Gravitational Mass = Inertial Mass?

[Kygron]

Ok, I just thought of this this morning and I've got to try out the idea on some people. Here's WHY the masses are equal:

 

The Setup (skip it if you know alot of physics):

 

Sorry, my mind works with analogies, I'll use standard ones, first, we have the sheet of rubber that has balls of different masses placed in it. The masses bend the rubber (warp the fabric of space-time) and display gravitational effects. It's a bad analogy because it relies on your knowledge of "real" gravity to power the motion, but hold that thought for a minute and I'll remove "real" gravity before I finish up.

 

Next, we extent that sheet of rubber until it models the whole universe as a balloon. This is the analogy that answers the question of "where's the center of the universe? There is none!" However, to continue to have that "real" gravity to power the model, we must have a massive object at the center of the balloon. Still with me?

 

Now we move to Einstein's elevator where he bends light but doesn't know if he's on a planet or accelerating through space. We learn that gravitational force can be replaced by acceleration.

 

Back to the model balloon, I get to fulfill my promise to remove the mass at the center. We exchange it for an acceleration, by inflating the balloon at an ever-increasing pace. The inertial masses on the surface resist the acceleration, causing dimples in the balloon, which produce a gravitational affect on the other masses. And wouldn't you know it... We live in a universe experiencing accelerated expansion!!!

 

The Conclusion:

 

The universe around us is expanding at an accelerating rate. The inertial masses resist this acceleration, warping space-time to produce gravity as they do. Gravitational strength is therefore produced by inertial mass and universal expansion.

 

I'm using this model to explain other phenomena to myself (like dark matter), but I'll start simple and ask for your feedback. I certainly surprised myself this morning saying "but that would require the universe to be accelerating... wait, it IS!"

[Obelix]

This seems a very interesting idea and worths formulating mathematically!

 

Yet I can readily think of one objection: Einstein started from Mach's assumption that the inertia of any specific mass is a result of the total gravitational interraction of ALL the masses in the universe with that mass. Hence, it is INERTIA that results from GRAVITATION. You, on the other hand say that it is the other way round. Maybe the idea is the same in the overall.

[5614]

Inertial and gravitational mass are the same thing, this is the Equivalence principle.

 

Kygron: you're setup seems interesting, but I have a few comments about it (these are just initial thoughts):

 

Firstly do you have to turn the rubber in to a balloon shape? Can't you just keep it flat? Either way you still need a gravitiational source pulling the balls down, although this is one of the flaws in the analogy. You're trying to fix a flawed analogy, why not just accept it is wrong?

 

[edit] after trying to argue that you don't need a mass in the centre I've convinced myself you do need a mass in the centre, at least if it's not expanding.

 

As for then claiming your balloon must expand, if it were expanding forever then in the end it will accelerate until points on the surface are moving at the speed of light with respect to each other, then what? The balls on the surface would be moving away from each other at >c.

[Kygron]

This seems a very interesting idea and worths formulating mathematically!

 

If anyone can, please do! I don't have the mathematical physics background for it.

 

Yet I can readily think of one objection: Einstein started from Mach's assumption that the inertia of any specific mass is a result of the total gravitational interraction of ALL the masses in the universe with that mass. Hence, it is INERTIA that results from GRAVITATION. You, on the other hand say that it is the other way round. Maybe the idea is the same in the overall.

 

I don't doubt that it is, or at least similar, I only wish to suggest an alternate viewpoint that has actual repercussions for current models.

 

Inertial and gravitational mass are the same thing, this is the Equivalence principle.

 

In that case I guess I should have picked a better title, oh well.

 

Firstly do you have to turn the rubber in to a balloon shape? Can't you just keep it flat? Either way you still need a gravitiational source pulling the balls down, although this is one of the flaws in the analogy. You're trying to fix a flawed analogy, why not just accept it is wrong?

 

No, it can be flat or anything else, the analogy is for illustration of concept.

 

As for then claiming your balloon must expand, if it were expanding forever then in the end it will accelerate until points on the surface are moving at the speed of light with respect to each other, then what? The balls on the surface would be moving away from each other at >c.

 

But isn't this the same problem we face with the current model?

 

Sorry for the bad start, the main idea I was trying to convey is: An accelerating universe is the cause of Gravity and other "unexplained" phenomena.

 

I'd love to see the effect this has on models of universal development, as I'm suggesting that G varies in space and time. (edit: but can still be calculated from non-gravitational data)

 

Thanks for the thoughts, please continue!

[5614]

But isn't this the same problem we face with the current model?

 

Sorry for the bad start, the main idea I was trying to convey is: An accelerating universe is the cause of Gravity and other "unexplained" phenomena.

 

I'd love to see the effect this has on models of universal development, as I'm suggesting that G varies in space and time. (edit: but can still be calculated from non-gravitational data)

Aye, my bad, my "then what" question I posed I should never have said, because there is no "then what". Having points moving away from each other at a relative speed >c is allowed, as no information is transferred. The only "then what" is that then these systems will never be able to communicate again.

 

As for taking the rubber sheet analogy, setting the rubber sheet to accelerate (expand if it is a balloon shape), and then claim that this is the cause of gravity (the objects on the surface would cause a dent due to their inertia), and then relay that analogy back to the real world... hmm, it's interesting. I can't (at the moment!) see any major flaw...

 

As we can't tell the difference between being in a gravitational field and being in an accelerating frame, then doesn't that mean that your model is mathematically identical to any gravitational field model? If so then it would make it a good analogy, but would it be possible to tell which is correct? Might we end up at relativity's "both views are equally correct"?

[Kygron]

As we can't tell the difference between being in a gravitational field and being in an accelerating frame, then doesn't that mean that your model is mathematically identical to any gravitational field model? If so then it would make it a good analogy, but would it be possible to tell which is correct? Might we end up at relativity's "both views are equally correct"?

 

It is my hope, in fact, that a simple transform can convert the current models to this new one, it would save alot of work (or not transform them, but incorporate this)

 

The difference is that I'm linking the gravitational force to the expansion rate of the real universe, the new model just demonstrates how to do the linking.

 

I've heard people suggest that certain universal constants may have been different in the early universe. However, how do you decide what they might have been? Were they greater, lesser? Can you even measure them? I'm giving a way that you CAN measure one of them, the gravitational constant, because you can measure the expansion rate of the universe.

 

Unfortunately, I don't know how to do the mathematics personally, but I have attempted to set this up so that they CAN be done and a definite "this works" or "this doesn't work" is achieved. (Some bad luck would get me: "this interferes with the calculation of the expansion rate.", or "we'd have to completely reprogram the computers to accept a variable G")

 

I'm hoping someone will be able to suggest some problems I'm running into, or suggest someone to present this idea to who would be interested in doing some of the mathematics. If only I had some grad students at my beck and call....

[5614]

This is an interesting thread. Here's another thought:

 

Am I correct in saying that the acceleration of the universe is accelerating? (I think this is true, but I'm unsure)

 

As in: [math]\tfrac{da}{dt} \neq 0[/math], where a = acceleration of the universe.

 

If so that would imply, by your model, a varying gravitational field strength, which has not been observed. This could be explained if the value of da/dt is very small, maybe over the last few hundred years the change has been too small for us to observe.

 

There must be numerical data about the acceleration of the universe, and how much that acceleration is varying by, if it even is.

[Klaynos]

This is an interesting thread. Here's another thought:

 

Am I correct in saying that the acceleration of the universe is accelerating? (I think this is true, but I'm unsure)

 

As in: [math]\tfrac{da}{dt} \neq 0[/math], where a = acceleration of the universe.

 

If so that would imply, by your model, a varying gravitational field strength, which has not been observed. This could be explained if the value of da/dt is very small, maybe over the last few hundred years the change has been too small for us to observe.

 

There must be numerical data about the acceleration of the universe, and how much that acceleration is varying by, if it even is.

 

This is exactly what I was wondering when I first read the thread, but I tbh don't know whether is is non-zero or not :|

[Kygron]

I searched a bit for info on the expansion rate. Best I've found was this paper that suggests in its introduction that the universe has had phases of deceleration.

 

For my model this would mean that there have been times when the gravitational field strength becomes 0 (not negative, it's the absolute value of the acceleration rate). This would be easily visible in starlight so it kinda messes things up for me.

 

Anyone know anything about possible deceleration? Or if there's been times of widespread supernova activity? Or if I'm lucky the rate at which gravity returns (second derivative of acceleration?) is gradual enough to let things continue just where they left off.

[JohnFromAus]

All this seems to relate to the so called "cosmological constant" in one of Einstein's equations which can be +ve 0 or -ve corresponding to an expanding - flat - or eventually collapsing on itself universe. There have been and probably still are projects going on trying to find the constants value - best a can remember is "close to 0" so could go either way.

Also how does the "red shift" of distant objects fit into this? ie The further away an object is the more it is "red shifted" - ie the faster it is receding.

 

Perhaps Im off the point here.

John

[Klaynos]

Well from memory there was very fast expansion for a short time after the big bang which then decelerated... But this is on the cusp of my memory so I wouldn't like to take it as gospel...

 

*goes to research*

 

*returns from research*

 

http://en.wikipedia.org/wiki/Cosmic_inflation

 

Short fast expansion

[Kygron]

Ugh! That was the first Wiki article I've seen where the dates are either pre-90's or the text is still in a "raw data" form: where ever it wasn't useless it was meaningless.

 

No offense to you of course, that just means I've hit the boundary of current research/personal ability. A good thing for my ego and a bad thing for my attempted contribution to science.

[Klaynos]

Well to sum it up, shortly after the big bang there was a very very fast expansion called inflation, which then slowed down...

[Kygron]

Well to sum it up, shortly after the big bang there was a very very fast expansion called inflation, which then slowed down...

 

Yes, yes, but I had assumed the acceleration decreased until it reached the current value, and now that paper I mentioned suggested that it decelerated for awhile and then re-accelerated to the current state. This latter explanation would not be so good for the model I presented in this thread.

 

This discussion has mentioned first through fourth derivatives of the size of the universe (WRT time), and I believe we've all (including myself) been confused at which one we're talking about at any place in the discussion. I'll try to be more clear in the future.

 

Hmm.... My model suggests that gravitational field strength was much greater during the inflationary period, but I seem to recall that inflation was suggested as a means of overcoming the gravity of the early universe. Looks like I may have to read the pre-90's section of that article after all.