I know that essentially it comes down to their being defined as such but since the first determines how an object accelerates in a gravitational field while the second specifies how it resists acceleration, doesn’t it seem odd that they would be absolutely identical? What am I missing about the distinction or is it true that in fact there isn’t any?
From my perspective (as a practicing physicist), the two quantities are in principle different, and it’s an odd coincidence that the two just happen to be equal to each other so far as we can tell. This “odd coincidence” was actually one of the inspirations for Einstein’s theory of General Relativity; it’s basically “baked into” the theory via what is nowadays called the Equivalence Principle. So if you accept General Relativity as an accurate description of the Universe, then the equality of gravitational and inertial mass follows from it.
To be perfectly nitpicky, it’s actually more accurate to say “we have never measured a difference between gravitational and inertial mass, and our experiments so far have had such-and-such level of sensitivity to any potential difference.” There are a few research groups, here and there around the world, who perform exceedingly precise experiments that are designed to be ever more sensitive to any possible difference between the two types of mass. These are serious research efforts, and they go to pretty heroic lengths to get the sensitivities that they do. My favorite anecdote comes from the group at University of Washington: their experiment is sensitive enough to tell when it has rained recently, because the extra mass of water in the soil of the nearby hills pulls on their apparatus enough to influence their data.
Nobody can really say.
If you take a realist view of general relativity, you could argue that gravitational inertial forces felt by a body are actually, on a basic level, indistinguishable. For example you could argue that the gravity we feel on the surface of the Earth is actually an inertial force because we are accelerated relative to free falling trajectories. But that’s putting the cart before the horse as the equivalence principle, of which this is just a re-statement, is a key assumption of general relativity.
It is puzzling that a gravitational field, which on certain levels is very similar to other fundamental fields, particularly the electromagnetic field, has this relationship to inertial mass which just isn’t found in other fundamental fields. One line of thought is that the similarity (with electromagnetism for example) is pretty much coincidental and gravity is an emergent phenomenon rather than one of the fundamental forces of nature.
The problem was raised in an article in the current issue of New Scientist. Basically what it seems to boil down to is that you can’t have a theory of gravity if there is no gravity and only inertia. Here is one pithy quote:
But the holy cow seems to have the 9 lives of cat and just won’t die.
Yes. Gravity is a pseudo-force. That is, it is an artifact of a frame of reference, just like a centrifugal force or coriolis force. Asking why gravitational mass is the same as inertial mass is exactly equivalent to asking why a centrifugal force is proportional to inertial mass.
So how would you respond to Prof Gripaios?
I’m not understanding why the concurrence of these two entities (gravitational mass and inertial mass) is considered a co-incidence. Their congruence has been measured to be exact down to 13 decimal places, for cosmos’ sake. It doesn’t get much better than that in science, doesn’t that mean that we are as sure as we can be that they are in fact the same thing? Just because it would be convenient for some purposes if they weren’t, is tough luck. What am I missing here?
In Weinberg’s “Gravitation and Relativistic Cosmology”*, he showed that, at least under certain assumptions, the equivalence principle falls out of a quantum theory of gravity (in the classical limit).
- It’s at work, so I can’t check the correct title, or look for what assumptions were made. Or even check if I’m recalling correctly.
If GR is correct, then it isn’t a coincidence. Gravity is truly curved space, so gravitational mass and inertial mass are two names for the same thing. If a quantum theory of gravity is correct, then there needs to be an explanation for why they are equal. Essentially, an explanation for why the equivalence principle holds to 13+ decimal places. i.e., why does quantum gravity look like curved space.
We have a good description of gravity that gives equivalence automatically. It’s in fact the only description of gravity we have. So the direct answer is that they are equivalent because gravity is (apparently) an inertial force stemming from the curvature of spacetime.
Completely separately, there is also active research into *quantum *gravity, and there are many problems along that road, but they’re quantum gravity problems, not gravity problems. A perfectly valid resolution to the tension between quantum gravity and equivalence is that quantum gravity isn’t how the universe works. (Of course, it would be nice to understand if there are resolutions other than discarding the idea, but there’s nothing that says quantum gravity has to work.)
Well, there has to be something that can explain, say, the behavior of a black hole with extremely low mass. If you can get a black hole down to the vicinity of the Planck mass, then things get screwey. And if you can’t get a black hole down to that mass, then you need to explain why not.
But then you’re left battling a lot of good arguments that classical gravity can’t be consistently coupled with quantum matter (like Eppley and Hannah, for example).
Indeed. I’m not actually arguing that gravity isn’t quantiz(ed/able). But the fact that equivalence doesn’t come out easily I see as a quantum gravity problem, not a problem with equivalence itself. The alternative view is to assert that an equivalence-incompatible quantum gravity theory is in fact correct and that we suddenly have no understanding why equivalence should hold. I would flip the burden: we know why equivalence holds; the task is to make any other description you come up with maintain that natural feature.
Looking back at my post, I see I was overly terse in one statement. My intention: “A perfectly valid resolution to the tension between quantum gravity and equivalence is that a theory of quantum gravity that doesn’t naturally provide equivalence isn’t how the universe works.” The burden of explanation as implied in the OP is that we already somehow know how quantum gravity works and that it doesn’t provide any explanation for equivalence, and I wanted to argue that the order should be reversed.
In general relativity both inertial and gravitational forces felt by a body are the result of how the Levi-Civita connection manifest itself in a local coordinate chart that is physically relevant to that body. The problem with saying that shows why the equivalent principle should be is that you have to assume the equivalence principle to model gravity in this way in the first place.
a) Coming from a strong physics background, I would not agree it is correct to lump gravity into the class of “pseudo” forces, as opposed to the others you mention.
b) Technically, one might answer the OP by saying a gravitational mass manifests gravitational behavior in a gravitational field. And, an inertial mass manifests its behavior everywhere (so far). I would also say a gravitational mass’ behavior is a subset of an inertial mass. And, since we are rather earth-centric, most people cannot understand the difference between weight and mass.
The article also talks about Unruh radiation and the possibility that it might well be the same thing as inertia. That would apparently not only break the equivalence but also get rid of the need for dark matter which no one seems to be able to locate - despite a virtual Noah’s arc of proposed particles to explain it.
I can’t read the article as I don’t have a subscription so I don’t know exactlty what they said. But surely, whilst it might seem that Unruh radiaition fits in nicely with inertia, it seems difficult to square the sheer size of the effect of inertia on a body even at low velocities with the very tiny Unruh effect.
Of course, now that the Pioneer Anomaly has been explained by perfectly ordinary forces, the same data now bear witness against any such hypothesis.
Well in fairness, they do devote several paragraphs to the fact that there are a number of proposed experiments, most of which are fairly cheap to do, that would resolve the issue, but which no one seems willing to fund for some reason.
edit: yet on the other hand, there is is funding to check equivalence on the ISS out to what? 15 decimal places? IDK. Seems like a bit of a contrast.
OK, agreed. I merely wanted to point out (perhaps superfluously) that there’s stumbling blocks in any direction you take to attack the problem, all of which are big enough that they’ve caused people to flat out claim it can’t work that way.