Exploring the Nature of Gravity: Free Fall, Curved Spacetime, and Planck Length

[KevinMcHugh]

TL;DR Summary

Why do we suppose QG exists

I've read that free fall is the natural state of an object, and that gravity is not a force. Although it is equivalent to acceleration. So objects in space move through curved spacetime. Mass curves spacetime, curvature tells matter how to move. Matter as we know it has mass on the order 0.03 eV upwards to the top. Dimensionally, on the order 10 EE-15 cm. So where is the need to describe the force of gravity at distances less than the Planck length?

 

[phinds]

Well, the center of black holes for one

 

[Heikki Tuuri]

We believe that there is an interaction between particles and spacetime geometry. It would be nice to understand - at least in principle - how that works.

Some people believe in the existence of Hawking radiation from black holes. If it exists it has to be a quantum phenomenon.

A quantum theory of gravity might uncover useful new technologies for space travel.

 

[KevinMcHugh]

Well, the center of black holes for one

Don't black holes have dimension on a macro scale?

 

[phinds]

Don't black holes have dimension on a macro scale?

Sure, if you take the Event Horizon as the "size" but so what? That has nothing to do with what's going on at the center and we don't KNOW what's going on at the center, which is why we call it a "singularity"

 

[KevinMcHugh]

We believe that there is an interaction between particles and spacetime geometry. It would be nice to understand - at least in principle - how that works.

Some people believe in the existence of Hawking radiation from black holes. If it exists it has to be a quantum phenomenon.

A quantum theory of gravity might uncover useful new technologies for space travel.

I understand particles interact with the Higgs field yielding mass, but how would particles interact with spacetime? Through creation and annihilation operators on the vacuum?

 

[KevinMcHugh]

Sure, if you take the Event Horizon as the "size" but so what? That has nothing to do with what's going on at the center and we don't KNOW what's going on at the center, which is why we call it a "singularity"

Thanks for the replies Phinds. What is the nature of the black hole that we can observe leads us to believe gravity is quantized?

 

[phinds]

Thanks for the replies Phinds. What is the nature of the black hole that we can observe leads us to believe gravity is quantized?

These is none, it's just that GR breaks down at the center and gives unphysical answers so the belief is that we have to have a theory of quantum gravity to ever understand what is going on.

 

[KevinMcHugh]

These is none, it's just that GR breaks down at the center and gives unphysical answers so the belief is that we have to have a theory of quantum gravity to ever understand what is going on.

Gotcha. So the math breaks down. How about philosophically? Does it make sense to quantize something that seems continuous? We don't quantize time or translations. Of course these may only appear continuous to our observations.

 

[Nugatory]

Does it make sense to quantize something that seems continuous?

Electromagnetic fields seem to be continuous as well, but they are treated quantum mechanically in the theory of quantum electrodynamics - and QED has proven to be one of the most successful theories of all time.

 

[phinds]

Gotcha. So the math breaks down. How about philosophically? Does it make sense to quantize something that seems continuous? We don't quantize time or translations. Of course these may only appear continuous to our observations.

The thought, as I understand it, is not that space-time is quantified but that something happens at the center of black holes regarding the MASS that we do not understand. GR says it all condenses to a point but a point is dimensionless. How could a finite mass be contained in something with no dimensions? We need a different theory to say what happens under such conditions. It MIGHT involve space-time but I don't know that it has to make it discontinuous.

 

[KevinMcHugh]

Electromagnetic fields seem to be continuous as well, but they are treated quantum mechanically in the theory of quantum electrodynamics - and QED has proven to be one of the most successful theories of all time.

Thanks for the reply. But we can certainly measure and quantify the photoelectric effect, so we have direct evidence of quantum effects. Am I to understand correctly that space and time are quantized in LQG?

 

[Heikki Tuuri]

I understand particles interact with the Higgs field yielding mass, but how would particles interact with spacetime? Through creation and annihilation operators on the vacuum?

Particles have mass-energy, and they bend spacetime. The bending of spacetime affects the trajectories of the particles.

 

[ohwilleke]

Summary: Why do we suppose QG exists

General Relativity and the Standard Model are mathematically inconsistent. Ergo, something necessarily has to be done to reconcile the two.

The Standard Model is proven at a lab scale with great precision in all its quantum mechanical weirdness. General relativity, in contrast, while it has strong experimental support has been tested only in less intimate, lab scale, ways. General relativity has only been tested in ways that can't really measure small scale quantum mechanical effects (because it is so weak). Thus, it is the more plausible theory to tweak general relativity substantially than is to do that with with the Standard Model which is tightly constrained experimentally at the laboratory scale. Ergo, quantum gravity should exist to reconcile classical General Relativity and the Standard Model.

Heuristically, it also makes sense that if classical electromagnetism has a quantum electrodynamics theory that is closer to the truth than the classical theory, and if quantum chromodynamics and the weak force have no real classical equivalent, that it is plausible that there should also exist a quantum gravity theory to which classical general relativity is a mere approximation.

 

[KevinMcHugh]

General Relativity and the Standard Model are mathematically inconsistent. Ergo, something necessarily has to be done to reconcile the two.

The Standard Model is proven at a lab scale with great precision in all its quantum mechanical weirdness. General relativity, in contrast, while it has strong experimental support has been tested only in less intimate, lab scale, ways. General relativity has only been tested in ways that can't really measure small scale quantum mechanical effects (because it is so weak). Thus, it is the more plausible theory to tweak general relativity substantially than is to do that with with the Standard Model which is tightly constrained experimentally at the laboratory scale. Ergo, quantum gravity should exist to reconcile classical General Relativity and the Standard Model.

Heuristically, it also makes sense that if classical electromagnetism has a quantum electrodynamics theory that is closer to the truth than the classical theory, and if quantum chromodynamics and the weak force have no real classical equivalent, that it is plausible that there should also exist a quantum gravity theory to which classical general relativity is a mere approximation.

I've since read a little Rovelli to help me understand. Where I'm having difficulty is with the minimum length. What matter or energy density is available to curve spacetime in that 10 EE-33 cm region? Can a quark even occupy such a small region?

 

[ohwilleke]

I've since read a little Rovelli to help me understand. Where I'm having difficulty is with the minimum length. What matter or energy density is available to curve spacetime in that 10 EE-33 cm region? Can a quark even occupy such a small region?

In classical GR, any true point particle with a non-zero mass gives rise to a singularity (it involves division by zero).

The Schwarzschild radius of an election's mass is about 1.353 * 10^-57 meters v. the Planck length of 1.616 * 10^-35 meters. https://en.wikipedia.org/wiki/Black_hole_electron

Schwazchild radius is proportional to mass, so a top quark pole mass mass black hole would have a Schwarzschild radius of 4.58 * 10^-55 meters (which is significant because the top quark is the heaviest fundamental particle in the Standard Model).

A black hole with a Plank length radius would have a mass of 3.85763×10^−8 kg, which is 1.772 Planck masses. https://en.wikipedia.org/wiki/Planck_particle Note that m(1 kg)=1.780×10^−27 GeV/c^2. So a Plank radius black hole would be roughly 10^17 times more massive than the pole mass of a top quark.

The Heisenberg uncertainty principle says that uncertainty in position times uncertainty in momentum measured at the same time is always greater to or equal than the reduced Planck's constant divided by 2.

The Heisenberg uncertainty principle also states that uncertainty in amount of energy times uncertainty in time measured at the same time is always greater to or equal than reduced Planck's constant divided by 2. The reduced Planck's constant is 6.582 * 10^-16 eV*second/radian. Mass and energy are basically equivalent with an E=mc^2 conversion factor for these purposes.

So, while you need some finite radius for a point particle in the Standard Model, for example, a la string theory, or some finite distance length to avoid the point particle problem, that scale can be much less than the Planck scale and the necessary scale is deeply within a domain where mass and position cannot be well defined to sufficient precision in a single measurement.

The point particle problem isn't the only mathematical inconsistency between GR and QM but it is one of the most obvious ones.

 

[KevinMcHugh]

In classical GR, any true point particle with a non-zero mass gives rise to a singularity.

The Schwarzschild radius of an election's mass is about 1.353 * 10^-57 meters v. the Planck length of 1.616 * 10^-35 meters. https://en.wikipedia.org/wiki/Black_hole_electron

Schwazchild radius is proportional to mass, so a top quark pole mass mass black hole would have a Schwarzschild radius of 4.58 * 10^-55 meters (which is significant because the top quark is the heaviest fundamental particle in the Standard Model).

A black hole with a Plank length radius would have a mass of 3.85763×10^−8 kg which is 1.772 Planck masses. https://en.wikipedia.org/wiki/Planck_particle Note that m(1 kg)=1.780×10^−27 GeV/c^2. So a Plank radius black hole would be roughly 10^17 times more massive than the pole mass of a top quark.

The Heisenberg uncertainty principle says that uncertainty in position times uncertainty in momentum measured at the same time is always greater to or equal than the reduced Planck's constant divided by 2.

It also states that uncertainty in amount of energy times uncertainty in time measured at the same time is always greater to or equal than reduced Planck's constant divided by 2. The reduced Planck's constant is 6.582 * 10^-16 eV*second/radian.

So, while you need some finite radius for a point particle in the Standard Model, for example, a la string theory, or some finite distance length to avoid the point particle problem, that scale can be much less than the Planck scale and is deeply within a domain where mass and position cannot be well defined to sufficient precision in a single measurement.

The point particle problem isn't the only mathematical inconsistency between GR and QM but it is one of the most obvious ones.

Thank you for that detailed answer. That clears up a lot.

 

[Elias1960]

So where is the need to describe the force of gravity at distances less than the Planck length?

The reason to care about QG is that we want to know the truth about how the universe works. For an instrumentalist, QG is of no value at all, given that GR and the SM predict all we need for developing the technology. But it is well-known that there are conceptual contradictions between GR and QT. And the SM is full of unexplained regularities. This makes it clear that some part of our knowledge about GR and QT is wrong, and that there is something interesting yet to be discovered.

 

[ohwilleke]

The reason to care about QG is that we want to know the truth about how the universe works. For an instrumentalist, QG is of no value at all, given that GR and the SM predict all we need for developing the technology. But it is well-known that there are conceptual contradictions between GR and QT. And the SM is full of unexplained regularities. This makes it clear that some part of our knowledge about GR and QT is wrong, and that there is something interesting yet to be discovered.

There may not be engineering applications per se, but there are good reasons to think that one possible way to explain phenomena attributed to dark matter and dark energy is as quantum gravity adjustments relative to GR, which would solve a lot of major unsolved problems in fundamental physics.

Also, understanding a true theory of quantum gravity (and most people think that classical GR is further from the truth than the SM), may open up details about gravity that we didn't know before that have applications as yet not envisioned.

For example, it took decades after the early 20th century discovery of experimental evidence for quantum mechanics to codify that in a workable QED theory and then apply that in applications that are ubiquitous and critical in technological applications like transistors today.

We are right now in the theory of quantum gravity where QED was in 1909 or so, and it could be a couple of generations before we have enough of a grasp of it to do anything fun with it.

 

[member 11137]

An article on another blog (Backreaction blog, S. Hossenfelder): "The five most promising way to quantize gravity" (06 September 2019) can also bring some elements in that discussion. I note: (i) a proposition for a sixth way: Gravitation can not be quantized; (ii) a long discussion around the equivalence principle.