The laws of physics through out the universe
How do we know laws of physics are the same throughout the universe? Intuitively I would say they would vary in two natural ways: the constants in the equations may vary or the math in the equations may vary. As a guess they could change over a long time. What is the furthest radius we can prove from earth, with absolute certainty, that the laws of physics do not vary? I am aware this may not be a radius but a more complex shape that cannot be simply described by a radius.
The nearest answer I can think of for a radius is a guess. And that guess is based on the furthest physics experiment we have done from earth. Which I think is an experiment with mirrors on the moon. Therefore if we assume (I don't know if this assumption is totally 100% reasonable) all physics laws hold because this experiment works. Then the radius is to the moon. This doesn't give an concrete answer for the radius, merely an educated guess.
Well, the experiments people did on Earth in the 18th century is far, far further in space (and time) than the Moon is from Earth today - and that's peanuts to how long life has existed here. Are you supposing that we "drag" our physics with us through time and space? This is starting to look awfully complicated, for something that has no problem to explain and no predictions to make. I'd hazard to call the idea unscientific - you're trying to replace something that's simple and seems to work with something that's very complex, and doesn't have any observations (or even reasoning) to go with.
The second paragraph you are referring to about the moon, as I wrote before in the question-it is merely an educated guess. Which of course means the second paragraph may not be correct about the radius because as I wrote before (in that paragraph) its a guess. But its the best answer I could guess for myself at the time I wrote the question.
I think it's not a good question, once you understand the core of the scientific method. It's a bad idea to think about things that can't be disproven - that way lies madness and dragons :) Look at all those crackpot theories out there - most of them either actively avoid a scientific test, or have no way to be disproven in the first place. And anything that is Earth-centric is suspicious - you think your approach is conservative, since we didn't observe something yet, but it actually introduces *more* complexity to the model, which inherently gives it more of the burden of proof.
@Luaan the question does not ask whether our knowledge is complete. Is asks whether there are already indications that certain laws as we know them might not hold somewhen (once upon time somewhere far far away).
This is assumed by the cosmological principle. Scientists generally trust whatever hypothesis requires the fewest assumptions — and assuming the Universe is homogenous is more supported than assuming it is not.
Nothing can be proved "with absolute certainty"; that is not how science works.
We adopt a working hypothesis that the constants of nature are exactly that; both constant in time and space. Then we conduct experiments that attempt to falsify that hypothesis or at least place limits on by how much things might vary.
For reasons that are explained in answers to this Physics SE question (see also this question), only the dimensionless parameters like the fine structure constant can be assessed for their variation - other constants like $G$, $c$ and $h$ are tied up in our system of (measuring) units so we are unable to say whether they are changing or not.
Taking the example of the fine structure constant, observations of absorption lines towards distant quasars put strong limits on by how much this can have varied in space and time (the two are inseparable, since it takes finite time for information to travel to us). So you can find lots of different attempts to do this in the literature - I dug out a few. Albareti et al. (2015) say the variation is less than a couple of parts in a 100,000 out to a redshift of 1 (a lookback time of about 8 billion years or so. Similar constraints exist for experiments carried out in different parts of the solar system. On the other hand, some authors do claim variations of a few parts per million on similar lookback times or in different directions (Murphy et al 2008; King et al. 2012), but these claims are disputed by many, if not most workers in the field.
There is a massive review of this topic by Uzan (2011), which you could read - this really is a broad question. My summary would be - at the moment there is no convincing evidence for any variation in space and time.
Closer to home, the natural Oklo nuclear fission reactors yield very strong evidence that the fine structure constant has been constant (to within a very tight bound) for the last 2 billion years.
@DavidHammen Absolutely correct. If someone wished to write an answer based on "lab-based" experiments, I would upvote it.