# Is there still no known origin of the law of inertia?

To quote Feynman at about the 21 minute mark of the first Messenger Lecture on The Character of Physical Law,

...that the motion to keep it going in a straight line has no known reason. The reason why things coast forever has never been found out. The law of inertia has no known origin.

This lecture was given in year 1964. I'm curious if there has been any progress since then to understanding the origin of the law of inertia. If yes, if a layman explanation can be provided.

Edit 1, adding the definition of scientific law for discussion in comments. From Kosso (2011, pp 8):

One more term should be clarified, ‘‘law’’. Theories differ in terms of their generality. The big bang theory, for example, is about a singular, unique event. It is not general at all, despite being about the entire universe. The theory of gravity, either the Newtonian or relativistic version, is very general. It is about all objects with mass and their resulting attraction. The most general theories, including the theory of gravity, are laws. In other words, laws are theories of a particular kind, the ones that identify whole categories of things and describe their relations in the most general terms. Laws start with the word ‘‘all’’, as in, All this are that, All massive objects are attracted to each other.

Being a law has nothing to do with being well-tested or generally accepted by the community of scientists. A theory is a law because of what it describes, not because of any circumstances of confirmation. And a theory is or is not a law from the beginning, even when it is first proposed, when it is a hypothesis. The status of law is not earned, nor does it rub off; it is inherent in the content of the claim. So neither ‘‘theoretical’’ nor ‘‘law’’ is about being true or false, or about being well-tested or speculative. ‘‘Hypothetical’’ is about that kind of thing.

See Kosso (2011) for the definitions of the terms Theory, Fact, and Hypothesis, if needed.

Edit 2, I acknowledge I do not know what definition Feynman held when using the term "law" in the Messenger Lecture (as I had quoted above). It seems he also referred to it as the principle of inertia (The Feynman Lectures on Physics, Volume I, Chp 7, Sec 3 - Development of dynamics):

Galileo discovered a very remarkable fact about motion, which was essential for understanding these laws. That is the principle of inertia—if something is moving, with nothing touching it and completely undisturbed, it will go on forever, coasting at a uniform speed in a straight line. (Why does it keep on coasting? We do not know, but that is the way it is.)

An interesting side note, according to user Geremia (link):

Galileo, Newton, or even the medieval physicist Jean Buridan (1295-1358), who developed the notion of impetus, were not the first to discover the law of inertia.

The first was John Philoponus ("The Grammarian"), who lived in the late 5th and 2nd ½ of 6th century A.D.

Edit 3, I agree that no "Laws" of physics have a "known" reason. But that is not the point of my question. My question is whether or not any progress has been made on understanding the origin (i.e. the mechanisms underlying) the law of inertia. For example, Darcy's Law can be derived from the Navier–Stokes equations. The Navier-Stokes equations arise from applying Isaac Newton's second law to fluid motion. I suppose this regression to more fundamental mechanisms or reasons can go ad infinitum (as explained here by Feynman. He also addresses the "why" question, Aaron Stevens).

Edit 4, I am not making Feynman into a Pope nor am I appealing to his authority. He has simply made a statement about the current understanding of the law of inertia. Of course, I attributed his statement to him. I then asked a question about his statement. I made no assumption as to whether his statement was correct or not. If anyone cared to make an answer pointing out his statement is incorrect I would be grateful to hear it.

• Comments are not for extended discussion; this conversation has been moved to chat. – tpg2114 Jul 2 '19 at 17:25
• @tpg2114 What about the comments that were actually suggestions to improve the post and not part of a discussion? – Aaron Stevens Jul 4 '19 at 22:45
• @AaronStevens I didn't see anything that wasn't reflected in edits, aside from your comment to make the post cohesive instead of adding in "Edit #..." parts. If there is something specific I overlooked, let me know. – tpg2114 Jul 4 '19 at 22:56

The law of inertia can be seen as the result of the translation invariance of the laws of physics. Of course it's a matter of taste whether you think translation invariance makes a more intuitively appealing axiom than the law of inertia itself.

• This does indeed begs the question of why translational invariance of the laws of physics should hold. To me, the law of inertia is more appealing because it's closer connected to our observations. If the law of inertia wouldn't hold, objects would behave in an unpredictable way. – descheleschilder Jul 3 '19 at 22:10
• The translational invariance of the laws of physics only tells us that momentum (=$mv$) is conserved (Noether), but doesn't say anything about the constancy of mass and velocity. Maybe the mass gets smaller and the velocity bigger. You also have to invoke the translational invariance in time (of the laws of physics) from which it follows that the energy (in this case, the kinetic energy $E_{kin}=\frac{1}{2}mv^2$) is conserved. So the law of inertia is not a result of translational invariance by itself. It has to be supplemented by the translational invariance in time. – descheleschilder Jul 4 '19 at 0:59
• @descheleschilder You are correct. The translation invariance is a result of the Noether theorem that is based on the Least Action Principle. – safesphere Jul 4 '19 at 4:12

The quote by Feynman is stating the obvious, that the law of inertia has no deeper explanation, other than when used, together with other laws, principles and postulates to set up a theoretical physical model for mechanics.

In general laws, principles, postulates are extra axioms used in physics models so that the theoretical model fits observations and predicts future ones.

At the moment there does not exist a Theory Of Everything (TOE)for physics. If one such does emerge in the future, it could be possible that the number of physics laws,postulates, principles will be reduced to that one mathematical theory and its axioms. We have not reached that level, if it is ever reached. In such a TOE it could be that inertia would be theorem and not an axiom, i.e. it would be more in mathematical formulation economical to have it as a theorem. (In a theory the place of axioms and theorems can be interchanged, one chooses the simplest mathematically as axioms)

• Well, one chooses (what one considers) the most convenient for a given application, which is not necessarily the same as the simplest. – tomasz Jul 18 '19 at 15:01

For me a lot of the answers here went over my head but I think I have an easy explanation for anyone else in my situation -- Relativity.

There is no absolute frame of reference which means that something is only "Moving" relative to something else. Nothing is ever moving in it's own frame of reference unless it is being acted upon by another force. (I'm not sure the concept of motion exists in your own frame of reference, only acceleration. That would make a good follow-up question)

As an example: If you fire a bullet from your spaceship, as soon as the acceleration stops the bullet is just sitting in space in it's own frame of reference and the ship is moving away from it.

If the bullet "Slowed" and you looked at it from the bullet's frame of reference it would look like the ship was accelerating towards the bullet--Why would it do that? Wouldn't it just stay still? If it turned (not in a straight line) it would look as though the ship suddenly accelerated to the side. The only sensible option is for both to sit still until something else accelerates them.

Once you think about it this way and subtract some earthbound constants like friction, gravity and a very commonly accepted point of reference it would be surprising anyone would expect any different behavior.

So in essence, the part of the Law of inertia that says a body in motion remains in motion is the exact same thing as the first part "A body at rest remains at rest". There is no difference between the two except for where the viewer is located.

The law of inertia can be expressed in terms of spacetime geometry as, "free massive particles follow timelike geodesics". The geodesic equation is an expression of the least action principle. Thus to say, "a free particle obeys the law of inertia", is the same as to say, "a free particle obeys the least action principle".

Another representation of the law of inertia using the least action principle is the Noether theorem stating that a momentum of a free particle is conserved in a space with a continuous translation symmetry.

The origin of the least (or more precisely, stationary) action principle is in quantum mechanics, "if we consider the classical description as a limiting case of the quantum formalism of path integration, in which stationary paths are obtained as a result of interference of amplitudes along all possible paths." (Principle of Least Action)

Thus the origin of the law of inertia is in the wave properties of matter. The stationary path of inertial motion is a result of a constructive interference of quantum waves (similar to the Fermat's Principle in optics).

• The last two paragraphs are circular reasoning and doesn't explain inertia motion. For its path formulation, QM needs a lagrangian that already comes from classical mechanics. – Cham Jul 4 '19 at 4:09
• @Cham The Quantum Medhanics Lagrangian does not come from Classical Mechanics. What you perhaps have meant to say is that Quantum Mechanics obeys the Least Action Principle just like the Classical Mechanics or General Relativity. However, the Principle of Least Action in Quantum Mechanics gets a clear explanation as the constructive interference. There is nothing circular in this reasoning. In fact, you don't even need to refer to Classical Mechanics at all for this explanation. – safesphere Jul 4 '19 at 4:20
• I don't agree. For a free point particle, the QM lagrangian is $L = \frac{1}{2} \, m \dot{q}^2$. What is this? Of course, it's the classical kinetic energy of the particle. It's a fact that we don't know how to formulate QM without implicit reference to its own classical limit. Even the canonical quantification (Hamiltonian formulation) is a procedure defined from classical mechanics itself (Poisson relations going to quantum commutators ...). – Cham Jul 4 '19 at 13:27
• @Cham You are welcome to disagree. However, a similarity in the Lagrangians doesn't change the fact that Classical Mechanics follows from Quantum mechanics, but not vice versa. It also doesn't mean that we don't know how to formulate Quantum Mechanics. We get an exact solution and this solution is a wave function with the properties that explain the law of inertia. Also, again, we don't even need to refer to or compare anything to Classical Mechanics for this explanation. – safesphere Jul 4 '19 at 14:29
• @Cham Quantum waves don't have inertia. They explain the Least Action Principle by constructive interference. Please see: en.wikipedia.org/wiki/Path_integral_formulation – safesphere Jul 4 '19 at 15:40

If one imagines on the origin of the universe as coming from nothing, one immediately realize that:

1. The net energy in the universe must be zero and the universe should be a free meal, i.e, if some energy is created by stretching up something at a point A, then, somewhere in the universe this thing (or equivalent) is going to be stretched down at a point B. This is the principle of conservation of energy in a nutshell.

2. The total amount of “movement” in the universe must be zero, not only because energy is zero, but because there is nowhere for the universe to go as well, i.e, if something is moving right next to point A, another thing(s) must be moving left near point B to counterbalance this motion. This is the principle of conservation of momentum in another nutshell.

People in the vicinity of point A or B may observe the existence of energy and motion, but it just doesn’t exist at the big scale. Therefore, if a state of motion is observed somewhere, such a state is demanded to remain the same until it is passed or transferred into another object. This explains why the state of motion should persist (half of the inertia principle). What this doesn’t explain, is why the motion appears to resist the change, in other words, why motion is not transferred from object 1 to object 2 at a zero time (the other half).

The fact is that there is another principle that seems to be a part of the universe’s behavior (I don’t know the reason why) but is well established.

1. The transfer of any peace of information (yes, motion is information) cannot be done at a speed higher than the speed of light in vacuum $$c$$.

Principle 3) demands motion to be passed at a finite amount of time, making an object appear to resist gaining or losing motion. Combining all this together, one realizes that inertia is a consequence of the basic structure of the universe.

Well, i think that a motivation for why bodies not subjected to forces obey the inertia principle can be stated: our universe has a space-time that, in this condition, looks homogeneus and isotropic. If anyone tries to write up the equation of motion for a body moving in such space-time, a lot of properties are strictly forbidden and the only solution left is a uniform straight motion. However, note that this answer is not totally complete, because now the focus has been shifted to the reason why the space-time of our universe looks exactly homogeneus and isotropic, in absence of charges or fields (i would add).

• "If anyone tries to write up the equation of motion for a body moving in such space-time, a lot of properties are strictly forbidden" - They are not forbidden by the spacetime itself. The equations of motion come from the Least Action Principle (expressed either in the geodesic equation or in conservation laws). The symmetries of the spacetime only give you the fact that the law of inertia in motion logically follows from the law of inertia at rest. The properties of spacetime alone without the Least Action Principle don't explain why things at rest remain at rest. – safesphere Jul 4 '19 at 14:37
• Absolutely yes. Equations of motion are descendants of the Least Action Principle but, above them, simmetries must be encoded in the Lagrangian from which you obtain them. Homogeneity and Isotropy, for a free classical-body, greatly restrict the possible Lagrangians that can be written up, leaving space only for redundant factors. – Andrea Mosena Jul 5 '19 at 9:07

Answering this question really requires a more philosophical take. For one, insofar at least as physics is concerned, the only way you can talk of an "origin" of something is to derive it from a more basic set of principles. Yet that assumes that there is such a more basic set of principles, and that may not be the case, and it's reasonable to imagine it is not the case: there can very easily be a finite set of groundwork, complete principles sufficient to generate all phenomena in the Universe.

The reason we can think this is that it is logically possible, and to show that we need only exhibit a consistent but imaginary example. Consider a Universe composed of a single kind of point particle whose laws of motion were literally just Newton's laws of motion, perhaps with some suitable forces. It's not our Universe, but it's a possible one (c.f. Modal logic). If you were to pose this question in such a Universe, it would have no answer in the way physics, as a mode of study, conceives of such a thing, because these would be its most basic laws with no deeper ones underlying them.

Hence, the only way physics would provide an answer to this is if it turns out that in the real Universe, there is a deeper set of laws in which inertia is not a fundamental phenomenon. Since we don't have a set of laws we can confide in as being complete, it is still possible, but then again, it may not be.

And past that, the question effectively amounts to "why is the Universe we live in the way it is?" even when all discoverable explanations have been exhausted, and this likely goes out of the realm of empirical science altogether. Empirical science does have limitations, and here is it (and those that say otherwise, and/or that say that nothing else is "worth" asking about are, in my mind, of a rather limited, if not hubristic, mindset, but that's for another discussion in likely another forum).

OK, this doesn't really answer the question. The answer is: "right now, we don't know. Moreover, it is reasonable to suspect that we may not ever be able to 'know', and we may very well come to a point where that is the most reasonable conclusion given the balance of evidence that will be available at that time."

There is still no answer to the question of why the law of inertia should hold (and you can say the same of every law from which it is supposed to be deduced). But suppose it didn't hold. What would this imply for the motion of an object in, say, empty space?

The law of inertia states that the momentum of the object stays the same forever, as long as no force acts on it. So the velocity vector of the object is constant during its motion. So what will happen if this is not the case?

I'm sure you can imagine that if the momentum of the object is not constant during its motion, the object would behave in a way that we have never seen. So while the "why" of this law is not known, it certainly is backed up by our observation. The world would look very different. Maybe in a parallel Universe, the law of inertia doesn't hold. Try to imagine how and if we could live there. One can say that the law of inertia is an empirical law, a law based on our observations.

Of course, the (ultimate) base of all our Natural laws is based on observation but empirical laws "beg" for a deeper explanation, like the empirical Bohr model for the energy levels in an atom was totally accounted for by quantum mechanics (which was fully developed years later) by means of the Schrödinger equation. There is no doubt though that Bohr played a role in the development of QM. But in the case of the law of inertia, there is no deeper theory (not yet, and I doubt there will ever be) that explains this law.

The main metaphysical point was made in the answer of anna v: in any theory based on mathematical reasoning the role of axioms and theorems (i.e. that which can be deduced from the axioms) can be interchanged. We normally put as axioms the simplest things we can that are sufficient to allow the theorems to be deduced. Determining which are simpler can sometimes be subjective or a matter of taste. Since the law of inertia is already a fairly simple statement, most other statements will be deemed more complicated and therefore less deserving of being called axiomatic in any given formulation of physics.

If we don't want to make the law of inertia axiomatic, then we have a choice of other things which we might argue are simple enough to warrant being used as axioms, from which inertia can be deduced. Here are some.

1. Symmetry of the Lagrangian with respect to translation in time and space (in classical mechanics), leading to conservation of energy and momentum.

2. The claim that the worldline of an object in free fall is a timelike geodesic of spacetime. (Such a worldline can also be described as a line of maximal proper time between any given pair of events on the line.)

3. Like (1.) but now invoking quantum mechanics.

I have a slight preference for (2) over (1) here, but of course since the world is quantum physical, one might argue that no classical reasoning can be adequate. However, it seems to me that the law of inertia could be asserted as axiomatic in any formulation of physics, and thus used to somewhat reduce the set of other things one would have to assert in order to give a complete statement of one's theory, whether present-day quantum theory or any future development.

• "Symmetry of the Lagrangian with respect to translation in time and space" - These symmetries are physically of space and time. The Lagrangian only reflects this fact. They alone are insufficient for the law of inertia. What you also imply without saying is that the Lagrangian describes reality. This is not given. You must prove or assume as an axiom that the Least Action Principle holds. Please see my answer where I attempt proving it based on the wave properties of matter. This obviously works, but what is the axiom in this case? What is the minimal expression of the wave properties? – safesphere Jul 20 '19 at 21:13
• The above comment covers your # 1 and 3 under the same LAP. Your # 2 also is not an independent axiom. The geodesic equation is an expression of the LAP for a free particle in a particular spacetime (using the metric as the Lagrangian). Thus all three of your options have the same foundation in the symmetries of spacetime plus the LAP and as such they are correct (albeit not independent at the lowest level). With quantum waves, the Least Action Principle is as beautifully intuitive as the Fermat Principle in optics, as a simple consequence of interference. What is the minimal axiom for waves? – safesphere Jul 20 '19 at 21:29