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### Author Topic: How are inertia and gravity related?  (Read 7060 times)

#### Pr. snoerkel

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##### How are inertia and gravity related?
« on: 01/07/2013 21:27:20 »
Inertia and gravity seem to be two quite different phenomena. However, as shown by somebody careless dropping lead balls off a badly built tower in Pisa, inertia and gravity are proportional.
So, somehow they must be related. Relativity has it that they both deform space-time, but that does not explain much. Does anybody have an idea?
« Last Edit: 04/07/2013 22:49:59 by chris »

#### Pmb

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##### Re: Inertia and gravity
« Reply #1 on: 02/07/2013 23:04:51 »
Inertia and gravity seem to be two quite different phenomena. However, as shown by somebody careless dropping lead balls off a badly built tower in Pisa, inertia and gravity are proportional.
So, somehow they must be related. Relativity has it that they both deform space-time, but that does not explain much. Does anybody have an idea?

Actually general relativity does explain this. It equates the gravitational field to an accelerating frame of referance. Spacetime curvature is merely geometric talk for tidal acceleration. But "deformed spacetime" is not what gravity is about. It's about equating gravity with non-inertial frames.

#### Pr. snoerkel

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##### Re: Inertia and gravity
« Reply #2 on: 03/07/2013 16:33:33 »
Maybe I phrased the question incorrectly- It is obvious that a mathematical correlation exists. indicating that there is a physical relation as well. But accelleration and gravity seems only related in the sense that gravity causes accelleration

#### Pmb

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##### Re: Inertia and gravity
« Reply #3 on: 03/07/2013 19:02:09 »
It's more than that. If you were in a frame of reference in which a charge was at rest but accerating from an electric field then you wouldn't be in an inertial frame. The same can't be said about gravity. Consider what Albert Einstein had to say about all of this. That the relation of gravity to inertia was the motivation for general relativity is expressed in an article Einstein wrote which appeared in the February 17, 1921 issue of Nature
Quote
Can gravitation and inertia be identical? This question leads directly to the General Theory of Relativity. Is it not possible for me to regard the earth as free from rotation, if I conceive of the centrifugal force, which acts on all bodies at rest relatively to the earth, as being a "real" gravitational field of gravitation, or part of such a field? If this idea can be carried out, then we shall have proved in very truth the identity of gravitation and inertia. For the same property which is regarded as inertia from the point of view of a system not taking part of the rotation can be interpreted as gravitation when considered with respect to a system that shares this rotation. According to Newton, this interpretation is impossible, because in Newton's theory there is no "real" field of the "Coriolis-field" type. But perhaps Newton's law of field could be replaced by another that fits in with the field which holds with respect to a "rotating" system of co-ordinates? My conviction of the identity of inertial and gravitational mass aroused within me the feeling of absolute confidence in the correctness of this interpretation.

#### yor_on

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##### Re: Inertia and gravity
« Reply #4 on: 03/07/2013 23:19:51 »
Sweet stuff

#### Pr. snoerkel

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##### Re: Inertia and gravity
« Reply #5 on: 04/07/2013 05:13:56 »
What is the physical explanation for the equivalent behavior, then?

#### Pmb

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##### Re: Inertia and gravity
« Reply #6 on: 04/07/2013 13:15:27 »
There is no explanation. It's a law of nature. That means we assume that it's true for all bodies but we cannot prove it by deriving it from more basic principles.

#### Pr. snoerkel

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##### Re: Inertia and gravity
« Reply #7 on: 04/07/2013 17:18:43 »
My point, exactly. However, could we develop such a basic principle, we might be able to advance our understanding of Cosmos. At this stage even some wild idea would be worth considering.

#### Pmb

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##### Re: Inertia and gravity
« Reply #8 on: 04/07/2013 17:31:34 »
My point, exactly. However, could we develop such a basic principle, we might be able to advance our understanding of Cosmos. At this stage even some wild idea would be worth considering.
The problem with that is that it's infinitely easier to say than do. If you were to figure that out and demonstrate it then you'd win a Nobel Prize. Don't you know that this is what physicists are always trying to do, i.e. determine the mechanisms of interactions such as this?

This is like me asking "Hey! What if we figure out how to travel back in time and then we can find the lottery numbers for last week and win a quarter of a billion dollars. Wouldn't that be great? Yes? Then let's do it."  ;D
« Last Edit: 04/07/2013 17:33:42 by Pmb »

#### Pr. snoerkel

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##### Re: Inertia and gravity
« Reply #9 on: 04/07/2013 20:13:25 »
It IS easier to say than to do. But without ambition, you go nowhere. With ambition, well maybe

#### Pmb

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##### Re: Inertia and gravity
« Reply #10 on: 04/07/2013 21:01:56 »
It IS easier to say than to do. But without ambition, you go nowhere. With ambition, well maybe
Looking for things like this is exactly what physicists do, i.e. it's their job by definition. I'm curious. Where did you get the impression that this wasn't being worked on already by every single theoretical physicist that exists?
« Last Edit: 04/07/2013 21:05:31 by Pmb »

#### Pr. snoerkel

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##### Re: How are inertia and gravity related?
« Reply #11 on: 05/07/2013 06:21:54 »
[Looking for things like this is exactly what physicists do, i.e. it's their job by definition. [/quote]
Professional scientists tend to work with projects with high probability of success, even though the result might not expand our understanding significantly. To do the opposite is a sure way to put a promising career behind you.
Moreover, often amateurs, not burdened by ruling paradigms, are better thinking out of the box. Think of Albert Einstein who did the most revolutionary thinking before he turned professional scientist.

#### Pmb

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##### Re: How are inertia and gravity related?
« Reply #12 on: 05/07/2013 21:11:42 »
Quote from: Pr. snoerkel
Professional scientists tend to work with projects with high probability of success, even though the result might not expand our understanding significantly.
Where did you get that idea from? I've never found that to be anywhere near true. E.g. right now a physicist I know is working on the multiverse. Why would he think it'd have a high probability of success and by who's measure?

#### Pr. snoerkel

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##### Re: How are inertia and gravity related?
« Reply #13 on: 06/07/2013 11:10:34 »
Well, it is true that generalizing is ALLWAYS, without exception, dangerous. However, I work with scientists (ok, no physicists) all the time. Most are interested in their career and their next paper, only (generalizing again). Nice to hear that not everybody is like that. Still, I believe that amateurs are sometime better thinking out of the box, simply because they are less aquainted with the tratidional thinking pattern.
But we are drifting away from the original subject, now.

#### Pmb

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##### Re: How are inertia and gravity related?
« Reply #14 on: 06/07/2013 16:35:19 »
Well, it is true that generalizing is ALLWAYS, without exception, dangerous. However, I work with scientists (ok, no physicists) all the time. Most are interested in their career and their next paper, only (generalizing again).
Oh. I see. I call that kind of thing bread and butter physics. I know physicists at Harvard and MIT, i.e. the real think tanks of this country and they do the kind of thing you suggested. While it's true that many scientists do what you say you should keep in mind that there are plenty of scientists who do what you suggested. These are smart people which means that they're also smart enough to know what you have in mind very well, as do I.

#### saspinski

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##### Re: How are inertia and gravity related?
« Reply #15 on: 12/07/2014 13:55:10 »
As far as I understand, general theory of relativity is an extension of the notion of inertia. Instead of forces causing the curvilinear trajectories of celestial bodies, those trajectories are the equivalent to uniform retilinear movement when the spacetime are not flat.
This is more intuitive than the concept of gravity as a force, because if you are in a free fall like an astronaut in the spac station, you don't feel any force. But on the other hand, the maths become much more complicated.

#### yor_on

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##### Re: How are inertia and gravity related?
« Reply #16 on: 13/07/2014 17:06:54 »
There are all kind of words for it :) If you by it mean that objects take a shortest path through a 'curved space' I think I will agree.
==

All defined from uniform motion naturally.
« Last Edit: 13/07/2014 17:10:49 by yor_on »

#### saspinski

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##### Re: How are inertia and gravity related?
« Reply #17 on: 02/08/2014 00:36:21 »
It is the path that requires no force to travel. It is possible to launch a rocket from the earth in September to arrive in October to the point in space that the earth will reach only in December. Supposing it had enough fuel for the required acceleration. It would be a shorted path that the earth orbit, but that path would not be a "free lunch".

#### alancalverd

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##### Re: How are inertia and gravity related?
« Reply #18 on: 02/08/2014 01:15:13 »

Professional scientists tend to work with projects with high probability of success, even though the result might not expand our understanding significantly. To do the opposite is a sure way to put a promising career behind you.

Not so! On the theoretical side, a fair number of physicists are still working on string theory which might improve our understanding but has negligible (probably zero) likelihood of experimental proof. In my youth I was tempted to join the hunt for "polywater", a high-temperature viscous polymer of water which occupied the minds of many who had read Kurt Vonnegut and apparently occupied the test tubes of a few lucky experimenters, but almost certainly could not exist, along with cold fusion and CO2-forced climate change.

Quote
Moreover, often amateurs, not burdened by ruling paradigms, are better thinking out of the box. Think of Albert Einstein who did the most revolutionary thinking before he turned professional scientist.
You may have put your finger on an important point here. "Burdened by ruling paradigms" describes the work of a priest or economist, not a scientist. Applied science generally gets divided between those seeking high yield (engineers) and those tasked with discovering why products and processes fail (scientists): the latter (me included) sometimes end up looking for holes in the box that constrained the original thinking.

#### PmbPhy

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##### Re: How are inertia and gravity related?
« Reply #19 on: 02/08/2014 01:21:22 »
Quote from: saspinski
It is the path that requires no force to travel.
That's not quite true. It's the path that requires only the gravitational force to travel.
In general relativity the gravitational force is interpreted to be an inertial force. In non-relativistic mechanics some physicists believed that inertial forces aren't real. However many of them do and when it come to GR Einstein perceived the gravitational force to be an inertial force and since he saw the gravitation force to be a real force he viewed all inertial forces to be real.

From the bible of general relativity, i.e. Gravitation, by Misner, Thorne and Wheeler, Box 6.1, page 164
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A tourist in a powered interplanetary rocket feels "gravity." Can a physicist by local effects convince him that this "gravity" is bogus? Never, says Einstein's principle of the local equivalence of gravity and accelerations.

From Introducing Einstein's Relativity, by Ray D'Inverno, Oxford/Clarendon Press, (1992) page 122
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Notice that all inertial forces have the mass as a constant of proportionality in them. The status of inertial forces is again a controversial one. One school of thought describes them as apparent or fictitious which arise in non-inertial frames of reference (and which can be eliminated mathematically by putting the terms back on the right hand side). We shall adopt the attitude that if you judge them by their effects then they are very real forces. [Author gives examples]

That the relation of gravity to inertia was the motivation for general relativity is expressed in an article Einstein wrote which appeared in the February 17, 1921 issue of Nature
Quote
Can gravitation and inertia be identical? This question leads directly to the General Theory of Relativity. Is it not possible for me to regard the earth as free from rotation, if I conceive of the centrifugal force, which acts on all bodies at rest relatively to the earth, as being a "real" gravitational field of gravitation, or part of such a field? If this idea can be carried out, then we shall have proved in very truth the identity of gravitation and inertia. For the same property which is regarded as inertia from the point of view of a system not taking part of the rotation can be interpreted as gravitation when considered with respect to a system that shares this rotation. According to Newton, this interpretation is impossible, because in Newton's theory there is no "real" field of the "Coriolis-field" type. But perhaps Newton's law of field could be replaced by another that fits in with the field which holds with respect to a "rotating" system of co-ordinates? My conviction of the identity of inertial and gravitational mass aroused within me the feeling of absolute confidence in the correctness of this interpretation.

From Newtonian Mechanics, A.P. French, The M.I.T. Introductory Physics Series, W.W. Norton Pub. , (1971) , page 499.
Quote
From the standpoint of an observer in the accelerating frame, the inertial force is actually present. If one took steps to keep an object "at rest" in S', by tying it down with springs, these springs would be observed to elongate or contract in such a way as to provide a counteracting force to balance the inertial force. To describe such force as "fictitious" is therefore somewhat misleading. One would like to have some convenient label that distinguishes inertial forces from forces that arise from true physical interactions, and the term "pseudo-force" is often used. Even this, however, does not do justice to such forces experienced by someone who is actually in the accelerating frame of reference. Probably the original, strictly technical name, "inertial force," which is free of any questionable overtones, remains the best description.

From The Variational Principles of Mechanics - 4th Ed., Cornelius Lanczos, Dover Pub., page 98.
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Whenever the motion of the reference system generates a force which has to be added to the relative force of inertia I’, measured in that system, we call that force an “apparent force.” The name is well chosen, inasmuch as that force does not exist in the absolute system. The name is misleading, however, if it is interpreted as a force which is not as “real” as any given physical force. In the moving reference system the apparent force is a perfectly real force, which is not distinguishable in its nature from any other impressed force. Let us suppose that the observer is not aware of the fact that his reference system is in accelerated motion. Then purely mechanical observations cannot reveal to him that fact.

Quote
It is possible to launch a rocket from the earth in September to arrive in October to the point in space that the earth will reach only in December. Supposing it had enough fuel for the required acceleration. It would be a shorted path that the earth orbit, but that path would not be a "free lunch".
In the first place we're talking not about the shortest path but an extremal path. And the magnitude of the spacetime interval between two points on a worldline in spacetime is not determined by the Euclidean metric but by the Minkowski metric. E.g. consider a photon which travels in flat spacetime between point A and point B. Suppose the spatial distance between A and B is d. The magnitude of the spacetime interval is 0. That's an example of how different Euclidean geometry is from Minkowski geometry.

#### PmbPhy

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##### Re: How are inertia and gravity related?
« Reply #20 on: 02/08/2014 01:56:59 »
Quote from: alancalverd
Think of Albert Einstein who did the most revolutionary thinking before he turned professional scientist.
Where on earth did you ever get the idea that this was a fact??

In any case that's a common misconception perpetuated by non-scientists who believe they know more than scientists because they haven't been brainwashed yet. I've seen this claim made countless times and have never ever seen any of the people who made it say anything which told me that they were thinking outside the box on any occasion. Anyway that claim is the furthest thing from the truth. And all scientists are quite adept at thinking outside the box, much more than amateurs are.

Quote from: alancalverd
Think of Albert Einstein who did the most revolutionary thinking before he turned professional scientist.
That's a false statement too. Einstein did of the work on special relativity and the other work in 1905 that he's famous for while he was a professional scientist. He was merely waiting for his Phd or putting his finishing touches on it that year but he was as much of a professional scientist than anybody could be. Knowledge, experience and ways of thinking for Einstein are the same, perhaps even much much more, of that than anybody who could be called a professional scientist. That term typically means someone whose educated in a field of science.

#### saspinski

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##### Re: How are inertia and gravity related?
« Reply #21 on: 02/08/2014 15:22:38 »

That's not quite true. It's the path that requires only the gravitational force to travel.
In general relativity the gravitational force is interpreted to be an inertial force.

I agree that it is useful for calculation to take gravity as a (inertial) force. And that is because we all live in a non inertial frame of reference. I am now sitting in a couch between two opposite forces: gravity and the normal force upwards. The sum is zero, and I am not accelerating.
Another way to analyse the situation is to note that my inertial behaviour would be a free fall. On one hand, it is against our understanding of inertia as a non acelerated movement. On the other hand it is consistent with the notion of inertia as the type of movement in the absence of forces.
Generally speaking, all geodesical paths in the spacetime are inertial movements if we understand inertia as absence of forces. By the way, my path in the spacetime, being in this couch, is not a geodesical one, so it is not inertial.

In the first place we're talking not about the shortest path but an extremal path. And the magnitude of the spacetime interval between two points on a worldline in spacetime is not determined by the Euclidean metric but by the Minkowski metric. E.g. consider a photon which travels in flat spacetime between point A and point B. Suppose the spatial distance between A and B is d. The magnitude of the spacetime interval is 0. That's an example of how different Euclidean geometry is from Minkowski geometry.

I was answering a remark from yor_on about curved space, not spacetime.
In a flat spacetime, the Minkovski geometry applies, and the geodesicals are straight lines. that correlates well to uniform retinear inertia movement.
In our case, over the earth surface, the Schwartzchild metrics (neglegeting the influence of sun, moon and other planets) applies, and the geodesicals are curved lines in the spacetime. That correlates well to orbital movements being regarded as inertial ones, and being "at rest" as non inertial.

#### PmbPhy

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##### Re: How are inertia and gravity related?
« Reply #22 on: 03/08/2014 03:20:00 »
Quote from: saspinski
I agree that it is useful for calculation to take gravity as a (inertial) force.
Einstein was more interested in what made sense theoretically and not what made things easy to calculate.
Quote from: saspinski
Generally speaking, all geodesical paths in the spacetime are inertial movements if we understand inertia as absence of forces.
You neglected to mention that all its necessary that all non-inertial forces be zero. It’s fine to have inertial forces acting. And remember that inertial forces being “real” was a very important part of Einstein’s thinking that led him to GR.
Quote from: saspinski
By the way, my path in the spacetime, being in this couch, is not a geodesical one, so it is not inertial.
Obvioulsy.
Quote from: saspinski
I was answering a remark from yor_on about curved space, not spacetime.
It’s literally impossible to have a curved space but non-curved spacetime.

Quote from: saspinski
In a flat spacetime, the Minkovski geometry applies, and the geodesicals are straight lines. that correlates well to uniform retinear inertia movement.
What exactly do you mean by "Minkowski geometry applies"? Geometry is independent of the coordinates used. If the Metric is not expressed in inertial coordinates then the geodesics aren't straight lines.

There’s a little known quirk in the language of GR regarding this metric. When Lorentz coordinates are used (i.e. spatial Cartesian coordinates are Cartesian and frame is inertial) then the metric has the form M = diag(1, -1, -1, -1). Only when it has this form is the metric called the Minkowski metric. This is the only metric that has this odd usage of terminology applied to it. Otherwise a metric is a metric regardless of which coordinates it’s expressed in. See http://mathworld.wolfram.com/MinkowskiMetric.html

#### saspinski

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##### Re: How are inertia and gravity related?
« Reply #23 on: 03/08/2014 22:02:57 »

What exactly do you mean by "Minkowski geometry applies"?

I mean M = diag(1, -1, -1, -1) is the metric used when gravitation is negligible. Otherwise the metric tensor changes.

Einstein was more interested in what made sense theoretically and not what made things easy to calculate.

I think he could not make GR easier to calculate. That is why classical Newtonian gravity is still used whenever it is possible.

You neglected to mention that all its necessary that all non-inertial forces be zero. It’s fine to have inertial forces acting. And remember that inertial forces being “real” was a very important part of Einstein’s thinking that led him to GR.

My point is: stars, planets, satellites move without any force acting on them (well, there are tidal forces...).  I don't see why the notion of inertial forces are useful. Except because it is easy to calculate using them in our non inertial frame of reference. Normal balances weight => equilibrium for practical use.
But if it were really equi + librium (equal force), the body would be in a free fall.

« Last Edit: 04/08/2014 00:09:19 by saspinski »

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##### Re: How are inertia and gravity related?
« Reply #23 on: 03/08/2014 22:02:57 »

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