Understanding Rest Mass and Its Relation to Velocity in Special Relativity

[sydneybself]

The velocity of an object can, theoretically, only be measured relative to the velocity of another object. If I understand the concept of rest mass correctly, it is the mass of a particle with zero velocity; if my understanding is correct, what is 'zero velocity' relative to? Is it relative to the velocity of light?

Special relativity was developed because of the problem with zero velocity. I'm confused!

 

[ZapperZ]

The velocity of an object can, theoretically, only be measured relative to the velocity of another object. If I understand the concept of rest mass correctly, it is the mass of a particle with zero velocity; if my understanding is correct, what is 'zero velocity' relative to? Is it relative to the velocity of light?

Special relativity was developed because of the problem with zero velocity. I'm confused!

The rest mass is the mass of the object at rest on one's own reference frame. That's it. Zero velocity means that the object isn't moving in that frame.

With SR, there are ways to measure this and the "covariant" mass, even if the object is moving. That's what is done in high energy physics for the many exotic particles that are created in particle colliders.

BTW, SR was not developed because "... of the problem with zero velocity". You should read Einstein's biography and the problem classical electromagnetism had at that time with Galilean transformation.

Zz.

 

[PeterDonis]

If I understand the concept of rest mass correctly, it is the mass of a particle with zero velocity

Not quite. "Rest mass" is really a bad term; a better term (and the one that is more often used now by relativists) is "invariant mass". The invariant mass $m$ of an object is the length of its 4-momentum vector, which is the same in all reference frames (see below).

The reason for the term "rest mass" is that, if you happen to be at rest relative to the object, the energy you will measure that object to have is simply $m$ (note that I'm using units in which the speed of light is 1, as is common in relativity physics). But as you note, "rest" is a relative term; someone moving relative to the object would measure it to have a larger energy than $m$. But the invariant length of the object's 4-momentum will always be $m$; the general formula is $E^2 - \vec{p}^2 = m^2$, where $E$ is the object's energy and $\vec{p}$ is its momentum. As an object's velocity relative to you changes, the energy you measure it to have changes, but so does the momentum you measure it to have, and they change in such a way that the formula just given remains true. So $E$ and $\vec{p}$ together form a 4-vector called "4-momentum", whose invariant length is $m$.

 

[ghwellsjr]

The velocity of an object can, theoretically, only be measured relative to the velocity of another object. If I understand the concept of rest mass correctly, it is the mass of a particle with zero velocity; if my understanding is correct, what is 'zero velocity' relative to? Is it relative to the velocity of light?

Special relativity was developed because of the problem with zero velocity. I'm confused!

You seem to have no confusion with regard to the velocity of that other object being zero. Why don't you just concern yourself with its rest mass?

Then you could switch roles and consider the velocity of the other object with respect to the first object which will now be zero and your confusion will be gone, correct?

 

[Nugatory]

The velocity of an object can, theoretically, only be measured relative to the velocity of another object. If I understand the concept of rest mass correctly, it is the mass of a particle with zero velocity; if my understanding is correct, what is 'zero velocity' relative to? Is it relative to the velocity of light?

Special relativity was developed because of the problem with zero velocity. I'm confused!

Rest mass means the mass measured by an observer who is no moving relative to the object.

If you on the Earth measure the mass of an object sitting on a table in front of you, you're measuring the rest mass. If I in a spaceship zooming past you at many miles per second measure the mass of an object in the spaceship with me, I'm measuring its rest mass.

 

[Nugatory]

Hah - thirteen minutes of silence and then four answers land within a minute of one another
Maybe a hint as to how long it takes to compose an answer to this question?

 

[ghwellsjr]

Hah - thirteen minutes of silence and then four answers land within a minute of one another
Maybe a hint as to how long it takes to compose an answer to this question?

Maybe a hint as to how often we refresh the subforum site.

 

[PeterDonis]

Maybe a hint as to how long it takes to compose an answer to this question?

Well, if we're going to judge that way, obviously the fair comparison is number of characters per unit time. Which post wins by this criterion is left as an exercise for the reader.

 

[ghwellsjr]

I think what's really happening is that when each of us first sees the new post and some time has gone by with no response, we all compose our responses and they show up close in time. I doubt that all of us would have posted what we did if we first had seen another adequate post.

 

[Glurth]

obviously the fair comparison is number of characters per unit time

LOL, the reponse of a true physisist!