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Or is there some way that they co-exist?

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Or is there some way that they co-exist?

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HallsofIvy

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JesseM

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Also note that string theory apparently "reproduces general relativity" in some sense (I don't understand the details, but it was discussed a little in this thread), yet also contains gravitons.I hear physicists saying that the "quantum of the gravitational force" is something called a graviton. Doesn't general relativity say that gravity isn't a force at all?

You don't have to accept that gravity is a "force" in order to believe that gravitons might exist. According to QM, anything that behaves like a harmonic oscillator has discrete energy levels, as I said in part 1. General relativity allows gravitational waves, ripples in the geometry of spacetime which travel at the speed of light. Under a certain definition of gravitational energy (a tricky subject), the wave can be said to carry energy. If QM is ever successfully applied to GR, it seems sensible to expect that these oscillations will also possess discrete "gravitational energies," corresponding to different numbers of gravitons.

Quantum gravity is not yet a complete, established theory, so gravitons are still speculative. It is also unlikely that individual gravitons will be detected any time in the near future.

Furthermore, it is not at all clear that it will be useful to think of gravitational "forces," such as the one that sticks you to the earth's surface, as mediated by virtual gravitons. The notion of virtual particles mediating static forces comes from perturbation theory, and if there is one thing we know about quantum gravity, it's that the usual way of doing perturbation theory doesn't work.

Quantum field theory is plagued with infinities, which show up in diagrams in which virtual particles go in closed loops. Normally these infinities can be gotten rid of by "renormalization," in which infinite "counterterms" cancel the infinite parts of the diagrams, leaving finite results for experimentally observable quantities. Renormalization works for QED and the other field theories used to describe particle interactions, but it fails when applied to gravity. Graviton loops generate an infinite family of counterterms. The theory ends up with an infinite number of free parameters, and it's no theory at all. Other approaches to quantum gravity are needed, and they might not describe static fields with virtual gravitons.

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Einstein tells us that gravity is a pseudo-force (like the centrifugal force): Massive objects only

On the graviton accounts, a massless elementary particle is introduced to mediate the force of gravity. These accounts are incommensurable with General Relativity (if we assume the principle of bivalence). In GR, there is neither room nor need for any mediation of gravity: it is a local phenomenon produced by the curvature of spacetime. It is worth noting that while the empirical evidence in support of GR is extensive (

Perhaps an expert could weigh in better than I on these matters; but the graviton seems to me hugely problematic. For example, even though a graviton (call it G1) is massless, it should still itself feel the force of gravity (like the photon does). However, then we must introduce new gravitons (G2) to transmit that force to G1. But then gravitons (G3) must be introduced to transmit the force to the G2. And on and on it goes: The problem of infinite regress.

As for your specific question, "If gravitons exist, does that mean spacetime is not curved by mass?":

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DaveC426913

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: blink blink : Surely "some clever physicist" that managed to wed quantum theory and general relativity would be celebrated as creator of one of the greatest solutions of the century.As for your specific question, "If gravitons exist, does that mean spacetime is not curved by mass?":Prima facie, yes. Although some clever physicist might be able to develop a theory where they both live happily together. However, such a theory would doubtless be unnecessarily complex and have no particular predictive power, and therefore should be rejected on grounds of parsimony.

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"Curved space-time" is nothing more, and nothing less, than a description of how distances behave. Philosophically, I'd say that the relevant question to whether curved space-time "exists" is the philosophical question of whether spacetime "exists". Whether or not the graviton exists or not is basically irrelevant. As long as space exists, and as long as what our standard rulers measure is "distance" (and our standard clocks measure time), space-time can be said to be curved. One would have to abolish the notion of spacetime altogether (perhaps replacing them with some sort of quantum foam: this has been proposed by Wheeler), or redefine the notion of distance, in order to get rid of this curvature.Or is there some way that they co-exist?

The notion of "existence" isn't a scientific question, but a philosophical one. Our philosophy forum is unfortunately not all that strong, but this seems like the best place for this question to me, so I'm moving it there.

Some other aspects of the graviton (specifcally, questions about whether or not it "exists" in quantum gravity) have been discussed in "Beyond the standard model", https://www.physicsforums.com/showthread.php?t=198464) but this doesn't seem to be what the OP is asking about. In case it is, though, I thought I'd mention it.

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Of course. But that's not what I said. I was talking about a consistent theory of gravity that included two: blink blink : Surely "some clever physicist" that managed to wed quantum theory and general relativity would be celebrated as creator of one of the greatest solutions of the century.

---

I don't think that's true. Photons"Curved space-time" is nothing more, and nothing less, than a description of how distances behave. Philosophically, I'd say that the relevant question to whether curved space-time "exists" is the philosophical question of whether spacetime "exists". Whether or not the graviton exists or not is basically irrelevant. As long as space exists, and as long as what our standard rulers measure is "distance" (and our standard clocks measure time), space-time can be said to be curved. One would have to abolish the notion of spacetime altogether (perhaps replacing them with some sort of quantum foam: this has been proposed by Wheeler), or redefine the notion of distance, in order to get rid of this curvature.

The notion of "existence" isn't a scientific question, but a philosophical one.

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I'm curious about that, I've heard during inflation it is believed that space expanded at faster than light speed, hypothetical warp engines if possible are believed to warp space to cause a region of space to move at faster than light speed. Yet I've also heard people believe, though it hasn't been proved without dispute, that gravity can only warp/change space at lightspeed.

So how is it the belief that space can change at faster than light speed(expansion during inflation), reconciled with the belief that it can't change at faster than light speed(gravity warping.)?

If there is no graviton, what exactly limits the speed of changes to space during gravity warping but not its expansion?

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JesseM

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Why are they prima facie incommensurable? This seems more like an "argument from incredulity" than anything else. Did you note what I said in my last post about how string theory "naturally" ended up reproducing general relativity, even though it was not originally constructed to be a theory of gravity, and that this was one of the major reasons physicists consider it to be a promising route to a theory of quantum gravity? I recommend reading through the thread on this which I linked to earlier.Of course. But that's not what I said. I was talking about a consistent theory of gravity that included twoprima facieincommensurable accounts: Curved spacetime and the graviton. If such a theory could be produced (e.g.one in which gravitons don't travel along geodesics), it would be interesting but scientifically bloated and useless.

But the electromagnetic force between charged particles doesn't depend on the measurable type of photons, it depends onKingOrdo said:I don't think that's true. Photonsreallyexist. They're hitting your face right now.

By the way, you mentioned that you objected to the idea that "gravitons don't travel along geodesics", but if you were talking about

Gravitons don't exist in general relativity, because GR is not a quantum theory. They might be part of a theory of quantum gravity when it is completely developed, but even then it might not be best to describe gravitational attraction as produced by virtual gravitons. See the physics FAQ on virtual particles for a discussion of this.

Nevertheless, the question in this form is still worth asking, because black holes can have static electric fields, and we know that these may be described in terms of virtual photons. So how do the virtual photons get out of the event horizon? Well, for one thing, they can come from the charged matter prior to collapse, just like classical effects. In addition, however, virtual particles aren't confined to the interiors of light cones: they can go faster than light! Consequently the event horizon, which is really just a surface that moves at the speed of light, presents no barrier.

I couldn't use these virtual photons after falling into the hole to communicate with you outside the hole; nor could I escape from the hole by somehow turning myself into virtual particles. The reason is that virtual particles don't carry any information outside the light cone. See the physics FAQ on virtual particles for details.

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They areWhy are they prima facie incommensurable? This seems more like an "argument from incredulity" than anything else. Did you note what I said in my last post about how string theory "naturally" ended up reproducing general relativity, even though it was not originally constructed to be a theory of gravity, and that this was one of the major reasons physicists consider it to be a promising route to a theory of quantum gravity? I recommend reading through the thread on this which I linked to earlier.

And, again, there are serious technical problem with including the graviton, like the infinite regress I mentioned above.

No. And I think you're missing the point. There are either gravitons or there aren't. There are, again, real photons. They are hitting you in the face right now. There are or there aren't real gravitons. If there are, they are in principle measurable. But one should not posit the existence of particles for which we have no need. Gravitation is very nicely described by Einstein, and--more important--his account has been very extensivelyBut the electromagnetic force between charged particles doesn't depend on the measurable type of photons, it depends onvirtualphotons which only appears in the Feynman diagrams that are summed together to make predictions in quantum electrodynamics, some would consider this nothing more than a mathematical technique that tells us nothing about what's "really" going on at the quantum level (see sections 3 and 4 of arnold neumaier's theoretical physics FAQ for example). Measurable photons are only seen in situations where you'd have an electromagneticwavecreated by accelerating charges in classical electromagnetism. Similarly, measurable gravitons, if they exist, would only be seen in situations where GR predicts gravitational waves. And the section of the virtual particles FAQ I quoted in my last post says that in this case, the notion of "gravitons" means little more than the idea that, in a theory of quantum gravity, the energy levels of gravitational waves would be quantized rather than continuous. Do you have reason to think there is something wrong with the assumption that a theory of quantum gravity would probably give gravitational waves with quantized energy?

I'm not talking about that. I'm talking aboutBy the way, you mentioned that you objected to the idea that "gravitons don't travel along geodesics", but if you were talking aboutvirtualgravitons it's worth pointing out that virtual photons aren't treated as traveling along geodesics either--see How does the gravity get out of a black hole? from the Usenet Physics FAQ:

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JesseM

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The reason mediating particles are not included in GR has nothing to do with "Occam's razor", it's just that they don't happen to appear in the theory's mathematical structure; the theory doesn't tell youThey areprima facie, and perhapsultima facie, incommensurable because they are two totally different accounts of why massive objects tend to move toward each other. General Relativity does not require mediating particles to explain these phenomena; therefore, in accordance with Occam's razor, they are not included.

Why a "redundancy"? You'd have a new theory that made the same predictions as GR in certain limits, just like with Newtonian mechanics and GR; the new graviton-based theory would also be expected to differ from GR at the Planck scale, so it wouldn't be precisely identical.KingOrdo said:If the graviton serves a role in gravitation isomorphic to the role the photon serves in electromagnetism, then we have a redundancy assuming General Relativty is true. This is (at least) aprima facieproblem.

I agree, but my point is that "if the graviton serves a role in gravitation isomorphic to the role the photon serves in electromagnetism", as you say, then there will be no real gravitons measurable in situations where there are no gravitational waves in GR, just like there are no real photons measurable in situations where there are no electromagnetic waves in classical electromagnetism. GR describes plenty of situations where spacetime is curved but no gravitational waves are generated, like the gravitational field around a spherically symmetric object such as a star or a black hole. If the graviton plays a role isomorphic to the photon, there would be no real gravitons detectable here, although the gravitational fields might be explained in terms of virtual gravitons (similarly, in situations where classical electromagnetism gives electromagnetic fields but no electromagnetic waves, quantum electrodynamics explains the fields in terms of virtual photons, but no real photons are predicted).KingOrdo said:No. And I think you're missing the point. There are either gravitons or there aren't. There are, again, real photons. They are hitting you in the face right now. There are or there aren't real gravitons. If there are, they are in principle measurable.

And in situations where GR

Quantum mechanics has also been extensively verified emprically. But the two theories give incompatible predictions about what should be happening at the Planck scale, and we have no empirical data on what is actually going on at this scale.KingOrdo said:But one should not posit the existence of particles for which we have no need. Gravitation is very nicely described by Einstein, and--more important--his account has been very extensivelyverifiedempirically.

You just said "photons" and "gravitons", you didn't specify you were talking about non-virtual ones (and virtual particles can be seen as 'real' in the sense that they are an essential part of quantum field theory's procedure for making predictions about measurable events). Do you understand that to explain why one non-accelerating charge pulls on other charges, no "real" photons would be necessary, and similarly no "real" gravitons would likely be necessary to explain the gravitational pull from a star or black hole?KingOrdo said:I'm not talking about that. I'm talking aboutrealparticles. When I say 'A', I'm referring to A--not B.

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No theories tell you "The reason mediating particles are not included in GR has nothing to do with "Occam's razor", it's just that they don't happen to appear in the theory's mathematical structure; the theory doesn't tell youwhymass and energy curve spacetime in the way they do, it just tells you a relationship between the two things. If you had a quantum theory of gravity which predicted that aneffectof gravitons (both real and virtual) was to disort distances in spacetime in the same way that GR predicts, then I don't see why this wouldn't show the two theories as commensurable.

Yes, I do think "GR is 'prima facie incommensurable' with Newtonian mechanics"--I think it'sDo you think GR is "prima facie incommensurable" with Newtonian mechanics because one explains gravity in terms of forces and one in terms of curved spacetime? And yet GR precisely replicates the predictions of Newtonian mechanics in certain limits--physics is primarily about mathematical predictions, not the conceptual images we attach to them. Even "pure" GR can be recast in a mathematically equivalent form where it's just a field in flat spacetime; this is discussed in Kip Thorne'sBlack Holes and Time Warps, for example.

Right. That would be fine, because it would show GR to be an approximation of the graviton theory, just like Newtonian gravity is an approximation of GR. But the point is that absent anyWhy a "redundancy"? You'd have a new theory that made the same predictions as GR in certain limits, just like with Newtonian mechanics and GR; the new graviton-based theory would also be expected to differ from GR at the Planck scale, so it wouldn't be precisely identical.

Right. So now you've asked me to prove a negative: That gravitonsI agree, but my point is that "if the graviton serves a role in gravitation isomorphic to the role the photon serves in electromagnetism", as you say, then there will be no real gravitons measurable in situations where there are no gravitational waves in GR, just like there are no real photons measurable in situations where there are no electromagnetic waves in classical electromagnetism. GR describes plenty of situations where spacetime is curved but no gravitational waves are generated, like the gravitational field around a spherically symmetric object such as a star or a black hole. If the graviton plays a role isomorphic to the photon, there would be no real gravitons detectable here, although the gravitational fields might be explained in terms of virtual gravitons (similarly, in situations where classical electromagnetism gives electromagnetic fields but no electromagnetic waves, quantum electrodynamics explains the fields in terms of virtual photons, but no real photons are predicted).

Why would it be "And in situations where GRdoespredict gravitational waves, the notion of "gravitons" basically just means that gravitational waves will have quantized energy levels rather than continuous ones, just like the discrete energies of electromagnetic waves in quantum electrodynamics are imagined to correspond to discrete numbers of photons. Do you think it's a priori impossible that gravitational waves could have discrete energy levels?

But I'm not interested in the

I think everyone here will agree that the term 'photon' commonly refers to real photons and not virtual photons. If I ever want to talk about virtual photons, I will use the term 'virtual photons'.You just said "photons" and "gravitons", you didn't specify you were talking about non-virtual ones (and virtual particles can be seen as 'real' in the sense that they are an essential part of quantum field theory's procedure for making predictions about measurable events). Do you understand that to explain why one non-accelerating charge pulls on other charges, no "real" photons would be necessary, and similarly no "real" gravitons would likely be necessary to explain the gravitational pull from a star or black hole?

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JesseM

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No theory tells you why something is ultimately true, but a theory can tell you "why" something is true in terms of some more basic elements of the theory; for example, we can use Maxwell's equations to derive the fact that electromagnetic waves can only travel at a single velocity, c. Likewise, in quantum electrodynamics the way that charges attract and repel each other as a function of distance is not treated as a fundamental assumption, but instead can be derived from the way charged particles exchange virtual photons. Something similar might be true of a quantum theory of gravity.No theories tell you "why". If the graviton account is correct, then you're in the same spot:Whydo these particles make massive things move toward each other?Whydoes gravity attract and not repel? Those are not scientific questions.

Perhaps you should define what you mean by "incommensurable", since it sounds like you're saying thatKingOrdo said:Yes, I do think "GR is 'prima facie incommensurable' with Newtonian mechanics"--I think it'sultima facieincommensurable, too. Sure, it is an accurate theory within certain limits. But so what? Putting the planets on circular orbits is accurate within certain limits--doesn't mean it's right.

But Einstein didn't construct GR because he wanted to explain the precession of the perihelion of Mercury, or any other specific observational problem that didn't fit with Newtonian mechanics (as this page mentions, in Newtonian mechanics it was already predicted the perihelion of Mercury's orbit would precess somewhat because of the gravitational influence of bodies other than the Sun, and although the known planets weren't enough to explain the amount of precession astronomers hypothesized that there could be another unobserved planet near the Sun which would make up the difference, so it wasn't completely obvious that this observation actually contradicted Newtonian mechanics). Einstein was motivated by purely theoretical concerns like the inconsistency between Newtonian mechanics and special relativity. Would the 1910 version of you say that he "doesn't want any relativistic theory of gravity", since there is no empirical evidence that necessitates it, in spite of the clear theoretical conflict?KingOrdo said:Right. That would be fine, because it would show GR to be an approximation of the graviton theory, just like Newtonian gravity is an approximation of GR. But the point is that absent anyempiricalevidence that necessitates the inclusion of gravitons (cf.the perihelion precession of Mercury in the case of GR (though of course here the theory came first)), I don't want them. This is a fine point, an a certainly arguable one, but I am very resistant to letting physics stray too far from its observational roots.

I'm not asking you to "prove" it, just give me a reason to think it is improbable in any way, any more so than any other broad hypothesis about new physics beyond what we already know. For example, do you consider "gravitons exist" more implausible than "GR will no longer work precisely at the Planck scale", or "Quantum mechanics will no longer work precisely at the Planck scale"? There seem to be strong theoretical arguments thatKingOrdo said:Right. So now you've asked me to prove a negative: That gravitonsdon'texist. I can't do that.

"Manifestation of the curvature of spacetime" is just a word-picture which one is free to discard even in GR itself, as I mentioned before; it would be better to say something like "all gravitational phenomena can be derived from the equations of GR", since these equations don't necessarily have to be interpreted in terms of "spacetime curvature". And as for your "buckets of observations", of course none of them is in conflict with the hypothesis of a theory of quantum gravity which diverges noticeably from GR at the Planck scale but which becomes almost indistinguishable from GR far from the Planck scale.KingOrdo said:Your theory is unfalsifiable. We don't yet have strong empirical evidence in favor of gravitational waves; but, assume they exist. Then GR takes care ofexplainingandpredictingthem very nicely. I can hand you buckets of observations justifying my belief that gravitation is a phenomenological manfestation of the curvature of spacetime.

The theoretical reasons for postulating gravitons go well beyond "best fit with perturbation theory" (in fact I think most physicists expect a complete theory of quantum gravity to be non-perturbative), they include things like the theoretical incompatibility between GR and quantum theory at the Planck scale, the fact that string theory is known to reduce to GR in certain limits even though it wasn't constructed to have anything to do with gravity, and a number of other hints in the direction of a theory of quantum gravity like the Bekenstein bound on the amount of information that can be contained in a black hole which can be derived from a number of different plausible theoretical assumptions.KingOrdo said:All you can give me to justify the graviton is some talk--albeit not incoherent talk--about best fit with perturbation theory and the assertion that, were I to build a Solar System-large particle detector, I could find the graviton. That's not enough for me.

I should not have used "a priori impossible" since that phrase has a specific philosophical meaning and this is the philosophy forum...I was thinking of "a priori" more in the statistical sense of a prior probability we should assign to something in the absence of evidence, and I erred in saying "impossible" when I just meant something like "very unlikely". So again, why do you think the idea of a quantum theory of gravity which reduces to GR in certain limits is even particularly unlikely (more likely to be false than true, say)? If you are really concerned with justifying everything in terms of observational evidence, then since we have no evidence about Planck-scale physics either way, it would make more sense for you to say something like "there is insufficient basis at present for judging this hypothesis to beKingOrdo said:Why would it be "a prioriimpossible"? Obviously it would not. Something is "a prioriimpossible" iff, roughly, there is some contradiction in its meaning. It isa prioriimpossible that I will one day be a married bachelor. It isnot[/i]a priori[/i] impossible that there is a God, and He is a massive chicken. Obviously nothing to do with gravitational waves isa prioriimpossible.

But I'm not interested in thea priori--this is science. I'm interested inempirical evidence. Show me a graviton--or some other empirical evidence that it exists--and I'm on board. Pure reason convinces me in philosophy, but not in science.

I don't think physicists are always so careful about using the word "virtual" when referring to the photons in Feynman diagrams, so I disagree that the word photon "commonly refers" only to non-virtual photons, but I suppose this isn't a very important point either way.KingOrdo said:I think everyone here will agree that the term 'photon' commonly refers to real photons and not virtual photons. If I ever want to talk about virtual photons, I will use the term 'virtual photons'.

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I read in Brian's Greene second book that this fact do not breaks the law of the light speed limit. I do not remember the exact arguments. I think that is because the inflation changes the scales, which preserves the light speed limit.

I'm curious about that, I've heard during inflation it is believed that space expanded at faster than light speed, hypothetical warp engines if possible are believed to warp space to cause a region of space to move at faster than light speed. Yet I've also heard people believe, though it hasn't been proved without dispute, that gravity can only warp/change space at lightspeed.

So how is it the belief that space can change at faster than light speed(expansion during inflation), reconciled with the belief that it can't change at faster than light speed(gravity warping.)?

If there is no graviton, what exactly limits the speed of changes to space during gravity warping but not its expansion?

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I agree, as long as you change the "No theory tells you why something is ultimately true" to 'NoNo theory tells you why something is ultimately true, but a theory can tell you "why" something is true in terms of some more basic elements of the theory; for example, we can use Maxwell's equations to derive the fact that electromagnetic waves can only travel at a single velocity, c. Likewise, in quantum electrodynamics the way that charges attract and repel each other as a function of distance is not treated as a fundamental assumption, but instead can be derived from the way charged particles exchange virtual photons. Something similar might be true of a quantum theory of gravity.

Well, by 'incommensurable' I mean, roughly, 'competing'. Liberalism is incommensurable with totalitarianism because they are two irreconcilable political philosophies. Either the things liberalism has to say about value in the world are true, or the things totalitarianism has to say are true--Perhaps you should define what you mean by "incommensurable", since it sounds like you're saying thatanytheory is "incommensurable" with any other theory that makes different predictions than it in any circumstances, even if the new theory reduces to the old theory in certain limits, limits which cover every circumstance in which the old theory has successfully passed experimental tests (as with Newtonian mechanics and GR). Would you say that any new theory of physics--say, a theory of particle physics that goes beyond the Standard Model--is "incommensurable" with existing theories? If so, presumably the fact that a new theory would be "incommensurable" with existing ones is not actually a good reason to think that no new theories will be found to supplant older ones, unless you think physics is already complete.

I'm not sure what that question means, but I do agree that in the case of historical GR, theoretical concerns were dominant. But doubtless we both agree that Einstein's theoretical motivations were far stronger than the current motivations for including the graviton. Anyway, GR could be easily falsified: Einstein made concrete predictions which any astronomer could check. Not the case with the graviton.But Einstein didn't construct GR because he wanted to explain the precession of the perihelion of Mercury, or any other specific observational problem that didn't fit with Newtonian mechanics (as this page mentions, in Newtonian mechanics it was already predicted the perihelion of Mercury's orbit would precess somewhat because of the gravitational influence of bodies other than the Sun, and although the known planets weren't enough to explain the amount of precession astronomers hypothesized that there could be another unobserved planet near the Sun which would make up the difference, so it wasn't completely obvious that this observation actually contradicted Newtonian mechanics). Einstein was motivated by purely theoretical concerns like the inconsistency between Newtonian mechanics and special relativity. Would the 1910 version of you say that he "doesn't want any relativistic theory of gravity", since there is no empirical evidence that necessitates it, in spite of the clear theoretical conflict?

My reasons for thinking the existence of gravitons improbable are these: (1) We don't need them to explain gravitation, (2) They have never been observed, and (3) They are unfalsifiable (at least with any currently conceivable technology). On the broader topics, I'm much more sympathetic to relativity theory than quantum mechanics. No one can dispute the extraordinary accuracy which QM describes the world, but there are obvious questions of interpretation. It's not clear what QM is evenI'm not asking you to "prove" it, just give me a reason to think it is improbable in any way, any more so than any other broad hypothesis about new physics beyond what we already know. For example, do you consider "gravitons exist" more implausible than "GR will no longer work precisely at the Planck scale", or "Quantum mechanics will no longer work precisely at the Planck scale"? There seem to be strong theoretical arguments thatoneof the last two must be true.

Right. But the fact that there's not evidence"Manifestation of the curvature of spacetime" is just a word-picture which one is free to discard even in GR itself, as I mentioned before; it would be better to say something like "all gravitational phenomena can be derived from the equations of GR", since these equations don't necessarily have to be interpreted in terms of "spacetime curvature". And as for your "buckets of observations", of course none of them is in conflict with the hypothesis of a theory of quantum gravity which diverges noticeably from GR at the Planck scale but which becomes almost indistinguishable from GR far from the Planck scale.

Yes, I think that's fair. I think my comments above should cover this point. But I will say that there is a sort of elegance to GR that you don't find in the pastiche of contemporary QG theories. Whether elegance is a good ground for making scientific adjudications, I cannot say. Maybe not.I should not have used "a priori impossible" since that phrase has a specific philosophical meaning and this is the philosophy forum...I was thinking of "a priori" more in the statistical sense of a prior probability we should assign to something in the absence of evidence, and I erred in saying "impossible" when I just meant something like "very unlikely". So again, why do you think the idea of a quantum theory of gravity which reduces to GR in certain limits is even particularly unlikely (more likely to be false than true, say)? If you are really concerned with justifying everything in terms of observational evidence, then since we have no evidence about Planck-scale physics either way, it would make more sense for you to say something like "there is insufficient basis at present for judging this hypothesis to beeithermore likely false than trueormore likely true than false".

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