Of Particular Significance

#### POSTED BY Matt Strassler

ON 07/25/2024

Every now and then, I get a question from a reader that I suspect many other readers share. When possible, I try to reply to such questions here, so that the answer can be widely read.

Here’s the question for today:

Below I give a qualitative answer, and then go on to present a few more details. Let me know in the comments if this didn’t satisfactorily address the question!

## First, A Qualitiative Overview

Let me first address this question for other forces:  for instance, “what is the source of gravity’s agency?” Then I’ll turn to electromagnetism, and then to the strong nuclear force. [The explanations given here are based on the ones used in the book.]

#### The Gravitational Force

What makes gravity happen? There are two answers to this question, both given in the book (chapters 13-14).

The first answer is from a field-centric perspective: the source of gravity’s effects is the gravitational field.  Object # 1 changes the gravitational field in its general neighborhood.  If object #2 wanders into that neighborhood, it will respond to the changed gravitational field that it encounters by changing its direction and speed of motion.  Watching this happen, we will say: the gravitational effect of object #1 pulled on and altered the motion of object #2.  But really, it was all done through the intermediary of the gravitational field: object #1 affected the gravitational field, which in turn affected object #2.  (The reverse is also true: object #2 affects the field around it and this in turn impacts object #1.)

The second, more complete answer is from the medium-centric perspective.  It was given by Einstein: space should be understood as a medium [albeit a very strange one, as described in the book], and the gravitational field is secretly revealing the warping of space itself (and of time, too).  In other words, what is “really” happening, from this perspective, is that object #1 warps the space around it, and when object #2 comes by, it encounters this warped space, which causes its path to bend.

Both answers are correct — they are two viewpoints on the same thing. But the second answer is more conceptually satisfying to most humans. It gives us a way of understanding gravity as a manifestation of the universe in action. The field-centric viewpoint is more abstract, and less grounded in intuition.

#### The Electromagnetic Force

For electric forces, we have a field-centric answer: the source of electrical effects (and magnetic ones too) is the electromagnetic field (whose ripples are photons, the particles of light.)  The story of how object #1 affects the electromagnetic field, which in turn affects object #2, has different details but the same outline as for gravity. (Object 1 affects the electric field around it; object 2 wanders by, and its motion is changed when it counters the altered electric field caused by object 1.)

What about the medium-centric answer?  Sorry — we don’t have one yet.  In contrast to the gravitational field, which describes the warping of space, we don’t know what the electromagnetic field really “is” — assuming that’s a question with an answer.   Perhaps it is a property of a medium, as is the case for the gravitational field, but we just don’t know.

This situation might seem unsatisfying. But that’s the limited extent of our current knowledge. Someday physicists may make progress on this question, but there hasn’t been any up to now.

There is a line of thinking (described in the book, chapter 14) in which the universe has more dimensions of space than are obvious to us, and electromagnetism is due to the warping of space along the dimensions that we are unaware of. This is called “Kaluza-Klein theory” and goes back to the 1920s; Einstein was quite enamoured of this idea, and it arises in string theory, too. But at this point, it’s all just speculation; there’s no experimental evidence in its favor.

#### The Strong Nuclear Force

The field-centric answer: the source of strong nuclear effects is the gluon field (whose ripples are gluons.)  Quark 1 affects the gluon field, which in turn may affect particle #2, which might be a gluon, an anti-quark, or another quark.  And in the proton, all the particles affect all the others, through very complicated processes involving the gluon field.

The medium-centric answer?  Again, we don’t have one yet. Kaluza-Klein theory might or might not play a role here too.

## What the Forces Have in Common

Let’s go a little deeper now.

You can’t take a first-year course in physics without wondering why gravity and electromagnetism both satisfy an “inverse square law”. If the distance between two objects is $r$, the gravitational force between them is

$F_g = -G_{{\rm Newton}} \frac{m_1 m_2}{r^2}$

where $m$ represents an object’s mass and $G$ is a constant of nature, known as Newton’s constant; the minus sign means the force is attractive. Meanwhile the electric force between them is

$F_e = k_{{\rm Coulomb}} \frac{e_1 e_2}{r^2}$

where $e$ represents an object’s charge and $k$ is a constant of nature, known as Coulomb’s constant. Note there is no minus sign: if the product of the charges is positive, the force is repulsive, while if it is negative, the objects attract each other. (Like charges repel, opposite charges attract.)

Neither of these laws, which were discovered before the nineteenth century, are the full story for gravitation or for electromagnetism; they were heavily revised in the last two hundred years. Nevertheless, the similar behavior is striking.

Remarkably, in the right settings, the strong nuclear force, the weak nuclear force, and the Higgs force also exhibit inverse square laws. Every single one. Again, there are differences of detail — minus signs, the constant in front, and what appears in the numerator — but always a $1/r^2$. What’s behind this?!

The answer? Geometry. The fact that a sphere in three spatial dimensions has area $4 \pi r^2$ is behind the inverse square laws in all the five elementary forces of nature (and some less elementary ones, too.) The reasoning is known as Gauss’s law, which I explained here (see Figure 1 and surrounding discussion). If we lived in four spatial dimensions, the force laws would instead behave as $1/r^3$; in two spatial dimensions they would show $1/r$; and in one spatial dimension, the force between two electrically charged objects would be a constant.

However, although each of the forces exhibits an inverse-square law sometimes, none of them does always. And each one deviates from inverse-square in its own way.

## How the Forces Differ

### Attraction and Repulsion

First, about attraction and repulsion. Gravity and the Higgs force between two objects are inevitably attractive forces, but electromagnetism and the nuclear forces (which all come from “spin-one” fields) can be either attractive or repulsive. [The reasons aren’t hard to show using math; I don’t know of a completely intuitive argument, though I suspect there is one.]

In electromagnetism it is simple: as I mentioned, like charges repel, opposite charges attract. But in the strong nuclear force, it is more complicated, because the strong nuclear force has three types of charges (referred to, metaphorically, as “colors”.) Quarks attract anti-quarks, but whether they repel other quarks depend on what charges they are carrying. Three quarks of different colors actually attract each other, and that’s what’s happening in a proton. [See here for some details.]

### Distance Dependence

Next, what about the distance-dependence? Electromagnetism exhibits the only force that is always close to $1/r^2$, deviating from it only by slow drifts (in math, by logarithms of $r$). All the other forces show dramatic differences.

#### The Weak Nuclear and Higgs Forces

At distances greater than $10^{-18}$ meters, 1/1000 of the radius of a proton, the weak nuclear force dies off with distance very rapidly — exponentially, in fact:

$F_{{\rm weak}} \sim \frac{e^{-M r}}{r}$

where $M$ is the mass of the W boson (the wavicle of the W field), and where I am just showing the distance-dependence and am dropping various constants and other details. The same is true of the Higgs force, except in that case $M$ is the mass of the Higgs boson. Essentially, in the language of the book, the mass of the W and Higgs bosons represent a stiffening of the W and Higgs fields, and stiff fields cannot generate forces that remain powerful out to very long distances. This is in contrast to the electromagnetic field, which is not stiff and can maintain an inverse-square law out to any $r$.

#### The Strong Nuclear Force

The strong nuclear force could not be more different. A distances approaching $10^{-15}$ meters, approximately the radius of a proton, the strong nuclear force dies off more slowly than the inverse square law, and eventually, for distances of greater than $10^{-15}$ meters, it becomes constant. One can again understand this in terms of Gauss’s law, but applied to a new physical situation that does not occur in electromagnetism (at least, not in empty space.)

This effect derives from the way that the gluon field interacts with itself, although it is far from obvious. I do give a glimpse of this story in the book’s chapter 24, where I briefly mention the feedback effect of the gluon field on itself. The full story is very subtle, eluded physicists for a number of years, and won a Nobel prize for David Politzer and for David Gross and Frank Wilczek. Today the effect is well-understood conceptually, and computer simulations confirm that it is true. But no one has completely proven it just using mathematics.

The effect is also responsible for why a proton has a larger mass than the objects (quarks, anti-quarks and gluons) than it contans, as I recently explained here.

#### Gravity

Gravity is different in the opposite sense: instead of deviating from the inverse square law at long distance, as the nuclear forces do, it does so at short distance. Somewhat as the long-distance effects in the strong nuclear force are caused by the gluon field interacting with itself, the complexity of gravity at short distance is caused by the gravitational field interacting with itself… though the former is caused by quantum physics, while the latter is not.

For elementary particles, the distances where gravity deviates from $1/r^2$ are far too short for us to observe experimentally. But fortunately, large objects such as stars magnify these effects at distances long enough for us to observe them.

The fact that the gravity of the Sun is not quite inverse-square, but has a small $1/r^3$ component, is what causes the orbit of Mercury to deviate very slightly from the prediction of Newton’s laws. This shift was calculated correctly by Einstein, using the new theory of gravity that he was then developing, and gave him confidence that he was on the right track.

Much more dramatic are the effects near black holes, where force laws are much stronger than the Newtonian inverse square law. These are now observed in considerable detail.

## Summing Up

Remarkably, despite all the diversity in the behavior of the five known forces, each one arises in the same way: from a field that serves as an intermediary between objects (which themselves are made from wavicles in these and other fields). This leads naturally, in three spatial dimensions, to laws that are inverse-square, modified by details that make the forces all appear very different. In this way, the huge range of behavior of all known processes in nature can be addressed using a single mathematical and conceptual language: that of quantum field theory. [This is a point I wrote about recently in New Scientist.]

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### 49 Responses

1. Joseph says:

Dr.Strassler:
Excuse my ignorance with the following question, I took a “basic” modern physics course, about 45 years ago, so I hope this question doesn’t seem too ignorant. The role of momentum in General Relativity. According to Einstein, the warping of SpaceTime is caused by the concentration of energy. Newton got part of it correct, in that the presence of “mass” (a manifestation of energy) causes warping. However, other energy also contributes to warping. For instance, the fact that a planet is rotating causes a contribution to the gravitational field. But, how about momentum ?(not kinetic energy) is the contribution of momentum to gravity, not only the magnitude of momentum, but also its direction of travel thru the field? In other words, two objects with the same magnitude of momentum…..but different directions of travel thru the field, will experience different gravitational effects?

1. My goodness, you’re asking quite sophisticated questions; no reason to excuse anything here.

You’ve asked the question in a way that is somewhat confusing.

The direction of motion certainly matters to gravity, but it also does to electromagnetism, too; a moving object has a magnetic field whose orientation depends on which direction the object is going. Nevertheless, it doesn’t mean that there’s anything really different if there’s nothing else in the entire space. If space is empty except for the one object, then all directions look the same and are equivalent, in which case, even though the gravitational field (or electromagnetic field) is oriented differently depending on the orientation of the object’s motion, all effects are otherwise the same.

On the other hand, if there is are other objects in the space, then yes, clearly the direction matters; some directions are toward other objects and some are not, and so both electromagnetic and gravitational effects depend on how the motion of an object is oriented relative to the positions and motions of other objects.

1. Joseph says:

Dr.Strassler:
Yes, that answers the question, thank you. I think I was trying to reconcile that ALL energy contributes to the gravitational field, such as the fact that the rotational kinetic energy of the earth contributes to the gravitational field of the earth, although if I remember correctly, it’s negligible for the earth. However, the rotational kinetic energy of a neutron star, rotating very fast, would make a measurable contribution.

However, translational kinetic energy does not seem to contribute to gravitational effects, but momentum, which has both magnitude and directional dependence does.

1. Joseph says:

Dr.Strassler:
I probably should mention that I understand that it’s the cross product of the velocity with the gravitational field that describes the momentum contribution to gravitational effects. However, if the body generating the gravitational field is not rotating, would there still be a cross product?

“Gravity without mass.”

So, could the medium-centric answer for all the “forces” be the electromagnetic field? In other words,

Space = Energy = Electromagnetic Field

And in keeping with Einstein’s GR, the “mass” that curves space is the energy density, i.e. how tightly curled up the EM fields is.

Based on this postulate, both Black Holes and the atomic nuclei are very tightly curled EM fields, extremely high energy densities, i.e. “gravity without mass”.

3. Bob Schwerzel says:

Just to dive a little deeper into the “medium-centric” approach to gravity (which also includes a gravitational field!), is it correct to assume that the curvature of space-time originates at the “local” level of each individual component of mass-energy within an object (quarks, gluons, electrons, etc.) and that the sum of these individual contributions somehow propagates out into the surrounding space-time as the overall curvature that Einstein’s equations describe? I have a hard time visualizing how a gravitational field alone could interact with space-time!

1. In saying “local”, I think you are imagining electrons etc as strict “particles” — pointlike objects that are point-like sources of gravity.

This is not the way field theory works; the objects in question are somewhat spread out (this is why I sometimes use the term “wavicles” instead of “particles”, so that we don’t have the wrong image in our heads when we try to imagine what is going on) and their gravity is not generally sourced at a point-like position. The mass-energy of electrons quarks etc is not constructed as a set of points.

Your last sentence is confusing to me: “I have a hard time visualizing how a gravitational field alone could interact with space-time!” The gravitational field is a property of space-time; it is not interacting with it anymore than air pressure “interacts” with air. It does, in a sense — but really, that’s not the right verb.

1. Bob Schwerzel says:

I don’t think I phrased my question as well as I could have. What I don’t understand is how mass causes space-time to warp – or is this just another way of saying that the gravitational field of the Universe is distorted by the presence of mass? I have a mental picture of each small component of, say, the Earth – each proton, neutron, etc. – contributing its own individual small amount of gravity, with the sum of all these adding up to the gravity of the Earth as a whole. But does this then imply that the space-time surrounding each of these individual components within the Earth is warped to some small extent, such that the sum of all these small warpings adds up to the overall warping caused by the entire Earth?

1. In Einstein’s theory, spacetime responds to the presence of energy and momentum. Yes, each individual object’s energy warps the space around it, though for the known elementary particles, this is to an ridicuously small degree, and not really large enough to be described by Einstein’s mathematics.

It takes an insanely large number of elementary “particles” to create a noticeable amount of warping; the warping around the Earth is very small. The math of Einstein’s theory doesn’t require looking at exactly where all the microscopic particles are located in order to get an excellent average description of the warping.

To get significant warping requires crushing a significant number of elementary particles into a clump the size of its Schwarzschild radius. If that radius is large enough compared to 10^{-35} meters, then Einstein’s theory can describe it just fine, again in a slightly averaged sense.

But for certain questions, Einstein’s theory can’t provide clear answers. In such cases we don’t know exactly what happens; quantum physics of the gravitational field, or other corrections to Einstein’s approximate description, can be important. String theory gives a possible answer in some cases; even though string theory isn’t necessarily the real world, it does give us examples of what kind of beyond-Einstein answers might make sense.

Does that help?

1. Bob Schwerzel says:

Thanks, Matt – that does help. I had wondered whether the fact that gravity emerges at the level of individual wavicles might somehow provide a path to a theory of quantum gravity? Is there a way for a quantum field theory of gravity to be consistent with Einstein’s results?

1. There’s no problem writing down a quantum theory of gravity that has gravitons interacting with other wavicles. Such a theory can compute many things, at the expense of being imprecise and incomplete. But it only breaks down at extremely short distances/high energies. While that’s a serious blow to having a complete theory — for instance, it makes it impossible to know what really happens at a black hole’s singularity or how the universe emerged, or to do high-precision calculations — it doesn’t cause a problem for your question.

String theory gives an example of how a complete theory of quantum gravity can work, and it is completely consistent with what I told you in the previous paragraph; if you didn’t know about the full structure of string theory, there are still many things that you could calculate in low-energy quantum scattering of wavicles.

4. Jason Stanidge says:

You wrote an article on how momentum and energy are defined by theoretical physicists from Noether’s theorem: https ://profmattstrassler.com/articles-and-posts/particle-physics-basics/mass-energy-matter-etc/mass-and-energy/

“Why is energy conserved? Because of a mathematical principle that relates the apparent fact that the laws of nature do not change with time to the existence of a conserved quantity in nature, which by definition we call energy’.”

Likewise: Why is momentum conserved? Because of a mathematical principle that relates the apparent fact that the laws of nature do not change with position to the existence of a conserved quantity in nature, which by definition we call momentum’.

I’m under the impression that theoretical and experimental physicists need to know how the energy and momentum of a system changes with some quantity, such as time. Defining force is a convenient way of doing this such as via Newton’s F = dp/dt. There are increasingly more sophisticated definitions, but still operating upon a definition of momentum for that system via Noether’s theorem above. Knowing about this I think helps in establishing a firm footing in the debate over what is and what isn’t a ‘force’.

1. Well, that’s a reasonable opinion, but hardly a establishment of a “firm footing”. Again, how do you address electromagnetism in the Kaluza-Klein context, where it clearly isn’t any more (or less) a force than is gravity?

1. Jason Stanidge says:

Trying to establish a firmer footing: I currently believe that if a theory can be written down using the principle of least action; then some of the terms in the resulting equations of motion can be labelled ‘forces’ when they resemble what’s commonly understood as a legacy force from a previous theory.

In basic mechanics, we define a quantity L = kinetic_energy – potential_energy that we mathematically minimize. The Euler-Lagrange equations automatically emerge; we then label the accompanying mathematical variables in it as force, energy, momentum etc from how they resemble the variables in Newton’s laws of motion.

Newton’s theory of gravitation can be written using a principle of least action, so can Einstein’s. Yet when I hold a pen above my desk and let go, the desk accelerating to meet the stationary pen is of more theoretical value for me than the pen accelerating to meet the stationary desk; as claimed by Newton’s theory. Since Einstein’s theory supercedes Newton’s; it will at the very least show how Newton’s force terms emerge from within Einstein’s theory and not vice versa.

Does Einstein’s theory of gravitation have ‘force’ terms in it?

I’m not competent enough to give an informed opinion for EM in the Kaluza-Klein context; but to start with I’d ask myself: is it founded upon a principle of least action and, if so, what do the force terms look like?

1. The Kaluza-Klein context is Einsteinian gravity in 4 spatial dimensions, one dimension of which is finite in extent. Or more than 4. Always action principles, or rather their quantum version; or Hamiltonians. Never force laws unless you decide you want to write things in that way. That’s true throughout modern field theory. Field equations are not force laws; just look at electromagnetism.

1. Jason Stanidge says:

I can see why you’re correct. I’ll give my further thoughts because it leads at the end to what I believe force represents from a *classical* viewpoint: how the two centers of energy/mass of two interacting fields are affected when the fields exchange energy and momentum with one another.

Solving Gauss’s law for a stationary charge +q gives the standard Coulomb electric field. I don’t even need to know how the electric field E is measured in the real world because here, it’s just maths. From this, I can get another solution to Maxwell’s field equations using the transformations of special relativity; or again solve Maxwell’s equations directly. Both methods give the same solution: an electromagnetic field moving with the same velocity v as the charge +q.

The equation of motion for the charge +q in the above is d/dt (mv) = 0 where m is the mass of the charge, and v is the velocity of its center of mass; where the charge is located. Similarly for the moving electromagnetic field: d/dt (m’v) = 0 where m’ is calculated from its total electromagnetic energy E’/c^2; and v is the velocity of a unique point calculated as the field’s center of mass/energy. Here, the center of mass of the charge and the center of mass/energy of the electromagnetic field coincide with one another.

Adding more charges, there’s now a net transfer of momentum and energy between the electron field of the charges and the electromagnetic/photon field. This leads to a change in the velocity of the center of mass for each of these two fields. However, the total combined center of mass of the two fields still moves with a constant velocity v: d/dt (mv + m’v’) = 0 or d/dt(mv) = -d/dt (m’v’).

I find the above adds weight to the idea of classical gravity having the property of a force in transferring or absorb energy/momentum from other fields.

What happens to the idea of a field having a center of mass/energy in quantum field theory and how are my above points affected?

1. If you take sufficiently simple, linear systems — electromagnetic fields coupled to a single object — you will often be able to write results in many simple ways. But even then, there are extreme subtleties with classical systems: here is someone’s talk about it that seems sensible, though I’d like to find you a more professional version.

I don’t think any aspect of your approach survives to quantum field theory. There are many, many things wrong with it. These issues are subtle, however, so I don’t claim I can point out all the flaws correctly with a cursory analysis. It might be that for some aspects, your approach can be generalized.

But even in classical physics for multiple charges, there is electromagnetic radiation going off to infinity, so I do not believe you can define the “center of X” for the system. This will certainly be true in accelerated quantum systems; if the forces on them are strong enough, they will be disrupted and will radiate.

I wrote “center of X” because “center-of-mass” is not “center-of-energy”. Indeed, mass is a Lorentz scalar, while energy is part of a Lorentz vector, and so it is not benign to call them the same thing; you need to choose. Once you have defined what you want, you need to give me an integral formula for it, and then we can try to compute it to see if it is finite. I doubt it will be.

Remember the field energy around a classical particle integrates to infinity. To make it finite you have to make the particle of finite radius, as in https://en.wikipedia.org/wiki/Classical_electron_radius . Once you do that, you have introduced new, unspecified “forces”, and the problem is now ill-defined.

Quantum field theory addresses this problem in a different way, but there are all sorts of subtle infinities which have to be subtracted off to define the problem, and very few settings in which this can be done in a completely controlled way. Quantum electrodynamics is not one of them.

Finally (for now), if you have a system of multiply charged objects that you say is subjected to a force — well, where and how does the force act? If it is a four-particle system, for instance, does the force act on particle 1, particle 2, particle 3 or particle 4? Or all four of them? Maybe there are huge forces on all four particles that almost perfectly cancel, so that the net force is tiny even though the particles are driven apart at near light speed, radiating away lots of photons? In your approach, all these are treated in exactly the same way. Quantum field theory (and even classical relativistic electromagnetism, for that matter) has no idea what to do with the limited information that you are providing.

Sorry I can’t be more systematic here, but it would take real work and time to really organize these thoughts.

1. Jason Stanidge says:

Thanks for your points. I don’t expect you to dive too deeply into this for my sake without your blog or you directly benefiting in some way.

It’s gradually dawned upon me that my above ideas are another symmetry of a physical system, in addition to time and space translations which you mentioned in your article on energy that I linked to at the beginning: changes to the velocity of the measuring laboratory aka boosts.

There’s various articles on this including from John Baez and Wikipedia; but I like this one from TH Boyer:
Illustrations of the Relativistic Conservation Law for the Center of Energy
https://arxiv.org/abs/physics/0501134

Is this a way of defining force for a field theory, on the same footing as energy and momentum, and hence extracting the Lorentz force law from Maxwell’s field equations?

In the various textbooks I’ve read on classical electrodynamics including Jackson’s; I’ve never come across anyone deriving the conservation of energy from Maxwell’s field equations directly using the idea of time translation invariance. It’s something I’ll have a go at as a private homework problem, and then the Lorentz force law if your comments are in agreement.

Panofsky-Phillips “Classical electricity and Magnetism” (2nd ed) defines the Lorentz force by paring down the expression derived from the Poynting vector representing field energy (and momentum, by way of the Lorentz force derivation) to “the resultant force that arises from spacetime average forces acting on material charges and currents”. [Pp 180-184.] They describe it as the suggestion of Lorentz and his “electron theory” that this is the only force that has “physical significance” of the longer expression [eq 10-40, 10-41].

In later chapters they derive that this is the correct covariant expression for the equation of motion of a charged particle in an EM field, so there’s that too. [Pp 251-252.]

The energy conservation of the EM field in vacuum is derived (by the reader) from that the divergence of the Poynting vector is zero, signifying absence of a net energy flow. “For example, in static superposed electric and magnetic fields in the absence of currents we may have non-zero values of the Poynting vector at various points in space, but its divergence vanishes everywhere, as can be seen from Eq. (10-33).” The Poynting vector is derived from an energy integral of Maxwell’s equations (from the scalar product of the H and E equations, specifically – I’m sure there are other ways).[Pp 178-181.]

If you want to go the other way around from covariance, it should be the one given in PP, I hope. Oops of severe typo in the earlier comment: that part would be pp 331-332.

3. Jason Stanidge says:

Thanks to Matt and Torbjörn Larsson for the concluding comments below which I’ve noted.

The material is of the type that non-experts can scrounge up since there is scant general descriptions answering Cox’s question. YMMV.

1. Jason Stanidge says:

Yes. Some of the readers here might not be aware of the slightly more technical articles Matt has written in the past on related topics. I couldn’t find anything on force like the energy-mass article; so I tried to give my opinion in a comment in a way vaguely on the same technical level that might be of some value to someone reading it. Bearing in mind me being corrected by Matt and learning something new.

Bear in mind that, for some reason where I’m the likely suspect, my misplaced reply was to Matt in another conversation. I’m sorry for the confusion!

The material is of the type that non-experts can scrounge up since there is scant general descriptions answering Cox’s question. YMMV.

The material is of the type that non-experts can scrounge up since there is scant general descriptions answering Cox’s question. Of course, YMMV.

So, no – it looks like it’s not my fault but the page script that has problems with placing replies.

“Gravity and the Higgs force between two objects are inevitably attractive forces, but electromagnetism and the nuclear forces (which all come from “spin-one” fields) can be either attractive or repulsive. [The reasons aren’t hard to show using math; I don’t know of a completely intuitive argument, though I suspect there is one.]”

I don’t know if it is “completely” (or at all) intuitive, but builds on my understanding of fields implementing Lagrangian action principles on energies to explain attraction and repulsion:

Asserting a lower energy bound gives different signs in the equation of motions for spin-zero and spin-one fields. It seems in the latter case the existence of antiparticles makes for the difference. https://physics.stackexchange.com/questions/433678/why-is-boson-spin-number-related-to-attraction-and-repulsion

Personally I’m not convinced that we should break out the medium-centric perspective for simplifying the non-linearities of gravity as a guideline, since I find the shared field-centric perspective more intuitive and conceptually satisfying. But that’s me.

Finally I know this is familiar but it may bear to point out: “each of the forces exhibits an inverse-square law sometimes” means that when you have a massless force carrier (electromagnetism, gravity) we can see cosmologically long range forces. The Gauss law link implies that bar constraints the field can do this, and I find that intuitive as well.

6. Julian Marc Collins says:

Hi Matt. I have long thought that gravity is fundamentally different in that unlike the other forces General Relativity is telling us that gravity is, in fact, not a force at all. It is simply objects moving under the influence of no force in a curved spacetime, which deceptively makes us think a force is acting when in fact no force is acting. Could this view not explain why all attempts to produce a quantum field theory for gravity have been unsuccessful, as this view would mean that such attempts are doomed to fail, as gravity is fundamentally different?

1. It always amuses me when experts say this about gravity.

What, pray tell, is a “real force”? You know, the thing that gravity is not… what is that?

Are electric forces real forces? How do you know that they are?

In Kaluza-Klein theory, electromagnetism arises from higher-dimensional gravity, and is just as “fake” (if you want to call it that) as gravity. We have no idea where the other elementary forces come. I have no idea what you imagine a “real force” to be, but electromagnetism probably won’t turn out to be that.

Regarding your question: the fact that gravity can be understood in terms of curved space time does not explain the difficulties with quantum gravity, which instead have to do with the fact that gravity becomes stronger in higher energy processes, unlike electromagnetism whose strength remains roughly constant. We had similar difficulties with Fermi’s theory of the weak interactions, which also became stronger at higher energy; those issues had to be solved with the introduction of the Glashow-Weinberg-Salam electroweak theory. There were also issues with the theory of interacting pions, and those were solved by realizing that pions, protons and other such things are made of quarks, anti-quarks and gluons. String theory or some other more complicated theory may solve the problems of quantum gravity.

Moreover we’re not even sure spacetime is real, or at least whether it is fundamental. So saying “simply… moving under the influence of no force in a curved spacetime” begs lots of questions too. In other words, this so-called “not-a-force” gravity may well turn out to be not-a-not-a-force.

7. Joseph says:

Dr.Strassler:
From a math standpoint, if gravity & electromagnetism didn’t follow an inverse square law, how would we ever separate things? In order to separate objects, the force must drop towards zero fast enough, as it does in an inverse square law. Wouldn’t the operations of the universe be very different if it was a 1/R^1 law?

1. Joseph says:

Dr.Strassler:
Disregard the above question, I just read your blog that you linked in the text, explaining Gauss’s law.

1. There’s still merit to the question.

There would be no specific problem if electromagnetism were a confining force, or even 1/R, because electrically neutral objects could separate from one another — just as protons and neutrons, which are neutral under the strong nuclear force, can separate.

I can’t currently remember coming across a sensible notion of a stronger-than-1/R^2 gravity force in 3 spatial dimensions — though if the scale at which the new force law took over were enormous (i.e. universe-sized) I’m not sure it would have much effect.

8. Jason Stanidge says:

I think many readers would benefit from a self contained article on how Coulomb’s law arises using the QFT model; and how this differs from the classical model that’s currently taught in high school and many university level classical electrodynamics courses. It’s possible to work this out from the various articles you’ve written on this in your blog and in your book, but they might be too difficult to find for some folk. For example:

In classical EM, the field is considered an intrinsic part of a point charge; thus contributing to its energy and mass. A charge’s Coulomb field has an existence independent of other charges.

In QFT, the EM field and electron field are separate but interact; giving rise to disturbances and wavicles in one another’s field. The rest-frame energy and hence mass of an electron is fundamentally a consequence of the Higgs field interacting with the electron field. For a Coulomb field to exist requires at least two electron/positron wavicles interacting with one another via the photon/EM field.

I think understanding the basics of the above is essential for anyone wanting to seriously understand your recent articles, for example.

1. Not everything in your third paragraph is strictly true.

Moreover, to do a proper explanation of Quantum Electrodynamics is much harder than you suggest here. There are many deep subtleties that you haven’t mentioned, such as the fact that the electron’s electric charge has to [formally, more than physically] be made infinite in order to even have a finite Coulomb field. So really we have to embed this theory into another one that regulates the infinities, or we’re just begging lots of questions. The electron’s interaction with the Higgs field is also subject to [formal] infinities.

In short, either you use the semi-classical model (which captures all of the physics that’s easy to explain, already clear in first-year undergraduate physics) or you do quantum field theory properly, and then it is a lot of work pedagogically. I’ll think about it, but I’m not sure it’s doable.

9. jansammer says:

“object #1 affected the gravitational field, which in turn affected object #2.” But what is a gravitational field? A region of space within which an object experiences a given force. Thus your
attempted explanation is nothing more than a definition of what constitutes a field. What needs to be explained is the *mechanism* whereby object #1 affects (or, better said, generates) the gravitational field in its vicinity. No such explanation is forthcoming, attempted, or even deemed necessary. But that’s exactly the crux. Unless you are able to account for the mechanism whereby object #1 affects the gravitational field, you’re just begging the question.

1. What I said in the post precisely addresses these issues. The field-centric explanation is a description (with detailed math), but not a satisfactory one to most people, because it lacks a mechanism. [Note however: no one said there had to be a mechanism; you are making an assumption that one exists, and one should be careful about such assumptions.]

But for gravity, the medium-centric explanation of Einstein does exactly what you claim is missing: it explains what the field is and what the mechanism is. So your complaint holds no water; answering you is exactly what Einstein was doing in general relativity over 100 years ago.

I wish we had a medium-centric explanation for other fields, but we do not have that yet. Physics is not over; we have many unanswered questions, and that’s why we continue to do research.

10. Jeff Cox says:

Very satisfying, Dr. Strassler and much appreciated. But what do we know about how fields come about? They have influence resulting in power resulting in wavicles. i get it. But how do fields arise? Do we know or speculate? –Jeff

1. That has a simple answer: we do not know.

Experiments and theoretical explorations have taught us that thinking about the world in terms of a set of fields is useful and powerful; we are very clear about what the fields do and can calculate their behavior with great precision and accuracy.

But we do not know why the world has the fields it has. The only field for which we have some explanation is the gravitational field (as representing the warping of spacetime.) The rest are just deduced from observations; there is no underlying theoretical explanation.

There are many speculations. String theory is an attempt to explain the fields, for instance, though it is vague about the details. It builds on an elaborate forms of the Kaluza-Klein approach mentioned in the book (chapter 14), with additional bells and whistles. There are others, too.

But fundamentally this is a matter of ongoing research, and I doubt that you and I will live to find out the complete answer. We will certainly need some additional clues from nature.

For a (potentially misleading but) partial description of “how” of potential dynamics of fields, specifically their importance and existence during different cosmological eras, this video by another particle physicist may be useful: https://www.youtube.com/watch?v=OHdUFPAK7f0&ab_channel=SixtySymbols

It mentions putative diminutive “probe fields” during inflation and how the inflation field, I take it, may completely ‘tear itself to pieces and vanish’ if it doesn’t linger on in diminutive form.

1. The linked video involves quite speculative physics, not properly caveated, and I do not endorse it.

11. Kris says:

Why would warping of extra dimensions affect movement in our three (or four) regular dimensions, and not only in the warped dimensions?

1. I think a lot of people somehow have this idea that our three dimensions represent one place, and any extra dimensions represent another place. Certainly a lot of movies talk about extra dimensions this way.

But this is all wrong. Extra dimensions are an extension of our place. They’re right next to us, just as our familiar dimensions are, and what is happening there certainly affects us.

For instance, suppose you were a worm living in a long thin tunnel. As far as you can tell, the world is one-dimensional: all you do is crawl forward. None of your senses tell you the tunnel has a width. But if the tunnel suddenly became narrower than usual, you would certainly discover that you could no longer proceed.

If you lived on the surface of a thin piece of metal and listened to the sounds produced inside the metal, you’d hear special sound waves corresponding to the metal’s thickness. Any change in that thickness would change the sounds you hear.

12. It is a great question, but one that is difficult for Dr. Strassler to answer beyond a descriptive level because no physicist has ever found a mathematical framework that explains the relationship between the electric force and the color force. Such a framework would presumably explain both the similarities and differences in a more insightful way.

13. David Farrelly says:

Very nice but just basically a description of how we (you) undestand the universe. I think the question that was asked has the answer “we don’t know why things are the way they are.” But you did a good job of explaining how to understand how stuff operates.

14. Thomas Hendrix says:

“…where e represents an object’s *mass* …” should be charge?

15. Is that a typo: “where e represents an object’s mass”, did you mean charge?

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