Relativistic mass

Main Question or Discussion Point

My textbook explains relativity with the help of relativistic mass...

My questions are-

1. Does relativistic mass has any effect in gravity? I mean do the object with more velocity attract things stronger than before?

2. I will see the object which going at a high velocity (from my reference frame) with a contracted length and its time dilated... I understand that(well after having the shock)... But I don't understand how its mass gets increased? Well energy and mass are equivalence and it has got extra kinetic energy... But If we say extra mass that would mean extra gravity... Well if you answer my 1st question this question will be answered too...

3. Two objects with invariant mass m1 and m2 collide and become one... Their relativistic mass was M1+M2... Now what would be their invariant mass? m1+m2? or M1+M2... Isn't it m1+m2... Then why we use the term 'relativistic mass'?

Another thing... Newton said F = d(mv)/dt
now we say m is the mass(relativistic)... But as he is dead long ago(with his mistakes which are apparently true at low velocities :tongue2: ) then would it be wrong to say that this is true if we divide the mass(invariant) by a gamma factor...

Related Special and General Relativity News on Phys.org
I think the modern view rejects the term "relativistic mass". The concept is troublesome mainly due to the fact, that it implies a change in the inner structure of an object. That is definetely not true, since the apparent increase of energy/impulse is just a relative measurement. Remember that measurements are not the same in different places of spacetime.

PS: Nevertheless the EFEs teach us, that extra kinetic energy does contribute to space distortion. So one could say, in GR an object that is moving really fast could curve a flat space, independently of whether it became "heavier" in its one reference frame...

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Hi EzioPi
1. Yes, otherwise, photons, with no rest mass, wouldn't be affected by gravity

2. It does not follow directly, this is why you don't see it.
You must assume (and it looks like reasonable assumptions, but before experimental confirmations, it's not enough as many other reasonable assumptions were shattered by the theory) that relativistic mass is conserved, and that momentum is conserved.
with those additional assumptions, you can perform a thought experiment of a totally inelastic collisions between two masses, and by shifting from the lab frame to the center of mass frame and applying some algebra you get to the formula that leads to the gamma factor.

3. this is precisely by doing this that you get to find gamma :)
Why the term relativistic mass ? since everything else so far (time, distance) is affected by movements, it is reasonable to think that maybe the mass you measure for a moving object is affected by its speed compared to you.
Following the algebra and with those extra assumptions, you find gamma (which could very well have been just 1, and there would be no need for the term relativistic mass)

Also notice that gamma looks a lot like beta but does not mean the same thing (in case this is where your confusion comes from)
Beta allows you to transform how time and distance are measured for two different reference frames while gamma is 'just for you' in your frame, but talking about a moving object with a certain speed (as seen from your lab)

Newton was really talking about momentum, and we still do, but it uses the relativistic mass instead of the rest mass.

Cheers...

mfb
Mentor
3. Two objects with invariant mass m1 and m2 collide and become one... Their relativistic mass was M1+M2... Now what would be their invariant mass? m1+m2? or M1+M2... Isn't it m1+m2... Then why we use the term 'relativistic mass'?
If you calculated M1 and M2 in the center of mass system, it is M1+M2. If not, the invariant mass might by anything between m1+m2 and M1+M2, depending on the setup.

Then why we use the term 'relativistic mass'?
As Trifis mentioned: Try to avoid it.

Well its easily assumable that Trifis and mfb are not comfortable using the term relativistic mass... And oli4 is with it... My question is why are we divided into 2 groups? Even if both ways are accepted wouldn't occam's razor tell us to choose one?

However, I am still confused as you guys are telling me to avoid it or explain things with it... Please,answer the questions below...

Those who prefer relativistic mass: oli4
Is it experimentally proven that mass really increases? Would a thing attract another thing based on their relative velocity? Is it experimentally proven that the same mass(invariant) acts like two for two things with different relative velocities...

Those who do not even like the term relativistic mass:
Trifis said extra kinetic energy distorts space time... Then the effect should be felt by everyone equally who are there whether they are moving or not... Does the effect vary for them? If they vary,then why?

Two objects with invariant mass m1 and m2 collide and become one... Their relativistic mass was M1+M2... Now what would be their invariant mass?

ZapperZ
Staff Emeritus
We may need a FAQ entry on this topic since this keeps popping up. I've posted a reply on this elsewhere, but here it is again.

Lev Okun has an extensive paper on why the term "Relativistic Mass" should be avoided:

L.B. Okun Am. J. Phys. v.77, p.430 (2009).

In particular, this is what he said:

Unfortunately, sometimes and especially in his popular writings Einstein was careless about the subscript 0 and spoke about the equivalence of mass and energy and omitted the attribute “rest” for the energy. As a result Einstein's equation E0=mc^2 became known in its famous but misleading form E=mc^2. One of the most unfortunate consequences is the concept that the mass of a relativistic body increases with its velocity. This velocity dependent mass is known as “relativistic mass.” Another consequence is the term “rest mass” and the corresponding symbol m0. These confusing concepts and notations prevail in such classic texts as the ones by Born and Feynman. Moreover, in these texts the dependence of mass on velocity is presented as an experimental fact predicted by relativity theory and proving its correctness.

To substantiate the formula m=E/c^2 some authors use the connection between momentum and velocity in Newtonian mechanics, p=mv, forgetting that this relation is valid only when v (is significantly less than) c and that it contradicts the basic equation m^2=(E/c^2)^2−(p/c)^2. Einstein's tolerance of E=mc^2 is related to the fact that he never used in his writings the basic equation of relativity theory. However, in 1948 he forcefully warned against the concept of mass increasing with velocity. Unfortunately this warning was ignored. The formula E=mc^2, the concept relativistic mass, and the term rest mass are widely used even in the recent popular science literature, and thus create serious stumbling blocks for beginners in relativity.
In support of Okun's view of what Einstein thought of this term, there's a paper Hecht that clearly stated this:

E. Hecht, Am. J. Phys. v.77, p.799 (2009).

Einstein's first paper on relativity appeared when the concept of speed-dependent electromagnetic mass had already become a topic of considerable interest. He accept this idea but changed his mind after being confronted by a far more compelling insight. We will show that after reading Planck's 1906 article in which the concept of relativistic momentum was introduced, Einstein came to realize that it was the relativistic equations for energy and momentum that were primary. From that perspective, it became clear that the inertial mass m was invariant, and he never again spoke of mass as being speed dependent.
Regarding the effect gravity on photons, we already have an entry in the Relativity FAQ in the Relativity Forum dealing with this, and why this is NOT the same as the effect on objects with actual rest mass!

Zz.

mfb
Mentor
Movement changes the gravitational field of an object, but you don't get the field of a heavier, non-moving object.
On the other hand, if you add energy to some internal degrees of freedom (heat the object or whatever), it is similar to adding mass. Actually, most of the mass of protons and neutrons is binding energy.

Two objects with invariant mass m1 and m2 collide and become one... Their relativistic mass was M1+M2... Now what would be their invariant mass?
As I said, it depends on the system and your reference frame. Two examples:

- m1 and m2 are at rest relative to each other, but moving quickly in your lab: You can calculate large relativistic masses M1 and M2, but in the center of mass system, the total energy is simply m1+m2.
- m1 and m2 are the same, but both particles travel in opposite directions. Your lab is the center of mass system, and the total energy is the sum of both particle energies, the invariant mass is M1+M2.

Everything else will be between those two examples.

bcrowell
Staff Emeritus
Gold Member
If you calculated M1 and M2 in the center of mass system, it is M1+M2.
Not true. E.g., two photons heading for a head-on collision have m1=m2=0, but the system as a whole has nonzero invariant mass.

mfb
Mentor
Ezio3.1415 used capital letters for relativistic mass (E/c^2) and I adopted that notation. The photons clearly have energy, so M1, M2 > 0.

Hi ZapperZ (and everyone else )
Thanks for this detailed and interesting post.
You are quoting very recent books which somehow critic older ones (which is fair enough, we must go on), well, I don't know about those books, but thank you so much for bringing them to attention, I might have a look at them (and 'go on')
But as far as older books are concerned, the list is quite big and very classic, Feynman, Born (didn't read this one), Hauser, Goldstein, ...
So in any case, I have a hard time imagining that since (at least) 2009, there is such a heavy shift that it actually invalidates all those writings, I suppose it is just a different way to say the same thing but with a twist on the rephrasing so that it orients the interpretation differently (and, I suppose, in a better way).
But I don't think this contradicts in any way the previous results, as mfb and trifis said before, maybe it's better to avoid the term and stick to the new angle of it, which is fine, but it does not invalidate the previous results.
Maybe we could compare it like saying 'Putting yourself in a system of units in which c is different than 1 is masochism', it probably is true but it does not invalidate the formulae where you had to take c² into account

Your comment on gravity effect on the photons was directed to me I guess
I didn't mean that photons get mass because of their speed and that because of that, the old classical Gmm'/r² formula would work (but I understand it was written so as to be read this way (if it even is what you were objecting to (also I apologize for my overuse of parentheses ()))).
What I meant was that, because they do have a "relativistic mass" (which in this case is really just the mass equivalent to their energy) they are another member of the gravity zoo: they 'attract' other masses and are attracted by them and all those effects (you will be hard pressed to find the gravitational effect of a photon on a star should be compatible in taking into account their relativistic mass (should you use this term) in your equations

Your post certainly sparked my interest, and I would appreciate others from you (or anyone else of course) to motivate me even more so to have a look at those books you just mentioned

The quotes you err.. quoted are not meaningful enough by themselves:
To substantiate the formula m=E/c^2 some authors use the connection between momentum and velocity in Newtonian mechanics, p=mv, forgetting that this relation is valid only when v (is significantly less than) c and that it contradicts the basic equation m^2=(E/c^2)^2−(p/c)^2
I don't get it... Where does this come from ?
p=mv is precisely valid when you take m as the relativistic mass instead of the rest mass (nobody forgot anything there)
just as the next equation is supposed to apply to the rest mass (m->m0)
(But I understand this might precisely be your point, except without the rest of the edifice it does not look like much, and can even be thought as being incorrect)
So I suppose in those more recent books it has been found (as hinted by Einstein himself apparently) that a different focus/language is more effective/simpler, and I am all for it.

But it does not invalidate answering someone using this other angle what the angle is about (unless the answer is wrong even under this formalism, that is, if you think Lagrange formalism is better than Newton's formalism, it's understandable, and may or may not be correct in this or another case, but, is answering a question about Newton's equations invalidated by 'Lagrange's equations are today's understood best way to answer those questions' ?)

Cheers...

Nugatory
Mentor
Well its easily assumable that Trifis and mfb are not comfortable using the term relativistic mass... And oli4 is with it... My question is why are we divided into 2 groups? Even if both ways are accepted wouldn't occam's razor tell us to choose one?
Like beauty, simplicity is somewhat in the eye of the beholder so Occam's razor doesn't conclusively settle the question... But the most widely held position these days seems to be that relativistic mass increase is not the cleanest/simplest way of understanding the phenomenon (relativistic mass is frame-dependent, invariant mass is not, frame-dependency is generally messier and less simple) so the razor is indeed being applied.

However, there are a number of situations in which it is convenient to use the notion of relativistic mass. For example:
Those who prefer relativistic mass: oli4
Is it experimentally proven that mass really increases? Would a thing attract another thing based on their relative velocity? Is it experimentally proven that the same mass(invariant) acts like two for two things with different relative velocities...
Yes. A classic experiment, done many times, is to apply a known (in the lab frame) transverse electric field to an electron moving at relativistic speeds (in the lab frame). We know the force on the electron (known electric field, known electric charge) so when we measure its transverse acceleration (in the lab frame) we can calculate its mass (in the lab frame).... And it is indeed the predicted frame-dependent relativistic mass.

Of course this situation is a bit unusual in that we're only interested in the observations we make in the lab frame. If we wanted a general frame-independent mathematical description of the physics, we wouldn't be using the frame-dependent relativistic mass and electric field; we'd do calculations involving the invariant mass and maybe even slip the frame-independent Faraday tensor into the picture. It would be more work for this particular problem, but the solution would be more general, cleaner, and generally would survive Occam's razor pretty well.

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ComplexVar89
mfb
Mentor
You can use the concept of relativistic mass, it will give the correct results if you are careful. But it is easier if you replace that "relativistic mass" by E/c^2 everywhere and talk about energy.
No particle physicist I met so far used the concept of relativistic mass anywhere, and we have relativistic particles all the time.

jtbell
Mentor
You can use the concept of relativistic mass, it will give the correct results if you are careful.
Of course, beginning students aren't careful, which is the big problem. As far as I know, the only non-relativistic equation that you can convert to a relativistic one by plugging in the "relativistic mass" is p = mv. For everything else, the relativistic equations look different from the non-relativistic ones, regardless of whether you use (invariant) mass or "relativistic mass." So what do you gain by using the "relativistic mass", except for being able to use E = mc2 for both stationary and moving objects?

No particle physicist I met so far used the concept of relativistic mass anywhere, and we have relativistic particles all the time.
Indeed, this was almost always true when I was a graduate student in experimental particle physics 30-35 years ago. The only place I saw "relativistic mass" was in a course about the history and design of particle acclerators. We used a textbook written in 1962, one of whose authors (Livingston) had worked with E. O. Lawrence on the first cyclotrons in the 1930s and had therefore learned his relativity very early on.

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1.
- m1 and m2 are at rest relative to each other, but moving quickly in your lab: You can calculate large relativistic masses M1 and M2, but in the center of mass system, the total energy is simply m1+m2.
- m1 and m2 are the same, but both particles travel in opposite directions. Your lab is the center of mass system, and the total energy is the sum of both particle energies, the invariant mass is M1+M2.
How does the invariant mass change from m1+m2 to M1+M2? How and why invariant mass is changing and turning to a amount which is also known as its relativistic mass? Sorry but I don't understand the process...

2. Something with mass is going at a high speed... Its kinetic energy will add to its gravity... Two identical bodies,one which is stationary with respect to our previous mass and the other have a relative velocity with respect to it... My question is on a given time will the gravitational attraction by our mass on the identical bodies will be different or not?

mfb
Mentor
1: It does not change, those examples are completely different.
In example 1, the "collision" is not a real collision at all, you just have two particles without relative velocity. The center of mass system is at rest relative to the particles, the total energy in that system is (m1+m2)c^2 and the invariant mass is m1+m2.
In example 2, you have two particles colliding head-on. The center of mass frame is your lab, and the total energy in that frame is (M1+M2)c^2, which corresponds to an invariant mass of M1+M2.

Two identical bodies,one which is stationary with respect to our previous mass and the other have a relative velocity with respect to it... My question is on a given time will the gravitational attraction by our mass on the identical bodies will be different or not?
You cannot compare them with a simple number. One object is moving relative to your test particle, its gravitational influence will be time-dependent.

pervect
Staff Emeritus
Based on the following paper, http://ajp.aapt.org/resource/1/ajpias/v53/i7/p661_s1?isAuthorized=no [Broken], I'll give you an oversimplifed answer and a warning.

The warning is that the answer is oversimplified, and that the waters are very deep here.

But the very very rough answer is that any sort of "gravity detector" is going to respond roughly to the energy of the passing particle. You seem to be determined to refer to the energy of the particle as the "relativistic mass". This is mostly a bad idea, except insofar as that it invites people to give you super-ultra-oversimplifed answers like the one I'm giving you. Thbis might actually be good for you, depending on your background. For the most part, using the phrase "relativistic mass" is sort of like raising a flag saying "I"m very new, and not very technically inclined, please don't get too technical."

One can see from the paper that there are some funny multiplicative terms that approach a factor of 2:1 at high velocities in the response of this particular detectior discussed in the paper that are related to velocity rather than energy. So don't expect much more than 2:1 accuracy from this simple approach.

I've also omitted any frame-dragging effects, which are sometimes called gravitomagnetic effects. These effects become important if you have two parallel comoving masses. You started to ask about that, but your question wasn't clear enough for me to answer, and at any right I'm trying to keep things ultra-simple. So I'l mention briefly that there is such a thing as "Gravitoelectromagnetism", http://en.wikipedia.org/w/index.php?title=Gravitoelectromagnetism&oldid=509366342, and that it can be relevant in describing the situtiation of two masses both moving in the same direction at high speed. It's usually easier to solve this sort of problem in the frame at which they are at rest, but if you're determined to consider the situatio from the viewpoint where they both move you can, but in such a case you must also consider the effects mentioned above.

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Hi guys,
Here is a nice article that, as I suspected, acknowledges what most of you said, that is, 'relativistic mass' seems to be a non fashionable term and has been so for quite some time now.
However, a point is made about the motivations for it and in any case, completely dismissing it is not necessarily such a good idea.
In any case, it's a nice read (though I just skimmed it) and I think it clarifies well the roles different masses play in different situations and when one or another "label" is most sensible. (rest mass, mass, proper mass, relativistic mass, ...)

pervect
Staff Emeritus
Relativistic and invariant mass are just the tip of the iceberg, and wind up having little to do with gravity in the end.

Concepts such as Komar mass, ADM mass, Bondi mass, and quasi-local mass wind up as being more directly related to gravity than either relativistic or invariant mass.

Unfortunately there isn't one single replacement for the Newtonian mass in GR - we wind up with at least three.

For the "managers overview", however, it's not a bad approximation to say that energy gravitates. You'll get errors this way, but they'll typical be modest, giving you the right order of magnitude. A more precise explanation would involve explaining that it's not "mass" that causes gravity in GR, it's the "stress energy tensor". "Mass" is what causes gravity in Newtonian theory, the "stress energy tensor", which includes energy but also includes momentum and pressure, is what causes gravity in General relativity.

Well its easily assumable that Trifis and mfb are not comfortable using the term relativistic mass... And oli4 is with it... My question is why are we divided into 2 groups? Even if both ways are accepted wouldn't occam's razor tell us to choose one? [..]
This has nothing to do with occam, as it largely corresponds to a dividing line between two equally capable calculation methods, and related tastes and interpretations.
Surely the physics FAQ may be useful, I think that it gives a balanced overview (disclaimer: I had a little hand in small improvements):

Yes I think so too; however, I notice what appears to be a disagreement about facts.

According to the author Peter Brown, based on Misner, Thorne and Wheeler, relativistic mass corresponds with what causes gravitation.
However according to pervect, who speaks of energy which I assume he think to be proportional with it, that is only:
[..] it's not "mass" that causes gravity in GR, it's the "stress energy tensor" [..], which includes energy but also includes momentum and pressure [..]
I don't know how to match that with Peter Brown's citation of Einstein:

Special relativity has led to the conclusion that inert mass is nothing more or less than
energy, which finds its complete mathematical expression in a symmetrical tensor of
second rank, the [stress- energy-momentum] tensor

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I think the problem is that some physicists are trying to keep things simple(invariant)... And they want to think of mass as a property of a particle that doesn't change and think of the effects caused by the velocity as the effect of extra kinetic energy... And some other are trying to change the definition of mass and say that the mass is not a thing which is constant... It varies for different reference frames and explain the things by the help of extra mass(relativistic mass) not extra kinetic energy...

I think the point is thinking of the effects as the result of extra mass or extra kinetic energy... That means we are to decide which one is better?

However, I don't think I am to say which one is better...

And some other are trying to change the definition of mass and say that the mass is not a thing which is constant...
They are trying not to change the definition of mass as implicit given by Newton's p=m·v. With this definition mass was invariant in classical mechanics. In modern physics the definition of mass has been changed to make it invariant in relativity too.

I think the problem is that some physicists are trying to keep things simple(invariant)... And they want to think of mass as a property of a particle that doesn't change and think of the effects caused by the velocity as the effect of extra kinetic energy... And some other are trying to change the definition of mass and say that the mass is not a thing which is constant... It varies for different reference frames and explain the things by the help of extra mass(relativistic mass) not extra kinetic energy...
I think the point is thinking of the effects as the result of extra mass or extra kinetic energy... That means we are to decide which one is better?
Ok, but it's more than this. Just a couple of examples: relativistic mass doesn't simply depend on speed, it depends on velocity, vector. It means that you have an increase of mass in the direction of motion but not of the mass in the orthogonal direction ("longitudinal" and "transverse" mass). Is it a useful concept of "mass"?
Relativistic mass is just a name for "energy" (divided c2). Why to give it another name?

Just a couple of examples: relativistic mass doesn't simply depend on speed, it depends on velocity, vector. It means that you have an increase of mass in the direction of motion but not of the mass in the orthogonal direction ("longitudinal" and "transverse" mass). Is it a useful concept of "mass"?
No, that's not useful and it is even not the relativistic mass but the "m" in F=m·a wrongly used for variable mass (as used in p=m·v).

Ok, but it's more than this. Just a couple of examples: relativistic mass doesn't simply depend on speed, it depends on velocity, vector.
Certainly not in SR, and this is explained in the earlier given references.
It means that you have an increase of mass in the direction of motion but not of the mass in the orthogonal direction ("longitudinal" and "transverse" mass). Is it a useful concept of "mass"?
Nonsense - as the physics FAQ explains, "longitudinal" and "transverse" mass preceded "relativistic mass".
- http://math.ucr.edu/home/baez/physics/Relativity/SR/mass.html
Relativistic mass is just a name for "energy" (divided c2). Why to give it another name?
Obviously the units don't match, they are physically different concepts just as force is a different concept from acceleration.

If one needs propaganda based on such bogus arguments, then the situation is very poor.