# Mass increasing with energy

The first of my two questions concerns the aspect of SR that deals with the mass of an object increasing as is moves faster and faster (or more appropriately, as the energy gets larger and larger). I'm a novice when it comes to higher level physics, and everything I know comes from reading books on it because I'm only in classical physics classes at the moment, so if I'm overlooking some critical aspect of the theory, please forgive me.

As the energy of a moving object increases due to velocity, according to SR, it's mass would increase with it's velocity as well. This was supposedly the factor that proved that according to SR, faster than light travel is impossible because at the speed of light, the relativistic mass of the moving object would be infinite, thereby making it's energy content infinite as well. But what I don't understand is that, relativistic mass increase, as I understand it, is something that a stationary observer would witness, not the object in motion itself. Much like time dilation is not felt by the object in motion, but witnessed by the stationary or uniformly moving onlooker. So how would this mass increase influence how much energy it takes to move the object in motion when the increase in mass is not felt by the object in motion, just witnessed by someone in a stationary reference frame? It's sort of like saying that, because I'm stationary and I observe your time to be stopped due to your traveling at the speed of light, you aren't able to set the alarm clock on your spaceship because I don't view you to be moving. I hope I got my question across effectively.

## Answers and Replies

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Swiss Army said:
As the energy of a moving object increases due to velocity, according to SR, it's mass would increase with it's velocity as well.
There have been many discussions on this topic in this forum so if you're not satisfied with the responses to your question in this thread then you can go through the others for more information etc.

The mass of which you speak is called the "inertial" mass or "relativistic mass". I'll refer to it simply as "mass." You can think of it as the ratio of the magnitude of a particle's momentum to the particle's speed. I.e. it is m in p = mv. To be precise - mass is defined such that mv is a conserved quantity. Force is then defined as F = dp/dt. These quantities involve both distance and time. Since time is dilated and lenght is contracted then this gives a value of m which depends on speed. The exact details are at

http://www.geocities.com/physics_world/sr/inertial_mass.htm

But what I don't understand is that, relativistic mass increase, as I understand it, is something that a stationary observer would witness, not the object in motion itself. Much like time dilation is not felt by the object in motion, but witnessed by the stationary or uniformly moving onlooker. So how would this mass increase influence how much energy it takes to move the object in motion when the increase in mass is not felt by the object in motion, just witnessed by someone in a stationary reference frame? It's sort of like saying that, because I'm stationary and I observe your time to be stopped due to your traveling at the speed of light, you aren't able to set the alarm clock on your spaceship because I don't view you to be moving. I hope I got my question across effectively.
When you consider the fact that mass is define through velocity such that mv is conserved then it follows that the m must be a function of speed. So you can say that mass increase is a result of length contraction and time dilation. Ask yourself how each observer measures the mass and then ask yourself how these observations are related. For instance - the relativistic mass is related to the ratio of the transverse component of force to the tranverse component of acceleration. If you understand how the force transforms and how the acceleration transforms then you should be able to understand how the ratio transforms and why that ratio is a function of speed - its all directly related to measurements of both distance and time.

JJ
Can someone explain this quote from Einstein? I can't yet understand why relativistic momentum is more correct than relativistic mass.

"It is not good to introduce the concept of the mass of a moving body M=gm for which no clear definition can be given. It is better to introduce no other mass concept 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."

hmmm...

I saw that quote from Einstein the other day and was wondering sort of the same thing.

JJ said:
Can someone explain this quote from Einstein? I can't yet understand why relativistic momentum is more correct than relativistic mass.

"It is not good to introduce the concept of the mass of a moving body M=gm for which no clear definition can be given. It is better to introduce no other mass concept 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."
Nope. I can't exlain it since only Einstein knows why he said it. But this does not mean that Einstein did not like the concept of relativistic mass. He said that he doesn't like a velocity dependant mass. Those are not the same thing. Einstein did use relativistic mass in his work many times. Relativistic mass is defined as the ratio of momentum to speed. This gives a mass to light and a mass for slowly moving bodies which depends on the gravitationl potential - neither of which depend on a variable speed other than the "c" in m = p/c.

JJ said:
Can someone explain this quote from Einstein? I can't yet understand why relativistic momentum is more correct than relativistic mass.

"It is not good to introduce the concept of the mass of a moving body M=gm for which no clear definition can be given. It is better to introduce no other mass concept 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."
His point is that mass should not be thought of as a relativistic variable. People want to say it is by manipulating the form of the relativistic 3-momentum, but that leads to erroneous interpretations of the physics at work (i.e. that mass must change with velocity).

He clearly mentions momentum and energy in the same breath for a reason. Together they give you a way to calculate the (rest) mass, which is the magnitude of the 4-momentum (E,px,py,pz). Don't discard his mention of energy.

So, to answer your question. He's not trying to be vague: he is saying "Don't talk about relativistic mass, because there ain't such a thing!"

DW
Swiss Army said:
I saw that quote from Einstein the other day and was wondering sort of the same thing.
He is saying exacly what it sounds like he is saying. Mass as was using the term and as modern relativity uses it does not change with speed. For more info read chapter 3 at
http://www.geocities.com/zcphysicsms/chap3.htm