What does it mean to say "Gravity is the weakest of the forces"?

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Solution 1

When we ask "how strong is this force?" what we mean in this context is "How much stuff do I need to get a significant amount of force?" Richard Feynman summarized this the best in comparing the strength of gravity - which is generated by the entire mass of the Earth - versus a relatively tiny amount of electric charge:

And all matter is a mixture of positive protons and negative electrons which are attracting and repelling with this great force. So perfect is the balance however, that when you stand near someone else you don't feel any force at all. If there were even a little bit of unbalance you would know it. If you were standing at arm's length from someone and each of you had one percent more electrons than protons, the repelling force would be incredible. How great? Enough to lift the Empire State building? No! To lift Mount Everest? No! The repulsion would be enough to lift a "weight" equal to that of the entire earth!

Another way to think about it is this: a proton has both charge and mass. If I hold another proton a centimeter away, how strong is the gravitational attraction? It's about $10^{-57}$ newtons. How strong is the electric repulsion? It's about $10^{-24}$ newtons. How much stronger is the electric force than the gravitational? We find that it's $10^{33}$ times stronger, as in 1,000,000,000,000,000,000,000,000,000,000,000 times more powerful!

Solution 2

When we say that gravity is much weaker then the other forces we mean that its coupling constant is much smaller than the coupling constants of other forces.

Think about a coupling constant as a parameter that says how much energy there will be in per "unit of interacting stuff". This is a very rough definition but it will serve our purpose.

If you determine the coupling constants of all different forces, you discover that, in decreasing order, strong, eletromagnetic and weak forces are much, much stronger than gravity.

You need around $10^{32}$ (that is 100,000,000,000,000,000,000,000,000,000,000) times more "stuff interacting" to get around the same energy scale with gravity if you compare it with the weak force. Moreover, the difference between strong, weak and electromagnetic forces among themselves isn't nearly as extreme as the difference between gravity and the other forces.

Solution 3

I don't think that any of the existing answers fully answer this rather subtle question (correctly). If we just consider the interactions themselves, and not particular particles that they couple together, then there is no meaningful sense in which gravity is any weaker than any of the other forces. This simply follows from the fact that the gravitational coupling constant $G$ has different units than the coupling constants of all of the other Standard Model interactions, so the fundamental "strengths" of the interactions are incomparable.

It's true that for some applications, it's simplest to work in Planck units where $\hbar = c = G = 1$ - but that statement simply reflects the fact that no dimensionless ratios can be formed out of those constants, so this simultaneous assignment is possible. It's therefore incorrect to say (as claimed in another answer) that the strength of gravity is "equal" to the strength of any other interaction in any nontrivial way. It's simply incomparable, neither weaker nor stronger. You could just as easily choose a system of units (like SI!) in which either coupling constant's numerical value is arbitrarily larger than the other's.

To meaningfully compare the strength of gravity to that of the other interactions, you need to consider the specifics of the Standard Model (SM) matter fields. The dimensionally meaningful statement is that $G M_H^2/(\hbar c) = (M_H/M_P)^2 \approx 10^{-34} \ll 1$, where $M_H$ is the Higgs mass and $M_P$ the Planck mass. (You get similarly small numbers if you plug in the mass of any other SM particle.) Different types of physicists will find different natural ways to interpret this inequality.

To a (phenomenological) particle physicist, the natural mass scale is the Higgs/SM scale $M_H$ (and the natural velocity and action scales are $c$ and $\hbar$). From this perspective, $G = M_P^{-2} \approx 10^{-34}$, and the natural question is

"Why is the gravitational interaction between SM particles so much weaker than the other SM interactions? Or equivalently, why is the Planck mass so huge relative to the SM scale?"

To a quantum gravity theorist, who is less concerned with the details of the Standard Model, the natural mass scale is the Planck mass $M_P$. From this perspective, $M_H \approx 10^{-17}$, and the natural question is

"Why is the Higgs mass so tiny relative to the Planck scale?"

This is what Wilczek meant when he said "The question is not 'why is gravity so weak?' The question is 'why is the electron mass so small?'." I'll leave it to the philosophers to debate whether this is actually a "better" formulation of the question. The "hierarchy problem" really encompasses both formulations of this question, but is usually formulated from the latter perspective, and phrased in terms of "unnaturally fine-tuned radiative corrections to the Higgs propagator" and a bunch of other jargon involving the renormalization group, whose details are orthogonal to the OP's question.

Another answer states another common misconception, which is that the weakness of gravity simply stems from the irrelevancy/nonrenormalizability of the gravitational interaction. To see why this explanation is seriously incomplete, it's useful to consider yet another type of physicist's perspective: that of a condensed-matter theorist. The key point is that irrelevant operators (in the technical sense of the word) are only irrelevant (in the colloquial sense of the word) at energies far below the microscopic "UV cutoff" energy scale.

In this case, the cutoff scale is the Planck scale, so it is indeed straightforward to show from general arguments that gravity is very weak at energies far below the Planck scale. But this doesn't really answer the question; it just pushes it back to the question "Why do SM particle interactions occur at energies so far below the 'natural' Planck scale?" In a generic system, we would expect the low-lying excitations (the elementary particles) to have mass gaps on the order of the microscopic energy scale (the Planck scale). Only very close to a phase transition does the mass gap almost close and field theory become applicable. So to a condensed-matter physicist, the natural formulation of the hierarchy problem is

"Why are the Planck-scale interactions so finely tuned to lie near a phase transition, thereby allowing us to use field theory to accurately describe the low-lying excitations (the elementary particles)?"

Solution 4

Gravity seems stronger because it's always attractive. Of the other 3 interactions:

  • Electromagnetism has positive and negative charges, so it only manifests macroscopically when there is a charge imbalance.
  • The weak and strong interactions are intrinsically short-ranged.

Solution 5

The Randall-Sundrum model explains it. The other forces are confined to the brane which we consider to be our universe. The brane is embedded in higher dimensional space where some of the dimensions may be compactified, but others could be larger or even infinite (a 5 dimensional anti-de Sitter space in which a (3+1)dim brane is embedded.All particles except the graviton are bound to the brane.) Higher dimensional space is called the bulk. If gravity is not confined to our brane and can penetrate into the bulk, that would explain its weakness. The problem with the extreme difference in strengths of the forces is termed the hierarchy problem (weak force=$10^{32}$grav force). There are other explanations involving supersymmetry.

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Comments

  • Smashery
    Smashery over 3 years

    I can understand that on small scales (within an atom/molecule), the other forces are much stronger, but on larger scales, it seems that gravity is a far stronger force; e.g. planets are held to the sun by gravity. So what does it mean to say that "gravity is the weakest of the forces" when in some cases, it seems far stronger?

  • David Z
    David Z almost 13 years
    +1, this is basically the answer I would have posted if I hadn't already seen it here. (I think it would not be inappropriate to include a small bit of mathematical detail, though.)
  • Gordon
    Gordon almost 13 years
    Yes, it answers what it means, but doesn't offer an explanation. I guess, though, he didn't ask for one...
  • Leandro Seixas
    Leandro Seixas almost 13 years
    Actually the Hierarchy problem is about the radiative corrections in the Higgs propagator. The large discrepancy of coupling constants is not a real problem.
  • Rafael S. Calsaverini
    Rafael S. Calsaverini almost 13 years
    I stand corrected then! :)
  • Smashery
    Smashery almost 13 years
    To explain the down-vote: the question isn't about why gravity appears weaker. It's the fact that, in my mind, gravity doesn't appear weaker.
  • Smashery
    Smashery almost 13 years
    To explain the down-vote: the question isn't about why gravity appears weaker. It's the fact that, in my mind, gravity doesn't appear weaker.
  • iamgopal
    iamgopal almost 13 years
    other forces don't scale ? sure ?
  • pho
    pho almost 13 years
    Then look for answers on a psychology site, not a physics site. We're supposed to be answering physics questions, not explaining how your mind works.
  • dmckee --- ex-moderator kitten
    dmckee --- ex-moderator kitten almost 13 years
    Though color (i.e. strong force related) charges come in 3 (plus 3 anti) flavors they share with electric charges the ability to form "neutral" bodies (indeed confinement requires this), the phenomena called "color transparency" (known in meson systems and theorized in baryons) takes advantage of this even inside the range of the strong force. In principle bodies could be assembled that are on aggregate "weak neutral", though not using a small integer number of bits.
  • Admin
    Admin almost 13 years
    Dear @Smashery please quit down-voting answers based on perfectly good physical arguments. Otherwise it appears you not looking for answers but only an affirmation of your pre-existing beliefs.
  • Brian Monson
    Brian Monson almost 13 years
    @Smashery this is the best answer to your question. To repeat myself, please do not down-vote unless you actually have a good reason to do so. And if you do do so, don't proclaim it. It hurts your credibility.
  • TheSheepMan
    TheSheepMan almost 13 years
    @Leandro that is a gross misstatement. from what I know of the hierarchy problem it is entirely about the vast difference between the coupling constants.
  • Hans Zimermann
    Hans Zimermann almost 13 years
    This answer might be useful in response to a different question. Here it does not seem to jive with what the OP is asking. Then again, after seeing some of the OP's comments it is not clear to me what he was asking.
  • spencer nelson
    spencer nelson almost 13 years
    @space_cadet Not sure why this is such a crazy request by @Smashery. He wants an explanation of how to reconcile everyday phenomena with commonly cited theory: "Gravity seems to be the most important force in my life, yet people say it's the weakest. Explain." Do you see how talking about Chan-Paton factors might not be a satisfactory response?
  • Brian Monson
    Brian Monson almost 13 years
    Hi @Spencer. If you were to ask a physicist today the question "why is gravity the weakest force" then of the many ways of stating the problem, one way is to note (as @Lawrence did) the tremendous difference between the natural mass scale of gravity and that of the standard model. This is what is referred to as the "hierarchy problem". Ask a postdoc or a professor about it and I'm sure they would be delighted to explain. The tidbit about S-duality is only one of many ways to find a resolution to this question, another one being the Randall-Sundrum model as @Gordon mentions in his answer.
  • spencer nelson
    spencer nelson almost 13 years
    @space_cadet I understand that this is the deeper reason, but it's also impenetrable to someone just trying to understand how physics interacts with daily life. Perhaps this is a discussion which should be had on meta - it seems like we are returning to the very-common 'how advanced should physics.se be' question.
  • Leandro Seixas
    Leandro Seixas almost 13 years
    No, is not about the difference of coupling constants, is about quadratic divergence of Higgs mass correction (first order radiative correction). I will find a question about it. This area of comments is not appropriate for a more detailed answer.
  • Brian Monson
    Brian Monson almost 13 years
    @Spencer I guess it boils down to a difference in perspective. When you get to a certain level you realize that there's no two ways about it. Either you discuss the physics aspect or the pop-science version. Or perhaps I am just a jaded cynic. In any case @Smashery is entitled to his perspective and so are you.
  • Smashery
    Smashery almost 13 years
    @space_cadet- No, it's not the best answer to my question (and this may sound arrogant; but I think, as the person who is having trouble understanding something, I should be the judge on whether it has helped me understand). This answer may be a completely accurate reason as to physical reasons why gravity is stronger; but if you read the question, I'm not disputing the fact that gravity is weaker: I already believe the physicists who say it is. I'm saying it doesn't make sense to me since gravity seems to have more of an effect on me.
  • Smashery
    Smashery almost 13 years
    What Spencer and others have done in their answers is shown me where my misunderstanding is: my forgetting that gravity is purely attractive, whereas the electromagnetic force has both attractive and repulsive forces. By reminding me that these positive and negative charges usually balance each other out, it all made sense to me. Yes, I'm a layman when it comes to these things; a good answerer will try to get inside my head and help me with my real misunderstanding.
  • Smashery
    Smashery almost 13 years
    Lawrence and Gordon are obviously knowledgeable; I thank them both for their efforts (and have upvoted their excellent answers elsewhere); but these answers here were not useful in helping me understand. The appropriate thing to do to filter out answers which do not help answer the question is to downvote them. My apologies if I have offended anyone by doing so.
  • Gordon
    Gordon almost 13 years
    @Smashery: Your headline question seems to ask why gravity is considered the weakest force. In your elaboration you seem to be asking why you think it should be stronger. Arrghh, I am not a telepath. An obvious reason would be that we evolved brains on one massive mother of a planet and gravity is accretive. Any number of other explanations as to why you think gravity should be stronger come to mind, but none of them are flattering.
  • Gordon
    Gordon almost 13 years
    @space_cadet: Thanks for the support. I thought he wanted to learn something, not that I am the Amazing Kreskin.
  • Smashery
    Smashery almost 13 years
    My apologies if you took the downvote personally; like I said elsewhere, you are obviously knowledgeable about the topic; but the gap in my knowledge was more that "to my intuition, gravity doesn't seem weak at all." Sorry if that wasn't clear in the question. I've since upvoted another of your excellent answers.
  • Brian Monson
    Brian Monson almost 13 years
    @Smashery you have surely not offended anyone :) However please do keep in mind that on a site such as this you should expect answers from experts. Obviously these are likely to be technical.
  • Marek
    Marek almost 13 years
    @Leandro: that is just one particular hierarchy problem. In general @space_cadet is right, the problem in general is with understanding the magnitude of coupling constants which usually requires some fine-tuning or new physics. The actual mechanism which explains it (in your case either fine-tuned cancellation of bare mass by quadratic radiative corrections or the usual SUSY solution) is only secondary. By the way, another instance of a famous hierarchy problem is the one of the smallness of cosmological constant.
  • jdm
    jdm over 12 years
    @Smashery, all: Actually the question why gravity is weak in some peoples mind and strong in others is interesting in its own right! Physicists usually decide gravity is weak because they compare the gravitational force with the EM force between, e.g., two electrons. There is some arbitrariness to this. I could also say "gravity is a strong force - but an electron only has very tiny gravitational charge!". It's like comparing apples to pears. There is a scale factor one has to decide on.
  • Georg
    Georg over 12 years
    ""gravity cannot felt by us in daily life "" Rofl I recommend You lay down under an apple tree for some hours!
  • TheSheepMan
    TheSheepMan over 10 years
    This doesn't answer the question. To answer the question, you would have to explain what system of units you have in mind such that all four coupling constants have the same units and therefore can be ranked in size.
  • Rafael S. Calsaverini
    Rafael S. Calsaverini over 10 years
    @BenCrowell When I first read the question, I assumed the person asking had no knowledge of physics beyond high school physics and I tried to adapt my answer to that context. Feel free to edit my question to add more detail if you want.
  • Abhimanyu Pallavi Sudhir
    Abhimanyu Pallavi Sudhir over 10 years
    Or jump out from the window.
  • Xtro
    Xtro over 9 years
    Try to walk or sit in the air :)
  • ashpool
    ashpool over 9 years
    This answer just shows how electromagnetic force is much stronger than gravitational force in an example. Do you mean that the meaning of the statement, "Gravity is the weakest force" is that it is the weakest in "many examples" ?
  • N. Virgo
    N. Virgo over 9 years
    It may or may not also have been Feynman who said words to the effect that the question "why is gravity so weak?" can be rephrased as "why is the mass of the proton so small?".
  • David Hammen
    David Hammen about 9 years
    This doesn't quite deserve the downvotes it received. There is a reason to downvote, which is that this answer is not an answer to the question. However, that you cannot feel gravity is exactly correct. You feel weightless when you jump out of a window. There's nothing to feel because you can't feel gravity. Nothing can. When you splat and hit the pavement moments later, that's not gravity. That's the normal force you are feeling.
  • Mahathi Vempati
    Mahathi Vempati almost 8 years
    Charge and mass are two different quantities. What amount of charge do you equate to what amount of mass to state that one force is stronger?
  • Rococo
    Rococo almost 7 years
    I don't understand. Your last line would imply that $q_E m_P/m_e q_P = 1.759/8.617$ ~ O($1$), right? But the lines above that would say that $q_E m_P/m_e q_P= 2.389*10^{22}/11.706$ ~ O($10^{21}$) . Right?
  • asmaier
    asmaier almost 7 years
    You are right. I missed a minus sign. $q_P/m_P = 8.617\cdot 10^{-11}$. I fixed the paragraph.
  • Ernie
    Ernie almost 7 years
    @Tinkidinki: Another way to think of this is that mass is a measure of what warps space to generate gravitational force, while electric charges create electrical fields that can move objects with mass against or through a gravitational field.
  • Michael Bray
    Michael Bray about 5 years
    I think there is recent evidence against this explanation. See: youtube.com/watch?v=3HYw6vPR9qU
  • tparker
    tparker over 4 years
    This answer is incorrect. Newton's constant, the coupling constant for gravity, has different units from the coupling constants for the other interactions, so it's meaningless to compare them. There is no meaningful sense in which gravity is fundamentally any weaker than the other forces, except in reference to specific Standard Model particles.
  • tparker
    tparker over 4 years
    Your claim that "the gravitational force and the electromagnetic force are actually of equal strength and range when they are compared at their natural scale" is trivial and misleading, because their apparently equality just comes from the fact that you are working in units designed to make them both equal to 1. In fact they have different units and are incomparable, so you make choose units in which their numerical values are as near or far from equality as you want.
  • tparker
    tparker over 4 years
    @Nathaniel I believe it was actually Wilczek, in physicstoday.scitation.org/doi/10.1063/1.1387576.