E=mc² is Incomplete

[@DrumsTheWord]

I need a good reminder occasionally just why geometry can be so useful in mathematics. Thanks for this!

[@coderamen666]

Wait until you see what general relativity is!

[@l0b5terlick55]

To think the whole reason we can't go at the speed of light is because of triangles. Screw you trigonometry.

[@drioustb9182]

+L0b5terlick luminarty comfirm

[@threeatenu62d3]

+Drious TB it is Illuminati

[@flawlesspiner1674]

+L0b5terlick XD How was that even trig?

[@SuHAibLOL]

Because Trigonometry is the study of triangles, typically right, and the functions derived from it, giving models for harmonic motion and billions of other stupid applications?

[@flawlesspiner1674]

sato But were sine, cosine, or tangent (ratio) even involved?

[@nightman365]

That triangle example made great sense. Thanks

[@crappyspidersucksthemost]

And why he took E as Hypotenuse?

[@oreowithurea5018]

@@crappyspidersucksthemost because the original equation is E² = (mc²)² + (pc)². Resembling the Pythagorean theorem where a² = b² + c², a = hypotenuse

[@ChannelTwentyTwo]

@@oreowithurea5018 just because a formula resembles the format a² = b² + c² we automatically take the discussion to a triangle approach simply because we know about pythagoras. But it's kind of an artibtrary decision for analysis right? My physics is not too sharp but is it more appropriate to say something like (mc²) and (pc) are simply vectors that are perpendicular? I don't know just a random thought.

[@Narvalo_Lastar]

​@@ChannelTwentyTwoI don't understand what describing it this way implies, using a triangle is just a kind graph of the equation

[@frankdimeglio8216]

​@@ChannelTwentyTwoThe stars AND PLANETS are POINTS in the night sky ON BALANCE. SO, consider WHAT IS the Moon !! SO, WHAT IS THE MOON will (and does) move away very, very, very slightly in relation to what is THE EARTH/ground. WHAT IS E=MC2 is the reason why what are OBJECTS may fall at the SAME RATE. Great. WHAT IS E=MC2 is taken directly from F=ma, AS gravity/acceleration involves BALANCED inertia/INERTIAL RESISTANCE; AS the rotation of WHAT IS THE MOON matches the revolution. Consider what is THE EYE ON BALANCE. (BALANCE AND completeness go hand in hand.) TIME is NECESSARILY possible/potential AND actual ON/IN BALANCE, AS ELECTROMAGNETISM/energy is CLEARLY AND NECESSARILY proven to be gravity (ON/IN BALANCE) !!!! Great. CLEARLY, ON BALANCE, I have proven WHAT IS the FOURTH dimension. (Again, BALANCE AND completeness go hand in hand.) Consider what is complete combustion AND WHAT IS E=MC2. CLEARLY (ON BALANCE), I have solved WHAT IS the coronal heating “problem”; AS ELECTROMAGNETISM/energy is CLEARLY AND NECESSARILY proven to be gravity (ON/IN BALANCE); AS TIME is NECESSARILY possible/potential AND actual ON/IN BALANCE !!! Great !!! By Frank Martin DiMeglio

[@eskewroberts7663]

THIS ANSWERS SO MANY QUESTIONNNNNSSSSSSS

[@mossab7136]

ikr

[@bejoysen4468]

It creates so many more though. Like why do photons have momentum and why don't I know shit about physics?

[@aogt1692]

Ive looked at some other sources and they say other variations for what E=MC*2 should be! Im still no closer to finding the legitimate answer

[@frede1905]

Bejoy Sen The momentum of a photon is p=h/a, where h is Planck's constant and a is the wavelength of the photon.

[@Shell-wr5ie]

Ikr

[@screamingiraffe]

The best "Why mass can't reach the speed of light " video I've seen so far. Nice work! A+

[@firstforfun]

Mass can reach the speed of light but not the mass we are use to ,the ONLY mass that can do it is the 0,000000000000001kg mass ,the quantum mass ,the mass that in the equation E=mc^2 (for light) its discarded because it is practically zero, but in reality it is not totally 0, if something exist in space-time always need to have mass,but in light is very very low at quantum level, it must have mass but in this case it is absurdly small, did you understand now?

[@chetopuffs]

First- For-Fun Source?

[@firstforfun]

@@chetopuffs all around of you,every thing you see and dont even see have mass,so everything that exist have mass

[@chetopuffs]

First- For-Fun Are you saying that a photon has mass? I mean really all I see are photons. Where did you learn this factoid? Can you define “Quantum mass”?

[@firstforfun]

@@chetopuffs yes i can ,quantum mass is the mass in the 0,0000000001 kg scale ,but have mass , everything have mass

[@Heeknot]

If we want to travel the speed of light we must kill all the triangles. It's simple people.

[@Strobeltproductions]

That would kill either all energy in the universe, all "stuff" in the universe, or all movement in the universe. Sorry, count me out.

[@Strobeltproductions]

***** Pffffft

[@samistarck6619]

Illuminati

[@Strobeltproductions]

Melon Crystal I delight in not knowing what this ever-popular term means.

[@gustavgnoettgen]

Perfectly balanced as everything should be

[@mybluemars]

So E=MC squared is also related to a right triangle? Arrgghh,, can't seem to get away from Pythagoras!

[@derPatte26]

And more! When our teachers back then in school said: You'll gonna need that the rest of your life! And you go like... Whatever! Sure triangles yes, ever single day! Keep talking blabla.... HE WAS RIGHT! DAMN IT! 🤬

[@spetsnatzlegion3366]

Pythagoras is the dominatrix that whips you with theory once you think the pain of physics is finally over

[@crappyspidersucksthemost]

Triangles explains everything! And why he took E as Hypotenuse instead of base or altitude? I Just Couldn't understand the logic behind comparing the formula to Pythagoras theorem!

[@hareecionelson5875]

@@crappyspidersucksthemost E^2 = (mc^2)^2 + (pc)^2 This does not necessarily mean Energy is the physical hypotenuse of a right angle triangle with a base and height, But it's useful to think of it that way, so we do. And maybe Energy is a hypotenuse of some cosmic triangle. It wouldn't be the strangest idea in science

[@ChannelTwentyTwo]

@@hareecionelson5875 as soon as we find an equation that resembles c^2 = a^2 + b^2, we automatically think in terms of triangles. but is it more appropriate to say that (mc^2) and (pc) are simply perpendicular vectors and that's why it works?

[@kapilesh14]

I am not going to lie this was probably the only video so far which I didn't have to watch twice to understand. I am an average intelligence guy with a little interest in Science but Henry nailed it for me in this video.

[@ThePCguy17]

damn right triangles. I will now prove them obsolete.

[@RandomDays906]

Yeah, go make those right triangles, wrong triangles! Now I'm waiting for ViHart to step in and say something about triangles.

[@DigGil3]

Dominic Boggio ThePCguy17 Buckminster Fuller would tell you that right triangles don't really exist in the real world and are rather special cases of the intersection of three circles that run across the surface of the Earth and which the result of these intersections is very tiny such as to make negligible that fact that the sum of their inner angles is larger than 180 degrees,

[@ThePCguy17]

DigGil3 And he would be unfortunately spouting thechnobabble (or would it be mathnobabble?) that doesn't actually have reasoning in it. I meant actually having a step by step proof. Or inventing a warp drive's power cell and bypassing the whole light speed problem.

[@DigGil3]

I thought you meant geometry... Sorry, the department for gravity-electromagnetism theory unification is next doors.

[@MusicalInquisit]

That is a cute joke.

[@earthman4222]

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

[@oncebittentwiceshy639]

I wonder, can we have "negative" mass ? Something that weights less than zero should pass light speed. Yes, I know - it sounds silly. Maybe I should go to bed . . . .

[@comediac92]

assuming that negative mass can exist, that would be similar to adding a minus sign to the mc^2 part of the equation, since the full equation is E=(mc^2)^2 + (pc)^2, this would translate to E=(-mc^2)^2 + (pc)^2. Since a negative number squared is a positive number, the object would still not be able to pass light speed

[@MichaelMeridius]

No, put simply you can't travel F.T.L. as you would require an infinite amount of energy regardless of your "negative mass". Objects with mass would not only need an infinite amount of energy but your mass would also increase exponentially. Your mass would be almost universally massive and this can never happen!

[@Lighthammer18]

Kate Hoover Einstein's equation suggests that we can have negative mass matter and also negative energies. Often called exotic matter-energy. However we haven't found any proof of negative matter, but the Casimir effect seems to produce some sort of negative energy, and from negative energy we could theoretically create matter with negative mass. This negative matter (Stretching to sci-fi here) could potentially be used to stabilize a worm hole, so it might be very important for space travel in the future.

[@MichaelMeridius]

Lighthammer18 I agree with the Casimir - Polder force (research) effect being demonstrably real and accurate, and a surprize to many scientists. It seems counter-intuitive that "empty" space (vacuum) is actually teeming with energy/particles popping in and out of our physical space time. This especially makes me laugh when creationists and the religious claim that "everything must have a cause and effect or something can't come from nothing" You picked a sound example that not only educates but also makes me laugh :) PS your "Sci-fi hypothesis" needs a bit of work though LOL ;0) I also think my site to site transporter technology (star-trek) needs more string and sticky tape as the Heisenberg compensators are playing up again !

[@ChrisYoungEntertains]

comediac Could you, hypothetically, have a particle with an imaginary mass (i.e. a multiple or fraction of i, the square root of -1), thereby solving the squaring to positive problem?

[@AlonTako]

dafuq dude i just understood so much in 2 minutes i might collapse into myself

[@Marconius6]

Pretty good explanation, and I love the animation you used too! My only complaint is you use the word "mass", I would have liked at least a passing mention of the fact this is "invariant mass" (which light doesn't have), as opposed to relativistic mass.

[@chadb2840]

I can suggest an equation that has the potential to impact the future: E = mc^2 + AI This equation combines Einstein's famous equation E=mc^2, which relates energy (E) to mass (m) and the speed of light (c), with the addition of AI (Artificial Intelligence). By including AI in the equation, it symbolizes the increasing role of artificial intelligence in shaping and transforming our future. This equation highlights the potential for AI to unlock new forms of energy, enhance scientific discoveries, and revolutionize various fields such as healthcare, transportation, and technology.

[@chadb2840]

What

[@notafeesh4138]

Was looking for this comment!

[@joshhummel1284]

that just blew my nerdy little mind

[@BananaNeil]

So, E=(mC^2)^2 + pC^2, and because with photons, m = 0, therefore E=PC^2, excellent. But P (momentum) = mV.... but m is still 0. so E is still 0. WTF physics?

[@Schmidt975]

BananaNeil p=m*v is only valid for classical (that is: slower than 0.1*c) particles.For light, for instance: p=h*f

[@LeconsdAnalyse]

***** You mean p=h/λ.

[@Schmidt975]

LeconsdAnalyse Oh yea, sorry ... I intuitively typed the energy of the photon instead of its momentum ;) Thanks for the correction :)

[@LeconsdAnalyse]

***** Do you mean lambda?

[@palella9910]

Umm... I may sound stupid, But using the equation, E^2=(mc^2)^2+(pc)^2, if you have that triangle, lets say that pc=d, and d=1/2 the speed of light, So and energy is= to k(k is a variable) and mass= t, then if you multiply d times 2, the speed of light, then the hypotenuse would grow(energy), but the energy would not equal infinity because the Energy to get to half the speed of light is not infinite, and you can't have 1/2 of infinity, because 1/2 of infinity is, well, infinity. So, everything in the universe, no matter what speed, takes an infinite amount of energy. To make it easier to understand, here: ~2.01k=mass + c(the speed of light). But, this doesn't make any sense, because infinity is unreachable, so in theory nothing in the Universe with mass can move! someone please help me understand this! sorry if I did a terrible job explaining it.

[@Fino260]

My mind has been blown today ! I was doing my physics exercices during a physic lesson, and to solve one, I did some calculations and other integrals. (took me some time) And guess what ? I found E^2 = (mc^2)^2 + (pc)^2 ! The funny part is that as I wrote E = (p^2c^2 + m^2c^4)^1/2 I did not realize immediately that it was the exact same formula as I had seen in this video for ages !

[@noahevans]

math is definitely math

[@chek49people]

herp derp that is science

[@noahevans]

are you inferring that science is not based on math?

[@Fino260]

herp derp Of course not ! Science is based on experiments, that is all ! Maths are only here to let us read the results.

[@dinul117]

Fino260 lol but then what's the point of the experiment if not to draw a conclusion from it via math?

[@clarenceho625]

thank you, finally an explanation that makes sense and doesn't end with "just because"

[@TayChinghern]

oh......I have no idea of what this wizard is saying

[@fairylightsarepretty6391]

ChingHern Tay me too but i don't know what e=mc2 even mean yet sighh

[@masood-msd2570]

Fairy lights are pretty HOW?!

[@tripleacity2284]

ChingHern Tay 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

[@softlysnowing3959]

ITs sImPLe. E(3) - pos(2, y, pc^2) is equal to the hypotenuse, times the quantum field of π^ω, plus the constant 4.378896458112134254601928717472..., ^ 8, if 4 > 3ba, ± 0.00000000000013. I hope you realized this was a joke.

[@disharai10tha41]

means if object is not moving we calculate its enery witn e mc2 formula if object have no mass like light than we calculate energy by e pc2 formula simple 😃

[@voidmain2453]

Best explanation I've seen!

[@iiiiitsmagreta1240]

It never fails to amaze me how everything in math and science just *works*. Like, the same principles that apply to trigonometry and measuring triangles also explain why we can't exceed the speed of light. Just, think about that.

[@nicsteyn1456]

Can someone please explain how photons have energy at all then? If momentum is equal to an objects mass * velocity (p=mv) then doesn't something that has no mass have no momentum? [EDIT: read down a little further and saw explanations for my first question] Also, if I remember correctly don't photons have an insanely tiny tiny amount of mass? Does this mean that even photons don't travel at the speed of light - or am I interpreting it entirely wrong?

[@ThisIsTaco1]

+Nic Steyn As far as I'm concerned, photons only have mass when they're not moving (because E=mc^2). That's why they behave like particles when they come into contact with objects, but behave like EM Waves when they move.

[@AmoryYomar]

+Nic Steyn Photons do NOT have mass at all. they also travel at the speed of light. HOWEVER photons DO have momentum. Their momentum is quite different than objects with mass as it's proportional to their frequency ( frequency of the light wave)and not to their mass. Overall the equation to calculate the momentum of a photon is different than that of objects with mass. There are 2 momentum equations used to calculate momentum, one is for mass-less particles and one is for particles with mass

[@nathanneiman]

First we need to state that this is a theory. According to Einstein a photon don't have mass but carry momentum. My understanding is that light is a wave and the photon a wave packet, not a real particle. If we abolish Einstein's postulate then photon can have mass, but we can't forget that light is a wave in a medium. So the mass is created when the electromagnetic energy goes through the medium.

[@Koray2013]

+Nic Steyn Photons have mass. That means they have energy. But because Photons only exist at lightspeed, they dont have an acceleration, despite their mass.

[@nathanneiman]

We can apply E=mc2 to photon to calculate a mass, but as I said before this contradicts Einstein's postulate. Supposing an existing structure in vacuum (Ether), the Electromagnetic energy integrating with the structure could give rise to what we call mass. In this way we can explain the momentum, otherwise is magic. Is important to note that light is only the undulation in the medium, not the mass, as well sound is the undulation in the air, so sound don't have mass. The distinction must be made between light as wave and photon as particle.

[@MatthewVandeputte]

Fuck me this is amazing

[@shlovaski8393]

exactly what part struck u most?

[@lancewedor5306]

Thanks for the offer!

[@TradeMyWish]

I never cared about this stuff but now I think is amazing all the sudden.

[@cloroxbleachfraganzia4126]

Okay. Give me your address.

[@JawadBhuiyan]

No problem... Turn around and bend over...

[@Michaelonyoutub]

This is the best explanation I have ever heard for e=mc^2. It makes so much sense now

[@SamirHabibTheKing]

Newton be like I KNEW IT, I TOTALLY KNEW IT

[@Theo_Caro]

Everyone: Shut up, Newton. No you didn't. You were too busy trying to be an alchemist!

[@frankdimeglio8216]

Gravity AND ELECTROMAGNETISM/energy are linked AND BALANCED opposites, AS E=mc2 is F=ma; AS ELECTROMAGNETISM/ENERGY IS GRAVITY. Gravity/acceleration involves BALANCED inertia/INERTIAL RESISTANCE, AS E=MC2 IS F=ma; AS ELECTROMAGNETISM/ENERGY IS GRAVITY. A PHOTON may be placed at the center of what is the Sun (as A POINT, of course), AS the reduction of SPACE is offset by (or BALANCED with) the speed of light (c); AS E=MC2 IS F=MA; AS ELECTROMAGNETISM/energy is gravity. The stars AND PLANETS are POINTS in the night sky. The ultimate unification of physics/physical experience combines, BALANCES, AND INCLUDES opposites. E=mc2 IS F=ma. This necessarily represents, INVOLVES, AND DESCRIBES what is possible/potential AND actual IN BALANCE. Gravity IS ELECTROMAGNETISM/energy. GREAT !!! GRAVITATIONAL force/ENERGY IS proportional to (or BALANCED with/AS) inertia/INERTIAL RESISTANCE, AS ELECTROMAGNETISM/energy is gravity; AS E=mc2 is F=ma IN BALANCE. BALANCE and completeness go hand in hand. It ALL CLEARLY makes perfect sense. By Frank DiMeglio

[@frankdimeglio8216]

@@Theo_Caro Gravity AND ELECTROMAGNETISM/energy are linked AND BALANCED opposites, AS E=mc2 is F=ma; AS ELECTROMAGNETISM/ENERGY IS GRAVITY. Gravity/acceleration involves BALANCED inertia/INERTIAL RESISTANCE, AS E=MC2 IS F=ma; AS ELECTROMAGNETISM/ENERGY IS GRAVITY. A PHOTON may be placed at the center of what is the Sun (as A POINT, of course), AS the reduction of SPACE is offset by (or BALANCED with) the speed of light (c); AS E=MC2 IS F=MA; AS ELECTROMAGNETISM/energy is gravity. The stars AND PLANETS are POINTS in the night sky. The ultimate unification of physics/physical experience combines, BALANCES, AND INCLUDES opposites. E=mc2 IS F=ma. This necessarily represents, INVOLVES, AND DESCRIBES what is possible/potential AND actual IN BALANCE. Gravity IS ELECTROMAGNETISM/energy. GREAT !!! GRAVITATIONAL force/ENERGY IS proportional to (or BALANCED with/AS) inertia/INERTIAL RESISTANCE, AS ELECTROMAGNETISM/energy is gravity; AS E=mc2 is F=ma IN BALANCE. BALANCE and completeness go hand in hand. It ALL CLEARLY makes perfect sense. By Frank DiMeglio

[@niklaspilot]

This is awesome! So you CAN actually describe complicated physics with basic mathematics.... :D WIN!!!

[@frankdimeglio8216]

ABSOLUTE MATHEMATICAL PROOF THAT ELECTROMAGNETISM/ENERGY IS GRAVITY: Time DILATION proves that ELECTROMAGNETISM/ENERGY IS GRAVITY, AS E=mc2 is DIRECTLY AND FUNDAMENTALLY DERIVED FROM F=ma. Einstein's equations are NECESSARILY QUANTUM GRAVITATIONAL, AS ELECTROMAGNETISM/ENERGY IS GRAVITY. In fact, the mathematical unification of Maxwell's equations AND Einstein's equations (given the addition of a fourth spatial dimension) proves that ALL of SPACE is NECESSARILY electromagnetic/gravitational IN BALANCE; AS E=mc2 is DIRECTLY AND FUNDAMENTALLY DERIVED FROM F=ma; AS time DILATION proves that ELECTROMAGNETISM/ENERGY IS GRAVITY. ACCORDINGLY, Einstein's equations predict that SPACE is expanding OR contracting in and with time. ALL of SPACE is NECESSARILY electromagnetic/gravitational IN BALANCE, AS ELECTROMAGNETISM/ENERGY IS GRAVITY. This is, in fact, CLEARLY proven by BOTH F=ma AND E=mc2. A PHOTON may be placed at the center of THE SUN (as A POINT, of course), AS the reduction of SPACE is offset by (or BALANCED with) the SPEED OF LIGHT; AS ELECTROMAGNETISM/ENERGY IS GRAVITY. (Very importantly, outer "space" involves full inertia; AND it is fully invisible AND black.) Gravity AND ELECTROMAGNETISM/ENERGY are linked AND BALANCED IN AND OUT of SPACE AND TIME, as this is CLEARLY proven by time DILATION, F=ma, AND E=mc2. This ALSO explains the cosmological redshift AND the "black hole(s)". Gravity/acceleration involves BALANCED inertia/INERTIAL RESISTANCE, AS ELECTROMAGNETISM/ENERGY IS GRAVITY. GRAVITATIONAL force/ENERGY IS proportional to (or BALANCED with/as) inertia/INERTIAL RESISTANCE, AS ELECTROMAGNETISM/ENERGY IS GRAVITY. "Mass"/ENERGY involves BALANCED inertia/INERTIAL RESISTANCE consistent with/AS what is BALANCED electromagnetic/gravitational force/ENERGY, AS ELECTROMAGNETISM/ENERGY IS GRAVITY. (Energy has/involves GRAVITY, AND ENERGY has/involves inertia/INERTIAL RESISTANCE.) ACCORDINGLY, FULL DISTANCE in/of SPACE, MIDDLE DISTANCE in/of SPACE, AND A POINT are all then in BALANCE; AS ELECTROMAGNETISM/ENERGY IS GRAVITY. Gravity IS ELECTROMAGNETISM/ENERGY. GREAT !!! This NECESSARILY represents, INVOLVES, and describes what is possible/potential AND actual IN BALANCE. Therefore, I have demonstrated the true mathematical UNIFICATION of physics/physical experience AS what is NECESSARILY electromagnetic/gravitational IN BALANCE; AS ELECTROMAGNETISM/ENERGY IS GRAVITY. By Frank DiMeglio

[@physicslover4951]

@@frankdimeglio8216 tldr

[@PoolPartyGuy]

1+1=2 is the most famous :/

[@maxwellsequation4887]

True

[@richardwilliam7140]

0 doesn’t exist is the real deal 😂😂😂

[@Patriotic_Hindu]

E in E = mC² stands for REST MASS ENERGY (E) Which literally describes that the momentum is zero because the object isn't moving

[@codyroth9387]

wait, I know I must be overlooking something, but isn't (translational) momentum "p" given by p=mv, where m is mass (v is velocity)? So therefore a massless particle has 0 momentum, regardless of velocity, and also as a result (according to the video) 0 energy? I know there must be a reason why this deduction is wrong, but what is that reason?

[@bliffity2692]

Your profile picture is not something that should be talking about complex physics.

[@codyroth9387]

Bliffity Translational momentum and basic talk of Energy is not complex physics. Fluid dynamics or quantum mechanics, on the other hand, is. I am also a Physics major, judging me by my profile picture is a pretty unintelligible way to make assertions about someone.

[@bliffity2692]

***** First of all I use the term complex lightly, and second of all I'm pointing out something doing something that does not correspond to what it appears to be which is a form of humor. It doesn't hold up if you look into it, but it's a joke. You're not supposed to look deeply into jokes. My comment is meant only for someone to glance at, think, "Oh, that's a bit funny," and forget about the next day.

[@pibroch]

Cody Roth, here's a copy of my recent answer on this page to a similar question, in case you have trouble navigating to it on your device: Momentum is not mass times velocity - that's what lead to your confusion. Mass times velocity is just a useful approximation for CALCULATING momentum for an object possessing mass that is moving slowly relative to c (the speed of light in a vacuum) - it doesn't DEFINE momentum. So it's completely useless even as an approximation for calculating the momentum of a photon, because a photon has no mass. Photons have measurable momentum: for example in Compton Scattering a photon, which is like a packet of kinetic energy, interacts with an electron which gains some of the energy of the photon. The first photon disappears and a new photon with less kinetic energy (longer wavelength) is created and emitted at an angle such that the total momentum of the system is the same as before the interaction - conservation of momentum. So the lesson for today: mathematical equations are invented to conform to our measurements of the natural world in terms of making successful predictions, not the other way round. If an equation doesn't make a good enough prediction for a particular scenario it's dumped. (And as far as we know it's possible that nothing in the natural world is governed by equations - we've no way of finding out - just because we can use an equation to make a prediction obviously doesn't mean the event being studied was in any way caused by the equation!)

[@codyroth9387]

Bliffity Alright, I see your humorous intent.

[@hanifrizki8130]

i dont even understand.... but i like it

[@ceilingphansandidealbands2590]

Same. I have a friend that thinks I'm so smart that when I was watching this she was like ugh I wonder if this would make since if I were you. I didn't have any idea what he meant either tho so...

[@johng7410]

Well you've sort of got 3 things at play here. Roughly speaking: * Energy is mass * Massless things (can) move at the speed of light * Mass stops you from going as fast as light. The formula is the math, but the concepts are more interesting. Essentially it means massless photons - the bits of light; and hypothetically gluons could travel at the speed of light. If you have any mass at all, then no light speed for you! Gluons get screwed here because gluons always travel with friends. Think of Gluons as usain bolt walking with a fat friend. And then the whole energy mass equivalence. It just means if you, say, burn wood you get fire. Mass of log - > heat. It's the science of three concepts.

[@killedinthezone1]

great explanation

[@InSiDeRLaLaLa]

indeed

[@mycelium9629]

30th like!

[@kevinpaulsen6103]

But isn’t momentum dependent on mass? Is the equation not E^2=(mc^2)^2+(mvc)^2? Because momentum = mass * velocity?

[@pibroch]

you've just demonstrated that you can have momentum without mass - well done

[@oreowithurea5018]

That's in Newtonian physics. Momentum has like 10 different definitions or formulas based on what branch of physics you're dealing with. In relativity, there is no fix time so we cannot apply classical formula

[@ianmacmillan6744]

Easily one of the best videos I've seen on U-Tube

[@Scripterrific]

mc vs pc? Sounds like an Apple commercial.

[@squibble311]

Mc² has to team up w/ pc to make E. top 10 anime plot twists

[@shrishsatheesh3274]

@@squibble311 any good anime recommendations?

[@squibble311]

@@shrishsatheesh3274 i have one dont

[@rodrocket712]

To all the guys asking questions in the comments. This is quite advanced stuff. Google it and look at reputable sources

[@rodrocket712]

Complicated for people with my level of education in these matters, I am just going doing my GCSE equivalent exams, so yeah, complicated for me, maybe not so for you. Had an interest in this stuff since I was 5.

[@AlchemistOfNirnroot]

+CxC_personal I'm doing my A Levels (final year) and only now have we touched E-mc^2, not the complete version either. And the hardest maths we do in physics is just rearranging exponential equations (not hard).

[@AlchemistOfNirnroot]

+CxC_personal e.g Q=Qe^-t/RC, e just means exponential and describes how the charge (Q) falls of exponentially with time. This is to do with capacitors, a component in a circuit used to store charge (Energy), but over time it will tend to zero. That's what the equation means, the R is the resistance and the C is the capacitance.

[@vleesevlons]

+LeconsdAnalyse They make the mistake at p

[@chaosjacky]

Does this mean, that any other matter with no mass (what is there apart from photons of light btw ?), travels at the speed of light ?

[@albertzhang5699]

Yes, the speed of light isn't just the speed of light, it should be called "The Speed of Massless Particles".

[@chaosjacky]

Albert Zhang And do you know any other massless matter than photons of light ?

[@allenjunge4127]

***** Well there are tachyons that way have a negative mass(?) and there are neutrinos that are massless.

[@albertzhang5699]

Allen Junge No, but if they did they would.

[@MrWorshipMe]

Allen Junge Neutrinos are not believed to be massless, since the only explanation for their flavor oscillations is that they have mass... although their mass was never measured, and is very very small (smaller than 1/500000 times that of an electron).

[@lancelovecraft5913]

I first saw this prior to taking any university physics class and now I am about to graduate college. I come back to this year after year because of the simple yet beautiful explanation

[@onebeets]

theory: einstein was just a really advanced 5th-grader

[@wasd2333]

E² = (mc²)² + (pc)² or Energy squared equals (mass times speed of light in vaccum squared) squared plus (momentum x speed of light in vaccum) squared is the new E = mc² which was Energy equals mass x speed of light in vaccum squared.

[@squibble311]

whats the purpose of the comment

[@frankdimeglio8216]

Gravity AND ELECTROMAGNETISM/energy are linked AND BALANCED opposites, AS E=mc2 is F=ma; AS ELECTROMAGNETISM/ENERGY IS GRAVITY. Gravity/acceleration involves BALANCED inertia/INERTIAL RESISTANCE, AS E=MC2 IS F=ma; AS ELECTROMAGNETISM/ENERGY IS GRAVITY. A PHOTON may be placed at the center of what is the Sun (as A POINT, of course), AS the reduction of SPACE is offset by (or BALANCED with) the speed of light (c); AS E=MC2 IS F=MA; AS ELECTROMAGNETISM/energy is gravity. The stars AND PLANETS are POINTS in the night sky. The ultimate unification of physics/physical experience combines, BALANCES, AND INCLUDES opposites. E=mc2 IS F=ma. This necessarily represents, INVOLVES, AND DESCRIBES what is possible/potential AND actual IN BALANCE. Gravity IS ELECTROMAGNETISM/energy. GREAT !!! GRAVITATIONAL force/ENERGY IS proportional to (or BALANCED with/AS) inertia/INERTIAL RESISTANCE, AS ELECTROMAGNETISM/energy is gravity; AS E=mc2 is F=ma IN BALANCE. BALANCE and completeness go hand in hand. It ALL CLEARLY makes perfect sense. By Frank DiMeglio

[@anthonydelille100]

Thanks for uploading this video. I never understood how fotons were able to move at the speed of light or even to move at all, but this makes a lot of sense. :-)

[@anthonydelille100]

Oh, now I just dicovered momentum = m.v If a foton has no mass, it also has no momentum at all and follwing, no energy. Is that even possible, if it's able to produce light? Can someone give me an answer please?

[@Pantopam]

light has a different equation for momentum, it's p=hf I think where h is Planck's constant and f is the frequency (1/wavelength)

[@anthonydelille100]

Allright, thnx :-)

[@mohammedalnafjan]

Pantopam I guess E=hf not p=hf

[@anthonydelille100]

E = h.f, p = h/lambda. f = 1/T, not 1/lamda

[@gustavgnoettgen]

This is the best mathematics I have ever seen on this equation. Great job, thanks!

[@spiderous]

Hey! Momentum = mass * velocity. When mass = 0 then p = 0* x = 0 so wtf with E = pc?

[@MichaelFoskett2]

+Interferencyjny You can't just use classical knowledge like p=mv for problems like this. The relativistic dispersion relation E^2 = (mc^2)^2+(pc)^2 is part of a bigger picture of special relativity that superseeds Newtonian dynamics (which is regained in the limiting case). So you have to take this new formula as like an axiom.

[@spiderous]

Oh, that's interesting. I've thought momentum is dependent on mass. Thank you for response. :)

[@UpcomingAssassin]

+Michael Foskett Not really an axiom, because it implies that it isn't proven and you just have to accept it. Unlike General Theory of Relativity, which is... you know... proven :P

[@MichaelFoskett2]

+UpcomingAssassin point taken 😅

[@SmartreviewDe]

+Michael Foskett p=mc² where m is relativistic mass and therefore never 0

[@chicopluma]

finally someone that explain's why things can't move at speed of light in terms I can comprehend

[@jshariff786]

If a physicist (or physics teacher) is ever saying "just because", they're not much of a physicist. The whole point of the science is to be able to explain results like this in terms of fundamental principles. That raises the question, where do the fundamental principles come from? Ans: from Experiment. So that's the point at which we need to fall back on "just because." But it's "just because so far every single bit of observational data ever collected throughout history points to this principle being true in nature." And soon as we get a datum that contradicts it, we'll begin to question it.

[@noanoxan]

Mind was properly blown away by triangles, once again. Fucking triangles.

[@TealJosh]

Yeah, trigonometry (my weakest spot in math) keeps pounding me to the ground over and over... **sigh**

[@oderalon]

-You were going to give a lecture on physics. You talked about poetry. -Poetry, physics, same thing. :)

[@alifbatah]

Is there anything proven to be faster than light?

[@bellabandgirl9641]

I dont think anything with mass can move the same velocety as light, but i think they proved that wrong in a video i saw, idk tbh haha

[@alifbatah]

BellaBandgirl I know that a nuetrino contains mass and could possibly go 2 x faster than the speed of light but the problem is they are proving immensely difficult to detect, so for now it can't be proven. I really want new age technology which would help us detect new things.

[@KambEight]

If something were proven to go faster than light, it would disprove a lot of modern physics. There was an erroneous experiment a while ago which seemed to suggest that neutrinos could do it, but it was later proved wrong.

[@BillyCLeWorth]

alifbatah Yes . Reading the last page of a book first thus knowing the outcome before the beginning . That is the only analogy I can readily come up with .

[@JackCodeKid]

Darkness

[@kovanovsky2233]

but isn't the equation for momentum is mass x velocity ?

[@niniiii981]

thats exactly what i tought

[@LeconsdAnalyse]

Yes. From the time of Leibniz and "vis-viva", and of course, Newton. And (linear) momentum has, as you already know, units of mv which can also be written as mv²/v, which is units of energy divided by units of speed. So, any object which has a physical attribute with these (more general) units is said to have (linear) momentum.

[@kovanovsky2233]

hmm, so if momentum is also Energy divided by speed, the momentum of light is Energy of light divided by speed of light? I looked up wikipedia that Energy of light (photon energy) is equal to Planck constant * speed of light / light's waveleght. Then momentum = planck constant * c / lambda / c which c cancels out and we left with momentum = planck constant / lambda is this correct ?

[@DoctorYammy]

+Kovanovsky Momentum is the energy an objects must have to remain in motion once it starts moving. What you described at the end was simply a mathematical equation describing the energy the light wave must have to remain moving

[@kovanovsky2233]

Doctor Yammy umm, so... is that a correct? is what I stated there momentum of light? or is it something similar but different? or am I missing something? I am just confused how to calculate momentum of light since light has no mass (as far as I know) and momentum equation is mass x velocity thanks for the replies though

[@kiritokun101]

thank god we dont have to learn this in school

[@76Eliam]

Depending on your country. I learned it in school, even if the complete equation was only used in the introduction before being simplified to E=mc²

[@TehBestOtaku]

You do if you take a physics class.

[@ericcartmann]

you learn it second year physics. In my school its in grade 12. Its really not that hard btw.

[@matthewwroblewski8752]

Introductory calc. (or maybe even just algebra depending on what you're trying to do) would be more than enough to work with an equation like E^2 = (mc^2)^2 + (pc)^2. I mean, MinutePhysics did a pretty good job of explaining it with just the Pythagorean theorem. BUT, knowing how to simply work exponents in E^2 = (mc^2)^2 + (pc)^2 and knowing (understanding) all of the physical implications of E=mc^2 is an entirely different ball of wax.

[@Edgewalker001]

You never had to learn trigonometry and physics? What kind of crappy school did you go to? XD Trigonometry is like the most useful aspect of math past multiplication for everyday use.

[@_Xeto]

To anyone who believes that triangles are the reason we can’t reach the speed of light, you are wrong. The triangle in the video is used as a visual analogy to explain energy, since the expression of the energy looks so much like the pythagorean theorem. But it doesn’t stem from any triangle, nor does it have any secret connection to any. The triangle just happens to behave in the same way, and it’s convenient to use it to show that you can’t quite reach the speed of light, if you have the tiniest amount of mass.

[@derekxiaoEvanescentBliss]

This doesn't exactly explain the "why" you can go at the speed of light but rather a math trick that physicists establish to demonstrate the concept lol

[@chivaswwe]

It's not a "math trick", its a math model which is the same as any other things that you'll find studying physics!

[@LeconsdAnalyse]

chivaswwe It's neither math trick nor math model, but actually a mnemonic.

[@frontierbrainanabel5070]

derek xiao What's your profile?

[@derekxiaoEvanescentBliss]

Konata Chan like as a student? Or like what is my profile picture

[@jamescuttell1333]

How can you have momentum and no mass? I was taught momentum is mass * velocity

[@philo-]

LeconsdAnalyse Thanks for that explanation, as I'm a student I'm going to watch some of your videos

[@pibroch]

How can you have momentum and no mass if you were taught momentum is mass * velocity? The answer is that what you were taught doesn't apply to objects with no mass! Countless experiments show that light has momentum and countless measurements show that light has no measurable mass. For a photon (which has no mass), momentum = Planck Constant/wavelength of the light. Also, "momentum = mass * velocity" is an approximation and doesn't work for objects approaching the speed of light. For an object with mass, linear momentum = mass * velocity/ sqrt(1- velocity²/speed of light²) BTW, in the video as well as in this reply, "mass" means the Newtonian concept of mass, which does not change with velocity. That is also what physicists mean when they use the term mass. ("Relativistic mass" is an energy term that is often confused with "mass" - for this reason it seems to be on the way out, and even Einstein recommended not using it when teaching physics. Particle physicists never refer to relativistic mass.)

[@DANversusWTP]

Most of the formulas you are taught in high school are not the whole truth.

[@lucianodsb]

James Cuttell, there's an experiment to notice that: turn the light on then feel the light pushing you back! Just kidding. That is a really common question, it was one of the questionings of Einstein's theories about the light behaviour back at his times. He noticed that if you assume that light has a momentum, all his equations matched perfectly and everything worked really well. When he were deducing the E^2 = m^2c^4 + p^2c^2 math formalism based on differential equations (Maxwell equations, Lorentz transformations), he noticed that the conservation of linear momentum were being broken at some point! So either linear momentum conservation - which is an untouchable and unquestionable law - didn't apply to that, - you would need some balls to face all those angry physicists telling you you were wrong, even being Einstein - , or photons had a linear momentum related to them. The latter was his assumption, and, surprisingly, that assumption matched every concept known so far, everything fitted perfectly like a jigsaw puzzle just when photons had linear momentum. It was basically a discovery made during a math equation development! This is what I know so far about the history of photons linear momentum...

[@jeremiahhoward4566]

light has no mass.

[@Alfosan2010]

I'm a simple man, I see E=mc², I press like.

[@lander9194]

Do you like my Nickname? I've made you waste 5 sec Give me my 5 seconds back

[@arjuniyer7847]

Lander Deckers give me back 5 seconds for reading your comment.

[@notmuchgd9842]

I wasted 2 seconds. You're lying.

[@michaeljones2926]

that was the fastest and most well explained math eauasion ever. i watched it 7 times. amazing, sir.

[@primarysecondaryxd]

I think the most famous equasion in the world is 2 + 2 = 4. That, or: Mind = Blown.

[@OnamKingtheKing]

Dominic Donahue 2+2=4 is an identity

[@pitou8271]

Dominic Donahue let's me ask you what is an equation?

[@hannahkan0622]

Dominic Donahue LOL!!

[@skya6863]

yiu yeung Kan whats 9 + 10?

[@jetison333]

Mårten Dejfors 21!

[@branot89]

If photons don't have mass, why isn't the speed of light unlimited? It sounds logical that photons do have a little bit of mass, but they are still the lightest thing in universe and therefote the fastest

[@theperpetual8348]

A photon does have limited energy though, as we saw, when m=0, E=V

[@renardmigrant]

This is just plain wrong, I don't know what else to say.

[@astroboy6608]

Photons are massless. Because of that, they can travel at the fastest possible speed, which is the speed of light (approx. 186,000 miles per second). Yes, it does seem logical that they do have mass, but that is incorrect.

[@christianmorales4247]

E=MC^2? E=PC? PC IS MASTER RACE. MICROSOFT MAKES PCs. MICROSOFT IS ILLUMINATE. LOOMANATEE CONFIRMED! wait, lemme adjust my tinfoil hat.

[@wasd2333]

+Christian Morales E² = (mc²)² + (pc)²

[@gregoryalban3700]

Christian Morales so true!

[@mateuszdziewierz4234]

If E=mc² and E=pc then E²=E²+E² becouse E²=(mc²)²+(pc)²

[@unitrader403]

@@mateuszdziewierz4234 the former two are simplifications for special cases in which either mass or momentum are (close to) 0, so you cannt mix them since they are mutually exclusive (except both are actually 0, in which case your "conclusion" holds up)

[@squibble311]

ωhaτ?

[@Kombivar]

The best explanation I've ever seen - even kids can understand, but played it about ten times slower :) thanks bro!

[@jet-ew2eg]

I wish I was high on potneuse

[@forloop7713]

Jaguar same

[@treyhestermann7332]

I'm pretty sure 2+2 is the most famous

[@rolfmaoqwerty]

Not an equation, but yes it's probably the most famous algebra problem

[@pgpulsegaming4041]

that's a sum not en equation

[@alejandrozapatamarcos456]

If-> p=m*v Then-> m=0 ; p=E/c? NO m=0 ; p=0 ; E=0 There is no momentum nor energy without mass, and vice versa

[@LeconsdAnalyse]

alejandro zapata You forgot the gamma factor in your expression for p, and that m is moving with constant speed 0

[@alejandrozapatamarcos456]

LeconsdAnalyse Thanks. Btw, what is the gamma factor in p?

[@LeconsdAnalyse]

alejandro zapata You're welcome. You wrote p=mv. It should be p=γmv, where γ=1/√(1-v²/c²) is the gamma factor in (the expression for) p.

[@alejandrozapatamarcos456]

LeconsdAnalyse Oh! The Lorentz factor, right? Thank you very much!

[@sumsar01]

If you have a particle with zero rest mass you will mostly likely be talking about a photon which have a impulse of p = h/lambda where h is planks constant and lambda is the wavelenght.

[@captainmal4336]

Probably the best video I've ever seen on KZbin. Thank you

[@theeye7776]

0:02 Wrong , its 9 + 10 now.

[@henryxu7529]

wait, but if a photon is mass less, and P=MV, if the mass is 0, then energy is 0. But light has energy! ??????????

[@alexanderm5728]

I'm four years late, but the expression p=mv is an approximation - it's only accurate for objects travelling at speeds that are very slow compared to the speed of light. For relativistic particles, you need another equation, p=γmv. For massless particles, it works out that p=E/c - which is equivalent to E=pc, as shown in the video.

[@QuantumPhyZ]

Im smarter than Einstein! 10+9=21 that is the missing equation there! Which talks about unknow laws of fisics!

[@QuantumPhyZ]

Masahiro Wakahaya Im actually in war with my grammar to

[@ZetaCheese]

dude, ik a lot of your comments are jokes, but in hopes this cranks out even another 10 seconds of video (i dont have the money for patreon, one day) you make really quality informative videos that's seems to be although short give a lot of ideas that dont seem to be presented anywhere else. Plus, I really like math, and physics seems really lightly covered in youtube and pop culture, this is great. Please, keep doing you!

[@AjourChannel]

This video, square.

[@AjourChannel]

LeconsdAnalyse Woof.

[@Vixikats]

Why can't girls find guys like you?...

[@General12th]

+Kaitlyn Amanda Guys like this exist everywhere. You just need to look for them. They usually hide themselves away in dark library corners or in the middle of a group of like-minded friends. Be adventurous! You'll find him eventually!

[@Vixikats]

***** I guess if I looked up from that dark library corner myself, I might see more people, then.

[@benalkan8559]

Amen

[@lucasnicoara7400]

J.J. Shank As one of them, I agree. But it's not like I'm hiding, I just don't really feel the need to meet more people. I have a small group of 4+ years very good old friends to hang out with, eventually party, but mostly staying home or hitting the gym.

[@pranaykhatwani]

Awesome video, but please make it available offline so I can watch these fantastic videos when I'm travelling.

[@iamcsxii4043]

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

[@themagicbush1208]

MinutePhysics corrects EVERYTHING i've learned in school. I fucking love this channel

[@HolyAvgr]

This is probably my favourite video. I found the triangle illustration to represent the triangular relationship to be gorgeous.

[@badroeddine639]

Best physics channel ever

[@DonutKop]

They really need to start saying the full equation... This is amazing

[@kunajayanmurugan2546]

I've gotta question. As you said based on the triangle, when m=0 , E=pc. But according to theory, when m=0, p should also be 0 based on the formula p=mv, right ?

[@wesleycyber]

Many say the m in E=mc^2 refers to relativistic mass while m-not (m with a zero subscript) is conventional for rest mass.

[@justincase1296]

I found a problem! P is the letter used for momentum if it is used for this as well the photons must have mass or they do not have energy. If the mass was zero the right side of the triangle would be zero. But momentum is measured with the mass and velocity of a object times each other. If the mass is zero then there is no momentum, making the bottom of the triangle 0 and energy would equal nothing since the right side is also composed of mass and would compress to nothing as well.

[@jgilgorri]

There are different formulations of momentum, actually. The momentum of a photon comes from its wave-like properties, not the particle-like properties.

[@justincase1296]

So if a object was hotter and had more energy it would have more momentum?

[@pibroch]

Justin Case If an object with mass gets hotter it means that on average the particles that make up the object have more kinetic energy. If the object has constant velocity its momentum stays the same regardless of whether it is getting hotter or colder. www.mansfieldct.org/Schools/MMS/staff/hand/atomsheat.htm

[@jgilgorri]

Pibroch That's classical physics. It's accurate enough to be used, but really, mass does increase (but by such a small amount it is immeasurable). Relativistic physics would show it (E=mC^2; one result of this is that more energy means more mass).

[@VArsovski10]

Nothing has a ZERO mass Ideally.. Even if something has a 1 x 10^-31 (i.e. 0.000000......000 - 31 times zeroes than 1) - it will have some Energy based on (speed of light)^2.. Though there was something (some theory) with a negative mass here - about the anti-matter I think, regardless - lim(0+) =/= 0.. You can NEVER assume something is 0 if it's multiplied by something near infinity.. It's more like 0xInfinity = 1 (for simplicity, just for the basic understanding), but the truth is that 0xInfinity = undefined.. Regardless - you can see that my assumption was that c^2 is near infinity (which really is - that's the power of 18th decade), and what has the mass much less than the power of -18th decade ? - nothing really.. Even particles are near that mass I believe (studied quite a long time ago, but pretty sure nothing has a mass like 10 powers less than a power of -18, more like 0.00000 28 zeroes than 1 grams - in mass don't exist, I think)

[@ByYeeqz]

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.

[@neurofiedyamato8763]

This was such an amazing yet simple explanation. I understand this so much better now.

[@minimi98526]

minutephysics is the best. I actually learn more here than in the entirety of highschool XD

[@non-productivegaming1208]

Literally, you are a Genius, I am also studying Physics and everyday I watch your video!!! Great help to my studies!!!!

[@GM-ds5rn]

One of the best episodes of minute physics, also can someone please get rid of trigonometry, I mean speed of light travel, amirite?

[@rajanidas6661]

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

[@TheGrooseIsLoose]

I’ve heard all of this before, but I’ve never put 2 and 2 together to realize that this is what shows that nothing with mass can reach the speed of light. It’s nice to finally understand that instead of just taking it for granted because I’m sure somebody with a PhD would be questioning it if it wasn’t super obvious for some reason.

[@anjuk6255]

Let's consider energy of light Since classically light has no mass Energy of light E=pc E=(mv)c E=0c E=0 Does that mean light has no energy.. how is that possible someone pls explain

[@phildobson8705]

Brilliant geometry but what is E measured in? How does the speed of Vibrations in Magnetic Feilds (light) tell us how much Energy is in a physical object?

[@cajeroautomatico]

Thank you minutephysics, that was an amazing visualisation & explanation!

[@nitukumari3360]

But how can a massless object have momentum? Since, p = mv

[@richardnk2008]

it really all did confuse me a bit, until you represented it as a right angle triangle :P that's a great way to explain it. and now that i have seen it represented in this way, i will probably never forget it, i remember pictures aloot better than i remember equations...

[@takoyuuki4270]

OMG THIS IS SUCH AN AMAZING CONCEPT!!! THANK YOU SOOOOOOOOOOOOOOOOOOOOOOOO MUCH FOR THIS!!!

[@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 PowerShell script for the above $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"

[@liamdacre1818]

Great video. I was really confused where the full equation came from but you explained it perfectly. (A^2 + b^2 = c^2)

[@LucisFerre1]

This is a *BEAUTIFUL* explanation/description of these spacetime factors. Thanks you.

[@mybluemars]

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

[@redflamelcd]

so beautifully explained it brought a tear to my eye

[@watermelonking]

This video is great! I love that it explains science in such a great way!

[@benYaakov]

At 0:52 , For photons E = Pc Now , P depends on mass , which is zero again , So E = 0 ? Can anyone tell where I am wrong ?

[@dantong5623]

we can think of P=mv in 4 dimensions, where P is 4-momentum, m is rest mass and v is 4-velocity. You are right in saying that photon has no rest mass, therefore, m=0. But, 4-velocity v is parametrized in proper time, basically 4-velocity = [distance (in time and space)]/(slippage of proper time). Photons do not experience time: there clocks are frozen, so their proper time slippage will always be 0. So you have for photons 4-velocity = infinite, and so your 4-momentum P=0*infinity, which means you have a poor parametrization of the world line. There's the problem: you can't use P=mv for photon. Actually for a photon, 4-velocity is not defined. We can however, express a photon's 4-momentum as a well-behaved vector by simply replacing the m terms in a normal 4-momentum formula with E/c^2. This 4-momentum vector has 0 length, reflecting the special nature of photons.

[@benYaakov]

@@dantong5623 :(

[@benYaakov]

So you meant that photons travels at infinite speed because clocks are frozen for them . So why people say that it travles with 300000 km / second .

[@dantong5623]

@@benYaakov 4-velocity of a photon is simply not defined. 3- velocity of photon, however, is well defined for an observer not moving at light speed because the definition of 3-velocity does not use proper time, but observer's time and space for definition and that 3-velocity is c. But, if you are an observer at light speed, then not only is your clock frozen, your space is also squeezed to a plane perpendicular to the direction of your travel, so if you calculate your own velocity with respect to an object, you basically get 0/0... I should've been more careful with the infinity. The infinity was to point out there must be something wrong with our formulation, so we must adjust it. This is sort of like how you can write cosx = sinx/tanx, and then think about what cos0 is. You can't use sin0/tan0...because sin0=tan0=0. But you can treat the question differently to get cos0=1 in a reasonable way. Now, the way we usually define velocity is analogous to cosx = sinx/tanx , and x=0 is where photon is. Hope this analogy helps.

[@pibroch]

You went wrong by believing that P depends on mass. It does not depend on mass. P=mv is just an approximation for objects with mass moving at slow speeds. It only provides an exact result for objects with mass standing still!

[@TheThibz1]

Oh damn, you just explained in two minutes so many things that I didn't understand in a lot of years of physics!

[@HackSawSees]

What a beautiful visualization.

[@larion_de]

Very elegant way of describing it

[@samikshyachand8433]

This is the best video I have seen till date!!

[@professormayonnaise3440]

why the formula of a moving object includes pc (i know p is the momentum) cause c is already there at mc(square) why we add it to the formula again? and what is the explanation for that formula? Henry Reich