“There’s something about sitting alone in the dark that reminds you how big the world really is, and how far apart we all are. The stars look like they’re so close, you could reach out and touch them. But you can’t. Sometimes things look a lot closer than they are.” -Kami Garcia

When we consider things like molecules, atoms, or even protons and neutrons, they all have finite, measurable sizes. Yet the fundamental particles that they’re made out of, like quarks, electrons, and gluons, are all inherently points, with no physical size to them at all. Why, then, does every composite particle not only have a size, but some of them, like atoms, grow to be relatively huge almost immediately, even with only a few fundamental particles involved?

From macroscopic scales down to subatomic ones, the sizes of the fundamental particles play only a small role in determining the sizes of composite structures. Image credit: Magdalena Kowalska / CERN / ISOLDE team.

It’s due to three factors that all work together: forces, the quantum properties of the particles themselves, and energy. Since the strong and electromagnetic forces work against each other, quarks and gluons can form finite-sized protons; protons and neutrons assemble into nuclei larger than the protons and neutrons combined would make; electrons, with their low mass and high zero-point energy, orbit around nuclei only at great (relative) distances.

The energy levels and electron wavefunctions that correspond to different states within a hydrogen atom, although the configurations are extremely similar for all atoms. The energy levels are quantized in multiples of Planck’s constant, but the sizes of the orbitals and atoms are determined by the ground-state energy and the electron’s mass. Image credit: PoorLeno of Wikimedia Commons.

Matter doesn’t need to be made of finite-sized particles to wind up creating the macroscopic Universe we know and love. Find out how on this week’s Ask Ethan!


  1. #1 Another Commenter
    September 16, 2017

    The Pauli Exclusion Principle goes a long way towards explaining why matter occupies space.

  2. #2 Patrice Ayme
    September 16, 2017

    Delocalization, plus the Pauli Exclusion Principle explains how matter makes space.

  3. #3 Michael Mooney
    September 16, 2017

    “Yet the fundamental particles that they’re made out of, like quarks, electrons, and gluons, are all inherently points, with no physical size to them at all.”

    Another Ethanism presented as a fact.
    A point is a virtual locus, not a very small volume, which is required for the occupancy of any particle, however small.
    (Same fallacy as Hawking’s “zero volume singularity.”)
    In layman’s language, the size of particles and the space between them determines the size of the composite.

  4. #4 Frank
    September 16, 2017

    “Yet the fundamental particles that they’re made out of, like quarks, electrons, and gluons, are all inherently points, with no physical size to them at all.”

    IMHO could we interpret this as meaning:
    Elementary quantum particles are not (solid/liquid) physical objects and they do not occupy any finite volume.
    Maybe because they are emergent properties, only really exist as similar to quasiparticles (clusters of information),
    defined (virtually exist) on an ND Cellular Automata Quantum Computer?

  5. #5 Frank
    September 16, 2017

    If anyone interested here some of my ideas about quantum computers:

  6. #6 Kasim Muflahi
    United Kingdom
    September 16, 2017

    I agree with the implication of the question i.e. it implies that electrons, quarks etc. shouldn’t be described as zero-volume points because they have mass; and mass is quantised so that it can’t exist in a zero volume point. If it did, it’d be a black hole.

    This also means that zero-volume singularities are physical impossibility despite the fact that GR predicts. In fact, the latter implies that GR has limitations i.e. a domain of validity and it’s being used beyond that domain.

    Consider the ‘ideal’ gas laws whose particles have mass but zero volume; its volume-temperature reaches zero at zero kelvin. But what happens to real gases? They liquefy or sublime to a solid. Either way, they cease to be gases and the gas law doesn’t apply. It means that real gas laws have a domain of validity.

    Taking that as a clue, I can say that something happens to GR at small distances that invalidate it. Hence, GR is being used beyond its domain of validity.

    It’s similar with fundamental particles; scientists are using point particles because it makes the maths easier. This implies that fundamental particles do have a finite size but using those sizes in the formulas make them unwieldy. Hence, the results of such equations, that use point particles, are approximations to reality. They could be wildly out..

  7. #7 Frank
    September 16, 2017

    We have both MM and Kasim here. Nice! 🙂
    I saw comments from Pentcho for some article on Quanta. 🙂
    (It looks like my comments (using a Disqus account) do not appear on Quanta for some reason.)

  8. #8 CFT
    September 16, 2017

    If particles were points, they wouldn’t be able to collide, and break apart in particle colliders. Strange that Ethan would take this perspective. Points would also not be stopped by other points, much less reflected by them, so I guess mirrors at LIGO don’t work anymore either, much less in a super size telescope. A point can not have a density either, so I guess a particle having mass is also a no go…This is basically why the gauge math is wrong and they had to come up with the bag end math of the Higgs field, to cover the fact their math didn’t do what particles in the accelerators were doing. Points aren’t particles, particles aren’t all the same non-size, and according to particle colliders, they do have mass.

  9. #9 Kasim Muflahi
    United Kingdom
    September 17, 2017

    It’s nice to be recognised but, Frank, are you gonna include CFT? He seems to agree with us.

  10. #10 Sean T
    September 17, 2017


    You have things completely backwards. The mathematics needed to deal with finite-sized fundamental particles is completely non-problematic and quite a bit simpler than the mathematics of point particles. Why point particles then? All attempts to measure the sizes of fundamental particles experimentally give the same answer – zero. AFAIK, a finite size is not completely ruled out, but the upper limit is very small, approaching the Planck length. In fact that was one of the features that made string theory attractive. String theory maintained that fundamental particles had a finite size.

    • #11 Kasim Muflahi
      United Kingdom
      September 17, 2017

      Would you agree that a singularity is a point particle that has the what’s left of the original star in zero-volume? Isn’t that what a point particle in physics is? i.e. all the mass and charge in a zero-volume point particle. AFAIK, this is a physical impossibility.

      The alleged fact that, when scientists try to measure the size of certain particle, they get zero; implies that the measuring technology isn’t advanced enough. When it does become up to scratch, we’ll not only determine the size of so-called point particles, but also their substructure.

      It’s better to assume that alleged point particles do have a finite size to hold the mass and charge. How was the charge to mass ratio of the electron measured?

      The mass of the earth, for instance, is considered to act as a point particle at the centre of the earth i.e. this is for convenience sake. The same applies for all other oint particles – just for convenience.

      Using the earth analogy, different regions of the earth exert different gravitational forces known as tidal forces. The same would happen with point particles if their actual size were known.

      So, even if scientists are taking tidal forces into account with macroscopic particles, they’re ignored with point particles thus rendering them approximations.

  11. #12 Sean T
    September 17, 2017

    Why do you think point particles cannot collide? A collision is an interaction occurring at close approach and over a short duration. Collisions need not involve actual physical contact. Two electrically charged point particles certainly can approach closely and interact via the electromagnetic force. That’s a collision.

    It also is advisable to keep quantum mechanics in mind. Point particles also behave as waves. Two waves certainly interact when approaching each other. Even a point particle has a finite wavelength. Point particles approaching closer than this wavelength will interact.

  12. #13 John
    September 17, 2017

    Sean T,

    As stated in the Forbes article, the LHC constrains the size of the point particles to less than 10^−19 meters. As the Plank length is just over 10^−35 meters, then I suggest we have somewhere around 16 orders of magnitude to go before becoming confident that the size of fundamental particles, the electron being an example, is equal to zero.

    This is, of course, only a small qualification to your comment.

  13. #14 Frank
    September 17, 2017

    Maybe because CFT is no fun?

  14. #15 Michael Mooney
    September 17, 2017

    @ Patrice Ayme #2
    Matter doesn’t “make space.” It occupies space. Particles, however small, occupy space. It requires ” ignore-ance” of fundamental geometry to claim, as Ethan does, that anything can exist in zero volume. But the most famous physicist since Einstein (Hawking) claimed that everything in the universe came out of an original singularity of “zero volume and infinite mass density.” (Also erroneously applied to black holes.) No wonder cosmology and astrophysics has in many cases become fantasy model building based on nonsense like that.

  15. #16 Michael Mooney
    September 17, 2017

    This will address the philosophical basis of Ethan’s misconception described in #14. He is a self described instrumentalists. So, if its too small to measure (presently), it has no “size,” just a point. That is the basic conceit and fundamental error of his philosophy.

    “Instrumentalism is thus the view that scientific theories should be thought of primarily as tools for solving practical problems rather than as meaningful descriptions of the natural world. Indeed, instrumentalists typically call into question whether it even makes sense to think of theoretical terms as corresponding to external reality. In that sense, instrumentalism is directly opposed to scientific realism, which is the view that the point of scientific theories is not merely to generate reliable predictions but to describe the world.”
    My criticisms in this forum are (and have always been) based on scientific realism as used in the above sense.

  16. #17 Kasim Muflahi
    United Kingdom
    September 17, 2017

    @Michael Mooney

    I concur. I’ve had similar arguments about scientists use predictions as proof of interpretation e.g. GR predicts that TIME passes more quickly in orbit than it does on the ground. The explanation given is that gravity makes TIME pass slowly and lack of gravity makes it pass more quickly. So, they use the difference between GPS clocks and ground-based clocks as proof of gravitational time dilation when it could be the effect of gravity on the clock’s mechanism.

    I’m not trying to change the subject but to illustrate the misinterpretation of observations. I’ve concluded that the mainstream interpretation of observations is at least debatable if not false. Hence, the interpretation of some particle as being point particles is at least debatable.

  17. #18 CFT
    September 17, 2017

    @Sean T,
    There is no way for a point to collide with another point, even in geometry, as there is no physical cross section. If it has zero size, what is carrying a charge? Or what is producing the wave you are measuring? Nothing? Just causeless amplitudes without a source? What makes you think it can happen in physics? If you have ever examined particle collisions, they indicate not only is something there with mass and a physical cross section, it is also spinning very rapidly, something which points can not physically or geometrically do.
    If your mathematical models of particles have no size (thus no internal structure), you don’t have models of particles at all. You have abstract mathematics carrying physical forces, dismally, which is not physically or logically possible…unless you subscribe to the very unscientific magic of mathematical Platonism.
    I refuse to subscribe to any variation of the dogma of mathematical mysticism. Math is not reality, reality is not made of math. Math is just an internally consistent man-made language being used to model a description of reality.

  18. #19 Axil
    September 17, 2017

    Recently, I have become fascinated by the concept of the tachyon. It is a particle with negative mass. This fasciation has been stoked by the recent release to the LENR community of a SEM micrograph of a sample of fuel that is being used in a LENR reactor. Here is one of those pictures:


    The tracks that the LENR active particle is taking correspond to the tracks that are predicted to come from a tachyon monopole. The sort of track has been seen many times in the photoemission studies of LENR ash samples. It is uncertain what that LENR active agent is but the indications are good that the LENR active particle is a metallic hydrogen nanoparticle that has been formed by a LENR fuel preparation process.

    My interpretation of this picture is as follows:

    The fuel is the microparticles of metal that the tape is supporting. There is an unseen active LENR reaction agent that is too small to see in the micrographs. I believe that this agent is metallic hydrogen since only hydrogen is present with the a unspecified transition metal. But these agents might be metallic hydrogen nanoparticles. The crystalline like fractal patterns seen on the tape surface and on the metal micro-particles are the LENR reaction trails produced by the metallic hydrogen as it converts matter into energy via a transmutation of elements process.

    The reactor builder states that:

    “The background is carbon adhesive tape that is commonly used for SEM.
    In the Full BSD electron topology one can see elemental composition of the sample. Higher atomic number, the brighter the color is.
    Yes, the shiny particles are metal hydrides.
    The tracks are made of a various elements. The starting element is usually of lower atomic number, while at the end it is higher.”

    Very little heat is produced by the LENR reaction because the carbon tape is not destroyed by the reaction. The energy from the reaction is stored in the structure of the metallic hydrogen as it moves along the surface of the tape and the metal.

    The LENR reaction is minimal at this quiescent stage but it can continue for weeks at this low level. During this stage, the metallic hydrogen is self-sustaining. When the fuel is activated by a high potential EMF field the LENR reaction produced by the metallic hydrogen increases exponentially. At his stage, the heat output is generated through an enhanced LENR reaction. A positive feedback mode is established as heat production increases the heat output. This is self-sustain mode.

    The metallic hydrogen when not activated produces a low intensity magnetic field that catalyzes the conversion of matter into energy. When the metallic hydrogen is activated, its magnetic potential increases greatly and the energy produced is substantial.

    When the activation signal is removed, the metallic hydrogen returns to low level activity and has a long shelf life. High intensity LENR heat production can begin when the activation signal is reapplied.

    According to one of the LENR reactor patents, the activation signal is an electrostatic field between 50 and 100 kilovolts.

    Metallic hydrogen is produced by high pressure processes such as formation in nano-pits and cracks as per high palladium loading or cavitation bubble formation as metallic water. But once formed, the metallic hydrogen/water is self-sustaining and act like free ranging particles.

    The herringbone track pattern as seen in this micrograph is predicted to appear as a tachyon interaction with a substrate. The negative mass seen might be produced by the activation field as the polariton cover in the spin wave that enshrouds the metallic hydrogen microparticle is constantly replenished and activated with a non- Hermitian open system’s based Parity/time state change as the polariton cover that surrounds the metallic hydrogen constantly decays and is replaced.

    Examples for tachyonic fields are all cases of spontaneous symmetry breaking. In condensed matter physics a notable example is ferromagnetism; in particle physics the best known example is the Higgs mechanism in the standard model.

    Inspired by this non-Hermitian P/T state change insight that might be in play with metallic hydrogen, in like manor, the Higgs boson is also a tachyon and its negative mass might be a manifestation of a continual state change that occurs in virtual particle creation and decay.

    Furthermore, as described by the description of the tachyon monopole in string theory, the generation of mesons is predicted to occur through hadronization. This kaon production is seen in the experiments of Leif Holmlid. There is a chance that the tachyon is dual with metallic hydrogen.

  19. #20 Michael Mooney
    September 17, 2017

    You are off topic. This thread is not about your fascination with tachyons. Start a blog about your personal interests… or “Ask Ethan!”

    I agree with Kasim Mulflahi, #17 and CFT, #18.

  20. #21 Axil
    September 17, 2017

    Why is the tachyon a critical keystone in particle theory?

    It is useful to compare and contrast string theories with conventional particle theories. Our goal should be to compare the predictions that have been formulated by string theory against the particles that are observed in the real world.

    What is the difference between a string theory and a conventional particle theory? Both kinds of theories describe particles and their interactions, but in the latter case the particles are the fundamental entities, whereas in the former case they are made of something more fundamental (the string).

    When constructing a conventional particle theory, the theorist is more or less free to decide what types of particles to include and what properties to endow them with, such as what their masses are, whether they are bosons or fermions, and how they interact with each other.

    These particle descriptions form the basis for theories that include quantum electrodynamics and the Standard Model.

    These particle descriptions are examples of realistic theories, meaning that they describe the real world. But there are countless other theories one can construct that are equally mathematically consistent (and also satisfy basic physical requirements like quantum mechanics and special relativity).

    Like particle theories, string theories describe the world in terms of particles and their interactions; unlike in particle theories, however, these are derived concepts. It is the function of the string theorist to derive complex particle behavior from a minimal subset of basic properties of the fundamental string.

    Calculation in string theory reveals that the masses of the different particles sometimes have crazy attributes. More precisely, we calculate the square of the mass of each particle and normally, the mass-squared is a positive number (if the particle is massive, like an electron) or zero (if the particle is massless, like a photon or a graviton). In some cases, however, the mass-squared turns out to be negative! Such a particle is called a “tachyon”.

    If the tachyon turn out to be real, that is, exists in reality, then this implies something profound about the validity of the string theory method of particle definition. This elevates the description of particles from strictly an observational practice to a mathematical definition of particles from first cause assumptions. This reductionist approach to discovering what reality is happens to be formational to the scientific edifice. Such a pursuit to derive basic causation is important to follow as a basic requirement of science.


  21. #22 Axil
    September 17, 2017

    Upside-down potential

    Consider a pendulum with its weight sitting at rest at the bottom of its arc. Let’s call that position x0. If a force is applied to the weight of the pendulum, it will swing and its position located at any time on its arc will correspond to real number values.

    Now consider an initial condition where at time t=0, the pendulum is pointing straight up with its weigh located at the top of its arc. Clearly, this is unstable, but at least in classical physics one can imagine that the pendulum can be so carefully balanced it will remain pointing straight up indefinitely so long as it is not perturbed.

    In an open system that is described by a non- Hermitian P/T complex number system something unexpected happens when there is a P/T state change occurs to perturb the pendulum from its straight up position.

    The weight of the pendulum does not fall to the bottom of its arc.

    Complex analysis shows that the pendulum repeatedly slides right back up to the top of the arc, and actually spends most of its time there. It is extremely unlikely to find the classical pendulum far from the origin; it is most probable to find the classical particle near x=0.

    At the quantum level, a particle in this upside-down potential is in a bound state strongly localized at the origin. The explanation for this surprising behavior is that we have extended real space to complex space. Complex numbers differ from real numbers in that the complex numbers are not ordered. If a and b are real numbers, we can say that a>b or b>a.

    However, even though the real numbers are embedded in the complex numbers, we cannot say that one complex number is greater than another complex number, so it makes no sense to say that the “bottom” of the potential is at x=0! One must think in new ways when working in the complex domain.

    We learn from this model that quantum theories need not obey the conventional mathematical condition of Hermiticity so long as they obey the physical geometric condition of space-time-reflection symmetry (PT symmetry).

    PT symmetry challenges a standard convention in physics—the widely held belief that a quantum Hamiltonian must be Hermitian. And, because PT symmetry is a weaker condition than Hermiticity, there are infinitely many Hamiltonians that are PT symmetric but non-Hermitian; we can now study new kinds of quantum theories that would have been rejected in the past as being unphysical. Moreover, PT-symmetric systems exhibit a feature that Hermitian systems cannot; the energy levels become complex when there is a change on P/T symmetry.

    The transition from real to complex energies is a key feature of PT-symmetric systems and it is called the PT phase transition. At this transition the system goes from a state of physical equilibrium (called a state of unbroken PT symmetry) to nonequilibrium (broken PT symmetry).

    The imitation of the LENR reaction is marked by a broken PT symmetry. This is one reason why the LENR active particle is an analog tachyon.

  22. #23 CFT
    September 18, 2017

    No one is free to create a particle with properties that negate its own existence and call it physics.
    No particle that exists is massless, if they were, they would have zero density and zero energy. Think about it. How on earth would anything that had no mass or energy interact with something that did? Wishful thinking? Magic? Lots of math? Folks want to pay lip service to E=MC^2 all day long, and then throw it under the bus the first opportunity their convoluted mathematical modeling demands it. No mass means no density or energy, which means no interaction, thus it can not be the causation of anything. Don’t confuse small, with nothing. They are not the same thing, even if calculus pretends otherwise.
    The very overextended, over-extrapolated particle zoo (which the tachyon is in) is a house of cards that has been teetering for over six decades. The LHC has been handily demolishing this fantastical menagerie one imaginary particle at a time, and only the fact that superstrings were intentionally concocted in the first place to exist at energy levels far beyond anything remotely measurable by humanity has kept them this side of the nothingness they were pulled from.
    In any case, when you have a not so little mathematical landscape problem of over 10^500 possible haystacks (universes) you have lost your needle in, you have no business discussing a ‘reductionist approach’ in the same breath. There is no way to even observe an alternate universe even if you had one, so there is no ‘observational practice’ either. Superstrings are far closer to mathematical onanism or metaphysics than physics.

  23. #24 Michael Mooney
    September 18, 2017

    Speaking of bullshit presented as science (like “stuff in zero volume”) one of my perennial faves (an aside) is this claim found in SR theory of length contraction:
    The faster you travel the shorter the distance traveled. It’s all subjective, you know. See Ethan’s blogs on the “science” of interstellar travel. Oh… space can also be folded like a blanket, so with enough energy “warping space” you can punch right through the folds… no need to travel light years of actual distance between stars.
    Fun with “science” according to Ethan.

  24. #25 Axil
    September 18, 2017

    A hypothetical particle with complex rest mass would always travel faster than the speed of light. Such particles are called tachyons. There is a strong chance that LENR is based on analog tachyons via metallic hydrogen nanoparticles.

    E = M(C^2)/(1 – (V^2/C^2 )^1/2

    If the rest mass m is Complex this implies that the denominator is Complex because the total energy is observable and thus must be real. Therefore, the quantity under the square root must be negative, which can only happen if v is greater than c. As noted by Gregory Benford et al., special relativity implies that tachyons, if they existed, could be used to communicate backwards in time[6] (see tachyonic antitelephone). Because time travel is considered to be unphysical, tachyons are believed by physicists either not to exist, or else to be incapable of interacting with normal matter.

    In quantum field theory, complex mass would induce tachyon condensation.

    We know that tachyon condensation exists as seminstated in Leif Holmlid’s experiments where metallic hydrogen produces mesons.

    It may be possible using LENR to produce a time machine.

  25. #26 Axil
    September 18, 2017

    Possible tachyon track in LENR ash from the martin fleischmann memorial project

  26. #27 Axil
    September 18, 2017


    Above is post about the the so-called θ-angle. The heavy hitters in science are sniffing around the root cause of the LENR reaction. Some new papers to read there.

    Of particular note is this bit of info and the associated document.

    “The new ideas about this question that Komargodski talked about are in the paper Theta, Time Reversal and Temperature from earlier this year, joint work with Gaiotto, Kapustin and Seiberg. Much of the talk was taken up with going over the details of the toy model described in Appendix D of this paper. This is an extremely simple quantum mechanical model, that of a particle moving on a circle, where you add to the Lagrangian a term proportional to the velocity, which is where the angle θ appears. You can also think of this as a coupling to an electromagnetic field describing flux through the circle.”

    It turns out that the stuff that I have been posting about has risen to a prominent place in physics.