Parth G | The Most Famous Equation In the World Is INCOMPLETE! E=mc2 Explained by Parth G @ParthGChannel | Uploaded 2 years ago | Updated 1 hour ago
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.
en.wikipedia.org/wiki/Mass%E2%80%93energy_equivalence
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Many of you have asked about the stuff I use to make my videos, so I'm posting some affiliate links here! I make a small commission if you make a purchase through these links.
A Quantum Physics Book I Enjoy: https://amzn.to/3sxLlgL
My Camera (Sony A6400): https://amzn.to/2SjZzWq
ND Filter: https://amzn.to/3qoGwHk
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Gorillapod Tripod: https://amzn.to/3wQ0L2Q
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
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.
en.wikipedia.org/wiki/Mass%E2%80%93energy_equivalence
Thanks so much for watching - please do check out my socials here:
Instagram - @parthvlogs
Patreon - patreon.com/parthg
Music Chanel - Parth G's Shenanigans
Merch - https://parth-gs-merch-stand.creator-spring.com/
Many of you have asked about the stuff I use to make my videos, so I'm posting some affiliate links here! I make a small commission if you make a purchase through these links.
A Quantum Physics Book I Enjoy: https://amzn.to/3sxLlgL
My Camera (Sony A6400): https://amzn.to/2SjZzWq
ND Filter: https://amzn.to/3qoGwHk
Microphone and Stand (Fifine): https://amzn.to/2OwyWvt
Gorillapod Tripod: https://amzn.to/3wQ0L2Q
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
