The Fundamental Origin Of Inertia

[Aethelwulf]

The Cause of Inertia

 

Abstract

 

In this work, I will investigate the possibility of a new definition for inertia and with it, explain what it really is all about.

 

Mass is Inertia

 

Mass may have a two sided-personality. It may be fundamental in two different ways. The first way we have all come to know from

reading popular magazine articles; the Higgs Field. Fundamentally-speaking, Higgs Bosons permeate the universe and give

massless particles mass through spontaneous symmetry breaking. This property of mass carries another load, the definition of

inertia, which while has a distinct definition different to mass in general, all experiments today have shown them to be the

same thing.

 

Mass was obtained in this fundamental field description, but with it the luggage of inertia itself. Is this the origin of inertia?

For many it is, since it is after all the story which describes the origin of mass. BUt that is only partially true. The Higgs

Boson doesn't give mass to plenty particles in nature, especially from dark matter. In the Heirarchy Model, it is these particles

which are extremely heavy and did not need to obtain their mass from the Higgs Field. But surely particles of Dark Matter

also have inertia?

 

Of course they do, so the Higgs Field, while perhaps the fundamental reason for providing a low percentage of mass in the universe

is attributed to the Higgs Field, it does not explain the origin of inertia. The reason must be even more fundamental,

if there is even such a thing. The investigation into inertia has a long history and still today there is no consensus which

can account for inertia. The law of inertia started with Newton, expanded by Mach and elaborated on by Einstein, all of them

contributed to the possible explanation behind what inertia is.

 

 

Machian Inertia says that inertia comes about from the interaction of all the bodies of mass in the universe.

 

 

What we found in classical theory was that all bodies of mass effect all other bodies in the universe according to the Newtonian

school of thought. We now know that gravity is the presence of curvature in the universe and the universe according to our

most current observations tell us that the universe is mostly flat. This remains a problem in cosmological physics.

 

Arguments for the treatment of taking into account all the bodies of the system, like in the Machian Principle states, accounts

for the inertia of bodies, still has a lot of theoretical evidence to back it up. General Relativity makes use of this noticing

the metric tensor was determined by the distribution of all matter.

 

Even Einstein said himself

 

''...inertia originates in a kind of interaction between bodies...''

 

Or does it?

 

We are going to challenge this idea by investigating the fundamental reason for inertia itself. The answer is surprisingly easy

which makes a fresh change to more exotic theories like those proposed by Sciarma. Einstein came closest to the answer arrived

to in this work; Einstein realized that inertia had something to do with energy content of the system. This relation is almost

forgotten when Einstein goes on to create his General Theory of Relativity, and motion began to be described by geodesics.

 

In it's most simplest form, inertia is

 

...''the resistance for a body to change velocity or a state of rest.''

 

Newton found the relationship in this intuitive form

 

[math]F = Ma[/math]

 

Where the mass is strictly the inertial mass. The weak equivalence principle states that mass and inertia are the same thing,

at least, all measurements to determine this fact have found inertial mass to be equal to the gravitational mass. It seems that

both are the same thing. The equivalence of inertial mass and gravitational mass can be given as

 

[math]F = M_g g = M_i a[/math]

 

The definition of two masses with acceleration

 

[math]F_{XY} = M_Xa_X[/math]

 

and

 

[math]F_{YX} = M_Ya_Y[/math]

 

such that

 

[math]F_{XY} = -F_{YX}[/math]

 

and

 

[math]\frac{M_X}{M_Y} = -\frac{a_Y}{a_X}[/math]

 

plugging this into our equivalence we get

 

[math]\frac{M_g}{M_i} = \frac{a_i}{a_g}[/math]

 

This is a well-known statement.

 

So, for instance, inertia would increase with an increase of mass if they are truly the same thing. Since energy depends on velocity,

we arrive at the question, ''If energy depends on velocity and a change in velocity would mean a change of energy, then

is inertia caused by the resistance to a change in energy?''

 

Which is more fundamental, velocity or energy? Energy might be seen as more fundamental, so it seems to be quite important then to ask whether inertia is

not resisting the change of velocity but resisting a change in energy as well. Just to note, momentum also is related to the

inertia

 

[math]p = mv[/math]

 

These equations are quite standard but it gives you some idea. Inertia has some other definitions, the first one here is the

inertial mass found in the classical Euler-Lagrange equation

 

[math]\frac{d}{dt} (\frac{\partial \mathcal{L}}{\partial \dot{x}_i}) = M(\ddot{x})[/math]

 

We're not going to do anything with this equation, but it is always nice to note.

 

Now, keeping in mind that energy depends on velocity, we have the relativistic relationship

 

[math]K = (\gamma - 1)Mc^2 = (\frac{1}{\sqrt{1 - \frac{v^2}{c^2}}} - 1)Mc^2[/math]

 

Mass will change proportional to the energy [math]E \propto M_{inert}[/math] and inertia is believed to be experienced when there

is a change of energy - the system simply would rather sit in it's lazy state.

 

A New Law

 

''It takes energy to slow down a system.''

 

This statement is strange because in physics we are not taught that it takes energy to slow down a quantum system. A quantum

system is subject to inertial effects as well, so our new law is becoming apparent: That is, that inertia is not just about

the resistance to change velocity, but as noted before, the resistance to change energy fundamentally. For this to be true, a system

at a constant velocity, it must cost energy to slow it down. Because of this, a system continues to move in a straight line and with

a constant velocity unless acted upon by some external force. I created a scattering formula for this.

 

We start off with this formula which was derived [1]

 

[math]\int (x(t_2) - v(t_1)) M\ dv = dE(v)[/math]

 

[math](v(t_2) - v(t_1)) M = \frac{dE(v)}{dv} = p[/math]

 

Using the dot product, the squared part of the formula arises as

 

[math]p^{2}_{e'} = p_{e'} \cdot p_{e'} = (p_{\gamma} - p_{\gamma'}) \cdot (p_{\gamma} - p_{\gamma'})[/math]

 

[math] = p^{2}_{\gamma} + p^{2}_{\gamma'} - 2p_{\gamma} p_{\gamma '}\ cos \theta[/math]

 

[math](v(t_1) - v(t_2))^2 M^2 = p^{2}_{\gamma} + p^{2}_{\gamma'} - 2p_{\gamma} p_{\gamma '}\ cos \theta[/math]

 

Is the final formula that I derived to describe scattering. Notice that the mass term can be equated directly with inertial effects.

 

So inertia turns out, that it requires energy to slow down and speed up a particle; this is the kinetic analogue of the classical

definition of inertia for velocity; the difference lies in counting the changes in energy. This is merely another case of

momentum being related to inertial effects through scattering events.

 

This in a sense defines inertia as well, because we have a given initial state. That state was changed when an external force was

applied through the scattering process.

 

Conclusions

 

I am very confident that what causes inertia is an innate property of all matter because of their energy content as

Einstein himself concluded. However, inertia arises, not as a resistance to a change in motion or rest, but has fundamentally

got to do with a resistance to change the energy of a system. As we have seen, to implement this idea, we require that there

be a fundamental condition in which it not only costs energy to speed up a particle but it also costs energy to slow it down.

 

In this theory, no one needs to use the Machian Principle to explain inertia - and any way, there have been inconsistencies

with the Machian Principle in the idea that all matter interacts with all matter gravitationally, and yet communication between

masses through curvature over very large distances seems troublesome in a universe which appears mostly flat in every direction.

 

Any relativistic simple set of equations describing an energy increase through a binomial expansion can sufficiently describe

inertia as the resistance to changes in energy; the great thing about this theory is that it does not change quantum mechanics in

any kind of way - in fact it is argued that this definition of inertia should in fact out-date the Newtonian definition.

 

In all respects, this definition of inertia:

 

1) Keeps inertia as it should be: An inert property of all matter.

 

2) Uses energy to define inertia, in a manner similar but not identical to Einstein's approach.

 

3) Explains inertia in a fundamental mechanical way.

 

The absence of inertia would be strictly speaking, an absence of mass within the system - to change the inertia you need to be

able to change (or lower the mass of a system) - this is also called inertia negation.

 

There is only one example of causing a particle with mass to behave as though it has no mass - the wikipedia article says differently

that there have been no cases known http://en.wikipedia.org/wiki/Inertia_negation , but there is. An electron in a superconductor

will behave as though it has no mass... photons also inside superconductors behave as though they have gained inertia (rest mass).

 

Apart from these special cases, there are no known other processes which can make an electron behave as if it has less mass than what it

actually has. Things like inertia dampers, does not seem to be part of science fact. Inertia dampers however could be science

fact if gravity is mediated by a particle commonly known as the Graviton. If one could build something which could shield the effects

of gravitons which would be responsible for the curvature of spacetime, then you could actually shield all curvature around

your system and may act like an inertial dampener. But, if gravity does not have a physical mediator (which seems very possible), then it is likely we will never

create one.

 

In my opinion, my theory is the simplest theory of inertia that could possibly be understood.

 

 

Notes

 

[1]

 

[math]a(t) = \frac{dv}{dt}[/math]

 

I integrated this

 

[math]\int_{t_0}^{t_1} a(t) dt = dv[/math]

 

I then multiplied [math]dp = F\ dt[/math] on both sides to obtain

 

[math]\int_{t_0}^{t_1} a(t) dt Ft = Ft \ dv = dE(v)[/math]

 

And noticed that one can rewrite this

 

[math]d \dot{E}(v) = \int_{t_0}^{t_1} a(t) F dt[/math]

 

Which is your power. Using the fundamental theorem of calculus, this is the same as saying

 

[math](v(t_2) - v(t_1))F = P[/math]

 

That is, the difference in the initial velocity and final velocity when a given force is present.

 

[2] http://www.padrak.com/ine/INERTIA.html by Paul Davis

 

[3] On the Origin of Inertia, Sciama, http://articles.adsabs.harvard.edu/cgi-bin/nph-iarticle_query?1953MNRAS.113...34S&data_type=PDF_HIGH&whole_paper=YES&type=PRINTER&filetype=.pdf

 

Sciama's theory requires that there be relationships between the analogy of electromagnetism and gravity. It also allows for a varying gravitational constant - which is at odds with General Relativity.

 

[4] http://arxiv.org/pdf/physics/0609026v4.pdf

Edited January 21, 2013 by Aethelwulf

[Aethelwulf]

Since I wrote this, I don't really think it is good to think of fundamental systems costing energy to slow down, even though this might be true. I originally devised that theory to explain inertia in terms of the least action of the system, that nature tries to find the most efficient way to assemble itself. If a particle costs energy to slow down, it could be argued it might rather not slow down, nor speed up since acceleration costs energy as well. Perhaps to simplify all of that, it is best to just keep inertia simply defined as resisting a change in energy without introducing new concepts like costing energy to slow down.

[phillip1882]

greetings Aethelwulf:

i still wonder at a fundamental question. if systems resist change in energy, and i tend to agree they do; then how do atoms endlessly accelerate toward one another? wouldn't this be a change in energy?

[Aethelwulf]

greetings Aethelwulf:

i still wonder at a fundamental question. if systems resist change in energy, and i tend to agree they do; then how do atoms endlessly accelerate toward one another? wouldn't this be a change in energy?

 

Hello.

 

Atoms may accelerate towards each other for different reasons...

 

One example might be an electromagnetic interaction. Such a case, we might expect a negatively charged atom accelerating towards a positively charged atom. The atom accelerates towards each other because of something similar as you might expect using the Coulomb Force. Notice, inertia is the tendency to remain in rest or in constant motion unless acted on by some external force. So yes, the force effects the atoms and there is a change of energy [math]\Delta E[/math] in the system.

Edited January 20, 2013 by Aethelwulf

[phillip1882]

hmm. an interesting idea. missing electrons would defiantly cause an attraction, but I'm more referring to something that has no charge, or at least not one that explains the way atoms interact. say a baseball thrown upward.

[Pmb]

One of the reasons this forum has not taken off well is that its so damn slow. Another is that the name of it is strange. What is Hypography anyway and who'd know what it was without a dictionary?

 

Then when you have topics like this, i.e. the Higgs mechanism - you reall cut your audience down even more drastically. I've been waiting for this forum to pick up but I can'gt see that happening at this point. It's a shame too. The other forums are fill with the same old arrogant bastards. One very irritating moderator in a new forum whined about a mere note I put in in the special relativity section to note that the speed of light isn't constant in non-acclerating frames. I only put that in because most relativistis view accelerating frames in flat spacetime to be part of special reltivity. Another poster was upset because he couldn't follow what I was saying and cursed me out of mussing up what he thought was a prestine SR sticky when in fact he needed some adjustments. One thing wrong with it was that the author of the sticky thought that inertial frames are defined as being non-accelerating. That's well known to be a bad definition (accelerating with respect to what, and so on) when in fact an inertial frame is universally defined as a frame in which the law of inertia (I.e. Newton's first law F = dp/dt = ma) holds true. So the moderator accused me of causing problems and warned me. Adios loser!

 

Sorry but I had to rant and this ended up being the place where I did it.

[phillip1882]

pmb, this to me is a place to learn and grow. if you have all the answers you probably shouldn't be here.

[Eclogite]

The other forums are fill with the same old arrogant bastards. One very irritating moderator in a new forum whined about a mere note I put in in ..........

But pmb, those same old arrogant bastards, of which I am one, find it impossible to get away from you, no matter which forum we moderate. :)

[Rade]

...I am very confident that what causes inertia is an innate property of all matter because of their energy content as Einstein himself concluded. However, inertia arises, not as a resistance to a change in motion or rest, but has fundamentally got to do with a resistance to change the energy of a system. As we have seen, to implement this idea, we require that there

be a fundamental condition in which it not only costs energy to speed up a particle but it also costs energy to slow it down.

Is it possible that this fundamental condition is related to interaction of fundamental entities that have asymmetric masses, one matter (let it have 3 mass units of energy) the other antimatter (let it have 2 mass units of energy). Symbolically let ^ = antimatter thus the fundamental interaction is {MMM} <-> {M^M^}, and we allow that this interaction is a quantum superposition between gravity for {MMM} entity and antigravity for {M^M^}. Thus the <-> interaction represents a gravity-antigravity source of motion that results in a resistance to change in the total energy of the system of 5 mass units, that is, it costs energy for gravity to speed up the interaction, while simultaneously it costs a bit less energy for antigravity slow down the interaction, with the net result that we observe a single {M} unit speeding forward though time and space (the missing 4 mass units present, but assigned to a virtual reality similar to the Dirac sea, thus outside direct human observation...but available for CERN type experiments). Well, perhaps a crazy idea, but I think your search for this fundamental condition may require crazy idea to explain it. Edited February 10, 2013 by Rade

[Aethelwulf]

Is it possible that this fundamental condition is related to interaction of fundamental entities that have asymmetric masses, one matter (let it have 3 mass units of energy) the other antimatter (let it have 2 mass units of energy). Symbolically let ^ = antimatter thus the fundamental interaction is {MMM} <-> {M^M^}, and we allow that this interaction is a quantum superposition between gravity for {MMM} entity and antigravity for {M^M^}. Thus the <-> interaction represents a gravity-antigravity source of motion that results in a resistance to change in the total energy of the system of 5 mass units, that is, it costs energy for gravity to speed up the interaction, while simultaneously it costs a bit less energy for antigravity slow down the interaction, with the net result that we observe a single {M} unit speeding forward though time and space (the missing 4 mass units present, but assigned to a virtual reality similar to the Dirac sea, thus outside direct human observation...but available for CERN type experiments). Well, perhaps a crazy idea, but I think your search for this fundamental condition may require crazy idea to explain it.

 

Finding it a bit hard to follow... but I did have one example in mind concerning costing energy to slow down. As I said before, we are often told that it costs energy to speed up a fundamental object, but we hardly (if ever) think it costs energy to slow down. But I will give you an example to consider, Bremsstrahlung radiation is given up to slow particles down - well more accurate to say, it slows down because it has given up energy. This is why it is often called ''deceleration radiation.''