Inertia and Relativistic Mass

BenTheMan said:
Right.

First, you did copy the first equation correctly. In Equation (4.4) Carroll defines

$$a = -\nabla \Phi$$

which is ok, but a bit different than I have seen it before, but makes sense, in light of the way forces and potentials are defined in electromagnetism. Perhaps this is the proper way to define gravitational potential, so that the analogy between electrical charges and gravitational "charges" is clear.

Second, your equation $$F = Mg\nabla\Phi$$ is still wrong. The correct Equation, from the lecture notes Eq. (4.2) is $$F = - M_g \nabla\Phi$$, which is the same as the first equation. For future reference, $$M_g \neq M g$$.

to all who are following, note that $$M_g$$ has units of mass, while $$M g$$ has units of force. This is important, because Reiku's next equation

$$\sum_i \gamma M_i c^2 = I_t = M_g$$

is definitely wrong. No matter WHAT $$I_t$$ is, the left hand side has units of energy, and the right hand side has units of mass.
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I think you can continue using it without the minus sign. If not, it's not a remarkable mistake.

And the left hand side must contain units of energy, if assumed $$I_{t}$$ (which is the total inertia) is related by: $$I_{t}=\Delta M_{i}$$ for the total inertial mass. And if the total inertial mass is a measure of how much relativistic mass is contained within the system, $$E= \gamma M_{i}c^{2}$$ says that there is a relativistic mass in inertial matter. It was clear to involve energy on one side if it relates to the total inertia of a system. Of course, the last equation is a small modification of the normal $$E=\gamma Mc^{2}$$, and i have involved it to mean inertial systems as well. If you don't like this, then its pure semantics.
 
Perhaps i should have said ''inertial energy,'' which is the energy contributing to the local system of a mass $$E_{i}$$.
 
If you don't like this, then its pure semantics.
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This is why your work is here.

It is absolutely, positively, NOT semantics. The equations that you've copied shamelessly from other work (without citing it) have been copied with little regard for meaning.

A minus sign is "semantics", SOMEtimes. Writing an equation which sets energy = mass is NOT semantics.*

==================
* I feel obliged to qualify this statement. Mass = Energy if you work in God's Units, where $$\hbar = c= 1$$. Because you have explicit factors of $$c^2$$ floating around, I assume that you're not working in those units.
 
BenTheMan said:
This is why your work is here.

It is absolutely, positively, NOT semantics. The equations that you've copied shamelessly from other work (without citing it) have been copied with little regard for meaning.

A minus sign is "semantics", SOMEtimes. Writing an equation which sets energy = mass is NOT semantics.*

==================
* I feel obliged to qualify this statement. Mass = Energy if you work in God's Units, where $$\hbar = c= 1$$. Because you have explicit factors of $$c^2$$ floating around, I assume that you're not working in those units.
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No, i'm not working in natural units.


Ben, i hardly copied anyones work. The force equation was something i worked from. There is a big difference.

And if you don't like the idea, its certainly semantics at play. In the end, you'd rather admit you wouldn't want me posting in the physics forum, but what's really elementary for you, is to just pick on something, and then use it to cast any work i do into psuedoscience or the cesspool.

The other day, i was wrong to rearrange the operator and the gradient, but it was an innocent mistake, and the rest of the work was fine. It was just acting out of your abuse of power to move it to the cesspool. What for? Two algebraic mix-ups when the rest was completely fine?

Today, you picked on one equation you said ''must be nonesense,'' and now you know it isn't. Now you're picking on something new. Give it a break. I agree with what i have done, and i associate inertia to relativistic mass. Again, if you don't like it, then it is semantics.
 
Today, you picked on one equation you said ''must be nonesense,'' and now you know it isn't. Now you're picking on something new. Give it a break. I agree with what i have done, and i associate inertia to relativistic mass. Again, if you don't like it, then it is semantics.
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So now that we've stopped talking about physics, I will be leaving this conversation.

Two things, and then you can have the last word, as I'm sure you will.

1.) It's not semantics, it's math. There's a difference. The sooner you learn that, the sooner you can start on the path of a legitimate physicist.

2.) I picked on the first equation I found that was wrong because I don't have the desire to read your essay all the way through. I read until I find a mistake, then I point it out. When you show me that it isn't a mistake, or when I figure out that I was wrong, then I'll move on. You pointed out that the definition $$F = M_g \nabla \Phi$$ was legitimate. I agree now. (This means that I was wrong. I can live with that.) The next mistake I found was when you equated energy to mass, in SI units (i.e. not natural units), by your own admission. If you cannot accept the fact that energy is measured in Joules and mass is measured in kilograms, then I don't know how to talk to you. Suppose I asked you how many inches are in a kilogram. Could you answer me? I don't know what any of your equations mean if they aren't dimensionally correct.

I could continue pointing out mistakes with your work, but why bother? For example, how in the hell can you write $$I = M + p$$, which (presumably) says that inertia is equal to mass plus momentum. You just told me that I has units of energy because $$\sum_i \gamma M_i c^2 = I$$. I has units of energy, M has units of mass, and p is a momentum. All three of these quantities have different units.

The next line says $$I = M(v + 1)$$. 1 is a number, and v is a velocity. Again, the units are wrong. If you were working in natural units, you would have written something like $$I = M(\beta + 1)$$ which would have made sense except...oops!...now I has units of momentum?

Reiku---this work is garbage. Every equation that you didn't copy from someone else's work is wrong, and it is wrong in the most basic way that physics equations can be wrong. I learned how to do dimensional analysis in high school chemistry class. Presumably, you've had an introductory chemistry class if you're really a university student, so you've done stoiciometry. I can't believe that the educational system in America is THAT much better than Her Majesty's Educational System. You are making some of the same mistakes that my first year students make the first week of class. I show them how they're wrong, and ask them the same questions that I'm asking you ("How many inches are in a pound?"). Most of them catch on. Some of them don't. The some that don't usually drop the course after they score around 30% on the first exam.

How can you honestly expect me to let something like this be associated with any sort of legitimacy? You can't expect to download some pdf file, copy some equations that you don't understand, and be taken seriously. Do you? If I buy a basketball, does that make me Kobe Bryant? If I buy a guitar, does that make me Jimi Hendrix?

Just a word to the wise---learn how to play before you book a concert in Madison Square Gardens.
 
BenTheMan said:
So now that we've stopped talking about physics, I will be leaving this conversation.

Two things, and then you can have the last word, as I'm sure you will.

1.) It's not semantics, it's math. There's a difference. The sooner you learn that, the sooner you can start on the path of a legitimate physicist.

2.) I picked on the first equation I found that was wrong because I don't have the desire to read your essay all the way through. I read until I find a mistake, then I point it out. When you show me that it isn't a mistake, or when I figure out that I was wrong, then I'll move on. You pointed out that the definition $$F = M_g \nabla \Phi$$ was legitimate. I agree now. (This means that I was wrong. I can live with that.) The next mistake I found was when you equated energy to mass, in SI units (i.e. not natural units), by your own admission. If you cannot accept the fact that energy is measured in Joules and mass is measured in kilograms, then I don't know how to talk to you. Suppose I asked you how many inches are in a kilogram. Could you answer me? I don't know what any of your equations mean if they aren't dimensionally correct.

I could continue pointing out mistakes with your work, but why bother? For example, how in the hell can you write $$I = M + p$$, which (presumably) says that inertia is equal to mass plus momentum. You just told me that I has units of energy because $$\sum_i \gamma M_i c^2 = I$$. I has units of energy, M has units of mass, and p is a momentum. All three of these quantities have different units.

The next line says $$I = M(v + 1)$$. 1 is a number, and v is a velocity. Again, the units are wrong. If you were working in natural units, you would have written something like $$I = M(\beta + 1)$$ which would have made sense except...oops!...now I has units of momentum?

Reiku---this work is garbage. Every equation that you didn't copy from someone else's work is wrong, and it is wrong in the most basic way that physics equations can be wrong. I learned how to do dimensional analysis in high school chemistry class. Presumably, you've had an introductory chemistry class if you're really a university student, so you've done stoiciometry. I can't believe that the educational system in America is THAT much better than Her Majesty's Educational System. You are making some of the same mistakes that my first year students make the first week of class. I show them how they're wrong, and ask them the same questions that I'm asking you ("How many inches are in a pound?"). Most of them catch on. Some of them don't. The some that don't usually drop the course after they score around 30% on the first exam.

How can you honestly expect me to let something like this be associated with any sort of legitimacy? You can't expect to download some pdf file, copy some equations that you don't understand, and be taken seriously. Do you? If I buy a basketball, does that make me Kobe Bryant? If I buy a guitar, does that make me Jimi Hendrix?

Just a word to the wise---learn how to play before you book a concert in Madison Square Gardens.
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That's just not true at all.

Granted its not common, but both mass and energy can be meaured in grams. For instance, it's known that in a standard dice, there contains about 10^84 grams of energy.

Now, the equation I=M+p must also be true, if relativistic mass is the cause of inertia in general. Momentum is related to energy such that $$E=\sqrt{c^{4}p^{2}+M^{2}c^{2}$$, so its equivalant to saying that inertia involves a system with mass and momentum. Your trying to make the equation look nonesense, by saying all the things have different units. That's not true. I've said energy and mass can both be measured in grams. The units of total inertia come under $$I_{t}$$ following the same units as $$M_i$$. But the momentum here is $$p=M_i v$$, for talking about an inertial system.

There's absolutely nothing wrong with it my eyes, and back off with the education. The scottish system is the hardest educational system in Britain, because the work has never changed since initiation, which the English system has.

Now, even more to the point, is that this is my own theory. I've been thinking about it for a while, and i have not accumilated it at random like your trying to make out. I chose each equation with great care and consideration into their properties. But because of the theory, i've had to make some equivalances you don't like, like $$M_g_t=\Delta \gamma M$$, because one side of the equation says total gravitational charge, while the other says a total change in relativistic mass. Just has to work this way, if the measure of inertia is the total change of relativistic mass in a moving system in some time can be deducted.

You simply don't like the equations, because you don't agree with my way of calculating the theory.
 
Let's look more closely at one of your obvious mistakes, Reiku.

Reiku said:
$$I=M+M(v+1)$$

$$I=M(v+1)$$
Click to expand...

Now, these two equations, written one after the other, directly contradict one another.

The first one, simplified, says I = M(v + 2).
The second one says I = M(v + 1)

Let's assume for a moment that both of them are correct.

Then, the two I's are the same, and we can write:

$$M + M(v + 1) = M(v+1)$$

or

$$M + Mv + M = Mv + M$$

from which it follows that

$$2M = M$$

which means either M = 0 (i.e. the mass of every object in the universe is zero), or

$$2 = 1$$

I have therefore "proven" using your analysis, Reiku, that 1 = 2.

Do you believe that 1 = 2?
 
James R said:
Let's look more closely at one of your obvious mistakes, Reiku.



Now, these two equations, written one after the other, directly contradict one another.

The first one, simplified, says I = M(v + 2).
The second one says I = M(v + 1)

Let's assume for a moment that both of them are correct.

Then, the two I's are the same, and we can write:

$$M + M(v + 1) = M(v+1)$$

or

$$M + Mv + M = Mv + M$$

from which it follows that

$$2M = M$$

which means either M = 0 (i.e. the mass of every object in the universe is zero), or

$$2 = 1$$

I have therefore "proven" using your analysis, Reiku, that 1 = 2.

Do you believe that 1 = 2?
Click to expand...

A slight typo on your first equation, James, but it doesn't effect the end result.;)
 
James R said:
Let's look more closely at one of your obvious mistakes, Reiku.



Now, these two equations, written one after the other, directly contradict one another.

The first one, simplified, says I = M(v + 2).
The second one says I = M(v + 1)

Let's assume for a moment that both of them are correct.

Then, the two I's are the same, and we can write:

$$M + M(v + 1) = M(v+1)$$

or

$$M + Mv + M = Mv + M$$

from which it follows that

$$2M = M$$

which means either M = 0 (i.e. the mass of every object in the universe is zero), or

$$2 = 1$$

I have therefore "proven" using your analysis, Reiku, that 1 = 2.

Do you believe that 1 = 2?
Click to expand...


I do apologize. It wasn't meant to be an obvious mistake at all.

They are the same units: for instance, if i wrote $$F_{r}=M+M_{added}v(+1)$$ i just meant that mass was added to the original mass. I should have wrote ''added'', but i did show later how they relate, because i did write $$F_{r}=M+M_{added}v(+1)$$.

But its the same system i was speaking about.
 
kenworth said:
thanks for that.but really the only thing that gets me off is being lied to.

tell me more about your mathematical certainties reiku,im almost there.
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I'm not certain about anything, but i like it. I like to describe inertia as the resistance to a change in energy; and i cannot describe it any other way, than the way i have, taking into account inertia, total inertia and change in mass.
 
I think its just how people are understanding my conclusions.

What does this read for instance?

$$M_i=p+Mc^{2}$$

I'm linking inertia mass to the energy of the mass plus momentum. I know $$Mc^{2}$$, but with $$M_i$$ on the left hand side, would necesserily mean that we are referring to the energy of an inertial system, instead of just the energy. I try to clarify this, by including $$M_i=p+M_i c^{2}$$. So i am talking about the energy of an inertial mass.
 
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