# What happens to the shape of an accelerating mass

## Main Question or Discussion Point

Hi:

When a mass is accelerated, what happens to its length and volume? I know that when the acceleration ends, its length is governed by the equation l = l0 x sqrt (1 - v^2/C^2), but what about during the acceleration?

Related Special and General Relativity News on Phys.org
bcrowell
Staff Emeritus
Gold Member
Time dilation and length contraction only depend on velocity, not acceleration. Some people call this the "clock postulate" for time dilation.

HallsofIvy
Homework Helper
The "shape" at any instant during acceleration is given by the velocity of the object at that instant.

Thanks guys. Taking the case of a neutron moving with velocity v, would its radius in the direction of v shorten while its radius perpendicular to v increases? It seems if this is so, then the neutron would assume an ellipsoid shape, more specifically an oblate spheroid shape, until it would become a disk at some point. Is this correct?

bcrowell
Staff Emeritus
Gold Member
Thanks guys. Taking the case of a neutron moving with velocity v, would its radius in the direction of v shorten while its radius perpendicular to v increases? It seems if this is so, then the neutron would assume an ellipsoid shape, more specifically an oblate spheroid shape, until it would become a disk at some point. Is this correct?
The radius perpendicular to the direction of motion is unchanged.

PAllen
2019 Award
Yes, such appearance as a disk has been dubbed a 'pancake', and, I believe Richard Feynman was the first to describe that the collision data for energetic electrons and nucleons could be explained on the assumption that the nucleon appeared as a pancake to the electron. This modelling assumption was part of his famous parton research which explained key behavior of the quark model of nucleons. Without modelling the nucleon as a pancake, the collision data could not be explained.

Last edited:
The radius perpendicular to the direction of motion is unchanged.
Thanks Ben. How then does the mass increase without the perpendicular radius increasing? I am assuming the neutron is the most dense unit of mass possible.

Yes, such appearance as a disk has been dubbed a 'pancake', and, I believe Richard Feynman was the first to describe that the collision data for energetic electrons and nucleons could be explained on the assumption that the nucleon appeared as a pancake to the electron. This modelling assumption was part of his famous parton research which explained key behavior of the quark model of nucleons. Without modelling the nucleon as a pancake, the collision data could not be explained.
That is extremely interesting to me, but I am not surprised by it. My own thoughts have led me to this conclusion (that of pancaking mass) which would max out at C

bcrowell
Staff Emeritus
Gold Member
Thanks Ben. How then does the mass increase without the perpendicular radius increasing?
Most physicists these days don't use the relativistic mass convention that you're using, but anyway, the density of mass-energy is higher as seen in the frame where the neutron is moving.

I am assuming the neutron is the most dense unit of mass possible.
No, that's not true.

Hi Ben. Tks for replying. Is the mass expansion and length contraction real then. I thought it was, from the observer's viewpoint. And what is more dense than a neutron?

PAllen