# Tagged Questions

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### Is the zero acceleration path also the shortest path between two points?

In flat, free, Euclidean space, the shortest path and the zero acceleration path are the same path, which is a straight line. However, in general relativity, is the zero acceleration path also the ...
109 views

### How exactly and WHY does matter affect space-time? [closed]

According to general relativity, inertial mass and gravitational mass are the same, and all accelerated reference frames (such as a uniformly rotating reference frame with its proper time dilation) ...
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### Is inertia actually a property of the force rather than the mass?

I ask this because it occurred to me that the inertial property of mass only actually arises in the context of forces (such as the EM force) as a resistance to their accelerating effect. Inertia plays ...
209 views

### Where does the idea gravity=curvature of spacetime really come from?

I have been searching for quite a while but mostly found the answer: Einstein's genius. Quite unsatisfactory. I know and understand that the idea gravity=curvature of spacetime works. Furthermore I ...
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### Can the equivalence principle be shown to follow from special relativity?

Einstein showed in various papers that the energy content of a body was a measure of its inertial mass. If you increase the internal energy of a system while keeping the center of energy at rest, its ...
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### Can we think of gravity as space itself moving?

So if you move through space with a constant acceleration you experience longer time dilation than when you're at rest, but you also experience the same time dilation when you're under the effect of ...
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### Where is Strong Equivalence Principle stronger than Weak Equivalence Principle

In my note, the two equivalence principles are stated as follows Weak Equivalence Principle: Gravitational and inertial masses are equal. Strong Equivalence Principle: There is no observable ...
219 views

### What is difference between Inertial mass and gravitational mass [duplicate]

I recently read that the mass we deal with in Equation $F=Ma$ is called inertial mass and the mass we deal with in $F=Mg$ is gravitational mass. Suppose I am taking a same ball in a free fall and in ...
205 views

### What makes matter travel along geodesics?

The relativistic explanation of gravity is geometric, the motion of a body in a field of space-time distortion can be described as being at rest and travelling along a geodesic of that field, but why ...
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### Is there a distinguished reference system, after all?

The equivalence principle, being the main postulate upon which the general relativity theory rests, basically states that all reference systems are equivalent, because pseudo forces can (locally) be ...
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### How does the Einstein Equivalence Principle imply a spacetime with a metric (and a connection)?

I have at hand the book by Clifford Will, "Theory and Experiments in Gravitational Physics", and the following Living Reviews in Relativity article. He quotes the Einstein Equivalence Principle (EEP) ...
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### Time dilation in a gravitational field and the equivalence principle

A clock near the surface of the earth will run slower than one on the top of the mountain. If the equivalence principal tells us that being at rest in a gravitational field is equivalent to being in ...
187 views

### Equivalence principle and acceleration vs a gravitational field

I picked this up on the net: Einstein came to realize the principle of equivalence, and it states that an accelerated system is completely physically equivalent to a system inside a gravitational ...
231 views

### Did people realize that gravity accelerated things before Einstein's elevator thought experiment?

I'm reading about the (very near) equivalence of gravitational mass and inertial mass in my undergrad GR course, and the text (Lambourne) describes this equivalence as the inspiration for Einstein's ...
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### Does GR imply a fundamental difference between gravitational and non-gravitational acceleration?

Does the equivalence principle imply that there is some fundamental difference between acceleration due to gravity and acceleration by other means (because there is no way to 'feel' free fall ...
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### The Equivalence principle of General Relativity and the Doppler Effect

I am studying General Relativity and am trying to understand the Equivalence Principle more thoroughly. Basically, it is said that if you are in a uniformly accelerated frame of reference in free ...
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### Is the equivalence principle in General Relativity an approximation?

I read in web that Einstein used the principle of equivalence to explain General Relativity but we know the gravitation is approximately equal in all of rested frame in gravitional field. In ...
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### Why acceleration is not relative in General Relativity?

I was thinking of it, If I say: "I'm moving at a velocity $v_1$ relative to a reference frame $M$ then the acceleration will be the derivative of $v_1$ relative to the reference frame $M$." In other ...
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### On Einstein's equivalence principles

There are two foundative Equivalence Principles in General relativity: Weak Equivalence Principle (WEP): the dynamics of a test particle in a gravitational field is independent of its mass and ...
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### Derivation of freely falling frame in Schwarzschild spacetime

Thinking about the equivalence principle, is there a nice, simple way to show that a local, freely falling frame in Schwarzschild spacetime is described by the Minkowski metric ...
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### What's the basic premise of General Relativity?

What is the basic assumption(s) required to explore general relativity? For example, if one merely assumes that the speed of light $c$ is the same for all observers, and the laws of physics are the ...
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### Why four velocity under covariant differential is considered to be zero?

In Einstein's general theory of relativity the elements of four velocity $U^{\mu} (\gamma c, \gamma v)$ under covariant differential is considered to be zero, why? $$\mathcal{D} U^{\mu}=0$$ in other ...
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### How (or why) equivalence principle led to Einstein field equations?

If equivalence principle was origin of general relativity what was the process that this principle led Einstein to developed his theory of general relativity?
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### Space time curvature real or theoretical (mathematical)?

Assuming one were in a capsule of some kind, with no window or instruments, and you swung into the gravitational field of a massive object (planet). Assuming no atmosphere to provide friction, could ...
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### Privileged coordinate system (or lack thereof) in general relativity

What does the following statement mean and why is it true? The Weak Equivalence Principle (WEP) implies that in general curved space-time there is no privileged coordinate system. I have looked ...
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### Switching from an accelerated frame of reference to a locally inertial reference system

Using the equivalence principle, show that the interval for an accelerated observer ($\textbf{g}$ uniform and constant) has the form  ds^2|_{\text{first order in ...
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### Use of Principle of Equivalence

Let $x^\mu$ be the coordinates of a reference frame, $K$, where all bodies feel the same constant and uniform acceleration $\textbf{a}=\textbf{g}=-\nabla\varphi$; let $\xi^\mu$ be the coordinates of a ...
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### Surely space-time Curvature does not explain gravity, it just describe its effects?

In special relativity co-moving objects see the other's 4-velocity as being only temporal. When they move relative to each other they see the other's 4-velocity has rotated so that it points less in ...
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### Equivalence principle question

I understand the equivalence principle as "The physics in a freely-falling small laboratory is that of special relativity (SR)." But I'm not quite sure why this is equivalent to "One cannot tell ...
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### Why does weak equivalence principle say gravity is equivalent to acceleration?

I am told that the weak equivalent principle, that $m_i=m_g$ (inertial and gravitational masses are equivalent) is equivalent to the statement that in a small system you can't tell whether you are in ...
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### What's the difference between the equivalence principle and curvature of spacetime?

Calculating using the equivalence principle only accounts for half the deflection of light, whereas the other half is from curvature of space-time. But isn't the equivalence principle the same thing ...
1k views

### How did Einstein derive general relativity?

How did Einstein derive general relativity (GR)? Did he use: the equivalence principle? The principle of least action? Anything else? Note, I'm not looking for a full mathematical derivation of GR! ...
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### Are there any well-known theories successfully unifying the inertial and gravitational mass?

From what little I know of general relativity, the equality of inertial and gravitational mass is an axiom of the theory. I suspect that this precludes GR from unifying them in the same sense as ...
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### Curvature of spacetime in only required to explain tidal forces?

I'm a bit confused about the equivalence principle in GR. I'm quoting from Wikipedia: An observer in an accelerated reference frame must introduce what physicists call fictitious forces to ...
1k views

### Why do objects follow geodesics in spacetime?

Trying to teach myself general relativity. I sort of understand the derivation of the geodesic equation ...
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### What does the equivalence principle mean in quantum cases?

We know that electron trapped by nuclear, like the hydrogen system, is described by quantum state,and never fall to the nuclear. So is there any similar situation in the case of electron near the ...
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### Equivalence principle and radiation from falling particle

I am currently having a hard time solving a problem of GR from Lasenby's book. I can't make it more clear than by quoting the exercise: 7.2 A charged object held stationary in a laboratory on the ...
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### Why can't we think of free fall as upside down rocket?

/\ / \ | | | m | | | ------ <--- floor (Rocket A) This rocket is accelerated (g) upwards then mass(m) falls on the floor. ...
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### How does Newton's 2nd law correspond to GR in the weak field limit?

I can only perform the demonstration from the much simpler $E = mc^2$. Take as given the Einstein field equation: $G_{\mu\nu} = 8 \pi \, T_{\mu\nu}$ ... can it be proved that Newton's formulation ...
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### Freefall in/out of an enclosed environment

I've just been learning about Einstein, relativity, and the equivalence principle in Physics. I'm fascinated with the idea of being inside a free-falling enclosed environment (such as, e.g., rocket, ...
286 views

### Why dynamic Casimir effect does not appear in static gravity field?

Dynamic Casimir effect tells us that a constantly-accelerated mirror should emit radiation due to interaction with vacuum. Following principle of equivalence, a similar mirror placed in static ...
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### Is the equivalence principle strictly fulfilled by general relativity?

The equivalence principle states The outcome of any local experiment in a freely falling laboratory is independent of the velocity of the laboratory and its location in spacetime. Any real local ...
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### Einstein's “happiest thought”

Einstein described his discovery of the equivalence principle as the "happiest thought of my life". Why? What, in broad conceptual terms, is the logical chain of reasoning that leads from the ...
681 views

### How are the comoving coordinates NOT a prefered reference frame?

Physics me this: The equivalence principle has rigorous physical definitions that say, for one, that the laws of physics are the same in all inertial reference frames. This is to say that the ...
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### Is relativistic motion equivalent to fluctuating gravitational fields?

The theory of relativity makes very precise predictions about how an object's motion through space-time affects the passage of time for both the object and observers in other frames of reference. I ...
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### How can a point-like particle “feel” gravity, if locally the curvature of spacetime is always flat?

I imagine a point-like particle can only experience the local properties of spacetime. But locally there is no curvature and no gravity, as it is often stated that Locally, as expressed in the ...
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### Can the equivalence principle be tested to high precision in a human-sized lab falling through the horizon of a black hole, in principle?

Can the equivalence principle be tested to high precision in a human-sized lab falling through the horizon of a black hole, in principle? By "human-sized lab" I mean a lab the size of the ...
959 views

### Is there a fundamental reason why gravitational mass is the same as inertial mass?

The principle of equivalence - that, locally, you can't distinguish between a uniform gravitational field and a noninertial frame accelerating in the sense opposite to the gravitational field - is ...