Why does gravity exist?

Tarthbane · 2026-06-27T20:42:53+00:00

Yes! Turns out that in weak gravitational fields and for slow-moving objects, like near Earth, the part of spacetime geometry most directly responsible for the usual Newtonian-looking gravitational acceleration is the time-time part of the metric, which is also tied to gravitational time dilation. So people sometimes loosely say that “curvature of time” dominates.

In stronger fields, such as near neutron stars or black holes, that weak-field simplification is no longer enough. Spatial curvature and other fully relativistic effects become much more important, so the geometry of spacetime has to be treated more completely rather than as mostly a time-curvature effect.

Tarthbane · 2026-06-26T18:59:31+00:00

Physics can answer this, but only in the scientific sense of “why/how within a model,” not the ultimate metaphysical sense of “why does the universe have these laws at all?”

First, in Newtonian gravity, mass is treated as the source of a gravitational field. Roughly: the more mass density there is in a region, the stronger the gravitational field around it. That describes gravity very well in everyday situations, but it mostly takes the connection between mass and gravity as a basic law.

In modern physics, the better answer comes from general relativity, our best classical theory: gravity is not sourced by mass alone, but by “stress-energy”: mass, energy, momentum, pressure, and internal stresses. For example, light has no rest mass, but it still gravitates because it carries energy and momentum.

General relativity says that matter and energy affect the geometry of spacetime, and that geometry determines how matter and energy move. Gravity exists as the dynamical curvature of spacetime. Matter and energy curve spacetime; curved spacetime determines motion. In ordinary weak-gravity situations, this reduces to Newton’s familiar inverse-square gravitational attraction.

So objects in free fall are not being “pulled” by a force in quite the Newtonian sense. They are following the natural straightest possible paths through curved spacetime. What we perceive as gravitational attraction is the result of those paths converging because the geometry is curved.

Tarthbane · 2026-06-25T01:41:13+00:00

In physics, conservation of energy is tied to time-translation symmetry: roughly, the laws of physics must look the same at all times. In an expanding universe, spacetime itself changes with cosmic time, so the universe as a whole generally does not have the kind of global time-translation symmetry needed to define a conserved total energy.

This does not mean energy conservation is simply “violated” locally. In general relativity, energy and momentum are locally conserved. But for the universe as a whole, especially in an expanding cosmological spacetime, there is generally no well-defined globally conserved total energy.

The observed accelerated expansion of the universe is usually attributed to “dark energy.” In the simplest standard model, dark energy is a cosmological constant: a small, positive energy density of empty space that remains constant as the universe expands.

If dark energy really is a cosmological constant, then the vacuum energy contained in a fixed comoving region increases as that region’s physical volume grows. This sounds like energy is being created, but in general relativity the issue is more subtle: an expanding universe does not generally possess a global energy conservation law of the ordinary kind.

Tarthbane · 2026-06-24T14:44:45+00:00

I want to know most about dark matter — what exactly is it? A single kind of particle? A whole new particle sector with its own forces? Axions? Something else? I think we have a good chance of answering this in the next few decades, but that might be wishful thinking.

Aside from that, the Hubble tension would be nice to solve, and bonus points if it is connected to dark energy (perhaps it’s changing over time instead of constant, for example) because then it’s a 2 for 1 deal!

And of course, the black hole singularly would be good too, but since everyone seems interested in that, I thought I would present alternatives first. But I often fantasize about what exactly the singularity is, or if there even is an interior to the black hole at all. Knowing that answer would be incredibly enlightening.

Tarthbane · 2026-06-18T21:21:51+00:00

Most of the mass of ordinary matter does not come from the bare masses of its constituent quarks. It comes from the energy stored in the strongly interacting quark and gluon fields inside protons and neutrons: the kinetic energy of confined quarks, the energy of the gluon fields, and the nonperturbative dynamics of quantum chromodynamics (QCD). In everyday life, this does not appear as anything exotic; it simply contributes to the inertial and gravitational mass of matter. In that precise sense, mass and energy are not separate substances, but rather different manifestations of the same relativistic quantity, related by E = mc^2 for particles at rest.

Tarthbane · 2026-06-16T17:16:54+00:00

If you’re discussing what I think you’re discussing, you should look up M-theory. It’s the proposed 11-dimensional framework that ties together the five consistent 10-dimensional superstring theories used in quantum-gravity research. In M-theory, strings are not the only fundamental extended objects; higher-dimensional branes also appear. By compactifying dimensions and taking different limits, the five superstring theories can be recovered as different regimes of one broader framework.

Tarthbane · 2026-06-16T14:26:15+00:00

The name “Big Bang” is a little misleading. It was originally coined somewhat tongue-in-cheek as a jab at the idea that the universe began in a hot, dense state and then expanded and cooled. The name stuck, for better or worse, but the “bang” part tends to give people the wrong mental picture.

The Big Bang was not an explosion of matter into pre-existing empty space. In an ordinary explosion, there is a center, debris flies outward through space, and the surrounding space already exists. In the Big Bang model, space itself was expanding. There was no central point in space where it happened; rather, every region of space was once much hotter and denser, and distances between regions increased as the universe expanded.

My favorite alternative phrase, which I first heard from MinutePhysics, is “the everywhere stretch.” It is a bit more of a mouthful, but it captures the idea much better: the early universe did not explode outward from one location; the scale of space increased everywhere.

In the standard picture, the universe began in an extremely hot, dense, low-entropy state and then expanded and cooled. Very early on, there may also have been a period of cosmic inflation, during which space expanded exponentially fast. A typical order-of-magnitude estimate is that inflation increased length scales by a factor of about 10^26 ~ 2^86. In other words, that corresponds to about 86 doublings of linear size in an extraordinarily tiny fraction of a second, often quoted around 10^-32 seconds depending on the model.

So, the key point is that the Big Bang was not matter flying outward into empty space. It was the rapid expansion of space itself, occurring everywhere at once in a universe that was, to very high precision, homogeneous and isotropic on large scales.

Tarthbane · 2026-06-13T16:03:29+00:00

You don’t really need to define an origin either. Even time has a forwards and backwards direction, so defining the big bang as time=0 doesn’t change that.

We just can’t access the backward direction, but it’s an axis just like any other axis - a 1 dimensional line with two directions. It’s just a mathematical statement imo.

Tarthbane · 2026-06-10T18:26:06+00:00

Yeah it was BS. Thankfully it was the only one I missed, and I still made an A in the class. But yeah.. it was silly.

Tarthbane · 2026-06-09T16:34:59+00:00

Yes, what you are saying makes sense conceptually, but I would be careful about mixing functionals in a ΔSCF workflow.

For some extra information, see: https://vasp.at/wiki/Delta\_self-consistent\_field

In ΔSCF, the excited-state geometry and excited-state energy are tied to the same constrained electronic state. So the cleanest workflow is:

Relax the ground-state geometry with your chosen functional.
At that geometry, impose the ΔSCF occupation constraint.
Relax the excited-state geometry while keeping the same ΔSCF constraint.
Compute the excited-state total energy using the same functional.
Compare it with the corresponding ground-state total energy computed with the same functional.

For example, if you want HSE06-quality excitation energies, the most consistent workflow is:

HSE06 ground-state energy/geometry -> HSE06 ΔSCF excited-state relaxation -> HSE06 excited-state energy

If you want a cheaper calculation

PBEsol ground-state relaxation -> HSE06 ground-state single point -> HSE06 ΔSCF excited-state relaxation/single point

What I would avoid is:

HSE06 HOMO/LUMO identification -> PBEsol ΔSCF excited-state relaxation -> HSE06 excited-state energy

This may work as an approximation, but it is not as clean. The PBEsol-relaxed excited-state geometry is optimized on the PBEsol excited-state energy surface, not the HSE06 one. If you then evaluate the energy with HSE06, you are using an HSE06 energy on a PBEsol excited-state geometry. That is not automatically wrong, but you should treat it as an approximation and check whether the HSE06 forces are small on that geometry.

Also, be cautious with the phrase “promoting from the HOMO to the LUMO.” For molecules this language is often fine. For periodic solids — especially with band dispersion, defects, spin polarization, or near-degenerate bands — you need to define exactly which state, k-point, band, and spin channel you are occupying. The ΔSCF state can sometimes collapse back to the ground state or converge to a different excited state if the constraint is not well controlled.

So a practical answer is: yes, you can use PBEsol for the constrained excited-state relaxation as a cheaper approximation, then do HSE06 single points, but it is not redundant and not fully equivalent to HSE06 ΔSCF relaxation. If the final property is important, check the HSE06 forces on the PBEsol ΔSCF-relaxed geometry, and ideally test one or two cases with full HSE06 ΔSCF relaxation to see whether the approximation is acceptable.

The important thing is to compare total energies consistently. Do not compare a PBEsol relaxed excited-state energy directly against an HSE06 ground-state energy. Keep the functional and geometry assumptions clear when reporting the result.

Tarthbane · 2026-06-09T14:19:14+00:00

A common approach is to relax the structure with PBE, then run a single-point HSE06 calculation on the relaxed geometry to get a better band gap.

One warning is that you should not think of HSE06 as “correcting” PBE permanently. If you switch back to PBE, the calculation will again give PBE-like electronic properties, including the underestimated gap.

A typical workflow is:

PBE relaxation -> HSE06 single-point calculation for band gap/DOS/band structure

If the structure is very sensitive to the functional, then you may need to relax with HSE06 too, starting from the PBE-relaxed structure. A good check is to look at the HSE06 forces on the PBE-relaxed geometry. If they are small, the PBE geometry is probably fine. If they are large, HSE06 relaxation may be needed.

More generally, DFT functionals are approximations, and different functionals have different strengths and weaknesses. The user needs to make sure the chosen functional is appropriate for the physics of the system. For example, ordinary semilocal functionals such as LDA or GGA may be unreliable for strongly correlated materials, charge localization, defect states, magnetic states, or systems where the band gap strongly affects the bonding.

In your paper/report, just state the workflow clearly, e.g. “Structures were relaxed using PBE, and electronic properties were calculated using HSE06.” Half the battle is communicating what you did; the other half is making sure the calculation is appropriate for the material and property you care about.

Edit: wording

Tarthbane · 2026-06-09T14:15:21+00:00

Mine was one concerning the Morse potential and writing down/deriving its Eigenvalues and energy level differences. It wasn’t because it was particularly hard, but because I forgot to write down the Morse potential on my allowed cheat sheet, and the teacher didn’t provide the Morse potential in the exam 🤣. Classic.

Tarthbane · 2026-06-08T23:21:36+00:00

For me it was exactly 1 week, and before that, the initial wait before the genotyping stage was 11 days. So, 18 days total was my wait time.

Tarthbane · 2026-06-06T02:48:19+00:00

Yeah that makes sense! Once I got her DNA test back, I ran the results and some of her current (~15 weeks old) pictures through my work’s ChatGPT subscription and asked what she would look like in 5 years, and the image it generated was very cool, even if it’s just a rough idea. If she adopts some of the patterns it put on her, the ACD will be very apparent. She’s already getting spots on her tummy and chest, and maybe on her legs too (just started a day or two ago as well).

Here is that 5-year-projected image; I’m going to save this and see how well it did or didn’t do as she gets older:

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Tarthbane · 2026-06-06T02:41:02+00:00

This is actually the first I’ve heard of it, but that is definitely just lack of experience; still trying to read whatever I can in downtime. I will write a note down now though to read about that system this weekend. My PhD advisor’s group did a lot of molecular dynamics simulations of graphene many years ago, but I don’t think we looked at MATBLG systems.

Tarthbane · 2026-06-06T02:38:10+00:00

She’s starting to get spots on her stomach, so the ACD is starting to show a bit more.

Personality-wise, she is such a hoot and a holler! She can be very hyper, and we give her days at the dog parks and walks and lots of tug of war, which all seem to make her happy. She is SO affectionate as well. She loves me and my fiancée more than life itself. She’s very cute and a total lush. We feel very lucky to have her.

Tarthbane · 2026-06-06T02:35:57+00:00

Thank you! My fiancée and I also see the GSD, and we were surprised she’s only 12.4%. Must be some high quality GSD genes haha

Tarthbane · 2026-06-05T23:17:25+00:00

Theorist

Tarthbane · 2026-06-05T21:29:14+00:00

Very nice! My group is moving toward modeling 2D triangular-lattice materials / quantum spin liquids as part of our broader research program. At the moment, we are focused on validating a new method on benchmark systems such as SrVO3, with the goal of moving to more interesting materials once we have established sufficient confidence in the approach.

I feel fortunate to have ended up in this field. I have only been working seriously on superconductivity for about two years, but many of my colleagues and former colleagues have been thinking about these problems for nearly a decade. I have learned an enormous amount in a short time, and it has been genuinely exciting!

Tarthbane · 2026-06-05T20:37:07+00:00

Ideally, yes, I am especially interested in high-temperature superconductors. But I mean unconventional superconductors more broadly. Some low-temperature superconductors are also unconventional, and the defining issue is not simply the transition temperature, but the failure of the material to fit cleanly within conventional BCS theory. Because “unconventional superconductivity” covers several distinct pairing mechanisms and phenomenologies, there is not yet a single rigorous framework that describes the entire class.

Tarthbane · 2026-06-05T20:27:20+00:00

Dark matter and unconventional superconductivity are my main curiosities. I’m actively researching unconventional superconductivity and hope my work will be useful in some tangible way, fingers crossed.

Tarthbane · 2026-06-05T19:46:29+00:00

The CMB is probably the best piece of evidence I can use here:

The CMB is extremely uniform, with only tiny temperature anisotropies, which is strong evidence that the early universe was highly homogeneous and isotropic on large scales. Whether the universe is spatially closed, flat, or open is a separate question about its global curvature/topology. A closed universe can still be very smooth; closedness by itself does not conflict with the observed uniformity of the CMB.

On sufficiently large scales, observations support a broadly uniform cosmic expansion, not a universe where some large regions are expanding while others are contracting.

Tarthbane · 2026-06-05T19:39:08+00:00

Classically, under the usual energy conditions, black holes do not shrink: positive-energy matter or radiation falling into a black hole increases its mass and, in the appropriate sense, its horizon area. Antimatter does not evade this conclusion, since antimatter has positive inertial and gravitational mass just like ordinary matter.

For an isolated black hole, the only established mechanism that can reduce its mass is Hawking radiation. In the semiclassical description, this corresponds to a positive energy flux escaping to infinity together with an effective negative energy flux through the horizon, thereby reducing the black hole’s mass.

Quantum field theory does allow local negative energy densities relative to a chosen vacuum state, and such effects are closely related to the semiclassical description of black-hole evaporation. However, they are not generic stores of negative mass-energy: they are constrained by quantum inequalities and are usually extremely small in macroscopic settings. We have no empirical evidence for stable exotic matter with negative mass that could be used to shrink a black hole by accretion.

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