Interesting Question About Relativity and the Absolute

[Curious6]

According to special relativity, distances are relative, as people measuring distance from different reference frames come up with different measurements and are equal on footing as regards their results. However, my question is then: how can we even define a given length, for example, the Planck length to be 10^-33 cm, if it is also subject to special relativity and therefore not even an absolute reference? Also (this is more of a philosophical question), can length even be assigned as a quality of an object or is it just an illusion from our reference frame?

Thanks for your insights.

 

[Curious6]

Let me try to rephrase the question in a more meaningful way: if space is relative, then can we say quarks (or strings, or whatever the smallest constituent of the world is) don't have a length, as it all depends on the reference frame? This however leads me to ask the following: an object existing must have some sort of inherent length to it, or can it vary infinitely depending on the reference frame?

Please, someone help me out, I'm very confused!

 

[nwall]

"Proper length" is the term used for a body's invariant length. Although a body's length will change with respect to an observer, it does have a proper length, and that is a body's length with respect to itself, or its length when at rest.

For example, if you lay down on a spaceship going at 90% the speed of light, you'll look squished up to us because your relative height will be smaller than it was when you were on Earth. But you won't look squished up to yourself. You'll still be able to measure your proper height and you'll measure the same height for yourself on the spaceship as you'll measure on Earth or anywhere (with the exception of extreme gravitational fields that may even distort your point of view).

 

[Garth]

For consistency the Planck length has to be that measured in the rest frame.

Garth

 

[Mortimer]

"Proper length" is the term used for a body's invariant length.

...and is in fact the pythagorean sum of measured spatial length: $$l_{spatial}=\frac{l_{proper}}{\gamma}$$
and $c$ times the velocity-induced non-simultaneity ("time-length"): $$l_{time}=c\frac{\gamma vl_{spatial}}{c^2}=\frac{vl_{proper}}{c}$$

or: $$\sqrt{\left(\frac{l_{proper}}{\gamma}\right)^2+\left(\frac{vl_{proper}}{c}\right)^2}=l_{proper}$$

($\gamma=1/\sqrt{1-v^2/c^2}$ as usual)

 

[Curious6]

OK, thanks for clearing up this doubt. It was this concept of 'proper length' I was doubting about.