# An idea on explaining the weak equivalence principle

1. Jun 1, 2009

### JK423

An idea crossed my mind on how to explain the weak equivalence principle(WEP) without using the gravitational law: F=G m1m2/r2
Part of what WEP sais is that assuming we are in a uniform gravitational field, if we let two objects of different masses, they will fall with exactly the same speed. The "heavier" will not fall on the ground faster than the the "lighter".
The usual way to prove this is this:
F=G m1m2/r2=m1a1
which means that the acceleration a1 will be independent of the objects mass m1.

My idea now:
1)Lets assume that all matter around us is composed at its very basis by a particle X of a spesific mass mx. But the point is, that all matter will be consituted by the smallest particle possible. Maybe its a particle even smaller than the quark, i dont know what that is, im just assuming.
2)Lets take an object and place it in a uniform gravitational field. Imagine that object to be constituted by a bunch of those particles X.
3)The gravitational field will exert force on every single one of those particles that constitute the object. Since all these have the same mass, they will all move with the same acceleration. As a consequence of that, the whole object will move with that acceleration.

Conclusion:
It doesnt matter how much mass this object has, or to put it differently:
It doesnt matter how many of those particles there are. Since every single one of them will move with a spesific acceleration, then the whole object will move with that acceleration.

I mean, i doesnt matter if that object is iron or cotton. It doesnt matter if the irons atoms are a lot heavier than the cottons. What matters is that, all matter (iron, cotton or even electrons and protons) are constituted by the very same ingredient. By a hypothetical particle with a spesific mass.
Making that assumption we can explain the universality of free fall without using the usual proccess (F=G m1m2/r2=m1a1)

What do you think about that?

2. Jun 1, 2009

### Cantab Morgan

The law of gravitation is not merely a description of something, it's also useful to make predictions. Newton's triumph was that he was able to use his laws to prove Kepler's laws of planetary motion with fewer starting assumptions.

So, you've offered a potentially interesting idea that describes how things under gravity behave, but does the idea lead to any interesting predictions? Unless you can do that, it really won't be a useful alternative or simplification of the law of gravitation.

3. Jun 1, 2009

### atyy

Doesn't highlight the key idea. Suppose you have a bunch of charges, each of which has the same charge but a different mass. Will they all have the same acceleration in an electric field just because they have the same charge?

4. Jun 2, 2009

### JK423

Yes Morgan youre right. Ofcourse that idea is not a theory, and ofcourse cant predict anything with numbers. Its just a good way for me to understand the nature of things. Even thought i dont know if the hypothesis of that particle X is true or not.

atty, i dont get your point. What does your question have to do with what i said? No, they wont move with the same acceleration. I dont talk about charges, i talk about mass and gravitation. Whats the key idea?

5. Jun 2, 2009

### atyy

Exactly! You don't talk about charge (governing force) and mass (governing acceleration due to force). You talk about mass (governing force) and mass (governing acceleration due to force). The key point is that you have assumed that in the case of gravitation, mass governs both things. In principle, gravitation could be due to gravitational charge - but as far as we know, gravitational charge (governing force) is always equal to inertial mass (governing acceleration due to force), so much so that gravitational charge is named gravitational mass.

6. Jun 2, 2009

### D H

Staff Emeritus
The key idea of the equivalence principle is that inertial mass (the m in F=ma) and gravitational mass (the mi in F=Gm1m2/r2) are one and the same thing.

In your original post you said
This is an invalid proof of the weak equivalence principle. First, it assumes Newton's laws are correct. That of course is not true in general. Using a non-general set of laws to prove a general result is not a good idea. There's an even bigger problem, however. Let's assume for the moment that the universe is Newtonian. This is still an invalid proof of the weak equivalence principle. In mathematics, if you assume the desired result to arrive at the desired result you do not have a valid mathematical proof. This "proof" of the weak equivalence principle does just that: it implicitly invokes the weak equivalence principle to prove that the weak equivalence principle is correct. The problem: This proof equates the m1 in Newton's law of gravitation with the m1 in Newton's second law. You cannot do so unless the weak equivalence principle is true.

7. Jun 2, 2009

### JK423

Ok i used the wrong words, we dont "prove" but we "show". We can show that F=G m1m2/r2=m1a1 using the experimental fact (so far) that mgravitational=minertial.
So we can show that an objects acceleration in a homogenous gravitational field is independent of its mass, using either general relativity or gravitational law+newtons 2nd law.
Assuming though that matter is basicly constituted by that particle X, we get the same result without using any law or theory. We just use the fact that all these particles in an object, experiencing the same force will gain the same acceleration (im not using Newtons 2nd law here).

8. Jun 2, 2009

### D H

Staff Emeritus
You are assuming Newton's 2nd and 3rd laws, Newton's law of gravitation, and the equivalence principle to arrive at your result. In your opening post, you said
The first sentence implicitly assumes Newton's second law and some law of gravity. The second sentence assumes the equivalence principle. The third sentence ignores Newton's third law.

9. Jun 2, 2009

### JK423

Ok now i think youre wrong..
Saying that the gravitational field will exert force on a particle doesnt imply Newtons 2nd law. The 2nd law says that this force is proportional to the acceleration. I didnt determine the form of that force, it could be anything! I used the fact though that a gravitational field will exert force on a particle with mass, but that doesnt imply the gravitational law.

Also, saying "Since all these have the same mass, they will all move with the same acceleration." i dont use the equivalence principle but i use the fact that two or more identical particles experiencing the same force will move with the exact same way. I dont say that their acceleration will be independent of their mass as the above principle states. Maybe there is a dependence. However, just because the particles are identical they will behave similarly.

10. Jun 2, 2009

### D H

Staff Emeritus
Sans things like Newton's laws or relativity, do you mean by "uniform gravitational field", "force", "mass", "acceleration", "particle"? You are doing one of these three things:
• Using the standard meanings of these terms, thereby implicitly assuming the standard laws of physics.
• Using your own non-standard meanings for these terms but not telling us. Is force something that turns particles green?
• Philosophizing, and doing so without defining your terms.

11. Jun 2, 2009

### JK423

Youre saying that we cannot use those terms without referring to a specific theory?
Cant we define those terms without using a formula for them? The formula just helps to calculate and make estimations. In quantum mechanics we still use the terms "mass" and "force" for example, but newtons law doesnt hold. That doesnt mean that in QM we redefined those terms....
You got me a little confused :P

12. Jun 2, 2009

### Cantab Morgan

Well those terms (mass, acceleration, etc) are quantitative. How would you measure them otherwise? On what principle would your measuring instrument function?

By the way, Eddington reportedly quipped that the definition of force is the left hand side of Newton's second law. I laughed at that. Until I tried to come up with a better definition, and then I laughed at myself.

Really? For example, what happened to mass in 1905?

Anyway, I appreciate that you're trying to build a mental model of the interesting behavior. But is imagining that all the massive particles are made of identical little particles buying you anything? How is it helpful to assume that protons and electrons and neutrinos are made out of the identical little pellets?

13. Jun 2, 2009

### D H

Staff Emeritus
I don't know what constitutes valid discourse in philosophy, but in physics the only truly valid discourse is mathematics. The laws of physics are written in mathematics. Everything else is just hand-waving. Newton's second law, for example, is not just a formula. It is essentially the definition of the term "force".

What quantum mechanics has done to some extent is to explain why mass arises. It has not done so fully yet; getting a better understanding of mass is one of the driving factors behind the Large Hadron Collider. Our modern understanding of mass completely falsifies one of your assumptions in your original post, "that all matter around us is composed at its very basis by a particle X of a spesific mass mx". This implicitly assumes the mass of a composite particle is mx times the number of the X particles that form the composite particle. A proton comprises two up quarks and one down quark. A proton's mass is about 180 times that of the combined masses of the three quarks that form a proton. The reason the quarks' masses don't add up to anything close to the proton's mass is because mass is bound energy. There is a lot of bound up energy when three quarks combine to form a proton.

This appeal to quantum mechanics is a bit of a false argument. Gravity is the one force that quantum mechanics has not come to grips with at all.

14. Jun 3, 2009

### Phrak

Actually it does matter what the stuff is made of, and this has been experimentally verified.
Freely falling light is not deflected in it's trajectory as proscribed by Newtonian gravity.

15. Jun 3, 2009

### JK423

In my mind, force is defined like: "force is an interaction that affects on a particles kinetic state". Should i care if its F=ma or F=2ma or F=f(a variable that affects its kinetic state)?? I do an experiment to see whats the formula! For example, i act on a particle with some kind of force (gravitational, electric, magnetic) of different magnitudes each time, then take measurements of speed,acceleration, directions etc and see whats the "pattern". Maybe ill find that Force is proportional to velocity, or to velocity^2 or (correct answer) to acceleration.
I hope that you understand what im trying to say.
When i say
"The gravitational field will exert force on every single one of those particles that constitute the object",
you (D H) tell me that i use the 2nd law. Do you know whats the formula of "force" in very small distances to say something like that? Maybe it changes to something else! But that doesnt affects the definition of force as something that changes the kinetic state of a particle. It only affects "the way" the kinetic state changes.
I agree with you that physics is mathematics and not words, but it just doesnt sound right to say F=ma - definition of force.
Maybe to you the whole definition thing is obvious. But right now if i told you "ok f=ma is the definition, youre right" i would be a liar because i dont get it. So, sorry if im being "annoying" perhaps, and thank you very much for your effort to help me understand.

I actually agree with Eddington. He doesnt say that the definition of force is the whole equation F=ma. Only the LHS. The RHS has to do with the way the particle behaves under the influence of that F in the LHS. Maybe it would be F=f(a) as i say above..
It only helps me understand why there is no mass dependency in gravitation. Just that.. Ofcourse im not trying to make a theory here, and cannot predict anything. Actually i can only predict that there is no mass dependency
Its not a necessity to assume that "a composite particle is mx times the number of the X particles that form the composite particle". The (bound energy of the Xs) = (mass) applies here as well. I could try to defend the idea but i wont cause its pointless. Defending questionable assumptions not mathematically expressed is pointless

16. Jun 4, 2009

### atyy

So what's your explanation for why the X particles stick together in small clumps sometimes (like a tennis ball) and in larger clumps other times (like a soccer ball)?

17. Jun 4, 2009

### JK423

atyy i have no theory here...
I just posted an argument trying to explain the equivalence principle.

18. Jun 4, 2009

### Cantab Morgan

Sure. In another universe, Aristotle might have been right, and we'd have F proportional to v or something like that. Or if we lived underwater, but didn't know it, we might come up with an Aristotelian style of Physics that would serve us well.

But think of it this way... Suppose you believed that the universe was predictable. (Let's exclude QM for a moment.) You look at the positions of, say, the planets, and you want to be able to predict their positions for arbitrary time later. Well, how much of the current state of the system do you have to know to make such a prediction?

Perhaps I just need to know the current position. Well, that turns out not to be correct, it doesn't tell me enough about their orbits to predict. So, I also need to know the initial velocities, the derivatives of the positions. Maybe that's not enough either. Perhaps I also have to know the initial accelerations to make my predictions. And maybe even more derivatives after that.

Well, in our universe, it turns out that you only need to know the positions and velocities to predict the future. The accelerations and so forth don't matter. Now, if you take that as an axiom, that might be more palatable to you as a first principle than F=ma. But guess what? You can show mathematically (with very mild assumptions) that your axiom implies that the laws of motion must be a second order differential equation, very much like F=ma.

I guess what I'm arguing is that if you don't like F=ma as a first principle, take instead the idea that a Newtonian universe is predictable given on the initial positions and velocities.

I don't think it's obvious either. Neither did our species apparently, which took millenia of civilization to come up with it. But the choice is not arbitrary either. Suppose you took another definition for, let's not call it force. Call it Spoo. And Spoo equals whatever formula you like. It is possible to come up with a Physics based on Spoo. But the equations using Spoo would be utterly intractable. Look at how beautiful our Coulomb's Law is for example. Expressing it in Spoo would be a nightmare.

I guess what I'm driving at is that the F=ma idea is valuable because of appeals to experiment.

19. Jun 4, 2009

### atyy

Well, some more questions, just in case you think it's fun to answer them. Wouldn't your explanation work if these were also all non-identical particles but with the same mass? In fact, wouldn't it work if they were all non-identical particles with different masses too?

20. Jun 4, 2009

### D H

Staff Emeritus
The equivalence principle is axiomatic, which means it has no explanation. It just is. Einstein did not try to explain this centuries old idea. He instead accepted this concept as given. What we saw was that simple truth has some very profound consequences.