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.

Neptune- The original Dark Matter.

The author feels that this technique of deliberately lying will actually make it easier for you to learn the ideas. - Donald Knuth

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.

Neptune- The original Dark Matter.

The author feels that this technique of deliberately lying will actually make it easier for you to learn the ideas. - Donald Knuth

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.

Of course when you said history my ears perked up. Now, the previous sentence contains an "idiom". Those that are English second language may not understand what the meaning of the phrase is though they knew the definition of every word.

We are in a similar situation in science. We keep discovering new words and we think we understand what they mean, but we may not know the total context of what it means. All we can do is build the structure one brick at a time.

Because of this thread I rewatched Roger Penrose's Princeton lectures and he covered the same material as Nereid did in her preceding post and they are correct in the point that we can not look at what we know today and have any clue as to what we will know tomorrow. We come to knowledge via many paths (pun intended), hard work and research is certainly one of the ways, but not the only one. Serendipity surely plays a role, but also remember how Sir Fred Hoyle deduced that the carbon atom had to have a resonance in a particular range. If it didn't we would not exist. And it was found to be so. Therefore the anthropic principal can play a role as well and it is Lee Smolin and, Barrow and Tipler, that have spoke to this; and of course others.

We have the tools to make progress and that is all we can hope for. If someone over reaches, we can learn from that as well. Though we can not directly test the quantum realm I would say, as Penrose would, "I wouldn't worry about that too much".

Yes and no. Certainly these are concepts that we've created, but the question is, do they have some kind of corresponding elements in whatever reality is?

This seems to be more or less an argument from incredulity. It seems unlikely to you that we'd be able to understand reality, so you're just assuming that we don't. And then it seems amazing to you that our theories work at all, because it's "overwhelmingly obvious" that they don't bear any relation to what the universe is really like. I'm saying, maybe it's not that amazing. Maybe the reason our theories work so spectacularly well is that they do correspond to reality. Not perfectly, of course. But neither are they completely unrelated.

This is the attitude that I find strange. You seem to be assuming a priori that the universe is incomprehensible. So when theory does well, and the universe looks like maybe it is comprehensible after all, you instead hold to your postulate and insist, no, those are just models, we don't understand reality at all. The universe is not really filled with baryons and leptons and photons that interact according to certain rules. Instead, it must instead be something that we cannot ever hope to understand that for some odd (and presumably equally incomprehensible) reason happens to behave just like it were made of baryons and leptons and so forth.

I'm certainly not suggesting that we have everything figured out, and I'd even acknowledge that maybe we never will. But you seem to be taking the extreme point that reality is completely unknowable, and I don't think you actually have any evidence for that apart from your own intuition.

It is sad that we've lost so much of that. And I wouldn't suggest that we're intrinsically smarter than any of those people (actually, on average we're probably not nearly as smart as the ones whose writings have actually survived, since their ideas were the ones later people thought were worth copying down). On the other hand, they hadn't really come up with the idea of actually testing their ideas to see if they worked. The ideas seemed "reasonable", but as we've discovered, being reasonable isn't a good way to tell if that's the way things actually work.

Let's look closely at some of these more recent examples, though. Once we thought atoms were the smallest components of matter, and that they came in a large number of varieties. Later we realized that in fact, they have internal structure. Many of the properties of various types of atoms (that up until then could only be determined experimentally) could actually be deduced from theory. But even though we now know that atoms are composite entities, does that mean taht it no longer makes sense to talk about atoms? Or that many of the things that we had figured out about how atoms behave wer suddenly no longer true? No, that's not the case. So then we discover that the protons and neutrons in the nucleus aren't fundamental either. But even with the existence of quantum chromodynamics, is it meaningless now to talk about protons? Again, no. For that matter, with the development of quark theory, that changed what we (think we) know about protons quite a bit, but atoms, not so much. Moreover, I'd be willing to make a Hawking-like bet that any new theory we develop will still have elements in it that correspond to protons, electrons, and so forth. So, unless you want to deny the existence of objective reality altogether, I'd actualyl say that protons are real things. To be precise, there is an element of reality that corresponds to what we call protons. Of course it's almost certain that we don't understand them fully. But I don't think it's realistic to think that in 500 years our descendents might be laughing, "can you believe it, they believed in protons!" in the same way we might laugh about phlogiston.

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Conserve energy. Commute with the Hamiltonian.

To Grey:

Here Here!

My point exactly.

The trouble with models I find is that they are essentially mathematical abstractions. I feel they can model "reality" up to a certain point, beyond which the models break down. 0 dimensional points in QM, 1-dimensional strings in string theory. It is like looking through a microscope. All is well till we get the limits imposed by the equipment.

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“He who asks a question is a fool for five minutes; he who does not ask a question remains a fool forever”
Chinese proverb
"All you need in this life is ignorance and confidence - and then success is sure." - Mark Twain.

It appears to me that Grey and Ken G are dancing back and forth across this fuzzy border between (frontier) physics and metaphysics, with regards to the "nature of reality". In general, from my experiencing the natural world as a scientist I fall behind Grey's point of view. Whatever an electron or proton or photon "really is", there are physical phenomena which behave and interact as these "things" do. At the same time, it is a virtual certainty that we will learn still more about their natures in the future.

To a physicist (or scientist in general), reality is what kicks back when we kick it. With our physicist hat on, we don't care what "reality really is" beyond our ability to build a model that accurately predicts how nature behaves (kicks back). Metaphysicians (or philosophers) delve into questions of "well, but what does it mean?" or "what is it, really?" or even wonder whether such questions are meaningful in the universe we live in. However, as noted by Ken G (if I understood correctly), most people who aren't scientists don't understand that these really are separate issues. So I think he is "raising the consciousness" here on this forum. Those are cool questions to wonder about as long as you don't go too far overboard "waxing Platonic" (unless you don't believe in any semblance of objective reality). And one should also keep in mind that metaphysicians don't have laboratories.

Without becoming metaphysical, I would just be happy to know what space and matter actually are, even with the limitations imposed by our senses. Just be able to keep "zooming" in to smaller and smaller scales...

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“He who asks a question is a fool for five minutes; he who does not ask a question remains a fool forever”
Chinese proverb
"All you need in this life is ignorance and confidence - and then success is sure." - Mark Twain.

This latter statement is precisely what we do in science, and as we do our understanding becomes deeper and the theories (models) more general. In the first statement, however, you raised the question of "what ... actually are". And that's a rather loaded question, unless you care to define precisely by what you mean by "what ... actually are".

To try to make this more clear, despite the success of Quantum Electrodynamics (probably THE most successful scientific theory we have in its abilities to predict fundamental physical quantities), I don't think you will find too many physicists who would say that anyone knows what a photon or an electron "really are", beyond what our "mathematical abstractions" (as confirmed by observation/experiment) describe them to be. That's not the same thing as "we know nothing" of what they are (or the post-modernist view that physics is a study of WASP values) or that we won't gain a deeper understanding of them in the future (we certainly will).

Let me try. By "what.....actually are", I mean not an abstract mathematical model, but a sensorial visualization of particles and space at tiny scales (even if not actually possible....)

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“He who asks a question is a fool for five minutes; he who does not ask a question remains a fool forever”
Chinese proverb
"All you need in this life is ignorance and confidence - and then success is sure." - Mark Twain.

As I said, a loaded question...(sorry, don't mean to be flip about it). At the same time, too, we don't have a proper theory yet on the nature of space-time on the quantum scale. And I guess this is the issue that started this thread.

May I suggest some reading (which optimizes on physical, conceptual understanding with minimal math) for some deeper insight into the nature of matter and space?

The Fabric of the Cosmos, by Brian Greene

QED: The Strange Theory of Light and Matter, by Richard Feynmann

Patterns in the Void: Why Nothing is Important, by Sten Odenwald

In one sense, they most certainly do ... that's one way of interpreting the agreement between theory and experiment/observation.

But then, what's "space"? "time"? "energy"?

And couldn't one have made a strong case, back then, that "phlogiston" (a concept) also had some kind of correspondence with whatever reality is?I think that this 'they didn't really develop a good scientific method' is partly bad press.

For example, I read (in one of Robin Dunbar's books?) that Archimedes gets high marks ... for the things which we now know he could have tested (i.e. where he could test, he did - that's how he got it right). His mistake lay more in providing 'answers' in cases where he should have said 'I don't know'.

Another example: the 'applied science' results of the ancient Chinese are astonishing; the shortcoming (from our 'scientific method' perspective) is more to do with a lack of writing down the methods (and some apparent reluctance to engage in theory building and testing).IIRC, we had a discussion like this earlier, here in BAUT (I couldn't find it quickly though).

That there will be elements which remain recognisable, across some centuries (and maybe even a millenium or two) is, I'm sure, nearly certain.

What's not, surely, is which elements? And, how important will those elements be? (Back in the 21st century, there was the concept of "protons" and "electrons". We can see a trace of those concepts in our modern 33rd century {insert nearest equivalent of physics here}, as follows {insert explication of correspondence here}. Of course, with {insert 33rd century concept here}, it's obvious that these "proton" and "electron" concepts are, while not outright wrong, quite misleading).

Anyway, there was another sense in which I intended my 'history hat' - the nature of science itself.

If you look hard enough, you can see unmistakable sign of (proto-)science in even ancient hunter-gatherers, and a good correspondence to many key elements of modern science in many pre-industrial revolution societies.

What will 'science' look like, 500 or 2500 years from now? Perhaps the 'mutual incompatibility between GR and QM' will be a classic example in 33rd century textbooks, used to show the precursors of a key change in the nature of science (which didn't occur for another 100 years)?

This distinction is important to try to explain, when addressing the question in the OP.

And, as I said earlier, the mutual incompatibility is quite easy to explain, in terms of the theories themselves ... you can even do it at several different levels.

What I'm interested in is an explanation which doesn't require an extensive description of the nature of modern physics, models, theories, etc.

Odenwald's book is good, in terms of presenting the nature of 'space' and how (completely) that nature depends upon theory ... but it's a whole book!

While it may be quite challenging, I like the approach of showing that 'space' and 'time' are different, in GR and QM. The hard part is describing the incompatibility - many (most) people seem to have difficulty grasping, even faintly, just how different each is, in either GR or QM, from one's everyday sense (one's intuitive sense is very hard to put aside), let alone appreciating the difference between GR and QM.

Perhaps 'energy' might be an easier way to show the incompatibility?

I have read the first two. These books are a bit like chinese boxes I find. The more you open, the more questions remain. Guess we don't have a theory yet on space-time because QM deals with forces and particles, and GR which deals with space-time is not a quantum theory.

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“He who asks a question is a fool for five minutes; he who does not ask a question remains a fool forever”
Chinese proverb
"All you need in this life is ignorance and confidence - and then success is sure." - Mark Twain.

In respect to the incompatibility of QM and GR in respect to space time, isn't it because in GR space is smooth even at short distances, while under QM, it is foamy, due the Heisenberg uncertainty principle?

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“He who asks a question is a fool for five minutes; he who does not ask a question remains a fool forever”
Chinese proverb
"All you need in this life is ignorance and confidence - and then success is sure." - Mark Twain.