This thread is motivated by a number of posts in the ATM section, where the usual things we think we understand are blithely tossed about as being meaningful in the Planck regime (or era, or at the Planck scale, or ...) - length (or space), time, energy, mass, ...

GR and QM are mutually incompatible, and this mutual incompatibility becomes extreme in the Planck regime.

But what does this mean, in respect of how we might use terms like 'time', 'space', or 'energy'?

It's easy to say that one theory (GR) is 'background independent', and the other (QM) 'background dependent', and that the scale at which these two theories become nonsense, when one is interpreted in terms of the other, is the Planck scale.

How best to demonstrate this incompatibility, using 'time', 'energy', 'space'?

What are some good explanations - other than those using the math of each theory - that you've come across which show this incompatibility?

Is John Archibald Wheeler on this forum?

If so, please HELP!!!

............

What bothers me about "incompatibility at the Planck scale" is that the Planck scale is a completely unknown and untested regime of physics. I personally don't care at all what any theory says will happen at the Planck scale-- it's irrelevant whether or not they are "compatible" at a completely untested energy scale. Even if they made exactly the same predictions at that scale, I wouldn't pay more than passing attention to those predictions. In the complete absence of experimental verification, as exists at that scale, any theory is purely amusement for an idle mind, and is virtually guaranteed to be wrong. Must we learn that same lesson over and over?

One non-math explanation - which you can find on quite a few webpages, in various forms (including those with some math) is the following*:IOW, all the usual terms we feel we have an intuitive feel for - energy, in particular - require a 'something' in which to make sense. Whether that something is Newtonian or Einsteinian, it is continuous, at least wrt 'space' and 'time'. In the Planck regime (at the Planck scale), 'space' and 'time' can't be continuous ... if we apply one of the key results from quantum mechanics.

Ergo, not only does either GR or QM (or both) 'break down' at this scale (in this regime), but so do all the other things we intuitively feel are 'universal'.

It's not very satisfying; has anyone come across any better (non-math) explanation?

*Source

Another way to look at the problem is that Einstein's gravity has no uncertainty principle built into it, it just depends on the energy density, etc. Normally that wouldn't matter, as the uncertainty in the energy density of macroscopic objects is minute, but it is possible to have high mass but not be macroscopic-- at the Planck scale. So there you have individual particles (virtual, as Nereid was talking about) that have an important gravity. But individual particles are subject to the uncertainty principle, and the uncertainty on the Planck scale is enormous (the more you corral a particle, the more uncertain becomes its energy-- that's the uncertainty that make virtual particles possible). So how would a theory of gravity handle an uncertain energy?

But as I said, I'll bet a hundred other things also break down at that scale, and we'd need experiments to know.

Well, I'm not John Archibald Wheeler and I'm not an expert on QM, but do know a bit about GR and I think I can provide an explanation (I'm sure there are others here who can correct me where I'm wrong (cough Eta C, hint Celestial Mechanic). I want to point out that no matter how much one wants to separate the math from the explanation, you must realize that the reason QM and GR are incompatible is because of the math. There are two approaches to consider. Getting the math of QM to work with GR or using the math of GR to work with QM.


In the case of the first, extremely simplified, in Quantum Elelectrodynamics(QED) (EM force), when you calculate the force between two electrons, most of the time the you simply consider a photon being emitted from one of the electrons and being absorbed by the other electron. This is known as a coupling. However, an energetic enough photon, can produce a electron-positron pair while moving between the electrons (they would then annihilate each other and the photon produced from their annihilation would be absorbed by the second electron, another coupling. This second coupling is considered a "perturbation" and should be a small correction to the main "one photon between electrons" coupling. It turns out the when calculating the charge, all the possible types of couplings have to be considered. You would think that these small corrections shouldn't be a problem, however when those "perturbations" are considered, the equations diverge and you end up with infinities in the calculations.
A way around this was found by Shin'ichiro Tomonaga, Julian Schwinger, Richard Feynman(They shared the 1965 Nobel Physics prize for it) which has been dubbed "Renormalization". Again, extremely simplified, renormalization basically subtracting out the infinities (I know, I know, that's not allowed I hear you screaming, but there is a lot more involved, I'm just trying, per Nereid's post to stay away from any advanced math and give a simplified version). A similar process was found to work with the color force on gluons for quark interaction and was named Quantum Chromodynamics (note the chromo to designate the color force).
You might think that it should be simple to just use the "Perturbative Theory" used in QM to find a gravitational theory. This would use the graviton as the mediator of gravitational force, much like the the photon is the mediator of the EM force. The problem is, the renormalization techiques using in QED and QCD, don't work for the graviton. The reason has to do with the properties the graviton has to have to be compatible with GR. And it has to be compatible to get the match that there is between GR predictions and observations. It's extremely technical (translation, I don't understand it enough to provide a good explaination) and math intensive. So throw out this approach(however, see near the bottom of this post)
If that approach doesn't work, how about trying to get QM to fit in with GR? Well, you run right in to the backround problem. In GR, the backround (space-time) is dynamic. Both time and space can change depending on the energy in a given volume (this is what we normally refer to as gravity). In QM, the backround used is Minkowski space, which is a flat space-time with no changes. Once you use a dynamic backround, problems arise in QM (such as the Unruh effect, which simply states that the vacumn, is dependent on the path through spacetime. In other words, the vacumn effects predicted by QM (virtual pair production for example) depend on the path the observer follows and two different observers may not see the same thing. QM at present can't explain this. Another problem comes about by trying to fit the Heisenberg uncertainty principle (HUP) into GR. To calculate the effects of the gravitational field in GR, you need to localize the amound of energy in a given volume. Under the HUP, we can't know the location percise enough, within that volume, to calculate the gravitational field generated by the energy.
Now, with all these problems, let me point out that while we don't have a full quantum gravitational theory, there have been some success in combining the two in limited ways. The Laws of Quantum Mechanics in Curved Spacetime were first developed by Hawking and the most notable result is Hawking radiation from black holes. In addition, there has been success in calculating the first order quantum mechanical corrections to the gravitational potential between two masses using QM perturbative methods. So far, this only works in the low energy regime, where the infinities don't materialize.

There are quite a few other techincal details to work out. Anyone interested in the techical details or the math can find these by searching the web.

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Some try to tell me, thoughts they cannot defend,... - Moody Blues.

That's a nice summary. Every time I hear explanations like this about how reality is behaving, it just strikes me as so overwhelmingly obvious that this is not "really" what reality is doing. It's just a model that works, and often works quite well, amazingly. But of course, it also breaks down at some point, simply because it isn't what reality is doing. This should neither surprise nor bother us-- science was never about understanding reality completely. But a separate issue is, are we kidding ourselves that we'll ever understand the Planck domain, given the known lack of experimental probes? I would argue, certainly yes. We just have to at some point come to terms with our own limitations, and the limitations of science as a philosophical endeavor. As for building bridges and particle accelerators, it's great!

Thanks Ken.


Of course they're models. The professionals and serious amateurs are well aware of it and are neither surprised or bothered by it. They are also able to use different pictures of the model to explore different possibilities. The problems usually crop up when those who don't realize they are models (which is a large percentage of people) try to fit "reality"(whatever that is) into these models. I would also point out that the general public are the ones who want a simplified explanation. Most can’t follow the math and the explanations of what is happening is all they have to go by, which sounds to them like it is reality. Those people usually end up mixing up the models or different views of the models to try and solve some perceived problem within the model.


I would point out the applied science of building bridges and particle accelerators was, at some point, a limitation of science as a philosophical endeavor. That’s probably why I’m not all that thrilled (and really could care less) about the philosophy of science. I’m more interested in if a model works or doesn’t mathematically, how well it matches observations, and the predictive power of the model.

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Some try to tell me, thoughts they cannot defend,... - Moody Blues.

To some extent that's true, but note there are many professionals and serious amateurs on this forum, yet I would argue that a significant fraction of all the posts in the Q&A section are of a more scientific/philosophical bent than simply questions about "what does theory A say about situation B". Questions like that are generally viewed as too dry for most posters, to be frank. Let's face it-- the philosophical implications of the theories are of higher general interest, and that's the part that is very often overinterpreted by both the askers and the answerers of the questions. A quick perusal of the open threads at the moment provides many examples, including this one. Why on Earth would we even want to know about the Planck domain at this point in humanity's scientific quest, anyway?
I agree, I guess the issue is, to what extent does this statement hold for the majority of visitors to this forum.

And that is certainly the most solid scientific stance, and personally I think it resolves a lot of the tension between science and other forms of inquiry (a common topic for this forum). Still, then why are we concerned about the Planck domain? There are no observations to match, nor meaningful predictions to make, in that domain. Indeed, when one tries to match that domain to any of the actual observables in the universe, say dark energy, the numbers can be off by a hundred factors of 10. My point is, the Planck domain is already pure philosophy, with very little chance of ever not being so (unlike bridges, for example).

Ladies and Gentlemen may I point out that already 100 views have occurred of this comparatively short forum. There are only two links given here, but I still spent over an hour reading them and related links from them. The subject of the Planck domain is the frontier of human conceptualizations, the unknown. Feynman points out in the sixties that it is a "quantum world", so that is how things work. The deeper we investigate the better. Even if our math is on the order of a 100 powers of ten off today, it will get better, I have confidence in the sagacity of you and the ones who will follow you. Philosophical or not it is of great interest and a viable pursuit of thought.

Please, keep it coming.

I'm on the other side of this, actually. That is, I agree that these are just models, and that we use them because they work. But why is it "overwhelmingly obvious" that this is not what reality is like? Perhaps the reason that it works so well is that it actually is pretty close to what "real reality" is. Maybe photons really do take all possible paths from their source to their destination, having infinitely many virtual interactions along the way, just like a Feynman diagram suggests. I'm not saying that the universe must be working that way. I'm asking why it's obvious that it can't be.

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Conserve energy. Commute with the Hamiltonian.

Along these lines, may I recommend Lee Smolin's book, The Trouble with Physics? (this site lists two ISBN's; I thought there was only one, per book? ISBN-13/EAN: 9780618551057; ISBN-10: 0618551050).

I've just finished reading it, and found it very refreshing.

Back to the topic ... I'm still looking for a non-math way to describe the incompatibility - Tensor's post is good, but I suspect most folks' eyes will glaze over when you try to explain why infinities in the expansion series terms is a (fatal) problem* ...

One approach I've considered is to try to show that 'time', 'energy', and 'space' (etc) are just as much 'models' (or 'theory-dependent') as, say, 'isospin' or 'colour charge'. IOW, there is no fundamental thing about the universe, independent of theory (or models), which you can assume exists, despite one's intuition and what one has picked up from being an intelligent, avid reader. You know what I'm talking about - whatever theory of gravity we have, or quantum theory, 'energy is conserved', or 'the first law of thermodynamics is valid', or 'space and time exist, period'.

*Apropos of which, I didn't realise that string theory hasn't got beyond showing that the second (or was it the third?) term is finite, much less showing that the infinite series isn't infinite ... well, that's what Smolin says ...

But what's a photon? What's a "path"? These are all human constructions, and we're just smart apes. How spectacularly unlikely is it that this is what reality "really" does? Then factor in the fact that it breaks down at some scale, so how does reality "get across" those scales to build these paths and these photons? Simply because we have five senses and a meager brain, and have had great successes with them, should we take this is as reason to suspect that reality will give up its secrets to us with millennia of effort and contemplation? I sorely doubt it. I don't even think reality has the slightest concept of a number, let alone a location or a path or a photon that would require such quantification. It just follows some immutable and spectacularly incomprehensible rules of being, i.e., it is what it is. Human conceptualizations are actually an effort to replace reality with something else, something smaller and more comprehensible (ergo Occam's razor), and the introduction of numbers and mathematics helped that process a lot for some sublimely profound reason. That this works so well in some situations is what is so amazing, but I do not see that as very good evidence at all that we are "close" to comprehending the most fundamental rules of existence. Not close at all, I should think (as per the "Planck domain").

All of a sudden I'm thinking I should dust off my college calculus book from way back.

Yes, that's very much the way I'm thinking about the question. It all has to do with the fact that we can standardize the measurement of certain things-- and we are then limited to try and cobble together a theory of everything by connecting these measurables. To me, that's kind of like trying to explain why a painting is great by looking at the pigments it used and the ratios of various proportions in the figures depicted. There may be much to be learned about the art of painting by considering such measurables, but they will never serve to reconstitute that art in its entirety.

To sum that up, one could define science as the study of the projection of reality onto the objectively measurable domain, but there is little or no reason to expect that projection to produce a one-to-one restoration of all that is happening "in reality". There is, however, the legitimate question of what elements of reality survive that projection, and what elements do not. I expect that a true "theory of everything" would not survive such a projection, but a more apropos question is, can there even be a theory of all the things that do survive the projection, or do the most sublime elements underlying even the projection require something that does not survive it? That's the element that I think people like Dawkins are overlooking.

When I get thoughts like these, I put on my 'history hat'.

That there were really, really smart people in ancient Greece, Rome, China, India, ... is where I start from. Sadly, much of what these really smart people worked out is lost to us - no written records survive.

However, from what does survive, we can get a sense of just how reasonable it seemed to those folk that 'air, water, fire, earth' was pretty close to what real reality is.

Or, to take a more recent example, phlogiston.

From ancient Greece to today is a mere ~2500 years (and ~500 from phlogiston); did the universe change so dramatically in such a short time? Or did we?

If we could fast forward 500, or 2500, years, how much like phlogiston, or earth/air/water/fire, would 'photons' and 'Feynman diagrams' seem?

An easier way to see this: between the proton and the top quark is what, ~2 OOM (in mass)? Add in the electron, and it's ~5 OOM. When the LHC comes on stream, we will get up to ~10 TeV, which will be another ~2 OOM.

Look at all the richness of the universe, in those ~6 OOM!

Yet we have detected cosmic rays with energies of ~10²⁰ eV ... there are more decades, in particle energy, between what the LHC will reach and these EHECRs as between the electron and top quark. What richness is there, in the universe, in these ~7 OOM?

Or take the Planck length, and compare it with the shortest distance we have been able to probe so far; then compare that with how rich the universe is, in classes of phenomena, between a thousandth of a proton's radius and (say) the solar system.

Well put, that's my page exactly. Granted, there's nothing wrong with being optimistic about what humanity may one day know about our universe, and there's nothing wrong with Grey taking the view that we should worry about phenomena only when we run into it in our theories or observations, but the danger is that such a present-ocentric view tends to lead to scientific hubris. I'm not saying there's any hubris in Grey's stated position, the hubris tends to appear more when science 'faces off' against non-quantitative or non-objective attempts at knowing something about our reality. When that happens, I feel all camps are best left to defend their own turf, but not to "invade" into the turf of the other approaches except on grounds that they are being intellectually dishonest or untrue to their own stated art. I pretty much cringe every time I hear the absurd phrase "theory of everything", and theories about the Planck domain give me a similar sensation.