Is gravity action at a distance or is it a local force?

[KurtLudwig]

Newton thought of gravity as action at a distance. Einstein showed that gravity is the curvature of space-time. Einstein's General Relativity is the best answer, but neither discusses gravity at the quantum level. I tend to think of gravitational force to be the result of matter interacting with the local gravitational field. Does string theory or loop quantum gravity have hypotheses on what gravity is or how it arises?

 

[bayakiv]

Connoisseurs of this forum will surely tell you what gravity is in terms of string theory or loop gravity theory. But if you want to know what gravity really is, then I can share my thoughts on this subject. But let's restrict ourselves to that limit of Einstein's theory when gravity is described by a scalar potential. In this case, Newton's gravitational potential can be interpreted as a hyperbolic angle of deviation of the vector field of accelerations of matter moving in Minkowski space. If you are satisfied with this answer, then you can go further, but for this we need to expand the Minkowski space to an 8-dimensional space with a neutral metric.

 

[dx]

According to string theory, at very very short distances spacetime is something called a calabi-yau manifold. These manifolds are defined by the condition of ricci flatness. There are fields in string theory called scalar moduli which describe the compact spaces. g_string = ⟨e^-φ⟩ where phi is such a scalar field. g_s² and g_s are the closed and open couplings.

 

[bayakiv]

Can not understand anything. A closed three-dimensional complex manifold is a layer above space-time, but how the layer forms the metric of space-time is not clear to me. Wouldn't it be easier to take a 4-dimensional complex manifold and already from it try to select an open 4-dimensional space-time and a closed space of extra dimensions. For example, if you look closely at the topology of the unit sphere of an 8-dimensional space with a neutral metric, you will notice that it is homeomorphic $\mathbb{R}^{4}\times S^{3}$. Another question is how to induce the metric on $\mathbb{R}^{4}$, but it is solved using a differential form (the field of accelerations of matter) given in space with a neutral metric.

 

[ohwilleke]

Gravitational Waves and Hypothetical Gravitons Propagate At The Speed Of Light

The affirmative detection of gravitational waves by LIGO and other gravitational wave detectors, coinciding to within error bars of photon evidence of a black hole-neutron star merger, strongly supports the view that gravity is a local effect that propagates at the speed of light, rather than an instantaneous "at a distance" effect.

General relativity, and every graviton based quantum gravity theory adopts this position.

Localization Issue In Classical General Relativity And The Issues It Poses For Quantum Gravity

This said, however, there are issues like the localization of gravitational energy, and the self-interactions arising from gravitational fields, which conventional general relativity theory as conventionally applied does not recognize.

Similarly, while individual gravitational interactions in general relativity conserve mass-energy, in general relativity with a cosmological constant the aggregate amount of mass-energy in the universe (apart from gravitational potential energy) increases with time at a global level, although it is arguably possible to describe a gravitational potential energy concept to address this which IMHO doesn't really work but a minority of GR theorists say overcomes the mass-energy conservation issue.

The theoretical aspects of GR that disfavor localization or don't conserve mass-energy area particularly problematic when trying to quantize gravity, because a quantum particle based theory pretty much entirely has to be a bottom up theory that derives all global properties from individual local interactions that the theory permits.

Entanglement and Locality

In quantum gravity theories, it is conceivable that gravitons could become entangled with each other leading to correlations in the properties of the entangled particles analogous to those seen in quantum mechanics in other contexts.

But entanglement effects always involve particles that share a light-cone in space-time, and as a practical matter, while we can measure the correlated properties of entangled photons or other Standard Model particles, we do not have the capacity to measure the properties of individual gravitons, either individually, or statistically, so there is no way to resolve entanglement questions related to quantum gravity in the straightforward direct way that we do with Standard Model particles.

The gist of entanglement is that the correlations observed require the sacrifice of at least one of three axioms that we can usually resort to in physics: causality, locality, or realism. So, while sacrificing locality is one way to get entanglement-like effects, it is not the only one. Arguably, they are all equivalent ways of expressing the same concept and the fact that this is not manifestly obvious simply indicates that our language is not aligned with underlying concepts of how Nature really works.

In the case of interactions involving photons, gravitons and gluons, I personally often find it convenient to, and tend to favor, sacrificing "causality" (i.e. the arrow of time) rather than locality, because fundamental massless spin-1 bosons always move at the speed of light, and hence, do not experience the passage of time in their own reference frame, so it makes sense that interactions mediated by fundamental massless spin-1 bosons should not experience an arrow of time either, thus disallowing CP violation (which empirically is not observed) in interactions mediated by these massless bosons, and essentially stating that the line in space-time that entangled massless bosons follow basically amount to simultaneous points in the space-time coordinates that are best suited to judging causality. But to some extent the decision regarding which axiom to sacrifice in entanglement situations is a stylistic one with no measurable real world effects.

But, lots of loop quantum gravity oriented quantum gravity theories adopt causality as a bedrock axiom and treat the dimension of time in some sense distinctly from space dimensions, so one must sacrifice either locality or reality to some degree in these causation affirming LQG theories.

Similarly, setting up a graviton entanglement experiment (or even a "natural experiment" that would entangle gravitons somehow so that we could measure these effects) is beyond our practical experimental and observational capacity.

Decoherence

Another possible angle to get at this issue which is attracting attention is to look at a phenomena in which a group of Standard Model particles acts "coherently" in the absence of outside interactions. In ordinary daily life, we are bombarded by all sorts of particles that leads to rapid decoherence except in rarified circumstances. But in a deep space vacuum, a coherent group of particles can be expected to travel vast distances with only slight non-gravitational interactions with the outside environment.

Theorists can use even very incomplete quantum gravity theories in which lots of quantities can't be calculated to then calculate the extent to which a flux of gravitons would lead to decoherence of that group of Standard Model particles sooner than it would in the absence of such interactions (see, e.g., here).

The rate at which decoherence emerges in objects in the deep vacuum is thus a physical observable that helps us tease out the mechanism by which gravity works.

Non-Local Gravity Theories

There are explicitly non-local formulations of gravity and papers on this topic address a lot of the issues that the OP question seems to be getting at. Rather than try to explain them myself, I'll defer to the articles from the literature below that discuss these theories.

Literature For Further Reading

Some recent relevant papers include:

* Ivan Kolář, Tomáš Málek, Anupam Mazumdar, "Exact solutions of non-local gravity in class of almost universal spacetimes" arXiv: 2103.08555

* Reza Pirmoradian, Mohammad Reza Tanhayi, "Non-local Probes of Entanglement in the Scale Invariant Gravity" arXiv: 2103.02998

* J. R. Nascimento, A. Yu. Petrov, P. J. Porfírio, "On the causality properties in non-local gravity theories" arXiv: 2102.01600

* Salvatore Capozziello, Maurizio Capriolo, Shin'ichi Nojiri, "Considerations on gravitational waves in higher-order local and non-local gravity" arXiv: 2009.12777

* Jens Boos, "Effects of Non-locality in Gravity and Quantum Theory" arXiv: 2009.10856

* Jens Boos, Jose Pinedo Soto, Valeri P. Frolov, "Ultrarelativistic spinning objects in non-local ghost-free gravity" arXiv: 2004.07420

The work of Erik Verlinde, for example, here, also deserves special mention. He has hypothesized that gravity may not actually be a distinct fundamental force, and may instead, be an emergent interactions that arises from the thermodynamic laws applicable to entropy and/or entanglement between particles arising from Standard Model interactions.

His theories approximate the observed laws of gravity, sometimes including reproduction of dark matter and/or dark energy-like effects, although some early simple attempts that he made to realize this concept have been found to be inconsistent with observational evidence.

Particular Theories

Does string theory or loop quantum gravity have hypotheses on what gravity is or how it arises?

In string theory, either a closed or open string gives rise in certain vibration patterns to gravitons which carries the gravitational force between particles in a manner rather analogous to photons that utilizes a "loophole" in key "no go theorems" related to quantum gravity that make a naive point particle analogy to photons not viable.

This is generally done in a 10-11 dimensional space, although the way that the deeper 10-11 dimensions are distilled to the three dimensions of space and one dimension of time that we observe varies quite a bit. In many versions, the Standard Model forces as manifested through string theory are confined to a four dimensional manifold or "brane" while gravitons and gravity can propagate in all of the dimensions.

The distinction between the dimensions in which the Standard Model forces can operate and those in which gravity can operate helps string theorists explain why gravity is so weak relative to other forces, relative to the generic naive expectation of versions of string theory that if all forces ultimately derive from universal string-like particles, they ought to be more similar in strength, especially at high energies.

There are multiple problems with string theory but the biggest one is that it is really a class of vast numbers of possible theories that do not uniquely give rise to a single low energy approximation that resembles the Standard Model, and nobody has figure out how to thin out the universe of possible low energy approximations of string theory to find even one that contains everything that the Standard Model contains, while lacking everything that we have no experimental evidence for at experimentally testable energies. So basically, there are almost no observables that can be calculated from string theory.

String theory, for example, tends to favor (and arguably requires) that its low energy approximations be supergravity theories (a class of theories that integrates supersymmetry theories with supergravity theories), Majorana neutrinos that undergo neutrinoless double beta decay, proton decay, and models in which the initial state of the Universe at the Big Bang has baryon number zero, lepton number zero, and engaged in baryogenesis and leptongenesis soon after the Big Bang with a high energy process showing CP violation, baryon number violation and lepton number violation, that generates far more particles than the only known Standard Model processes that do so. The existence of a massless spin-2 graviton is pretty much the only prediction of string theory that has any support from observational evidence, and of course, that itself, is only indirect and in its infancy. But the mathematical intractability of quantum gravity by other means under various "no go theorems" has been one important motivation for string theory's popularity.

In loop quantum gravity, the universe is fundamentally made up of nodes that have a small finite numbers of connections to other nodes, and gravity is quantized primarily by quantizing space-time, rather than primarily by quantizing particles against a background that is smooth, continuous and local.

In LQG, locality is ill defined at this most fundamental level and is only an emergent property of the collective interactions of all of the nodes in a sense similar to that of temperature and pressure in the thermodynamics of gases being emergent properties of individual gas atoms randomly moving around a particular speeds that can be described globally in a statistical fashion. Particles move from node to node according to simple rules.

For example, LQG imagines that in space-time, most nodes in what we perceive to be a local area of space-time will connect to other, basically adjacent, nodes in the same local area, but there is no fundamental prohibition on a node having some connections to nodes in what we perceive to be the same local area, and other connections to nodes in what we perceive to be a local area billions of light years away.

The number of space-time dimensions is likewise an emergent property in LQG, and the number of space-time dimensions that emerge in this fashion aren't necessarily integer quantities. A system of nodes could also be described with a fractal dimension that is not an integer defined in a manner similar or identical to the mathematical definition of a fractal dimension.

Some edge examples of LQG theories think of matter and particles themselves as deformations of space-time itself that are emergent, rather than as something separate that is placed within a space called "space-time."

As in classical general relativity, gravity is fundamentally a function of the geometry of space-time, but in LQG, that geometry is discrete and broken rather than smooth and continuous, and locality is (as discussed above) ill defined. In LQG, the "background independence" of the theory, realized by not having a space-time distinct from gravity, is a hallmark axiom of the field and line of reasoning involved. This has the nice feature of "automatically" and obviously giving LQG properties like co-variance that impose tight constraints on the universe of gravity theories formulated with more conventional equations of gravity, like the Einstein field equations, which have this property, even though this is not obvious without extended and non-obvious mathematical proofs. But it has the downside of expressing how gravity works in equations that are not very conceptually natural to the uninitiated, which can make understanding what LQG really says in more familiar contexts challenging.

One of the biggest practical challenges for LQG when confronted with experimental evidence, is that many naive versions of it should give rise to slight Lorentz Invariance Violations (i.e. deviations from special relativity) at the Planck level due to the discrete rather than continuous nature of space-time, because Lorentz Invariance is formulated as a continuous space-time concept. Strong experimental constraints disfavor Lorentz Invariance Violations to levels that naively extend below Planck length scale distances. But, the problem of discrete formulations of space-time leading to minor deviations from Lorentz Invariance is not a universal property of all LQG theories and can be overcome with different conceptualizations of it that evade this problem.

Like string theory, LQG is very much a work in process that is striving to find ways within its general approach and family of theories that reproduce either classical general relativity in the classical limit, or a plausible modification of classical general relativity that can't be distinguished from general relativity with current observational evidence. There are a host of intermediate baby steps and confirmations of what is predicted that have to be surmounted before it can gain wide acceptance and produce a full spectrum of "big picture" results, in part, because so much of this class of theories is emergent, and has to be discovered, rather than being put in by hand as higher level operational and useful theories in practical situations.

Footnote Regarding Loop Quantum Gravity Terminology

There are two senses in which the term "loop quantum gravity" (LQG) is used, and I'm not being very careful about distinguishing the two in this post. Some of what I say about LQG is really specific only to the narrow sense theory that I discuss below, while other things that I say about LQG applies to the entire family of LQG style quantum gravity theories.

In a strict and narrow sense, loop quantum gravity refers to a specific quantum gravity theory that involves quantizing space-time that is largely attributed to Lee Smolin and Carlo Rovelli, although assigning credit to any scientific theory that a community of interacting researchers help formulate is a perilous and always somewhat controversial thing to do.

But the term is also frequently used as a catchall term for quantum gravity theories that share, with the narrow sense type example of loop quantum gravity, the feature that space-time itself or closely analogous concepts are quantized. LQG theories are distinguishable from quantum gravity theories, like string theory, that simply insert graviton particles that carry the gravitational force into a distinct pre-determined space-time with properties sufficient to be Lorentz invariant and observe other requirements of gravity theories that approximate general relativity in the classical limit.

For example, "http://www.thephysicsmill.com/2013/10/13/causal-dynamical-triangulations/" (CDT) is a quantum gravity theory that is in the loop quantum gravity family of theories, but is not precisely the same theory as the type example of LQG after which this family of theories is named.

"Spin foam" theories are another example of LQG family quantum gravity theories.

 

[KurtLudwig]

The above answer by ohwilleke is a tremendous answer, which I will read over and over again. Thanks KurtLudwig

 

[Fra]

Except for LQG and strings, there is also the entertained idea that gravity is to be understood differently than other forces, and possibly as an emergent or statistical phenomenon - if this is so, the whole idea to "quantize" the gravitational field may prove to be misguided. After all there is a drastic assymmetry between atomic physics and cosmological scale interactions, so it is by no mean "obvious" that quantizing gravity is the right way to think.

For examlpe Verlindes paper, https://arxiv.org/abs/1001.0785. However no matter what issue you have with Verlindes specific idea there may be other, different ideas along the same road. Here the idea is to understand einsteins field equations not as a statemet of physical law in the regular sense, but as a kind of statistical equilibrium statement (in some context).

/Fredrik

 

[bayakiv]

@ohwilleke , Thanks for the introductory lecture. Now I understand that in string theory, gravity is trying to represent a gauge force. However, let me doubt the prospects of these attempts. The point is that mathematically, gravity is represented by a local deformation of the isotropic cone of Minkowski space, and therefore it is induced not by local-group connections, but by local deformations of the Dirac algebra. In turn, the local deformation of the Dirac algebra is a consequence of a local change in the shape of the foliation layer, which is orthogonal to the covector field (differential form) of matter accelerations.

 

[ohwilleke]

I don't have high hopes for string theory either. There may be specific mathematical innovations in it that prove fruitful, but as a whole, I suspect that it is probably the wrong approach.

 

[bayakiv]

The weak point of string theory is its lack of support in the form of a clear philosophical concept. Of course, string theory is based on modern physical theories and new mathematics, but this is not enough. A truly new breakthrough physical theory should be based on a well-forgotten old ethereal concept, raised to a new level. In other words, the concept of a mathematical description of moving matter should serve as the basis for a new breakthrough physical theory.

 

[bayakiv]

I don't have high hopes for string theory either. There may be specific mathematical innovations in it that prove fruitful, but as a whole, I suspect that it is probably the wrong approach.

In fact, this erroneous approach can be easily corrected if the trajectories of moving matter are taken as strings. Take at least one-dimensional quantum gravity. What do we want to have there? Obviously the gravitational field of the particle and its wave function. And it is desirable that all this follows from a single concept - strings or something else. So the concept of a flow on a torus stretched over a sphere with punctured poles easily copes with this task. Indeed, a particle there is a feature of the flow in which it is closed (i.e., its streamlines are closed), the action is quantized there, since this is the coordinate of the sphere's latitude, the wave function of a particle is a complex function, which is the mathematical expectation of a random value of the particle's latitude, and the gravitational field is the scalar field of the hyperbolic angle of deflection of the flow from the vacuum direction. It should only be added that here it is meant that the pseudo-Euclidean plane is mapped onto the torus so that its isotropic lines are wound around the defining circles of the torus.

 

[CherylJosie]

This response is mind-blowingly comprehensive. Thank you so much for putting in the time and effort.

I'm not a physicist but I am curious at a level that far exceeds my grasp. I have a few observations/questions that I'd appreciate some clarification on. Okay, it's not a few, and it's not all observations and questions, it's a collection of dream-like suppositions arising out of my ignorance and curiosity. Anyway...

Similarly, while individual gravitational interactions in general relativity conserve mass-energy, in general relativity with a cosmological constant the aggregate amount of mass-energy in the universe (apart from gravitational potential energy) increases with time at a global level, although it is arguably possible to describe a gravitational potential energy concept to address this which IMHO doesn't really work but a minority of GR theorists say overcomes the mass-energy conservation issue.

The theoretical aspects of GR that disfavor localization or don't conserve mass-energy area particularly problematic when trying to quantize gravity, because a quantum particle based theory pretty much entirely has to be a bottom up theory that derives all global properties from individual local interactions that the theory permits.

I've seen some articles in the popular literature suggesting that we might inhabit a huge black hole. For lack of a better understanding, I conceptualize the 'big bang' as the appearance of a black hole viewed from the reference frame of an observer that exists inside a singularity after its formation, i.e. a 'white hole'.

If we do inhabit a black hole that is constantly accreting matter from beyond the event horizon, would this potentially explain how "the aggregate amount of mass-energy in the universe (apart from gravitational potential energy) increases with time at a global level"?

I ignorantly conceptualize existence within a black hole as a separate 'universe' where the universe is expanding as the event horizon expands, causing a red-shifted expanding universe by virtue of continual accretion.

Since time dilation within a relatively strong gravity field is so pronounced, would it somehow speed up the perception of gravity changes originating from beyond the event horizon, assuming that quantum gravity is in fact limited to the speed of light and subject to the time dilation of relativity?

What about the 'rubber sheet' stretching of spacetime? Does that stretching also alter the localized perception of gravity originating from beyond the event horizon by making it appear to slow down and/or shrink away into the distance until it vanishes?

Is there a constant that these two divergent spacetime effects of concentrated gravity converge to in the limit of their ratio, or does the ratio blow up to infinity/shrink to zero?

Could time dilation in a gravity well explain the perceived 'rapid inflation' period where the universe nearly instantaneously becomes huge?

I'm specifically asking about the body of literature and any theoretical work along these lines, since I have no relevant experience and wouldn't recognize it in mathematical form if it bit me. I'm specifically not presuming any relevant knowledge of the topic on my part. I'm just asking probing questions to see if anybody thought this through already, and what they came up with, because I'll never get there on my own.

Similarly, setting up a graviton entanglement experiment (or even a "natural experiment" that would entangle gravitons somehow so that we could measure these effects) is beyond our practical experimental and observational capacity.
...
The work of Erik Verlinde, for example, here, also deserves special mention. He has hypothesized that gravity may not actually be a distinct fundamental force, and may instead, be an emergent interactions that arises from the thermodynamic laws applicable to entropy and/or entanglement between particles arising from Standard Model interactions.

Is it accurate (on any level) to rephrase that as, "gravity, space, and time are properties of quantized matter just as mass is a property of quantized matter, and the expanding universe can be conceptualized as white hole spacetime enlarging from accretion of new matter from outside the event horizon of a black hole?"

In loop quantum gravity, the universe is fundamentally made up of nodes that have a small finite numbers of connections to other nodes, and gravity is quantized primarily by quantizing space-time, rather than primarily by quantizing particles against a background that is smooth, continuous and local.

In LQG, locality is ill defined at this most fundamental level and is only an emergent property of the collective interactions of all of the nodes in a sense similar to that of temperature and pressure in the thermodynamics of gases being emergent properties of individual gas atoms randomly moving around a particular speeds that can be described globally in a statistical fashion. Particles move from node to node according to simple rules.

For example, LQG imagines that in space-time, most nodes in what we perceive to be a local area of space-time will connect to other, basically adjacent, nodes in the same local area, but there is no fundamental prohibition on a node having some connections to nodes in what we perceive to be the same local area, and other connections to nodes in what we perceive to be a local area billions of light years away.

If spacetime is a property of matter rather than an 'ether' in itself, does quantum entanglement imply this same remote yet paradoxically localized connection to distant nodes as being a form of spacetime warping? Does the proximity of particles that is required for entanglement imply anything about the possibly brief formation and evaporation of microscopic black holes as particles collide, then separate, maintaining some of the properties they shared while 'crushed together' into a 'nascent universe' where they were once so local to each other that from the external reference frame they were briefly crushed into a singularity? Can the local connection to remote areas through quantum entanglement be conceptualized as a sort of 'taffy pull' where those shared properties stretch across what appears to be our spacetime, but in the local universe of a microscopic black hole that has evaporated, are still local to each other even though their local universe 'no longer exists'?

The number of space-time dimensions is likewise an emergent property in LQG, and the number of space-time dimensions that emerge in this fashion aren't necessarily integer quantities. A system of nodes could also be described with a fractal dimension that is not an integer defined in a manner similar or identical to the mathematical definition of a fractal dimension.

Some edge examples of LQG theories think of matter and particles themselves as deformations of space-time itself that are emergent, rather than as something separate that is placed within a space called "space-time."

I'm wondering about how singularities help us to resolve discrepancies between relativity and quantum mechanics. In particular, I'm wondering about the relationship between the surface area and the volume of a singularity. In N dimensions, the ratio of surface area to volume of a sphere approaches infinity as the radius of the sphere approaches zero, meaning that a spherical singularity is all surface and no volume. I'm presuming that a non-rotating Schwartzchild singularity resolves to a sphere of zero radius? Sorry, I'm really ignorant, but it seems that this simplification is perhaps useful.

In polar coordinates, the three dimensions are expressed as two angles and one radius. When the radius shrinks to zero, one of the three physical dimensions represented by that polar coordinate system shrinks to zero and essentially vanishes inside of a singularity. However, from the reference frame of an observer falling into the singularity, do they ever 'hit bottom' or does the expansion of spacetime from the accretion of new matter mean that the distance along that radius to the singularity keeps increasing even as the observer falls in? If the accretion of matter is quantum because the matter that accretes is quantized, does that mean that the expansion of spacetime within the 'nascent universe' of a black hole is also quantized?

Fractal surfaces can have finite 'radius' and still have infinite surface area. Does the loss of a dimension inside of a black hole imply a quantized 'fractal iteration' of universe through the function of singularity that has zero volume and is all surface?

Taking this ignorant speculation to extremes, what about the classical definition of polar coordinates compared to a more encompassing definition of polar coordinates? In rectangular/Cartesian coordinates, there are three axis, and we conceptualize polar coordinates e.g. as being one 360 degree angle wrapping around one rectangular axis, plus a second 360 degree angle wrapping around a second rectangular axis, plus an absolute magnitude of radius. What about the third, unused rectangular axis? Can we also conceptualize a third, 'redundant' polar angle that wraps around that otherwise unused rectangular axis? Does spacetime described in such a redundant system have any useful properties related to theoretical physics? Is it possible that 'quantum states' could be mathematically represented with the help of 'spin' around an otherwise 'unused polar axis'? If all three polar axes are rotating simultaneously, yet pointing to one fixed location in rectangular spacetime, could reversing the direction of all three of the spins result in an identical point that is represented by an opposite composite 'spin' on all three polar coordinate axes?

If that composite 'spin' is representing a quantum state via the mass density of a probabilistic distribution from a center of mass, then the polar coordinates don't have to necessarily point to a fixed point in spacetime from the reference frame of the observer or the particle. The composite spins of those three angles could also be in motion as the probabilistic distribution of the mass/particle changes. So the same multi-variate(?) redundant polar coordinates could describe particles in motion as well as particles 'at rest'. What if those redundant polar coordinates can represent actual physical properties of matter that don't conceptualize well into non-redundant rectangular/Cartesian coordinates?

How about adding the possibility of a negative excursion on the radius? What does that do to our understanding? Can we identify yet another 'parallel' representation of spacetime that is represented by a negative excursion on the radius and a 180 degree phase shift of all three of the 'spins'? Does geometry provide for any other such redundant polar coordinate systems that might be helpful in conceptualizing the standard model from a quantum perspective? Or is the coordinate system immaterial to the capabilities of the math?

I'm thinking also in terms of spacetime possibly being a property of quantized matter rather than an entity to itself. If spacetime is a property of matter, then changes in spacetime are the direct result of the changes in the matter that it is a property of. For example, does time begin when a 'black hole' universe accretes its first quantum particle(s) into a singularity, forms an event horizon, and creates a 'light cone' from which there is no escape? Could that explain why there's no escaping a black hole, if there's no spacetime beyond the event horizon from the 'white hole' reference frame, and nothing to escape into because there's no spacetime outside of it given that it suddenly appeared from nowhere in an instant as far as the reference frame of observers inside of the black hole is concerned?

What does this imply about the possibility of time travel? I'm thinking specifically of the simplistic concept where an observer travels into the past or the future and steps out of the Tardis in the same physical place from the non-inertial reference frame of someone on the surface of the planet that is whirling through its rotation as it orbits the sun that is spinning along in an arm of the Milky way that is receding from all distant red-shifted matter. Just as no time is the same in the past or the future, if spacetime is a quantity of matter, then no space is the same in the past or the future either. At a minimum, piloting the Tardis through spacetime requires skill in both time travel and space travel for it to produce any meaningful result.

Does time travel i.e. beyond the reference frame of the observer require a violation of conservation of energy, entropy, and causality based on the quantum nature of spacetime in string theory being possibly a property of matter that is suddenly out of sync with the spacetime it is manifesting as a property of itself while trying to escape its own manifested properties? Ugh, it's difficult to put into words... I'm specifically implying a discrepancy between Einstein's statements about the possibility of time travel through a continuous spacetime that is distinct from matter, and what quantum theory indicates about the possibility of time travel if spacetime is actually a discrete property of quantized matter. I'm thinking specifically of Einstein's statement that we could see the past with a powerful enough telescope if we looked through the curvature of the universe. Does that mean we are looking around the circumference of an ever-expanding black hole singularity shell universe inside of an event horizon and seeing the universe as it was millions/billions of years ago, in the same 'physical location' as we are now, looking at the backs of our own heads? I've never understood this statement and I'm not even sure I've got it correct, but I'm conceptualizing that the past is outward and the future is inward if we inhabit a singularity, so Einstein's statement would translate into a spiral at best? I'm just not getting this.

I'm also arriving at fatalistic interpretations of free will in the process, because if spacetime is a function of matter, that means that free will may be an illusion, or total creativity may be possible, or maybe both, in typically ironic dualistic internal contradiction...do physicists ever stray into philosophy?

As in classical general relativity, gravity is fundamentally a function of the geometry of space-time, but in LQG, that geometry is discrete and broken rather than smooth and continuous, and locality is (as discussed above) ill defined. In LQG, the "background independence" of the theory, realized by not having a space-time distinct from gravity, is a hallmark axiom of the field and line of reasoning involved. This has the nice feature of "automatically" and obviously giving LQG properties like co-variance that impose tight constraints on the universe of gravity theories formulated with more conventional equations of gravity, like the Einstein field equations, which have this property, even though this is not obvious without extended and non-obvious mathematical proofs. But it has the downside of expressing how gravity works in equations that are not very conceptually natural to the uninitiated, which can make understanding what LQG really says in more familiar contexts challenging.

One of the biggest practical challenges for LQG when confronted with experimental evidence, is that many naive versions of it should give rise to slight Lorentz Invariance Violations (i.e. deviations from special relativity) at the Planck level due to the discrete rather than continuous nature of space-time, because Lorentz Invariance is formulated as a continuous space-time concept. Strong experimental constraints disfavor Lorentz Invariance Violations to levels that naively extend below Planck length scale distances. But, the problem of discrete formulations of space-time leading to minor deviations from Lorentz Invariance is not a universal property of all LQG theories and can be overcome with different conceptualizations of it that evade this problem.

I'm still ignorantly wondering about the polar coordinates and Schwartzchild singularity. It seems to me that the fundamental conflict between relativity and quantum mechanics is on the level of scale, or 'size'. Relativity deals with huge things and quantum mechanics deals with tiny things.

In polar coordinates, the difference in scale lies along one dimension only, the radius. An expanding universe that is accreting matter from beyond its event horizon implies that the scale is changing as the radius grows. If a sentient being were the first quantum particle to exist at the center of a nascent 'big bang', would such being note a rapid change in the physical constants as the universe accretes additional matter and expands? Would the change be monotonically increasing, monotonically decreasing, alternating between increasing and decreasing, continuous or discrete steps? Would it all depend on the mathematical frame one is trying to understand the problem within? Could such observation even be undertaken given the severe time dilation inside the gravity well of a nascent singularity?

Also, my admittedly sparse (nonexistent) understanding of the Schwarzschild metric is that it resolves the 11 dimensions of string theory down to 6 dimensions that I can't fathom how they work. Is it possible that those 6 dimensions are somehow geometrically representative of 3 space dimensions, and 3 time dimensions? I.e. if spacetime is a property of matter, would the two be 'linked' in terms of how many dimensions each one exhibits? Maybe our limited 3D human perception is accurately perceiving those 11 dimensions in the physical realm and they aren't so spooky invisible after all? Maybe what is confusing us is that time seems to be a single dimension because it's a property of matter that manifests as change, whereas gravity is a property of matter that manifests as a force? Maybe it's our limited ability to perceive change that has us visually confused about how many dimensions there are?

Could these 6 dimensions be expressed in 3 polar coordinates each, and per my prior discusssion have additional 'dimensions' corresponding to the two angular polar dimensions that are otherwise unused in polar coordinate notation of spacetime that splits the total number of dimensions equally between space and time? Maybe there's actually 8 dimensions and we just forgot to think of them in terms of redundant polar coordinates that have three angles plus a radius, and can represent single points in spacetime with multiple values on those dimensions, at least 4 each considering the redundant angular dimension plus the redundant negative excursion on the radius?

Do the 'spins' of particles have anything to do with mathematical representations of spacetime in polar coordinates?

Since I'm ignorant of the math, I don't have any knowledge in these things, so I'm just asking rather than hypothesizing. Have I elucidated anything that anybody has already considered?

Another question is that if spacetime from the reference frame of the inside of a 'big bang' begins when a black hole forms at a singularity, but is also forming outside of the reference frame of the observer on the outside (we can't see into a black hole, so there's a 'light cone' blocking our perception), does that imply that spacetime has a 'unidirectional flow' as a singularity accretes matter from beyond the event horizon? I've seen descriptions that the future of an observer falling into a black hole converges at the singularity. Does that imply that the universe outside of the black hole has ceased to exist for that observer? If so, can the observer on the indside still feel the influence of gravity from objects beyond the event horizon? Can the observer on the inside ever be impacted by anything falling in behind, or is spacetime so severely stretched that once the event horizon is crossed, there's no way for anything falling into accelerate so much that it catches up? What does a non-Schwartzchild rotating black hole do to this concept of 'untouchable' prior matter that fell in first?

What does Hawking radiation say about the progression of spacetime inside of a black hole, if the black hole evaporates? Has time reversed itself since the future lies inward but the radiation escapes outward? Is the evaporation real as mass is lost to the 'outside world', or is the loss of mass merely the effect of a singularity that is accreting no new matter from its surroundings, progressively collapsing on itself to the point that it vanishes from the perspective of the 'parent universe' as spacetime inside of it deforms so radically that the 'doorway' between the black hole 'child universe' and its 'parent universe' closes behind the 'tear' that singularity ripped in the fabric? If so, what does that imply about the conservation of energy and causality/entropy? Is the gravity that was once perceptible from inside the event horizon now a lost quantity, after the matter that manifested that gravity as a property of itself has finished 'tearing through the fabric' of spacetime and passing on to 'the elsewhere' as that tear closes behind it, sort of like 'spacetime/matter death'?

Footnote Regarding Loop Quantum Gravity Terminology

There are two senses in which the term "loop quantum gravity" (LQG) is used, and I'm not being very careful about distinguishing the two in this post. Some of what I say about LQG is really specific only to the narrow sense theory that I discuss below, while other things that I say about LQG applies to the entire family of LQG style quantum gravity theories.

In a strict and narrow sense, loop quantum gravity refers to a specific quantum gravity theory that involves quantizing space-time that is largely attributed to Lee Smolin and Carlo Rovelli, although assigning credit to any scientific theory that a community of interacting researchers help formulate is a perilous and always somewhat controversial thing to do.

But the term is also frequently used as a catchall term for quantum gravity theories that share, with the narrow sense type example of loop quantum gravity, the feature that space-time itself or closely analogous concepts are quantized. LQG theories are distinguishable from quantum gravity theories, like string theory, that simply insert graviton particles that carry the gravitational force into a distinct pre-determined space-time with properties sufficient to be Lorentz invariant and observe other requirements of gravity theories that approximate general relativity in the classical limit.

For example, "http://www.thephysicsmill.com/2013/10/13/causal-dynamical-triangulations/" (CDT) is a quantum gravity theory that is in the loop quantum gravity family of theories, but is not precisely the same theory as the type example of LQG after which this family of theories is named.

I'm thinking in terms of duality. Is a photon a particle or a wave?

Is a graviton something unto itself, or a property of matter?

Does duality come into play when discussing the standard model and the reconciliation of relativity with quantum mechanics? If so, is that duality expressed in mathematical form, aside from the implicit duality of two radically different mathematical descriptions (relativity and quantum mechanics) of a single physical spacetime?

"Spin foam" theories are another example of LQG family quantum gravity theories.

My primitive concept of 'foam' is a 'bubbleverse' where black holes can form within black holes, and from the outside perspective, they are all empty shells of zero radius, finite event horizon, and infinite surface area that is paradoxically expanding from the inside perspective even though it is already huge by the time 'enough time passes' for intelligent observers to develop and look outward.

From the inside perspective, all the matter in the singularity is constantly receding as it plunges toward the singularity, continually stretching the spacetime that is a property of that accreting matter, stretching spacetime inward along that unidirectionally expanding radius as that matter falls in. At the same time that matter attempts to traverse the distance to the singularity and collapse inward on itself, new matter that accretes behind the matter that is already inside is also simultaneously stretching the radius from the outside as the universe expands and red-shifts. The distance from the singularity to the event horizon continually grows, subjectively rapidly and infinitely? Or not? How does this all work? Are microscopic singularities part of quantum foam?

I'm conceptualizing that the dividing line between bubbles is a fractal iteration of gravity concentrating so severely that it changes the nature of spacetime. It stretches so radically in its local vicinity that it exists as a separate entity from the rest of creation, i.e. it IS creation of a new universe even as it is death of matter vanishing from the old universe, in a philosophically twisted, metaphysically dualistic description of real phenomenon that are completely beyond my comprehension.

My primitive concept of the foam multiverse includes the joining of 'bubbles' that encounter each other and merge, from within the same reference frame of a particular universe as discrete 'child bubbles' forming on the surface of the 'parent bubble' and colliding with each other, whereas from the reference frame outside a nascent universe, bubbles could also merge as a 'child bubble' grows to consume its entire parent.

In such a 'multiverse', since time is dilated severely in the reference frame of the observer inside of a black hole, and we all might inhabit a black hole 'big bang', would that imply that spacetime outside of that reference frame is essentially all swallowed up already by the time the observer looks? Does that mean that from the inside looking out, the 'foam' appears to be an infinitely expanding universe, whereas it is actually a series of 'black holes inside of black holes' all constantly merging with each other even as they form new 'black holes inside of black holes' that swallow up matter and vanish it as the 'singularity evaporates'? Did Hawking describe the evaporation of a black hole from the perspective of a living outer universe, or did he describe what it looks like the death of the universe from the reference frame of the oldest black hole in existence as its matter all condenses into one singularity and the universe it used to exist in vanishes completely while it 'rips through the fabric of spacetime' and the hole created by the singularity closes behind it?

Are there any theoretical bases to my geometrical interpretations? I know I'm reaching here. I'm trying to develop a hand-waving understanding of the current state of the science that I'll never grasp on a mathematical or theoretical level. I don't have the capacity, and the popular literature/documentary series are geared toward an audience that has even less capacity than I do. This forum is my only avenue of exploration.

Thank you for reading through this fantastical and 'creative' foray into things I am unworthy of, and thanks even more for any explanations that might clarify my understanding. I hope my attempted conceptualizations are at least entertaining to those more adept, even if they don't align with the current state of the art in any fashion and turn out to be useless. I'll never develop them into anything, so if anyone else can, have at it. I'd be glad if they turn out to have any value at all even if only for their science fiction appeal to aspiring Asimovs.

 

[ohwilleke]

I've seen some articles in the popular literature suggesting that we might inhabit a huge black hole. For lack of a better understanding, I conceptualize the 'big bang' as the appearance of a black hole viewed from the reference frame of an observer that exists inside a singularity after its formation, i.e. a 'white hole'.

If we do inhabit a black hole that is constantly accreting matter from beyond the event horizon, would this potentially explain how "the aggregate amount of mass-energy in the universe (apart from gravitational potential energy) increases with time at a global level"?

This isn't entirely wrong but it isn't a very useful way to think about it, and it has nothing to do with dark energy phenomena.

Could time dilation in a gravity well explain the perceived 'rapid inflation' period where the universe nearly instantaneously becomes huge?

No.

How about adding the possibility of a negative excursion on the radius?

In calculating the probability of a particle in quantum mechanics going from point A to point B, a function called a propagator, you sum up the probability assigned to each possible path of the particle including paths that are forbidden in classical GR such as paths for massless particles slightly above or slightly below the speed of light. This is somewhat analogous to what you are thinking.

Could that explain why there's no escaping a black hole, if there's no spacetime beyond the event horizon from the 'white hole' reference frame, and nothing to escape into because there's no spacetime outside of it given that it suddenly appeared from nowhere in an instant as far as the reference frame of observers inside of the black hole is concerned?

In classical GR, the math just works out that way. There is a singularity in the equations.

Considering quantum mechanics, quantum tunneling manifesting as Hawking radiation should be possible, but it is at such a low level for stellar sized or bigger black holes (less than the ambient temperature of the universe due to cosmic background radiation) that it is indiscernible.

Hawking radiation only exceeds the ambient temperature of the universe due to cosmic background radiation for hypothetical black holes called primordial black holes (because the only time they could form would be in the immediate wake of the Big Bang) that have a mass less than the mass necessary to create one from the gravitational collapse of a star. There is no positive evidence that there have ever been primordial black holes, and if they ever did exist, the smaller ones would have evaporated to nothing by now. There is increasingly strong observational evidence that dark matter phenomena are mostly not due to primordial black holes.

What does this imply about the possibility of time travel?

Time travel is impossible. This is so even if it is possible for quantum correlations to be transmitted over paths that don't fully obey the arrow of time, and even if in a LQG fundamental node-like geometry, not all paths strictly follow an arrow of time.

Relativity deals with huge things and quantum mechanics deals with tiny things.

As applied it usually works out that way. But relativistic concerns to apply to quantum systems, and quantum mechanics probably contains the key to the overall pattern of the large scale structure of the universe.

Also, my admittedly sparse (nonexistent) understanding of the Schwarzschild metric is that it resolves the 11 dimensions of string theory down to 6 dimensions that I can't fathom how they work.

It probably isn't even fruitful to try to fathom how they work. There isn't even a consensus within string theory about how this works, although there are some leading hypotheses (Kaluza-Klein mini-nodes of dimensions and brane theory are the two main ways). Mathematically, 11 dimensions is easy. But finding a way to associate this with physical reality is not.

Do the 'spins' of particles have anything to do with mathematical representations of spacetime in polar coordinates?

No. All of the laws of physics are, at a fundamental level, coordinate system independent. It can be more convenient to use one coordinate system than another in a particular context to make a calculation, but the coordinate system you use doesn't matter.

What does Hawking radiation say about the progression of spacetime inside of a black hole, if the black hole evaporates?

Virtually nothing.

Hawking radiation makes assumptions merely about the environment an infinitesimal distance in from the event horizon. We don't have a good model of spacetime inside of a black hole that can be tested in any observable way.

One of the core foundations of black hole research is that black holes have only a handful of properties (mass, spin, charge) and are otherwise indistinguishable from each other.

I'm thinking in terms of duality. Is a photon a particle or a wave?

Both.

Is a graviton something unto itself, or a property of matter?

A graviton is not a property of matter. The coupling of a graviton to matter could be called a property of matter and a property of the graviton, but the graviton itself is not a property of matter. If gravitons exist, it is a particle-like resonance with zero rest mass and spin-2 that couples to other particles proportionately to their mass-energy.

Are there any theoretical bases to my geometrical interpretations?

You are all over the map in terms of being gushing with ideas and we don't have answers to anything.

 

[ohwilleke]

In fact, this erroneous approach can be easily corrected if the trajectories of moving matter are taken as strings. Take at least one-dimensional quantum gravity. What do we want to have there? Obviously the gravitational field of the particle and its wave function. And it is desirable that all this follows from a single concept - strings or something else. So the concept of a flow on a torus stretched over a sphere with punctured poles easily copes with this task. Indeed, a particle there is a feature of the flow in which it is closed (i.e., its streamlines are closed), the action is quantized there, since this is the coordinate of the sphere's latitude, the wave function of a particle is a complex function, which is the mathematical expectation of a random value of the particle's latitude, and the gravitational field is the scalar field of the hyperbolic angle of deflection of the flow from the vacuum direction. It should only be added that here it is meant that the pseudo-Euclidean plane is mapped onto the torus so that its isotropic lines are wound around the defining circles of the torus.

There are no obvious answers. We don't know how to do it.

 

[ohwilleke]

The weak point of string theory is its lack of support in the form of a clear philosophical concept. Of course, string theory is based on modern physical theories and new mathematics, but this is not enough. A truly new breakthrough physical theory should be based on a well-forgotten old ethereal concept, raised to a new level. In other words, the concept of a mathematical description of moving matter should serve as the basis for a new breakthrough physical theory.

This is pretty much exactly backward. String theory has clear support in the form of a clear philosophical concept. What it lacks is a way to operationalize that philosophical concept to a description of physical reality that resembles real life, has any observational motivation, or can be calculated with in ways that can be tested against observable phenomena.

 

[Fra]

Maybe it depends on how you see it. I think of string theory, and I know many professional string theorists do as well, as a kind of "conservative attempt" at a unified theory of interactions. It is conservative in the sense that is builds on the same paradigm as the standard model and QFT. It merely raises the question that: what if point particles are not points, but just looks like points from a distance. And that we really have vibrating string, whose vibrational modes can encode the different elementary particles. This is essentially a simlpe mathematical idea, that when worked on turns out complicated, and one fines that this idea seems to work only in certain dimentions, and that there are also many ways to do this, allowing possible particle spectra that we also do not see. From this perspective it seems string theory lacks a guiding principle, how to tame the extra possiblities introduced.

The weak point as I see is that string theory, is in beeing conservative, it brings over many of the already existing foundational and conceptual problem of quantum mechanics - unsolved, and the role of the observer. String theory at least in its principles offers no ambition to solution there. Instead I suppose that is they every survive their random walk in the swamp without getting lost, in the end the various dualities may receive "interpretations" and new insights that was never a plan in the original constructing principles.

/Fredrik

 

[dx]

It is conservative in the sense that is builds on the same paradigm as the standard model and QFT. It merely raises the question that: what if point particles are not points, but just looks like points from a distance. And that we really have vibrating string, whose vibrational modes can encode the different elementary particles.

On first sight, it may appear like string theory is building on the paradigm of quantum field theory, but actually this is not exactly correct. QFT is based fundamentally on what are called local operators. This is the reason it is inconsistent with general relativity, because in general relativity there are no gauge invariant local operators. String theory solves this by introducing what are called vertex operators, which are not defined on spacetime, but are defined on a two dimensional Riemann surface called the worldsheet. The superconformal field theory on the worldsheet must be viewed as being more primary than spacetime, and it is possible to describe quantum mechanics in a context which is not directly connected to spacetime. This generalization of local quantum field theory is capable of encompassing general relativity. A local operator inserted in the interior of the worldsheet corresponds to the emission of a closed string, and a local operator inserted on the boundary of the worldsheet corresponds to the emission of an open string.