Straight line through spacetime.

[stevmg]

Not quite, this is the resultant of doing the Taylor expansion of the correct formula:
E=\frac{m_0c^2}{\sqrt{1-(v/c)^2}}.
Like any Taylor expansion, it is valid only for \frac{v}{c}<<1.
It is not valid at large speeds.

So we are clear in future reference:

m₀ is "rest mass"

m(v) = m₀/SQRT[1 - (v/c)²] You have stated before andI have read that the term "relativistic mass" is in disfavor. It is not "inertial mass" is it?

My only references are AP French and you follks. I have no other sources here.

 

[starthaus]

So we are clear in future reference:

m₀ is "rest mass"

m(v) = \frac{m_0c^2}{\sqrt{1-(v/c)^2}} is called what?

relativistic mass.

You have stated before and I have read that the term "relativistic mass" is in disfavor.

correct

It is not "inertial mass" is it?

nope.

 

[stevmg]

So, what is it? What's it called? Does it have a new name? I haven't found one in the few books that I have.

 

[starthaus]

So, what is it? What's it called? Does it have a new name?

It still has the old name but we prefer not to call it by it.

 

[DrGreg]

Just to get this clear

E = \frac{m_0 c^2}{\sqrt{1-v^2/c^2}}​

is the energy of a particle. This is the same E that appears in

E^2 = (m_0 c^2)^2 + (pc)^2​

and it's also equal to rest energy (m₀c²) plus kinetic energy. If v/c is very small, the kinetic energy approximates to ½m₀v².

If you want to give the quantity

M = \frac{m_0}{\sqrt{1-v^2/c^2}}​

a name, you can call it "relativistic mass", but the modern preference is not to use M at all but to use E instead. (The two are related by E = Mc² and so are "almost the same thing".)

 

[DrGreg]

It is also worth mentioning that the modern physicists who don't use relativistic mass will refer to rest mass (=invariant mass) as just "mass".

Old timers who do use relativistic mass will refer to relativistic mass as just "mass".

Hardly anyone uses the term "relativistic mass" except in discussions like this comparing alternative definitions. So when an author refers to "mass" (without qualifying it as "rest ..." or "relativistic ..." etc) you will need to work out which of the two camps they fall into. It's unfortunate, but there are no Physics Police enforcing the use of one term or the other.

 

[Passionflower]

Old timers who do use relativistic mass will refer to relativistic mass as just "mass".

Indeed, together with their endlessly annoying claim that if one uses an infinite amount of energy to accelerate an object with mass it will actually travels at c.

 

[starthaus]

Indeed, together with their endlessly annoying claim that if one uses an infinite amount of energy to accelerate an object with mass it will actually travels at c.

Riight :-)

 

[stevmg]

Just to get this clear

E = \frac{m_0 c^2}{\sqrt{1-v^2/c^2}}​

is the energy of a particle. This is the same E that appears in

E^2 = (m_0 c^2)^2 + (pc)^2​

and it's also equal to rest energy (m₀c²) plus kinetic energy. If v/c is very small, the kinetic energy approximates to ½m₀v².

If you want to give the quantity

M = \frac{m_0}{\sqrt{1-v^2/c^2}}​

a name, you can call it "relativistic mass", but the modern preference is not to use M at all but to use E instead. (The two are related by E = Mc² and so are "almost the same thing".)

It is also worth mentioning that the modern physicists who don't use relativistic mass will refer to rest mass (=invariant mass) as just "mass".

Old timers who do use relativistic mass will refer to relativistic mass as just "mass".

Hardly anyone uses the term "relativistic mass" except in discussions like this comparing alternative definitions. So when an author refers to "mass" (without qualifying it as "rest ..." or "relativistic ..." etc) you will need to work out which of the two camps they fall into. It's unfortunate, but there are no Physics Police enforcing the use of one term or the other.

Indeed, together with their endlessly annoying claim that if one uses an infinite amount of energy to accelerate an object with mass it will actually travels at c.

Riight :-)

Hardly anyone uses the term "relativistic mass" except in discussions like this comparing alternative definitions. So when an author refers to "mass" (without qualifying it as "rest ..." or "relativistic ..." etc) you will need to work out which of the two camps they fall into. It's unfortunate, but there are no Physics Police enforcing the use of one term or the other.

Ha! Ha! Now that is clear... Seems like my original question as to the definition of "mass" or "relativistic mass" was a legitimate one as there is no consistency and no "Physics Police" to enforce one.

It is also clear as to why one cannot use the induction method of proving the momentum-energy equations for a system of particles. To wit,

E² - (cp)² = E₀² would be true for one particle. If you were to have two particles of the same mass but going in opposite directions at v treating the combination of the two particles as a "system" would yield a total momentum of 0 and thus (cp)² would be zero in that equation as if the velocity were zero. But, in actuality, the velocity of these particles is not zero and an erroneous answer would result.

I will have to go through Space-Time Physics as suggested by starthaus to see if I can wrap my brain aound this. No more comments from me until I have done so and that may take a very long time.

Until later.