Can tidal forces disproove Einstein's equivalence principle?

[Yora]

The equivalence principle states that there is no difference between being in a space ship that stands on the surface of the Earth, and a space ship accelerating in space at 9.8 m/s^2.
The downward force is exactly the same and, as an often used phrase tells us, there is no possible experiment to tell the difference.

Here is a proposed experiment. We have a device that measures the force acting on with incredible precision. So precise that it can tell the difference between being on the surface of the (perfectly spherical) Earth, or raised 2 meters above it. If I take the device up one deck while our ship is standing on Earth, it will detect that it is now a few meters away from the Earth's center of gravity. If I move it to a higher deck and put it on the floor in an accelerating space ship, it should detect no such difference.

Does this disprove the equivalence principle?

Is the claim that no experiment could possibly tell the difference false?

Does the principle only apply to specific points, but not larger spaces?

[InvisibleBison]

I don't know much about physics, but it seems to me that you're trying to disprove the assertion that you can't tell the difference between situation A and situation B by showing that you can tell the difference between situation B and situation C. In other words, being 2 meters above the surface of Earth is not the same thing as being on the surface of Earth.

[Grey_Wolf_c]

I'm fairly certain Einstein's thought experiment does not allow you to move away from the point experiencing the force. Otherwise, it is trivial to determine that gravity vectors are radial, whilst acceleration ones are parallel.

GW

[asda fasda]

I would say no, as I understand it the equivalence principle shows that standing on the surface is theoretically the same as acceleration.
The equivalence principle goal was to show that in free fall although you feel accelerating in fact you are in the weightlessness state, and standing on the ground is in fact accelerating against none interrupted movement.

The rocket ship experiment is just an illustration and moving up generally breaks assumption of "stands on the surface of the Earth" of this principle and would be the same as saying but "I can decrease acceleration in the rocket and I cannot decrease the force working when I'm standing on the ground so the 2 situation isn't equivalent".

although I'm not sure I'm presenting this correctly, I'm not a physicist, but I recommend "space time" show on you tube, it has few great episodes on gravity, especially yesterday I just have watched one the explain gravity as effect arising from time dilatation, that was weird stuff : )

[NichG]

It makes more sense as a statement of what can be allowed to enter into a mathematical formulation of the laws of physics than a statement about a physically real experiment. You can, for example, have non-gravitational tidal forces (such as any rotating rigid object would experience). The equivalence principle is saying that you can't write down a valid theory of physics which treats accelerations (including tidal ones) separately according to their source. So e.g. you couldn't say that some real property or outcome of an interaction depends only on gravitational tidal forces but not ones arising from rotation or some arbitrary pattern of electric fields or whatever. Once it's an acceleration, it has to enter into the theory in the same place as all other accelerations.

[Radar]

Does the principle only apply to specific points, but not larger spaces?

This one is true. The equivalence concerns either a point or a uniform gravitational field and all real sources of that are only approximately uniform at any given place. Technically you can create non-uniform acceleration by rotation (as was mentioned), but it would not be possible to shape it in the same way.

I think NichG has written it precisely as it is: what we see as gravity is just another inertial force - an indicator that we are in an accelerating frame of reference. That assumption redefines the Newtonian first law of dynamics and is the reason for using differential geometry as a natural language for describing general relativity.

[erikun]

The equivalence principle, as stated by Wikipedia, states that the inertial mass and the gravitational mass are of equal value when the acceleration on a body is equal to the gravitational force on a body. Or more conveniently, that the inertial mass multiplied by the acceleration would be equivalent to the gravitational mass multiplied by the gravitational force.

(Inertial Mass) x (Acceleration) = (Gravitational Mass) x (Force of Gravity)

In this case, I'm using "Force of Gravity" where the article mentions intensity of the gravitational field. The two would be the same, since "the position an object is in within a gravitational field" would be equivalent to the force that is being applied to it by gravity; that's basically what the gravitational field represents.

For using the proposed device, I am assuming that it is capable of detecting the difference in forces as an object moves up and down within a gravitational field. That is, the device can detect 9.80000012 m/s^-2 at sea level and 9.8000001185 m/s^-2 when standing one floor higher (or whatever the actual values would be) to such accuracy. But the reason that there is a difference is because the two locations are at different points in the gravitational field. Gravitational Mass has not been lost in walking up to the second floor of the ship, I'd hope, which means that the difference detected is the difference in the force that gravity is applying at the different locations. The device is being pulled up higher in the gravity well of Earth, meaning that the gravity on it is lower.

Meanwhile, on the constantly accelerating space ship, the whole mass of the ship is moving at a constant 9.80000012 m/s^-2. I hope. This means that any floor of the space ship would be detecting 9.80000012 m/s^-2, since there is no variation.

This does not create any conflict in the equivalence principle because the two no longer end up equivalent. Gravity is a field, and has different values within that field. Anything from height above sea level, to the location of the moon, to even standing above a large iron deposit, can change the specific level of gravity being experienced on a body. The common "9.8m/s^-2" is just an approximation, rounded off to roughly equal to what you might expect at sea level on Earth. The actual value ranges between 9.764 m/s^-2 and 9.834 m/s^-2, so it would not be possible to have a single acceleration space ship which could represent every variation of gravitational acceleration found on Earth, since the ship can only maintain a single acceleration at one time. It would not be surprising that moving about Earth's surface to find different levels of gravity would change the value that the force-detecting machine would detect, but this doesn't violate the equivalence principle due because it would be changing the force of gravity affecting the machine as it moves around.

[Jay R]

No, that doesn't violate the equivalence principle. The difference between gravity at the surface and gravity a little higher than the surface is identical to the difference between one level of acceleration and another slightly lower level of acceleration.

A person in a room on the surface with no windows cannot feel the difference between accelerating at roughly 9.81 m/sec² and being on the ground.

A person in a room slightly higher than the surface would have a slightly lower force of gravity. That would feel exactly like a slightly slower acceleration in a ship.

So the equivalence principle states that a person on the surface of the earth moving up a couple of meters is equivalent to a spaceship at 9.81 m/sec² undergoing a brief slightly higher acceleration (the force to move up), followed by a slightly lower acceleration (force of gravity two meters higher).

But remember that the difference in gravitational attraction 2 meters higher is less than one part per million. Throughout the process, the force would still be estimated as 9.81 m/sec².

[halfeye]

No, that doesn't violate the equivalence principle. The difference between gravity at the surface and gravity a little higher than the surface is identical to the difference between one level of acceleration and another slightly lower level of acceleration.

A person in a room on the surface with no windows cannot feel the difference between accelerating at roughly 9.81 m/sec² and being on the ground.

A person in a room slightly higher than the surface would have a slightly lower force of gravity. That would feel exactly like a slightly slower acceleration in a ship.

So the equivalence principle states that a person on the surface of the earth moving up a couple of meters is equivalent to a spaceship at 9.81 m/sec² undergoing a brief slightly higher acceleration (the force to move up), followed by a slightly lower acceleration (force of gravity two meters higher).

But remember that the difference in gravitational attraction 2 meters higher is less than one part per million. Throughout the process, the force would still be estimated as 9.81 m/sec².

Agreed, and the gravity at the surface of the Earth is much more variable than that due to different densities of rock.

[Grey_Wolf_c]

In the same spirit, there is something about relativity that has always bothered me. If there is no preferential frame of reference, and I can pick any I want and the laws still all apply, how is it I can choose my plane of reference as me standing on the planet, and I can measure the speed of a sufficiently distant star as it moves across the sky as a ludicrous faster-than-light speed, on the basis that it is (a) very far away and (b) it is in fact the Earth spinning around under me? How are rotational planes of reference accounted for?

Thanks,

Grey Wolf

[Radar]

In the same spirit, there is something about relativity that has always bothered me. If there is no preferential frame of reference, and I can pick any I want and the laws still all apply, how is it I can choose my plane of reference as me standing on the planet, and I can measure the speed of a sufficiently distant star as it moves across the sky as a ludicrous faster-than-light speed, on the basis that it is (a) very far away and (b) it is in fact the Earth spinning around under me? How are rotational planes of reference accounted for?

Thanks,

Grey Wolf

Even within relativity theory (special or general) there are still two significantly different classes of frames of reference: inertial and non-inertial. The former is the nice and clean one where all those laws about light speed being the absolute limit actually work. The latter is a that one uncomfortable uncle that everyone knows but nobody wants to talk about as the theory stops being elegant once the observer is accelerating (and rotation is acceleration in a way). Keep in mind that observing the world from a non-inertial frame of reference "breaks" pretty much every physical theory including plain old Newtonian mechanics where you either break the third or second law of dynamics depending on whether you introduce artificial inertial forces or not.

It is of course possible to work with non-inertial frame of reference in relativity but I can bet this formulation of the theory is significantly ugly and difficult to deal with.

[Grey_Wolf_c]

Even within relativity theory (special or general) there are still two significantly different classes of frames of reference: inertial and non-inertial. The former is the nice and clean one where all those laws about light speed being the absolute limit actually work. The latter is a that one uncomfortable uncle that everyone knows but nobody wants to talk about as the theory stops being elegant once the observer is accelerating (and rotation is acceleration in a way). Keep in mind that observing the world from a non-inertial frame of reference "breaks" pretty much every physical theory including plain old Newtonian mechanics where you either break the third or second law of dynamics depending on whether you introduce artificial inertial forces or not.

It is of course possible to work with non-inertial frame of reference in relativity but I can bet this formulation of the theory is significantly ugly and difficult to deal with.

OK, that makes sense, and now you mention it, that distinction is somewhat familiar to me, but it only inevitably raises the question of how can you tell you are in an inertial frame? Or rather, in a universe in which everything is spinning and circling something else, how can you even speak of a non-inertial frame of reference? Isn't that practically a theoretical-only frame of reference roughly equivalent to being the only non-moving thing in the entire universe, and if so, how is that not effectively a "magical" "preferential" frame of reference? Or at the very least as theoretical as the classic joke about a spherical cow in a vacuum?

(To be clear: I am well aware that these objections are so basic that they must have an answer; I am not one of those kooks who thinks that because they have a vaguely logical objection, I have somehow "disproven" general relativity)

GW

[Radar]

OK, that makes sense, and now you mention it, that distinction is somewhat familiar to me, but it only inevitably raises the question of how can you tell you are in an inertial frame? Or rather, in a universe in which everything is spinning and circling something else, how can you even speak of a non-inertial frame of reference? Isn't that practically a theoretical-only frame of reference roughly equivalent to being the only non-moving thing in the entire universe, and if so, how is that not effectively a "magical" "preferential" frame of reference? Or at the very least as theoretical as the classic joke about a spherical cow in a vacuum?

(To be clear: I am well aware that these objections are so basic that they must have an answer; I am not one of those kooks who thinks that because they have a vaguely logical objection, I have somehow "disproven" general relativity)

GW

It's fine, those are very valid questions. First of all, let's settle how to see, if you are in an inertial or a non-inertial frame of reference. It is actually doable (up to precision of a given experiment obviously) precisely because of all the weird effects non-inertial frames of reference introduce. While velocity is completely relative even if you are in an inertial frame of reference (different inertial frames of reference can move with respect to each other), acceleration can always be detected locally. Basically, if you need to introduce inertial forces (so you see everything experiencing forces proportional to their mass and seemingly without a source) to make sense of what you see, you are in a non-inertial frame of reference. Rotation also introduces inertial forces just as acceleration, so both can be calculated for any frame of reference you start with.

So, where can we find inertial frames of reference? Any nonrotating object in a free fall in vacuum is a good inertial frame of reference. Since we are on Earth, we obviously do not fall into that category, but for many everyday purposes, assuming that we do is good enough. That being said, since we can always discern by how much do we deviate from a truly inertial frame of reference, we can always translate the data we got from an experiment to some artificial inertial frame of reference (as in there was no such observer, but there could be) and analyze our data there, since more often than not, it is far simpler. Classical example of how picking the inertial frame of reference makes things better is the solar system model and specifically the transition from Ptolemy to Copernicus. At that time dynamics was not a known field of science and the notion of observed laws of nature on Earth also working for celestial bodies was not established yet, but the very reason why Copernicus got a far simpler model then Ptolemy was that he associated the frame of reference with the Sun, which is a solid approximation of an inertial frame of reference.

[Jay R]

OK, that makes sense, and now you mention it, that distinction is somewhat familiar to me, but it only inevitably raises the question of how can you tell you are in an inertial frame?

In an inertial frame of reference, Newton's First Law holds. That means that a particle not being acted upon by outside forces travels in a straight line at constant velocity. By contrast, in the non-inertial stationary planet one you brought up, photons from the stars are coming down to earth in a spiral. Since the starlight that just hit you tonight was already on its way to you from the star last night, it was on the other side of the earth 12 hours ago. And it was over your head last night, and behind the earth a day and a half ago, and ....

It doesn't travel in a straight line. In the years or centuries it took to get here, it has been circling the stationary earth every 24 hour, just like the star has.

Or rather, in a universe in which everything is spinning and circling something else, how can you even speak of a non-inertial frame of reference? Isn't that practically a theoretical-only frame of reference roughly equivalent to being the only non-moving thing in the entire universe, ...

Correct! Einstein first pointed this out. "The weakness of the principle of inertia lies in this, that it involves an argument in a circle: a mass moves without acceleration if it is sufficiently far from other bodies; we know that it is sufficiently far from other bodies only by the fact that it moves without acceleration."

... and if so, how is that not effectively a "magical" "preferential" frame of reference? Or at the very least as theoretical as the classic joke about a spherical cow in a vacuum?

(To be clear: I am well aware that these objections are so basic that they must have an answer; I am not one of those kooks who thinks that because they have a vaguely logical objection, I have somehow "disproven" general relativity)

It is not magical; it is certainly preferential.

To deal with a non-inertial frame of reference, we have to invent fictitious forces -- like whatever is making the starlight come down in a spiral. Another example of such a fictitious force occurs when your car is accelerating. You naturally think of your car as a frame of reference, so it feels like a force is pushing you back in your seat when you accelerate quickly. Go back to the "inertial frame of reference" of the stationary street, and that feeling is just the very real acceleration of your car pushing you forward.

You are correct that there is probably no completely true inertial frame of reference. The inertial frame of reference of the stationary street I just used is exactly the same frame as the non-inertial frame of reference of the stationary planet we used earlier. But within the limits of the car experiment, we can treat it like an inertial frame of reference, just as, within the limits of low velocity, we can treat it like classical physics, despite the fact that there is an extremely small Lorentz contraction from accelerating the car.

Most real uses of the "spherical cow in a vacuum" approach to physics are tools to explore the basic underlying forces first, before adding on the complications. And very often, we then don't have to complicate the model. The relativistic changes to the car are far too small to interfere with my point about acceleration -- probably too small to measure with any tool we currently have. So we can use the stationary street model as both an inertial frame of reference and as Newtonian motion, even though we know that both are only approximations.

[Lord Torath]

In a Finite Element Analysis class I attended recently, the presenter quoted: "All models are wrong. Some models are useful."

Newtonian physics is wrong. We know that it breaks down when things get really big (or really tiny) or move really quickly. But when dealing with the masses and velocities we typically encounter on the surface of Earth, it's a very good predictor of behavior.

The Theory of Relativity is wrong. We know that it breaks down on very tiny scales. But outside of that situation, it is extremely accurate.

But both these models are extremely useful in conditions where their predictions are very close to reality. They are only 'wrong' in the sense that in certain circumstances, the results they provide do not coincide with what we see in real life. Everywhere else they perform flawlessly. (Yes, okay, I'm essentially saying they perform perfectly except when they don't. A bit of a tautology, I concede. But when you know exactly where they don't perform well, you can use them everywhere else, and focus on finding other models to describe what happens in the problem regions, which is kind of how we got Quantum Mechanics.)