hoponpop

You may be overthinking this, or I may be under thinking it. Lol I think you're right to decompose and go to the projection theorem, but from there isn't it just a matter of proving the projection theorem for each M and Mperp? : /

I like Feynman's stuff for that. I liked his statistical mechanics lectures: ISBN-13: 978-0201360769 And his statistical thermodynamics thing (can't find that anymore). Probably pretty low level to a lot of people on here, but hey...

Does time slow down, or do other dimensions change? Most generally, solely along the x-axis: v=x/t So, exaggerating for the sake of simplicity, if the speed of light were do double due to influence of an independent mass, we have: 2v=a(x/t) Mathematically, it is (here) indistinguishable whether time is halved or distance is doubled. 2v=(2x)/t=x/(.5t) There are actually infinitely many solutions to this. Any fix for this? Why time and time alone? Or, more broadly, why is it said that time changes as opposed to anything else? What fundamental aspect of time makes it more likely to change than distance

Lol awesome. Where else can you get that? My background is in biomedical engineering, but I'm currently in law school with no one to talk to about fun things like this.

Given only a single discrete object, is it possible to describe that object solely in terms of its structure? Let us define a discrete object P as an arbitrary piece of matter. What it is is unimportant. Let P constitute a matrix P' propagating infinitely in every dimension. Let us define each point in the matrix P' as P'(x,y,z,t, ...). Further, let every point in the matrix P' constitute a second similar matrix, P", also propagating infinitely in every dimension. Let us define every point in the matrix P" as, e.g., P"(x',y,z, ...), wherein x' denotes the x component of the previous matrix P' is being expanded upon. Let this pattern continue infinitely for every point in every subsequent matrix. Effectively, we have created as complete a description of a discrete system as (I can see) is possible. So, the question comes down to this: Does there exist a function that defines P solely in terms of its (infinite) constituents, even if everything is known about it? I have no idea. Edit: Actually, I think I only described a point. Hmmm... Where from here Edit Edit: I think that no matter how definitively you describe a point, even if you know everything about that point, you effectively know nothing about it without comparing it to something else (e.g., putting it in a coordinate system).

Not saying anyone has suggested otherwise (re. time being relative), just laying out how I got where I did. I guess I'm making a big deal about nothing here. I still have a problem with (at least my understanding of) Einstein's conception of time, though, so I will continue to think about that. Good debating with you, swanston. You certainly know your shit. Lol

Even if you assume a perfect clock, Einstein extends relativity to time. He doesn't go as far as to classify time as a unit of measure, but he acknowledges that time is relative. Take that a step further: even if something is absolute, any description of it is relative. Now we're getting into philosophy, but language is essentially an abstract representation of systems of matter. Numbers are a subset of language. The only thing special about numbers is that they represent a "universally" understood system of relationships. A measurement is just a description that makes use of that relationship, and is thus understood as "definite," or "absolute." However, you still have to define what that measurement is relative to. "8 inches tall" imparts a very definitive structure to an object. The more narrowly you want to describe something, the more you compare it to other things. That is the nature of language. Time is different. There is no implied "starting point" (e.g., ground for "8 inches tall"). So, while you can very well ignore that and have a legitimate theory, the theory is much broader if it encompasses the relativity of time.

I like this. I agree that there is no problem with the theory (at least not that I've pointed out). I am also not arguing that the theory of special relativity doesn't work in practice. I agree that my very general description of the definition is simultaneity is inaccurate; you are correct that relative velocity is as generally as it can be stated. swansont got me thinking though: The issue of measurement and the theory of relativity are integrally tied. §2 of "The Electrodynamics of Moving Bodies" is actually titled "On Relativity of Length and Time." However, the fact that length and time are relative is not applied (or, seemingly, considered) in defining arrival or position of the hands on the clock. Each of these definitions is important. If arrival is defined as the point at which the train ceases motion, then we need to introduce another reference point. Time, even if defined to the picosecond, is not 100% accurate. However, no matter how precisely time is defined, it is still relative, an we need yet another reference point. Add another reference point and we've related three otherwise (potentially) independent events. This can go on forever. In my mind, any complete theory can and will be criticized as a tautology (see, e.g., Haig-Simon Equation), so I like where this is headed. Maybe set up a bunch of matrices A, B, C, ... and relate them to each other, and look at the elements of the matrices for patterns.... More to come. Please blow up anything you can find that I'm wrong about. That's how we refine.

Einstein's "On the Electrodynamics of Moving Bodies" (https://www.fourmilab.ch/etexts/einstein/specrel/www/) draws its conclusion based, at least in part, on Einstein's interpretation of simultaneity (generally, the point from which seemingly simultaneous events are observed dictates their perception, e.g., as simultaneous or "not simultaneous"). Einstein never explicitly defined simultaneity in this paper, but rather merely analogized to the arrival of a train when the hands of a clock were at a certain point. The problem that I see with this is the degree of imprecision implicit in this definition (e.g., when does "arrival" occur, how is the position of hands on a clock measured/does a smaller gear tooth size effect simultaneity, etc.). Applying these theories at much higher speeds than observed in daily life would greatly amplify the effect of aforementioned imprecision on any calculation involving the same. The only impact that I can see this having is on significant digits. However, I am hopeful that someone much smarter than me can tell me why I'm wrong about all of this.