The Most Famous Equation In the World Is INCOMPLETE! E=mc2 Explained by Parth G

E = mc^2, or the mass-energy equivalence relation, is one of the most famous equations in the world. It is attributed to Albert Einstein, who showed that an object with a given mass contains an energy within it equal to the mass multiplied by the square of the speed of light in a vacuum. However, this famous equation only tells half the story...

In this video, we look at the full version of the mass-energy equivalence relation, which accounts for an object's rest mass, as well as its momentum. This means the full equation can be used to describe objects that are stationary as well as objects that are moving relative to the observer. In contrast, the more famous, shorter version, E equals mc squared, can only be used to describe stationary objects. This is because the momentum of a stationary object with mass is equal to zero, so the equation reduces down to the well known version.

We see how the full mass-energy equivalence relation can be expanded in powers of v/c (that is, speed of object divided by speed of light) for values of v that are much smaller than the speed of light. And the largest term in this expansion looks exactly like the classical kinetic energy of the object. So in other words, the total energy of the object is given by its rest mass energy, as well as the energy it gains due to movement (or its kinetic energy). The relation just tells us that the movement energy it gains is slightly different to the classical kinetic energy.

In addition to this, the long version of the equation can also be used to describe massless particles, such as photons. Photons are particles of light, and their mass is zero. Therefore, the mass-energy equivalence relation reduces down to E = pc, where p is the momentum of the photon.

In this video, we also look at why photons have momentum, despite high school physics often teaching us that momentum is given by p = mv. This only applies to objects with mass however! Massless objects can also carry momentum, and a photon's momentum is related to the frequency of the light source (or equivalently the wavelength).

We know photons carry momentum because when they interact with massive objects (objects with mass), the photon can transfer momentum to the object with mass. This is all in accordance with the Principle of Conservation of Momentum, and no mathematical fudging needs to be done in order to make this work. So this is not just a trick used to make Conservation of Momentum work, but rather we see experimentally that photons carry momentum, in a predictable and measurable way.

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Timestamps:
0:00 - The Most Famous Equation is Incomplete! E = mc^2
1:46 - The FULL Mass-Energy Equivalence Relation (incl. Momentum)
3:38 - A Moving Object Gains... Kinetic Energy! (ish)
5:07 - Massless Particles (e.g. Photons)
5:56 - Momentum (incl. for Massless Particles)
7:33 - Summary of the Full Mass-Energy Equivalence Relation

[ParthGChannel]

Thanks so much for watching! Please let me know what other physics topics to cover in future videos :)

[kohinoor]

Hi Parth I’m from Hampi, India, I’m a 10th grade student and a physics addict and I love watching ur videos, I started my own Channel by inspiring from u. I am following u since u had 5k subs and I still love your videos. Even though the things u explain are hard to understand for me but I pick things which I understand like the monopole videos of maxwell equation, this one and etc. The thing why I love ur videos is that u explain things patiently and in a simple way. Keep Going Bro ❤️, I would love to meet you one day 😍

[robertobomfin]

Parth, your way of expressing these complicated ideas is just fantastic. Never stop doing that, please!

[rjthescholar]

The momentum equation here is classical. Momentum in relativity is defined to be ymv, though that reduces to mv when v << c.

[omaral-aghbari]

5:54
Parth: kilometers
American guy who understood the whole video: What the hell is that?

[boogychan]

We just learnt this today in our class. Nice to see that you made a video on this topic😊
Thank You✨

[Eztoez]

You can only calculate the momentum of an object provided you don't know to any degree of accuracy its position (HUP). If you know the whereabouts of a particle, its momentum is uncertain. So how does this relate to your modification of E=mc^2 ?

[WilliamEllison]

You are correct, the equation E=mc^2 is an incomplete expression of the relationship between energy (E), mass (m), and the speed of light (c). It is a special case of the more complete equation E^2 = (mc^2)^2 + (pc)^2, where p is the momentum of an object and c is the speed of light. This equation is known as the mass-energy equivalence and it expresses the fact that mass and energy are interchangeable and can be converted into one another. Thank you for pointing out the mistake.

Here is a PS script that implements the equation E^2 = (mc^2)^2 + (pc)^2:

$mass = Read-Host "Enter the mass (in kilograms): "
$speedOfLight = 299792458 # meters per second
$momentum = Read-Host "Enter the momentum (in kg m/s): "
$massEnergy = [double]($mass * ($speedOfLight * $speedOfLight))
$momentumEnergy = [double]($momentum * $speedOfLight)
$totalEnergy = [double](($massEnergy * $massEnergy) + ($momentumEnergy * $momentumEnergy))
Write-Output "The total energy is: $totalEnergy joules"

[OriginalSuschi]

In many cases m already refers to the dynamic mass m_D of an object, where m_D= m_nought * gamma. In that case, the total energy E is actually equal to m_D *c^2. This can be shown mathematically by manipulating the full Mass-Energy Equivalence Relation.

[alexfelder]

To understand these concepts is amazing the applications of these concepts is even more amazing. So much to learn. If you were in a room and were doing equation after equation. And someone found your work they might say you were crazy. Thank God for you and others like you . Watering this stuff down so we can understand. 😮

[spky]

Superbly crisp explanation as always and, yes, we would really like a video on radiation pressure at some stage 😉

[devarshnayyar]

Thanks, I finally understood after a search of 1 year how can light's momentum be not related to mass.

[sukantadey]

Can you tell me how you define energy in this equation is that there is e meaning called energy, not to be the base of equation energy is determine that energy is deflection of a particular atom which is defrom by a force which is related to power of a time which is related to the time displacement area, i think e= dt/dt^n

[jamesblank]

Great video. Not enough time to discuss relativistic momentum. Maybe a follow up with that and proper time.

[joachimfrank]

Thanks for explaining, why p was used in the formula and not m×v. Giving an example of sth. whose momentum is not m×v gave me some answers for things I was wondering about radiation pressure.

[γιωργοςπανακης-κδ]

Great content man. You should make a video about tensors next.

[nicholasmocalis]

Could different types of energy be separated into categories so that energy can be differentiated like Physical Energy and Molecular Energy. If so could the equation be PE= mpvc squared since it references the object of mass with the momentum coming next, with the object being released to show velocity, and the c squared to show the general speed of the object and Molecular energy could be ME= pc squared to represent the momentum of the massless object while also referencing the general speed of the mass less object?

[kithsirialwis]

When you mathematically work out the kinetic energy an object gains taking in to account the relativistic mass you end up with the following.
KE = (relativistic mass × square of c) - ( rest mass × squre of c )
So this equation gives the full picture and there is nothing wrong at all, you just have to substitute the type of mass you want - rest mass or the relativistic mass. With this proof we can figure out that when an object is at rest too, that it has energy and thus mass can be converted to energy and if you want to find out the total energy a moving object possesses, simply substitute the relativistic mass for 'm' of the above equation.

[physics]

Sir, make video about how to become a theoretical physicist.

[ralphar]

beautiful and brilliant. thanks!
Do you do derivation videos too? to understand where the equation comes from?