Is relativistic mass real?

One of the oddest features of special relativity is the inability to go faster than the speed of light and this is absolutely true. The most common explanation is that the mass of an object increases with speed, but this particular explanation simply isn’t true. In this video, Fermilab’s Dr. Don Lincoln explains the truth behind this. (And, no, don’t send him emails about how this proves relativity is wrong. He is a strong believer in properly-understood relativity.)
Dig in deeper here: arxiv.org/pdf/...

[@kripashankarshukla4073]

Earlier, I found relativistic mass concept very difficult but after watching this video, I finally understood the whole concept. You are just awesome.

[@sangvinhun]

layman: so, how do we go from newtonian mechanics to relativistic? physicist: just put in the lorentz gamma factor into every equation bro

[@llhique6409]

No u have to put a gamma raise to power 3 in force equation I.e. Newton's second law 🤓🤓

[@s_patzz8212]

I like this. It's FUNNY... and it's TRUE!

[@arthurd8340]

rapper: ain' no god bro physicist: let there be Light fool

[@kashyapnadig]

In the numerator or the denominator?

[@davidwright8432]

Equations are fine! they're just more precise (and so more useful) than saying exactly the same thing, in any spoken language. Please use them often! With, of course your usual clarity of explanation. Thanks!

[@stevee8884]

His T-shirt says: "It's all fun and games until someone divides by zero"

[@peterbourke]

is that a negative zero?

[@LegendThriller74]

@@peterbourke I can infinitely say it isn't negative zero🤣

[@andrewcaldwell0311]

Danny Byrge I’m infinitely confused lol

[@infarredpyro]

If you make it magnatic fild of wold attack by electromagnatic superhigh Around time of your unless ability gravity and spacetime of the wold The energy source releases the particles. pressure Atom and matter Keep away The time gap creates a black hole and is the fourth dimension. 4D That energy must be enough to conquer the world mass.

[@infarredpyro]

🤣🤣🤣🤣

[@Dimblenick]

In fact, i want more equations

[@feynstein1004]

Seconded

[@blurryvision4815]

Omar Adel thirded?

[@twistedsim]

tripled

[@bautibunge737]

Foured

[@JoshSideris]

Not before understanding something intuitively! Just learning the equations alone is why you get some people thinking that **F=G(m_relativistic*m_2)/r^2** works.

[@dlam2864]

1:43 i think all your viewers are "physics minded"

[@P-G-77]

or simply very curious ... like me ... I'm not a physicist or a mathematician but certain subjects interest me so much that I took the trouble to learn certain notions. In fact, I would like some videos to be even more present on youtube.

[@hxhdfjifzirstc894]

I'm just here for the jokes.

[@davidmarilley6060]

Important post since we hear "rest mass" too often. Thanks for giving it a rest.

[@anno96]

Finally. I was confused af when I learned that when something move at the speed of light it should have an infinite mass, while the photons have 0 mass, and after that I thought when u move a bigger mass it would be harder to move than a lighter mass so imagine that you should move an infinite mass that would be infinitely hard, but that turned out to be not true thanks to your explanation 😃

[@aidanandrewson7223]

I very much love these videos in any format, so I'd do what feels comfortable for you

[@Trident_Euclid]

Aidan Andrewson same

[@bullymaguire2061]

collab with pbs spacetime...

[@misterright8626]

This guy is better than Spacetime.

[@martixy2]

Let's not go there.

[@benjfactor]

Whatever happened to the first guy on spacetime?

[@yce1234]

I enjoy the more technical, mathematical, deeper discussion. Good work!

[@matthiasburger2315]

Thank you for this video! I remember my prof at university explaning this (in 1995) and adding: "Imagine a Lorentz-Transformation of an object with mass m. Time and velocity changes under this transformation - what would identify this object as itself, when its mass would change, too? Mass needs to be invariant under Lorentz-Transformation."

[@ZachDxn]

Fantastic video! I love that you give the equations but still make the theory easily understood for people who aren't interested in them. More formulas would be great as long as you can continue to explain the concepts without needing them.

[@PenaUrkuri]

Too technical? not at all! you explained the equations used in really simple terms. Bring more equations in! they don't take away they ad to it. I am a teacher my self from Finland, history thou not physics, and primary sources are always welcome. Like a historian might bring up radiocarbon dating method physics need to show what tools it uses. Not everyone might understand the whole thing, but in general scientific understanding videos, like all fermilab videos, aim is to show and tell how we do these things and how science works. Keep up the good work!

[@timwcronin]

Pena Urkuri I would've actually preferred to see the equation under inertia when you had it up! (1:50)

[@theultimatereductionist7592]

AGREED, Pena Urkuri!!

[@oomegalinux]

I liked the fact that this video was more technical than others. In fact, I'd like to see more equations, but this is just me. I think is not bad to put the equations as long as you explain the idea behind them. Then people that can understand the equations and the ones that don't will benefit from the videos.

[@USA2Brazil]

Agreed, though I would like to see a deeper brakedown on the equations done on a part by part series basis.

[@-danR]

A simple gedankenexperiment is better than any number of equations. A particle in a super-future accelerator is travelling so fast that its 'relativistic mass' is 100 times the mass of the earth. Therefore it attracts the earth in such a high gravitational field, due to its...mass..., that the earth could revolve around the particle more than vice-versa (of course, they revolve around a common center, but never mind). Now, I'm sure there are people that would, barring the technical challenges, say "yup, that's relativity". To insure they are also dissuaded, now consider _two_ such particles, now travelling side by side. Either one has the gravitational field that at some 100,000 kilometers distance they would attract each other with a force 100 times that of the earth at the same distance. The relativistic 'mass' disappears in the mind, without a single equation. Of course no such attraction would exist. And the mass would not exist.

[@quecisneros]

I am a theoretical chemist earlier in my career an organic chemist and I love these explanations with more fundamentals and formulas already known and yet with a digestible way to explain them to the general public. I believe these should be taught to more people so that they now how modern World functions and spell the act of charlatans off. I love your explanations I am a fan.

[@charlesrgordon]

I thought the video was eloquent and informative, and thanks for introducing gamma

[@threadthathasnoend1212]

I really liked this video and would love to see more similar to it. I'm not in physics but I do have a passing interest. Thank you for what you guys do

[@yukterez]

There wasn't too much math but too little, we want to see what effects the kinetic energy of a moving objects excerpts on the gravitational field, because we know gravity couples not only to the rest mass but also to the momentum (a box of gas weights and gravitates more if you heat it up because of the kinetic energy of the gas atoms divided by c²)

[@celiogouvea]

Yukterez Net so why it weight more if there are the same amount of subatomic particles? I don't understand that! I think "mass" is some kind of resistance in between matter and dark matter (space-time), the more speed, the more resistance so, we think the mass increases but, in fact is the resistance. The momentum could be the action = reaction, in the case of gravity the action > reaction due to differences of dark matter densities.

[@ronaldderooij1774]

@@celiogouvea Energy is just a number. It is a potential of something. Nothing more. Yes, more energy at one spot creates bending of spacetime. It is in Einstein's equations. But you have to derive them. Good luck with that.

[@ffggddss]

@Yukterez Net: The math for the gravitational effect of kinetic energy of a (relativistically) moving object would likely be overwhelming; you'd have to break out Einstein's Field Equations to show that, with the stress-energy tensor containing the large momentum term. I think you'd want to start with the Schwarzschild solution for, say, the Earth, and do some kind of perturbation for the "cosmic bullet." Maybe after some appropriate approximations it could be reduced to a dull roar? I'm not prepared to attempt that, but maybe someone is... Fred

[@ericsu4667]

Relativistic mass is not real, of course. Conservation of momentum shows that mass is also conserved. sites.google.com/view/physics-news/home/transformation

[@jomen112]

@@ericsu4667 If you treat mass and energy as the same, i.e. being momentum, then mass is conserved. But if you think of mass as a special state then it is obviously not conserved. E.g. in matter/anti-matter annihilation both viewpoints are valid. This non-conservation view of mass indicate to me that it is not a core property of nature, rather momentum is a more basic concept.

[@wwttwtlee2489]

I think that relativistic mass is a very useful concept in relativity. In SR, we have F = dp/dt where t is the proper time and p = mv in which m is the relativistic mass. The equation tells us the the larger the m, the larger the force required to produce a given acceleration. This shows that m has the meaning of inertia of a body.

[@tom_something]

5:39 - This formula can be derived geometrically. In fact, I once did so without knowing what exactly it was after someone postulated to me that everything travels through space-time at the speed of light, and all we can change is the direction, not the magnitude, of that 4D vector. And I'm no math whiz. Let C, the speed of light, be 1. 1 what? One lightyear per year, if you'd like. This is the speed at which you're going through space-time. For any of us on Earth, that's going to be pretty much all time, and no space. We're not going through space very fast, so almost all of our traversing is happening through time. There's another video on this channel about that. That's four dimensions, which is kind of a pain. But you can collapse it down to two dimensions by having one dimension represent time and another dimension represent the three spacial dimensions. You're allowed to do that for what we're about to do. So now your velocity vector is always the same magnitude, or length, and it's just pointing in different directions based on how quickly you're traveling through space. You can split that vector into a right triangle. Side A is your spacial speed, as a fraction of C. Side B is the rate at which you're traveling through time. And side C, the hypotenuse, is... well, C, the speed of light. And we already decided that we're going to use a unit system where C can be 1. That's OK. We can do that as long as we're consistent. So, good old C^2 = A^2 + B^2 C = 1 A = speed divided by C. Since C is 1, it's just going to be some number between zero and one. B = the rate at which we travel through time. We want to solve for B to answer the question, "at what rate do we travel through time depending on the rate at which we travel through space". B = sqrt(C^2 - A^2) And remember, A is equal to velocity divided by C, and C is 1 therefore... B = sqrt(1 - (v/C)^2) Look familiar? It's the inverse of the equation shown on the board. That makes sense. If our traversal through time is 0.5, or half its normal speed, then the equation on the screen represent the factor by which time has slowed down. Not "time" as in the speed the thing is moving. Rather, the speed at which the object's attributes can be changed. The factor by which inertia is effectively increased even though its mass--and its gravitational influence, and also any other factors that are supposed to scale with mass--remain unchanged. And that's gamma. And again, I'm hardly a math whiz. It's just a right triangle.

[@marcmarc172]

I'm a huge fan of the channel and I really enjoyed this video in particular. I thought you were, indeed, gental when you used those few equations. I love how much you smile throughout the videos; it brightens up my day. Keep up the great work!

[@polarnorth]

gentle

[@wgm-en2gx]

I prefer a little math in these types of explanations. However, I might be more math oriented than some.

[@ericsu4667]

Relativistic mass is not real, of course. It is merely a concept from Lorentz Transformation which violates conservation of momentum in elastic collision in any reference frame that is not center-of-mass frame. vixra.org/abs/1802.0099

[@ericsu4667]

his comment is about relativistic mass which does not exist.

[@ericsu4667]

Do you know about Lorentz transformation in detail?

[@ericsu4667]

I am actually asking you how much you know about physics, relativity, and Lorentz transformation. It all depends on your major in college.

[@aremijfaye5160]

What 's wrong with this: E=gamma*m*c^2 With a bit of manipulation we can get E^2 -v^2*E^2 /c^2=m^2 c^4 When v increases, the left hand side term decreases, which means the right hand side (m^2c^4) is decreasing. Which simply means the rest mass decreases. Does it mean an increase in velocity implies a decrease in rest mass?

[@fvckyoutubescensorshipandt2718]

I used to the think the energy used to accelerate was literally converted to mass it took so much of it. These days I like to look at it from the time dilation standpoint; the faster you are moving the less time you have to accelerate. If you are in a ship that can do 1G (9.8m/s^2) acceleration at rest (or close enough to it from a relativistic standpoint) that doesn't do very much when you are already going 90% lightspeed and the time dilation makes your acceleration slow to about 4.45 m/s^2 with the same apparent thrust/energy. At 99% it's down to 1.4m/s^2, 0.47 m/s^2 at 99.9% and just gets about 3x slower for every 9 added = accelerate forever you will just get closer and closer but never reach it. Sounds easy enough until you realize the amount of energy/antimatter needed for a 10,000-ton ship, even with 100% conversion efficiency. To keep that acceleration up 24/7 for 9 months ship time (about what it takes to hit 99.9%) just to reach Proxima Centari (and fly right past it since you aren't slowing down) is many times the weight of the ship itself. (~22x assuming 100% efficiency). Not to mention it'd have a kinetic energy of 24M megatons of TNT, comparable to the asteroid impact that took out the dinosaurs (well, same order of magnitude). Rocket problem all over again, just with antimatter instead of chemicals. Also kinda hard to find 220,000 tons of antimatter lying around.

[@wayneyadams]

I have never used the term relativistic mass in my classroom. It leads to all sorts of crazy misconceptions. I have had students who said all you have to do is get a body moving fast enough to increase its mass to the point where a black hole will be created. I usually tell my students that the force required to accelerate the body a known amount increases as the body travels at higher velocities. In other words, the inertia increases and we simplify the concept by calling it a mass increase, but the actual amount of matter does not change. A physics student performs a simple experiment where he applies a force to a body and measures its acceleration. Just as he is doing the experiment, ALF (Alien Life Form) flies over at some relativistic velocity and observes the experiment. Since motion is relative, ALF observes the experiment being performed in a moving frame of reference. When he does his calculations, he finds the force required to accelerate the body to be greater than the result the physics student obtained. The faster ALF is traveling, the greater the difference. It's as though the mass had increased giving rise to greater inertia, but there has been no actual mass change. Particle accelerators have to adjust for this inertia increase as they accelerate particles to velocities close to the speed of light. One more important point, inertia is never equal to mass unless the body is stationary in the observer's frame of reference. it's just that the relativistic effects are so small that they are insignificant and undetectable. That is also so true for time dilation, length contraction, and velocity addition. There are not separate equations that suddenly kick in at high speeds. The reason the relativistic effects are negligible in our everyday world of low speeds is because of the (v/c)^2 term. v/c is extremely small and (v/c)^2 is ridiculously small. For instance, the Space Station orbits at about 17,600 MPH which gives us (v/c)^2 = 0.00000000069. if we subtract that from 1 we get 0.99999999931. In fact my calculator gives 1 when I do the calculation because the value is smaller than the precision of the calculator. Wayne Adams B.S Chemistry M.S. Physics R&D Chemist 9 yrs. Physics Instructor 33 yrs.

[@xXZ31t6esTXx]

Don't worry about putting ecuations in your videos as long as they are simple like this one! :-)

[@xXZ31t6esTXx]

I mean I could watch a whole set of videos explaining Eistein's ecuations but only if they start from highschool educ

[@chrisherrick2397]

My definition of simple stops at tensor calculus.

[@finnelhumano6096]

Sometime ago I saw a 2+hour long lecture in youtube on general relativity that explains all the math involved from linear algebra and, I think some multivariable calculus

[@finnelhumano6096]

Sometime ago I saw a 2+hour long lecture in youtube on general relativity that explains all the math involved from linear algebra and, I think some multivariable calculus

[@rz1653]

It is all about exposure. Even tensor algebra gets simple once you get used to the ideas.

[@RTlnx]

I think the base level is perfect. I'd actually enjoy more 'advanced' videos where these more basic ones are further explored. Perhaps confine the math to those 'advanced' videos instead of having to apologe for using maths in many videos?

[@rykehuss3435]

Try PBS Spacetime, Sixty Symbols, Numberphile etc

[@merloon]

PBS Spacetime will melt your brain

[@T33K3SS3LCH3N]

A professor used this relativistic momentum idea to explain to us why photons have "mass" for the purpose of momentum despite not having any rest mass. I'm glad I knew about this video for a more complete explanation. So if I put the two together properly, it's that in p = γ * m * v, the multiplication with m=0 at light speed can still give a non-zero result because γ becomes an infinity that happens to yield an actual result for this equation. At least as a rough plausibilisation which clearly can't be entirely correct since not every massless particle has the same momentum.

[@AliothAncalagon]

Zero times infinity is still zero. What are you talking about? Relativistic mass is real. You found one possible answer yourself why denying this makes no sense. Most physicists simply don't like how its used, because calculating around with it induces mistakes quite quickly and doesn't usually offer much use.

[@ffggddss]

Short answer to the title question: No. It isn't that mass increases with speed; it's that momentum increases faster than p = mv, and kinetic energy increases faster than T = ½mv². And the particular way they do this, differs, making the usual "relativistic mass" formula erroneous. It is the true formulas for these quantities: p = γmv = mv/√(1-[v/c]²) T = (γ-1)mc² that makes the speed of light, c, unattatinable for objects with mass. Post-view: I'm glad you also brought up the gravitation of a relativistically-fast-moving body; to work that effect out, you need to delve into Einstein's field equations of General Relativity. And that situation is again different from simply assigning the fast-moving body some "relativistic mass." It seems to me that the central principle here is that of relativity itself - that every inertial reference frame is equally valid for describing and working out the physics of any given situation. And this is a principle that already arose from Newtonian mechanics, where it takes the form of Galilean Relativity. With that foundation, assigning a body a relativistic mass is tantamount to abandoning the whole concept of the mass of a body, because mass then becomes no longer a property of the body, but of the body together with its state of motion/choice of inertial frame. It also occurs to me that this philosophical point is perhaps harder for the non-technical audience than the equations we're sparing them. Fred, also a strong advocate of properly-understood relativity; a former student of the J. A. Wheeler paradigm of relativity, as laid out in _Spacetime Physics_ by Taylor & Wheeler, and in _Gravitation_ by Misner, Thorne, & Wheeler

[@karlscheel3500]

Thanks for removing the confusion regarding relativistic momentum! ALL physics professors should ditch the concept of relativistic mass and ALWAYS include gamma when explaining Einstein's famous equation! It would make it MUCH easier for ALL students to grasp! It's quite easy for the average person to see mathematically, that as you approach the speed of light, you get closer to division by zero in the gamma term, which is ALWAYS equal to infinity.

[@mydogbrian4814]

- But infinities in equations are non sensical terms, like black hole singularities with "g". So then; = is the gamma hypothesis truly valid?

[@mydogbrian4814]

The video was fine. Its Nice to know that some concepts that us morons cherish is actually dumbed down hogwash. So, gamma tells us how "p" increases. But why isnt it directly proportional to v all the time?

[@PaulFreemanTheTall]

@My dog Brian : The infinity is a sign that the concept has reached a boundary, ie that no greater speed is possible. So its not meaningless or an error but a sign that there is a physical limit. This becomes clearer when you watch his space time video on why its not possible to move faster than the speed of light.

[@AnujMishra9]

Fantastic video. And i think , in order to understand these concepts this much amount of technicality is absolutely essential. I would love to see even more videos from you explaining these difficult concepts using some equations.

[@vdweghp]

Apology accepted, now I can get smug about 'NO NO NO, there's no such thing as mass increasing at high speed, it's just the Lorenz factor increasing' :D

[@namanjain989]

Relativostic mass stands on the Idea that E=mC^2 then m=E/c^2 so more kinetic energy then more mass but that equation works only when the object isn't moving

[@NiallsSongs]

This is the first video of yours I've watched and I found it excellent. The balance between scientifically correct and intuitively accessible content was perfect for my needs. I'm looking forward to watching more. Thank you.

[@sarthakpapney3125]

sir really this video is very good and interesting like your other videos and sir please keep making videos, i know that your videos got less views than your videos deserve but I love your videos and many others like me who love Physics also love you and your videos so sir please please keep on making them..,I Love Fermilab and I want to come there in future.. and sorry sir for my bad english

[@deluxeassortment]

I'm glad you cleared this up. I always had an issue with the idea that the actual mass of something grew with velocity. If that were true, event horizons would cause runaway spacetime curvature!

[@frankbarbehenn]

I valued the equation because it clarified the distinction between inertia and the substance of matter we call mass. The substance is not gaining more molecules nor are the molecules gaining more “material” somehow. Rather it is getting harder and harder to “push” that material as it gets closer to the speed of light.

[@electricananda]

It was not confusing at all! Please more equations in future videos. There's stuff that's meant for everyone to understand, not excluding even those who have a fear of equations, and there's some university level lecture stuff, but really no middle ground. So far I've found that Fermilab's videos have a good selection of topics, but leave at least me hoping for longer, in-depth information on the topics introduced. (Maybe consider starting another channel?)

[@papyrophobia]

Please feel free to delve deep, but beware the balrog.

[@GulfsideMinistries]

I'm not a physicist. I barely got through Algebra! But I know enough that I took a few minutes and worked out some examples of the equation you invited us to play with and saw you were right (as I expected you were). I learned several neat things in this video, so thank you for it. Not too technical at all. Keep up the good work!

[@mohitsinha2732]

Another argument against relativistic mass is that when we write the relativistic acceleration & Force equations we will have to declare separate longitudinal & transverse relativistic masses! Which is a very strong argument against considering relativistic mass as the same object will have two relativistic masses (longitudinal & transverse)!

[@Mysoi123]

True, if relativistic mass were real, then it shouldn’t be depend on the direction of the force!

[@daGama1915]

Think you could go more technical. Videos like this, with a simple and a less simple part, would be welcome

[@astropredo]

For me it is amazing!! Keep pushing!

[@user-cp3ju2fz4z]

o.O

[@thanigaivels807]

How harder you may push, you can't reach speed of light😜

[@P-G-77]

True agree 100%

[@wwttwtlee2489]

In SR, we have the law of conservation of mass-energy. We can either consider the conservation of the total energy (mc2) of an isolated system or equivalently the conservation of relativistic mass just by dividing the previous equation by c^2.This shows the equivalence of mass and energy.

[@Jack__________]

Don’t dumb down your content for any reason... I appreciate the hard ideas even if I don’t fully grasp them immediately, and contemplating what it all means is the joy of life.

[@pawelkrol6547]

It wasn't really technical. I love these equations. They help you get a better understanding of what is truly going on. I like it this way, please do not fall into the trap of treating your viewers as morons. We can do math. :)

[@user-cp3ju2fz4z]

Yes we can \ - . - / We make math great again.

[@TimBorny]

This was an excellent balance of assumption of knowledge and explanation of concepts. You produce some of the best videos on these relatively complex physics concepts. Keep it up! (and definitely don't dumb it down...)

[@tomcapizzi7264]

I have been stressing this point in our discussion group. Mass is a relativistic invariant. Even Einstein was a proponent of the idea of relativistic mass. He wrote about it in his books on Relativity. I have proposed an alternate description. The Newtonian formula for momentum is based on low speed data. Although it is not obvious until velocity is a significant fraction of c, it is incorrect, because it is only an approximation, since gamma is very close, but not equal, to 1. The measurement of excess momentum is one of the reasons relativistic mass was invented. As pointed out in the video, momentum can grow if velocity gets big, rather than mass. Gamma times velocity is a known quantity, called celerity or Proper velocity. It is also an absolute fact that celerity times mass equals momentum, for ALL values of celerity, which is unbounded by light speed. Since celerity is approximately equal to velocity, the momentum reduces to the Newtonian value naturally as the low speed approximation. I have also taken issue with Einstein's gedanken experiments. In one form or another, they all start with rigid measuring rods and synchronized clocks, and they all conclude with contracted rods and dilated clocks. This does not prove Special Relativity. When the conclusion contradicts the premise, it only proves the original assumption was incorrect. It implies nothing about the conclusion of the argument, it could be true or false. The point I am making is that it is NOT possible to measure all of a moving objects length or the full duration of its elapsed time. I would argue that it is similarly NOT POSSIBLE to measure a moving object's total speed either. Velocity is the observable portion of celerity (which is true total space velocity). If we form a right triangle with time displacement as the base and space displacement as the altitude, the hypotenuse is gamma ct, and the combined hypervelocity is gamma c. The cosine component is just c, the velocity in time, while the sine component is gamma beta c = gamma v = celerity. The ratio of opposite to adjacent is the slope of the hypotenuse, which is the tangent of the angle of elevation to the horizontal, also referred to as the tilt angle. This angle is the gudermannian of a hyperbolic angle known as rapidity, w. This quantity is important because every Lorentz boost can be characterized by a value of rapidity. The product of two Lorentz boost matrices (in the same direction) is another boost matrix, and it is characterized by a rapidity which is the sum of the rapidities of each matrix factor. And every value of rapidity, which is unbounded, maps to a tilt angle by way of the gudermannian function. As the rapidity approaches infinity, the tilt angle approaches 90 degrees. Using the rapidity and its corresponding tilt angle, the following identities are universally true: cosh w = sec tilt = gamma sinh w = tan tilt = gamma beta tanh w = sin tilt = beta coth w = csc tilt = 1/beta csch w = cot tilt = 1/ (gamma beta) sech w = cos tilt = 1/gamma Then hypervelocity = gamma c = c cosh w, celerity = gamma beta c = c sinh w, and velocity = beta c = c tanh w = v. Clearly, as w approaches infinity, sinh w approaches infinity, and celerity approaches infinity. At the same time, the tanh w approaches 1, and the tilt angle approaches 90 degrees, resulting in v = beta c approaching c. So, the reason we cannot observe velocity greater than c is that it is the visible part of celerity which would have to be greater than infinity. There is more at my web site, specialrelativity.today

[@johnlary8792]

Thank you for improving my understanding of physics. No problem with your use of equations. No problem with your tackling fundamental errors or explaining more deeply than popular physics explanations. Please continue to drill down into fundamental ideas, even if more equations are needed. It's worth the work.

[@leesaxon7279]

Great explanation, very useful. I was not at all bothered by the (slightly) more technical nature of this one, and I think you could go even further. There definitely is a point where it becomes "math majors only," and I think PBS Spacetime has been crossing that line lately, but you're definitely doing a good job keeping it in intuitive territory.

[@siddhartharaja9413]

Love you sir ,you are a real gem!please continue making such great videos for curious science students!

[@Ambienfinity]

Love all your videos. This was as technical as you felt you needed to make it in order to explain the concept fully. I watched it twice just to make sure I'd understood the concept of gamma in all this!

[@lastfirst6626]

A line of reasoning that led me to think that the physical mass doesn't increase was that a rocket's propellant's mass would increase and so should be able to provide the needed reaction to keep the rocket accelerating beyond the speed of light.

[@JimButler1234567890]

I appreciated this video and the detail that you went into. Without the details, one cannot hope to really understand the distinction in concepts like this . Thank you very much for this.

[@nejx8711]

Fermilab: *towards the end of the video* “but don’t worry, I’ll make a video explaining the REAL reason you can’t go faster than light” Me: *looks at recommended* “How to travel faster than light, by Fermilab” Also Me: Hmmmmmmmm...

[@tunnar79]

@Star Trek Theory *too much.

[@tunnar79]

@Star Trek Theory How high were you at the moment of writing that comment?

[@michael.forkert]

Speed or velocity is the distance covered in a certain time span. To determine the speed with a stopwatch, you have to know in beforehand, where to start and where to stop the stopwatch. To determine that the Light is 299,792,458 meters per second fast, you necessary had to have measured the distance in beforehand, which the light had to cover in one second. Speed or velocity is distance divided by time (Miles, Feet, Meters per second, minute or hour. If you don't know the distance, you have to divide by a certain amount of time, in beforehand, you never will be able to determine any speed of any object or wave, including the speed of light. If they put you in the middle of a. desert with just a stopwatch, you can walk or run, but you will not be able to determine your speed or velocity. So...

[@sylvainbrosseau6239]

You're very good at this. First you take up a confusing topic, one that people may not have recognized being problematic. Then you use a proper perspective and simple way to explain it. Then your speed rate of talking is perfect. Not like those video with the guy talking too fast and linking sentences together in fear you'll leave the video. You're very good at this.

[@Trp44]

Not understanding this doesn't keep me from enjoying listening to it.

[@WarrenGarabrandt]

You might enjoy his audiobooks then. They are very good.

[@samarthsai9530]

Yes Sir we want more Math more and more equations. Great video sir.

[@paulomanuelsendimairespere3901]

A photon has got momentum and a 'gravitational field', then he has to have mass. For me, that is clear.

[@gregvondare]

Over the last hundred or so years of advanced physics, we've been asked to accept all sorts of strange, non, even counter-intuitive ideas. Some of which you mention in this video: clocks running at different rates, mass changing with speed, and objects shrinking along their axis of acceleration. With sufficient math to back up these concepts, most of the enlightened members of my generation (Boomers) went along. Then, we were asked to accept even more odd and bizarre effects on the quantum level. Again, we took the word of our physics gurus (mostly Feynman) and learned the more advanced math behind concepts of HIggs field theory, quark triadism, virtual existence and the ferocious activity of the vacuum. Now, with string theory and a rush of new ideas such as branes, q-foam and the concept of an infinite, bubbling, uberverse, we have come to an outer limit of complete unreality and some features so arcane they can't even be expressed by conventional mathematics nor tested in any laboratory (although Dr. Bohm made an interesting argument with his ideas of relevating). So, what I'm saying at great length is that retroactively abandoning some of the wonky concepts of 20th century physics is no harder, really, than it was to accept them in the first place. The only interesting question is: what's next on the chopping block? As we lumber toward a theory of quantum gravity, something venerated must face the axe. Dr. Don, what's your call?

[@tonywilliams4020]

I'd prefer a bit more depth than even this to be honest, but keep it up, whatever you feel is best.

[@Javierm0n0]

High five to whoever owns the dorito with the wing. (Rx-8) Answer, the info wasn't hard to follow at all.

[@stylis666]

I had a dorito once and then I developed taste.

[@Super1337357]

boost goes in, apex seals come out :)

[@roberthigbee3260]

Error alert - I know, I must have a lot of nerve to correct this guy, but this is the 2’nd video of his where he said the same wrong thing with the same misleading example clip. A big mass is harder (takes more force) to accelerate in a given amount of time than a small mass, but he does not say that. He says you can “push this toy car easily, but a much bigger car is harder to push”. Here’s the thing - that dude pushing the car is doing so at a constant velocity and the effort he is putting in has nothing to do with the car’s mass. He is pushing to overcome the friction in the internal parts he is causing to rotate by pushing on the back end of the car to just maintain a constant velocity. In space, it takes zero effort to keep either a bowling ball or a tractor trailer moving at a constant velocity of, for example, 5 miles per hour once you have accelerated each to that speed. If you accelerate the bowling ball and tractor trailer to 5 mph over a 5 second time period then, yes, the force you exert on each object will be different and much larger for the more massive object. Mr. Fermilab knows this. He is just in love with his cute car video clip and wants to seem “hip” with us less knowledgeable folk to such an extent that he gets sloppy here and there. Keep up the good work Mr. Fermilab, but tighten it up a bit please! Thanks!

[@rainertheraven7813]

The changes of mass at different 3D-speeds are easy understandable when you assume that all of us are traveling through 4D spacetime with lightspeed. Mass is a 4D concept and must be infinite in 4D spacetime, since spacetime is static without any change. The mass at 3D-speed zero derives from the inner speed of matter.

[@jerrylong381]

Well, there goes my theory that dark matter is only the increased mass of everything in the universe moving at very high velocities.

[@kingarmorgator]

I'd say if anyone really had a problem with the equations or subject matter they'd be watching something else. Do what you do.

[@D_D-_]

if a thing moves faster, then its kinetic energy is larger. Then according to E=MC^2, doesn't it mean the mass increases as its energy increases? Can anyone help to answer this?

[@Rohan_Choudhary5]

Yes,my dear.It's mass would increase as it gets faster and faster. If a body of mass M,moving with some speed ,its total energy would be E=(gamma factor)×MC^2. Here gamma factor depends on speed of body.Actually, gamma factor remains, 1 ,if the body is at rest or moving with low speeds compared to the speed of light. So,this equation reduced to E=MC^2. We call this as " mass- energy " relationship. As we also know that kinetic energy of a body =1/2MV^2, where M is the mass of body which is constant .But as V increases,it's kinetic energy increases, and according to mass-energy relationship, this increased energy is equivalent to some mass. So mass would increase. This is what we called relativistic mass .As now, the mass changes according to speed of body,the formula for kinetic energy wouldn't be the same as previous. New formula of Kinetic energy ={(gamma factor) × MC^2} minus {MC^2 }.

[@ibazulic]

Relativistic mass is a mathematical concept, it does not exist. For an object that is moving, the total energy of an object is equal to its rest energy + kinetic energy, which is in fact p*c where p is the momentum of a particle or an object. While p can be written as m*v, this does not work when photons are, for example, checked because they do not have mass. So in the case of a photon, the equation E=gamma*m*c would give 0, because mass is 0 and that doesn't make sense because photons clearly have energy (which is why we have the photoelectric effect for example). There are more problems relating to the relativistic mass, this is an excellent article to read: www.sciencedirect.com/topics/mathematics/relativistic-mass So yeah, the mass of an object is always sqrt(E^2-p^2c^2)/c^2. If the object is not moving, then its mass is E/c^2 which is what we should get. The 2nd term is the kinetic energy of a moving object.

[@78tag]

Your explanation of the equations involved here are clear enough to make it easy to follow what you are saying without having to understand the equations. It's like discussing quantum physics - no one really undertands it but that doesn't stop us from discussing it.

[@haarmegiddo]

Now we are owned a video that explains why is the Lorentz factor in that equation in the first place :)

[@MikeRosoftJH]

The simple explanation is that the entirety of the special relativity can be derived from the assumption that speed of light is the same for all observers. (Don can sure give us a more complete explanation.)

[@kenlogsdon7095]

MikeRosoftJH - It may be a bit more accurate to state that the Principle of Relativity which states that all physical laws are the same regardless of frame of reference, together with the axiom that there exists a finite rate of interaction due to the spacetime interval, eg, the "speed of light", is the basis for the geometric Lorentz transformation for inertial reference frames.

[@Goreuncle]

+Haar Megiddo *owed

[@AbdennacerAyeb]

Equations is better for better understanding.

[@user-cp3ju2fz4z]

"is better" is equal to "for better" but in respect there are different parameters, how weird.

[@Bobby-fj8mk]

Dr Don Lincoln - you didn't convince me. If the relativistic mass was 10 times the rest mass then you could measure that if a particle hit a target. I did watch your next video "Why can't you go faster than light?" My understanding is that the extra energy you use to accelerate a particle close to the speed of light is turned into mass. That's what a whole bunch of professors always told me and you are telling me the opposite.

[@thewaytruthandlife]

dear mr Lincoln; a) doesnt the kinetic energy not represent some mass ? I mean p=gamma*m*v and E=1/2 *gamma*m*v^2 (and therefor E=mc^2 (or its more correct version) is pretty much close the same. b) from what I understood (correct me if I am wrong) is that the mass of for example protons /neutrons ect largely is represented due to the kinetic energy of the subatomic particles that make up these particle and that, for about 98%. so that we basically can say we consist for the majority of kinetic energy, mass wise speaking… c) can we not say the more kinetic energy an object contains the harder it gets to deliver some more kinetic energy to speed things up ? because of the energy content (and therefor impulse but also mass) d) so inertia is basically the resistance of an object containing kinetic energy to gain more kinetic energy.

[@KetilDuna]

Beautifully explained, as always - thank you.

[@peterparahuz7094]

0:33 ha ha ha. "unsolicited correspondence", another words "stop sending me mail!"

[@mrv1264]

Or, "stop sending me comments that question the status quo or that which is politically correct in the physics community."

[@avrenna]

Correspondence is probably still welcome as long as you aren't a schizophrenic layman who doesn't understand the equations but still thinks he's smarter than Einstein and the thousands of physicists and thesis-writing post-grads since, believing that he's found a brilliant new way of "looking at things" that no one has ever considered before.

[@NoizyInSeattle]

In science discussion forums, I see "Einstein was wrong" quite a bit. They never really explain why they think so.

[@quantumcat7673]

"Momentum act differently at low speed" (than at very high speed) The equation is the same for any velocity lower than c so it does act the same way albeit in a feeble effect. What happens when the velocity goes up is the energy density of the object augment hence also the curvature of space. That is why relativistic effects occur at very high speed, because potential energy becomes denser.

[@wwttwtlee2489]

In the stress-energy-momentum tensor of the field equations in GR, the energy is mc^2 and the momentum is mv where m is the relativistic mass. This takes the role of gravitational mass that causes 4-D spacetime to curve manifesting gravitational phenomonon.

[@mennonis]

I feel like it was not hard to follow, although I'm an electrical/software engineering student, but I have not had general physics classes in over 5 years (turns out computers dont care about gravity?)

[@mennonis]

so i welcome more videos like these

[@foobargorch]

maybe one day... watch?v=lKXe3HUG2l4

[@GottfriedLeibnizYT]

Yes ! a new Don video !

[@johnlary8792]

Thank you for correcting my 75 year old brain's erroneous ideas about relativistic mass. My college major was molecular biology and biophysics at Yale, and all of my physics courses spoke of relativistic mass. Adding the gamma term to the momentum equation is a simpler and more elegant explanation that hiding gamma term inside the mass to yield "relativistic mass." Keeping gamma as a separate term allows preservation of the idea that gravitational mass and inertial mass are equal.

[@dorothygale5896]

There was a young man named Bill Wight, Whose speed was much faster than light, He set out one day, In a relative way, And returned on the preceding night.

[@thomasdoyle4246]

I will have to watch it again, maybe a couple of times. Don't change your approach. I love that you take the time to explain these complicated science explanations of reality.

[@Ammmo30]

"How about a bullet from a sniper rifle?" *Shows someone shooting an AR-15* (Love the video btw)

[@drottercat]

I suppose that knowing your AR15s from your sniper rifles is not important to people interested in realtivity.

[@Ziplock9000]

@@drottercat Well said

[@tom_something]

The _observation_ of an increase in mass is something I'd call "relativistic fairness". Imagine you have a rocket in space that accelerates by pushing out protons at a very high speed, one proton per second. Protons don't have much mass, but we're pushing really, really hard on them. So hard, in fact, that by the time they leave our engine, we observe them to be moving away from us at 90% of the speed of light. Wow, that's fast! But it's only one proton. I haven't done the math, but even at that speed, I don't think one proton for second is going to do much for us. So let's increase the output power by a huge factor. By such a huge factor, in fact, that without relativity, we would observe the protons to leave our engine at 900% of the speed of light, a tenfold increase. That would make a huge difference in our thrust, right? But unfortunately, because of relativity, that proton does not appear to travel away at 900% of the speed of light. It's only traveling at.... somewhere between 90% and 100% (non-inclusively) of the speed of light. That's not fair! We pushed much harder on the proton, and the proton barely moved faster! The universe agrees. That isn't fair. Our hard work (pun intended) should be rewarded. And, in fact, it _is_ rewarded. From our perspective, as that proton proceeds further and further down the engine, accelerating faster and faster in our retrograde direction, our engine observes that the proton is harder and harder to move, as though it has more mass. So even though we still only observe the proton to be moving a little bit closer to the speed of light away from us than before, stellar observations suggest we are moving faster. What's more, I think our engine is observed to get longer. And since force times distance is energy, this also helps to explain our boost in acceleration. From the perspective of an observer who starts near us at our initial velocity and remains at that velocity, we also observe that the proton increases its mass, helping to propel the ship. But we do not see the engine get longer, so from our perspective compared to the ship, the resulting ship's speed through the universe as measured against the stars is not quite as fast. But we also observe that a clock on that ship is moving more slowly than ours. And that explains why from their perspective they might think they're moving faster than we observe them to be moving. In relativity, just throw the word "observed" in front of everything. Even light, for that matter. It's not that light _definitely_ moves through a vacuum at the speed of light. It's that for all observers the light is measured to move at the speed of light. This gentle language adjustment makes it easier to apply the principle of relativity.

[@apertureonline9566]

Well, so here’s how I interpret these concepts: we can’t simulate significantly complex objects yes due to low mass and the fact that space tears at you gravitationally. It’s also past traveling faster then the speed of light because a worm hole has light, but it’s extremely important to understand those limitations and what we can do. Which is a big issue regarding velocity

[@apertureonline9566]

Can I use this math to understand how far we can go when we measure in light years? No.

[@HoD999x]

i want more equations

[@user-cp3ju2fz4z]

1+1=2 F(x)= (4x^3 - 3x) / (45x^32 + 6x^2x) 2=2 1,5+0,5=2 0,8+1,2=2 -5+3=2 Enough ?

[@Hythloday71]

Oh dear, so is length contraction even real ?

[@gokbok2568]

Indeed, just try and jump in cold water!

[@GottfriedLeibnizYT]

Yes. The fabric of spacetime gets distorted and the length of the body changes accordingly.

[@ffggddss]

Yes; but in a sense somewhat similar to constancy of mass, no it isn't. What *does* change, is the 'length component' in the frame wrt which the object is moving. There is a spacetime 'hyperbolic rotation' connecting the two frames, in which the distance and time components both change in a way that preserves the spacetime interval, ds² = dx² - c²dt² This is analogous to a spatial rotation, in which two spatial components both change, but in a way that the spatial interval, ds² = dx² + dy², is preserved. If you stand in front of a rectangular building, you see its full width in front of you. If you walk partway, say 60º, around it, that same front face of the building now looks half as wide. Did it actually shrink? No. Its actual width is still the same; its apparent width is only half that. In the case of 'boosting' a meter stick into a moving frame, the proper length of the stick is still a meter; but its apparent length is shorter. Masses, proper lengths, and proper times, are all constants; they are invariants; apparent lengths and times *do* vary.

[@foobargorch]

Science is the best way to esecalate a dick joke, well done!

[@snnwstt]

Nope, it is a matter of perception to who observe it, as parallel tracks of a railway seems to converge at infinity when you look at them ( perspective geometry in case of the railway). They seem to converge, but never really do. It is a little bit as thinking that the whole world expand while it would be you who shrink (yes, it would takes less energy to have only you shrinking instead of the whole universe to expand, .. but then, why the other parts of the universe would not shrink too?) But if you were shrinking because you were speeding ? Anyhow, you could come with a perspective geometry which will describe the same effects around you, with no one really shrinking. Does )( look like parallel segments of straight lines? Take || and a piece of lens like fisheye lens, the || will become, to you, through the lens, curves like )( . That would be your perception, but in reality, they didn't changed at all just because you look at them through fisheyes lens, isn't it? Same for speeding objects, they may appear smaller when you look at them, but they, in their local frame, it is you who become smaller, not them.

[@synapticmemoryseepage4447]

A pleasure to happen upon this viddy today. Yesterday, I read "37.9 Relativistic Momentum" in 'Physics For Scientists and Engineers Second Edition: A Strategic Approach', which covers momentum in terms of relativity. The book does not appear to mention relativistic mass, and following the development of the equations for relativity is really easy.

[@egbun]

You’re the best physics 'splainer of all. This was the perfect level of simplification. Only one question was left hanging in my mind: although mass doesn’t increase to infinity near the speed of light, does momentum increase to infinity? So a grain of sand could move the entire universe?

[@szokebalazs2244]

This should be the minimum I really like this”show” but you could add more equations.

[@omsingharjit]

thanks for teaching right lesson

[@jd-gw4gr]

the gamma term added to the momentum is a fudge factor to get experimental observations to agree with the hypothesis which of course is based upon an assumption that mass can not travel faster than the speed of light paradoxically is a hypothesis.

[@outbackjoeaustralia]

This seems inconsistent with some other phenomenon. For example an atom has more mass than the rest mass of the quarks it's made of because the quarks are moving. Or heating up something makes it heavier because the atoms move faster. Or even adding chemical energy, like recharging a battery, makes it heavier. If an object becomes harder to accelerate and is attracted more to gravity has it acquired mass? How do we define mass? Isn't it arbitrary to choose to say acceleration energy requirements increase due to some momentum effect rather than choosing to say it's because of more mass? We could say an atom has a mass equal to the sum of the quarks that make it but instead we say it has a higher mass. More explanation needed please.

[@BrMiller]

The two ways we think of mass in every day life are that more massive objects have a greater gravitational influence and that more massive objects are harder to accelerate. How much space time curves is determined by amount of energy there is. All energy results in this space time curvature; light, energy from the Higgs mechanism, the binding energy between quarks and in fact kinetic energy all do this. In relativity, the formula for acceleration of an object given a force is a = F*sqrt(1-v^2/c^2) * c^2 / E, where E is the energy of the object at rest. The acceleration of the object will be less if it is moving faster. When an object has a higher temperature, the particles within it will be moving faster, so when a force is applied there is less acceleration than when the object is cooler. As far as you are concerned that object is in fact more massive as it is harder to accelerate and it will curve space time more. Them saying relativistic mass isn't real is more of a matter of definition. When physicists say mass they are usually referring to the mass of an object when it isn't moving. This means the mass of an object is constant in reference frames. Temperature is constant in all reference frames, so even though an increase in mass due to an increase in temperature is caused by the relativistic mass of moving particles, they still consider the thermal energy to be a part of the rest mass. It doesn't matter where this rest mass comes from as long as it is constant in all reference frames. You can argue relativistic mass does exist, however its usage is unnecessary. You can say p=m(relativistic)v and m(relativistic)=γm, but you could just say p=γmv. Mass as a whole doesn't really exist as motion can be explained simply with energy and momentum. What energy we decide is mass is arbitrary. Generally we say the energy of an object when its net kinetic energy is zero is its mass, but fact is all energy has mass like properties and we could just as easily include kinetic energy as a part of its mass.

[@netspirit79]

That's not a sniper rifle. It's a normal, everyman's AR-15

[@chrisristau8803]

Bible in a science video....wth is going on over here?

[@shannont8169]

Even for 4 years ago, this anti religion attitude is outdated. this isn't the early 2010s anymore.

[@infinitytoinfinitysquaredb7836]

Gamma shows us how possible it would be to get close to light speed given a proper energy source and enough time. The graph/equation shows that it only takes 15.5% more energy to increase your speed 1 MPH at 50% of light speed as it did going from 0 ---> 1 MPH, and at 90% of light speed energy consumption is about 130% greater (significant not insurmountable). And this video was easy to understand. Feel free to ramp up the math whenever necessary.

[@BenRush]

"To those who do not know mathematics it is difficult to get across a real feeling as to the beauty, the deepest beauty, of nature ... If you want to learn about nature, to appreciate nature, it is necessary to understand the language that she speaks in." -R. Feynman

[@schadenfreudebuddha]

I dunno, some of MY relatives are pretty massive.

[@TheReaverOfDarkness]

I like having the equations, even if I don't understand them. When combined with the layman's explanation, it expands the range of prior expertise I may have and still appreciate the video.

[@jamiboothe]

Please add any algebra formulas or equations that pertain to your subject, but also keep up with explaining these very complicated ideas in ways that do not need math, to understand. I once heard someone say, "If you can`t explain it simply, you do not know the subject well enough to be explaining it". I am not sure who said it and the quote may be paraphrased, but you get the idea. Thanks for the excellent videos.

[@ZeeshanAli-xe5co]

So Gama is just a placeholder number to keep the Newtonian eq working which is p = mv. The question is why there is gama or why we need gama when speed increases