Kinetic energy: Newton vs. Einstein | Who's right?
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- Опубліковано 11 чер 2024
- Using Newtonian physics, physicists have found an expression for the value of kinetic energy, specifically KE = ½ m v^2. Einstein came up with a very different expression, specifically KE = (gamma - 1) m c^2. In this video, Fermilab’s Dr. Don Lincoln shows how these two equations are the same at low energy and how you get from one to the other.
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Yep, I love it. That is the proper level of Maths. The most impressive thing is the derivation from first principles and ends up with an equation that "matches" the classical results, both for momentum and KE. I was in shock the first time that I did the Taylor expansion of the relativistic KE.
Me too, I thought this is sooo cool
Did you then compare, say, the first two terms of the Taylor expansion to, say, the first ten terms to see that a great, local approximation generally only requires the first two terms?
@@RME76048 You can see that very easily as the thrid term already contais 1/c^2 and the fourth 1/c^4
Dark matter /energy paradox SOLVED
m.ua-cam.com/video/ZQNWVQc5sNI/v-deo.html
Turned out correct formula is E=mc²D² where D is time dilation (discovered by Einstein as well, and used twice in his two theories, but not third time - and that led to his biggest mistake switching to expanding Universe and now staying with time dilation alone). Free "Time Matters eBook" shows it well. Last 100 years of physics (apart of nuclear physics, thx to 1932 neutron discovery) were lost because of this simple Einstein's inconsistency.
I'm finishing out a 40+ year career as a control systems engineer in the auto industry and recently decided to catch up on all of the developments in physics and astronomy that I have missed over that time. Your videos are excellent and are my favorite learning tool thus far. I still have about 60 videos to go and am looking forward to them all. Thank you so much for sharing your knowledge. I feel like I'm back in school!
You chose the best teacher.
Then, I suggest you also follow this channel. ua-cam.com/users/howfarawayisit
I think you'd like it.
Well, if you're back in school ... 😇 ... it's "Your videos", not "You're videos" which is "You are videos".
@@KaiHenningsen I'm an old man. I'm confused.
Love the math, but the physics I love even more!
Wow, connecting high school physics with Einstein using the binomial theorem. Very cool.
I'm OK with the math even if you got heavily into motivating it. But from a less math-centric point of view, I think the level employed in this video still does an excellent job of showing how the math justifies the typical verbal explanations and analogies.
I think it's pretty much understandable as long as they add the verbal explanation. It's not that it's so difficult, it's more like most of people don't have the time to check the equations as if they were going use it professionally tomorrow.
Thank you for that explanation.
Yes please! It's a rare treat to find someone that is both good at math and good at explaining these topic. That was a reasonable amount of math, and I would enjoy more videos with that in them.
Nice video! You point out that most man-made objects travel slowly enough that the Newtonian formula for kinetic energy is very accurate, but I’m a bit surprised that you didn’t mention that particle colliders accelerate particles to near the speed of light so the relativistic formula for KE is very relevant. It explains how we can keep increasing the KE of a particle while it’s velocity changes only very slightly.
Classical physics doesn't fit in the quantum realm. Particle colliders are man-made but they're to accelerate the particles not ordinary objects. I think that's why he didn't mention it.
Wonderful! Elegantly presented too! Thank you Fermi Lab
& Dr Don.
Thanks for your explanation. I only had ‘classical dynamics’ in college because my field of study were large macroscopic objects where this works perfectly. But I always wondered where things started to deviate, where linear relationships might start to vary or whether constants were in fact constant throughout the history of the universe (mostly wondered about the gravitational constant).
,😁
I'm a big fan, Don! Great video, I think your explanation is clear and interesting. Thanks!
I loved the math in this episode! I've read the English translation of Einstein's own book on relativity and had no trouble with the math there or here, and taught myself calculus in the last few years with a lot of help from the Internet, especially a series of videos from the UA-cam channel 3Blue1Brown, so that I could follow the physics here and on PBS SpaceTime more closely.
Wow! That’s impressive! Something similar is on my todo list for when I retire. For now I have too many interests, and days are too short and busy. Kudos if you can follow pbs spacetime: I have given up because most of what they talk about flies over my head.
I recommend channel "eigenchris" for relativity math
where can i get a copy online is it free?
Been a long time follower. This was great, as always, and I'm fine with this level of maths. Could probably handle a bit more complexity.
I appreciate and respect your work sir!
You inspired me about physics.
Support from India.
I graduated from Penn State with a degree in Electrical Engineering back in '82. At the time of graduation I could do calculus and differential equations in my sleep. I can now follow along easily, but I'd be hard pressed to setup the equations and initiate the process like I used to. This is a great series to help scrape off some the mathematical rust.
Don't hesitate to get more "math-y" in the future. Adding in some calculus and DE's would be great.
This is so accessible and provides such insight. TY!
Don you’re my hero! Thanks for your public service!! Enjoying The theory of everything in Wondrium. Awesome!!
This is exactly the type of "Physics thinking" that so many non-physicists aren't trained in, and don't understand. It reminds me of the "sin x = x" for small x approximation. It is the kind of thinking I learned while getting my Physics degree and I am happy to see you spreading the same technique! Great video, keep up the good work!
Thanks for connecting all of this in my head! I love it when I know different equations and then after many many years someone tells me how they are related! Im like of course duh. Then I realize it takes a great teacher to show it.
Looking good Don Bot! Thanks for the math infusion on the big KE
You have a great sense of humor for this kind of thing.
It's not stand-up comedy quality, but it works well for this.
I once had a dentist in Lititz PA who told not-the-funniest jokes as part of his dentistry.
The jokes sucked, but when somebody is drilling on your teeth, it works surprisingly well as a convenient distraction.
This video has the power that E=mc² had, has and will have in physics! Great! Explained in highschool classrooms will make students love math and physics more than ever! Bravo!
Amazing! Thanks a bunch for the explanation.
Love it!! That was a very succint and clear explanation. Please have MORE math heavy videos
Thanks you for that Don. The maths was less than I had to know for passing what in England and Wales was called 'O'-level at 16 years old in the 1960s. I have watched the video twice and, with pauses and the back-button the second time around, it makes sense to me 55 years later. Excellent. If you stick with this kind of maths level I'm fine.
Thanks Dr Lincoln!
More math videos !! This one was brilliant
Great video. Thanks again.
Great video.
Good amount of math! Very clear and interesting!
A more intuitive way of writing relativistic KE would be:
KE = 1/2 mv^2 + 3/8 mv^2 (v/c)^2 + 5/16 mv^2 (v/c)^4 + ....
This way you can see very easily that the contribution of the 2nd and higher order terms get very small very quickly for v
Fascinating! Absolutely loved it
superb presentation, I'm grateful
Thanks a lot Don! Especially for the math. I looooove it!
Really Good Video! Much Praise!
Congrats Dr. Don! Another excellent and scientifically precise video.
Here is my suggestion: I'd love to see a video where you explain the blend between quantum physics and special relativity a.k.a. the dirac equation, but made a little more digestible.
I second that but would like to see it done with Geometric Calculus, SpaceTime Algebra and the Real Quantum Mechanics notation and concepts of David Hestenes.
Very good. Great explanation, thanks.
I loved it ! I’de love to get more of these videos :)))
I have a love-hate relationship with maths because I like them but I always make dumb mistakes and end up messing up the result. But I love to see these kind of explanations, and since you walked us through the process very patiently, I was able to follow through.
Thank you!
Clear and consise. Great, I love it.
Excellent video thanks.
The calc figure might be similar, but kinetic energy is very different under Newton and Einstein Furthermore, in many cases, we have built things that the difference is important.
Another awesome video. Bravo
Thank you for your explanations. In my view the maths here was easy to follow.
Wonderful video, Don 😀 More math, please!
More math centric videos please. Cast your vote guys 🫰
Fantastic video as usual! More math please.
Be careful what you wish for 😊
Thanks Doctor Lincoln, the maths was interesting not too much of a problem either. Keep up the good work.
Excellent, as always !
Very happy with this level of maths, another enjoyable and educational video.
Understood every equation in this video intuitively 👍🏼👍🏼
Well done DON ☆☆☆☆☆
It was even for an old undergrad , not that big of a mathofobical nightmare to understand .
Or its your ability to teach us such things , remarkable fast !
Grtzz from the Netherlands Johny geerts
Thanks for the video. I would very much like to see some more math.
Thanks, Don!
I like the math. I don't understand it directly but you explain it well and that gives depth of meaning to the videos.
Thank you Don for sharing kindly your knoledge as usual. I would like you in next videos, to deepen in the subject space, how all is space, even the very constuitives of the matter, how spands, is it created or streched or is the same, and the quantic space, and is there a space that contends our universe, and why with expansion we se galaxys like there were and not how they are, if not its allways like that? Total thanks Don, I am allways looking forward for your videos. I hope you are helthy and happy
Thanks DrDon 🙂
Don, you're simply the best!
Great video. I like the math, especially because of the way you explain it.
Definitely would enjoy more math-centric videos!
Though one may not say that the maths was elementary but it wasn't difficult either, plus without the maths, not sure how could have this video been made. It was just perfect, rightly balanced for viewers to understand, derive and co-relate the classical and Einstein's equivalent equation of KE. Awesome, Dr. Lincoln, thank you!
As long as the math focuses more on relationships and terms like in this video, I find it very informative. When it starts to dig deep into explanations and proofs, then I lose interest. For example, I like Mathologer's videos, but the second half of his videos that are sometimes more technical are things I often don't understand or skip unless there are geometric visuals accompanying it.
Visuals are always very helpful for me, such as when you show a neutrino changing, and not just explaining it with words.
I loved it thanks for the amazing explanation:D
Math comes into play in beautiful fashion in a few iconic results of Physics. I have a couple in mind, but since I forgot one, I will say a result that blew my mind. In the 3-body problem, there is a solution in a given configuration in which the 3 bodies orbit the center of mass along a number 8 shaped form. That blew my mind.
As I haven't used calculus since my school days, some decades ago, I quickly got lost and started to tune out. I stuck with it though and soon found that I was following quite well. Though I did get lost for a time, I managed to get the overall gist of it.
Love this stuff!
This was great and very clear
Lovely video with appropriate maths! Without some maths, it is very difficult to comprehend physics!!! Pls do incorporate more and more maths in future videos...
Please more maths. Viewers who don’t understand the maths equations still can listen and get the idea because of your excellent explanations.
Another amazing video
I teach maths so having maths in the video is welcome. Though I didn’t go deep into it but it’s good to know the overall conversion from relativistic to classical energy. Also, it shows how maths is fundamentally important in physics. Thank you.
More math and technical details in videos please!
It's fascinating how you can view the relativity equations as adding correction terms to the classical ones, and those terms are based on the relative speed with respect to light. It's so elegant.
In the 'old days', working with the design of color TV CRTs which used 30kV screens, we found that as the screen became larger and we were moving to HDTV, one could not calculate/simulate the sharp e beam focus required without at least 'perturbing' the electron mass. Other things like build and voltage accuracy and current density were bigger problems but you know, engineers like to get it right. ...which is defined as good enough
The math was very helpful and insightful.
MORE math please! That was fantastic, a very engaging synopsis of the math. I don't care if a lot of it scrolls quickly as you get to key points to stop and explain in more detail. I'm not a mathematician or physics (comp sci) but I love seeing the nitty gritty of the math. I've seen too many physics videos with abstract descriptions that are repetitive and boring. Seeing the math is much more enlightening about what's really going on. I'd love to see Durac's equation derived and used in calculations and even some of Schrodinger's wave equation.
Dare I ask for a mathematical synopsis of GR field equations? 🤣🤓😂
Appreciated❤️ want physics with mathematics ✨
Good for the layman and for the scientist. For sure i enjoyed the presentation and the math.
THANK YOU PROFESSOR LINCOLN...!!!
LOVE MATH... BUT TODAY CANNOT GO BEYOND BASICS... BECAUSE HARD TO REMEMBER EQUATIONS AS WELL AS LOOSING THE CAPACITIES FOR MENTAL PLACEMNTS due to several factors ...!!!
THANKS AGAIN...!!!
Love it!
Please give your all.
Go ahead Dr. Lincoln !! More math !!
More math and physics centered videos please!
Omg, I never imagined I would learn so much in 8 minutes of video. Now I get the formula for total E of a body. The binomial expansion is my old acquaintance, so I'm good.
this is great, we were never taught this in high school
Please make more like this
Cool guy connecting two things which I never expected to .
I also appreciate your struggle to find each time interesting endings that fit well with "physics is everything" :-) ; as for me i would say more like "everything begins with physics"; or is it ?
I’m curious why it’s referred to as a relativistic correction, when isn’t it really more of a classical truncation?
Dr Don, I'm a maths phobe, but I do enjoy these videos.
*More please!*
Yes, please show your work! Don't apologize for speaking the true language of science.
Love the math. I now have an inkling as to why the particle accelerators release so much energy when the beams collide.
Thanks Dr Lincoln. Any chance of doing something on black holes and how can they possibly form within a finite time?
Great video Dr Lincoln. Yes please, adding math to the videos makes them even more valuable. Like you said, Physics is everything but without math, it is just.. physics.
More math please! It isn’t 100% necessary to create an approximate understanding of a physics argument but it is necessary to create a deep understanding, and sometimes fundamental
Thank you for a very interesting video, Dr. Lincoln. There is however a minor mistake. The fastest man-made object, the Parker probe, will reach 190 km/s at closest approach to the Sun (expected for 2024, its current record is 160 km/s) . Eleven kilometers per second was, for example, the re-entry velocity of an Apollo capsule on its way back from the Moon.
Very well done
Amazing video.
Thanks professor.
Yes the was great! More math please
We want more, way more math-centric videos Dr. Lincoln. Please, keep 'em coming!
math or no math ur presentations are always very digestible!
More math please. An addendum video to go even a bit deeper would be awesome.