Sources? (Want to see exactly what you mean.)
According to special relativity, time dilation occurs between two reference frames that are traveling at relativistic speeds with respect to each other. (I.e., going really, really fast.) If you go fast enough, locally, time will slow down, meaning if you go fast enough, you can essentially travel to the future.
The Hafele-Keating experiment from 1972 showed this effect by putting atomic clocks on jets and flying them in opposite directions around the Earth, and then comparing their times to a control atomic clock on the ground. Naturally, because we're only capable of going so fast, the effect is only traveling a few nanoseconds into the "future," but there was a noticeable and measurable effect that — within the limits of measurement error — agreed with the theory. This is a repeatable experiment.
Some say 4th dimension, while others say each different universe is a different dimension, because they may actually occupy the same space. So if the idea of a multiverse means, everything is happening now, just in a different dimension, maybe we should go back to the Vedic way of thinking. They have always believed in a multiverse - http://www.bibliotecapleyades.net/vida_alien/vidaalien_signtimes08a.htm. As far as your statement that " We are indeed capable of traveling forward in time at different rates," I will need to see some examples, please.
Eh, this confusion is mainly the result of different interpretations of the word dimension. A dimension is basically just another coordinate orthogonal to any of your any previous dimensions. However you want to interpret it, time is nothing more than a fourth dimension as far as coordinate systems go, because as far as humans are concerned, I only need four coordinates to describe any even uniquely (after I define a frame of reference, anyway): three in space and one in time.
By the way, if you read that page you linked, the time dilation equation for how time can pass at different rates depending on your reference frame is described about a quarter way down the page.
I don't much like the term "multiverse" since it gets confounded by a lot of people spouting nonsense, but I don't have a problem with the many-worlds interpretation of the collapse of the Schrodinger equation.
Basically, the idea is that the any quantum system is indeterminate until it's measured, and exists in a superposition of multiple states. Something can be alive and dead, or in two places at once, described by a probability distribution, but the actual state isn't determined until it's measured. The indeterminate nature of quantum states until they're measured is also a repeatable experiment. (Google the quantum version of Young's double slit experiment.)
The most widely-accepted interpretation of this probabilistic nature of quantum systems is to take them at face value: they're probability distributions. Just like you don't know whether a coin will land heads or tails until it's landed, you don't know whether a quantum system is in a certain state or not until it's measured. That's sort of the gist of the Copenhagen interpretation of quantum mechanics.
The many-worlds interpretation instead postulates that each possible outcome corresponds to a different universe. This is kind of neat, and since there's no real way of knowing what interpretation is correct yet, I don't have a problem with it. However, lots of people misinterpret it, and believe this means that there's a universe for every possible outcome of the world, history, etc. This isn't true, because the interpretation
only applies to quantum systems, and something as complex as, say, the neurochemical interactions in the brain to make a decision, aren't quantum systems. So there isn't going to be a separate universe for every decision you might make, etc.
None of that means "everything is happening now," though, even if the many-worlds interpretation is true. It just means (if it's true) there's a difference universe for each state of a quantum system. You would still have to travel among them linearly, in effect, through time. It would just mean you would have different, branching paths to choose from instead of one path. All of that's a big "if."
Some say that, but how do we truly know that? There is no evidence or proof. No repeatable experiment to accumulate data for the scientific method, which is required by science.
You're right, we don't have any tests for that particular part of the theory, since we don't have nearly enough energy to attempt it. However, it's a mathematical consequence of the rest of special relativity, and we have mountains of data that supports the parts of the theory we can test. That gives strong evidence that the rest of the theory is likely correct as well.
As third dimensional beings, we measure everything using materials of our dimension.
As sarcastic as it may have seemed, Dr Zoidberg was right. We're fourth dimensional beings at least, not third dimensional, because we do travel through time; we just have little control over the rate, and, for the time being, no control over the direction. Though I'm not sure what you're point is here. "The human experience" doesn't really fall neatly into any particular dimension or anything, and isn't really an accurate tool for measuring anything.
On a final note, if we consider the geometry of time like we consider the geometry of space, we could, perhaps, think of time as having a nearly infinite slope. Like a very steep mountain, it's almost impossible to do anything but slide down in one direction. It's been a while since I last did any tensor calculus or dealt with geodesics, but we know from general relativity that things like mass and energy can affect the the geometry of space-time. If time has a constant but nearly-infinite gradient in the direction of the future, it makes sense that all we need to do is find enough energy to alter the local geometry enough to result in a negative gradient for time, toward the past. Which would be consistent with the fact that any world line with a slope less than the speed of light in special relativity is effectively traveling back through time, but doing so would require an infinite amount of energy.
We'd need a lot of energy, of course.
(ETA: Forgive me, real physicists, for where I've screwed up. Like I said, it's been a few years.)
