient Egyptians worked this out with their pyramids lol
    Seriously this answers heaps of questions 😎

  • J
    J 7 months ago

    After six years I finally understood this

  • KatanaX
    KatanaX 7 months ago

    E=mc2=deconstruction. Mc2=e=construction.

  • KatanaX
    KatanaX 7 months ago


  • Miachel De santa
    Miachel De santa 7 months ago

    If mass is zero then p is also zero then how is a photons energy measured

    • Jamie Anderson
      Jamie Anderson 7 months ago +1

      by measuring photon's wavelength which is inversely proportional to its energy

  • Eric Steele
    Eric Steele 7 months ago

    i love this channel

  • Kshitij Desai
    Kshitij Desai 7 months ago

    Isn't momentum mass times velocity

  • jimmy alderson
    jimmy alderson 8 months ago

    What 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 shrivastav
    Varun shrivastav 8 months ago

    If mass is zero the momentum will also zero

    • Jamie Anderson
      Jamie Anderson 7 months ago

      Obviously not as all photons have energy.

  • Krushna Thakare
    Krushna Thakare 8 months ago

    What is time ?

  • ItzJake Roblox
    ItzJake Roblox 8 months ago

    Wait 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 ,
    sauronfupoc , 8 months ago


  • Ken Behrendt
    Ken Behrendt 9 months ago

    Actually, 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 Stalin
    Joseph Stalin 9 months ago

    Pc Master race confirmed

  • ketsuu thebest
    ketsuu thebest 9 months ago

    what is momentiup

  • Matheus Barreto
    Matheus Barreto 9 months ago

    Can someone explain me why V = c (pc/E)?

  • ErnestoStaccolanana
    ErnestoStaccolanana 9 months ago

    I needed a momentum to understand this

  • Andrew ramirez
    Andrew ramirez 9 months ago

    Im confused, if mass is 0 then shouldn't momentum be zero?

    • Cqsi
      Cqsi 9 months ago +1

      Andrew ramirez waves like light, does not have any mass, but momentum ;)

  • Matthew Palmore
    Matthew Palmore 9 months ago

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

  • Marek Basovník
    Marek Basovník 9 months ago

    The 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 #breakthrough
    Atharva #breakthrough 10 months ago

    but is p in the triangle = mc or gamma. mc ????

  • Junhan
    Junhan 10 months ago +1

    He is also speaking with the speed of light

  • Earth Man
    Earth Man 10 months ago +1

    I had been missing the momentum P variable. You helped me shape my understanding of relativity SO MUCH.

  • Mathew Farry
    Mathew Farry 10 months ago

    The 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.

    • pibroch
      pibroch 7 months ago

      You haven't watched the video.

  • Maldo Gabriel
    Maldo Gabriel 10 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 Voloshin
    Konstantin Voloshin 10 months ago

    1:16 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 :)

  • kormannn1
    kormannn1 11 months ago

    knew something was wrong with this equation!

  • Bennett Austin
    Bennett Austin 11 months ago

    You’re a god

  • Baring Fan Account
    Baring Fan Account 11 months ago

    I'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?

    • pibroch
      pibroch 7 months ago

      Correct. But the momentum of something without mass is not dependent on mass.

  • Aethin
    Aethin 11 months ago

    E=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.

    • pibroch
      pibroch 7 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 Clarke
    Joe Clarke 11 months ago

    How does light have momentum if it had no mass? Me confused

  • PanosGaming YTTV
    PanosGaming YTTV 11 months ago

    Can't it be E=γmc²?

    • pibroch
      pibroch 7 months ago

      That is 100% correct!

  • 'Eternal Optimism...

    What 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.
    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)

    MF DOOM Year ago

    You know Einstein explained this in his relativity theory

  • ꧁Prasoon ꧂
    ꧁Prasoon ꧂ Year ago

    Hahaha! You’re funny.

  • Raina Gautami
    Raina Gautami Year ago


  • iamcsxii
    iamcsxii Year ago +1

    Sorry,I’m only ten years old lol

  • iamcsxii
    iamcsxii Year 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 Anderson
      Jamie Anderson Year ago

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

  • iamcsxii
    iamcsxii Year ago +2

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

  • kingp
    kingp Year ago

    Ohhhh 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 ΦΖΞ
    Dj Savic ΦΖΞ Year ago

    What is the practical application of
    E² = (mc²)² + (pc)² if we already have
    E = γmc² ???

    • Jamie Anderson
      Jamie Anderson Year ago

      The second equation does not work for objects with no mass - it is incomplete.

  • Artur Zagraienko
    Artur Zagraienko Year ago

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

  • Mehul Manian
    Mehul Manian Year ago

    But 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 Dziewierz

    C²umanati confirmed

  • Andron Schultz
    Andron Schultz Year ago

    My fellow Illuminatirs where are your presence?

  • Rasmus Suonio
    Rasmus Suonio Year ago

    If 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 Suonio
      Rasmus Suonio Year ago +1

      Or p≠0 but negative momentum doesn't exist.

    • Rasmus Suonio
      Rasmus Suonio Year ago +1

      *if p>0

    • Rasmus Suonio
      Rasmus Suonio Year ago

      Yes and of p>0

    • pibroch
      pibroch Year ago

      The 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 Suonio
      Rasmus Suonio Year ago

      I 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.

  • Zogurtool
    Zogurtool Year ago

    0:12 everything is squared.

  • Kapitan Benon
    Kapitan Benon Year ago


  • AstoundingJB
    AstoundingJB Year ago

    Nice 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

    • pibroch
      pibroch Year 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 Eagle
    Desert Eagle Year ago

    I am not sure about geometry analogy

    • pibroch
      pibroch Year ago

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

  • Prajyot Singh
    Prajyot Singh Year ago

    If it's a massless particle, wouldn't it's momentum be zero hence making it's energy zero

    • pibroch
      pibroch Year ago

      No - 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 Pavit

    I hate triangles and especially Pythagoras for this!!!!!!😠😠😠😠😠😠😡😤

  • Raju Maharjan
    Raju Maharjan Year ago

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

  • Rot
    Rot Year ago

    Omg this is so impressive

  • Hawk Eye
    Hawk Eye Year ago

    Bro if mass is 0
    Then how it has momentum

    • Hanif Shakiba
      Hanif Shakiba Year ago

      Hawk 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 Agrawal
    Harshit Agrawal Year ago

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

  • João Vítor Marcenes

    Yeah, but isn't p = m • v?

  • Sazzad Hussain
    Sazzad Hussain Year ago

    Damn....now i will my whole class with this equation

  • Aaron Wang
    Aaron Wang Year ago

    Negative Mass

    DUB VERSE Year ago

    How you make these type of video?

  • Matt Bruce
    Matt Bruce Year ago

    This one is one of your best videos! Great work! :)

  • Medi König
    Medi König Year ago

    Wow, brilliant !

  • Triple A City
    Triple A City Year ago

    That is not the case with light and spacetime, but yes if we talk about mass energy

  • Harsh kumar
    Harsh kumar Year ago

    Can anyone explain that how can v=C.pc/E

  • PureLSD
    PureLSD Year ago

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

  • Simply Curious
    Simply Curious Year ago

    To 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).

  • Peter Parker
    Peter Parker Year ago +1

    illuminati confirm