Hi Einstein,
We have multiple reference frames in existance that appear to be independant of each other. We don't get to choose these reference frames. They already exist. My question is "What defines these reference frames?"
I agree. And this relates to one of the more important aspects of the mathematical argument presented in the link I provided above. Namely, that since the Lorentz transformation does not preserve magnitudes when performing the transform (as a proper transformation should), then the basis for time dilation as described in special relativity is in question. Einstein used "relative simultaneity" to argue that it was the observer's measurement apparatus that undergoes distortion, but it is clear that (due to general relativity itself) you could also claim that the source wave that the observer was measuring could have also undergone distortion (grossly related to the weak equivalence principle). But I like the way the author explained it on
THIS PAGE:
"Electromagnetic phenomena (e.g., light waves) are endowed with the curious distinction of exhibiting a constant propagation velocity regardless of an observer's relative velocity. For this unique phenomenon to occur either the measuring instruments employed by the observer are distorted as a result of the observer's relative velocity or the light wave itself distorts, as a consequence of and in proportion to the observer's relative velocity. The special theory of relativity supposes the former, an alternative theory proposed herein, supposes the latter."
But a line of force is clearly 2-D. It doesn't extend into the third spatial dimension.
OTOH, one could point out that a "line of force" is a ficticious quantity in our observed 3-D universe. We replace the "real" force which does, indeed, act over more than just a line with a resultant force vector. IOW, the concept of a force acting along a line is a mathematical convenience as is the concept of a "center of gravity". Think of a pressure. It acts over a surface, but we can reduce it to an "equivalent" line of force acting through a central point.
But there are three 2-D planes orthoganol to one another in normal 3-D space.
Yes, I completely agree.
I do have some thoughts on time and mass that tend to tie together your idea that mass and time are vector quantities, even though both are considered scalar.
I'd like to explore these with you. As I always say, I think I have sound math for this concept (MassTime) that would be like a mirrored-opposite to the concept of SpaceTime.
Doesn't a scalar quantity changing in intensity do so in either a positive on negative direction? So if the magnitude of the scalar quantity is changing, it has direction. That would give it vector status.
I understand what you are implying, but the entire definition of "positive or negative" is with respect to an arbitrary reference point. But even that "rate of change" metric you are describing is not a true vector as it only has a 1-dimensional nature to it (i.e. + and - are relative measures of the same, single dimension).
The concept I am getting at when I say mass and time are vectors is much more direct. But for it to make sense we must generalize the concept of "vector" such that it is not exclusive to SPACE or spatial dimension. We must realize that both Mass and Time are, indeed, dimensional aspects of Energy. And each one has readily identifiable sub-dimensions which are triple orthogonal sets. The example for Mass is that we are aware, from chemistry and physics, that atoms are comprised of particles that have +, -, and neutral charges. So just like we break-down a spatial vector into "X, Y & Z" components, we could equally break down Mass (and we do) into its e-, p+, and n0 components. IOW, the total number of electrons in a specific isotope of a specific atom represents the negatively charged vector component of the overall vector that describes that Mass.
When you do the same thing with Time, and its sub-dimensions of Past, Present, Future there is an interesting result when you combine this with my theoretical equation for Information as a higher level metric of Energy: We find that INFORMATION (in the form of stories, photos, or movies) can describe three different "forms" of the past. The "simple past" is described by Information which relates an event as it actually happened. It would be like the line in the center of a light cone. Yet Information could also describe two other forms of the past: (1) Possible past (one that did NOT happen but which could have happened in accordance with our known laws of Energy) and (2) Impossible past (one that could NOT have happened as it violates our known laws of Energy).
This is just a verbal description of the underlying math which shows how Information can describe things outside the realm of possibility given our universal parameters. And it underlies the importance of information and its relationship to the observer in any formulation of a GUT.
RMT