The discussion revolves around the concept of treating the speed of light (c) as a dimensionless constant in the context of spacetime. Participants explore the implications of different unit systems, particularly natural units versus SI units, and the philosophical and practical considerations of defining time and space measurements.
Participants express a mix of agreement and disagreement. While there is acknowledgment of the validity of treating c as dimensionless under certain conventions, there remains contention regarding the implications of unit choice and the fundamental distinctions between time and space.
Limitations include the reliance on specific definitions of units and the unresolved nature of how different conventions affect the interpretation of physical dimensions.
The shadow idea is not for defining perpendicularity, it is only for illustrating the fact that perpendicularity is independence to a higher extent: it is instead of some shadow, no shadow at all.Ibix said:Then how do you define the word "perpendicularly" when you write "the light will come perpendicularly to the analyzed vector"? You rely on it in your definition of orthogonality.
If you read my posts, you will find out that I am not positing the simile for Minkowski space, at least not for the orthogonality that is based on the dot product with negative sign, which is not the same thing, sure. I just said that the shadow simile pops up however also in Minkowski space under forms that would deserve discussion.Orodruin said:You (or that simile) are presupposing a Euclidean space. Spacetime is Minkowski, not Euclidean, so it does not work as a mental guide in spacetime.
And no, it does not sound like it would be a good textbook simile even in Euclidean space. At least not at higher level. It may have more of an intuition point in lower level maths but even then it is flawed as presented in this thread.
Not if they are null vectors.Saw said:The two vectors at the extremes are orthogonal, i.e. totally linearly independent
I don't understand what you are talking about. This looks like a personal theory of yours. Personal theories are off limits here.Saw said:here the orthogonality concept has been generalized in a way that picks up the dot product leg, but drops the full independence leg.
So it is a personal theory of yours. See above.Saw said:I can understand that you are suspicious about this speculation, which is what it is, I can perfectly concede that.
Since the "positions" that everyone but you in this thread are taking are the standard "positions" about vector spaces in both math and physics, your apparent expectation that we should "move" from them is mistaken. Particularly when, as you admit, you are expounding your own personal theory. Get your speculations published in a peer reviewed journal and then you can discuss them here.Saw said:I have convinced myself that I will not move you an inch from your positions.
Since the "concepts" you refer to are your personal theory, yes, it is indeed over. Thread closed.Saw said:I said that I would not insist on these concepts that mentors are clearly rejecting and so this is over!