If the universe was just a sequence of random arrangements of random phenomena, then no physics would be possible - there would be no reproducible experiments, and so no way to predict the future based on the present.

Specific things may be variables rather than constants, but we can only ever define that in relation to some other constant. If the hyperfine transition of the cesium-133 atom starts taking longer, how could we measure that, except in relation to some other periodic activity, e.g. the hyperfine transition of hydrogen atoms (or, if we go back to Galileo, human heartbeats)? So we could equally say that the hydrogen transition has got faster or the cesium transition has got slower. Now if 111 elements "agreed" on how fast time was passing and one other element differed, it would probably make sense to say that it was the one element whose transitions were slowing down rather than the 111 elements whose transitions were speeding up. But ultimately there is no single objective measure of time in the universe; rather there are a number of periodic patterns in the universe that are mostly consistent with each other, and most easily explained by there being a single, consensus concept of time passing. If one particular pattern starts going against that consensus, it makes sense to say that that particular pattern is changing, and since we want our definition of the passage of time to agree with the consensus, if the pattern that changed happened to be the "official" definition of time (hyperfine transitions of cesium-133) then we would almost certainly just switch to a different pattern in nature that followed the consensus. But if the consensus itself broke down, well, at that point it no longer makes sense to talk about a single concept of "time" - rather we'd have to talk about the specific patterns we were talking about. And if the patterns went away entirely, physics itself would become impossible.

In relative terms I agree. However, what if some outside force were causing the 111 elements transitions to speed up, but that outside force had no effect on the 1 who was immune to that cause? How can we ever be sure of anything? If we go into things assuming that the 111 elements are correct and the 1 was incorrect, we could be tying ourselves to assumptions that may be invalid.

Think to Geordie's epiphany: "It never occurred to me that space was the thing that was moving."

> what if some outside force were causing the 111 elements transitions to speed up, but that outside force had no effect on the 1 who was immune to that cause? How can we ever be sure of anything?

If two models generate the same predictions, they are the same model, and the simpler (in the Kolgomorov complexity sense) is best understood as the truth (in so far as that concept is meaningful at all). A force acting on everything in the universe except one atom, or a (equal and opposite) force acting on that one atom, is the same thing[1], just as a universe where all distances are multiplied by two is indistinguishable from the current universe. Again, there's no way to make an observation from outside the universe; we can only make relative measurements, observe patterns, and use them to make predictions.

[1] ultimately, this comes down to: they generate the same sense-impressions that I subjectively experience - but for simplicity let's assume an objective universe exists, other humans exist, and we can observe the same things - I believe this assumption is justified as the most parsimonious explanation of the patterns I perceive in the sense-impressions I experience

> is best understood as the truth

No! It's preferred as an explanation because it is more elegant and convenient, NOT because it is more true. It is the same true!

That's just getting into semantics, which is pointless. What is "truth"? Ultimately, that depends on your point of view. If you base it off of experience (which is how you learn about everything in the first place), then the experience is "truth". If you base it off of something "outside" of yourself, that reference point itself becomes "truth". But of course, that reference point - be it real or not - is still something you imagine is there, and therefore might not be real, and the burden of referencing everything to that "source" of truth still falls on that one thing you are trying to avoid: experience. Sorry for being overly philosophical. For a continuation of this thought, try web searchs for "solipsism" and "world of mind".

Elsewhere in the thread someone gave the example of heliocentrism versus geocentrism. You can form a heliocentric model that makes accurate predictions, you just have to add epicycles to everything. But I would say that heliocentrism is not merely more elegant and more convenient, but also more true. Wouldn't you? For a more extreme example, in the story from http://lesswrong.com/lw/i4/belief_in_belief/ I think we would say that it isn't true that there's a dragon in the garage.

In that case however we have other data than just the model to suggest that geocentrism is false, whereas the topic of this thread is models in physics mathematics that merely differ in complexity, with no apparent difference in "truth".

> Just as a universe where all distances are multiplied by two is indistinguishable from the current universe.

Uh, wouldn't you have a speed of light problem? I think most of the fundamental forces are all inverse square laws, which would also make things weird.

I'm sure you have a much better understanding that my casual interest. But, uh, simple linear scaling seems detectable.

I mean a universe in which the speed of light was multiplied by two, and so was every linear distance measure.

so the earth is twice as big, but the same mass? seems like there are some detectable changes there. but maybe you're increasing mass in a really tricky way. it'll need to be more than double to have the same effect. at a given distance.

The other one that seems like it would be tough is strength of a magnetic field. inverse cube law, rather than inverse square. seems really hard to do something and get the same answers.

i'm an idiot. by distance you mean something more like a pure scalar value. if you double all the secret constants in the universe, we can't tell the difference.

You double k1 and k2. Now something involving k1*k1/k2 is twice it was before.

Why would it matter though? I read a analogy somewhere (in a Carl Sagan's book, I think) about how a goldfish in a convex fish bowl might create a set of rules for motion of objects that will work fine in predicting motion of objects as seen from inside the fish bowl but will be totally different from the true laws that people outside that bowl will formulate. As long as the rules keep working for the fish, why would the fish care if they are wrong? More importantly, how would you know that you are living in the outermost layer of reality? (not sure what the technical term should be)

As Vladimir Bartol famously opined: "Nothing is true."

How do we know for sure that we're not in the Matrix? Can we be sure? Does the very fact that we question our reality confirm our sentience or are our thoughts merely the output of algorithms we've been programmed with from the outset?

> How do we know for sure that we're not in the Matrix? Can we be sure?

If we observe no effects then the most parsimonious explanation for our experiences is that we're not. We can't ever be sure, because someone could be in the Matrix and have absolutely identical experiences to our own. Occam's Razor tells us what's most likely (and you can get more specific than that, putting numbers on it - see Kolgomorov complexity), but it's not 100% reliable.

> Does the very fact that we question our reality confirm our sentience or are our thoughts merely the output of algorithms we've been programmed with from the outset?

Try reexpressing that question in terms of something you could empirically observe. If you can't, the question probably isn't meaningful.

That concept of surety we cannot grasp with the observation tools we have available, but it's also not necessary to grasp it; the assumption that the 1 element was changing rather than the 111 only becomes functionally "incorrect" if it contradicts some other observation we make.

Beyond that, the grand truth of what's actually happening becomes a bit uselessly murky. The real function of Occam's Razor is to allow us to simplify models for our own benefit (because simpler models are easier to interpret and use), not necessarily because the simple answer is the Actual Truth(TM), which we can't know outside of observation.

There's a thought experiment in college philosophy: how do you know the universe wasn't created from nothing precisely six seconds ago, with all matter and energy in the universe arranged with the precise concentrations and momenta they would need to become the present universe in precisely six seconds?

> The real function of Occam's Razor is to allow us to simplify models for our own benefit (because simpler models are easier to interpret and use), not necessarily because the simple answer is the Actual Truth(TM), which we can't know outside of observation.

What about assigning greater prior probability to hypotheses that are simpler in some sense? Is there perhaps something to that too?

I'd say it's legitimate, just because simpler models have turned out to be true more often in the past, as best as we can tell.

Maybe even _that_ reasoning relies upon simple hypotheses being more likely. In this case, the simple, and therefore favoured, hypothesis would be that "models with a simplicity that is similar to that of other successful models are more likely to be true".

Assuming that other successful models are also true and not just a wolf in sheep's clothing.

Let's forget that I said "true", and switch it to "successful" instead.

That sounds like a more complex hypothesis to me.

Maybe it's simpler than "models with a simplicity that is dissimilar to that of other successful models are more likely to be true", though it's not obvious what should be considered simple and not.

Kolgomorov complexity seems like the obviously correct measure, though AIUI it's only defined relative to some fixed Turing machine.

I have an idea of doing a PageRank-style weighting of Turing machines, based on how simple/complex simulating one under another is. That would align with my intuition that most basic universal Turing machines are equally valid, but one that has (say) a short instruction that outputs one particular long sequence of symbols is probably not a valid machine to use.

Surely this is the same paradigm that would have opined Copernicus's heliocentric incorrect and the geocentric model accepted by the masses the correct model(?)

Is it not scientific method to prove correctness, not simpleness?

The geocentric model isn't simpler; that was the problem underpinning the shift to a heliocentric model.

The geocentric model required the addition of several epicycle adjustments with no observable cause. Re-framing the local system with the sun at the center eliminated most of the epicycles.

(... and the remaining errors in the heliocentric model relative to the observed motion led to the discovery of the moons and, eventually, Newton's gravitational theory. The driving function, overall, is simplification of the model by removing special cases and the need for acausal "I don't know why; this is what we observe" rules).

> and most easily explained by there being a single, consensus concept of time passing

... assuming everything holding that consensus is in the same intertial frame. ;)

First, people look really hard to discern whether or not the constants are constant. So far, they are. See [1-3] for quick examples.

Second, if the constants were changing, we could simply reference to the value of the constant on a certain date. As the rate of change is now guaranteed by existing experiments to be small, any shift would be very tiny, and easily calculable.

The question of the constancy of constants remains a very good one. That question is, by its very nature, its own constant of science.

[1] https://arxiv.org/abs/1501.00560

[2] https://www.nist.gov/publications/precision-atomic-spectrosc...

[3] http://iopscience.iop.org/article/10.1088/0264-9381/24/17/01...

We have not yet seen any indication that universal constants (or any other laws of physics) would change over time, therefore Occam's Razor suggest that we continue with the assumption that they don't until contrary evidence appears.

> If the measurements used to define these constants are defined in terms of the constants themselves, how would we see change?

Either the constants change such that we can measure the effect (e.g. the mass of atoms changes but the calibration of scales does not change accordingly), or they change such that our measurement apparatuses are equally affected. In the latter case, we will not be able to see the change, but then again, you could go into epistemology and argue that nothing has happened at all.

Yep. Too far down this road, and you arrive at Wolfram's observation that, hypothetically, the entire universe could be a simulation running as a cellular automaton with a single updating agent stepping the state of the universe interaction-by-interaction. It could take an arbitrarily-long time to run one "step" of the universe in that agent's timeframe, and life existing in that universe would have no way of knowing, because all of our processes for measuring time await the touch of that updating agent to progress.

If the universal constants change, we have far more to worry about than our measurements being inaccurate.

Also, we can view the past for many of these constants (gravity, for example) by looking in telescopes to places many millions or billions of light years away- and what we see reflects gravity and the speed of light being the same as it was then. Why would it change now? Occam's Razor applies.

>"we can view the past for many of these constants (gravity, for example) by looking in telescopes to places many millions or billions of light years away- and what we see reflects gravity and the speed of light being the same as it was then."

Isn't this circular? The concept of a light year (and the determination of how far you are looking into the past, etc) assumes a constant speed of light.

There are also phenomena such as the natural fission reactor at Oklo that demonstrates that the fine structure constant hasn’t changed over the past 2b years.

Part of the definition of this constant is c and pi. It is very hard to alter one constant without altering another.

https://en.wikipedia.org/wiki/Natural_nuclear_fission_reacto...

It's circular-ish, but we also see alignment in observable cosmic phenomena that strongly suggest the constants hold (such as the periodicity of pulsars being related to how fast they are moving relative to us, which we can measure via redshift).

Actually, the determination of how far you are looking into the past depends on both the constant speed of light _and_ the accelerating metric expansion of space:

https://en.wikipedia.org/wiki/Metric_expansion_of_space

The traditional values are no better. The metre is traditionally defined as one ten-millionth part of the distance between the geographic north pole and the equator along the Paris meridian. The planet does, and will continue to, slightly change its shape for the same reason that the traditional second - the sixtieth part of the sixtieth part of the twenty-fourth part of a day - has gotten quite a bit longer. The gram is traditionally defined as the mass of a cubic centimeter (or millilitre) of water at a specific temperature and pressure (and let's hope that we don't see changes in the behaviour of water molecules over time as well).

There's a sort of mythos about the metric system being all "sciency", but it's just as arbitrary as any other system when you get right down to it. A metre is one ten-millionth part of an arbitrarily selected measureable distance because, well, it's "about yay big", close enough to the yard (an ad hoc body measurement) everyone had been using anyway. (The nearest familiar alternatives would have been either two rods or a hand, or the French equivalents.) It's just easier to do the math in a lot of cases because base ten. Anchoring the values to something anyone can, in principle, measure anywhere in any reference frame, at least makes sure that we're all talking about the same thing - even if that thing changes. That said, there's no evidence for the proposition that they do change, and quite a bit to suggest they don't.

> The metre is traditionally defined as one ten-millionth part of the distance between the geographic north pole and the equator along the Paris meridian.

Not anymore: "The metre is defined as the length of the path travelled by light in a vacuum in 1/299 792 458 seconds." [1]

[1] https://en.wikipedia.org/wiki/Metre

In the case of the meter it definitely is. Space time is stretching so the meter will slowly get longer, but you won't notice

Interesting question, in that kilogram & second are only really handy ways for humans to be able to compare things to other things reliably. Using constants is presumably a more reliable way for the higher level comparisons to be reproducible. It's turtles all the way down...

Someone already provided a better answer than I can but just as another example. Constants can sometimes be a tricky name because in programming we think of constants as having a set value, but that’s not entirely what physicists mean. They mean values that have no units. Pure numbers as it were. Sure these may change or we may measure them better but by redefining our units in terms of these constants we kinda sidestep that. There isn’t anything to measure if that makes sense. The only thing to measure is what a meter is.

That isn't the case. Most physical constants do have units, such as G=6.67408(31)×10^−11 m^3⋅kg^−1⋅s^−2

You should read Liu Cixin’s The Three Body Problem I think you’d enjoy it.

Somewhat related but I believe there is some discussion that non observable parts of the universe (i.e. Really far away) may behave differently. Unfortunately these outer/early edges are going faster than the speed of light (I think) so we will probably never know.

Any such discussion is entirely in the realm of not science. Non-observable means not falsifiable means not science. Saying the non-observable universe is going faster than the speed of light is like saying God’s beard is orange.

Ok briefly observable but not anymore and never will be. And galaxies can move faster than the speed of light: https://m.phys.org/news/2015-10-galaxies-faster.html

I was going to correct that technicality on observable but was on mobile earlier.

Also you can absolutely have a theory that explains the observable universe reliably (i.e. Verifiable) but at the same time makes suggestions about the unobservable universe (for example most cosmos theories say the actual universe is bigger than the observable). We just don't have the technology or time to observe it yet.

Your link clarifies the statement. Space is expanding. Galaxies aren't actually moving FTL.

Yes I meant we can't see or go there because it's expanding / moving faster than we can get there (light).... I'm still not sure if I'm completely wrong or just misunderstood (given the downvote).