DaleSpam said:
I am not advocating any concept. They make no experimental predictions...
Here is an experimental prediction that could only be made by assuming the concept No. 5 is correct.
So, at the end of this text is a space-time diagram with a sequence of events. The diagram represents a sort of sequence of thought experiments in which three observers in a Lorentz space send messages back and forth as they move through 4-dimensional space. Before the experiments begin, the three observers get together and plan the experiments, documenting the exact sequence of events to be enacted. Predictions about the exact results of data that are to be recorded and transmitted among the observers for each planned event are documented in advance of the experiments. At the end of the sequence of experiments, the three observers get back together and compare notes to see if their experimental results verify existence in any of the Lorentz space planes of simultaneity (volumes) under dispute.
In the sketch below the brown, light brown, and blue observers are initially together in the brown rest frame, synchronizing space-time markers which are available as displays of actual distance traveled in 4-dimensional space, referenced from their starting point. The plan is for each to advance through a sequence of world line events, maintaining a display of distance traveled, photographing data and transmitting data back and forth among the three observers (speed of light transmission).
All three are together at event 1 (events in the space-time diagram are brown, light brown, or blue circles) where they synchronize their distance markers). It is planned that the light brown guy and the blue guy will move to a new position that puts them in brown’s instantaneous plane (3-D volume) of simultaneity at event 8. Light brown and blue have used Lorentz transformations to assure that their distance markers display the same values at event 8 as the brown guy’s markers display at event 2. Light brown and blue both transmit pictures of their displayed values so that brown can validate their numbers when he (brown) arrives at event 3 in the space-time diagram (brown calculates how far he has traveled along the 4th dimension since leaving event 2.
At event 9 the light brown guy transmits a photo of his distance display, which is received by blue at event 14 and received by brown at event 4. The blue and brown guys do calculations that demonstrate that events are still occurring in agreement with theoretical physics and agree with their pre-test predictions for that event. At this point the brown guy is able to confirm that the light brown guy existed in his plane of simultaneity back when he (the brown guy) was at event 3). From the data received from the blue guy at event 4 he is also able to determine that the blue guy was also in his (brown’s) plane of simultaneity back at event 3. Thus, the pre-test predictions for the experiment hold up.
Just one experiment doesn’t seem enough, so they continue acquiring data.
The blue guy arrives at the brown guy’s position at event 5. So, here the blue guy and the brown guy simultaneously occupy the same position at the intersection of their X4 axes. Special relativity tells them that if the light brown guy really still exists, then the light brown guy must exist at event 11 in blue’s instantaneous 3-D space volume, while simultaneously existing at event 12 in brown’s simultaneous space. However, as PeterDonis points out, they can’t really be sure, because they have no way of getting information from those events instantly while they are at event 5. They must wait until later for confirmation from the light brown guy.
Brown gets his confirmation when he arrives at event 6, receiving the picture of light brown’s event 12 photo of his distance traveled along the 4th dimension, which is exactly the same distance that the brown guy recorded for his own trip when at event 5. Thus, brown concludes that the light brown guy must have been in his simultaneous space which included both event 5 and event 12 simultaneously.
The blue guy has to wait until his event 16 for confirmation that light brown was at event 12 simultaneously with event 5 (when both blue and brown guys were simultaneously at event 5). Of course the blue guy saved a copy of brown’s distance position along brown’s X4 dimension when they were together at event 5. So, now he had confirmation that light brown was in brown’s simultaneous space, i.e., both brown and light brown were in the simultaneous space of events 5 and 12. These observations agree with those predicted before the start of the experiment.
But, now, blue asks whether the light brown guy was in his (blue’s) simultaneous space when blue was at event 5. Fortunately, light brown included a photo of his X4 position corresponding to event 11. Light brown and blue both used Lorentz transformations to figure out what each other’s positions should be along their respective X4 axes when blue arrived at brown’s position, event 5. Light brown transmitted his computations that he had made about what blue’s X4 position should be when light brown was at event 11. And blue computed the X4 reading that light brown should have when he (blue) was at event 5.
Light brown and blue wanted to be sure science was working right, so they took photos of their respective X4 distances corresponding to blue’s simultaneous space at blue’s event 16. Light brown did calculations (by prearranged agreements) at event 13. At event 17 blue found that light brown was in his (blue’s) simultaneous space when blue was at event 16 and light brown was at event 13.
All three observers get together at the end of the experiments and review all of their data. They conclude that sure enough, when the brown guy and blue guy were at event 5, the light brown guy simultaneously existed at event 12 (in brown’s simultaneous space) and event 11 (in blue’s simultaneous space). They then conclude that the light brown guy is actually a 4-dimensional object, and-- by extension--they all are. Thus, we have a model in which objects are 4-dimensional extending into a 4th spatial dimension.
DaleSpam said:
However, "eternalism" is my favorite when there is no reason to pick one of the others.
The only problem is that it does not make the predictions that were made using concept number 5 as described above.
DaleSpam said:
If you will note, there is no distinguishing feature between eternalism and spatial eternalism other than your idiosyncratic and unexplained labelling. It makes it hard to distinguish as a legitimately different concept.
The “eternalism” includes just pure time as the character of the 4th dimension. It is clear that having just pure time as your concept for the 4th dimension (without any spatial essence in that direction), you do not have the 4-dimensional space within which 4-dimensional objects can occupy. The thought experiment diagrammed in the sketch below and discussed in the above text emphasizes the agreement with the experimental predictions that 4-dimensional objects exist. "Eternalism" does not imply the existence of 4-dimensional objects.
