A little bit ninjaed, but I wrote quite a bit before finding that I had been, and it's difficult to excise the repeated stuff.I can't disprove the concept of a 4th dimension, though I do have a few questions and not willing to accept it completely. Does this prove that there is a 4th dimension? Not really. It certainly does not conflict with the concept of a 4th dimension, though. There are so many factors that come into play, that wobble could have been from just about anything.
That's not quite right. If the simplest explanation for something (e.g. gravitational 'leaking') is that there's a 4th (...5th, ...6th) dimension into which it dissipates, then not being able to disprove it allows it to be an acceptable theory for how the problem concerned is solved. Being unable to disprove a 4th dimension when there's no reason to suppose one doesn't make it desirable to believe in it after all, however. (I think I've not double-negated anything in that last sentence, but it looks awkward. YKWIM, I'm sure.)
But time, by definition, is linear.
By that, you mean unidirectional, I think. (Measurement of time is variable according to who is measuring it. And, by that definition, measurement of someone else's time (e.g. while observer/observed/both approach, pass and recede from the observed/observer/one another at any significant speed) could very well show time around the observed passing at different speeds at different observer-times, thus not 'linear' in any accepted manner.)
And that traveling through it would always end in a paradox leads me to believe that you can't travel through it at all.
First of all, you're right if you go back and kill your own grandfather, that's a causality-breaking paradox, but if you were to go back and
be own your grandfather (making out with your hot grandmother-to-be... yeah... I'll let that one sink into your mind a bit... indeed...) that it's a causality-
making paradox which is not strictly prohibited by any of the relevant rules of physics.
But I've already pontificated about all the various ways in which time travel might reinforce or 'branch' a time-line, in past threads on the subject. I've got a surprisingly large tolerance for just about any of the fictionally-used versions of time-travel, except for the Fading Marty McFly one, but I do tend to personally favour the You Go Back And Do What You've Been Back And Done idea as the most elegant. (IMO, YMMV.)
Which is not to say that there might not be a form of time-travel which takes one into the 'forbidden zone' of lightspeed-limited travel. A wormhole takes you, by a shortcut
and with a time-travel element, on not just an FTL journey (as it would have to be if taking a non-wormhole direct route through normal space), but to a 'when' that a suitably neutral-framed observer (e.g. sitting equidistant between embarkation and destination point, in the same relative frame of reference[1]) eventually sees the appearance of the arriving you at the destination prior to seeing the disappearance of the departing you from the starting point. But unless you 'drop into' the historically-facing time-cone from the departure point, you're not dropping into your own past and giving any reason for a paradox.
(It's as much a paradox as the fact that a lighthouse beam, sweeping the sky, can (eventually) shine on one distant planet and then shortly afterwards shine on another distant planet, with the 'end' of the spotlight apparently travelling faster than light... But it doesn't take information at Planet A and convey it to Planet B at FTL speeds, it just (at lightspeed) tells Planet A that it is being shone upon (or was shone upon, a length of time proportional to the distance between Here and Planet A, ago) and also tells Planet B that it is (/was being) shone upon from Here. There's no A->B communication involved, merely two independent H->A and H->B communications that obey the cosmic speed limit.)
Arriving right next to a supernova, that hadn't, at the time of departure, announced itself to the origin point, wouldn't allow you to broadcast a signal to pre-departure self and tell you not to go back in time. Because that signal could not out-pace the initial output of the supernova that you hadn't yet known about.
Which is not to say that perhaps one couldn't travel back into one's own (known!) past. If nothing else, travelling sideways-in-one-direction and back-a-bit-in-time could be followed by a second jump sideways-in-the-other-direction and back-a-bit-in-time to allow one to arrive at your origin point but two 'bits' of time past-wise. (Minus jump preparation time, of course.) But there's no reason to suppose that you even have to go sideways at all, when you go back. This is where the [ABBREV=You Go Back And Do What You've Been Back And Done]YGBADWYBBAD[/ABBREV] idea (or the many others, like the 'branching timelines' one, or the 'into a different version, and change that instead' one which I think that's what you consider to be "4th Dimensional Travel").
That's if I understand your objection, leading up to the bit you talk about in the "This is the part of the theory of relativity or any iteration thereof that is wrong (I can't see it any other way)." part of your post.
However, none of the aforementioned world-views are authoritative. It's all just vaguely viable speculation. They explain the known facts
for the facts which are known to me, and moreover they fail at the Occam's Razor fence as not being the simplest explanation, given that it's quite possible that there is absolutely no possibility of wormhole travel (effectively
or actually through time... or even just less bothersome but still sub-FTL in all respects), up until the point at which something (c.f. Quantum Tunnelling, although that is actually probably happening without any fancy wormhole stuff anyway) shows to want to do something apparently not 'normal'.
[1] Other observers in other parts of the universe and/or in other frames of reference might have their own ideas about order, and not necessarily agree that the effect preceded the cause. Or even see it in a more extreme way. Either way, it's essentially a Picard Manoeuvre, I suppose.