Your Daily Equation#6: Relativistic Mass

Episode 06 #YourDailyEquation: Why is the speed of light the fastest possible speed? In this episode, Brian Greene tells a simple story--involving medieval jousters--to motivate the relativistic mass equation, and then uses that equation to explain the speed limit set by light.

Even if your math is a bit rusty, join Brian Greene for brief and breezy discussions of pivotal equations and exciting stories of nature and numbers that will allow you to see the universe in a new way.

The World Science Festival (WSF) is an innovative multi-media organization that produces original live and digital content straddling the arenas of science, technology, the arts, media, performance and education. With the goal of radically transforming public perceptions of science, WSF creates world-class programming, both live on stage and televised, featuring inspired collaborations, outstanding talent and novel production techniques that bring scientific discovery, insight and perspective to a broad general audience.

[DrJeeps]

I'm a psychology professor with an interest in physics. I love these daily equations. Please keep on doing as many as you can. Thank you for your ability to promote and explain the beauty of physics!

[rjohn]

Thanks Brian- I'm 73, never took physics or calculus, and I was able to follow- not saying I could do it but I got the principles and will now watch all of these. Hate being house-bound when you've ignited my inner Cliff Klaven.

[navstar]

Just happened on this series... A Daily Equation - what a great & practical format for many of us folks. Liked the jousting analogy & KE explanation in this one 👍. Many thanks for the videos Brian😊!

[ffggddss]

"Relativistic mass" is a broken concept, because it works only for the special relativistic (SR) formula for momentum, p[rel]. When learning relativity, it is a mental crutch that attempts to preserve the Newtonian form of momentum by making mass depend on velocity. In fact, it isn't that the mass is changing; it is that the functional dependence of momentum on velocity, differs from the Newtonian p = mv; namely,
p[rel] = mv/√(1–[v/c]²) = m(γv).

And it is this change in the formula for momentum that makes attaining v=c impossible for any body with non-zero mass.
The culprit is still that factor, "γ, " but it is properly attached to the "v, " not to the "m."

That this is so, can be seen by trying to plug this "relativistic mass" into the Newtonian formula for kinetic energy, KE = ½mv². It gives the wrong result. The actual formula is
KE[rel] = (γ – 1)mc² = (1/√(1–[v/c]²) – 1)mc² ≠ ½γmv². (Dr. Greene's derivation of the Newtonian KE from E = mc² is exactly right, however.)

"Mass of a body" is a property of the body itself, not of its state of motion – or, in fact, of the state of motion of some arbitrary observer! Because it is a central principle of SR that physics "looks" the same in any inertial frame of reference. Two observers in uniform relative motion to one another should assign the same value to the mass of a body.

Fred

PS. See the excellent, less technical explanation of this by Dr. Don Lincoln on the Fermilab channel.

[TheAdithya]

Thanks for the explanation! The example, despite being a bit contrived illustrates nicely the need for an increased mass - to conserve momentum. A less contrived way to show that a mass increase is required is to use the impulse momentum theorem viewed from an objects instantaneous rest frame and comparing it with the equation that arrives from a static frame at rest.

[BadassRaiden]

I think the biggest thing i like about these, are that, now that school is out for most children and young adults, no one is learning anything. And if worst case scenario the education system falls apart (probably not likely but hey) then we still need not just the information out there to go and find, but we need those individuals who would pull information they know and understand, and instead of just lazying about and being the keepers of that information, they share it like this, often times information most people wouldnt bother to try to understand. This way, the most mind blowing of information, isnt lost in the crisis (again, probably not gonna happen, but i hear a lot of people talk about how thankful they are the internet is still operating). I once heard, maybe NGT talk about it, but something was said along the lines of, "if everyone who was knowledgeable enough to make a cell phone from scratch, how long would it take for us to reinvent it, if all those people disappeared?" Of course we arent only talkin about people disappearing but the information they carry with them being lost in time. It seems many civilizations succumb to this tragedy. Im just saying, teachers and professors, those with knowledge who's profession is to teach others, i think they should all be doing stuff like this, sharing their knowledge freely and openly.

[hardlyconfused]

Disagree. This is what I read from Wikipedia:
In Einstein's first 1905 paper on E = mc2, he treated m as what would now be called the rest mass, and it has been noted that in his later years he did not like the idea of "relativistic mass".
I know Wikipedia may not be 100% accurate, but please correct me if the references are not correct.

[irenemedvedev]

Thank you very much from New York. Looking forward to new episode every day!

[martijn]

Can't wait for this. Thx Brian for the stuff you have shared during the years. Amazing how many implications there are for all basic ingredients of physics when relativity is set in motion.. .time, space, and now mass.

[enotdetcelfer]

Wow, really wish I had learned this in school like this, it makes so much more sense to see the series expansion and to realize all the types of energy that goes into your "total mass" great stuff I hope you do more of these!

[RichardAlsenz]

Read Gauss!
Gauss to Bessel Goettingen 9 April 1830 …
The ease with which you delved into my views on geometry gives me real joy, given that so few have an open mind for such.

My innermost conviction is that the study of space is a priori completely different than the

study of magnitudes; our knowledge of the former

(space) is missing that complete conviction of necessity (thus of absolute truth)

that is characteristic of the latter;

we must in humility admit that if number is merely a product of our mind

[snarzetax]

"Alright, I'm going to have to answer this phone." I felt that. 😆

[gioivanmijares]

After how many videos about mass, finally I understand it now Thank You!!!

[WalterBislin]

Very nice example with the 2 riders. Never seen before.

[Eponick]

This series is great! Something to look forward to every day in these stressful times. This made me realize I've never heard a relativistic reasoning of escape velocity. Probably because its simpler in Newtonian terms but this would be much more interesting.


For instance: How does the increasing energy/mass of the rocket affect the curve as you accelerate to escape velocity? Would a substantially larger mass have a much higher escape velocity or is it negligible?


I know I can look it up but I may try to work it out on paper first.
Thanks for everything you and the folks at WSF do!


EDIT:
Apparently I incorrectly assumed the mass of the escaping object mattered... Not sure how it doesn't matter at thought-experiment level masses, though. Ignoring factors like solar system instability if you were hauling a cube that was equal to the mass of mars it would have to greatly increase escape velocity since the earth would be pulled towards the ship as you accelerated.
May try to work this out, but a fun side note (if i'm correct) you weigh approximately 1.6x your weight at 11.186km/s relative to your weight on earth.

[jsbllrt]

Brian, this classes are so amazing! Thank you very much!! Cheers from Buenos Aires!

[seamusandpat]

Thanks for this wonderful series. I am enjoying it so much.

[bluefinance]

Could we please do the equation of the Wave function or the Harmonic oscillator

[ibite]

Thanks for these videos, very well explained, could explain afterward to my daughter who is 9 and she did not get excited by but understood and accepted the consequemces of the relativistic effects and was able to explain it back afterward. Good enough for me.

[putinscat]

1) Matter warps space. 2) Space warps at the speed of light ( meaning if the Earth moves from point A to B, the space warping around it at those points has the speed of light restriction in the change of warpage ) 3) Now accelerate an object close to the speed of light, and try to see the resistance to change of the space warpage with an object that is moving at almost the maximum limit. This resistance of the entire universe's gravity warping thru very fast moving matter is why mass seems to increase, and why you can't get to speed of light limit. 4) Only by warping space around an object could you move faster.