The Special Relativistic Action, Explained
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- Опубліковано 31 жов 2021
- In special relativity, the action for a particle has a beautiful, geometric interpretation: it's the length of the worldline that the particle traces out as it moves through spacetime. Get the notes for free here: courses.physicswithelliot.com...
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This video is part 2 of a series about the principle of least action. The first video was about a particle in Newtonian mechanics. The third is about a particle in general relativity, and the fourth is about a string in string theory.
Part 1 Introduction to the principle of least action: • Explaining the Princip...
Part 3 The action in general relativity: • How Einstein Uncovered...
Part 4 The action for string theory: • The First Thing You'll...
Tutoring inquiries: www.physicswithelliot.com/tut...
If you find the content I’m creating valuable and would like to help make it possible for me to continue sharing more, please consider supporting me! You can make a recurring contribution at / physicswithelliot , or make a one time contribution at www.physicswithelliot.com/sup.... Thank you so much!
About physics mini lessons:
In these intermediate-level physics lessons, I'll try to give you a self-contained introduction to some fascinating physics topics. If you're just getting started on your physics journey, you might not understand every single detail in every video---that's totally fine! What I'm really hoping is that you'll be inspired to go off and keep learning more on your own.
About me:
I’m Dr. Elliot Schneider. I love physics, and I want to help others learn (and learn to love) physics, too. Whether you’re a beginner just starting out with your physics studies, a more advanced student, or a lifelong learner, I hope you’ll find resources here that enable you to deepen your understanding of the laws of nature. For more cool physics stuff, visit me at www.physicswithelliot.com. - Наука та технологія
I was a full-time minimum wage worker, going to school on borrowed money and trying to do Aerospace Engineering at a school known for AE studies. I could not keep working and do all the long labs required as they conflicted with my work schedules. So I majored in Physics and worked in Chemistry (in life) in an industrial research setting. The first books I bought the summer before my first year of college were the three-volume Feynman Lectures and the 2-volume set of D'Abro "The Rise of the New Physics" that new cost $3.00 each, Feynman's Red Books were $5.00 each at the University Bookstore. My course textbooks had not yet arrived and I was nervously wanting to get a head start for fear of falling behind. Little did I know then, on the job, I would have plenty of time to catch up. Now in my retired years, I have plenty of time to review, great job Elliot I like your style and value your explanations.
Thank you Michael! Let me know what else you're interested in learning about!
I am also trying to self-teach and re-purpose myself into an aerospace engineer :) Living in the times there is so many fantastic lecturers willing to share their knowledge available to us 24/7 with all modern day visualization methods is truly a privilege I am grateful for.
I recently found this amazing channel of a guy explaining aerodynamics and thin airoil theory, in case you want to revisit (there are others more formal, but this one is easy to follow):
ua-cam.com/video/QkaG-hDmRiQ/v-deo.html
Good stuff! When I was in school, relativity was almost always ignored by my instructors. I had to teach it to myself. My self-guided studies of relativity have never been Lagrangian-based. I really appreciate this content!
@pyropulse I completely agree! The best teacher that I had in grad school was actually the laziest lecturer that I ever had. He told me that it was only the material that I taught to myself that I would remember well. He was completely correct. The math, the special and general relativity, and the quantum that I know well (to this day) was all self-taught.
Do you consider watching this video self teaching?
@@Nekuzir It's kind of self-learning. No teacher told me to watch it and i'm doing it during my free-time
Your lectures are amazing . these lectures are very didactic and clear, unfortunatly unlike those of many of the professional physicists
Thanks Yair!
Thank you once again. Your videos mean a lot for those who wanna learn things out there.
Such incredibly clear explanations. Bravo!
Great video! Many, many thanks for your valuable job.
Thanks Alessandro!
Good job Elliot
great video Elliott!!
Thanks Max!
Thank you for the video.
excellent video, you're very inspiring :)
Thank you!! Wonderful.
great video thank u , can u do for us a video about conformal field theory
Thanks Mustapha! Maybe! Though that's a little more of an advanced topic
Do we really want to cross out that mc^2, or do we want to keep it in the expression to allow for interactions where mass is transferred?
way to go Elliot. Keep the good work. Physics is amazing. also I noted you have a big screen behind you and as well as a PS5! ahahaha.
Thanks!
I was kinda expecting that you will add a nonzero potential towards the end, which would give more interesting dynamics.
After all, in the U=0 case, objects just seem to follow the good old Newton 1st law.
It is possible in principle to add arbitrary U(x)?
Might in a future video! To introduce a force like electromagnetism, you would add terms q (V + A.v), which geometrically corresponds to integrating the electromagnetic potential A^\mu = (V, \vec{A}) along the worldline. To incorporate gravity, you would replace the Minkowski metric with a curved metric: ua-cam.com/video/h2SEK6Jjv3Y/v-deo.html
From this can’t we deduce that for QM this world line would be Feynman’s path integral?
Thank You. A definition of "metric"
Sir, How the Spacetime interval(S) is related to Action (S) just by a constant (mc)....as action is integral of lagrangian with time and lagrangian of relativistic particle is just kinetic energy (no potential).... Why we equate to Spacetime interval with some constants....and why they have same "S" as representation?
In variational calculus, you first need to find a quantity you want to minimize the integral of; and in this case we want to minimize the metric, as explained in the first part of the video. The fact that action is represented by S and the metric by s is just an coincidence, distance intervals are fairly commonly written with s. As for the mc factor, it's just a term needed to make things equate reality. Notice as it is just a constant, the minimization of the integral can be done regardless of such factor, but in order to obtain equations of motion, we need to multiply by something that tunes it into a proper Lagrangian, which is mc in this case. This happens usually when looking for the expression of the Lagrangian of any system. There is no absolute principle to know which will it be, you need to find it according to what you know in each separate case
I think we draw world lines like that to remind us t is a parameter that we treating like x.
We’re so use to the notion of x(t) and we want to challenge ourselves to change our perspective
12:16 It might be better to say that the length of a line can be considered the shortest distance, or that if one marks out the shortest distance between to points it will be on the line determined by the two points. For, strictly speaking, a line is not a distance.
Might be splitting hairs, but Euclid is delicate stuff.
12:00 But from the twins perspective, they were on a stationary ship, and you zoomed off on a fast moving Earth, so they should see you as "younger", no?
at 8:25 i am not sure about this now, confused, since people in youtube are saying like your way, but
isnt this einstein metric ds2 = -c2dt2 + dx2 and
isnt this minkowski metric ds2 = c2dt2 + dx2 and he treated t-axis as i* t-axis (complex number times time)
You b smart. Live with courage and be true to yourself (and honest with yourself) and you will live a rich and meaningful life. Peace
I am no expert but the math seems pretty good here. Everyone likes to point out how at "non-relativistic" velocities displacement is Newtonian and so on. OK, but when does velocity become relativistic? Seems as if there is always a little relativity going on, sometimes more significant than one might think.
We say it is not noticeable, but that does not mean it is not there. It's everywhere. And everything is moving in a least-action sort of way.
This is probably a case of me just being nitpicky, but in almost every textbook on the subject, I have seen the Minkowski metric being defined by the equation ds^2 = c^2·dt^2 - dx^2, rather than the equation ds^2 = -c^2·dt^2 + dx^2. I realize this is mostly inconsequential, as all it does is change our sign conventions, but it still was confusing for me to see you treat the latter as the Minkowski metric, and I feel as though this approach made it overly complicated to explain what was happening. Using the former, one could have simply written ds = sqrt(c^2·dt^2 - dx^2) without further worries, and this also has the advantage that it matches the mathematical definition of what a metric is (with some caveats). I am merely pointing this out so that people can see that an alternative convention exists, one that is more convenient mathematically, and has no bearing on the physics.
Hi Angel-- both conventions are in common use, and you'll encounter each one depending on the book. In my opinion the convention I use here, ds^2 = - c^2dt^2 + dx^2 + dy^2 + dz^2, is much more natural though, because at a fixed time it reduces to the usual Pythagorean theorem for distances in space.
Thanks a lot for this. This is very good. But shouldn't you be playing the PS5 instead?
🤣
Who in the world would choose a length that is always below zero!
And how we can then just say "ok let's add a minus sign here, cause it's inside the root"?
Mad stuff :)
There are many ways to formulate SR. The ds^2 = -cdt^2 + dx^2 + dy^2 + dz^2 is commonly called (-1, 1, 1, 1) and is probably the one you will encounter the most... but it's not the only one. (1, -1, -1, -1) is also possible. I've also seen (i, 1, 1, 1).
But the Twin Paradox introduces some nasty accelaration into the picture ;-)
That's fine! Contrary to popular belief, special relativity is perfectly able to deal with acceleration - so long as it happens in flat spacetime.
The twin paradox can exist without acceleration too, on the simplest of cases, such as two inertial twins running at opposite directions and communicating through EM waves, in a perfectly symmetrical manner. But it's not a logical contradiction, just a counterintuitive consequence of relativity, contrary to what pop-science youtubers will say. You can also define the twin paradox in a spherical universe, in which two twins go inertially around the universe and come back to the starting point. The details do not matter, all perfectly symmetrical scenarios generate the twin paradox.
@@tomkerruish2982 With the only exception that the acceleration can't be due to a gravitational force?
@@jacobvandijk6525 Yes, because then it's not happening in flat spacetime.
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Not helpful.
The guy is confused when at 11:20 he calls Inertial proper time as being dilated. Yes it is longer than accelerated proper time but it is measured by an observer in one place so it cannot be cited as an example of time dilation.
1) CT is just "light seconds"
2) @9:16 square root of a negative number is an imaginary not a negative number.
3) Very confusing definition of "proper time" Basically it is the time measured by an observer using a clock at relative rest to the observer. It is the un-dilated time measured at one point =To =T/gamma (where T = dilated time).
4) Without clarifying he is comparing proper time between inertial and non inertial frames when INERTIAL proper time is indeed longer than ACCELERATED proper time as seen in the twin paradox. However neither proper time is ever a DILATED time which is the time on a clock MOVING relative to the observer hence measured at 2 DIFFERENT places. So at 11:20 he wrongly called the inertial proper time as dilated time.
I'd like to hear a response to this.
Your hair combing looks like Heisenberg's.
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