Questions of Length, Distance, Direction, and Relativeness

[E-motion]

Questions of Length, Distance, Direction, and Relativeness

 

Webster's New Twentieth Century dictionary defines the word dimension many ways. I use the definition below as a reference for two reasons, it's specific to Physics and it's consistent with the origin of the word.

 

dimension n. [OFr. dimension; L. dimensio, a measuring, from dimensus, pp. of dimetiri, to measure off; dis-, off, from, and metiri, to measure.]

7. In physics, a fundamental quantity, as mass, length, or time, in terms of which all other physical quantities, as those of area, velocity, power, etc. are measured;

 

The SI unit of Length is the Meter. The Meter is the basic unit of Length in the metric system, equal to 39.37 inches: it was meant to be and virtually is, one-ten-millionth part of the distance along a meridian from the equator to the pole. Today, it's still virtually equal to 39.37 inches but is more precisely defined as a specific number of wavelengths of radiation emitted from a particular element. A wavelength being the distance between corresponding points of two successive waves.

What does Length, as a "fundamental quantity," quantify? I would say that it quantifies whatever the Meter, or any other of its units of measurements, measures: the distance between two relative points of reference. Simply put, distance is quantified between things (length) and between the ends (length), sides (width), and/or tops and bottoms (heigth) of things. Is there a difference between (l), (w), and (h) other than relative direction?

Length is relative because the entire quantifying process is relative. All the units of measurement were derived from and are the distance's between two arbitrary and relative points of reference (even the length of the human foot is the distance between toe and heel), and any distance actually measured is dependent on first estabishing two relative points of reference in order to measure the distance between.

Is distance itself relative? If so,to what? Where does distance end?

[Tom Mattson]

Length is relative because the entire quantifying process is relative.

 

No' date=' it isn't. The relativity of length has nothing to do with the fact that lengths are defined between two points of reference. It comes from the metrical structure of the spacetime we inhabit. If the metric of Galilean relativity were descriptive of our actual universe, then lengths would not be relative, despite the fact that reference points define lengths.

 

Is distance itself relative?

 

That depends on what you mean by "distance". If you mean a spatial "distance" between two points, then yes it is. If you mean "distance" in the more general sense (eg: that which is given by a metric in a metric space), then no it isn't.

[wormholeman]

I will try to answer your question. Distance relative; distance is a measurement, if there are two distances, then it can be relative I would think, because it can be compared. Distance simply ends at the point where the observer stops measuring.

[brokenbin]

Distance is NOT relative. Distance is just a simple measurement, a quantity. In order to be considered relative, distance should be able to be described by the space-time diagrams. http://www.astro.ucla.edu/~wright/st_diags.htm When distance is connected with another quantity, time, then it is considered relative. But just by itself, it cannot be relative.

[wormholeman]

Like this?

[Tom Mattson]

Distance is NOT relative. Distance is just a simple measurement' date=' a quantity.

[/quote']

 

As I was saying before, that depends on what you mean by "distance". If you mean "spatial interval" then it is relative. If you mean, "spacetime interval" then it is not.

 

In order to be considered relative, distance should be able to be described by the space-time diagrams. http://www.astro.ucla.edu/~wright/st_diags.htm

 

You can describe distances in that way. Consider the distance between the two ends of a rod of length L that is moving with speed v along the positive x-axis in some frame S, and let frame S' be the rest frame of the rod.

 

Let Event 1 be the measurement of the x-coordinate x₁ of the left end of the rod, and Event 2 be the measurement of the x-coordinate x₂ of the right end of the rod. If the measurements are made simultaneously in S (that is, t₁=t₂) then the difference x₂-x₁ is the length of the rod (aka: the distance between the endpoints of the rod) in S. And this distance is relative.

 

From the Lorentz transformation:

 

[imath]\Delta x'=\gamma (\Delta x -v\Delta t)[/imath].

 

If [imath]\Delta t=0[/imath] (simultaneous measurements) then we have:

 

[imath]\Delta x'=\gamma\Delta x[/imath].

 

We understand [imath]\Delta x'[/imath] to be [imath]L_0[/imath], the "proper length" of the rod, and [imath]\Delta x[/imath] to be [imath]L[/imath], the length of the rod in Frame S. They aren't the same.

 

When distance is connected with another quantity, time, then it is considered relative. But just by itself, it cannot be relative.

 

Unfortunately this is too vague to be meaningful. In some sense the measurements of the length of the rod is "connected" to time inasmuch as the two frames are at two different velocities, and velocity is the derivative of position with respect to time. But I really have no idea of what you are trying to say here.