Wednesday, August 28, 2013

At the edge of our knowledge

I have had a question for a while now, and I mull it over from time to time. Not really knowing what to do with it, I want to put it here and let other people play with it too. I suspect that this question may make a strong point about epistemology and knowledge in general, and I'm looking forward to feedback.

The motivation for my thinking is the current debate between quantum loop gravity and string theory, the details of which are not needed for this discussion (which is good, because I don't know them!). All that's needed is that we have two theories here that posit fundamentally different mechanisms of behavior for reality--two different and incompatible claims as to what is really going on--and yet our ability to measure is not sufficiently refined to choose which is the better theory. The way I originally had this explained to me (by a physicist working to advance string theory) is that the theory is a couple of decimal places ahead of what we can currently measure.

Now, I expect measurements will catch up with those theories eventually, but it makes me wonder about something. Suppose that we're far in the future, and we have much more refined instrumentation and technique for making measurements. In fact, we're very near being able to measure at the Planck scale, or if needed, something beyond that--a place where it becomes physically impossible, for whatever set of reasons, to make better measurements.

Suppose, then, that we have two different and incompatible explanations of reality that make identical predictions down to this limit, perhaps even that could be resolved with a few more decimal places of accuracy in measurements (that we cannot have due to physical limitations). This is what I'm wondering about.

Is it conceivable that we could hit a place where our theories are able to make more accurate predictions than we can experimentally verify? More importantly, if so, could such theories actually be different and incompatible (or must there be some uniqueness requirement that prevents it)? Of key importance, does this, if such a limitation exists, present a strong argument that we have no basis upon which to claim that our theories actually describe reality?

Even if there is no real physical limitation for obtaining more accurate data, this problem may still exist in a softer sense. It is conceivable that our theoretical models will always be able to be at least a few decimal places of accuracy ahead of what we can measure, rendering a soft version of the same question.

Anyone that wants to play with it, in comments or otherwise, is strongly encouraged to do so.


  1. This comment has been removed by a blog administrator.

  2. It's a great question and I'm pleased to see that you are open-minded about it. I am honestly too stupid (or at best, uneducated enough) to help you try to figure it out, but if or when you do, it will be interesting to find out the answer. For no reason (other than fun) I'd like to place bets that both theories are wrong, and wait and see what happens. Can either of these theories answer the ontological question "Why is there something rather than nothing?" Lastly as a nit-pick, isn't string theory technically now M-theory, or are there some differences of which I'm not aware? Also it's interesting to me that top scientists seem radically opposed, from the string theory wiki entry: "According to Hawking in particular, 'M-theory is the ONLY candidate for a complete theory of the universe.'[3] Other physicists, such as Richard Feynman,[4][5] Roger Penrose,[6] and Sheldon Lee Glashow,[7] have criticized string theory for not providing novel experimental predictions at accessible energy scales and say that it is a failure as a theory of everything."

    1. It's important not to get bogged down in particular theories here for this question. I realize current theories will be outstripped, updated, etc.

      The question is really about how we interpret the situation--if it is possible (and if not, why?)--where we have two different, incompatible theories that cannot be resolved empirically. This is entirely hypothetical and might not even be possible, though I haven't seen a good argument for why it isn't.

      A second, related question I neglected to mention in the original (and may edit in) is how we might go about choosing between such theories, should such a situation arise.

  3. Hi there,

    The question of what status to grant our theories if there are fundamental limits on what we can observe is an interesting one. To start at the end, as it were, with your question in bold, I'd suggest that a limit on what can be observed need not force us to stop saying that our theories describe reality. After all, we know that in high gravity Newtonian mechanics ceases to describe reality accurately, but this doesn't change the fact that it is an incredibly good at modelling large portions of reality. Likewise General Relativity can't tell us what happens at the centre of a black hole, but does a very good job of handling just about everything else at the macro scale. Perhaps all we need to recognise is that physical theories always come with implicit caveats about the domains and scales of reality that they claim to model.

    Even recognising this, the question still stands of course: what should we say about theories whose only disagreements lie below a threshold which we know for fact marks the limit of measurement? The first theory says A should be the case below the threshold, the second theory says it should be B. A and B represent different states of affairs, but the observable portion of the universe would look identical whichever was the case (otherwise we could make the measurement indirectly). This seems to me to be similar to the situation with Deism, and we should adopt as true the theory with the least ontological commitments, as a matter of wise convention.

    If we were faced with the more interesting case that both theories were equivalently minimal in what they posit, we may have to bite the bullet and say that there is simply no fact of the matter. What we're left with here is something like a deep physical version of Quine's Indeterminacy of Translation, where two descriptions of reality are indistinguishable but nonetheless different.

    As a bit of a footnote, Daniel Dennett has suggested that if there is a indeterministic component in the universe (perhaps provided by quantum tomfoolery), then situations like this could even arise at the macro-level, without there needing to be any limits on what is observable (particularly in relation to intention systems - see his paper Real Patterns, linked below).



    1. Your thinking matches mine very closely here. Thanks for your comment!

  4. James, this situation already exists in quantum mechanics. The rival interpretations in quantum mechanics are all compatible with the data and there is no test that can decide between them.

    Consider what happens when a photon approaches two slits. What happens next? Is there a pilot wave that senses the two slits and guides the photon through one of them (hidden variables interpretation)? Does the Universe split in two and the photon goes through one slit in one universe and the other slit in the other (many-worlds interpretation)? Or is it meaningless to say which slit the photon goes through (Copenhagen interpretation)?

    If there is no experiment that can determine which interpretation is correct what can we say about the nature of reality? Are we entitled to make a judgement on metaphysical or aesthetic grounds?

    1. I don't disagree--and I think the question of how we choose between such theories/interpretations is a very interesting one.

      However, this problem could be circumvented by finding something that subsumes QM entirely, so these interpretations might be artifacts of something fundamentally wrong with the assumptions of QM, so I don't want to jump on board and say "this situation already exists" as I've posed it. I want the situation, for philosophical reasons, to literally be beyond redemption by any possible empirical method, as a thought experiment.

      I'm also directly interested in if such a situation is possible. I strongly suspect it is, and I think that makes a powerful case that our physical models, theories, and interpretations are literally best-guesses at trying to make sense of reality and may or may not actually describe the "true nature of" reality.

      Particularly, I want to establish that we have an epistemic gap between our models, etc., and reality and that that is totally okay (i.e. we need not stuff some kind of religious explanation in there to try to account for it) because that epistemic gap is very narrow. I also want to unseat Platonism and uncareful realism, though I do have confidence that there is a real physical reality that we are a part of.

  5. I think it's unnecessary to assume that our ability to precisely measure our reality is what establishes our epistemological horizon. A much simpler argument exists for that: It is impossible to distinguish between a "physical" reality and one that is simply a computational simulation existing in an underlying reality. If we exist in a simulation, we have no access to the underlying reality that encompasses our own. Consequently we could make infinitely precise measurements about what we perceive to be reality, but nonetheless, be completely in error about how reality actually functions. Furthermore, if our reality IS a simulation, it could be structured in a manner that misleads us from it's actual implementation, thereby undermining even that knowledge.