I How does inertia, a property of mass, arise?

[KurtLudwig]

TL;DR

Newton's First law states that an object will continue to move in a straight line or remain at rest. Only when the its velocity is changed, either its speed or its direction, does the property of inertia show itself.

Do todays physicists have a deeper understanding on mass and inertia on how inertia arises?

 

[kuruman]

You skipped the second half of Newton's first law which is "... unless an unbalanced force acts on it." Setting that aside, can you explain what you understand by inertia? I am asking because different people have different understandings of inertia. Also, presumably, you wish to deepen your understanding, so we have to know how deep it is right now.

 

[KurtLudwig]

Inertia shows itself when you hit a pothole on the road, when you make a sudden turn without slowing down, when a tire is mass unbalanced and rotates. Inertia is a property of mass, but it is shows itself only when that mass is being accelerated.

Do physicists have a deeper understanding of inertia now that physicists know about the Higgs field and boson? What causes inertia? I have read about Mach's principle.

I am at the level of an undergraduate in physics and at calculus 3 (vectors and tensors) in mathematics. I first read about the subject on Wikipedia, before asking questions.

Many, many years ago, I worked on inertial guidance systems, with rotating gyros. Later, I dynamically balanced gas turbines and generators. I understand mathematically how unbalances and resonances arise, but not the physics. I can calculate on where to attach a weight or grind off mass to correct dynamic unbalances.

When I read further, physics turns into mathematics: linear algebra, matrices, tensors, differential equations, set theory, and broken symmetries.
Newton's First law was just an observation of a smooth stone sliding on ice. The Greek philosophers could have never observed inertia.

 

[anorlunda]

Aren't you neglecting Newton's 2nd law, f=ma? To change the velocity of an object, to accelerate it in other words, you need a force proportional to the mass.

Your body experience that every time you ride in a car that accelerates or brakes.

Actually, in physics there is something deeper. Newton's laws of motion can be derived from the Principle of Least Action. But that's hardly necessary. Physical laws much match the observations we make in everyday life. Newton did a better job at that than his predecessors. Einstein improved on Newton's Laws when General Relativity extended it beyond everyday life up to universe scale considerations.

 

[kuruman]

Here is an example of how inertia "arises" that is very well understood in terms of Newton's first law. You are driving your car at a constant speed. A book rests on the back seat. You have to veer suddenly and without braking to the left because you almost missed your turn. The book slides across the seat to the right. Why do you think that is?

From what you have said, and this is only a guess, you would view this event as some form of inertia "arising". I view it as a manifestation of the first law: There is an unbalanced friction force between the car's tires and the road to cause it to change its direction of motion to the left. There is an unbalanced friction force between your body and the car seat to cause you to turn to the left. However, the force of friction between the book and the seat is not enough to cause it to turn to the left, so according to the first law it retains its state of motion and keeps going in a straight line. Because you are moving to the left, you interpret the book's behavior as motion away from you to your right. Having had physics, you interpret this behavior as inertia "arising". Does inertia arise? I would say no. The book's state of motion remains the same throughout your decision to change your state of motion. The relatively low force of friction between the book and the seat did not communicate this decision to the book whereas the relatively high force of friction between your body and the seat did.

 

[sandy stone]

Related to the concept of inertia is the idea of conservation of momentum. Physicist Emmy Noether showed that this in turn is a consequence of the fact that the results of experiments do not depend on where they performed. In physics-speak, the invariance of physical laws with respect to translations leads to the conservation of momentum; pretty astonishing when you think about it. Perhaps this is what you're looking for.

 

[Nugatory]

Actually, in physics there is something deeper. Newton's laws of motion can be derived from the Principle of Least Action.

(Anorlunda already knows all this, I'm writing for others reading the thread)

That is indeed true, but it's still just the next turtle (google for "turtles all the way down"). We can use Newton's laws to answer the original question, and then use the principle of least action to explain the origin of Newton's laws... but where does that principle come from? Why should the universe we live in care about it?

We can work our way down through a sequence of ever bigger stronger turtles more powerful and generally applicable laws of physics, but we're always going to end up with something that we accept because observation tells us that that's how the universe works, not because of some deeper explanation.

 

[anorlunda]

I think it was Leonard Susskind who put down the problem of infinite turtles in all circumstances, perhaps tongue in cheek. He was discussing the cosmological principle. He said (my paraphrase):

It's true because it is a principle. Principles are things we observe to never be violated. Principles are not derived from more fundamental things. Other principles that we use include causality and least action.

Of those, I think causality is the strongest. AFAIK, nobody researches what the next turtle under causality might be, we just use the principle to reject any claims that would violate causality.

 

[KurtLudwig]

Thank you for all your answers.

 

[paradisePhysicist]

If you push a block, on a vacuum on ice, it will continue to move based on Newton. But this only applies to solids, if you push a blob of water instead, the water will no longer behave as 1 blob of water but the water behind the water will be traveling faster than the front blobs of the water.

So the cause of Newton behavior is 2 things: the tendency of molecules of a solid object to maintain the same relative distance of neighboring molecules, and 2, the tendency of a molecule to maintain the same speed in space. 2 could be explained by consciousness, if molecules did not maintain the same speed in space then molecules would have either accelerated or decelerated millions of years ago and planets would have never formed, if there were no planets then no consciousness.

 

[Buckethead]

Newton's first law has the problem of turtles all the way down in the part "moves in a straight line" as we are forced to ask "what is a straight line?" A straight line can be defined as what a massive object does when it is "moving" and not being affected by an outside force, but there is your turtle. An object in orbit is not being affected by an outside force and is moving in a "straight line" as per Newton's law, but it is indeed not really a straight line in the traditional sense. Here it might be better to say an object moves in a geodesic unless acted upon by an outside force.

Indeed inertia is one of the greatest mysteries in nature in my opinion.

 

[paradisePhysicist]

Maybe a molecule in orbit, but an object in orbit is subject to multiple forces, example:

 

[trainman2001]

I like the book in the car example. If we were filming the car turning and the book sliding from above, would we then clearly see the book actually continuing in the original direction of travel, i.e., straight ahead? Starts to sound like Einstein to me. Different descriptions of motion depending on the P.O.V. of the observer. Similar to the tossing a ball straight up and down in a passenger car of a moving train, and the "actual" trajectory of that same ball for the observer standing besides the track, seeing the ball following a string of parabolic arcs back to the tossers hand.

 

[Buckethead]

Maybe a molecule in orbit, but an object in orbit is subject to multiple forces, example:

Tidal forces. OK, I'll go with molocule.

 

[paradisePhysicist]

Tidal forces. OK, I'll go with molocule.

Also the wikipedia says this of tidal force: "It arises because the gravitational field exerted on one body by another is not constant across its parts: the nearest side is attracted more strongly than the farthest side. It is this difference that causes a body to get stretched. Thus, the tidal force is also known as the differential force, as well as a secondary effect of the gravitational field. "

I think that is not the full story; while the gravity vector strengths are different in most cases, also the object is subject to stretching, or rather, compressive, forces due to that the directions of the different gravity vectors are at different angles. Example is a space station that matches the Earth's curve exactly:

 

[Ian J Miller]

In my opinion, this is a little like asking why Newton's second law is in that form, or why the equivalence principle is there. I think the short answer is we don't know, we don't know why mass responds to forces in exactly that way but we have equations that tell us what happens, and unless someone has a really bright idea, I am happy to live with that restriction. I know how to calculate, and for the moment, that will have to do.

 

[synch]

[ It is based mainly on gut feeling, but the idea might help discussion ] I think that inertia is not so much a property of mass itself but more a property of the existence of the mass.

 

[Vanadium 50]

What does that even mean? (And why should "gut feeling" matter?)

 

[vanhees71]

I've no clue either. I think "inertia" is just a fundamental property of matter. It's very well observable by everyday experience that you need a large force to accelerate a "bigger" body than a "smaller" one (of the same material). In Newtonian mechanics it's mass which quantifies in concise mathematically feasible fundamental laws what "bigger" or "smaller" in this context of inertia means. There's no explanation given by the natural sciences, why Nature behaves as we observe her. Rather the natural sciences describe how Nature behaves in a quantitative way as far as reproducible objective phenomena are concerned, no more no less.

 

[MikeGomez]

I've no clue either. I think "inertia" is just a fundamental property of matter. It's very well observable by everyday experience that you need a large force to accelerate a "bigger" body than a "smaller" one (of the same material). In Newtonian mechanics it's mass which quantifies in concise mathematically feasible fundamental laws what "bigger" or "smaller" in this context of inertia means. There's no explanation given by the natural sciences, why Nature behaves as we observe her. Rather the natural sciences describe how Nature behaves in a quantitative way as far as reproducible objective phenomena are concerned, no more no less.

I think that inertia is more than "just" a fundamental property of matter.

In the view of General Relativity, an apple does not fall to the ground. The ground accelerates towards the apple, and even though the surface of the planet is accelerating in different directions at different locations, the planet does not grow in size. If I understand correctly, this is explained in GR as the EFE's describe the relationship between mass (energy) and spacetime.

So in my opinion, I think that a better way to say it is that inertia is a fundamental relationship between matter and spacetime.

 

[vanhees71]

GR is a relativistic gauge theory that describes the gravitational interaction, which can be reinterpreted as a dynamical geometric model of spacetime as a Lorentz (or rather Einstein-Cartan) manifold. The apple and the Earth are simply interacting through the gravitational interaction though a fully self-consistent solution of the apple+Earth as a closed two-body system is very difficult (it's already very difficult in the simpler case of electromagnetism). It's of course fully sufficient to describe the spacetime around the Earth and than the motion of the apple around the Earth as a "test particle".

 

[wrobel]

So in my opinion, I think that a better way to say it is that inertia is a fundamental relationship between matter and spacetime.

and what does it practically imply?

 

[wrobel]

There's no explanation given by the natural sciences, why Nature behaves as we observe her. Rather the natural sciences describe how Nature behaves in a quantitative way as far as reproducible objective phenomena are concerned, no more no less.

indeed! physics and metaphysics must be separated with a high and enduring wall

 

[vanhees71]

Metaphysics is something you can turn to as a retired physicist, not before!

 

[jbriggs444]

In the view of General Relativity, an apple does not fall to the ground. The ground accelerates towards the apple, and even though the surface of the planet is accelerating in different directions at different locations, the planet does not grow in size. If I understand correctly, this is explained in GR as the EFE's describe the relationship between mass (energy) and spacetime.

So in my opinion, I think that a better way to say it is that inertia is a fundamental relationship between matter and spacetime.

General relativity is not relevant here. It has nothing to do with inertial mass.

All general relativity accomplishes here is gives you a "place" to sit where objects can be subject to a force and experience a constant proper acceleration without moving outside the lab.

If you have one brick, it takes a support force to hold that brick in place. Two bricks, twice the support force.

If you go far from Earth and climb into a rocket ship that is accelerating at 9.8 m/s² then it takes that same amount of force to support one brick. And still twice as much force to support two bricks.

Nothing to do with curved space-time.

 

[vanhees71]

In relativity what measures inertia is anyway not (only) mass but all kinds of energy and stress, and that's precisely what GR tells us: both the inertial as well as the gravitational meaning mass has in Newtonian physics in relativity is in fact measured by the energy-momentum-stress tensor of "matter and radiation".

Nevertheless GR doesn't tell us in any way, why the phenomena are as they are observed. It only describes them in a much more comprehensive and in some sense imho simpler way than Newtonian mechanics does. In Newtonian mechanics the perfect agreement between all three kinds of mass (inertial, active, and passive gravitational mass) is simply an observation, while in GR it's built in the model from the very beginning (with the above qualification that it's not mass but energy, momentum, and stress).

 

[MikeGomez]

If you go far from Earth and climb into a rocket ship that is accelerating at 9.8 m/s² then it takes that same amount of force to support one brick. And still twice as much force to support two bricks.

Nothing to do with curved space-time.

Clocks tick at a faster rate at the top of the accelerating rocket ship than at the bottom, identically to an equivalent situation on earth. The reason this has nothing to do with curved spacetime is due to the definition of curved spacetime, not the definition of acceleration or inertia.

 

[MikeGomez]

GR is a relativistic gauge theory that describes the gravitational interaction, which can be reinterpreted as a dynamical geometric model of spacetime as a Lorentz (or rather Einstein-Cartan) manifold. The apple and the Earth are simply interacting through the gravitational interaction though a fully self-consistent solution of the apple+Earth as a closed two-body system is very difficult (it's already very difficult in the simpler case of electromagnetism). It's of course fully sufficient to describe the spacetime around the Earth and than the motion of the apple around the Earth as a "test particle".

Right, but he point wasn't about a two body system. It was that the planet is accelerating in all directions at once. Instead of an apple, it could be a dust particle or smaller, or I think at least in principle an infinitesimally small point in spacetime. The surface of the planet still accelerates towards that point.

 

[MikeGomez]

Nevertheless GR doesn't tell us in any way, why the phenomena are as they are observed. It only describes them in a much more comprehensive and in some sense imho simpler way than Newtonian mechanics does. In Newtonian mechanics the perfect agreement between all three kinds of mass (inertial, active, and passive gravitational mass) is simply an observation, while in GR it's built in the model from the very beginning (with the above qualification that it's not mass but energy, momentum, and stress).

Wikipedia states "Although some theorists have speculated that some of these phenomena could be independent of each other, current experiments have found no difference in results regardless of how it is measured:"

I agree that there is very little hope for such speculation. Eotvos performed his experiment 100 years ago, and since then scientists have created increasingly more accurate apparatuses which fail to detect any difference between types of mass.

 

[MikeGomez]

Nevertheless GR doesn't tell us in any way, why the phenomena are as they are observed. It only describes them in a much more comprehensive and in some sense imho simpler way than Newtonian mechanics does. In Newtonian mechanics the perfect agreement between all three kinds of mass (inertial, active, and passive gravitational mass) is simply an observation, while in GR it's built in the model from the very beginning (with the above qualification that it's not mass but energy, momentum, and stress).

You say GR describes the gravitational interaction, but I've read that mathematically "gravity" and "inertia"
enter the EFE's in the same way.

In any case, aside from experimental evidence as well as the mathematics, we also have Einstein's view there is
no difference between gravitation and inertia.