Kinetic energy: Newton vs. Einstein | Who's right?

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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[jaimeduncan]

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.

[robertbaraszu]

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!

[Mutual_Information]

Wow, connecting high school physics with Einstein using the binomial theorem. Very cool.

[davidg]

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.

[russelltaylor]

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.

[jacksonstarky]

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 YouTube channel 3Blue1Brown, so that I could follow the physics here and on PBS SpaceTime more closely.

[saintsolaris]

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.

[timrwilson]

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.

[joecanales]

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).

[rahularyaphysicist]

I appreciate and respect your work sir!
You inspired me about physics.
Support from India.

[richardturietta]

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!

[earthwormscrawl]

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.

[segoldGA]

Don you’re my hero! Thanks for your public service!! Enjoying The theory of everything in Wondrium. Awesome!!

[riccardofecchio]

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!

[IngTomT]

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<<c

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!

[det]

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.

[litigioussociety]

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.

[physicsman]

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.

[joseraulcapablanca]

Thanks Doctor Lincoln, the maths was interesting not too much of a problem either. Keep up the good work.