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30

I just read your blog post and it's clear to me where you've gone wrong. The equivalence principle only allows you to transform to an inertial frame locally. This means that if your spacetime is curved, then the falling observer can only choose Minkowski coordinates for an infinitesimal region around her. Think of a curved surface and having to choose a ...


15

While everyone agrees that jumping in a falling elevator doesn't help much, I think it is very instructive to do the calculation. General Remarks The general nature of the problem is the following: while jumping, the human injects muscle energy into the system. Of course, the human doesn't want to gain even more energy himself, instead he hopes to transfer ...


13

You could think of it this way: 1) Take a free particle, put it at some spacetime point, and leave it evolve. 2) Imagine the motion is not geodesic, that is $a_\mu\equiv v^\nu v_{\mu;\nu}\neq 0$, or in other words the acceleration is not zero. Note: We know that $a_\mu v ^\mu = 0$, or the 4-acceleration is normal to 4-velocity. 3) Imagine you are that ...


10

A derivation of Einstein's equation isn't why the Equivalence principle is central to GR. The reason that the equivalence principle is central to GR is in the fact that you can represent the gravitational field with a metric tensor at all--you can replace a force equation with a geodesic equation for a test mass precisely due to the fact that the geodesic ...


10

That this works for a test mass is essentially a postulate, which, as indicated by Alexey Bobrick's answer, is related to the equivalence principle. On the other hand, it is hypothesized that this behaviour can actually be demonstrated to be a direct consequence of Einstein's equations for physical masses. To prove this, however, requires actually solving ...


10

These are two different effects. Satellites don't fall down because they are moving on a circular orbit. Actually, they are falling down all the time, since circular motion is accelerated (though the velocity doesn't change absolute value, it changes direction!), so it is kind of "falling around the earth". The second question is, why doesn't an astronaut ...


9

As an addition to already posted answers and while realising that experiments on Mythbusters don't really have the required rigour of physics experiments, the Mythbusters have tested this theory and concluded that: The jumping power of a human being cannot cancel out the falling velocity of the elevator. The best speculative advice from an elevator ...


9

indeed there would be a (very small) and homogenous pressure within the blob, coming from surface tension. This pressure is calculated by the Kelvin Equation and is significant in small droplets (reason for small droplets to have a higher vapour pressure than bulk liquid) In Your 100 m blob, this extra pressure is negligible of course. There is another ...


9

The reason that jumping can make a relatively large difference is that the kinetic energy is proportional to the square of the velocity. Thus relatively small changes to the velocity can result in relatively large changes to the kinetic energy. In addition, the velocity which a human can achieve in jumping is a substantial percentage of the velocity of fatal ...


8

Dbrane's answer contains the essential points. However I should point out that General Relativity is more sophisticated than your models suggest. The Inertial Frame concept (as used in the Equivalence Principle) is really only valid infinitesimally (whence it matches Minkowski space and "idealised gravity-free universe"). Some authors have critized the EP ...


8

His starting point was to realize that Newton's gravity didn't satisfy his principles of the (special) theory of relativity because it wasn't Lorentz-invariant and it included action at a distance, faster-than-light effects of gravity that could spread immediately. So he was looking for a better theory that would be compatible with the principles of ...


7

Equivalence principle states (very roughly) that movement of objects doesn't depend on their mass (so long as they are massive, of course). These important observation is what introduces (pseudo)Riemannian geometry into the theory of gravitation, because it essentially tells us that matter that is not acted on by other forces follows the geodesics of the ...


7

There are several qualitative and quantitative differences between gravity and magnetism. When you attract 'neutral' bits of metal with a magnet, or attach it to something like a plate of metal, what's happening is that individual atoms of the metal react to the magnetic force. In a ferromagnetic metal, one with a similar electronic structure to Iron or ...


7

In 1921 Einstein gave a series of lectures in Princeton, that you can read today under the title "The Meaning of Relativity". It is an early and very special description of General Relativity, where he emphasizes much the concepts and reasoning that lead him to the theory. Nobody is able to know what was really inside Einstein's mind, but in that lectures ...


6

Well, it depends... If you just made the sun much heavier, so the earth would have to move faster in it's orbit, you wouldn't feel any different. It's just that the year would be shorter and the tides higher. If you just put a rocket behind the earth and somehow put it on rails so it couldn't go to a different orbit, then you'd feel it. You'd be heavier in ...


5

Dear Carl, my overall moral answer is the opposite one to the first two answers, so let me write a separate answer. My overall message is that with the right minimal extra assumptions, a correct theory respecting the equivalence principle has to agree with GR at cosmological distances. There are various modifications or competitors of GR, see e.g. this ...


5

Dear user, the equivalence between the inertial mass and gravitational mass tells us the following thing about the Higgs mechanism: Any inertial mass produced or modified by the Higgs mechanism also has to produce or modify a source of gravity of the same magnitude. And vice versa, a gravitational mass produced by the Higgs mechanism also has to produce an ...


5

Gravity does not attract all objects with the same speed but rather with the same acceleration. This means that any two objects in the same gravitational field will change their speeds by the same amount in any given time period. Of course, if both objects start with the same speed then their speeds will be the same as they accelerate - if you drop two ...


5

What the elevator story illustrates (and the meaning of the equivalence principle) is that you cannot distinguish $locally$ between an accelerated system and a gravitational field. Einstein uses too another example in the Princeton lectures in 1921: in a rotating platform, you would feel a centrifugal force near the outer edge. As with you at the surface of ...


5

Imagine you live in a universe governed by extremely simple rules, like Conway's Game of Life, for example. Once you discovered those rules, you might wonder, "Why do cells come alive if they have three living neighbors? Why do they die if they have one? How does that work?" (By "how" here I am referring to "what underlying mechanism makes it work?", which ...


5

They should feel the same. You only feel forces in orbit if there is something causing sensations, and nothing does in either case. Even on earth, you don't feel the "force" of gravity; you feel the force of the floor pushing you up so that you don't start falling under gravity's influence. In orbit, there is no floor, so you don't feel gravity. You ...


5

The Weak Equivalence Principle, or WEP for short, states that under identical initial conditions, the motion of particles of different masses in a given gravitational field is identical. Or in other words, there are no physical effects that depend on the mass of a point particle in an external gravitational field. This is just the equivalence between the ...


5

I think these are two separate questions that should be approached separately. 1) "Why isn't $m$ in in the first equation?" The mass of a body does change the force acting on it. But the mass of a body also changes its acceleration. If you increase the mass of an object it feels a larger force, but it's also harder to move. The equation for gravitational ...


4

You're choosing a "freely falling" inertial frame. There's a natural set of coordinates for a non rotating black hole for this called "Gullstrand-Painleve" coordinates. They correspond to the natural coordinates for a particle falling into a black hole from infinity. See the wikipedia article. In these coordinates, the speed of light is different for light ...


4

If you fill the cockpit with water, the pilot will feel a buoyant force. Humans have about the same density as water, so ignoring the scuba suit, the pilot will feel a buoyant force about equal to his own weight. The plane's maneuvers don't change this result much. By the equivalence principle, when the plane accelerates, the water in the cockpit and the ...


4

This is a tricky question. Fundamentally, this is the motivation of general relativity (and all metric theories of gravity)--if all masses interact with a gravitational field in the same way, then, in a sense, the motion of a particular mass is determined by the local gravitational field, independently of the mass. This then leads you into explaining the ...


4

In special relativity, unaccelerated observers cannot do any experiment to determine their state of motion in any absolute sense--all meaningful motion is relative to something else. We want to generalize the principle of relativity, that laws of physics are independent of inertial motion, as far as possible. Mathematically, this suggests using tensors, ...


4

No one else has taken a crack at it, so I'll just point you in the direction of the answer. He won't notice unless the pseudo-forces due to rotation (centrafugal, Coriolis and Euler) are large enough to notice. So take a human being to have a height of 2 meter. Using the conventions in the wikipedia pages and assuming that the angular velocity of the can ...



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