I wonder why we come to accept irrevocably without recourse that inertia must equal matter. Certainly when Newton postulated about inertia, there seems to be a lot of evidence he would have given the photon an essence of inertia as well; even though it has a finite speed, it does have a constant one, and it would seem the photon had a ''finite inertia.'' The Weak Equivalence Principle, brought around by general relativity in 1926 states that not only is matter the presence of inertia, but matter is inertia, so all conclusions of having a finite inertia for the photon seems weak, since it has only energy and no mass. But what if inertia is not matter? What if Inertia is simply the non-interaction of a second mass, or by technicality, a strong curvature/fluctuation in space and time. Inertia does not necessarily have to be a product of mass, nor does mass need to be an influence of inertia. To help provide evidence of this, a little thought is required. Indeed, inertia is therefore the resistance to speed up or slow down unless acted upon by some external force, but what if it is not a resistence at all? What is stopping a mass from accelerating or decelerating, as some ''resistence'' would issue you to believe? A peice of matter would continue to move in a straight line until some external force shatters it's position and perhaps trajectory... So inertia would be simply be a system moving in a constant direction without the presence of some external object to deter this motion. So why should inertia explicitely be mass itself? What if inertia is simply the natural condition of a moving system, and not necesserily one that is made of matter?
I can see the argument. Without gravity of some sort where is the inertia? inertia: an object in motion tends to stay in motion unless acted upon by another force. so in a sence inertia does not exist it is the other forces pushing and pulling that do all the work. Inertia is just the absence of a force.
Inertial confinement fusion.. the term always puzzled me http://en.wikipedia.org/wiki/Inertial_confinement_fusion
The heated outer layer explodes outward, producing a reaction force against the remainder of the target, accelerating it inwards, and sending shock waves into the center. A sufficiently powerful set of shock waves can compress and heat the fuel at the center so much that fusion reactions occur. Isnt this the basics of a nuclear bomb? just using lasers instead of high explosives?
It doesn't. Inertia is the tendency of an object to resist acceleration. It turns out, of course, that more mass means more inertia. Or, to say it another way, mass is a measure of inertia. Gravity is not required for inertia. Objects in free fall obviously have inertia.
But we do? Einstein was the first to postulate an equivalance between matter and inertia; the Weak Equivalence Principle.
As James noted, inertial mass (the m in p=mv and F=ma) is defined as the measure of inertia.That m=F/a is not surprising at all -- that is how mass (inertial mass) is defined. The surprising thing is that inertial mass is equal to gravitational mass. That is not a tautology, it is an axiom. Physicists do accept definitions so long as they are useful, but they are not so wont to accept axioms. They test them to death. That is exactly what physicists have done since Galileo's time. That inertial mass is gravitational mass now stands as one of the most accurately tested concepts in all of physics. See [post=1996429]this post[/post].
That inertial mass is equal to gravitational mass is a direct consequence of the equivalence principle.
I don't know what you mean by without recourse. Anyway, when you take Newton second law, you know that when you apply a force on an object, its acceleration is proportional to the force. This proportionality constant is a property of this object and we call it inertial mass. Why inertial? you can see that when you apply a force to an object, the acceleration that it gets is a = F/m (a is the acceleration, F the force and m is the mass). The larger the mass, the smaller the acceleration. So we see that the mass in Newton second law is a measure of the inertia of the object. Now, you can show by using Newton third law (this is an high school exercise) that when you take an object with mass m1 and put it together with another object of mass m2, and apply a force F on them, they will get an acceleration a = F/(m1 + m2). So we see that under the assumptions of Newton second law and third law, mass is an aditive property. So that intuitively, if we think of matter consisting of some basic constituents, the mass also measure the number of these constituents. This is why we intuitively see the mass also as the quantity of matter. Next we can also look at the gravitational force. Same as for the electric field, gravitational force has its sources. Electric forces has also its sources that we call electric charge, gravitation source are the gravitational charges, with the difference that electric charges can be positive or negative but gravitational charges are allways positive, i.e., the electric force can be be attractive or repulsive, the gravitational are allways attractive. It happens that the elctric charge and the mass of objects are not related, however, the gravitational charge and the mass are related. The gravitational charge of an object is allways proportional to its mass. So that instaed of speaking of gravitational charge we call it gravitational mass, and we can set this proportionality constant to be equal to 1 and measure the gravitational mass in the same units as the inertial mass. The fact that the inertial mass and gravitational mass are equal are shown in Eotvos experiments.
After reading this a number of times, it still does not seem to make any sense. :mPlease Register or Log in to view the hidden image!
I think the equivalence principle describes the equality. But I think we must be careful not to imply that there is a causal connection between a principal and the effect that it describes.
Einstein's equivalence principle: The outcome of any local non-gravitational experiment performed in a freely falling frame of reference is independent of the velocity of that frame, or of where and when the experiment is performed. The strong equivalence principle extends "any local non-gravitational experiment" to cover "any local experiment, whether gravitational or not". Both forms also postulate Galilean equivalence: The gravitational motion of a small test body depends only on its initial position in spacetime and velocity, and not on its constitution. As James noted in post #8, Einstein saw these as resulting from the equivalence of gravity and acceleration. Gravity and acceleration can only be equivalent if inertial mass is equal to gravitational mass. Suppose they are not equivalent. Imagine a spring to which we can attach various objects. Attach object A to the spring, stretch the spring by a measured distance, and measure the acceleration. Now do the same for object B. The two objects have the same inertial mass if the resulting accelerations are equal. If the two objects have different gravitational masses they will undergo different gravitational accelerations, violating Galilean equivalence.
The reason I put so much importance on the difference between a principal that describes an effect and the cause of the effect is that we can get into a habit of associating the cause with the principal. This takes away the most important thing about any effect. That important thing is the cause of the effect. In the case of inertia, the cause must be some fundamental property of the massive object. Knowing the principal, and knowing the maths that describe the property in detail still does not explain what is that fundamental property. My speculation is that the property of inertia derives from the more fundamental property of the stability of the frequency of electromagnetic fields.
You don't get inertial until you approach \( N_A \), or count a large number of m as atoms. So you can't measure G without it, or N(G) does not exist below it. Where is this G in the part below the space N measures?
No, I'm pretty sure this is wrong. I'm pretty sure that you can measure inertia of a single neutron, for example.
