- What we mean by length---a spatial separation
measured at once instant in time---means that
length is
reference frame dependent
if simultaneity is---which it is
by the time dilation effect
(time flow rate variation effect)
of special relativity.
- The length dependence on
reference frame is called
the FitzGerald contraction
after its sort-of discoverer
Irish
physicist
George Francis FitzGerald (1851--1901).
FitzGerald is only
a sort-of discoverer because though
he had the idea of a contraction in the direction of motion
and the FitzGerald contraction formula,
he did
**NOT**have a consistent theory of all related effects---the consistent theory is, of course, special relativity itself (see Wikipedia: George Francis FitzGerald: Length contraction). - The length of an object
in its own rest frame
is its proper length.
Proper length is an intrinsic property of an object unlike length in general that depends both on proper length and reference frame of length measurement.

- The formula for the
FitzGerald contraction is
### L = L_0*sqrt[1 - (v/c)**2] ,

where L is measured length along the direction of motion, L_0 is proper length, and v is the velocity of motion.If v = 0, L = L_0. If v = c, L = 0.

- To illustrate the
FitzGerald contraction,
say a pole vaulter
runs along with his/her pole level
and passes through a shed open at both ends.
The pole's proper length is greater than the length of the shed.

But the pole vaulter runs very fast and in a ground-frame observer's observation the pole is contracted to be less than the shed proper length and the whole pole is inside the shed for some time interval.

The pole vaulter's frame perspective is that the shed was contracted.

Yes, the ends of the pole were inside the shed, but

**NOT**at the same time in his/her reference frame. - Yours truly does
**NOT**think that FitzGerald contraction has ever been verified for a macroscopic-scale object in the lab. No one ever mentions such a verification. It seems a very hard thing to do.However, many results depend on the FitzGerald contraction, and so it has been indirectly verified endlessly.

Also it's a basic result of special relativity, and so all of special relativity depends on it.

Caption: *Pole Vault*.

Does this pole vaulter feel his FitzGerald contraction during his approach?

Explanation of the FitzGerald contraction:

Image link: Wikipedia: File:Salto con l Asta.jpg.

Local file: local link: pole_vault_fitzgerald_contraction.html.

File: Relativity file: pole_vault_fitzgerald_contraction.html.