When E=mc2 FAILS (because it is incomplete) | Mass-Energy Equivalence in 60 Seconds #shorts

In this #shorts I answered a question about the mass-energy equivalence relation, Einstein's famous equation E=mc2.

The question was that if a photon has no mass, then this equation tells us that it must also have no energy. But a photon is often called a "packet of energy" - so where's the fallacy?

Well as it turns out, the relation E = mc^2 only applies for an object at rest, that has some mass (i.e. m is not equal to zero).

The full equation actually accounts for the (rest) mass of our object being considered, as well as its momentum.

And it turns out that photons do have momentum, despite not having mass. This means that the energy of the photon is not in fact zero!

The full equation (as accurately as I can write it here) looks like this:
E^2 = (mc^2)^2 + (pc)^2, where E is the energy of the object being considered, m is its rest mass, p is its momentum, and c is the speed of light.

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[ParthGChannel]

Hi everyone! Thanks so much for watching :) In response to a question I've seen a few times now, a photon does not have mass but still has momentum because the equation p = mv only applies to an object that has mass in the first place! Photons are particles that do not have any mass, but still display behaviours shown by objects carrying some momentum. For example, in systems with photons in them, the Law of Conservation of Momentum holds perfectly if we account for the photon's behaviour, but fails if we ignore the photon's behaviour. Hope that helps!

[dbz]

I'm a medical student but I was good in physics till high school
So, I love your videoes too much...
It's pretty fun to know about physics this way😊

[DrDeuteron]

Energy is in the eye of the beholder.


(A photon has no rest frame, and hence: energy, momentum, wavelength, frequency...are not properties of _it_ ).

[py]

Reading the comments here I believe the host could have explained a bit more in the video about why photons have momentum without having static mass.

[robertschlesinger]

Very interesting, informative and worthwhile video.

[mohamadalialloush]

Question: what is the real nature of forces, like what they really are( well we know that there is some disturbance in the space, but we need more)

[kamlesh]

In the eq. E=mc², m is not the stationary mass but it is exactly relativistic mass of the object, which is also true for photon

[Prashanth-ynzd]

How can photons have momentum when the mass is zero

[imyasharya]

Wait, it doesn't has mass but has momentum? That's definitely made me go nuts. AFAIK, momentum is mass times velocity, isn't it?

[yourkashii]

P= m.v explain please if phone have m = 0.then p will be zero..🤔🤨

[pasijutaulietuviuesas]

E^2 = (mc^2)^2 + (pc)^2 = (mc^2)^2 + 0 -> E = mc^2.
E^2 = (mc^2)^2 + (pc)^2 = 0 + (pc)^2 -> E = pc.
p = h/λ -> E = hc/λ.
f = c/λ -> E = hf.

That is why when talking about photons, their energy is calculated with E = pc (in terms of momentum) or E = hf (in terms of wave frequency).
Massless particles always travel at c. Anything travelling at less than c has mass.

Massless: E = pc = hf.
Motionless: E = mc^2.
Massive and in motion: E^2 = (mc^2)^2 + (pc)^2.

[nehaka]

Sir, to have momentum of photons, it requires mass because p( momentum)= m(mass) × v (velocity). And you say that photons have momentum.

[shadiwahb]

Isn’t the energy of a photon E=hf or E=hc/λ which would therefore make its rest mass irrelevant in this case. Also if we consider that E=pc then the momentum of a photon, p=E/c and since E=hf=hc/λ then we can say that the momentum, p=hc/λ divided by c which is hc/λc and since the c’s cancel then can we say that the momentum of a photon is given by planks constant divided by the wavelength (h/λ)

[areeba]

Thank you bro I am thinking this for a long time you tell me very easy ☺️

[trueriver]

Actually the word "mass" is used in two ways. The first way is to refer to the rest mass (more pedantically the mass measured in a co-moving inertial frame) and that is the way you use the word in this video

The other use of the word "mass" can be applied to a moving object and includes the mass equivalent of the kinetic energy as well as the rest mass. In this usage, which is quite common in older textbooks, the mass of the photon is entirely that of its kinetic energy. Einstein used "mass" in this sense and his original paper on special relativity gives the formula for the total mass of a moving object as gamma times the rest mass -- so used the word in both senses in the one equation (at least his English version did: sadly I can't read it in German)

The expression "proper mass" means rest mass and usually means that the writer uses "mass" to mean the total mass of the object as observed in motion.

My guess is that the viewer who asked that question has been reading different texts that employ the two distinct usages. It's confusing for the newcomer.

The other odd thing about a photon is that when observed in different inertial frames the same photon has different masses (in the second sense) but as we know is still moving at the same speed. It changes it's kinetic energy without changing either its rest mass or its speed. Newton has just left in dismay...

[shreya]

Hello . Why are the planetary orbits elliptical ? Also, how is gravitational force responsible for revolution ?

[hoofheartedicemelted]

Question. In laser optics the laser wavelengths are measured in "nm". Is there a certain type of laser that would operate as low as 400hz? I'm a noob so my conversions might suck. I'm just asking as you are obviously smarter than me. Thank you for any help sir.

[pandu]

Very good question and answer is seems to be simple but it has a lot of complex and meaning. Hmm interesting🤔

[heavymetalnewsdesk]

The actual explanation is even simpler. E=mc2 is the formula for kinetic energy and means resting mass has no kinetic energy. E is Energy, M is the mass of the object you are calculating. C is the constant speed of the object you are calculating. If m is resting then C=0. so E=500lbs (0 x0) for instance

[jperez]

I have never satisfactorily found an explanation how they constructed the steam tables. If you were the first to do it in the beginning, how did they do it?