# Relativistic Mass

#### Charlie G

I have just recently began to understand relativity, right now I get time dilation and lenght contraction but I do not get relativistic mass. The book I am reading does not defy it very well (or perhaps I should read the chapter again) but it gave it as the explanation of why objects with mass cannot reach the speed of light. The book says that as the object increases its speed its mass increases making it require more energy to speed up, ultimatly ending in it requiring an infinite amount of energy to raise its speed.

As of now I only have a ninth grade education and according to it mass cannot be created or destroyed, however the book implies that mass is being created. I thought it may be an illusion, but the book claims relativistic effects are real and arent illusions. Right now the best explanation I can think of is the kinetic energy of the moving object is being converted into mass at such high speeds(giving rise to high energies required for mass conversion).

Related Special and General Relativity News on Phys.org

#### feynmann

I have just recently began to understand relativity, right now I get time dilation and lenght contraction but I do not get relativistic mass. The book I am reading does not defy it very well (or perhaps I should read the chapter again) but it gave it as the explanation of why objects with mass cannot reach the speed of light. The book says that as the object increases its speed its mass increases making it require more energy to speed up, ultimatly ending in it requiring an infinite amount of energy to raise its speed..
If one spaceship move to the right at half the speed of light and another space-ship move to the left at half the speed of light. Now what's the speed of space ship relative to each other? The relative speed must be lower than the speed of light. Does this have anything to do with the mass of space-ship? If not, then the mass is Not the reason that speed can not exceed the speed of light.

Last edited:

#### Fredrik

Staff Emeritus
Gold Member
First of all, the concept of relativistic mass isn't used much by physicists. It's a pretty useless concept actually. It can be defined as $E/c^2$ where E is the energy of the particle, so the relativistic mass is just the energy expressed in different units.

For a massive particle, you can also define it as $\gamma m$, where m is the (rest) mass. Then you can prove that $E=\gamma mc^2$.

#### Charlie G

Oh, I think I get it now, so the relativistic mass is essentially the objects kinetic energy, expresses in units of mass using the energy-mass equivalence equation, added to its rest mass?

#### JesseM

Oh, I think I get it now, so the relativistic mass is essentially the objects kinetic energy, expresses in units of mass using the energy-mass equivalence equation, added to its rest mass?
Yes, kinetic energy is $$(\gamma - 1)mc^2$$, so if you divide that by c^2 to convert it to units of mass, and then add the rest mass m, you get $$(\gamma - 1)m + m = \gamma m$$ which is the "relativistic mass".

#### Charlie G

Great, thx for the help:)

#### feynmann

Oh, I think I get it now, so the relativistic mass is essentially the objects kinetic energy, expresses in units of mass using the energy-mass equivalence equation, added to its rest mass?
That's not exactly true. The pressure also contribute to inertial mass. So it is harder to accelerate a box filled with gas than a solid object

#### JesseM

That's not exactly true. The pressure also contribute to inertial mass. So it is harder to accelerate a box filled with gas than a solid object
Pressure is not really a separate term though, it'd be included in the rest-mass energy of any bound system composed of multiple particles, like a box filled with gas (it should be some combination of internal kinetic and potential energies). The rest mass of a composite bound system is not just the sum of the rest masses of all the particles that make it up.

Last edited:

#### bernhard.rothenstein

I have just recently began to understand relativity, right now I get time dilation and lenght contraction but I do not get relativistic mass. The book I am reading does not defy it very well (or perhaps I should read the chapter again) but it gave it as the explanation of why objects with mass cannot reach the speed of light. The book says that as the object increases its speed its mass increases making it require more energy to speed up, ultimatly ending in it requiring an infinite amount of energy to raise its speed.

As of now I only have a ninth grade education and according to it mass cannot be created or destroyed, however the book implies that mass is being created. I thought it may be an illusion, but the book claims relativistic effects are real and arent illusions. Right now the best explanation I can think of is the kinetic energy of the moving object is being converted into mass at such high speeds(giving rise to high energies required for mass conversion).

Different textbooks and papers give different names to the same physical quantity. I quote for you from Hans C. Ohanian Special relativity a typical approach.
The relativistic momentum is sometimes written as
p=m(V)V
where m(V) is a "velocity-dependent-mass" defined as
m(V)=m/sqr(1-VV/cc).
In contrast the ordynary mass m that appears in the right side is called rest mass.
Other textbooks call velocity dependent mass, relativistic mass, telling that a relativistic mass as well as a nonrelativistic mass characterize the inertia of a point mass, the only difference being that in the relativistic case the inertia of the point mass depends on velocity, while in the nonrelativistic case, this dependence can be neglected. A.N Matveev "Mechanics and Theory of Relativity".
Some physicits consider that the use of the concept of relativistic mass does more harm than good, avoiding it. Others defend it.
I think that when we speak about a physical quantyity the best thing is to define the way in which we measure it. One possible way to measure the relativistic mass is to consider the circular motion of a charged particle in a magnetic field
rqB/V=[m/sqr(1-VV/cc]
where r is the radius of the circle, q the eletric charge of the particle B the magnetic field
(Ohanian p.145) and to find names for m and for m/sqr(1-VV/cc). I think that there is a little chance that large communities of physicists will accept the names given,

#### rcgldr

Homework Helper
Aren't relativistic mass effect considered responsible for the varying mearsured values for G the gravitaional constant? Is the stuff at the web site below just conjector or generally accepted? Does this imply that there is an absolute velocity (at least with respect to the center of the universe)?

Last edited by a moderator:

#### clem

Ohanion oversimplifies to reach a large UG audience. He has become quite wealthy, but cannot be used as an authority for relativity. Use a graduate text for that. "Large communities" disagree on many things, but it is a confused minority that uses "relativistic mass".

#### bernhard.rothenstein

Ohanion oversimplifies to reach a large UG audience. He has become quite wealthy, but cannot be used as an authority for relativity. Use a graduate text for that. "Large communities" disagree on many things, but it is a confused minority that uses "relativistic mass".

#### jtbell

Mentor

To the person who started this thread: you've inadvertently stepped into a can of worms (or stirred up a hornets' nest, or something like that) by bringing up "relativistic mass." See this post for an attempt to explain what I mean by this.

Last edited:

### Physics Forums Values

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving