See the sibling comment for another version of this argument, but finding the weird mathematical coincidences between the competing mathematical theories of nature is very useful. In other words, there are mathematical and logical tests that can be as important as experimental tests for the progress of our understanding of nature.
It turns out it is the exact opposite: general relativity effects prevail [0]. Thanks for forcing me to check!
> Special Relativity predicts that the on-board atomic clocks [...] should fall behind clocks on the ground by about 7 microseconds per day [...] due to the time dilatation effect of their relative motion.
> Further, the satellites are in orbits [...] where the curvature of spacetime due to the Earth's mass is less than it is at the Earth's surface. A prediction of General Relativity is that clocks closer to a massive object will seem to tick more slowly [...]. A calculation using General Relativity predicts that the clocks in each GPS satellite should get ahead of ground-based clocks by 45 microseconds per day.
> The combination of these two relativitic effects means that the clocks on-board each satellite should tick faster than identical clocks on the ground by about 38 microseconds per day (45-7=38)!
[0] http://www.astronomy.ohio-state.edu/~pogge/Ast162/Unit5/gps....
This is a sincere question, and I care to hear your opinion: do you believe that a reader of phys.org would need more than a glance at the article to know this is a discovery about the mathematics of general relativity, not an engineering breakthrough in the creation of a scifi-like hyperdrive?
That's an overstatement. Measurements are more important than theory. We cannot form theories without measurements, and yes theories inform our measurements, but science always begins and moves forward with measurements.
Edit: Unrelated, but I see you’re a fellow Greg Egan fan, good to meet you! Planck Dive has to be one of my all time favorites.
Same with GR: it was a purely mathematical construct for a while until we could test it, but there were too many theory clues that it must be right.
And this is not selection/survival bias: it is extremely rare for humanity to find a robust mathematical construct for which we can have a high degree of certainty that it describes the universe well. In the few cases where we have had that certainty, due to mathematical proofs in seemingly disjoint fields, we ended up being right.
To push it to stuff like super strings and quantum gravity: few respected scientists would claim that their pet mathematical construct is correct, but many of them will say "the vague commonalities between all these diverse and seemingly unrelated mathematical constructs definitely point to an underlying fundamental construct".
We use scientific models because they are useful not because they are fact. Even if our model does not always match our observations it can still be a useful model in some circumstances. It's very important when talking about science that we understand that it isn't fact. It is a model. It might be a good model. It might be a bad model. It might be a useful model for our application. It might be a poor model for our application. That's it.
When you see a headline that says "X is Y" and it's about a scientific model, what that means is "If our model is consistent with the real world then the model predicts that we should find that X appears to be Y in the real world". But that's a bit too long to put in a headline and you would have to do it for every scientific conversation.
It is extremely unfortunate that on the first day of junior high school when you start doing "proper" science classes that they don't sit people down and explain what a scientific model is. Mostly I think it's because the teachers don't know, because their teachers never taught them.
Double-plus goodthink, comrade!
There are some results around QG, such as holography, which seem to be universal. That is, they make sense with strings, loop quantum gravity or any of about ten other lines of work that people can do quantum gravity calculations with today.
If you can prove that all of those have to say the same thing, that is a powerful result and probably means something about our world.
It seems pretty reasonable that wormholes could exist so long as they don't form closed-timelike curves, so I think these people are getting at the quantum roots of the "cosmic censorship principle".
"Wormholes" are two entangled black holes that have been subsequently moved light years apart, preserving the entanglement during the move. They are a great mathematical toy for exploring the nature of entanglement.
But that's it. We have trouble preserving the entanglement of just a few ultra cold particles for a few milliseconds. I am far^^^far more likely to fall onto the floor by quantum tunnelling through my chair than a useful wormhole ever appearing. Postulating they actually exist is not in the slightest bit reasonable.
Here is a fantastically interesting article that maybe has some new insight on the nature of spacetime; top comment on HN thread about it is some person loudly and incredibly pretentiously mistaking their own misunderstanding of the intricacies of 'truth' in science (and how there are different levels) for some flaw in the work itself.
You know, the underlying sentiment here is a good one. How do we know what we know, what do our theories really tell us, etc. All excellent questions. But you didn't express that at all, instead you say these things shouldn't be 'touted as discoveries about the real world.'
That's all you man! No theorist ever has wanted people to think this of their work, it slaughters the beautiful intricacies of it and leads to public relations disasters like this.
Don't go misunderstanding shit and then confidently be blaming it on other people man. Rhetoric matters.
The whole "it's just a theory" thing has done so much harm to public understanding and appreciation. It's an impossible starting point for a conversation, if you think "it's just a theory", you're not wrong, as much as entirely missing the point. How do you start with that and get to an understanding that things aren't always absolutely right or wrong, that contexts and assumptions matter, that things can be true in one setting (the math) and uncertain in another (the real world). That for most things what we are more than anything is uncertain. That there are many different kinds of uncertainty.
How are the subtle intricacies of things (that the answer to almost everything starts with "well, that depends...") supposed to survive forums where conversations are heavily selected for ability to grab attention? Not a rhetorical question, if you got ideas I want to hear them.
PS noobermin, I don't mean to be overly-critical of you although it sure sounds like it. I'm using 'you the pronoun'. Just something I think about a lot that you catalyzed me into trying to express...
This, to me, shows a rather sophisticated understanding of scientific truth, namely that we should demand that a scientific theory (as opposed to a mathematical construction) should be falsifiable. AFAIK, there is no question that the mathematics of string theory et. al is sound; the question is whether these theories are physical, and whether they are falsifiable. These are the exact objections the top-level comment makes when referring to "unestablished and untested theories".
From a sibling comment:
> There are some results around QG, such as holography, which seem to be universal. That is, they make sense with strings, loop quantum gravity or any of about ten other lines of work that people can do quantum gravity calculations with today.
> If you can prove that all of those have to say the same thing, that is a powerful result and probably means something about our world.
OTOH, it does matter if you are able to make a statement of the form "Any mathematical construct that accurately describes X must have property Y." It is not clear that quantum gravity (or the linked article) meets this latter standard.
Here are a few premises on which I based my statement (I will pick one particular venue of scientific research, so I will not speak in all generality. You can of course disagree and say that it does not generalize at all, but I think this would be a philosophical discussion, i.e. it does not matter at all that we have different opinions, as both are equally valid ways of pursuing scientific truth):
1. Computational complexity is a science on its own. Computational complexity also makes useful statements about the limits of the physical laws in our universe (a la "extended Church-Turing thesis" or Aaronsons "NP-complete problems and physical reality").
2. NP=P vs NP!=P is a question that has a definite answer within the relm of science but we do not know the answer yet. The answer will constrain what the permitted laws of physics are due to point 1 above.
3. There are a lot of clues that NP!=P coming from very separate disjoint fields of math. Mainly because we already know there are a lot of "phase transition"-like phenomena when we apply approximate algorithms to problems that can be parameterized to be NP-complete only if some ε is larger than some critical value.
4. These "phase transitions" are purely mathematical constructs, but due to the previous points they constrain what is permitted in the universe as strongly as any 5-sigma measurement in a particle accelerator.
To bring this back to the discussion of speculative theories of quantum gravity: if all of the competing theories of quantum gravity (all of them being very speculative and unproven) have a handful universally agreed on predictions (although derived in completely separate ways), this is as strong of a constraint as any 5-sigma measurement in a particle accelerator or cosmological observation.
Or if you permit me to attempt to phrase is it in yet another way: there are a ton of theory assumption behind any 5-sigma (or 10-sigma) experimental measurement. These assumptions are the same ones that inform the purely mathematical constraints. If both the math constraints and the interpretation of an experiment are based on the same assumption, why are you taking the interpretation of the experiment any more seriously than the pure math.
Sorry for the length of this text - I am finishing my dissertation this week (doctorate in physics), so this is very much on my mind at the moment.
Because math models the experiment, it does not define it's results.
Even math as fundamental as the laws of thermodynamics does not constrain what is permitted; they are axioms which describe the universe as best we are able to view it. If all competing theories of quantum gravity agree on a point, it would mean almost[1] nothing until that point is observed.
From the outside it feels like there is a fallacy common in at least some branches of physics (string theory...) where over-fitting math is equated with insight.
[1]I suppose you could break out Bayes' theorem and try to work out a prior for comparable theories being wrong, degree of independence between theories, etc...
And there it is hardly over fitting when the same results come from vastly different mathematical constructs.
The irony here is that, although I am a professional software engineer, the entirety of my post-secondary education is in mathematics. I did some research in graph theory when I was in grad school, so I am actually quite familiar with this notion of "phase transition" that you're referring to. But, I also don't consider mathematics to be a science, because I define "science" in the same way as Wikipedia: "...a systematic enterprise that builds and organizes knowledge in the form of testable explanations and predictions about the universe." There are many things mathematics can describe that are inherently unphysical, which, IMO, makes mathematics itself not a science, however excellent a tool for science it is. And, it's on this basis that I'd come at all of your points 1-4.
Regarding QG theories and their explanatory power, I would say that the fact that they have a handful of universally agreed upon predictions does not make any one of them correct in the least. The value in any one theory of QG is not in the areas where it agrees with other theories of QG; it's in where that theory disagrees with established theory in a way that we can see in a lab, a telescope, or an accelerator. What we're trusting here is the physical behavior of the universe, and we're hoping that it's correctly predicted by the mathematical construct that is the theory.
The fact that its theoretical is mentioned in the article for anyone that bothered to read past the first few paragraphs. For the rest of us, it just makes for interesting party conversation whether the theory pans out or not (which couldn't be proven by actually transiting a wormhole within any of our lifetimes)
So no harm, no foul -- anything that makes theoretical science interesting in the popular press is a win in my book.