Of Particular Significance

The Impossible Commentary: Is Gravity a Force? Is it an Illusion?

Picture of POSTED BY Matt Strassler

POSTED BY Matt Strassler

ON 10/26/2023

[This is a tricky one… it’s easy to make confusing statements about Einstein’s theory of gravity (general relativity), and so I am especially hopeful of getting readers’ feedback on this subtle issue, to make sure what follows is 100% clear and correctly stated.]

  • (Quote) On Earth’s surface, we are roughly 4,000 miles from Earth’s center. But if you ascended another 22,000 miles, where you’d find the GOES weather satellites that monitor Earth’s weather patterns, you’d find your weight (but not your mass!) reduced to one-fortieth of what it is on Earth… And if you traveled out into deep space, far from any large object, you’d weigh virtually nothing. Yet all the while, your body’s mass—the difficulty I would face if I tried to speed you up or slow you down—would never change.
  • (Endnote) Confusingly, astronauts orbiting Earth inside nearby space stations appear to float as though weightless. From Newton’s perspective, they are not truly weightless; if they were, they’d coast, leaving the Earth’s vicinity and moving rapidly into deep space.
    Instead, they and their spaceship are pulled by gravity into a common orbit around the Earth. Since they travel on the same path as their container and as the camera which films them, they seem and feel weightless. (This subtle issue is turned on its head in Einstein’s view of gravity.)

Astronauts in a space station seem to float, as though they are weightless. Are they truly weightless? Or are they only apparently weightless?

The same issues arise for people in a freely falling elevator, accelerating downward with ever greater speed. They will feel weightless, too. But are they?

Newton would have said they are apparently weightless, subject to gravity but all falling together along with their vehicle. A naive (but instructive!) reading of Einstein might lead us to say that they are truly weightless… that the gravity that Newton claims is present is a pure illusion, a fictitious force. But a precise Einsteinian would say they are almost but not quite weightless — and the lack of perfect weightlessness is a clue, a smoking gun in fact, that they are indeed subject to gravity.

Newton’s Viewpoint

The Newtonian view is that a space station, elevator, and any person within them is subject to the pull of a gravitational force due to the Earth, and that this force is proportional both to the mass M of the Earth and the mass m of the object being pulled. Meanwhile, Newton’s second law of motion states that the acceleration due to a force is inversely proportional to the mass of the object being pulled. Since the force of gravity is proportional to the object’s mass while the acceleration caused by the force is inversely proportional to the mass, the effect of Earth’s gravity on an object’s motion is independent of the object’s mass. (This simple view holds as long as the object’s mass is small enough that it in turn does not affect the Earth’s motion! Otherwise the discussion becomes somewhat more complicated.)

M is the Earth’s mass, m the object’s mass; a is the object’s acceleration, and its acceleration agravity due to gravity’s force Fgravity is independent of its mass. (GN is a constant, irrelevant here.)

As a result of this, a freely falling elevator and the people inside it accelerate together, traveling always at exactly the same speed. Since all their motions are the same, nothing causes the people to move either toward the elevator’s ceiling or toward its floor. And so, if these people are in the middle of the elevator, perhaps even upside-down or sideways from our perspective, nothing seems to pull them in any direction. They will sense themselves as floating inside the elevator, as though there were no gravity. They will feel weightless, even though they and their elevator are falling more and more rapidly thanks to the pull of gravity — thanks, in other words, to their weight.

The same is true of a person orbiting the Earth inside a space station; indeed, an orbit is just a special way of falling forever, where one moves around the Earth fast enough that falling downward combined with moving forward leads to circular motion. (See the book’s Figure 9.) Just as do people in a falling elevator, astronauts in an Earth-orbiting space station move in exactly the same way as does their spacecraft, with nothing drawing them toward any of the craft’s walls. That’s why they will feel as though they are motionless and floating — as though they are weightless.

Figure 1: (Left) In the presence of uniform gravity (green arrows), an elevator falls faster and faster, with an acceleration a, and so does a person inside the elevator. Since the person and elevator accelerate at exactly the same rate, the person does not move toward any of the elevator’s walls, and so feels as if floating. (Right) In fact, the experience of the person at left is identical to that of a person in the absence of any gravity inside a floating stationary elevator; neither the elevator nor the person is pulled in any direction.

From our perspective, watching our friends in free fall or in orbit, we know that they are subject to the Earth’s gravity. The elevator would not be falling, nor the spacecraft orbiting, were there no gravity from the Earth; and were the people inside these conveyances not subject to gravity, they would not travel in concert with their vehicles and would not feel weightless. Their experience of apparent weightlessness is caused by the universality of gravity, not by the absence of gravity, according to Newton.

Einstein’s Viewpoint — The Equivalence Principle

Now, what does Einstein say about all this? Einstein makes a claim known as the principle of equivalence. Its simplest form is this: if the effects of gravity are constant across all of space, then one cannot say that there is any gravity at all, because there is no physical distinction between a spatially-uniform gravitational force and a special form of pure motion: constant acceleration. This has led some people to say that gravity is an illusion, a fictitious force.

The classic example of a fictitious force is what is called centrifugal force — a force pushing away from a central point — such as the force that seems to push you toward the right side of a car when it turns to the left, and vice versa. The fact that centrifugal forces can be viewed as fictitious is made clear by the fact that there always exists a perspective from which the centrifugal force is exactly zero. As your car drives past me and turns left, I see no sign of your apparent centrifugal force. Instead, what I see is the car experiencing a centripetal force — a force toward a central point — created by the friction between the road and the tires; this is what makes it turn left. You, not feeling this force, tend to go straight, and thus you move to the right relative to the car. From your perspective, the car moving left underneath you due to a leftward force acting on the car feels as though you are subject to a rightward force; but this is an illusion.

Yes, the Newtonian force of gravity is somewhat illusory in Einstein’s view. As Einstein realized, Newton’s force is relative — that is, it is perspective-dependent, much like centrifugal force. That means that it doesn’t make sense to specify its strength and direction in the way that Newton would have recommended; different observers will view it differently.

But still, gravity is not like centrifugal force; it’s not an illusion. There are aspects of gravity that are intrinsic and not relative — they are independent of one’s perspective — and because of this, gravity is not to be viewed as fictitious. It’s certainly not a Newtonian force. But it is most definitely a force in the modern physics sense. (And it’s not alone in being partly ficticious: even electric and magnetic forces have aspects that are relative and others that are intrinsic. For instance, from your perspective, a stationary electrically charged particle is surrounded by nonzero electric field but has zero magnetic field; however, if I travel rapidly past you, I will claim that the magnetic field around the particle is nonzero. Both of us are right.)

A separate argument sometimes made in this context is that in Einstein’s view, gravity is a manifestation of the curvature of space and time, and so, it is claimed, gravity isn’t a real force. But this has no bearing on the question of whether the gravity is fictitious. Space-time curvature causes effects that we can choose to interpret as forces, and there are aspects of those forces which are not illusory.

Einstein’s view does imply that for persons inside an isolated bubble (such as a closed elevator or a space station far from other objects), the force of gravity cannot be measured unambiguously. Here’s another example. Suppose, for instance, there are persons in an elevator who feel just as they normally would in a stationary room on Earth — as though they were held by uniform gravity to the elevator’s floor, as in Fig. 2. No experiment can reveal whether they are indeed held by a constant gravitational force to the floor (as we are, almost exactly, at the Earth’s surface) or whether the elevator is subject to no gravity at all, and instead is undergoing a constant acceleration due to a force that pushes the elevator but not the persons inside. The floor, in contact with the persons’ shoes, is pushing them, causing them to accelerate upward with the elevator, and the experience of that upward acceleration is indistinguishable from the experience of constant downward gravitational pull.

Figure 2: (Left) In a stationary elevator, held to the ground by uniform gravity (green arrows) but prevented from falling by forces from the ground (blue arrows), a person can stand on the elevator’s floor, pulled downward by gravity but prevented from falling by forces created by the floor itself (red arrows). (Right) The experience of the person at left is identical to that of an observer in an elevator which is being pushed by forces (blue arrows) that give it acceleration a, and whose floor simultaneously pushes (red arrows) on the person’s shoes, causing the person to accelerate also at acceleration a . (The acceleration a is the same in magnitude, but opposite in direction, to that of objects falling on the planet at left.)

Similarly, if they feel weightless, like the person in Fig. 1, some of them might imagine they are gently floating in space, far from any object that could cause gravity. But others might worry that perhaps they are falling down an elevator shaft just outside a giant star, moments from certain death. If they try to think of experiments to determine which of them is right, they will fail, because of the principle of equivalence: no experiment of any type can distinguish motion caused by a uniform gravitational force from perfect weightlessness. This is the central pillar of general relativity, Einstein’s giant step beyond Galileo’s relativity. But that’s a subject for another book.

It might seem, then, that whether gravity is present or absent is not subject to experimental test, and that its presence is wholly a matter of perspective. But this is only true if the gravitational force is perfectly uniform across the bubble. Certain variations in gravity across the bubble can be measured unambiguously.

[Caution: here I am oversimplifying; it’s not only uniform gravitational fields that are fictitious. For instance, any choice of non-Cartesian coordinates on flat space-time , such as Rindler coordinates, creates such forces. To fully understand when and why certain combinations of gravity and acceleration are fictitious, while others are not, requires more of the math and concepts of general relativity.]

Gravity created by the presence of real-world objects is never perfectly uniform. The strength of Earth’s gravity varies with one’s distance from the Earth’s center, and its direction varies with one’s location. Let’s see now that these gravitational forces are not fictitious.

Einstein’s Viewpoint — TidAl FORCES

The essential point is that gravity around any finite object is not uniform. It varies, and that makes all the difference, as illustrated in Fig. 3.

Let’s consider our friends in the elevator who want to know if they are truly weightless in deep space or are falling in an airless shaft toward the Earth’s center. If they are armed with precise instruments (or if the elevator is unusually tall) they will notice that there are in fact gentle forces in the elevator — that objects tend to fall toward the elevator’s floor and to rise toward its ceiling. This is because gravity’s pull is slightly stronger near the floor, and slightly weaker near the ceiling, than it is on average across the elevator. The effect is straightforward to measure with precise instruments, even though it is far too small for a human to feel. [It would not be too small if the observers were falling just above a neutron star, however.] One consequence is that any object that extends vertically along the elevator tends to be slightly stretched. Not only that, this stretching effect will change over time. (If the elevator is falling from space toward the Earth’s surface, the tidal effect will grow. If the elevator shaft is already underground, as in a mine, it will shrink.)

Figure 3: (Left) In the presence of gravity (green arrows) that is weaker near the elevator’s ceiling than it is near its floor, the person’s feet and head will be accelerated at different rates, causing the person to stretch until the body’s internal forces counter the stretching. (Right) Like the person in Figure 1, this person will feel weightless on average, but will feel real tidal forces that grow toward both floor and ceiling and point oppositely, causing the stretching effect.

These subtle forces are tidal forces — aspects of gravity that, unlike gravity’s overall strength in a small isolated bubble, are not matters of perspective. Tidal effects are intrinsic, not relative; there’s nothing illusory about them. They actually stretch and squeeze physical objects, and you can’t make them disappear simply by changing your viewpoint.

This is the key insight: by measuring the presence of tidal forces, the inhabitants of the elevator can confirm that they are not weightless. They will not be able to determine exactly what is happening to their elevator purely from measurements of the tidal forces, but they can use them to rule out various possibilities, including the hypothesis that they are drifting in deep space, unaffected by any other objects.

The Global Perspective

In this discussion of whether gravity is an illusion, we have focused on what is observable by an observer with a narrow perspective inside an isolated bubble. Why, however, are we privileging the inhabitants of an elevator or space station? Yes, from their point of view, they are almost weightless; but we, viewing from outside, have access to vastly more information, and it makes no sense to pretend we don’t have it. For instance, we might be able to observe thousands of falling elevators and spacecraft all around the Earth, each with its floating space crew. From their motions and from the real tidal forces they experience, we can map out the area around the Earth, and see that it is accompanied by tidal forces and motions completely consistent with a spherical gravitational effect centered on the Earth itself, one that causes objects to accelerate toward the Earth’s center. Whether we describe this effect as a Newtonian-like force is a matter of perspective, but the tendency of objects located anywhere nearby to approach the Earth and crash into its surface clearly is not. (A collision cannot be made to un-happen simply by changing one’s point of view!)

Figure 4: By observing many elevators and the real tidal forces experienced within them, we can map out the region around our planet and obtain a global view of our planet’s gravitational effects, which are by no means fictitious, even though they can be viewed as ultimately due to the curvature of space and time.

So it’s misleading to say that gravity is an illusion and that the space station astronauts are truly weightless. The space station astronauts can measure the tiny tidal forces around their station, and confirm they are not exactly weightless and are subject to some source of gravity. Meanwhile, their space station is one of many satellites of the Earth, and we, watching them all, can confirm that they are subject to Earth’s gravitational effects (even if we view those effects as due to spacetime curvature and avoid using the word “force” altogether.) Though the strength of gravity’s pull as Newton defined it is perspective-dependent, and not reliable, there is nothing debatable about the statement that it’s Earth’s gravity that keeps the space station and its inhabitants in orbit. (For a related discussion, see here, here and here.)

Additional discussion of tidal forces will be found in a later note.

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48 Responses

  1. Hi, Matt — This whole discussion has been very enlightening to me, in particular the way it has brought home to me how truly pervasive gravity is. I’d seen the elevator/spacecraft (i.e., the “enclosure”) example before, but I hadn’t really appreciated that because it illustrates the effects of gravity on the occupants of the enclosure, it also highlights the impossibility of building a “Newton cage” that could somehow exclude gravity from its interior in a manner analagous to the way a Faraday cage excludes the electromagnetic force from its interior.

    I think it’s striking that the force of gravity can penetrate the walls of the enclosure so as to affect the occupants while simultaneously attracting the enclosure itself, apparently without being attenuated by the walls.

    What does its say about the nature of the gravitational field, or the curvature of space-time, that it can simultaneously penetrate and attract any enclosure, whether it’s an elevator, a spacecraft, or a cave in a mountainside?

    1. This is a very good question and I have been thinking about it — partly because I had to consider whether to explore it in my book. (I chose to ignore the issue, a weak point which I’ll have to address here someday.)

      From Einstein’s perspective, the answer is geometry. Space-time geometry is something you can’t shield; it’s not even right to think of it as “penetrating” walls, since it forms the very context in which the elevator’s walls and what’s inside the elevator are placed.

      But the question is much more subtle in quantum physics, where spacetime geometry can fluctuate, and specifically in the gauge-gravity (“AdS/CFT”) correspondence, where gravity can be viewed as emergent. Even understanding what objects are and how causality works is not at all obvious once you enter these realms.

      So I suspect this very simple question has a set of very subtle answers that are still not entirely known.

  2. In a region of almost uniform gravitational field, similar to the electric field between two large parallel plates with different voltages (away from the edges), the tell-tale of tidal forces from varying gravitational field would not apply, or at least be very difficult to measure, such that hapless travellers whose ion drive failed in this region could be truly weightless, up to observational accuracy. As gravity is unipolar, only one large enough uniform matter disk is needed.

    But perhaps there is a GR wrinkle that invalidates such a (very implausible) scenario?

    1. Yes, that’s right. If you’re near a huge isolated plane or disk of matter, you will not feel a tidal force unless you are close to the plane’s edges. Of course, you will hit the plane eventually as you accelerate toward it, and then it’s over. Between two planes you are safer, but of course the two planes will attract each other and won’t remain stationary.

      The only important wrinkle that I can think of so far is practical: to create a stable disk of matter large enough to cause interesting amounts of constant gravity yet strong enough to avoid collapsing isn’t easy. You couldn’t make a stable disk out of ordinary rock with mass as large as the Moon, even if you spun it. There are plenty of strangely-shaped small asteroids, but their gravity is measly.

      So unless you’re happy with barely noticeable gravity, you would need to build the disk out of some kind of imaginary material … and in this sense, the question is pretty academic.

  3. Returns me to Veritasium’s cringeworthy choice of “Why gravity is not a force” as name and slant of their 2020 video on the equivalence principle. It’s undeniably effective to convey a nutshell of the equivalence to people with high-school Newtonian-physics-fed apprehension of physics; but it does so without challenging Dunning-Kruger-laced naiveté that it thus reinforces on …algebraic representations in physics not being universally subject to the caveat famously advertized for natural language, “the map is not the territory”.

    We there change maps to cover the same territory with distinct projections, and there’s a choice between teaching stereopsis and discussing the parallax and its impact (as you neatly do), or to instead address cyclopes by presenting the parallax as an update to the single “real” map (instinctively understood to evolve towards some Omniscient Cyclope’s definitive complete map — the promised land of 20/20 hindsight and a common sense assumption that really begs challenging).

  4. “Their experience of apparent weightlessness is caused by the universality of gravity, not by the absence of gravity, according to Newton.”

    So the inertial frame for Newton would be the Earth whereas for Einstein it’s the frame of free falling weightless observer, and that the Earth is accelerating upwards. I find this to be a mind-boggling, huge difference in perspectives.

    1. This isn’t the right way to think about it. What you’re doing here is extending the viewpoint of observer in the elevator rigidly across the Earth. That’s unnecessary and unwise; general relativity does not force you to extend a viewpoint rigidly across all of space, the way special relativity does. What you’re doing is like saying that the fact that I can’t feel myself orbiting the Sun forces me to think of the Sun as orbiting me. Not so; that’s extending the equivalence principle to a false equivalence. As I emphasized, there *are* tidal forces, and those are viewpoint-independent. We can in fact tell that the Earth orbits the Sun (just go to the beach and watch the Sun-tides, which combine with the Moon tides to give the spring and neap tide cycles) while the Sun does not orbit the Earth (the Earth-tides effects on the Sun are much smaller.)

      I discussed this issue in another long thread over a year ago, culminating in this post. https://profmattstrassler.com/2022/06/01/coordinate-independence-kepler-and-planetary-orbits/

      1. Also, your figure 4 clearly shows that ‘the Earth’ accelerating upwards for every observer can’t be globally true so I think you’re being very diplomatic by describing my comments as ‘unwise’.

        On the other hand, I have to be careful that I don’t throw the baby out with the bathwater here because locally, when a patch of the Earth’s surface reaches a falling elevator, it *is* accelerating upwards in the inertial frame of the elevator, assuming tidal effects are tiny, and this can be made increasingly exact by taking the elevator and Earth’s surface patch both to a point. Every point on the Earth, apart from the one at the center, is being deviated from its geodesic path by its neighbouring points getting in the way and hence accelerating that point in the frame of a point-like free-falling observer there. As a correction to what I wrote above:

        “The inertial frame for Newton would be the Earth, whereas for Einstein it’s the frame of a free falling weightless observer that can be made arbitrarily small, and that some point on the Earth’s surface is accelerating upwards, once inside this inertial frame. I find this to be a mind-boggling, huge difference in perspectives.”

        Also, I’m not saying that these points being accelerated implies that there’s no gravitational force for the reasons you’ve posted above. That is, energy affects space-time which affects the path taken in space by falling elevators, points of the Earth etc; and these effects can be physically measured as a consequence of gravity.

        1. Correction:

          “The inertial frame for Newton would be the Earth, whereas for Einstein there are multiple inertial frames of free falling observers distributed around the Earth, and that some point on the Earth’s surface is accelerating upwards once inside. I find this to be a mind-boggling, huge difference in perspectives.”

  5. As always I learned things by a post (and comments) here. Setting aside the various complementary aspects of “force” and the interesting analysis of fictitious forces, my reason why gravity is a force among others would naively be that it can be described by a Lagrangian. Thus it can be quantized below the forbidding Planck scale, as other fundamental forces, see e.g. “Quantum gravity as a low energy effective field theory”, John F Donoghue (2017), Scholarpedia, 12(4):32997.

    Among other things it obeys energy conservation locally, and a uniform field would be interpreted – ambiguously and so contingent, but not fictitiously – as a constant potential energy. What could be fictitious is what Robb’s comment alludes to as Einstein’s distaste for the geometric description of gravity, a handy tool to describe relativistic tidal forces but to my knowledge not tested in the way the gravitational potential is. (The field was recently shown to have an Aharanov-Bohm effect.) The way I would describe the difference between gravity and the other forces is that their fields strive to make particles deviate from geodesics, while gravity strives to make them not do so. (But here the geometric interpretation is, again, handy, as noted in the comments.) Gravitational and inertial mass equivalence is not a fundamental property* it seems to me, Donoghue derives is as related to non-local quantum field effects in macroscale systems:

    “It is interesting that the bending angle depends on the type of massless particles. The particles no longer simply follow geodesics. This violates some ways that we talk about the equivalence principle. However it is not a violation in a fundamental sense. It is a manifestation of the fact that in quantum loops, massless particles propagate long distances. The long-distance propagation of massless photons and gravitons is not localized, and consequently can be interpreted as a tidal correction in that the massless particle is no longer describable as a point source. There is then no requirement from the equivalence principle that such non-local effects be independent of the spin of the massless particle. However, it is interesting that quantum effects predict such a difference, without any free parameter, modifying one of the key features of classical general relativity.”

    *Shades of the black hole firewall paradox, where equivalence was one of several conflicting properties complicating retaining unitarity of quantum field physics.

    1. This is a long but interesting comment. Here are few thoughts.

      A Lagrangian formulation doesn’t prove anything; there are forces that don’t seem to exist in particle physics in our universe, but can exist in principle, and have been widely studied in the past three decades, that have no local Lagrangian formulation. (These would be forces induced by systems of particles with strong, scale-invariant interactions.) Such forces do arise approximately in certain material systems near phase transitions.

      Einstein’s equivalence principle, in modern language, is generalized to diffeomorphism invariance in general relativity, which is a form of gauge invariance… similar in many ways to the gauge invariance found in the electromagnetic, strong and weak nuclear interactions. The whole discussion then boils down to determining what phenomena are gauge invariant. A fictitious force arises in GR when all diffeomorphism-invariant quantities are zero. The most prominent gauge-invariant quantity in GR is the Ricci scalar R, which in the geometric language is a measure of curvature. R is zero in a constant gravitational field but non-zero in the presence of tidal forces.

      I think a lot of your other points, though interesting, are going off in a different direction, and in this sense distract from the key concepts behind this post. In particular, while Donoghue’s paper sounds, like most of his work, as though it is well worth reading, it is addressing more subtle concepts that aren’t needed here.

      1. I hope you don’t mind, but I’m taking advantage of this more technical thread since it’s already here to ask some questions you might have time for, and the answers will probably just require a short yes or no. I’m under the impression that GR can be mathematically formulated by the principle of least action which involves in part, integrating a function called the Lagrangian, and that gauge invariance automatically arises as a consequence of adding to the integral a total derivative of a function which becomes zero when integrated between the limits.

        “The whole discussion then boils down to determining what phenomena are gauge invariant.”: is this equivalent to determining what phenomena can be described by a principle of least action?

        “diffeomorphism invariance in general relativity”: does this come automatically from the principle of least action for GR?

        1. No, the principle of least action (which is about how the system behaves) is not related to gauge invariance (which is about the variables that you use to describe the system). Gauge invariance/diffeomorphism invariance arises from using redundant variables to describe a physical system.

          Simple example: suppose you describe an on-off switch using an integer “n”, where n=odd represents “on” and n=even represents “even”. The variable “n” is redundant since it can describe “off” using 0, 2, 4, -2, etc. Shifting “n” by 2 would be a gauge transformation that changes “n” but does not change your description of the on-off switch.

          Meanwhile, if you want to understand what might cause the switch to flip, you might write a Lagrangian to do it and use the principle of least action to compute what the switch does. It might be convenient to use “n” as your variable, but the action needs to be gauge invariant, just as the physical system is. The quantity Exp[i pi n] would be gauge-invariant and could appear in the action.

          Why would we use redundant variables? Because sometimes the equations are much easier to solve than when we use non-redundant ones.

  6. Hi Matt,
    Excellent posts. Long time lurker. One thing that has always confused me about the equivalence principle is why a quantum interference device would not be able to differentiate free fall in a gravitation field from no gravity. Wouldn’t a two arm interferometer be able to pick out the direction of the potential gradient due to phase difference between the lower and higher m*g*h paths? Thanks in advance.

    1. One preliminary point. First, interferometry is already a classical phenomenon — after all, Michelson and Moreley were earlier than quantum physics. All you need is waves, and those waves need not be quantum.

      Your question, however, is a good one. I agree that it requires some thought, and I haven’t thought about it before. I think the easiest way to understand it is probably to take the reverse point of view. (a) Start with no gravity, and work out what the waves are doing in a static interferometer — i.e. an inertial frame — where clearly there is no phase difference. (b) Now go to an accelerating frame and view exactly the same phenomenon from that perspective, and work out how the phase difference ends up being zero from that point of view. This will then answer your question.

      Understanding (b) isn’t trivial, though it should be straightforward if one proceeds carefully. (The fact that the waves do not appear to travel in straight lines in the accelerated frame may well be important.) I haven’t quite seen my way through to the answer yet, but I’ll see if I can come up with the solution, and in the meantime, perhaps another reader can propose an answer.

  7. Whew.
    I started with the tides and their bulging. I found clarity in the explanation of the twice daily highs and lows. Importantly, I can upgrade and consolidate my mental model of this physical system using narrative and visual imagery aided by minimal algebra. The read was worth the time.
    The stimulus to rethink gravity as waves may be personally irrelevant and serve only to confuse some more of my neurons as did the tedious jargon used by J(C)F, but heh, the comments are a wide forum and often provide that extra layer of insight and education or distraction.

  8. This is a very nicely explained piece. I know I am going to be linking many others back to it in future.

  9. while I read the text, I thought “it ‘ll come soon ..”, but it didn’t : no clock in sight!
    Maybe leaving time out of the picture was intentional? (I was hoping for a link with the escape velocity and its time contraction effect at work even though our feet remain fixed to the floor). The focus was clearly on explaining the subtle difference between relative effects like ‘apparent weight’ and absolute effects like tidal stretch, and that was very well done.
    Nice outreach.

    1. Yes, leaving time out was indeed intentional. The effects on time are considerably smaller than the tidal effects I’ve focused on. The tidal effects are present even for Newtonian physics (although viewed differently) while the effects on time are absent, appearing only after Einstein’s revision of the notion of time. For the same reason, tidal forces have obvious effects at human scale (on ocean tides, for instance) while the more subtle issues concerning time only show up in advanced technology, such as GPS.

      1. In fact, there are no physical effects due to time. It’s about the speed at which time is perceived, not a physical change in inertial speed either. Only accelerating interaction matters.

        In gravitational potentials, the aging differences are due to accelerating real forces, which in locality appears as the curvature of time, but for a passing lightlike particle, the same appears as the curvature of space.

        I think that time is special only in the world lines of the bodies, i.e. in the proper times. Otherwise, they can be converted to each other by selecting the coordinates – space and time.

        1. On the contrary, it is not that spatial events evolve forward over time, but that time evolves spatial events forward. It is spacetime, not space and time. What affects space, affects time and vice-versa. The 2 cannot be separated. What can be explained in terms of space, can also be explained in terms of time. When we see light curve around a massive body, it is not because the space is curved, it is because the photons are evolving down the time dilation gradient, just like all other particles.

          You speak of “other” forces, but there are only 3 recognized forces; the strong force, the weak force and the EM force. I am saying time is also a force, the fundamental force of the universe, evolving all spatial events forward. We therefore see that all the following equations have a direct relationship to the difference in the rate of time, dRt, between the invariant 1 s/s rate of Einstein’s “far distant observer outside all gravitational fields” and the coordinate point.

          Notice that all velocities are dependent only on c and the dRt, and that formulas containing m as an element result in terms of mc^2, just like Einstein’s energy formula.

          VCo = (c√(dRt) for simple, nearly circular, orbits within a Kepler Zone.
          VEo = √(((2((c^2(dRt)) – ((c^2(dRtα))) for elliptical orbits within a Kepler Zone.
          VGo = ((c√(dRt))/(√3), for galactic rotation velocities for stars outside the Kepler Zone. This is the fundamental compensatory velocity formula.
          E = mc^2√(1 + dRt) for Einstein’s energy formula.
          F = ((mc^2)(dRt))/(r) for centripetal force & gravity.
          F = ((Mm)(r1)(c^2)(dRt1))/((M⊙)(r2)^2) for the force in Newton’s for 2-body systems.
          Mo = ((c^2(r – To))/G for the mass inside a stellar circle.
          M/R = c^2(1 – (1 – (3(VGo)^2/c^2))^2))/2G for the Mass/Radius ratio of stars outside the Kepler Zone in spiral galaxies.
          G = ((rc^2(dRt))/M for the empirical gravitational constant.

          If we look at the Earth/Moon system, we see that the tides are caused by the shift in the position of the Earth/Moon barycenter, which is ~75% the radius of the Earth. As the Moon orbits the Earth, the barycenter within the Earth shifts along with the Moon. The time dilation gradient is different along the Earth/Moon axis and is not as steep in the direction of either body as it is orthogonal to that axis. This reduces the force in time, which is dependent on the dRt, and it is not forcing the oceans to evolve downward as much as it is in other areas. Put simply, they have less weight along that axis and so we see a bulge that follows the orbit of the Moon.

          Matt, I see you removed my post of last night. I am assuming it was because it was off-topic. I am sorry about that. I hope this post is OK with you. If not, I will simply drop out of this conversation. I don’t want to bomb your site. 🙂 Thank you. .

          1. Please do try to keep your replies at a reasonable length. And please, it’s not really appropriate to introduce your own personal views on physics onto a website whose purpose is to explain mainstream physics to non-experts. (For instance, the notion that “time is a force” is… let us say… far from mainstream.) You’re welcome to try to convince other experts that you are right, but on this website there are many non-experts reading, and it is my responsibility to make sure that non-mainstream comments don’t start to dominate. I have to draw that line somewhere, and long comments are an obvious place, along with comments with lots of links.

            1. OK, Matt. I’ll not post anymore on your site. Sadly, the mainstream you are explaining has been on the wrong track since Hubble saw his shift. Hence it is full of “dark” unknowns like a singularity no one can explain, or dark energy in a universe accelerating itself out of existence, which no one can explain, and dark matter no one can find, even at CERN, because Einstein explained what we see due to how light travels, and not what is actually happening. He got sooooo close, when he called his time components his “energy components”. Quantum physics, on the other hand, has made great progress over those hundred years because it deals with what is actually happening, an evolving quantum continuum, a holographic energy field. A few years ago you posted that the Standard Model was dead, and now you are back promoting it, even though there has been no progress since you said it was dead. The simple fact is, it deals with physical particles, which we now know do not exist. Only waveforms exist.

              James Webb killed LCDM and, along with it, the Standard Model. I describe the eternally evolving, perceptually infinite, quantum continuum.

              I do thank you for your site and the time you spend on it. It has a great deal to offer and I have gleaned much from you over the years.

              Esa, my, “time evolves spatial events forward” and “It is spacetime, not space and time”, statements are not contradictory. The time aspect evolves the space aspect forward….one affects the other. Spatial mass slows time, so time accelerates the mass. Very simple, really.

              Again, thank you, Matt. Good luck finding a way out of all the the dark things the mainstream has been so lost in for so long…..There actually is LIGHT at the end of that tunnel….A whole universe of LIGHT. 🙂

              1. You are, of course, entitled to your opinion. But every website has its purpose. You are welcome to engage with mine, if you do so reasonably, and as long as you keep in mind its purpose, even if you disagree with it.

                [[Meanwhile, I do not recall posting that “the Standard Model was dead”, nor do I recall ever saying those words to anybody, anytime, anywhere, excepting in regards to the fact that it does not include gravity and must be extended; and I will happily pay you $100 if you can find that statement on this website.]]

                1. Sorry, Matt. I was sure you said it as you are the only particle physics person I have followed. I was greatly pleased at the time. 🙂 Perhaps you said it facetiously and I misunderstood. I remember it was when you returned from CERN. It must be at least 4 or 5 years ago, now. Maybe more.

                  Anyway, if i am wrong, I apologize. I didn’t mean to put words in your mouth.

                  Thank you for letting me continue, but I see no point in me continuing here. I follow your posts and when I saw the topic thought I could contribute to the discussion, but now i realize this is not a forum, per se, but your personal blog. Again, sorry, I didn’t mean to disturb the flow. 🙂

                  I did send you an email a couple of years ago with a paper showing how all molecular structures could be diagramed using just the up quark and electron, but never heard back from you. Of course it grew out of my time dilation model. If you are interested I will send it again. Just send me an email and I will send it to you in reply.

                  Thanks again.

                2. It’s my own blog/website, yes; but again, its purpose is to explain mainstream particle physics and related subjects — to make it clear what mainstream physics says and doesn’t say, so that everyone can understand it and can then agree, disagree, criticize or support it from an informed point of view. You are correct that it’s not a discussion forum for out-of-the-mainstream physics; I have nothing against such sites, but this isn’t one of them.

          2. You said “time evolves spatial events forward” and “It is spacetime, not space and time”. Those sentences contradict each other.

            Pure time can only be found in the proper time of the body. Spacetime is a continuum, where only the interval is an essential, independent that how much components separate when measured; space or time – it varies from different perspectives.

  10. Based on the principles of general relativity, one can very well see from the opposing point of view for Newton and animal instinct as follows:

    a) Gravitation is not a real force, but proper acceleration forces are
    b) Local physical changes do not fall but rise like buoyancy
    c) Tidal forces are not caused by differences between spacetime geodesics, but we would say that tidal forces are from spacetime structure and cause curvature with geodesics

    Are there valid reasons that that kinda change of perspective cannot be fruitful?

  11. I would like to see how and ideally why this relativity is unique to gravity and no other kind of (apparent) force, for example an explanation of why iron filings in an iron box would know they are falling towards a magnet, or whatever situation seems equivalent to the gravity experiment, but is actually different because this phenomenon is unique to gravity, and not simply an alternative but equivalent model to what was around before.

  12. Dr. Strassler:
    One of the things I have always found curious, that even in General Relativity, momentum is conserved. You can argue that gravity is not a real force, but even in Eienstein gravity, is not gravity a paired effect? Earth affects the moon with the same “force” as the moon affects earth. Is momentum conservation more fundamental than forces? I have always thought so, if my definition of a “real force” is one that obeys Newton’s third law….which is tantamount to conservation of momentum, would you argue that gravity is a real force….or gravity is a real effect. I would go with real effect.

    In other words, Newton’s third law is often stated as equal, but opposite forces. However, if you view Newton’s third law as conservation of momentum, it still applies in General relativity…even if it’s not a “real force”. In fact, can’t I argue that it’s conservation of momentum that makes gravity behave and look like a real Newtonian force?
    Does my argument hold any merit?

    1. I don’t think your statements are correct; conservation of energy and momentum are quite subtle in the context of a general curved spacetime, and I don’t understand this subtlety fully enough to explain it correctly. For instance, one thing you’re neglecting is that the Earth and Moon radiate gravitational waves which carry off both energy and momentum, so certainly the Earth-Moon system alone does not conserve either one. In more complicated spacetimes it becomes difficult to even define a global notion of momentum. Momentum and energy density are conserved, but only locally (i.e. in small regions where these complexities can be neglected.)

      1. Dr. Strassler:
        Thank you for the detailed response, I always appreciate & respect your interpretation of things. To me, the fact that electromagnetic waves carry momentum is evidence of the fundamental of momentum conservation. When you turn on a flashlight, the flashlight recoils, although nothing of “mass x velocity” is coming out the front, but the photons carry momentum . When a molecule fires off a photon, the whole molecule recoils. Gravitational waves carrying momentum is also, I believe, a manifestation of this requirement also. Can’t wait to read your book, already pre-purchased an Amazon.

        1. It is true that electromagnetic waves carry momentum and that momentum conservation is satisfied by electromagnetism. But gravity is different, as it is in so many ways. This is because momentum (and energy) have to do with motion across space and time, which are flat for pure electromagnetism but curved for gravity. Once the curvature is large and complex enough, it becomes impossible to define momentum and energy uniquely, which then makes defining their overall conservation impossible. Only in a small region can one locally define these quantities and show they are conserved within that region.

          In sufficiently simple space-times, it is still possible to define energy and momentum and in those cases, as far as I am aware, they are conserved. But if you can’t unambiguously define them, you’re in trouble.

          As I said, though, I’m not the expert on this, and so there might be better and more accurate ways of explaining the situation that a real expert in general relativity’s ins and outs could tell you.

  13. “ there is no physical distinction between a spatially-uniform gravitational force and a special form of pure motion: constant acceleration.”

    I don’t think I’ve ever seen the equivalence principle stated that way. It’s a nice way of putting it, particularly with regard to the discussion of tidal forces that follows.

    Is gravity really different from other forces in that regard? If the universe were permeated by a uniform electric field, would the net force be zero for any (all?) frames? What about a net charge at all points?

    Probably more related to future posts, but the geometric description of gravity, which apparently Einstein was not overly fond of) has always struck me not as a feature that sets gravity apart, but rather as reminiscent of dynamics as stationary action paths through Lagrangian and Hamiltonian phase spaces.

    1. Gravity really is different. A uniform electric field would cause some objects to accelerate in one direction, others to accelerate in the opposite direction, and still others not to accelerate at all. Moreover, the acceleration rates would not be the same, because the electric charge of an object is not correlated with its mass. Thus a uniform electric field cannot be traded for pure motional acceleration; objects do not all accelerate in the same way, as they do for gravity. Only because gravity is universal can it be viewed as due to geometry.

      That said, one can formulate electromagnetism as due to extra-dimensional geometry. At some point I’ll have to figure out how to explain why that works, and this question will come up again at that point.

  14. One could just as well attribute tidal effects to variations in the curvature of spacetime rather than gravitational “forces”.

  15. All that without once using the word,”microgravity,” as astronauts describe it. The real tricky one is after describing gravity as the curvature of the fabric of spacetime is answering the next logical question: What is the fabric made of? Similar to the search for a magnetic monopole some may claim dark energy as the dipole for gravity. But such claims lead to more questions, as they should. It is good to know something but damn, look at all we don’t know.

  16. I have clearly demonstrated that the universe is a holographic energy (quantum) field. It is not space and time, but spacetime, a single thing with 2 aspects, space and time. I have also demonstrated that when we drop an object in a gravitational field, it is not an object falling through space, but a density in the continuum evolving down a time dilation gradient. ALL gravitationally induced velocities are directly related to the difference in the rate of time, dRt, between the invariant 1 s/s rate of time of continuum as a whole and the rate of time at the coordinate point. V = c*sqrt(dRt) inside the Kepler zone, which is inside the corotation ring of a large spiral galaxy, and (c*sqrt(dRt))/sqrt3 outside the Kepler zone. The velocities are merely compensation for the slower rates of time in masses, keeping them up with the evolution of the continuum as a whole, which evolves forward at c in the forward direction o time. My latest paper, “Time Dilation Cosmology”, became the 3rd most viewed paper in the Journal of Modern Physics in the past year in just 2 months and is now the 3rd most viewed in the last 15 months. It can be found at: https://www.scirp.org/journal/paperinformation.aspx?paperid=125191 if anyone would like to pursue it further in a discussion here. I should add that I am Managing Editor of the Journal of Cosmology. Thanks, Matt.

  17. In physics, things are defined to make problems appear simple, and the best definitions can change depending on the problem, or even how it is approached. Is gravity a fictitious force? If you want to calculate a low Earth orbiting satellite’s trajectory, it’s generally best to treat it as a real, Newtonian, force, with some relatively small relativistic corrections if you care about further accuracy. If you want to calculate photon orbits about a black hole, it’s best to go fully general relativistic and force never enters into it. At a deep level, of course, these are really based on the same physics, but it can be very fruitful to treat them as if they weren’t. It’s one elephant, no matter how the blind men’s descriptions differ.

    1. Agreed. For a professional physicist, I think the real point of this post is that the 1/r^2 law of Newton is less important to Einstein than is the 1/r^3 tidal force; it’s the latter, not the former, which shows up in gauge invariant quantities such as the Ricci scalar.

  18. Matt, would it be fair to say that forces can always be regarded as “fictitious” in the sense that they are never ontological in their own right? Rather, “forces” are interpretations of the effect of something else, whether that is the curvature of spacetime, or the effect of virtual particles, or of ripples in quantum fields. If so, it would follow that one could always give alternative accounts, either in terms of, or not in terms of, the force.

    1. Well, let’s start by being clear about these two definitions of “fictitious.” My definition was that a fictitious force is one that is strictly zero from some point of view, and therefore cannot have any real physical effect that isn’t perspective-dependent.

      Your proposed definition is really quite different, as it is terminological: it says that I can describe even a real force (such as a tidal force), one that has a perspective-independent impact (such as ocean tides), in ways that never use the word “force” and have a different conceptual basis. This is true, and in a way it has been true for centuries — Newton’s laws were reformulated by folks such as Lagrange, Maupertuis, Hamilton, Jacobi, etc. in ways that view “force” as a derived concept. But in this sense, all physics concepts are — well, maybe not “fictitious”, but “contingent”… contingent on the conceptual language that I use to describe the world, which we know (from centuries of experience) is not unique.

      So is it “fair to say” it? As long as you’re clear about what you mean. What’s really essential is that gravity is a real effect, even though some aspects of it are fictitious, and whether you phrase its origin as “spacetime curvature” or “quasi-Newtonian force” doesn’t matter in the end.

  19. In a similar fashion, tidal locking is considered a “phenomenon”, which could be a candidate as a possible
    “force” in and of itself , certainly not an illusion, by which a body has the same rotational period as its orbital period around a satellite . So, the Moon is tidally locked to the Earth because it rotates in exactly the same time as it takes to orbit the Earth. In opposition, celestial objects that retrograde in orbit would find difficulty in tidal locking to a satellite unless the satellite is retrograde. So is this considered a reverse or opposing “force”? Certainly not an illusion because it is empirically verified

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[UPDATE May 10, 4:00 pm Boston Time, 10:00 pm EU time: AURORAS MAY BE ACTIVE NOW!] I don’t use exclamation marks in blog post titles

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