# Confused by different definitions of position

1. Apr 5, 2015

### Sabra

Hello,

I am self-studying an introductory mechanics textbook and while I feel I understand the material there pretty well, I came across across an online definition of position which seems at odds with the explanations and definitions in my book.

The definition that confused me is:

""Position is scalar; it has neither magnitude nor direction.

EDIT: A position vector refers to a location relative to an arbitrary reference origin. This is not the same as position. Being arbitrary, the reference origin can be moved, without moving or changing the position (location) of the object, but this will change the position vector. Think of it this way: put an object on a glass table. Place a grid, with an arbitrary zero point under the table with the object centered on the zero point. The postion vector is zero relative to the origin on the grid. Now, move the grid such that the zero point is no longer under the object. The object's absolute position on the table is unchanged, but its vector relative to the grid is now different. ""

"Absolute position" seems to contradict the principle that no reference frame is inherently more correct than another. Also, if this "absolute position" is not defined relative to any reference point, how would you identify it?

I think this definition is wrong (and appropriately, position should be a vector quantity, not a scalar one). Am I right?

I'd very much appreciate it if someone could shed some light on this for me. Thanks!

2. Apr 5, 2015

### sk1105

This isn't absolute position either - it's defined with respect to the table. Imagine moving the table under the object. The object's 'absolute' position with respect to the walls of the room is unchanged, but the vector relative to the table is now different.

I'm a little unsure of what exactly your textbook is saying, but I suppose it is colloquially possible to specify a kind of absolute position without magnitude and direction ("the object is here", "the object is there") and have people know what you mean (although you could still argue that 'here' and 'there' are relative to the person talking). However, you are right that all reference frames are equally valid, so to describe a position without reference to some chosen origin would be meaningless in a mathematical context.

3. Apr 5, 2015

### FactChecker

I'll take a stab at it, but I am guessing at what the author had in mind and may be giving him more credit than he deserves.

I would say that an object has a position/location even if we are not there to give it position coordinates. That may seem like a silly statement to make, but it leads to some consequences that are not immediately obvious. One motivation of tensors is to define something that has the same physical meaning and rules regardless of the coordinate system used. Once one coordinate system is used to measure a tensor object, there are specific rules that must be followed if the coordinate system is changed. Those rules allow us to say that that tensor has a physical meaning independent of coordinate system.

4. Apr 5, 2015

### Staff: Mentor

Which textbook?

5. Apr 5, 2015

### Sabra

Just to clarify, the quote about "absolute position" came from an online source - my book defines position as a vector and does not mention "absolute position". The quote just made me think I had misunderstood the book, so I wanted to check here.

sk1105 - That's what I thought. Thanks very much for your reply!

FactChecker - I think it's likely the online source is mistaken. I didn't know that about tensors - I'll hopefully study them in the future. Thanks!

Edit: jtbell, didn't see your post there. The textbook is Newtonian Mechanics by A.P. French. But like I said, the quote that says position is a scalar and talks about absolute position is not from the book.

Last edited: Apr 5, 2015