Does Mass Increase as You Approach The Speed of Light?
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- เผยแพร่เมื่อ 14 ต.ค. 2024
- Why can't you reach the speed of light? Does mass increase as your velocity increases? Find out now on Dragon Ball Z.
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Simplified for the lazy person:
1:27 - 2:25 - He draws an arrow with a certain length. Then he rotates that arrow counter clockwise.
2:25 - 3:42 - He shows that the new rotated position of the arrow is mathematically linked to the original position using triangle magic.
4:33 - 6:51 - He shows that the length of the arrow doesn't change if you simply move it around. Its direction changed with the angle, but the length always remains the same. The "length" value (e.g - 1 meter) is specifically a "scalar", or the quantity that doesn't change if it moves. The scalar can be discovered via the *dot product* spell (this is important for later).
Okay. So at this point, you have to understand what the 4th dimension is. 4D is just time. If you rotate an arrow you drew on a piece of paper, then you rotated the paper 90 degrees, you're specifically rotating that drawn 2D arrow 90 degrees in 3D space (just focusing on the arrow, not the paper). If you get a real arrow and spin it around freely, you're rotating a 3D arrow in 4D time. Each milisecond that goes by as the arrow spins means that the arrow is pointing at a different angle than before. Changes in a 4D graph can cause changes in the 3D objectlocated in it (example - an apple rotting away with time is a bunch of 3 dimensional changes observed due to changes in the 4th dimension - go watch Dr. Strange).
8:32 - 11:40 - When math magicians have to go up in dimensions, they can't draw that shit out on paper anymore, so they have to write down these weird algebra magic spells. These spells are written down in brackets [ ] . The higher the dimensions, the longer the spells get, and the more you have to write down into those brackets [ ] . He wrote an algebra spell which shows a 4D arrow [it's the same arrow as before - just shown in 4D], as well as some numbers that'll represent the components of that arrow. He shows that the concept of 'scalar' transfers over, in the sense that there are certain properties that don't change with everything else around it changing. To describe this in 4D, physics wizards call it the "Lorentz Invariant" (the *dot product spell in 4D*, or the thing that doesn't change in 4D) that undergoes "Lorentz Transformation" (the stuff that does change in 4D).
*This next part is very important*
12:01 - 13:02 - Remember the way he showed the arrow moving in a 2D graph at 2:25 with dotted lines? Well now he is writing an algebra spell to show this arrow moving in a 4D graph.
13:07 - 15:16 - If you look at Einstein's equation, it describes that energy is equal to the characteristics of mass and momentum. Momentum itself is a real-world (3D) characteristic, so using the same algebra spells from before, he shows that momentum is equal to the energy of the object with relation to its existing momentum. If you apply the *dot product spell* to this, you essentially get mass (if you take away momentum in an object, you're essentially telling that object to stay perfectly still. it still has energy [everything has energy], but it doesn't want to move at all. this concept is called *mass*).
BUT WAIT - The dot product spell is the *Lorentz Invariant*, which means that it is something that doesn't change when things change in 4D. So mass is one of these things.
TLDR - Mass doesn't change when you move things. The only reason why people say that "mass" changes is because they are using an old Newtonian idiot definition of "mass" which describes "inertia" (or resistance to acceleration), when there is another definition of mass in use - one far younger and more powerful.
I'm gonna use triangle magic instead of trigonometry now
Thank you
Thank you you have simplified it but a little to much?
holy shit this explanation is awesome
the explanation is amazing!
How kind you are, thank you ヾ(｡>﹏
As an engineer, I'm satisfied with your shirt
I was about to comment that 😂😂
Disgusting
@@PapaFlammy69 pi^2 = g is called "engineer units" !
@@zoisantonopoulos7999 Cry
Gregory Toomey no gravity 😂 because gravity g~9.80 and pi^2~10 so pi^2 = g
"I'll prove this is the case" : gives 4 very specific examples.
The Mathematicians aren't going to like this one.
Just mildly tweaking on the floor....
The proof is supposed to be that since the mass can be expressed as the dot product of a four vector, is must be an invariant quantity. The rest was just showing why people invented a different kind of mass to begin with.
@@AndrewDotsonvideos it's like a decade since I was a graduate student so I can't really remember, is this roughly the same method to show that the magnitude of a scalar is invariant in polar co-ordinates compared to Cartesian co-ordinates because that was the other question that occurred to me when you did that hand-wave-y proof.
@@AndrewDotsonvideos I am not a physics major, so that comment is Chinese to me. Interesting Chinese, but Chinese nonetheless.
@@matthewmcneany what you are proposing only proves that the quantity is invariant under the polar-cartesian coordinates transformation. You have to show that a scalar quantity is invariant under all possible physical transformations of the coordinate system (namely rotations, boosts and translations of the origin which togeher form the Poincaré group). Once you accept that only quantities with one or more free Lorentz indeces change under a transformation, the simple fact that a scalar quantity has no free Lorentz indeces proves that it is an invariant quantity (under all above mentioned transformations)
"Hello fellow smart people"
"Ight imma head out" - me, a non-mathematician
Kaasplankje5678 this class is taken as a physics major into to Black hole theory and General Relativity
@@javieralarcon007 I've just started my economic master and I have to learn basic linear algebra etc (finding derivatives, primitives, convex, concave, solve simple equations, portfolio optimalization, profit maximalisation, derivatives and ''“Linear and Dynamical Systems, Optimizationand Games''. I learned all this in like, 8 weeks, but spent about 70 hours each week on this, and 4 other courses which are (only 1 of the 4, the other 3 are mandatory because of the expectation of academic competences) /is (the statistics) equally time consuming. #plzsendhelp #notfun For real, if someone wants to help me out over skype or something and you now a lot about frame math (linear and dynamical systems), let me know! Id be happy to take your advice any day!
Every course is mandatory, I meant that only statistics consumes as much time as mathematics does. The other subjects consume study time, but not practice time like math and statistics do.
I'm an engineer and I just came to read the comments
Giving him the benefit of the doubt. Hopefully he's not as narcissististic as the statement implys. Samething here. Granted it's important physics and math. They have their place. But physicist and mathematicians as stars. Peddling there stuff like it's the most important thing. Hard to respect them when it seems it's for the money or worse yet tax payer moneys. I've followed and been involved in physics since I was eight years old. Read cosmos when I was 10. No I didn't get it. Like Max Planck, two slit experiment was well just the way it worked. He didn't know the implications of what he found. I was like 30 before I started getting it. I remember reading The life and of Albert Einstein in high school. Went on some extreme tangents before I figured out what was up. Fricking dry reads. The more I looked the experiments I saw more history I looked at. Then I sorta made own theory. Which I cleverly called the Solid State Universe Theory. As implied matter like energy running through a solid... So reducing and creating a tensor network. And low behold Einstein had already done that. The more I learned and the more I learned where to look. Yeah I started seeing Einstein's tracks had already been there. Here thinking it's some novel deduction. Anyways it really increased my respect for him and his genius. So what's this guy then Hmm wanted to be an engineer and physics well didn't work. Now just a fantastic vetter. As in making sure they're respecting the greats. I know you know Einstein created quantum mechanics and he wanted it viewed from a certain orientation and Neil's Bohr and the weirdly concerned physicist's, at Copenhagen, thinking physics would end if they didn't get it their way. Yeah they stole it and made it their way. Thou I don't think either were fully wrong. I'm convinced that there's hidden variables and nonlocality working conjunction. Now you got Brian Green peddling Michio Kaku, Sean Carroll just goes on and on. Ahh fine with it dosent give the masses any meat to chew on, no conclusive direction Idk the way its gotten. All that math will be worth something someday but they just charge like they have it and know it, when they clearly don't. I'm with Einstein. Discretnizing quantifying a space through Penrose tiling or quantum tensor spin networks work because quantizing is well all one can do. But something infinitely divisible such as a field or electron photon. There's so many things that come into play and how they fit. We have an observational time limit. Say borderless universe yet the infinite border may be the red shift shift to dissolution and separation of interaction. Like it to quiet back down.
I love watching videos like this on days when I have assignments due for a completely unrelated major.
Yahiko Tendo Which one?? Now I’m curious u.u
Oh god he's one of those "natural units" guys now...
Well, wait untill he shows atomic units
I’m never going back
Natural Units >> SI
You mean a physicist?
@@AndrewDotsonvideos In understanding SPACE, what is gravity, TIME, AND time dilation (ON BALANCE), it is important is it to understand what is a BALANCED displacement of what is SPACE. ELECTROMAGNETISM/energy is gravity ON/IN BALANCE.
Consider what is E=MC2. TIME is NECESSARILY possible/potential AND actual ON/IN BALANCE. Consider TIME AND time dilation ON BALANCE. (c squared CLEARLY represents a dimension of SPACE ON BALANCE.) Indeed, the stars are POINTS in the night sky ON BALANCE. The rotation of WHAT IS THE MOON matches the revolution. Consider what is THE EYE, AND notice what is the TRANSLUCENT AND BLUE sky ON BALANCE. NOW, consider what is the BALANCED MIDDLE DISTANCE in/of SPACE. CLEARLY, BALANCED inertia/INERTIAL RESISTANCE is fundamental (ON BALANCE). “Mass"/ENERGY IS GRAVITY. ON BALANCE, consider what is the orange (AND setting) Sun. “Mass"/ENERGY involves BALANCED inertia/INERTIAL RESISTANCE consistent WITH/as what is BALANCED electromagnetic/gravitational force/ENERGY, AS ELECTROMAGNETISM/energy is CLEARLY AND NECESSARILY proven to be gravity (ON/IN BALANCE); AS gravity/acceleration involves BALANCED inertia/INERTIAL RESISTANCE (ON BALANCE) consistent WITH E=MC2, F=ma, TIME, AND time dilation ON BALANCE. This CLEARLY AND NECESSARILY represents, DESCRIBES, AND INVOLVES what is possible/potential AND actual ON/IN BALANCE, AS ELECTROMAGNETISM/energy is CLEARLY (AND NECESSARILY) proven to be gravity (ON/IN BALANCE). Notice what is the fully illuminated (AND setting/WHITE) MOON ON BALANCE. Great. TIME is NECESSARILY possible/potential AND actual ON/IN BALANCE. Indeed, inertia/INERTIAL RESISTANCE is proportional to (or BALANCED with/AS) GRAVITATIONAL force/ENERGY; AS ELECTROMAGNETISM/energy is CLEARLY AND NECESSARILY proven to be gravity (ON/IN BALANCE). This CLEARLY explains what is E=MC2 AND F=ma ON BALANCE, AS TIME is NECESSARILY possible/potential AND actual ON/IN BALANCE !! (Consider TIME AND time dilation ON BALANCE.) Great. Indeed, consider WHAT IS THE EARTH/ground ON BALANCE. I have mathematically proven why the rotation of WHAT IS THE MOON matches the revolution, AS ELECTROMAGNETISM/energy is CLEARLY (AND NECESSARILY) proven to be gravity (ON/IN BALANCE). Consider TIME AND time dilation ON BALANCE, AS the stars AND PLANETS are POINTS in the night sky ON BALANCE; AS c squared CLEARLY represents a dimension of SPACE ON BALANCE. (Consider what is THE EYE ON BALANCE.) I have mathematically proven what is the fourth dimension, AS ELECTROMAGNETISM/energy is CLEARLY AND NECESSARILY proven to be gravity (ON/IN BALANCE) !!! I have explained why what are OBJECTS may fall at the SAME RATE.
By Frank Martin DiMeglio
I wish I can understand this lol. Hopefully I'll rewatch it when I've progressed in physics.
¿What u don't know?
same lmao
@@matiascontreras8597 Like how dot product of four momentum was lower index- upper index thing instead of lower index-lower index thing. I don't know what metric tensor is 😔
@@om5621 The index position has to do with covariance and contravariance. Contravariance can be loosely thought of something that scales opposite ("contra") to unit vectors. If you have the velocity v = v1 * xhat + v2 * yhat, then its x-component is v1. Let's say |xhat| = 1, per definition. Moreover, we let v1 = 1. Now if you change |xhat| to, let's say, 2 (by redefining it), then xhat is twice as long as before. In order to make v refer to the same vector, v1 has to be made half the size, i.e. v1 = 0.5. This is a direct consequence of the unit of v being distance/time, and xhat being distance. This sort of opposite scaling is what makes the v1-component (and v2) contravariant. Covariant vectors would scale in the same way, (i.e. xhat from 1 to 2 would result in v1 from 1 to 2). Examples of covaiant vectors are the gradient vector of a function, but also, reasonably, unit vectors such as xhat.
@@om5621 The whole idea is that something invariant (that doesn't change when you change the coordinate system) has to match upper- and lower indices. A vector should of course be invariant. For instance, the velocity vector we defined as v = v1*xhat + v2*yhat should always refer to the same vector, no matter if the unit vectors (coordinate system) are changed. But this isn't a problem since xhat is covariant and v1 is contravariant, so their respective changes cancel out. In index notation, by defining {x_1, x_2} = {xhat, yhat}, and {v1, v2} = {v^1, v^2}, we get v = x_i v^i. If we'd have covariant components (i.e. v = x_i v_i) then both would scale in the same way, and v wouldn't be invariant, making it pretty useless (there are ways around this).
I'd like to say, I'm just an Engineering student but I've always been fascinated by the upper level physics that we don't get into (basically past intro to E&M (and yes, I know "upper-level" is a bit of a stretch)), and I really enjoy when you make these kinds of videos. Keep it up!
Now I see why I can't loose weight even when I'm running.
Try decreasing your momentum of your kinetic energy. That way, maybe you will start running backwards and start losing weight xD
Yeah but as you're running you have length contraction in the direction of motion, so you get immediately slimmer
40 year old mom joke
I love how digestible you made such a complex topic. A physics 1 class and a little bit of math is all someone needs to understand how all this works with your explanations. Great video!
Thanks!
Excellent. The confusion is persistent, and it is great you contribute to dispelling it so clearly.
Your videos really be hitting different once you understand the subject that’s being talked about. 3rd year physics degree student here and this video also helped me to clarify some ideas for my Electrodynamics midterm in 2 days, thanks for your uploads they really help a lot :-)
This is the best explanation I've found for this. The way you explain it seems to keep a simplicity while talking about something complex. Please consider doing a full series on Relativity so plebs like me can understand it better.
Summary if I understood it right. People are confusing mass, which is invariant with frames, with momentum which can infinitely change depending on the chosen frame.
Now THIS is podracing Andrew
Teacher: "What's another way we can think about this coordinate system?"
Andrew: "let's try spinning, that's a good trick!"
thank you for explaining vectors under rotations so clearly!
It’s cool cause u upload videos so people who r interested can watch and try understand but it also probably helps u get a better grasp of it too
We just covered relativity in my sophmore E&M course. This really cleared up my confusion surrounding "relativistic mass," thank you!
Without having done four-vectors, this was super clear!! Very well explained, thanks for the insight!
I'd gladly like to see how you would go about proving that something is a four vector!
Kevin Somenzi thanks!
@@AndrewDotsonvideos :)
It's either made up of already known quantities, or you have to experimentally verify that it is indeed a 4 vector.
Gosh, I was a real a noob back then haha; now I'm almost done with my masters in theoretical!
i lost you at "whats going on smart people"
Relativistic mass is a sometimes convenient fictional computing device, but so is rest mass. "Rest mass" is really just energy: the sum of a small energy contribution from coupling with the Higgs field, plus a large contribution from a bunch of other things like confinement energy of the quarks and binding energy of the nucleons.
"m" is really the component of the total energy that doesn't change with velocity, and "E" is the component that does. If you replace m in the equations with E_non-k and E with E_k, the equations make much more intuitive sense, and there are no worries about fuzzy concepts like mass (inertial mass, rest mass, relativistic mass....).
Hi Andrew,
You have a talent for teaching. I hope to reach your level of teaching one day.
It seems to me that every (relevant) relativistic effect works against light speed.
If A observes B moving away at relativistic speeds, then A will also observe a length contraction effect on B. Hence from A's perspective, B will appear to be moving over "shorter distances" than it would without relativistic effects.
A will also observe time dilation on B, so B's "time intervals" will be longer from A's perspective. So, the time it takes B to do a thing will be longer from A's perspective than it would without relativistic effects.
So, A is also percieving B to be moving shorter and shorter distances in a longer and longer amount of time than it would without relativistic effects, and these effects are unbounded.
That means that a speed increase of 2000 km/s at non-relativistic speeds might be percieved by A as a speed increase of 2000 cm/year (or whatever) at relativistic speeds, and this never stops.
You can just postulate that the speed of light is invariant and derive all of relativity from it. Its easy enough that i actually got taught special relativity in high school.
Here is a good thought experiment. Imagine a photon clock - two mirrors and a photon bouncing between them. Now imagine we give it a boost perpendicular to the direction of photons motion. Since the speed of light is constant, light will take more time to go between the mirrors as it will be travelling in a diagonal. If you used that clock to measure time, you would see it tick slower when it moves at relativistic speeds. Use the Pythagorean theorem to derive how much time must be dilated for that to make sense.
Mikhail Mikhailov It's not just that the theory can be derived from the postulate that the speed of light is invariant. The theory IS that the speed of light is invariant. Sure, there are other theories that start from different postulates yet achieve different conclusions, putting them in the same equivalence class. But strictly speaking, those theories are still different. A theory is defined not by its conclusions, but rather by the pair of the set of conlusions and the set of axioms.
@@angelmendez-rivera351 You are a nerd. What next, will you tell me that SU(2) and representations of SU(2) are different objects or some other nonsense like that? :3
Anyway, fair point.
@@mikhailmikhailov8781
You also have to postulate that all inertial observers are equally right and what an inertial observer is.
*He is using "natural units" now.*
He has crossed over guys.
thoroughly enjoyed this. I've been learning intro mechanics on my own and I'm glad that my text didn't go "there". We just stuck to p = ymv and left it at that. Definitely less confusing that way. Just keep gamma out in the open and it's not too bad to include it once you get used to it.
You're the best, Andrew. Keep it up!
Mr35diamonds thanks!
Cheers for that. Always wondered about this common assertion-misconception but never bothered to check its validity.
You're alive! I double checked your channel two days ago lol. But thanks for doing a relativity video!
Mara I live!
Actually very clear and thorough explanation, amazing!
Hi Andrew, first of all I love your videos and this was the perfect 100k special which focuses on a very common misconception among physics learners like me.
Second, I know that people who are not serious about physics will mostly prefer informative but less mathematical videos. But you included most of the math behind this whole thing, which is really good for the Physics students here who watch your videos. This type of videos are really helpful for people who are studying or want to study higher level physics because it's the actual interpretation of how (theoretical) Physics works.
(Phew! that was a long one though ;-)💓)
Great video, really clear and intuitive explanation. More Special Relativity videos please.
This was a really good explanation. I had introduction to SR last year and this was just one of those floating questions I had in my head that I accepted would probably be answered some day... that day is today!
Bless you bro, was waiting to here your response to my suggestion. Did not disappoint.
Very good job here, Andrew - you did a much better job of explaining this than the guy on the FermiLab channel!
I think that another reason for confusion about this issue is the fact that mass and energy are, of course, very tightly intertwined in the sense that you can make mass out of energy and make energy out of mass, and they are related by good old E=mc2. (m being the rest mass, obviously.) So this relation between mass and energy (and inertia) isn't conceptually all that simple. I personally have a niggling suspicion that there's something very deep there but I'm nowhere near bright enough to wiggle it out....
Thank you for being one of my motivators to get me back into physics!!
This is awesome. I was trying to understand why a professor I respect a lot kept saying that saying "rest mass" or "relativistic mass" is a silly thing, but unfortunately I didn't understand his explanation. Yours was _very_ clear. Thanks a lot!
At the beginning of the video you wrote that x' = xcos(theta) + ysin(theta), which are the components of the vector, I think this is the relationship between the unit vectors of your coordinates system and not between the components, so you should have x^' = x^cos(theta) + y^sin(theta) which indeed yields the same result for this case, but I think is the correct way of doing it. Please correct me if I'm wrong.
Im a highschool senior and I understood you until dot products (have no idea what they are). And I roughly know about the Lorentz factor (learned from you how to get it from pythagorean theorem), and obviously F=ma and p =mv but thats about it. I will revisit this as I progress in my physics career.
I enjoy your videos. Do a video on Tau and how common and not so common equations, math, and plots would work out with it.
Hey, Andrew, I know 'rapidity' isn't used much in real physics, but if you define an 'angle' q such that beta = tanh(q), you can write the Lorentz transformation as a rotation matrix. That idea has really helped me understand SR. Have you covered that in your studies? Would you be willing to do a talk about it?
The other day I heard my engineering professor say "2π=6" un-ironically
David Bordenkircher At least he didn't unironically use e = 10 in a paper.
@@angelmendez-rivera351 since when e=10?
Reynan Henry In a physics publication, a physicist approximated e with 10 and used it for their calculation. Granted, this can be justified rather rigorously, but on first inspection, it looks comical as all hell.
do you have any link about that? Im curious
@@angelmendez-rivera351 Of course Astrophysics (related subjec). Everybody know in terrestial physics at most pi=3, but astrophysics related subjects its 1=e=pi=10
In my physics class, we went the other way around:
We defined still mass, ie the mass of a non moving object as m0.
Then defined relativistic mass as m=gamma*m0
Then defined relativistic momentum as p=m*v=gamma*m0*v
Then defined relativistic force as F=dp/dt=m*dv/dt + m0*dgamma/dt*v
And then used those definition to calculate energy and find E ˆ 2=m0ˆ2 * cˆ4 + pˆ2 * cˆ2
You are such a kind teacher andy, but mass depends on velocity in one sense, but inside your own reference frame your own mass is always invariant.
Clearest breakdown of mrel I've ever seen. Great stuff. What about taking the next step from Lorentz lambda for just x and looking at it for all components...?
Hey, just a quick nitpick.
The metric you used is not THE metric. That's the metric for Minkowski space: a "flat" spacetime. Depending on what you're looking at, that may not be your metric (in fact, things get fun if you don't use that metric. The Schwarzschild metric, for instance, is usually used to give your first look at a black hole). I know you were using it for clarity, but it's something you may wish to mention for the sake of completeness.
Good video :)
Im an engineering student and I understood everything, specially everything thats written on the back of your shirt
And the front lol
Happy Diwali Andrew
Things are always better when math included ... really enjoyed the video keep up the good work
Short answer: no. Relativistic mass has largely been deprecated in favour of relativistic momentum.
That's my argument against "Superman can travel at the speed of light so he can punch with infinite mass" damnit....
@@elsephiroth666 the speed of light in fictional stories is a meme lmao. I remember a scene in the original Dragon Ball where people argued that tiny ass goku can move at the speed of light cause he jumped away from a blinding light.
Special relativity aside, people also don't realize light would circle around our Earth several times in a second. Haven't seen a piece of fiction that does not underestimate lightspeed.
the sad part is that relativistic mass has been deprecated even before relativistic mass was invented.
Wow! In a half hour you explained what it took me an academic year to figure out! Thank you.
Best explanation I have yet seen for mass not increasing.
Me: watches the video
My engineering brain: aight imma head out !
Great vid btw keep em coming Andrew
B..but he has a pi^2 = g tshirt
@@subinmdr I can't believe I didn't notice that
Weird flex, but okay.
Your brain is not engineering brain then
I'd like to see the proof that p^mu is in fact a 4-vector please :)
Wow this has been bothering me for a while now thanks for clearing this up
thank you very much for this. my physics is poor and my maths worse but i do enjoy the subject and watch many videos which are above my understanding in the hopes it will slowly sink in. this video has made many things that i half knew, or thought should be the case, much clearer. thank you again.
I feel like my intelligence grew 1% after watching this video. We have been taught this "mass variation" thing as if the mass itself increases from school itself(it was like 2 1/2 years ago). It had only the postulates and the equations with no derivation. It didn't make sense at all. Now, we haven't started special relativity in college yet (I have to wait one more semester it seems). But I couldn't control my urge and started studying from various book and from youtube. This video feels like the crown gem of the whole syllabus. Thank you Andrew for this video. Now if our professor makes the same mistake you mentioned, I can point it out. Please make a video on the mass-energy equivalence also if possible. with the derivation
My dad and I have these HUGE arguments about time travel to the past and travelling faster than the speed of light. I'm not giving in Andrew
Zayn Charania What side are you on?
I can settle any time travel arguments. I'm good at 4th dimensional thinking
Just being an EE makes me happy I can kinda follow along:) love your videos
This is probably my favourite science video on TH-cam even though I'm not familiar with everything he explains
Thanks a lot! Can I ask why?
@@AndrewDotsonvideos Of course man! I love maths and science, so this is my favourite science video. Veritasium made my favourite math video :). Anyways, it was just your clear passion and complete understanding of the topic that made it easy to follow. Also, I learnt about vectors and scalars last year in Physics, so to learn them in a new way that is far more interesting than just a definition was fascinating.
@@aidanwebster75 Thanks for the feedback! Tbh, I would phrase things a bit differently if I were to re-record the video. "Mass is lorentz invariant BECAUSE its the square of a 4-vector" was what I kind of insinuated, but is not really a proof. If anything it's just making an analogy to the "length" of a 3-vector (v dot v) being rotationally invariant, which no one would argue with. In the end, mass is the total energy of a particle in its rest frame. If I go to a new frame where the particle moves with velocity v, it now has kinetic energy, and so the total energy is gamma mc^2, which people then called "relativistic mass"(times c^2). What they did, imho, is create a new word for something that already exists, total energy. Energy depending on how fast you go is almost an obvious statement, and you avoid misleading students into thinking mass depends on how fast you go. One day I'll do a follow up to this video, thanks again for watching!
@@AndrewDotsonvideos that's actually really interesting! I look forward to it😋
I've just started my first year in engineering so this will help me understand vectors better and use what I learn on something interesting instead of just learning the equations and theory from class. So that's pretty cool.
I love these videos, even though I'm not necessarily getting everything here yet. Great job!
Taking a stat mech course next year as an elective 4 my chem e degree. It would be hype if one of your next videos was about something in the subject you think is cool
I like how your series is now "first lecture of every physics course"
Bruhhhhh.....I was going CRAZY with what was written on your SHIRT than what you were talking about
Well this makes me feel better, since I also said in my videos that mass does not change, while plenty had disagreed.
I am thoroughly in love with these videos.
I just watch this so that I can look smart
This definition of a scalar has made vectors make so much more sense to me.
Great presentation, and yes all textbooks with relativistic mass are junk. Usually when I watch a video on this topic, the ‘energy momentum tensor’ is mentioned. Is that just a different way to describe the same math you performed? Anyway, my layperson understanding of this is that General Relativity is all about energy and momentum, and that everything in the universe is moving and has energy and momentum including photons. Mass (real rest mass) is simply a Lorentz Invariant number that is calculated in the rest frame and scalar to all frames. If you please, can you correct my understanding if this is off track? Thanks!
R C You are on the right track. However, the one thing I have to correct us that you are confusing the energy-momentum tensor with the stress-energy tensor. The stress-energy tensor is what is used in general relativity. The energy-momentum tensor is simply what Andrew called in his video the four-momentum, which is what most people call it. Basically, the energy-momentum tensor is a tensor of order 1, meaning it is a four-vector. Contracting the tensor with itself, which in this case is known as the inner product, which is a generalization of the dot product, yields a tensor of order n - 1. Since n = 1, that means the inner product gives a tensor of order 0, which is what we call a scalar, and in the context of Lorentz transformations, an invariant. Actually, this is true of all four-vectors: when they are contracted with themselves to form an inner product, the result is an invariant. If the chosen four-vector is the 4-position, then the invariant is (ct)^2 - r^2, where r^2 = x^2 + y^2 + z^2. If the chosen 4-vector is the 4-velocity, then the resulting invariant is equal to c^2. And if the chosen 4-vector is the 4-momentum, a.k.a the energy-momentum tensor, then the invariant is equal to (mc)^2 = m^2·c^2, which is also equal to (E/c)^2 - p^2. So, the mass is a Lorentz invariant that characterizes a system of a matter, since for every system of matter, (mc)^2 is different, but c is independent of systems of matter, since it is a property of spacetime itself.
Thank you Angel Mendez-Rivera
I’m in AP Physics II and this was really interesting and wasn’t too confusing. I am looking forward to learn more in college
AP Phys 1 here. hows it like?
Amoxyl AP 1 is harder, relatively speaking. depending on what year in HS you're in, AP 1 is the hardest class u've ever taken, and the AP test is hard as well. if it's easy for you, go ahead and take AP physics C instead of 2. calculus explains a lot of the phenomena that you're told just "to memorize" in AP 1 and 2
My explanation is the following: If you use time from your point of view when you're moving really fast and you use space from the point of view of a none moving target and use v=Delta X/Delta T'
Where Delta X is the distance you covered from the none moving target point of view and Delta T the time you were travelling from your point of view. In this case v can reach infinity and has v approcahes infinity your velocity using a none moving target time and space approches c. Or basically, you can get to a star millions of light year away and only ages a seconds, from that mixed perspective, you're going faster then c. But anyone else will have aged a millions year.
That sentence ending at 1:13 is more eloquent and well-conceived than anything I'll ever hope to say did you just pull that out of your head
great video as usual!
Nice video! I’ve been meaning to ask you how you did on the GRE?
@Andrew Dotson
Hey Andrew, not sure if this is necessarily the right vid to leave this request on, but I recently came across the concept of fractional derivatives and a tie-in to the fractional Schrodinger equation. Having only recently learned the normal Schrodinger equation and having no background in complex analysis yet, I do not have a solid grasp on those concepts. Would it be in the realm of feasibility for you to do an overview of fractional calculus and its applications to Physics (even if a fair few of us might not yet understand it)?
My birthday just passed and I'm going to set this video equal to birthday gift from you. Thanks
You forgot the simplest definition of a vector: a member of an additive abelian group V together with a field F and an external binary operation FxV->V which follows certain axioms. Or equivalently: a vector is a member of a vector space
Great video yo!
Love the vids, is it true that you get homework in American collages?
Hey that's a great video, I totally loved it ❤
Great video sir! I have one question, at 24:27 why do you take the dot product of v and the chain rule of dγ/dt?
@@panoschristodoulou1208 it should not be a dot product, d gamma /dt is scalar and should still be scalar after applying chain rule, i just had bad notation here. Sorry about that, good question.
Oh, I'm glad I took linear algebra my first semester, now I actually understand a video :D
* My teacher told that this is a fact that must be learnt more like a postulate*
It's unfortunate. Because I think the beauty of SR is its economy in matter of postulates. You can construct the whole theory starting from only 2 postulates.
Really just start with light always travelling at the same speed regardless of reference frame and that at low speeds (relative to c) predictions must agree with Newton's laws. That's really all it take to build SR.
Where was this video when I was going through undergrad! I remember struggling with this concept initially.
cheers for this video your explanation helped a lot as I see misleading information all the time
Now, thats a great vid, the only thing i didnt get is how does the lorentz matrix is made, but i do get the rest of the concepts. Can you give a tetxt book on it? I am curious.
I wish I knew about this video when I was doing linear algebra😥 This guy explains it so well
Thank you! I've always been told that relativistic mass is not a useful or correct quantity but I now finally understand why.
Hi Andrew . I m Claudia I have an off topic question. A friend of mine, Alexa wants to be a theoretical physicist . We are in the 2nd year at the faculty of physics in Romania. I was thinking that you can help her by describing this field in depht from your point of view and also share your path in career or maybe what will come next. Can you consider doing it ?
Or bring Theodore Ree for help . Thank you a lot and keep what you re doing. ♡
It’s been a while since you uploaded. I’m glad you’re back.
He was just busy with graduate physics stuff
gagers78 I didn’t say he should always upload. All I said is that I’m glad you are back with another video. So...
@@user-uu9dm5pz7z yeah i wasn't having a go
gagers78 maybe I should have said it differently.
@@user-uu9dm5pz7z nah it's just me not thinking before i comment.
Great content nicely explained. I expect that I am not the first to say, you look quite a lot like astrophysicist Mat O'Dowd from PBS SpaceTime.
First year engineering student. Understood the video for the first little while, blinked, and became very lost lol. Love your videos
hey andrew can you make video explaining Lorentz invariant measure in QFT?
Nicely made Andrew. i think a layman would be able to understand at least to some degree so long they have some math background
You're brilliant at explaining
Energy and Mass are interchangeable; however, you won't necessarily increase both. Example: a 100 gr bullet traveling at 3000 ft/s has more energy than a 100 gr bullet traveling at 2000 ft/s, but the mass of both bullets are the same.
Please do more videos about how to improve physics instruction...
As a former physics undergrad who never completed their degree, I definitely thought there were some issues with how it was all taught.
Did you call me smart?
Well, that's your first mistake.
Thanks for clearing my doubt
Dude. I study A-level physics, maths and chemistry. Physics is my main and i think your channel is awsome man.
Hello Andrew. My question is why mass increases with velocity when pushed by a force but you can drop a mass toward a gravitational body (even a black hole) and there will be no increase in mass. In fact if a mass is dropped from a great distance toward a black hole it will approach the velocity of light without increase in mass. If you are so smart you will give me an intuitive answer. Thanks