Understanding Mass in Relativity: Misconceptions and Explanations

[Naty1]

Dalespam posted in another thread (as have others in other threads) responding to a comment:

but since as speed increases so does mass

.

No, it doesn't, energy increases

I still find that very confusing unless this is simply a modern convention.

In SIX EASY PIECES for example (copyright 1997) pages 87 to 91 Richard Feynman seems to say repeatedly mass DOES increase with speed. For example:

The mass of the object which is formed when two equal objects collide must be twice the mass of the objects which come together...the masses have been enchanced over the masses they would have been if standing still...the mass they form must be greater than the rest masses of the objects even though the objects are at rest after the collision!

and separately:

when we put energy into the gas molecules move faster and so the gas gets heavier...kinetic energy does not affect the mass according to Newton's laws...but there is no place in relativity for strictly inelastic collisions...conservation of energy must go along with conservation of momentum in the theory of relativty...because of the kinetic energy involved in the collision, the resulting object will be heavier, therefore it will be a different object...

Explanations appreciated.

 

[N721YG]

Rest mass + energy needed for relativistic speed = relativistic mass.
Relativistic mass is only observed from outside the inertial frame.
All non accelerating frames are at rest so maybe relativistic mass is an illusion.
Next - Someone that knows what they are talking about.

 

[DrGreg]

I refer the honourable gentleman to the answer I gave a few threads ago:

I think it's necessary to remind some participants that there is more than one definition of "mass" in relativity.

- invariant mass, or rest mass, or proper mass, which excludes the kinetic energy of the object's centre of momentum
- relativistic mass, sometimes called inertial mass, which includes the kinetic energy of the object's centre of momentum.

Be sure you know which sort of mass is being talked about.

Most modern physicists use "mass" to mean "invariant mass" but some people use "mass" to mean "relativistic mass".

Photons have zero invariant mass, but non-zero relativistic mass. The quoted Wikipedia article on the photon refers only to invariant mass, which is described simply as "mass", consistent with modern usage.

Whichever definition you choose, mass is a form of energy, like other forms such as kinetic energy, potential energy, heat energy, sound energy, etc. So mass doesn't get converted into energy, but it can be transformed from mass-energy to some other form of energy. The total energy from all sources (as measured by a single observer) remains constant.

The problem is that not everybody agrees which convention to use. Feynman was referring to relativistic mass, but many users in this forum insist on following the modern convention of referring to invariant mass a.k.a. rest mass. It's the one I prefer myself, but both conventions are valid, as long as you know which one the author is using. The confusion arises when two thread-posters are using different conventions and maybe not realising it.

 

[Naty1]

Relativistic mass is only observed from outside the inertial frame.
All non accelerating frames are at rest so maybe relativistic mass is an illusion.

I don't like that explanation (much) because KE and relativistic mass vary by the same Lorentz transformation amount ...so for anyone to explain relativistic mass increase is less real than KE energy increase due to inertial observation frame makes no sense to me.

 

[Naty1]

DrGreg...thanks for your input...I DID see that earlier post and forgot about it...if that's the convention generally used, that's just peachy by me...(If you just tell me the same thing a few more times I might even remember it!)

Until I was just rereading Feynmann's book this morning I had also forgotten how blatently he describes KE and relativistic mass being "one"...when he says because the resulting object of a collision is heavier due to energy content, "it will be a different object" lights went off...

His writing is just great!

 

[hartlw]

So let's say we have two isolated particles and an arbitrary reference frame (I don't see how in this case you could define an Inertial Reference Frame). Can you write equations of motion?

 

[jtbell]

In a similar vein to Dr. Greg, I offer this post and this one, which I've written previously on this subject.

 

[N721YG]

I don't like that explanation (much) because KE and relativistic mass vary by the same Lorentz transformation amount ...so for anyone to explain relativistic mass increase is less real than KE energy increase due to inertial observation frame makes no sense to me.

I said "Relativistic mass is only observed from outside the inertial frame.
All non accelerating frames are at rest so maybe relativistic mass is an illusion."

DrGreg said "...but many users in this forum insist on following the modern convention of referring to invariant mass a.k.a. rest mass. It's the one I prefer myself,..."

I am in no way in DrGreq's league but it sounds like we are saying something similar. It seems that maybe KE should be ignored (until impact) unless there is an ether to compare speed to.

 

[Dale]

I still find that very confusing unless this is simply a modern convention.

It is simply the modern convention. Unfortunately there is a lot of historical work out there that uses "relativistic mass" either explicitly or implicitly.

The reason the modern convention is used is because of the four-momentum. Relativistic mass is the timelike component of the four-momentum, which is also (and more commonly) known as energy. Invariant mass is the norm of the four momentum, which does not have another common name. So just from a communication standpoint it makes more sense to use the word "mass" to refer to the norm and "energy" to refer to the timelike component.

Secondly, even though laypeople and pop-science books tend to use relativistic mass it is a source of confusion. Mass is generally thought to be a property of an object rather than an observer, so the idea that motion increases mass leads to a feeling that motion is still absolute. Also, since mass is usually thought to be a property of an object it does not make sense that it could have multiple different values at the same time as relativistic mass does.

IMO (and in the opinion of the modern physics community) there is no reason to use "relativistic mass" instead of energy. E.g. "An object cannot accelerate to the speed of light because it would have infinite energy" works just as well as "An object cannot accelerate to the speed of light because it would have infinite (relativistic) mass"

However, in the end it is just a convention, as is the use of any word.

 

[N721YG]

So let's say we have two isolated particles and an arbitrary reference frame (I don't see how in this case you could define an Inertial Reference Frame). Can you write equations of motion?

Wouldn't their motion relative to each other define the inertial frame?