Your disagreement with your phycist friedns is that they are already taking the angle between the times of the observers into account while you are using viewpoint of “ah, there is a difference and with this new thing we can make it go away”.
Not the impression I get, but there does tend to be a bit of a communication barrier, given how … odd my abstractions of these things to be.
If I have a number like 1.01001100011100001111.… where there is supposed to be a digit pattern of ever expanding size this fails to be a rational number but is very strctured. However transcendental numbers include every digit combination (and none of them have an end). Most of these numbers don’t have a structure. It gets a bit muddled whether the “structuricity” or “self-similiarity” is essential or essential clue or totally optional. But being a number and being irrational doens’t give this structuricity.
Sorry, I didn’t mean to imply that the behavior of numbers in this way is significant in some sense; rather, it’s just an example to try to explain the idea that it isn’t strictly necessary to these ideas for self-similarity to behave exactly like this. A logarithmic spiral works, and exhibits a particularly neat kind of self-similarity, but I think a hyperbolic spiral might also work under some other constraints, and it wouldn’t exhibit the same kind of neat self-similarity. Or the shape might not be a smooth spiral at all, but some jagged monstrosity.
That is, the numbers are just trying to describe the “kind” of thing I’m trying to gesture at, lacking good language to define or describe it.
If you are thinking in euclidean terms it might seems that x,y,z,t can be relabeled into each other. However with relativity there is an “odd signature” going either (+---) or (-+++). One can easily relabel like signs. But part of what gives the space its properties that there are “timelike” dimensions and “spacelike” dimensinos. SImple relabeling over all is not sufficient, in order to get full exhangeability something more tricsky would need to be done.If you are not taking these thinks into account you might have a lot of sign errors and some effects will go different direciton than expected.
They aren’t actually exchangeable. But also they kind of are. This one is difficult to explain.
Somebody traveling close to the speed of light, relative to us, has in a sense exchanged travel-in-time for travel-in-space. There is an “exchange” happening. But from the perspective of that person, we’re the one who have conducted an exchange.
If they are traveling towards our Left, we could say that their “time” dimension is pointed partially Time-ward, and partially Left-ward. This doesn’t mean Left and Time have been exchanged, however; that’s just our perspective.
Rather, I’d say it’s more correct to say that Time is like Left, in that it doesn’t point in any specific direction; you have to be inside space-time, with an orientation, in order for Time to point anywhere. And it doesn’t have to point in any particular direction; just as we can’t agree on what direction Left points, likewise we can’t agree on what direction Time points. In general I’d say that Time pointing in any particular direction would be privileging a reference frame.
(But also, as mentioned in the other thread, I think Time and Distance are kind of the same thing, but also kind of not; Time is Distance turned inside out and upside down, sort of. That gets weird, because it kind of implies that you need singularities in order for Time to exist at all, which causes a bootstrapping issue with the universe. Granted that bootstrapping issue isn’t any worse than the universe already had, so oh well there.)
Edit:
Huh. Thought about this a little bit more, and was preparing to analogize this to the holographic principle. Then I considered timeless physics instead, since it seemed closer to what I’m doing here.
And then I noticed those two ideas are kind of the same thing. So, the holographic principle, noticing that distance is unnecessary given that all the information we need is already encoded in time, says we can describe the universe as two spacial dimensions plus a time dimension. Timeless physics, noticing that time is unnecessary given that all the information we need is already encoded in distance, says we can describe the universe as three spacial dimensions. So there’s a generalization of both the holographic principle and timeless physics, I think.
Not the impression I get, but there does tend to be a bit of a communication barrier, given how … odd my abstractions of these things to be.
Sorry, I didn’t mean to imply that the behavior of numbers in this way is significant in some sense; rather, it’s just an example to try to explain the idea that it isn’t strictly necessary to these ideas for self-similarity to behave exactly like this. A logarithmic spiral works, and exhibits a particularly neat kind of self-similarity, but I think a hyperbolic spiral might also work under some other constraints, and it wouldn’t exhibit the same kind of neat self-similarity. Or the shape might not be a smooth spiral at all, but some jagged monstrosity.
That is, the numbers are just trying to describe the “kind” of thing I’m trying to gesture at, lacking good language to define or describe it.
They aren’t actually exchangeable. But also they kind of are. This one is difficult to explain.
Somebody traveling close to the speed of light, relative to us, has in a sense exchanged travel-in-time for travel-in-space. There is an “exchange” happening. But from the perspective of that person, we’re the one who have conducted an exchange.
If they are traveling towards our Left, we could say that their “time” dimension is pointed partially Time-ward, and partially Left-ward. This doesn’t mean Left and Time have been exchanged, however; that’s just our perspective.
Rather, I’d say it’s more correct to say that Time is like Left, in that it doesn’t point in any specific direction; you have to be inside space-time, with an orientation, in order for Time to point anywhere. And it doesn’t have to point in any particular direction; just as we can’t agree on what direction Left points, likewise we can’t agree on what direction Time points. In general I’d say that Time pointing in any particular direction would be privileging a reference frame.
(But also, as mentioned in the other thread, I think Time and Distance are kind of the same thing, but also kind of not; Time is Distance turned inside out and upside down, sort of. That gets weird, because it kind of implies that you need singularities in order for Time to exist at all, which causes a bootstrapping issue with the universe. Granted that bootstrapping issue isn’t any worse than the universe already had, so oh well there.)
Edit:
Huh. Thought about this a little bit more, and was preparing to analogize this to the holographic principle. Then I considered timeless physics instead, since it seemed closer to what I’m doing here.
And then I noticed those two ideas are kind of the same thing. So, the holographic principle, noticing that distance is unnecessary given that all the information we need is already encoded in time, says we can describe the universe as two spacial dimensions plus a time dimension. Timeless physics, noticing that time is unnecessary given that all the information we need is already encoded in distance, says we can describe the universe as three spacial dimensions. So there’s a generalization of both the holographic principle and timeless physics, I think.