Deriving E=mc^2 using 4-vectors and Special Relativity

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  • Опубліковано 14 гру 2024

КОМЕНТАРІ • 34

  • @gabitheancient7664
    @gabitheancient7664 Рік тому +3

    3:10 it seems like a way to interpret this is that the way time varies in relation to the universal time is the lorentz factor (which is the factor that we use to transform things through different frames), which is interesting

    • @TheBrainFiller
      @TheBrainFiller  Рік тому +1

      Yeah that’s an interesting take! Thanks for watching

    • @cyberjack1406
      @cyberjack1406 25 днів тому +2

      Short of. There is no universal time as time is well relative what you call universal time is just the time of any other observer who measures those velocities but other than that yes that's pretty much its meaning.

  • @shivanbr3496
    @shivanbr3496 2 роки тому +3

    The king has returned!

  • @LingqiaoMu
    @LingqiaoMu 2 місяці тому +1

    so useful and clear!!! thanx!!!

  • @gabitheancient7664
    @gabitheancient7664 Рік тому +1

    Always found most derivations weird because no one explained what is energy and just put it in there
    Now I get that relativistic energy is defined in a way that resembles newtonean mechanics and is also conserved
    Very good video

    • @TheBrainFiller
      @TheBrainFiller  Рік тому +1

      Yes, quantities are invented in physics because they’re useful and nothing is more useful to a physicist than a conservation law

    • @gabitheancient7664
      @gabitheancient7664 Рік тому +1

      @@TheBrainFiller and it has the same units of newtonian energy since it's defined with a mass and a velocity
      because of school and other youtube educators it's being hard to realise these things are like, made up for useful scientific reasons and not something someone excavated out of the ground

  • @fun_g
    @fun_g Рік тому

    Amazing videos bruv i just binge watched some of them please start uploading again

    • @TheBrainFiller
      @TheBrainFiller  Рік тому

      Thanks for watching! Yeah, I have a couple things in the pipeline. So hopefully 🤞in the next few weeks.

  • @andreasgschiel8111
    @andreasgschiel8111 6 днів тому

    A very good video! I think the P^t Notation is very unluckey because I confused it at first with the 3 Space coordinates because in the course I am taking right now we use latin letters for space and greek for time-space, in this notation it would be just P^0 but maybe you haven't used this notation, it makes knowing what is what very clear for me.

    • @TheBrainFiller
      @TheBrainFiller  6 днів тому

      Ah right yeah index notation for coordinates sure I know what you mean. Yes in this video I just referred to coordinates explicitly as t, x, y, z but x0,x1,… etc is useful sometimes

  • @nader6632
    @nader6632 2 роки тому +1

    thank you
    this is so clear💙

  • @andreasgschiel8111
    @andreasgschiel8111 6 днів тому

    2:50 I am pretty sure forgot the dt^2 Terms in the second equation in the space coordinates

    • @TheBrainFiller
      @TheBrainFiller  6 днів тому

      Ah appreciate it but looks more like potentially unclear notation to me. In my mind the squared next to the dx, dy, dz is implicitly also on the dt in the denominator but I could have put brackets to make it clearer! Thanks for watching

  • @tusharmathur6384
    @tusharmathur6384 2 роки тому +2

    nice video sir well i am only in high school so i was not able to understand it but thanks for your efforts

    • @TheBrainFiller
      @TheBrainFiller  2 роки тому +1

      Yeah that’s totally understandable but I would use the maths in this as a good way of judging your progress in the future. You’ll probably learn about vectors and dot products before the end of high school. You’ll also definitely do derivatives at some point (as someone who seems interested in maths/physics). The physics in this video is admittedly not often taught in high school (sometimes is though to be fair) but you will think about using vectors in physics.
      Point being in the years to come you’ll be able to see why the stuff you’re learning now will apply to other stuff (actually this is why I really liked watching Andrew Dotson’s videos on UA-cam in high school, where he vlogs about what he’s learning in his physics degree and does some brilliant skits).
      Thanks for watching and good luck in your future learning

  • @mrslave41
    @mrslave41 2 місяці тому

    5:39 where is this from? 😮

    • @TheBrainFiller
      @TheBrainFiller  2 місяці тому +1

      Where did I get that time component of the momentum inner product? At 4:16 I computed the inner product of 4-momentum with itself and the expression at 5:39 is just a rewriting of that. Hope that helps!

    • @mrslave41
      @mrslave41 2 місяці тому +1

      @@TheBrainFillerwow 😮. amazing 🥲

  • @mrslave41
    @mrslave41 2 місяці тому

    6:58 where did total energy come from?

    • @TheBrainFiller
      @TheBrainFiller  2 місяці тому +2

      Ultimately it’s something that’s made up we just choose to call gamma m c^2 the total energy but it’s well motivated. What I mention in the video is if you take the low speed limit on that quantity it looks like mc^2+1/2mv^2 so it looks like some constant term plus the kinetic energy. But here’s another reason, we know that this overall 4 momentum inner product is conserved by computing it and seeing we get a constant. Moreover, we know that the 3 momentum is conserved as a fundamental law of physics. If the 4 momentum is conserved and the 3 momentum is conserved then the time component of 4 momentum must also be conserved. So this thing in the time component of 4 momentum has units of energy, looks like kinetic energy at low speeds and is conserved…those seem like exactly the properties of something we’d call the total energy yeah? Hope that helps

    • @mrslave41
      @mrslave41 2 місяці тому

      @@TheBrainFiller i’ll take a look 👀 later. looks daunting 🥺. can i interview you / do a collab on my channel?

    • @Oschar157
      @Oschar157 2 місяці тому +1

      @@TheBrainFillerthis was helpful, was going to ask the same thing, thank you. Great video

  • @ααυα6α
    @ααυα6α 27 днів тому

    Bro why did u stop making vids

  • @jacobvandijk6525
    @jacobvandijk6525 Місяць тому

    HERE WE SEE HUMAN ARROGANCE IN A NUTSHELL.

  • @youngphilosophy6178
    @youngphilosophy6178 Рік тому

    You mean dv^2 not v^2, right. The differentials add up to a differential.

    • @TheBrainFiller
      @TheBrainFiller  Рік тому +1

      If you’re talking about 2:50 then each term is divided by dt so each term is a component of the velocity not a differential of the velocity. Thanks for watching and let me know if that clarifies things

  • @alanli1669
    @alanli1669 5 місяців тому

    Where are the new videos!?

    • @TheBrainFiller
      @TheBrainFiller  5 місяців тому +1

      I don’t know man…I don’t know. I have ideas but I lack the mental energy/space for whatever reason.

  • @prakashc5086
    @prakashc5086 Рік тому +1

    Calculus des differentielles😊

  • @andrewiglinski148
    @andrewiglinski148 Рік тому

    Dude there are some really obvious errors in this…