On Wellsian Time Machines

There is nothing "tripping me up" here at all.

I've already posted the very sources on the "vector quantity" definition as it applies in physics. Why are we bringing that up again?

As to the Einstein equation, well, gee, ANY thing that has a velocity has to have SOME diection to that velocity even if the direction changes. (Which I've ALSO said before.) But that DOES NOT MAKE IT synonymous with the term "vector".

Vector applies only to specific defined direction.

Since this is not always possible to ascertain in quantum physics, (due to the Heisenberg Principle) "vector quantity" is used to descibe the fact that a particle can either be determined to be traveling in a given direction at some point, OR... to be traveling at a given velocity at some point. But it is not possible AT THIS TIME to know the two simutaneously. Hence, the term "vector quantity".

This only applies in quantum physics and in NO other definitions of the term "vector". And certainly not in the Einstein equation which has nothing to do with quantum physics. Nowhere is "vector" used to describe velocity as a quantity itself. Only velocity in a SPECIFIC direction. There are NO "vectors" involved in the Einstein equation. They aren't needed. It works for all POSSIBLE vectors.

Since I've already provided all the references you could need that explain what a vector is, I'm not sure what it is you are getting at at this point.

Unless you take issue with THEM, in which case I can only suggest you take your argument TO them. I did not define the term. They did.

I can only repeat it as it is defined and show you the references to it/them.
 
A very quick search turned up the following supporting my definition of 'vector quantity' and 'velocity'.
http://bartok.ucsc.edu/peter/114A/tensors/node3.html
(a mathematical approach)
http://www.phys.uidaho.edu/~pbickers/Courses/310/Notes/book/node129.html
(online course materials)
http://members.edventures.com/terms/v/vector_quantity/definition.html
http://www.rit.edu/~pnveme/pigf/Vectors/vector.html
http://physics.mtsu.edu/~phys231/Lectures/L6_-_L11/L6/Vector_Components/vector_components.html
http://www.britannica.com/bcom/eb/article/5/0,5716,119065+5+110308,00.html
(if momentum is a vector, logically so is velocity)
http://www.quickgetaway.com/Book/8positio.htm
(velocity being a vector is acknowledged in many different areas!)


At any rate, there's your definition of 'vector quantity', as in something that is a vector.

Velocity is a vector, to fully describe a velocity you must give a speed and a direction.

'Vector quantity' means the same in quantum physics as in normal physics, and its definition has nothing to do with the Uncertainty Principle.

Einstein used 'velocity', ie the vector, in his equations, but nowhere are the results of the equations dependent on direction. They get cancelled out by squaring and scalar multiplication. By doing this, Einstein's making a mathematical point: no matter what direction you plug in, the same magnitude gives the same result.

Anyway, if taht doesn't convince you that velocity is a vector and thus has a magnitude and a direction, I don't know what will.
 
NoName:

Very good. Nice references.

I'd also say that we've been able to show references from different sources that do not always agree with each other. And depend on interpretation in some cases.

For instance, in the cartesian Vector (your first one) note that contained therein is the following phrase:

"Let us emphasize that a set of quantities with a subscript, e.g. -A1-, is not necessarily a vector. One has to show that the components transform into each other under rotations in the desired manner. "

(I don't think this message board handles the symbols all that well, please forgive the substitutions)

And further:

"We shall then need to define two types of vectors, one transforming like the -X1- and the other transforming like the derivatives -a0/ax1- where -0- is a scalar function.

This no doubt leads to the kind of discussions we are having now. All in all, I'd say a good dialogue. Informative for anyone who reads it.

Frankly, I would still contend that your second reference goes to MY point that Velocity is a Vector Quantity, meaning that it is a component OF a vector, but not synonymous with it. (In this case anyway.) Ahh semantics.

In your fourth reference we find this:

"Vectors have magnitude (and unit) and direction. Velocity is the vector that would correspond to speed. 40 mph traveling east can be vector. This sense of direction allows the vectors to be represented geometrically with an arrow, the head in the direction of the vector and its length scaled to represent its magnitude."

Although I do take issue with the second sentence above as leading to the kind of confusion we are discussing here. Again, in this case, (the classic MECHANICAL definition, Vector is a velocity in a defined direction. I would question the conclusion drawn by the author of the above quote to use the second sentence in this case. The third sentence is MY point exactly.

Well, anyway, I'm sure you get the point.

I still contend that other than in Quantum Physics, (for reasons stated before) the term Vector is best applied when a defined direction is involved.

We agree that velocity itself cannot be truely defined unless SOME direction is considered, but the difference is whether a "specific defined" direction is applied, or general non-specific ones as in the Einstein equation we are using. The former represents a Vector, the latter does not.

I suppose we could go on with this as long as you like, but as far as I'm concerned, we merely interpret the details of this differently. Neither of them being "wrong" or "right".

I would also contend that the references provided by BOTH of us back this view up. Since there ARE seeming inconsistencies across the board on these.

Perhaps we could explore why THAT is so.

Peace.
 
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