Why is the relativistic mass a rejected concept?

[kmarinas86]

http://www.weburbia.com/physics/mass.html

Of the two, the definition of invariant mass is much preferred over the definition of relativistic mass. These days when physicists talk about mass in their research they always mean invariant mass. The symbol m for invariant mass is used without the suffix 0. Although relativistic mass is not wrong it often leads to confusion and is less useful in advanced applications such as quantum field theory and general relativity. Using the word "mass" unqualified to mean relativistic mass is wrong because the word on its own will usually be taken to mean invariant mass. For example, when physicists quote a value for "the mass of the electron" they mean invariant mass."

If it is not wrong, why not go about setting it straight and making it clear? Are we going to totally ignore the physical implications of having a relativistic mass, such as its dependence on the work done on the body relative to a given inertial frame? Why not at least see how the relativistic mass affects GR? After all, the energy of an object should increase directly in proportion to its relativistic mass, should it not?

Ouch! The concept of 'relativistic mass' is subject to misunderstanding. That's why we don't use it.

Why does the failure of some students affect the scientific models so?

Second, it makes increase of energy of an object with velocity or momentum appear to be connected with some change in internal structure of the object. In reality, the increase of energy with velocity originates not in the object but in the geometric properties of space-time itself.

Are the experimental predictions of the former different than the latter? If so, what experiment could be conducted to tell the difference?

Yet the mechanical formalism often proves harder to swallow and is at the root of many peoples failure to get over the paradoxes which are so often discussed.

If they cannot understand it, too bad! Don't limit physics just because of that. Just make better solutions to these paradoxes so they will understand. That does not require that you reject relativistic mass as something that does not exist.

 

[PeterDonis]

After all, the energy of an object should increase directly in proportion to its relativistic mass, should it not?

It would be more accurate to say the energy of an object *is* its relativistic mass (times the speed of light squared, if you're using conventional units; but one of the first things usually taught in relativity physics is to use "natural" units, in which the speed of light is 1). So rather than use another word for energy, which could potentially cause confusion with invariant mass, why not just use the word "energy"? That's basically the logic as I understand it.

 

[atyy]

It isn't a rejected concept. Rindler's textbook uses it.

http://hussle.harvard.edu/~gabrielse/gabrielse/resume.html wrote a paper with "relativistic mass" in the title!

And this site hosted by the Albert Einstein Institute http://www.einstein-online.info/elementary/specialRT/emc .

 

[kmarinas86]

It would be more accurate to say the energy of an object *is* its relativistic mass (times the speed of light squared, if you're using conventional units; but one of the first things usually taught in relativity physics is to use "natural" units, in which the speed of light is 1). So rather than use another word for energy, which could potentially cause confusion with invariant mass, why not just use the word "energy"? That's basically the logic as I understand it.

The following equation (the energy-mass equivalence relation) doesn't seem to allow that:

m_0 c^2 = \left(E^2 - \left(pc\right)^2\right)^{1/2}

According to what the textbooks say, the E in this equation is not the same in every frame. Instead of m_0 c^2 converting into pc in different frames, or vise versa, we have E^2 and pc being either increased or decreased simultaneously. If I do not go any further than this, than I am left with the unsettling impression that E is either unphysical or dependent on some other property of the observer, such as its own energy content, which it does not see it its own frame (i.e. kinetic energy), which makes itself evident upon collision with mass m_0. Both conclusions would be troublesome to me, as they don't seem to add up.

So what is the real meaning of E here? Wouldn't having a global (or universal) inertial frame defined by a system center of momentum frame (similar to the cosmic background radiation) allow total system E to be invariant rather than total system m_0 c^2? In what empirical study has that been shown to be untenable?

 

[atyy]

My understanding is the same as PeterDonis's. The relativistic mass is just another name for the total energy. The main advantage of the relativistic mass is to suggest that in a relativistic theory of gravity, the total energy, being a form of "mass" should be a source of gravity. In fact, the correct generalization is that the stress-energy tensor is the source of gravity.

Apart from that, and the ability to understand language that is still used, I do find it easier to calculate without the relativistic mass, and use only rest mass or rest energy.

 

[PeterDonis]

The following equation (the energy-mass equivalence relation) doesn't seem to allow that:

m_0 c^2 = \left(E^2 - \left(pc\right)^2\right)^{1/2}

Re-write the equation this way (by squaring both sides, rearranging terms to put the E term alone on the left, then take the square root again):

E = \left( \left( m_{0} c^{2} \right)^{2} + \left( p c \right)^{2} \right) ^{\frac{1}{2}}

E is the total energy, and if you divide it by c^{2}, you get the relativistic mass. You are correct that it is frame-dependent; that's one reason why many physicists don't like to use the term "relativistic mass", since "mass" conveys the impression to many people of something that should be a frame-independent property of the object. "Energy" doesn't appear to give rise to the same connotations; the fact that an object's energy is frame-dependent is just a consequence of the fact that its velocity (or momentum) is frame-dependent (as the rewritten equation above makes clear).

 

[kmarinas86]

Re-write the equation this way (by squaring both sides, rearranging terms to put the E term alone on the left, then take the square root again):

E = \left( \left( m_{0} c^{2} \right)^{2} + \left( p c \right)^{2} \right) ^{\frac{1}{2}}

E is the total energy, and if you divide it by c^{2}, you get the relativistic mass. You are correct that it is frame-dependent; that's one reason why many physicists don't like to use the term "relativistic mass", since "mass" conveys the impression to many people of something that should be a frame-independent property of the object. "Energy" doesn't appear to give rise to the same connotations; the fact that an object's energy is frame-dependent is just a consequence of the fact that its velocity (or momentum) is frame-dependent (as the rewritten equation above makes clear).

Wouldn't E simply be the maximum amount of energy that may be transferred to a separate body in that given reference frame? The actual amount of energy transfer would seem to be a function of the elasticity of the collision with the separate body. The more elastic the collision, the greater the energy change \Delta E would be observed of the separate body on impact. This seems to be the direct result of having \Delta E include the part of the initial energy of the affected separate body that is impedance-matched to the incoming object. It makes no sense to me that the motions of this separate body, which is a receiver (measurer) of \Delta E, would not somehow contribute some of its own energy into \Delta E in the form of \Delta pc, through gauge bosons, such as photons, which travel at c with a momentum transfer of \Delta p. It seems that there would be a scalar product involved in such a collision to determine the limits of the amount energy exchanged if there are additional degrees of freedom, would there not?

 

[ZealScience]

The following equation (the energy-mass equivalence relation) doesn't seem to allow that:

m_0 c^2 = \left(E^2 - \left(pc\right)^2\right)^{1/2}

According to what the textbooks say, the E in this equation is not the same in every frame. Instead of m_0 c^2 converting into pc in different frames, or vise versa, we have E^2 and pc being either increased or decreased simultaneously. If I do not go any further than this, than I am left with the unsettling impression that E is either unphysical or dependent on some other property of the observer, such as its own energy content, which it does not see it its own frame (i.e. kinetic energy), which makes itself evident upon collision with mass m_0. Both conclusions would be troublesome to me, as they don't seem to add up.

So what is the real meaning of E here? Wouldn't having a global (or universal) inertial frame defined by a system center of momentum frame (similar to the cosmic background radiation) allow total system E to be invariant rather than total system m_0 c^2? In what empirical study has that been shown to be untenable?

I actually have the same problem as OP's. To this post you say energy is relative, yes, true, because this is the basic idea of relativity. But in that sense, rest mass is also hard to define. Because you also have to consider the molecular kinetic energy, various types of potential energy. What about gluons? Gluons has much greater mass than quarks, if you get rid of them, you won't worry about losing weight!

SDo if you really want to measure the "rest mass", then you have to make them at the same temperature the same state in order to standardize their molecular energy (though trivial comparing to it's whole mass). But this is not possible for measuring "rest mass" of small particles (quarks, mesons), or super massive celestial bodies (super massive BHs, neuton stars, or huge stars). So I am quite with "relativistic mass".

 

[tom.stoer]

There are several reasons.

One was already mentioned above: mass is a property of a particle, it can e.g. be due to the internal dynamics of a particle, but 'relativistic mass' is a purely kinematical property of the motion of a particle.

Then look at the introduction of 'rekativistic mass', e.g. via the momentum p(v) = m(v)*v; it seems that via the relativistic mass one can rewrite Newtonian formulas such they become valid in SR. But looking at energy there is no similar and consistent trick to make E = m(v)*v²/2 a relativistic equation.

I mean, there's nothing totally wrong with 'relativistic mass'; you can take any equation you like, pick a subset of symbols from this equation and give it a name if you like. The question is if it's useful and it it becomes accepted.

 

[Phrak]

The invariance of intrinsic mass is a good argument in favor of redefining Newtonian mass, but there are stronger heuristic arguments as well.

In inertial and gravitational interactions there is a physical quality that we can call inertial or gravitational charge in a manner parallel to electromagnetic charge. In each case* there remains one real valued, scalar quantity that cannot be reduced to dimensions of time and space.


*The argument is restricted to special relativity where mass is not identified as a function of the metric.

 

[PAllen]

I think the real issue is the temptation to plug relativistic mass into a Newtonian formula and assume the result is now correct for relativistic speeds. This leads to errors in almost all cases, as shown by another recent thread. If, instead, you use the normal relativistic equations, writing them in terms of relativistic mass adds no clarity or simplification. Pedagogically, the former issue is paramount.

 

[Dale]

. That does not require that you reject relativistic mass as something that does not exist.

You misunderstand. Nobody is rejecting the concept, just the name for the concept. The better name for the concept is "total energy", for all of the reasons cited above.

 

[harrylin]

The concept is only rejected by a number of people (such as Okun and followers). It's currently unpopular among particle physicists, but less so among physics teachers.
See also the physics FAQ:
http://math.ucr.edu/home/baez/physics/Relativity/SR/mass.html

 

[harrylin]

I actually have the same problem as OP's. To this post you say energy is relative, yes, true, because this is the basic idea of relativity. But in that sense, rest mass is also hard to define. Because you also have to consider the molecular kinetic energy, various types of potential energy. What about gluons? Gluons has much greater mass than quarks, if you get rid of them, you won't worry about losing weight!

So if you really want to measure the "rest mass", then you have to make them at the same temperature the same state in order to standardize their molecular energy (though trivial comparing to it's whole mass). But this is not possible for measuring "rest mass" of small particles (quarks, mesons), or super massive celestial bodies (super massive BHs, neuton stars, or huge stars). So I am quite with "relativistic mass".

I agree that relativistic mass has useful features, just as rest mass; as long as people know and understand the difference between rest mass and relativistic mass, the use of both permits to enhance physical insight (the same for proper length and time vs. coordinate length and time).

 

[Hurkyl]

If they cannot understand it, too bad! Don't limit physics just because of that. Just make better solutions to these paradoxes so they will understand.

Physicists did: invariant mass and 4-momentum.

 

[tom.stoer]

The concept is only rejected by a number of people ... It's currently unpopular among particle physicists, but less so among physics teachers.

Yes, and this is another problem.

Teachers seem to be happy with that concept, but science advisors aren't b/c they - not the teachers - have to answer silly questions like "do (why don't, ...) particles turn into black holes b/c of increasing mass near speedof light?"

 

[atyy]

Then look at the introduction of 'rekativistic mass', e.g. via the momentum p(v) = m(v)*v; it seems that via the relativistic mass one can rewrite Newtonian formulas such they become valid in SR. But looking at energy there is no similar and consistent trick to make E = m(v)*v²/2 a relativistic equation.

In the Newtonian context, the kinetic energy is defined via work-energy. So presumably one should try that route, ie. redefine force so that Maxwell + Lorentz force law is covariant, then define relativistic KE via work-energy.

 

[pervect]

Relativistic mass does not fit in well with the "geometric object" paradigm. Geometric objects are complete in the sense that if you know all the components of them, you can transform them to any reference frame or set of coordinates you want.

Energy, or relativistic mass, is not a geometric object by itself, because if you only know the energy of something, you don't have enough information to transform it to another reference frame. If you know the energy-momentum 4-vector, on the other hand, you do have all the information you need to transform it.

The level of abstraction here is rather high, but perhaps thinking in terms of "objects" as in "object oriented programming", one might gain some insight. The "geometric object" encapsulates all the needed properties of the object, and the coordinate system becomes a "view" of the object. So you can clearly draw the line between the idea of "changing views", i.e. coordinate systems, and "changing the object itself".

So if you're a programmer, or familiar with the programming, you can think of the geometric object as a "class", and the description in some particular coordinate system as a particular view. A view would be analogous to a method implemented in the class. Changing coordinates then corresponds to changing tje view, you just provide the information on the view that you want to the object-class, and the methods in that class output for you the information you need on how it looks in that view.

Invariant mass is, to my mind, a clear winner, in part because it's a geometric object, but also because it better relates to the concept of mass as a "quantity of stuff". Without re-reading some of Max Jammer's books, I'm not quite sure where the historical origins of the idea of mass as "a quantity of stuff" are, but it's an old and widely understood idea. And this idea of mass as "a quantity of stuff" is much more compatible with the concept of invariant mass, because the invariant mass depends only on the object, while the energy depends on the both the object and the viewpoint chosen, the viewpoint being the specific coordinates or reference frame used.

 

[atyy]

Invariant mass is, to my mind, a clear winner, in part because it's a geometric object, but also because it better relates to the concept of mass as a "quantity of stuff". Without re-reading some of Max Jammer's books, I'm not quite sure where the historical origins of the idea of mass as "a quantity of stuff" are, but it's an old and widely understood idea. And this idea of mass as "a quantity of stuff" is much more compatible with the concept of invariant mass, because the invariant mass depends only on the object, while the energy depends on the both the object and the viewpoint chosen, the viewpoint being the specific coordinates or reference frame used.

How would you weigh this stuff?

 

[jtbell]

By comparing it to another piece of stuff, using e.g. a balance scale.

 

[PeterDonis]

Wouldn't E simply be the maximum amount of energy that may be transferred to a separate body in that given reference frame? The actual amount of energy transfer would seem to be a function of the elasticity of the collision with the separate body. The more elastic the collision, the greater the energy change \Delta E would be observed of the separate body on impact. This seems to be the direct result of having \Delta E include the part of the initial energy of the affected separate body that is impedance-matched to the incoming object. It makes no sense to me that the motions of this separate body, which is a receiver (measurer) of \Delta E, would not somehow contribute some of its own energy into \Delta E in the form of \Delta pc, through gauge bosons, such as photons, which travel at c with a momentum transfer of \Delta p. It seems that there would be a scalar product involved in such a collision to determine the limits of the amount energy exchanged if there are additional degrees of freedom, would there not?

To do calculations, as other posters have noted, it's much easier to deal with "geometric objects" whose transformation properties from frame to frame are well-defined. E by itself is not such an object, but the energy-momentum 4-vector (E, p_x, p_y, p_z) is. (Note that I was using "natural" units there, where c = 1; in conventional units each momentum component would be multiplied by c to give it the same units as E.) If you do a collision calculation using 4-vectors, all the issues you talk about do indeed come into play.

None of that, IMO, affects the question whether "relativistic mass" is a useful term. Referring to E as the "total energy", or as "the E (or timelike, or zeroth) component of the energy-momentum 4-vector" makes sense. I don't see how calling E (or E divided by c^2) the "relativistic mass" would be an improvement, and for reasons already given, it seems to me that it would be worse because it would invite more confusion.

 

[atyy]

By comparing it to another piece of stuff, using e.g. a balance scale.

pervect suggested that the rest mass captured the idea of "amount of stuff". If we compare hot and cold boxes in which the molecules have more and less kinetic energy, will the scale still give only the rest masses?

 

[kmarinas86]

pervect suggested that the rest mass captured the idea of "amount of stuff". If we compare hot and cold boxes in which the molecules have more and less kinetic energy, will the scale still give only the rest masses?

If there were a sender and a receiver of light which receded from each other, with the sender traveling faster than the receiver in one particular frame of reference, the frequency of the light would appear to drop upon reflection, would this not? This would mean that the change of the energy content of the photon \Delta pc must now be something absorbed by the receiver. However, since receiver itself does not travel at the speed of light, doesn't this change the energy content and thus the m_0 of the receiver? Generally speaking, this would mean that all collisions and/or reflections with photons are inelastic, except in the very special case where the sender and the receiver travel at the same speed in the same direction. It would seem that when compared to a global inertial frame, the absorption of more energy (net in a particular direction) would correspond directly with the relativistic kinetic energy of this receiver relative to this global inertial frame. So the relativistic mass may reflect the exact amount of energy of the object, but only when calculated with respect that COM frame, and any attempt to treat relativistic mass as something "of physical stuff" relative to an arbitrary observer, except one that is at rest to that COM frame, would be incorrect.

Invariant mass is, to my mind, a clear winner, in part because it's a geometric object, but also because it better relates to the concept of mass as a "quantity of stuff". Without re-reading some of Max Jammer's books, I'm not quite sure where the historical origins of the idea of mass as "a quantity of stuff" are, but it's an old and widely understood idea. And this idea of mass as "a quantity of stuff" is much more compatible with the concept of invariant mass, because the invariant mass depends only on the object, while the energy depends on the both the object and the viewpoint chosen, the viewpoint being the specific coordinates or reference frame used.

The invariant mass cannot capture the quantity of all stuff, unless if you exclude photons as "stuff". The m_0 of photons is zero, but any absorption or emission of light by matter, especially as is known to occur with nuclear reactions and photovoltaic interactions, will change the system's m_0. It appears that the quantity m_0 is only invariant with respect to the frame of reference, yet it is not a constant over time.

m_0 c^2 therefore does not seem to capture to full concept of an "invariant energy" which would include the energy of light and not just that of mass. This means that the system's \left(E^2 - \left(pc\right)^2\right)^{1/2} is not constant with time either.

 

[harrylin]

Yes, and this is another problem.

Teachers seem to be happy with that concept, but science advisors aren't b/c they - not the teachers - have to answer silly questions like "do (why don't, ...) particles turn into black holes b/c of increasing mass near speed of light?"

That's only due to overly simplified explanations - but admittedly, probably by those same teachers...

 

[harrylin]

pervect suggested that the rest mass captured the idea of "amount of stuff". If we compare hot and cold boxes in which the molecules have more and less kinetic energy, will the scale still give only the rest masses?

Regretfully not* - you have found the counter example of the question if a fast object turns into a black hole.

* in theory, for this is extremely hard to measure

 

[kmarinas86]

The invariant mass cannot capture the quantity of all stuff, unless if you exclude photons as "stuff". The m_0 of photons is zero, but any absorption or emission of light by matter, especially as is known to occur with nuclear reactions and photovoltaic interactions, will change the system's m_0. It appears that the quantity m_0 is only invariant with respect to the frame of reference, yet it is not a constant over time.

m_0 c^2 therefore does not seem to capture to full concept of an "invariant energy" which would include the energy of light and not just that of mass. This means that the system's \left(E^2 - \left(pc\right)^2\right)^{1/2} is not constant with time either.

This brings me to a final point: Is any variable in the equation m_0 c^2 = \left(E^2 - \left(pc\right)^2\right)^{1/2} constant with respect to both the frame of reference and mass-to-light (or light-to-mass) conversion of energy?

 

[ZapperZ]

The invariant mass cannot capture the quantity of all stuff, unless if you exclude photons as "stuff". The m_0 of photons is zero, but any absorption or emission of light by matter, especially as is known to occur with nuclear reactions and photovoltaic interactions, will change the system's m_0. It appears that the quantity m_0 is only invariant with respect to the frame of reference, yet it is not a constant over time.

m_0 c^2 therefore does not seem to capture to full concept of an "invariant energy" which would include the energy of light and not just that of mass. This means that the system's \left(E^2 - \left(pc\right)^2\right)^{1/2} is not constant with time either.

This is a rather naive and silly complaint. That's like saying, if I took a bite out of a cake, the cake now has a different mass, and so, no "invariant mass". This is not what is being discussed here.

Again, if one has a strong idea about this, one should really put one's money where one's mouth is. Lev Okun has published a very good paper arguing why the concept of relativistic mass should be rejected.

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

I don't see any valid rebuttals to that so far. In fact, there's also plenty of evidence that Einstein, after his initial paper, has moved to reject the notion of relativistic mass.

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

I'd like to see published counter arguments against such ideas beyond just a matter of tastes!

Zz.

 

[kmarinas86]

This is a rather naive and silly complaint. That's like saying, if I took a bite out of a cake, the cake now has a different mass, and so, no "invariant mass".

Your analogy is an inaccurate reflection of what I stated. The "invariant mass" of your "cake" is not changed by biting into it, but rather it is simply split into two kinds of pieces: 1) the cake pieces that come off 2) the cake that remains. Only when you can get that cake pieces' atoms and molecules to lose some mass through the metabolism of one's body, in the form of radiative heat, would I question the time-invariance of this so-called "invariant mass".

 

[atyy]

This is a rather naive and silly complaint. That's like saying, if I took a bite out of a cake, the cake now has a different mass, and so, no "invariant mass". This is not what is being discussed here.

Again, if one has a strong idea about this, one should really put one's money where one's mouth is. Lev Okun has published a very good paper arguing why the concept of relativistic mass should be rejected.

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

I don't see any valid rebuttals to that so far. In fact, there's also plenty of evidence that Einstein, after his initial paper, has moved to reject the notion of relativistic mass.

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

I'd like to see published counter arguments against such ideas beyond just a matter of tastes!

Zz.

In addition to those I posted in #3:

http://www.frankwilczek.com/Wilczek_Easy_Pieces/342_Origin_of_Mass.pdf

http://www.sp.phy.cam.ac.uk/~dar11/pdf/dehmelt-lecture%5B1%5D.pdf

Phys. Rev. E 81, 056405 (2010) "Relativistic mass and charge of photons in thermal plasmas through electromagnetic field quantization"

 

[atyy]

Yes, and this is another problem.

Teachers seem to be happy with that concept, but science advisors aren't b/c they - not the teachers - have to answer silly questions like "do (why don't, ...) particles turn into black holes b/c of increasing mass near speedof light?"

Regretfully not* - you have found the counter example of the question if a fast object turns into a black hole.

* in theory, for this is extremely hard to measure

Well, if we have point particles combined with GR, they are of course black holes since a point particle will have a radius less than its Schwarzschild radius (even without "moving at near the speed of light").

 

[harrylin]

In addition to those I posted in #3:

http://www.frankwilczek.com/Wilczek_Easy_Pieces/342_Origin_of_Mass.pdf

http://www.sp.phy.cam.ac.uk/~dar11/pdf/dehmelt-lecture%5B1%5D.pdf

Phys. Rev. E 81, 056405 (2010) "Relativistic mass and charge of photons in thermal plasmas through electromagnetic field quantization"

And from the physics FAQ (which rebuts one-sided opinions):

- Putting to Rest Mass Misconceptions, Physics Today 43, May 1990, pgs 13 and 115
http://dx.doi.org/10.1063/1.2810555

- In Defense of Relativistic Mass, Am. J. Phys. 59, November 1991, pg 1032
http://ajp.aapt.org/resource/1/ajpias/v59/i11/p1032_s1

 

[harrylin]

Well, if we have point particles combined with GR, they are of course black holes since a point particle will have a radius less than its Schwarzschild radius (even without "moving at near the speed of light").

I don't know about that... (someone else?!). However, my reply seems to have been misunderstood: I compared a misunderstanding due to a poor explanation of "relativistic mass" with a similar misunderstanding due to a poor explanation of "invariant mass".

 

[Phrak]

pervect suggested that the rest mass captured the idea of "amount of stuff". If we compare hot and cold boxes in which the molecules have more and less kinetic energy, will the scale still give only the rest masses?

I don't think this is the right idea. It's not a closed system; the hot box has gained more gravitational stuff.

stuff = \int_\Sigma P_{\mu\nu\sigma}d^{3}x

 

[kmarinas86]

Regretfully not* - you have found the counter example of the question if a fast object turns into a black hole.

* in theory, for this is extremely hard to measure

I thought a system lost mass when potential energy is lost to external heat after passing through the intermediate stage of kinetic energy of a body in gravitational fall. So if an object were accelerated to \gamma=2 when passing by a black hole, wouldn't that mean half of the object's internal kinetic energy was converted into an "externalized" kinetic energy of the whole object? The internal kinetic energies would simply be deflected toward a common course, possibly by following geodesics that converge as they approach the black hole. Similarly, if the object was accelerated to \gamma=3 when passing by the black hole, wouldn't that mean 2/3 (i.e. 1 - 1/\gamma) of its inertial mass then exists as the kinetic energy, while still being a part of the "invariant mass" m_0? The energy of the object now available for collision, rather than locked up inside atoms and molecules, would be capable of being dissipated through friction, and would ultimately be lost to the rest of the universe as heat, resulting in a mass defect. In this case, the stuff of the object is never "increased" as a result of this acceleration.

 

[atyy]

I don't know about that... (someone else?!). However, my reply seems to have been misunderstood: I compared a misunderstanding due to a poor explanation of "relativistic mass" with a similar misunderstanding due to a poor explanation of "invariant mass".

Oh sorry, were you being serious? I thought you were joking. OK, I did misunderstand then. Would you mind explaining again?

 

[ZapperZ]

Your analogy is an inaccurate reflection of what I stated. The "invariant mass" of your "cake" is not changed by biting into it, but rather it is simply split into two kinds of pieces: 1) the cake pieces that come off 2) the cake that remains. Only when you can get that cake pieces' atoms and molecules to lose some mass through the metabolism of one's body, in the form of radiative heat, would I question the time-invariance of this so-called "invariant mass".

You are applying an incomplete conservation law, i.e. your accounting process is flawed. You are only using the conservation of the invariant mass, when the actual conservation law is the conservation of mass/energy. But that is still besides the point because this is NOT what is being discussed here, i.e. we 're not talking about a conversation of mass-energy, but rather the accounting of mass ONLY. Considering that, in high energy physics experiments, where mass-energy conversion happens ALL THE TIME, only invariant mass is used, and it is the ONLY thing that actually has any meaning.

So go ahead and submit your "questions" as rebuttals to all those high energy physics papers.

Zz.

 

[kmarinas86]

You are applying an incomplete conservation law, i.e. your accounting process is flawed. You are only using the conservation of the invariant mass, when the actual conservation law is the conservation of mass/energy. But that is still besides the point because this is NOT what is being discussed here, i.e. we 're not talking about a conversation of mass-energy, but rather the accounting of mass ONLY. Considering that, in high energy physics experiments, where mass-energy conversion happens ALL THE TIME, only invariant mass is used, and it is the ONLY thing that actually has any meaning.

So go ahead and submit your "questions" as rebuttals to all those high energy physics papers.

Zz.

In two contributions to this thread, you think that you have a monopoly over what others are discussing? Mind you, not even most posts here are the same things I discussing, so I do not claim such a monopoly.

To my surprise in fact, only one person in this thread so far, you, seem to be direct about the rejection of relativistic mass, whereas most here either wondered about its existence and/or have discussed the pedagogy of this subject.

All I glean from this so far is an absolute total lack of evidence of scientific consensus on the part of participants in this thread regarding the subject of relativistic mass.

 

[atyy]

I don't think this is the right idea. It's not a closed system; the hot box has gained more gravitational stuff.

stuff = \int_\Sigma P_{\mu\nu\sigma}d^{3}x

I agree. I should have made the scenario two closed boxes that have equal weight on the balance. In one box, a stationary particle decays into moving parts.

 

[Hurkyl]

All I glean from this so far is an absolute total lack of evidence of scientific consensus on the part of participants in this thread regarding the subject of relativistic mass.

Why not glean "there are so many problems with using the notion of relativistic mass instead of invariant mass and 4-momentum that everyone can pick a different reason to reject it when asked"?

I mentioned pedagogy simply because everything boils down to it -- relativistic mass in general simply isn't as good a tool for understanding and explaining things as invariant mass and 4-momentum. All the comments are either explaining why it's not as good, or demonstrating the community has accepted that it isn't as good.

 

[ZapperZ]

In two contributions to this thread, you think that you have a monopoly over what others are discussing? Mind you, not even most posts here are the same things I discussing, so I do not claim such a monopoly.

This is because you were using what I noticed to be something beyond what the actual topic is.

To my surprise in fact, only one person in this thread so far, you, seem to be direct about the rejection of relativistic mass, whereas most here either wondered about its existence and/or have discussed the pedagogy of this subject.

All I glean from this so far is an absolute total lack of evidence of scientific consensus on the part of participants in this thread regarding the subject of relativistic mass.

So where is the "total lack of evidence of scientific consensus" when you read the mass of the top quark, the mass electron neutrino, etc.? After all, many of the high energy collider experiments continually have mass-energy conversion. This, you did not address. Rather, you focused on the fact that I have only posted twice in this thread, as if that in itself is a point in your favor.

I pointed out two AJP papers addressing why the use of the term "relativistic mass" is faulty. In fact, Lev Okun even has a stronger opinion on this than I do (read his "Relativistic Mug" preprint). I don't believe you've supported your assertion with any valid citation.

Zz.

 

[kmarinas86]

You are only using the conservation of the invariant mass, when the actual conservation law is the conservation of mass/energy.

http://en.wikipedia.org/wiki/Invariant_mass

The invariant mass, rest mass, intrinsic mass, proper mass or just mass is a characteristic of the total energy and momentum of an object or a system of objects that is the same in all frames of reference related by Lorentz transformations.
[...]
This equation says that the invariant mass is the pseudo-Euclidean length of the four-vector (E, p), calculated using the relativistic version of the pythagorean theorem which has a different sign for the space and time dimensions. This length is preserved under any Lorentz boost or rotation in four dimensions, just like the ordinary length of a vector is preserved under rotations.
[...]
Since the invariant mass is determined from quantities which are conserved during a decay, the invariant mass calculated using the energy and momentum of the decay products of a single particle is equal to the mass of the particle that decayed.

Now that you know that Wikipedia's description of "invariant mass" is wrong, then why don't you go fix it?

 

[harrylin]

Oh sorry, were you being serious? I thought you were joking. OK, I did misunderstand then. Would you mind explaining again?

Misunderstanding (as we know from elsewhere) due to a poor explanation of "relativistic mass":
"do particles turn into black holes b/c of increasing mass near speed of light?"

Misunderstanding (as we know from this thread) due to a poor explanation of "invariant mass":
"if we compare hot and cold boxes in which the molecules have more and less kinetic energy, will the scale still give only the invariant masses b/c invariant mass is the amount of stuff?"

Cheers,
Harald

 

[ZapperZ]

http://en.wikipedia.org/wiki/Invariant_mass
Now that you know that Wikipedia's description of "invariant mass" is wrong, then why don't you go fix it?

That's it? That's all you got? Asking me to go correct something that I don't care for in the first place? And this is what you use as a source?

I could ask you the same thing. Since I've given you published sources, if you don't think they are correct in their assertion to drop the idea of relativistic mass, why don't you write a rebuttal?

I noticed you still refuse to address my point about high energy physics experiments.

Zz.

 

[harrylin]

[..]
All I glean from this so far is an absolute total lack of evidence of scientific consensus on the part of participants in this thread regarding the subject of relativistic mass.

The consensus or not of the few people here is not relevant!

What matters is the quality references that we provided. And if you checked out the physics FAQ which gives a summary overview, you would now understand why relativistic mass is disliked by many but appreciated by others, and not generally rejected.

 

[kmarinas86]

I can see why m_0 is invariant, but let's look at what we are actually seeing:

m_0 c^2 = \left( E^2 - |pc|^2\right)^{1/2}

So here is the thing. E does not contain a norm, and yet |pc| does. If the momenta which make up |pc| are not aligned, then E is greater than |pc|. So even if we converted all mass into photons, we would still preserve this difference.

As far as I know, \frac{E}{c^2} is the relativistic mass. If this is not invariant, then neither is |pc|. However, if the momentum of the whole system were a constant with time, implying a system closed to any other environment, I would fail to see how |pc| would vary with time. This would make the system's m_0 c^2, E, and |pc| not a function with time.

However, then it is claimed that one could increase this E by choosing a different reference frame. Now realizing that this is the "relativistic mass" and considering a recent argument of mine against the "physicality" of this E, I now realize that I myself rejected the relativistic mass.

Wouldn't E simply be the maximum amount of energy that may be transferred to a separate body in that given reference frame? The actual amount of energy transfer would seem to be a function of the elasticity of the collision with the separate body. The more elastic the collision, the greater the energy change \Delta E would be observed of the separate body on impact. This seems to be the direct result of having \Delta E include the part of the initial energy of the affected separate body that is impedance-matched to the incoming object. It makes no sense to me that the motions of this separate body, which is a receiver (measurer) of \Delta E, would not somehow contribute some of its own energy into \Delta E in the form of \Delta pc, through gauge bosons, such as photons, which travel at c with a momentum transfer of \Delta p. It seems that there would be a scalar product involved in such a collision to determine the limits of the amount energy exchanged if there are additional degrees of freedom, would there not?

In the quote above, here I said that E is not something of the object itself, but rather the maximum value of energy change that may occur of that object when colliding with a body in the same inertial frame of reference as the observer. In other words, I claimed that relativistic mass is not tied to anyone body.

 

[pervect]

pervect suggested that the rest mass captured the idea of "amount of stuff". If we compare hot and cold boxes in which the molecules have more and less kinetic energy, will the scale still give only the rest masses?

In Newtonian physics, I'd just use a balance, as others have remarked. And in Newtonian physics you wouldn't expect the answer to change when you add heat to the box, so this is something new that arises in relativistic physics. We've subtly changed our philosophical idea of "stuff" - from being just matter, to being energy. So now, the amount of "stuff" in the box is the amount of energy in the box, not just the amount of gross matter. A subtle, but important, evolution from the original Newtonian idea.

In special relativity, we can define a satisfactory answer for the "amount of stuff", which we have newly interpreted as the total energy, of a system, IF the system is isolated. Due to the relativity of simultaneity, the amount of energy in a non-isolated system depends on the observer when the system is interacting with the environment. In GR, the situation is even worse - there isn't any general answer for total energy unless one has some preconditions.

Even in special relativity, the problem can be tricky. The surest way of getting the correct answer is also the most technical. The sure way is to use another geometric object the stress-energy tensor, to compute the energy, and momentum, of the system. Then, for isolated systems, one can show that E^2 - p^2 is invariant, it's independent of the "view" or coordinates or frame one takes. We say that the energy-momentum of the box transforms as a four vector, even for an extended object - but ONLY when the extended object is isolated. So E^2 - p^2, or rather its square root, turns out to be a good way to "weigh" a box.

However, the general reason why we use the stress-energy tensor is, I think, a mystery to most students. The answer goes back to geometric objects again. The stress energy tensor is a geometric object, it's a frame-independent way of thinking about the distribution, or density, of energy and momentum.

The easy way of getting the correct answer, without using the stress-energy tensor, is to compute E^2 - p^2 in the rest frame of the box. In this case, one can omit the walls of the box. But one has to presuppose the result that E^2-p^2 is invariant.

If you compute the total energy and momentum of the box in some other frame, you have to be sure to include the walls of the box. This is part of having a closed system, without a box, some collection of bouncing non-interacting particles would fly apart. There must be tension in the box to hold it together.

This tension in the walls doesn't contribute to either the total energy or the total momentum in the rest frame of the box. But in other frames (or views, as I called them eariler), it does! So to have frame independent physics, one has to include these contributions from the walls of the box.

I have posted a worked example somewhere of a "box of bouncing particles" using SR that shows that if you omit the walls and include only the energy and momentum of the particles, E^2 - p^2 of the sub-assembly (the contents of the box excluding the walls) is NOT constant, a consequence of the system being NOT isolated unless you include the walls.

 

[atyy]

In Newtonian physics, I'd just use a balance, as others have remarked. And in Newtonian physics you wouldn't expect the answer to change when you add heat to the box, so this is something new that arises in relativistic physics. We've subtly changed our philosophical idea of "stuff" - from being just matter, to being energy. So now, the amount of "stuff" in the box is the amount of energy in the box, not just the amount of gross matter. A subtle, but important, evolution from the original Newtonian idea.

In special relativity, we can define a satisfactory answer for the "amount of stuff", which we have newly interpreted as the total energy, of a system, IF the system is isolated. Due to the relativity of simultaneity, the amount of energy in a non-isolated system depends on the observer when the system is interacting with the environment. In GR, the situation is even worse - there isn't any general answer for total energy unless one has some preconditions.

Even in special relativity, the problem can be tricky. The surest way of getting the correct answer is also the most technical. The sure way is to use another geometric object the stress-energy tensor, to compute the energy, and momentum, of the system. Then, for isolated systems, one can show that E^2 - p^2 is invariant, it's independent of the "view" or coordinates or frame one takes. We say that the energy-momentum of the box transforms as a four vector, even for an extended object - but ONLY when the extended object is isolated. So E^2 - p^2, or rather its square root, turns out to be a good way to "weigh" a box.

However, the general reason why we use the stress-energy tensor is, I think, a mystery to most students. The answer goes back to geometric objects again. The stress energy tensor is a geometric object, it's a frame-independent way of thinking about the distribution, or density, of energy and momentum.

The easy way of getting the correct answer, without using the stress-energy tensor, is to compute E^2 - p^2 in the rest frame of the box. In this case, one can omit the walls of the box. But one has to presuppose the result that E^2-p^2 is invariant.

If you compute the total energy and momentum of the box in some other frame, you have to be sure to include the walls of the box. This is part of having a closed system, without a box, some collection of bouncing non-interacting particles would fly apart. There must be tension in the box to hold it together.

This tension in the walls doesn't contribute to either the total energy or the total momentum in the rest frame of the box. But in other frames (or views, as I called them eariler), it does! So to have frame independent physics, one has to include these contributions from the walls of the box.

I have posted a worked example somewhere of a "box of bouncing particles" using SR that shows that if you omit the walls and include only the energy and momentum of the particles, E^2 - p^2 of the sub-assembly (the contents of the box excluding the walls) is NOT constant, a consequence of the system being NOT isolated unless you include the walls.

Yes. The only question, and it is a matter of taste, is how does one motivate the change in the definition of "amount of stuff"? And really, doesn't one need GR to appreciate this definition of "amount of stuff"? (Well, I suppose generalizing Newtonian conservation laws applied to fields would be enough - but maybe not - I think there's this issue of being able to choose non-symmetric stress-energy tensors) If so, wouldn't part of the motivation be a heuristic for guessing the stress-energy tensor as the source of gravity in a relativistic theory of gravity? It can be done without relativistic mass, but would you prefer to do it that way?

BTW, I happened to learn SR on my own from WGV Rosser's text that advocated using only rest mass. When I went to university, I was converted, reluctantly, to accepting relativistic mass - I believe we used Purcell, but am not sure what Purcell actually does, since that book was so impenetrable to me. Does anyone know whether Purcell used relativistic mass? Or was that worse than SI units;) Jackson the betrayer (see his latest edition)!

 

[pervect]

Well, the idea of having gravity depend on a single scalar quantity - "relativistic mass", or "quantity X" - would be nice. But in the end, it winds up depending on a rank 2 tensor, so it never really seems to happen.

And it seems that the well-meaning shortcuts wind up biting one in the back eventually. A lesser but common example of this is when students start asking why you don't turn into a black hole if you move too fast - after all, your "relativistic mass" goes up.

Their logic is sound, the problem is taking a flawed concept (relativistic mass) too seriously. It may be a motivator, but in the end it doesn't quite work right.

Having gravity depend on the scalar rho+3P works better than having it depend on "relativisitic mass", in my opinion. But that's not perfect either, though it works reasonably well for static systems. And it's a relatively advanced concept (the Komar mass concept) anyway.

Also, if we take the energy as mass concept too seriously, we wind up with having 1kg on a mountaintop being different than 1kg in a valley, due to the difference in gravitational potential energy. (We had a recent thread, I was more or less uncessesful in cautioning an enthusiastic but rather misguided poster about this idea). And that's not good. Especially when we start trying to push that idea to it's logical conclusion. Where is the place that 1kg is "really' one kg? The Earth's gravitational field has some effect, but the Suns' gravitational field has more. And the galaxy's gravitational field has more than that. And so on, and so on. In the end, we can't find any place that 1kg is really 1kg. Eliminating gravitational self energy is tempting, but it isn't a good idea, either.

In the end, we are left with a bunch of competing ideas for mass, all of them different (the Komar formula, rho + 3P, for instance, is NOT exactly the same as either the relativistic mass OR the invariant mass), none of which is fully satisfactory.

 

[Hurkyl]

2) I said that E is not something of the object itself, but rather the maximum value of energy change that may occur of that object when colliding with a body in the same inertial frame of reference as the observer. In other words, I claimed that relativistic mass is not tied to anyone body.

There's already a notion of relativistic mass. If you're going to start inventing new concepts, you should give them different names.

5) Therefore, while those against the validity of relativistic mass focus on the Lorentz boosts of a particle, those for the validity of relativistic mass focus on the proper acceleration of a particle.

Eh? The way I've seen it presented, accelerated particles are pretty much the biggest strike against relativistic mass. With 4-vectors and invariant mass, you get an equation F=ma. When 3-vectors and relativistic mass, you don't get any simple relationship (except in the special case where force and velocity are in the same direction).

 

[atyy]

Well, the idea of having gravity depend on a single scalar quantity - "relativistic mass", or "quantity X" - would be nice. But in the end, it winds up depending on a rank 2 tensor, so it never really seems to happen.

And it seems that the well-meaning shortcuts wind up biting one in the back eventually. A lesser but common example of this is when students start asking why you don't turn into a black hole if you move too fast - after all, your "relativistic mass" goes up.

Their logic is sound, the problem is taking a flawed concept (relativistic mass) too seriously. It may be a motivator, but in the end it doesn't quite work right.

Having gravity depend on the scalar rho+3P works better than having it depend on "relativisitic mass", in my opinion. But that's not perfect either, though it works reasonably well for static systems. And it's a relatively advanced concept (the Komar mass concept) anyway.

Also, if we take the energy as mass concept too seriously, we wind up with having 1kg on a mountaintop being different than 1kg in a valley, due to the difference in gravitational potential energy. (We had a recent thread, I was more or less uncessesful in cautioning an enthusiastic but rather misguided poster about this idea). And that's not good. Especially when we start trying to push that idea to it's logical conclusion. Where is the place that 1kg is "really' one kg? The Earth's gravitational field has some effect, but the Suns' gravitational field has more. And the galaxy's gravitational field has more than that. And so on, and so on. In the end, we can't find any place that 1kg is really 1kg. Eliminating gravitational self energy is tempting, but it isn't a good idea, either.

In the end, we are left with a bunch of competing ideas for mass, all of them different (the Komar formula, rho + 3P, for instance, is NOT exactly the same as either the relativistic mass OR the invariant mass), none of which is fully satisfactory.

Well, let's exclude the more Komar, AdM, Yau, Yorke etc proposals for the moment. My own thinking is that while the relativistic mass is an important motivator, it should also be shown to be limited - ie. we search for a covariant analogue of the relativistic mass = energy - which for particles would be the invariant mass or the energy-momentum 4-vector. However, we also wish to define it for fields, which leads to the stress-energy tensor, which is good for particles and fields. And this is what we expect to take the place of "gravitational mass", since mass=energy heuristically.

An analogous paedagogical discussion might involve Bohr-Sommerfeld quantization. I know ZapperZ dislikes it, so he's being consistent in having everything very clean. But then this comes back in the field of quantum chaos, so perhaps it's best to learn these restricted ideas as advanced ideas. But don't we want students to have the joy of being confused by things like the EP (now can one argue that the relativistic mass is a worse heuristic than the EP)?