Difference between mass (relativistic & non)

[kc7rad]

Just a question from a physics noob (my degree is in computer science... about 17 years ago). I'm just a curious semi-educated spectator! :-)

I see relativistic mass and non-relativistic mass discussed. Other than the moving object's ripples in gravity and Lorentz contraction and time dilation, is there any functional difference in the properties of its mass?

Ok, I'll step away and go read more on the speed of gravity or something. Maybe I will get some coffee!

TNX
Ken

 

[pervect]

Just a question from a physics noob (my degree is in computer science... about 17 years ago). I'm just a curious semi-educated spectator! :-)

I see relativistic mass and non-relativistic mass discussed. Other than the moving object's ripples in gravity and Lorentz contraction and time dilation, is there any functional difference in the properties of its mass?

Ok, I'll step away and go read more on the speed of gravity or something. Maybe I will get some coffee!

TNX
Ken

For more info on relativistic vs invariant mass, see either of the following. Note that I've excerpted quotes, to encourage readers who are interested and motivated to clink on the links and read the entire article.

http://math.ucr.edu/home/baez/physics/Relativity/SR/mass.html

Does mass change with velocity?

There is sometimes confusion surrounding the subject of mass in relativity. This is because there are two separate uses of the term. Sometimes people say "mass" when they mean "relativistic mass", mr but at other times they say "mass" when they mean "invariant mass", m0. These two meanings are not the same. The invariant mass of a particle is independent of its velocity v, whereas relativistic mass increases with velocity and tends to infinity as the velocity approaches the speed of light c. They can be defined as follows:

<snip>

or the Wikipedia article

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

The term mass in special relativity can be used in different ways, occasionally leading to confusion. Historically, mass can refer to either the invariant mass or the relativistic mass.

* The rest mass or invariant mass is an observer-independent quantity.
* The relativistic mass or apparent mass depends on one's frame of reference.

In particular, the relativistic mass increases with observed speed while the rest mass is an invariant property of an object: it does not change with a change of reference system.
<snip>

I don't understand what you mean by "ripples in gravity", or why you think that Lorentz contraction and time dilation have anything particular to do with whether one uses relativistic or invariant mass.

I'd also generally not recommend the locked article on "the speed of gravity" recently moved here. If you are not just trolling and want some genunine info, we can provide some detailed and correct references - I'd suggest starting with:

http://math.ucr.edu/home/baez/physics/Relativity/GR/grav_speed.html

(This is the same as the link at the end of the article just before it was locked by the moderators for not meeting PF guidelines, it's about the only part of the article I'd recommend).

 

[bernhard.rothenstein]

mass proper and relativistic

Just a question from a physics noob (my degree is in computer science... about 17 years ago). I'm just a curious semi-educated spectator! :-)

I see relativistic mass and non-relativistic mass discussed. Other than the moving object's ripples in gravity and Lorentz contraction and time dilation, is there any functional difference in the properties of its mass?

Ok, I'll step away and go read more on the speed of gravity or something. Maybe I will get some coffee!

in order to see how fierce the debates between physicists could become concerning the two concepts you mention, have a look at
L.B.Okun, Physics Today, June 1989 p.31
L.B.Okun, Physics Today, May 1990 p.147
and others by the same author as well as to the papers generated by them.
sine ira et studio

 

[pmb_phy]

Just a question from a physics noob (my degree is in computer science... about 17 years ago). I'm just a curious semi-educated spectator! :-)

I see relativistic mass and non-relativistic mass discussed. Other than the moving object's ripples in gravity and Lorentz contraction and time dilation, is there any functional difference in the properties of its mass?

Ok, I'll step away and go read more on the speed of gravity or something. Maybe I will get some coffee!

TNX
Ken

Relaticistic mass is greater that proper mass (aka rest mass). For gruesome details please see

http://www.geocities.com/physics_world/mass_paper.pdf

Pete

 

[Meir Achuz]

There is a right and wrong in physics. The use of "relativistic mass" in SR is just wrong. E used it early on, but even he disowned it.

 

[JesseM]

There is a right and wrong in physics. The use of "relativistic mass" in SR is just wrong. E used it early on, but even he disowned it.

No, it isn't objectively wrong in the sense of leading to any incorrect physical predictions, as long as it's used correctly. The debate about whether to make use of "relativistic mass" in SR is essentially an aesthetic one, since any statement made using the concept of relativistic mass can be replaced with an equivalent one using concepts like relativistic momentum and energy.

 

[pmb_phy]

No, it isn't objectively wrong in the sense of leading to any incorrect physical predictions, as long as it's used correctly. The debate about whether to make use of "relativistic mass" in SR is essentially an aesthetic one, ...

Bravo! Well said JesseM. There is absolutely nothing wrong with using rel-mass in SR, nothing!

..., any statement made using the concept of relativistic mass can be replaced with an equivalent one using concepts like relativistic momentum and energy.

That is true if and only if the object under scrutiny is an isolated system. If the system is not isolated then then E will not always equal mc^2.

Pete

 

[pmb_phy]

E used it early on, but even he disowned it.

Who is E? I'd like to ask E directly why he disowned it.

Pete

 

[Parlyne]

Who is E? I'd like to ask E directly why he disowned it.

Pete

Good luck with that. He's been dead for the last half century.

 

[JesseM]

That is true if and only if the object under scrutiny is an isolated system. If the system is not isolated then then E will not always equal mc^2.

Even so, any physical prediction you made using the equation E=mc^2 could be replaced with some different but equivalent set of equations that would lead you to the same predictions--that was all I was saying, that predictions made using the concept of relativistic mass will never differ from predictions made without it (although it may be that it makes the reasoning that leads to the predictions become simpler in some situations).

 

[robphy]

Even so, any physical prediction you made using the equation E=mc^2 could be replaced with some different but equivalent set of equations that would lead you to the same predictions--that was all I was saying, that predictions made using the concept of relativistic mass will never differ from predictions made without it (although it may be that it makes the reasoning that leads to the predictions become simpler in some situations).

This bears some similarity to saying that there is a choice of coordinate system involved...any of which leads to the same physical result. Aesthetically (borrowing your word from your first reply), modern geometrical formulations prefer coordinate-free reasoning... preferring, whenever possible, observer-independent quantities (e.g., scalars not involving the observer's 4-velocity) over observer-dependent quantities (where the observer has to be somehow factored out to see what is really there... or else be transformed to see what another observer would measure, then discern what is really there).

 

[pmb_phy]

Even so, any physical prediction you made using the equation E=mc^2 could be replaced with some different but equivalent set of equations that would lead you to the same predictions--that was all I was saying, that predictions made using the concept of relativistic mass will never differ from predictions made without it (although it may be that it makes the reasoning that leads to the predictions become simpler in some situations).

Perhaps when the person is well versed he will make no false predictions. However I disagree in general because on numersous occasions on this forum I've witnessed people assuming/quetioning whether an object will become a black hole (because of increased in mass) of it moves fast enough. People tend to image things in their minds before sitting down and doing the math. However those are not experts asking since an expert would never be ignorant enough to make such assumptions.

Pete

 

[pmb_phy]

This bears some similarity to saying that there is a choice of coordinate system involved...any of which leads to the same physical result. Aesthetically (borrowing your word from your first reply), modern geometrical formulations prefer coordinate-free reasoning... preferring, whenever possible, observer-independent quantities (e.g., scalars not involving the observer's 4-velocity) over observer-dependent quantities (where the observer has to be somehow factored out to see what is really there... or else be transformed to see what another observer would measure, then discern what is really there).

If the observer is factored out then this something that is "really there" has no meaning for me since it can't be measured without at least one observer. Also different coordinate systems will yield different observations. E.g. for a particle at rest in an inertial frame will be observed as having a spatial acceleration whereas an observer at rest in the inertial frame will observe only a particle at rest of moving with constant 3-velocity.

Pete

 

[robphy]

If the observer is factored out then this something that is "really there" has no meaning for me since it can't be measured without at least one observer.

Let me clarify with an example.
The electric field is akin to the relativistic mass in the following way:
$$E_a=F_{ab}v^b$$ (similarly, $$m_{rel}=g_{ab}p^av^b$$), where $$v^b$$ is the unit 4-velocity of the observer. The "thing" with the observer-independent reality, if you will, is the field tensor $$F_{ab}$$ (similarly, the 4-momentum of the particle $$p^a$$). Hence, the emphasis is placed on the geometrical object representing a physical quantity, rather than on its components in a choice of coordinate system (which transform as...).

Nothing above prevents you from contracting with your 4-velocity to make a measurement. But, geometrically speaking, it is better (i.e. clearer, more economical, free-from-observer-dependencies) to talk about the object itself rather than the object's-components-and-the-observers-that-made-the-measurements.

 

[Andrew Mason]

There is a right and wrong in physics. The use of "relativistic mass" in SR is just wrong. E used it early on, but even he disowned it.

I'd be interested in knowing why you say this. Also your source for saying that Einstein eventually disowned its use. Relativistic mass is implicit in E = mc², which he seems not to have disowned.

AM

 

[pmb_phy]

The "thing" with the observer-independent reality, if you will, is the field tensor $$F_{ab}$$ (similarly, the 4-momentum of the particle $$p^a$$).

Ummm ... that's pretty obvious rob. However you're giving the impression that all quantities in relativity are tensors. They are not. If you believe so then please explain how energy is not an observer dependant quantity.

..it is better (i.e. clearer, more economical, free-from-observer-dependencies) to talk about the object itself rather than the object's-components-and-the-observers-that-made-the-measurements.

Anything described using the term "better" is simply a matter of taste rob.

Pete

 

[Meir Achuz]

I'd be interested in knowing why you say this. Also your source for saying that Einstein eventually disowned its use. Relativistic mass is implicit in E = mc², which he seems not to have disowned.

AM

This is from a John Baez website:

In a 1948 letter to Lincoln Barnett, Einstein wrote

"It is not good to introduce the concept of the mass M = m/(1-v2/c2)1/2 of a body for which no clear definition can be given. It is better to introduce no other mass than `the rest mass' m. Instead of introducing M, it is better to mention the expression for the momentum and energy of a body in motion."

 

[Andrew Mason]

This is from a John Baez website:

In a 1948 letter to Lincoln Barnett, Einstein wrote

"It is not good to introduce the concept of the mass M = m/(1-v2/c2)1/2 of a body for which no clear definition can be given. It is better to introduce no other mass than `the rest mass' m. Instead of introducing M, it is better to mention the expression for the momentum and energy of a body in motion."

Thanks for the quote! This John Baez http://math.ucr.edu/home/baez/physics/Relativity/SR/mass.html" goes through the arguments for abandoning the concept of relativistic mass but does not really explain the advantages.

Personally, I think relativistic mass is a useful concept because:

1. It retains the beauty and simplicity of the equation $E=mc^2$ as an exact relation.

2. Photons do not have rest mass but they transport rest mass across space. The mass they transport is $E/c^2$. If we do not have a concept of relativistic mass, where does the mass go between the time the photon leaves one matter object and is absorbed by another?

3. electrons moving at very close to c can be accelerated only by applying increasingly greater force (adding large amounts of energy for very tiny changes in speed). This can be explained only by introducing the concept of relativistic mass.

4. You would have to define momentum as something other than the product of speed and mass. How do you explain momentum increasing if speed is limited, other than by saying mass increases?

5. It makes the math much simpler. For example, kinetic energy (ie. change from rest energy) is just a function of its change in mass: $KE = \Delta E = \Delta mc^2$

The biggest argument seems to be that it confuses students. If it is any consolation, I was taught the concept of relativistic mass and it did not confuse me at all.

AM

 

[Meir Achuz]

At least you now know that even Albert abandoned you.
Each of your 5 points are spurious. The only good reason is your last sentence. Now to quote Aristotle: He wasn't confused by having heavier objects fall faster. Nor, would I venture, would it confuse our beginning students. One last word: Right is an advantage over wrong, even if students are not confused by wrong.

 

[Andrew Mason]

At least you now know that even Albert abandoned you.
Each of your 5 points are spurious. The only good reason is your last sentence. Now to quote Aristotle: He wasn't confused by having heavier objects fall faster. Nor, would I venture, would it confuse our beginning students. One last word: Right is an advantage over wrong, even if students are not confused by wrong.

It is just a pedagogical debate. Even those who argue against relativistic mass do not say it is wrong. They just think it is a poor way to teach relativity.

In physics a concept is only wrong if it is inconsistent with evidence. Relativistic mass, as a model to explain relativistic phenomena is consistent with the evidence. It is just as 'right' to speak about relativistic mass as it is to speak about time dilation or length contraction.

AM

 

[pervect]

While relativistic mass is not wrong, anyone with a philosphical preference for observer independence will chose invariant mass over relativistic mass, as invariant mass is observer independent for systems with zero volume (i.e point particles) and for isolated systems (regardless of their volume).

This is the simple point that robphy was trying to make, and one I want to echo. It also contains some advanced points in the interests of creating an argument ooops, I mean in the interests of accuracy.

On the same basis, a person favoring observer and coordinate independence will prefer the stress-energy tensor over invariant mass, for the stress energy tensor is ALWAYS observer independent.

Note that general relativity is written in terms of the stress-energy tensor, thus it's energy (and pressure, and momentum) that causes gravity and not mass in general relativity. The idea that "mass" causes gravity is strictly a Newtonian carry-over.

 

[Hurkyl]

Personally, I think relativistic mass is a useful concept because:

If you don't mind discussing it...

Several of the things you said are actually reasons I prefer to use rest mass, and not relativistic mass.

In the 4-vector formalism, the equations p = mv and F = ma are only true if m denotes the rest mass.

And in the 3-vector formalism, the notion of mass as "resistance to motion" doesn't work -- IIRC, $F = \gamma m_0 a$ only when the force is applied in the direction the object is moving. But when the force is applied in a perpendicular direction, it's $F = \gamma^3 m_0 a$.

 

[Andrew Mason]

And in the 3-vector formalism, the notion of mass as "resistance to motion" doesn't work -- IIRC, $F = \gamma m_0 a$ only when the force is applied in the direction the object is moving. But when the force is applied in a perpendicular direction, it's $F = \gamma^3 m_0 a$.

But doesn't the difference between the force in the forward and perpendular directions have to do with length contraction being in the forward direction only?

AM

 

[clj4]

But doesn't the difference between the force in the forward and perpendular directions have to do with length contraction being in the forward direction only?

AM

No, it has to do with the unfortunate insistance of preserving the expression F=ma. The presence of $$\gamma^3$$ is due to the formulas of "transverse acceleration" vs "longitudinal acceleration" (see paragraph 10 of the Einstein 1905 paper). Here, the different powers of $$\gamma$$ have been tacked to the inertial mass, creating the "transverse" vs. "longitudinal" mass.