# 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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• Science & Technology

• Claudio Costa 19 days ago

Seems interesting!

• BakonKing Month ago

Assume nonzero curvature and go faster than light.

• Laggy Acer Month 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 Month ago

How Momentum is mass times velocity and light has no mass

• Brendan Ha Month ago

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

• William Harvey Month 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 Month 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 Month 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 Month 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 ! 2 months ago

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

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

• Prateek Panwar 2 months ago

Why that bulb is cracked

Admit it, You didn't rechecked the video

• Huzaifa Nihal 3 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 2 months ago

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

• SimonDaBug 3 months ago

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

• Nirvana One 3 months ago

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

• Jerico Reyes 4 months ago

After six years I finally understood this

• KatanaX 4 months ago

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

• KatanaX 4 months ago

Mc2=E

• Abhirup Chattopadhyay 4 months ago

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

• Jamie Anderson 4 months ago +1

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

• Eric Steele 4 months ago

i love this channel

• Kshitij Desai 4 months ago

Isn't momentum mass times velocity

• jimmy alderson 4 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 5 months ago

If mass is zero the momentum will also zero

• Jamie Anderson 4 months ago

Obviously not as all photons have energy.

• Krushna Thakare 5 months ago

What is time ?

• Osu! Autoplays 5 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 , 5 months ago

• Ken Behrendt 5 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 5 months ago

Pc Master race confirmed

• ketsuu thebest 6 months ago

what is momentiup

• Matheus Barreto 6 months ago

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

• ErnestoStaccolanana 6 months ago

I needed a momentum to understand this

• Andrew ramirez 6 months ago

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

• Cqsi 5 months ago +1

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

• Matthew Palmore 6 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 6 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 6 months ago

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

• Junhan 6 months ago +1

He is also speaking with the speed of light

• Earth Man 7 months ago +1

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

• Mathew Farry 7 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 4 months ago

You haven't watched the video.

• Maldo Gabriel 7 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 7 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 7 months ago

knew something was wrong with this equation!

• Bennett Austin 7 months ago

You’re a god

• Baring Fan Account 8 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 4 months ago

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

• Aethin 8 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 4 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 8 months ago

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

• UltimateGaming 9000 8 months ago

Can't it be E=γmc²?

• pibroch 4 months ago

That is 100% correct!

• 'Eternal Optimism... 8 months ago

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.
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)

• MF DOOM 9 months ago

You know Einstein explained this in his relativity theory

• Prashun Raj Dhital 9 months ago

Hahaha! You’re funny.

• Raina Gautami 9 months ago

Awesome

• iamcsxii 9 months ago +1

Sorry,I’m only ten years old lol

• iamcsxii 9 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 Anderson 9 months ago

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

• iamcsxii 9 months ago +2

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

• kingp 9 months 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 9 months ago

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

• Jamie Anderson 9 months ago

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

• Artur Zagraienko 9 months ago

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

• Mehul Manian 9 months 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 9 months ago

E²=(m[c²])²+(pc)²
A²+b²=[c²]
C²umanati confirmed

• Andron Schultz 10 months ago

My fellow Illuminatirs where are your presence?

• Rasmus Suonio 10 months 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 10 months ago +1

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

• Rasmus Suonio 10 months ago +1

*if p>0

• Rasmus Suonio 10 months ago

Yes and of p>0

• pibroch 10 months 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 10 months 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 10 months ago

0:12 everything is squared.

• Kapitan Benon 10 months ago

.

• AstoundingJB 10 months 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 10 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 Eagle 10 months ago

I am not sure about geometry analogy

• pibroch 10 months ago

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

• Prajyot Singh 10 months ago

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

• pibroch 10 months 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 10 months ago

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

• Raju Maharjan 10 months ago

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

• Rot 10 months ago

Omg this is so impressive

• Hawk Eye 10 months ago

Bro if mass is 0
Then how it has momentum

• Hanif Shakiba 10 months 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 10 months ago

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

• João Vítor Costa 10 months ago

Yeah, but isn't p = m • v?

• Sazzad Hussain 10 months ago

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

• Aaron Wang 11 months ago

Negative Mass

• DUB VERSE 11 months ago

How you make these type of video?

• Matt Bruce 11 months ago

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

• Medi König 11 months ago

Wow, brilliant !

• Triple A City 11 months ago

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

• Harsh kumar 11 months ago

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

• PureLSD 11 months ago

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

• Simply Curious 11 months 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).

• OHD

• Peter Parker 11 months ago +1

illuminati confirm

• Triple A City 11 months ago

Oh...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

• pibroch 11 months ago

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

• Jagjit Singh 11 months ago

If photon doesn't have mass how can it have momentum as p=mv

• pibroch 11 months ago

p does not equal mv for a photon so it is not used for a photon.

• Space noodles 11 months ago

because its v is huge

• Full Activity Year 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 Jain Year ago

For those who think p=mc. This is not true.
Here p=h/lambda

• But 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 Jhaveri Year ago

Very nice

• bigseba123 Year ago

wow

• Aaron Wang Year ago +1

Can't that be written as E = mc^2 + pc?

• Max Buskirk Year ago

So the area of the triangle is 0.5mpc^3.... what could this mean?

• Firal Rally Year ago

Sounds relatively simple

• Shane Gary Year ago

Prepare 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 Gary Year ago

E=mc squared+John 14:26= infinity Forever...

• Call_me_kev Year ago

E=mc2 MAYBE the most important equation in the world

• Pedro Year ago

Wait, 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 Das Year ago

You 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

triangles... are every where. doritos fidget spinners doges cats dogs memes and now science.

ILLUMINATI CONFIRMED

• Suby125 Year ago

This was quite the eye-opener. Excellent explanation

• Wizard Perry Year ago

How can momentum exist without mass?

• +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 Goel Year ago

That was unreal , amazing GGG !!!!