# How does relativity explain inertia

brupenney
Hi: Will someone please answer this question: How does relativity explain inertia. What resists accelerational force; if there were nothing resisting the motivating force, why would a force be needed at all to set it in motion.

Tks

Staff Emeritus

The short version is that relativity says F=dp/dt, where p is the momentum, i.e. force is the rate of change of momentum with respect to time. This is identical to Newton's formulation so far.

The difference is that in relativity, p = mv/sqrt(1-v^2/c^2) rather than p=mv, i.e. the formula for momentum versus velocity is different.

I have a nagging feeling that this explanation is too complex (though I don't know your background, perhaps I'm being overly concerned). Alas, I don't see any way to simplify it. It's not really terribly complex after all, though you do need to know what momentum is and also a bit of algebra. Perhaps I could omit the algebra, but then there wouldn't be any way to clearly state why the momentum was different in relativity.

brupenney

The short version is that relativity says F=dp/dt, where p is the momentum, i.e. force is the rate of change of momentum with respect to time. This is identical to Newton's formulation so far.

The difference is that in relativity, p = mv/sqrt(1-v^2/c^2) rather than p=mv, i.e. the formula for momentum versus velocity is different.

I have a nagging feeling that this explanation is too complex (though I don't know your background, perhaps I'm being overly concerned). Alas, I don't see any way to simplify it. It's not really terribly complex after all, though you do need to know what momentum is and also a bit of algebra. Perhaps I could omit the algebra, but then there wouldn't be any way to clearly state why the momentum was different in relativity.

Tks. I understand what you're saying. I was asking a question beyond that. Imagine a mass unmoving in space. Unless it is held there by some force, why should a force be needed to move it? The math of inertia just describes, doesn't explain. Is the mass trapped in spacetime, which exerts a restraining force, so that a force is required to move it from its position? If time isnt the restrainer, then space would be, but this would mean space must be material, which goes against accepted physics I believe.

Mentor

Tks. I understand what you're saying. I was asking a question beyond that. Imagine a mass unmoving in space. Unless it is held there by some force, why should a force be needed to move it? The math of inertia just describes, doesn't explain. Is the mass trapped in spacetime, which exerts a restraining force, so that a force is required to move it from its position? If time isnt the restrainer, then space would be, but this would mean space must be material, which goes against accepted physics I believe.

The mass doesn't have to be "stationary" like you describe it. It can also be moving at a constant velocity, and still not require any force. Only if its velocity is changed is a force required. That's what inertia is all about. In a way, the concepts are basically the same for both Newtonian mechanics and relativistic mechanics.

someGorilla

The math of inertia just describes, doesn't explain.

What would an "explanation" look like for you? Can you think of a kind of explanation which gets to the bottom of the matter and leaves nothing more to wonder about? I, for one, can't. Physics provides descriptions. Sometimes we call these descriptions explanations when we find them illuminating or inspiring, but you'll never get down to "what" things are and "why" they work like that, you can only have the "how" of nature's inner workings.
As for me, I like it that way

Mentor
A simple explanation is that inertia is the result of all the other masses in the universe acting on the object of interest.

In relativity inertial mass is equated to gravitational mass and so far experiment has confirmed that assumption.

Mentor

Imagine a mass unmoving in space.

Unmoving according to whose point of view (reference frame)? One of the key principles of relativity theory is that there is no "absolute reference frame." If you're in a spaceship that is stationary with respect to the object, then the object is stationary with respect to you. If I'm in another spaceship coasting past yours (and the object) at constant velocity with respect to you, then the object is moving at constant velocity with respect to me. Either of our points of view are equally valid. There is no way we can consider one of us to be "really" at rest, and no way to conclude that the object in question is "really" at rest or not.

Staff Emeritus
Gold Member
Tks. I understand what you're saying. I was asking a question beyond that. Imagine a mass unmoving in space. Unless it is held there by some force, why should a force be needed to move it?

Your thinking here is just backwards. Why would it need to be "held there" to prevent it from moving? Or to put that another way, why would we have to worry about the object spontaneously beginning to move, in the absence of any "restraining" forces? Answer: we don't have to worry about that; it doesn't need to be restrained against spontaneous movement. As already explained to you in the very first reply, Newton's second law, or its relativistic equivalent, state that the net force on an object is equal to the rate of *change* of its momentum. If there is no net force, then there can be no change in momentum. So if the momentum was zero to start with, then it will remain zero. This is an experimental/observational fact to which there has never been an exception, and hence it is taken to be a fundamental law of nature.

brupenney
Thanks guys for taking the time to reply.

Staff Emeritus

Tks. I understand what you're saying. I was asking a question beyond that. Imagine a mass unmoving in space. Unless it is held there by some force, why should a force be needed to move it? The math of inertia just describes, doesn't explain. Is the mass trapped in spacetime, which exerts a restraining force, so that a force is required to move it from its position? If time isnt the restrainer, then space would be, but this would mean space must be material, which goes against accepted physics I believe.

That feature is common to both relativity and Newton's laws. In particular Newton's first law is often stated as "an object at rest will remain at rest". No force is needed for it to remain at rest. Sometimes people describe this by saying "Matter is fundamentally lazy". It turns out (at least according to Wiki) that the root Latin word of "Inertia" means "lazy".

See for instance http://en.wikipedia.org/w/index.php?title=Inertia&oldid=511134187

Inertia comes from the Latin word, iners, meaning idle, or lazy. Isaac Newton defined inertia as his first law in his Philosophiæ Naturalis Principia Mathematica, which states:[1]
The vis insita, or innate force of matter, is a power of resisting by which every body, as much as in it lies, endeavours to preserve its present state, whether it be of rest or of moving uniformly forward in a straight line.

So this is a classical physics question. I'm not aware of any explanation for it more fundamental than Newton's laws.

Staff Emeritus
Gold Member
A simple explanation is that inertia is the result of all the other masses in the universe acting on the object of interest.

In relativity inertial mass is equated to gravitational mass and so far experiment has confirmed that assumption.

This is the Machian interpretation, which was finally embodied in an actual physical theory in the 60's by Brans-Dicke gravity. BD gravity was falsified empirically in the 70's (for all interesting values of its omega parameter), so the Machian approach is basically dead.

georgir
As a theory of Gravity, relativity can not and does not attempt to explain inertia regarding other kinds of forces.

And when talking about gravity only, there is nothing to explain at all. Gravity affects all objects equally. A feather and a star will fall in the same way. They affect things differently, but they react to things exactly the same. So the concept of different inertia depending on mass never even arises.

Austin0

What would an "explanation" look like for you? Can you think of a kind of explanation which gets to the bottom of the matter and leaves nothing more to wonder about? I, for one, can't. Physics provides descriptions. Sometimes we call these descriptions explanations when we find them illuminating or inspiring, but you'll never get down to "what" things are and "why" they work like that, you can only have the "how" of nature's inner workings.
As for me, I like it that way

Everything you say here is completely true but did not stop Newton, Mach, Einstein et al from expending much time and brainpower attempting to find an answer to exactly the OP's question, so he is in good company.

someGorilla

Everything you say here is completely true but did not stop Newton, Mach, Einstein et al from expending much time and brainpower attempting to find an answer to exactly the OP's question, so he is in good company.

Yep. It's funny how we look for sensible and meaningful explanations and once they're there, coherent and (more or less) complete, we wonder if they are so meaningful after all... The thing that really strikes me is how the search for coherence, meaning and elegance is effective. It works! That is something that might never be explained. Ok, enough OT.

nitsuj
Hi: Will someone please answer this question: How does relativity explain inertia. What resists accelerational force; if there were nothing resisting the motivating force, why would a force be needed at all to set it in motion.

Tks

Look into what mass of an object mostly is (kinetic), I think through that you'll answer your why question. it was one of my biggest "eye openers".

harrylin
Hi: Will someone please answer this question: How does relativity explain inertia. What resists accelerational force; if there were nothing resisting the motivating force, why would a force be needed at all to set it in motion.

Tks
The shortest version is that relativity doesn't explain inertia; relativity accounts for it.

nitsuj
lol now that's just mean....well maybe not mean but definitely coy.

altergnostic
No one knows the cause of inertia. It is something we observe and its effects are described by physics, but what causes it is unknown, Newton defined it as a law. Einstein actually called it a phantom in the Born-Einstein letters, and was glad he could bypass the concept of inertia from the equations of general relativity. With Newton and Special Relativity, we need a force to change a body's velocity (a force would always cause an acceleration), in GR there are no forces, it is the spacetime that is curved, so the body is considered to follow a geodesic with constant velocity instead of being accelerating. These are all mathematical models and maybe someday someone will shed more light on what is it about mass that makes it resist a force. I have seen an interesting but rather bizarre aproach, which took the dimensions of gravity as proposed by maxwell and took the cubed length literally to mean that all bodies are expanding, so any force you appled on a body would need to work against the body's innate 3D motion. The author himself was bothered by the idea though.