# Density Increasing

Gold Member
When an object moves by you, I know that its density is supposed to increase (at least that's what I was told by my physics teacher); however, I don't understand why. I understand why the density is greater in a moving reference frame relative to an observer at rest, but why does it continue to increase as it moves by you?

Thanks.

Your physics teacher is probably thinking that if a box of mass M and dimension x by y by z travelling in the z direction has its z dimension reduced by the Lorentz contraction. So the volume of the box has apparently shrunk. But mass is conserved.

Gold Member
I don't quite follow. I understand that the observer at rest would see the length of the box contract in its direction of motion, and that, assuming work was done on the box, the mass of the box appears to increase as well. However, I do not understand how the density continues to increase as the box approaches the observer.

Dale
Mentor
2021 Award
If it approaches inertially then the density will be constant (but higher than the density in the rest frame).

Gold Member
That's what I thought. Perhaps that's what my teacher meant by density increasing as the block passes by you. Thanks.

George Jones
Staff Emeritus
Gold Member
As others have said, the mass-energy density rho' in the observer's frame is constant (if velocity is constant) and greater than the density rho as measured in a frame in which the stuff is at rest.

For completeness, I'll make things a bit quantitative, even though jgens does not need an answer at this level.

The two densities differ by two factors of gamma = 1/sqrt(1 - V^2 / c^2), roughly, one for Lorentz contraction and one for the transformation of energy between the two frames. Consequently,

rho' = rho/(1 - v^2 / c^2).

A more sophisticated way to look at it is that density is the zero-zero component of the stress-energy tensor, and there is a factor of gamma for each of the two indices.