# System with $N$ atoms

Suppose a system (eg: rocket) consists of $$N$$ atoms. It starts moving away from the origin of an inertial frame at speed 0.9c. Will $$N$$ changes and if it changes where does this change come (if increases) or goes (if decreases)?

Update: Let's suppose there is no fuel in the rocket and it attains this speed through a sequence (can be a large number) of gravitational slingshots, and the mass 𝑚0 we are talking about is calculated after receiving the first slingshot

Follow-up Question: Since $$N$$ will not change and Total Mass = Sum(mass of all atoms in the system), and according to the equation

$$m = \frac{m_0}{\sqrt{1-\frac{v^2}{c^2}}}$$there is △m increase in Total mass. I want to understand how does this △m came into the system, does the particle mass increase or something else

A rocket uses fuel to move so the fuel particles escape the system; if you roughly know $$\Delta m$$ and the mass of the fuel particles you can estimate the number of particles that have escaped the rocket. Particle number is Lorentz-invariant so the particles composing the rocket will remain the same in any inertial reference frame.

If the rocket isn't propelled by fuel nor by any $$\Delta m$$ the number of particles composing the rocket stays the same.

The relativistic mass $$m=\gamma m_0$$ originating from relativistic speed is not the "real mass" of the system, thus is not associated to particle number. Instead the particle number is associated with the rest mass $$m_0$$ which is conserved and frame-invariant.

• Let's suppose there is no fuel in the rocket and it attains this speed through a sequence (can be a large number) of gravitational slingshots, and the mass 𝑚0 we are talking about is calculated after receiving the first slingshot Sep 17, 2021 at 9:58
• @ancadancad In that case there is no change in $N$. Sep 17, 2021 at 9:58
• I agree with @Steeven, since particle number is invariant Sep 17, 2021 at 10:00
• I totally agree with particle number being invariant, but could you explain the comment of this answer physics.stackexchange.com/a/666534/314115 Sep 17, 2021 at 10:04
• @ancadancad The concept of "relativistic mass", while not "wrong" as such, is not considered useful and hasn't been for a long time. See this thread for the details. Sep 17, 2021 at 12:37

No there will not be any change. Particle number is Lorentz invariant i.e. the number of Atoms that make up a particular object is the same no matter from which frame of reference you measure it.

• But a rocket uses fuel to move so the fuel particles escape the system Sep 17, 2021 at 9:41