I asked this question already but I did not see your answer. If you answered it already I may have missed it. Either way, can you specify your answer to the following question: Are you using the word objective to mean something other than observer-independent? If so, what do you mean by the word objective?
Do you agree that directional orientation is not observer-independent? For instance, will one observer's right be another observer's left? Can one observer's right be another observer's forward?
Do you agree that directional orientation is not reference-frame-independent? For instance, is it true that from one reference frame the blue car is on the left but in another reference frame the blue car is on the right?
Do I agree? Not exactly, because the 0D "reference point" and the "1D line" connecting two 0D "reference points" are mathematical constructions (i.e conceptual fictions) used to describe objective physical relationships, but they don't actually physically exist. 0D points don't actually exist; they are made-up to make reference frames. However, nonetheless, I think I agree with the spirit of what you are saying, which I think can also be said as follows: In classical physics, all observers will agree on the relative distance between two reference points, which means 'distance' is an objective, observer-independent, and reference-frame-independent measurement (in classical physics).RJG wrote: ↑May 3rd, 2021, 6:32 amYes, but don't stop there. Not only do 1D relationships (distance between objects) objectively exist, but also 2D relationships.Scott wrote:For example, in regard to the 2D world in the OP, it is objectively true (i.e. true in an observer-independent and reference-frame-independent way) that the red car and the blue car are closer together than the red car and the green car. All would-be observers would agree on that fact; that fact is true in all would-be reference frames; and that fact is true without any observers or reference frames (or with our eyes closed).
In the 2D world in the OP (represented in the image), it is objectively (independent of human perception) true that:Therefore, in this 2D world:
- 1. There exists a Red car and a Blue car.
2. There exists a 1D relationship (distance line) from any reference point on the Red car to any reference point on the Blue car.
3. There exists a 2D relationship (X-Y coordinates or polar (distance/angle)) from any reference point and axis on the Red car to any reference point on the Blue car....agreed?
- 1. Objects (Red and Blue car) exist independent of human perception; i.e. they objectively exist.
2. 1D (distance) relationships exist independent of human perception; i.e. they objectively exist.
3. 2D (X-Y or polar) relationships exist independent of human perception; i.e. they objectively exist.
To put it more simply -- in a 2D universe, if objects exist then the relationships (both 1D and 2D relationships) between these objects likewise exist.
In other words, insofar as two observers agree on how to measure the distance between two real objects (e.g. what 2D border to treat as the surface of each object, and/or which point to treat as the center of each object), then their distance measurements will agree.
Generally and roughly speaking, it seems we agree on the above.
Scott wrote:In a 2D world, you can draw/imagine two perpendicular axises through any point, and you can label those two axises X and Y, but there infinite ways to draw them through any point and infinite points through which you could draw them. So even if the origin point is specified ,there are still infinite potential reference frames that could be created.
I am not sure what you mean by "X-Y relationships".
Perhaps, you are meaning to refer to the mathematical law that in unbent 2D space there exists for each 1D line a perpendicular 1D line. If so, I agree that that is a mathematical law, as objectively true as the fact that the ratio of a circle's circumference to its diameter is pi.
No. Three main things illustrate why that is false.
1. Through any reference point, infinite 1D lines could be drawn and any of those infinite drawn lines could be labeled as being an axis. Which of the infinite lines is selected out from the other infinite options to be treated as an axis in the reference frame is not observer-independent and is not reference-frame-independent.
2. Any 1D line drawn through a reference point specially selected out as an axis is equally entitled to be labeled as the Y axis or the X axis. In other words, any 1D line drawn through a reference point is equally able to be considered the leftness-rightness axis as the forwardness-backwardness axis. Whether the axis is assigned as being the leftness-rightness axis or forwardness-backwardness axis is not observer-independent and is not reference-frame-independent. Even if I draw a line on the image in the OP and tell you to treat that line as a reference line or axis for the reference frame, there is no way to say whether that 1D line is an X axis or a Y axis. Whether the line gets labeled as the X-axis or the Y-axis is not observer-independent and is not reference-frame-independent.
3. Even if you imagine a 0D point, and imagine a specific one of the infinite 1D lines through that 0D point as being an axis, and arbitrarily label that 1D axis as being the X-axis versus the Y-axis (and thus the other perpendicular line as being the Y-axis), you still have not created a full reference frame with which to use to determine left and right. In addition to arbitrarily labeling one of the arbitrarily selected 1D lines as the X or Y axis, you then need to also choose the positive direction on that axis (forward, backward, down, right, etc.), not just a line. Then you may have created a full reference frame in a 2D world. To illustrate, even if I draw two perpendicular lines on the image in the OP and tell you one of those two specific lines is the X-axis (the axis of left and right), and the other line is therefore the Y axis, and their intersection is the origin point of the would-be reference frame, I still even with all of that haven't provided a full reference frame from which for you to say whether the blue car is on the left or the right because you won't know which direction on the X-axis itself is left (negatively numbered) and which direction is right (positively numbered). That is not an observer-independent and reference-frame-independent choice. In other words, you need to specify a vector with directional oriental to get directional orientation and thereby have a created reference frame.