# I Stretching a rubber band increase its mass but how?

1. Nov 27, 2016

### Patrick Pihl

Stretching a rubber band increase its mass due to e=mcc, but how?

2. Nov 27, 2016

### PeroK

What do you think is the definition of the mass of an object?

3. Nov 27, 2016

### Patrick Pihl

Number and kind of particles in the object?

4. Nov 27, 2016

### PeroK

A better example than the rubber band is the hydrogen atom: one proton and one electron. The mass of the atom, however, is less than the mass of the proton plus the mass of the electron. The difference is the binding energy released when the atom is formed. The same energy is required to ionise the atom by separating the two particles.

From this, you can see that the mass of a collection of particles is not simply the sum of the masses of each individual particle.

5. Nov 27, 2016

### Orodruin

Staff Emeritus
This is not correct. The classical definition of the (inertial) mass is related to an objects resistance to acceleration. In relativity, it is related to the energy content of an object in its rest frame. It then turns out that this also is the inertia of the object, which is one of the great insights from special relativity!

6. Nov 27, 2016

### Mister T

When you transfer energy to the rubber band to stretch it, you increase its energy. If the energy increases by $E$ the mass increases by $E/c^2$. You correcty noticed that stating this doesn't explain how it happens.

To understand how it happens you need to understand what mass is. It's not a measure of the quantity of matter, it's a measure of the rest energy. Stretching the rubber band increases the rest energy. It turns out that in this case $E/c^2$, the amount it increases by, is very very small compared to the rubber band's mass. So small in fact that the most precise measuring devices cannot detect it. Ignoring it is therefore justified when measuring the mass, so that is the approximation people use.

But just because the approximation is valid doesn't mean it constitutes a valid way of defining mass. There are plenty of other examples where the opposite is true. That is, the contribution to the mass is very very large compared to the mass of the object. Perhaps the most famous example is the atomic nucleus.

7. Nov 28, 2016

### Patrick Pihl

Thank you all! That gives me a slightly better understanding :)
I should have thought about that myself when knowing that mass also increase with speed.

8. Nov 28, 2016

### Orodruin

Staff Emeritus
It does not. What is called "relativistic mass" is an antiquated concept. See my PF Insight on relativisic mass (link in my signature). When we talk about mass today we talk about the invariant mass of a system.

9. Nov 28, 2016

### Staff: Mentor

It's not just a matter of "today." Even forty years ago when I was a grad student in experimental elementary particle physics, everyone that I worked with used "mass" to mean "invariant mass" a.k.a. "rest mass."

10. Nov 28, 2016

### Mister T

That's an increase in relativistic mass. We're talking instead about an increase in mass.

You can't increase the mass just by increasing the speed. This confusion is best remedied by never introducing relativistic mass.

11. Nov 28, 2016

### DrStupid

Too late - unless you have a time machine.

12. Nov 28, 2016

### Ibix

I do. It turns out relativistic mass is imaginary.

For anyone not getting the joke: it turns out that travelling faster than light allows time travel (unless you restrict the allowable velocities somewhat). But anything with a real rest mass travelling at v>c would have an imaginary relativistic mass.

13. Nov 28, 2016

### Staff: Mentor

And if anyone is curious about how faster than light implies time travel.... Google for "tachyonic anti-telephone" and (more seriously) for "closed time-like curve".

Of course, and kidding aside, the correct conclusions are not that time travel might be possible or that objects might have imaginary masses, but rather that equations derived under assumptions that are equivalent to "no FTL travel" cannot be used to predict what would happen if FTL were possible.