What if gravity worked differently?

[Baggio]

Hi,

I'm stuggeling trying to understand the physics behind this. I just don't know where to start. Everything I read just goes into too much detail. And my lecturer didn't explain it well at all he basically just gave us this http://www.warwick.ac.uk/~phsep/px311/notescosmology/cosmology4-7.doc (page 6) without explaining what was going on.

Can someone help me?

 

[selfAdjoint]

This is a perfect example of something that can have easy or no math and still be confusing because the discussion is all at a higher level than the student casn support. Certainly not your fault.

Let's start with the first section

Newtonian Gravity and its problems


1. The interaction is instantaneously long-ranged – inconsistent with special relativity
2. The gravitational mass for no reason obvious in the theory (although checked to very high precision in expts).

The familiar Newtonian inverse square formula didn't copy, but that was just in there for swank anyway. The important thing is these two statements.

The first one says that Newton's formula has no description of how gravity spreads or propagates from one body to another. It just assumes that it is instantaneously ther even between two stars far away from each other. But this implies that things can cause other things to happen in no time at all over huge distances, and (special) relativity says that's impossible. "Spacelike related" things can interact, and simultaneity isn't defined for far apart bodies. OK? Newton's theory of gravity violates relativity.

The second statement is something that bothered nineteenth century physicists a lot. You have thing called "mass" and its only definition's are
$$F = ma$$
and
$$F = G\frac{m_1m_2}{r^2}$$

And the two formulas HAVE NOTHING TO DO WITH EACH OTHER!

Why are there two independent definitions of mass, and why do the two kinds of experimental measurements yield the same numbers up to high accuracy? It's a puzzlement!

 

[TheAntiRelative]

Why are there two independent definitions of mass, and why do the two kinds of experimental measurements yield the same numbers up to high accuracy? It's a puzzlement!

Could it be because the space displaced is related to the amount of curvature?

 

[dextercioby]

SA,the principle of equivalence is a postulate both in Newtonian gravity & GR.So there's no justified amazement.


Daniel.

 

[selfAdjoint]

SA,the principle of equivalence is a postulate both in Newtonian gravity & GR.So there's no justified amazement.


Daniel.

Daniel, if you folow the document the OP linked to, it is going though the main logical steps in Einstein's journey to GR. When Einstein started down that path, there wasn't any Equivalence Principle. and the amazement was manifested in every nineteenth and early twentieth century physicist who could lift his nose from "the next decimal place". I am going through the document section by section to try and bring its rather perfunctory description to life.

 

[dextercioby]

I don't know how it was called (my CM teacher called "principle of equivalence"),but it was known since Newton that gravitational mass and inertial mass were the same object...If it wasn't known since then,how would the celestial mechanics have been developed...?

Daniel.

 

[Zanket]

Since Newton it was known that the values for either were equal within the margin of error of tests. Einstein postulated that they would be found equal in every test because they are the same thing from different perspectives. That’s a more advanced approach that led to predictions beyond Newton. In Einstein’s view (my words), the Earth’s surface accelerates upward to maintain its position (to be in equilibrium) against inward accelerating space, like the push (acceleration) you feel against your hand when you squeeze a tennis ball.

 

[Zanket]

And my lecturer didn't explain it well at all he basically just gave us this http://www.warwick.ac.uk/~phsep/px311/notescosmology/cosmology4-7.doc (page 6) without explaining what was going on.

Can someone help me?

That doc doesn't look conducive to learning. I suggest you go to a large bookstore or library and look at all the laymen's books on relativity, shifting among them until you understand the key concepts like the equivalence principle.

Or browse the web for better info. Encarta (the Microsoft software encyclopedia) has a great movie clip of the equivalence principle that is worth a chapter.

This site is one of the most succinct I've seen. It covers the basics of the tidal force, the equivalence principle, and gravitational time dilation, all in just a few paragraphs and pictures.

 

[yogi]

Zanket - I don't think Einstein thought of gravity as you have described in post 7

 

[Zanket]

It's an interpretation of the equivalence principle. We feel the Earth's surface accelerating upward. It's accelerating against something it's in equilibrium with, otherwise presumably the Earth would expand or shrink. I don't see anything squeezing the Earth, so I can say it's inward accelerating space. Check out free-fall coordinates here.

 

[pmb_phy]

This is a perfect example of something that can have easy or no math and still be confusing because the discussion is all at a higher level than the student casn support.

I disagree. Taylor and Wheeler did a decent job in their text Exploring Black Holes. I hope to work on making the description easier some day myself.

Please also note that it mass is not really defined as f = ma (this was Mach's and Euler's notion. Not Newton's). Its quite argueable that Newton's mass was defined as f = d(mv)/dt (details can be found in Max Jammers texts).

The first one says that Newton's formula has no description of how gravity spreads or propagates from one body to another.

Sure it has a description. It simply has no explanation. Then again GR doesn't either. It too has only a descripion. GR is accurate and consistent with relativity whereas Newton's isn't.

Why are there two independent definitions of mass, and why do the two kinds of experimental measurements yield the same numbers up to high accuracy? It's a puzzlement!

They do not define the same thing. They define different things. One is gravitational mass while the other is inertial mass. One of the gravitational masses is active (i.e. source) gravitational mass while the other is passive (i.e. that on which gravity acts) gravitational mass. They need not have the same units and as such they don't really have to be referred to as mass. Its simply easy to refer to each as mass. The principle of equivalence states only that the two are proportional.

Pete

 

[yogi]

Zanket - what you are describing is more like in-flow theory - I can't say if IT is right or wrong since it predicts the same results as GR - but my comment was directed to the fact that Einstein didn't think of things that way - GR contemplates a static space modified (condidtioned) by matter. Inflow theory contemplates a dynamic of some sort - usually an aether.

Pete - how could they have different units.

 

[pmb_phy]

Pete - how could they have different units.

Change the units of G and you'd have to change the units of the M's. Adjust the magnitude of G then you can use a proportionality constant to change the equality to a proportionality and still have a valid equivalence principle.

Pete

 

[yogi]

Pete - so you are saying for example "25 clubs" of gravitational mass would be equal to "20 kgm" of inertial mass, but we would then need to change the magnitude of G to G* and the units of G* would be [(M^3)/(sec^2)]/club. So fundamentally, the two entites are different animals - coincidentally equal, but not equivalent in fact.

 

[JesseM]

Pete - so you are saying for example "25 clubs" of gravitational mass would be equal to "20 kgm" of inertial mass, but we would then need to change the magnitude of G to G* and the units of G* would be [(M^3)/(sec^2)]/club. So fundamentally, the two entites are different animals - coincidentally equal, but not equivalent in fact.

If they were proportional, so that any object with x kg of inertial mass will always have 1.25x clubs of gravitational mass, then it would just be a difference of units, inertial mass and gravitational mass would still be equivalent. For them to be independent, you shouldn't be able to use inertial mass to determine gravitational mass at all, just like you can't determine how many coulombs of charge on object has just by knowing its inertial mass.

 

[yogi]

But the fact is - we have two separate experiments that must be satisfied in the sense that each defines a force. I think Pete is saying, its possible that the two different entities are not physically the same thing at some fundamental level.

But isn't that where history started on this issue - with all the many experiments aimed at measuring even the slightest difference between gravitaional and inertial mass

Recall Feynman's musings - that perhaps gravity, like centrifugal force, is in reality a pseudo force that manifests itself because we do not have the right coordinate system. This line of thought points in the direction of absolute equivalence, i.e., that G forces are in reality due to accelerations of cosmological origin

 

[JesseM]

But the fact is - we have two separate experiments that must be satisfied in the sense that each defines a force. I think Pete is saying, its possible that the two different entities are not physically the same thing at some fundamental level.

OK, I just looked back over Pete's posts and it looks like that's what he is arguing. But actually, I'm a little confused about this, thinking about that comment you mentioned by Feynman:

Recall Feynman's musings - that perhaps gravity, like centrifugal force, is in reality a pseudo force that manifests itself because we do not have the right coordinate system.

Doesn't general relativity already say this, so this isn't really a "musing" but just a description of the theory? For any coordinate system where someone is at rest and experiencing a gravitational force, can't you find another coordinate system where this is just a pseudo-force due to acceleration?

 

[Chronos]

Whose reference frame are you speaking about?

My bad, I just saw your post JesseM.

 

[Zanket]

Zanket - what you are describing is more like in-flow theory - I can't say if IT is right or wrong since it predicts the same results as GR - but my comment was directed to the fact that Einstein didn't think of things that way - GR contemplates a static space modified (condidtioned) by matter. Inflow theory contemplates a dynamic of some sort - usually an aether.

OK, good to know. My book Relativity Visualized says, "In a nutshell, Einstein's view of gravity is that things don't fall; the floor comes up!" But that's the only source I have like that.

 

[Chronos]

Gravity is not a force, it is the geometrical relationship between objects. EM fields are superimposed over that background.

 

[Zanket]

The principle of equivalence states only that the two are proportional.

Then what is the big whoop about it, given that this was known in Newton's age? What does the principle offer that was new?

 

[pmb_phy]

Then what is the big whoop about it, given that this was known in Newton's age? What does the principle offer that was new?

What Newton did was to restrain his laws to inertial frames. Einstein came along and said "Hey guys! If I'm in a free-fall frame then, since inertial mass = gravitational mass, all objects at rest with respect to me will remain at rest if they are close enough to me. Therefore the gravitational field has vanished. This implies that the gravitational field is frame dependant." He then took this idea and extended it. If you take his books and papers on GR then you'll notice that he doesn't conclude/derive mass = gravitational mass, he starts with this as an axiom, just as Newton does.

As I recall (with my poor memory) Sir Aurthur Eddington mentioned something to this effect. I can search for the article but it'll take a long time to find. Perhaps days.

Pete

 

[pmb_phy]

Gravity is not a force, it is the geometrical relationship between objects. EM fields are superimposed over that background.

I disagree. It was Einstein's GR which changed Newton's mechanics on this point.

In Newtonian mechanics inertial forces (i.e. the dp/dt which arises from observering nature in a non-inertial frame) were considered to be "fake" in some sense of the term (pseudo-force etc.). However since Einstein believed that the gravitational force was a "real" force and the gravitational force, according to GR, is an inertial force then what used to be referred to as "pseudo"/"fake" forces is now to be considered as "real."

Pete

 

[pmb_phy]

If they were proportional, so that any object with x kg of inertial mass will always have 1.25x clubs of gravitational mass, then it would just be a difference of units, inertial mass and gravitational mass would still be equivalent. For them to be independent, you shouldn't be able to use inertial mass to determine gravitational mass at all, just like you can't determine how many coulombs of charge on object has just by knowing its inertial mass.

What really ticks me off is that I made an entire web page on this since it came up often. Now I can't find it.

I'm sorry to say that I'm not feeling all that well today so I'm out of gas. Otherwise I'd take a shot at Latex. Think of it like this

F = GMm/r^2 = (G/qQ)(Mq)(mq)/r^2 = G' M'm'/r^2

Choose q and Q as you like. They don't have to have units of mass and they don't have to be equal.

Pete

 

[Zanket]

What Newton did was to restrain his laws to inertial frames. Einstein came along and said "Hey guys! If I'm in a free-fall frame then, since inertial mass = gravitational mass, all objects at rest with respect to me will remain at rest if they are close enough to me. Therefore the gravitational field has vanished.

Is it true to say, then, that the equivalence principle as told by Einstein was not new info (that is, it was just the “inertial mass = gravitational mass” part that was already noted), but rather was just leveraged to make new predictions re gravity?

If yes, then I don't understand what Einstein was getting at here when he said:

We then have the following law: The gravitational mass of a body is equal to its inertial mass.

It is true that this important law had hitherto been recorded in mechanics, but it had not been interpreted. A satisfactory interpretation can be obtained only if we recognise the following fact: The same quality of a body manifests itself according to circumstances as "inertia" or as "weight" (lit. "heaviness").

What does the last sentence mean if the equivalence principle is nothing more than “inertial mass = gravitational mass”? I have interpreted the last sentence to mean that inertial mass and gravitational mass are the same things from a different perspective, and not different things that just happen to be equal.

 

[yogi]

Zanket - yes - I know Epstein has a few paragraphs titled the floor comes up claiming Einstein sanctioned this notion - but he also says don't take it too literally - its a tutorial aid - from the perspective of an observer experiencing gravity on the Earth's surface - it would be the same if the floor came up - but it can't come up everywhere unless the Earth is expanding at an accelerating rate - there is such a theory of gravity - but it doesn't take a lot of thought to see why its not possible - it belongs in the same category as the angel theory (invisible angels everywhere holding things on the Earth to keep them from floating off into space) - actually put forth as a serious idea by one of the creationists) Chronos gives you the conventional definition according to GR.

 

[yogi]

There are two approaches to gravity and inertia - one is to take the position that inertial mass and gravitational mass are equal but they are fundamentally different things that are displayed by the experiments. Taking this view, the search for reality should be in a direction which will distinguish them on a fundamental level. The other apporach is that gravity and inertial are simply different sides of the same coin - what we measure as inertia is the acceleration of mass relative to space - and what we measure as gravity is the acceleration of space acting upon an inertial mass.

 

[Zanket]

Zanket - yes - I know Epstein has a few paragraphs titled the floor comes up claiming Einstein sanctioned this notion - but he also says don't take it too literally - its a tutorial aid - from the perspective of an observer experiencing gravity on the Earth's surface - it would be the same if the floor came up - but it can't come up everywhere unless the Earth is expanding at an accelerating rate ...

Yeah, I didn't take it literally since that obviously doesn't compute. When I learned about free-fall coordinates (accelerating inward space interpretation of GR) and about how what we feel pushing upward is the electromagnetic force (not gravity), and with some insight from JamesR, it made sense to me that Epstein had not given the full picture, and that the full picture is that the Earth is not expanding because the electromagnetic force that pushes outward is in equilibrium with the accelerating inward space of gravity.

 

[yogi]

Anyone know how Galileo explained the fact that a large heavy rock fell at the same rate as a small light rock?

 

[ohwilleke]

IIRC, and this is going back to the main discussion of the thread, the reason GR was necessary is because SR in Minkowski space has inconsistencies that violate the equivalence principal.

 

[Zanket]

Anyone know how Galileo explained the fact that a large heavy rock fell at the same rate as a small light rock?

That's in Epstein's book. The large heavy rock comprises pieces each the size of the small light rock, so all must fall at the same rate.

 

[JesseM]

That's in Epstein's book. The large heavy rock comprises pieces each the size of the small light rock, so all must fall at the same rate.

Would this argument give the wrong conclusion when thinking about objects falling through a liquid though? Since the buoyancy force is not proportional to the mass of the object but only to the volume, wouldn't two balls of the same shape and volume but different masses fall through a liquid at different rates?

 

[yogi]

But Jesse - the insight that is revealed is that in a vacuum, Galileo found a very simply explanation that didn't involve the mathematics of combining G with F = ma
I think there is a big lesson to be learned by his logic - its actually quite profound - and it escaped the greatest minds of science since Aristotle who pronounced with certainty that the heavier object would fall faster - and everyone bought into it for nearly 2000 years.

 

[JesseM]

But Jesse - the insight that is revealed is that in a vacuum, Galileo found a very simply explanation that didn't involve the mathematics of combining G with F = ma

But the point is that in Galileo's time no one knew how gravity worked in a vacuum, or even whether space was a true "vacuum" at all. It's logically possible that more massive objects could fall faster than less massive ones, as demonstrated by the fact that they do just that in a fluid, so his thought-experiment, which purports to show that it isn't possible, must be flawed.

 

[Zanket]

Would this argument give the wrong conclusion when thinking about objects falling through a liquid though?

It seems it would. I don't know how Galileo reconciled his argument with that.