# Questions tagged [inertial-frames]

A specific reference frame that describes its coordinates in a manner that does not depend on time and is isotropic.

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### Twin paradox problem from a perverse perspective

Reformulation of the problem I want to study twin paradox but considering that the reference frame of the twin that travels to Alpha Centauri has no velocity. Instead of considering that the twin who ...
2answers
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### What's the nicest proof that two isolates masses orbit their center of mass? [duplicate]

Although it seems intuitive, I haven't found proof of this fact in my textbooks from a purely mathematical standpoint. I was wondering if anybody knows of a particularly elegant proof of this fact, ...
2answers
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### Why didn't Lorentz conclude that no object can go faster than light?

Based on Lorentz factor $\gamma = \frac{1}{\sqrt {1-\frac{v^2}{c^2}}}$ it is easy to see $v < c$ since otherwise $\gamma$ would be either undefined or a complex number, which is non-physical. Also, ...
1answer
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### How does the Equivalence Principle imply that derivatives of the metric vanish in a freely falling frame?

Why do the first derivatives of $g_{\mu\nu}$ vanish in a freely falling coordinate system? I would like to start from the Equivalence Principle that for any point in spacetime there exists a locally ...
1answer
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### Relativistic effect in a current carrying wire

In many places I read that in the rest frame of a current carrying wire (electrons in motion), the spacing between the positive ions is length contracted and equal to the length contracted spacing ...
1answer
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### Transformation of $4-$velocity

Notation: a greek index indicates four labels; spacetime coordinates $\mu = (0,1,2,3)$. A latin index indicates three labels; spatial coordinates $i = (1,2,3)$. $$* * *$$ A quantity, to be ...
2answers
436 views

### Wigner Rotation of static E & M fields is dizzying

I am looking for a formula to describe the set of inertial frames in which an electromagnetic field with non-parallel, non-perpendicular, and non-zero $E$ and $B$ transform to an electromagnetic field ...
1answer
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### Energy can be created

Consider a device which converts kinetic energy into electrical energy ( just like piezoelectric generator). Now I install this on two trains of very high mass approaching each other (moving in ...
1answer
51 views

### Why acceleration due to gravity is not reliably defined?

In Sean Carroll's Spacetime Geometry, there is the following line on Page No.50 in 2014th edition: "The acceleration of a charged particle in an electromagnetic field is uniquely defined with respect ...
5answers
202 views

### Is Relativity of simultaneity just a flaw in perception?

So I went through a couple of different books on special relativity ( including Einstein's own book) and I just can't seem to accept relativity of simultaneity as a real thing. I'll explain my ...
2answers
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### Is force really defined by the second axiom of Newtonian mechanics? [duplicate]

Many people claim that force is defined by the second axiom of Newtonian Mechanics, which is: "In an inertial reference frame, the rate of change of momentum of a particle equals the sum of the ...
1answer
467 views

### Newton's theory of gravity is covariant under Galilean transformations

We know from classical mechanics that the gravitational field equation for the scalar potential takes the form $$\nabla^2\phi=4\pi \rho,$$ where $\rho$ is mass density (which, can depend on time and ...
2answers
242 views

### Can an object have constant speed and tangential acceleration without undergoing circular motion?

Is it possible for an object to be moving with constant speed and a constant magnitude of acceleration tangent to this velocity but NOT move in a circular path? If there are other situations could I ...
1answer
142 views

### How length is an invariant in Euclidean space?

The special theory of relativity shows that intervals are invariant under Lorentz transform in the Minkowski space -time. But how can we prove (any postulates or theory) that the length is an ...
2answers
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### What does $U^{-1}(\Lambda)\phi(\Lambda y) U(\Lambda) = \phi(y)$ physically mean?

In QFT, let $U(\Lambda)$ denote a unitary representation of the Lorentz group. Let $\phi(x^{\mu})$ be scalar field operators in the Hilbert space; in other words: U^{-1}(\Lambda)\phi(x^{\mu}) U(\...
1answer
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### Reference frames and Newton’s second law

I have an understanding Issue. We were told that apparent weightlessness was due to the absence of Normal Reaction force.The example chosen was a man in a lift...the latter moving with different ...
1answer
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### Do Events Conditional to Simultaneity Occur in Every Reference Frame?

Imagine a train with a table that contains a light on both ends (so that the line between the two sources of light is parallel with the line of motion of the train) and a light sensor in the perfect ...
1answer
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### Einstein's Simultaneous Lighning and the Lorentz Transformation

I am reading Einstein's book, "Relativity: the Special and General Theory" translated by Robert W. Lawson, and I have some questions concerning Special Relativity -- specifically, the thought ...
2answers
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### Relativistic effects on charge

Does charge of the body gets affected by relativity or is constant in all frames of references?
1answer
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### Is it correct to use Newton's third law on all these scenarios? [closed]

So I was thinking about Newton's third law for sometime lately, and my problem is more about the concept, I'm fine with solving problems. I thought of these scenarios and tried to apply Newton's three ...
0answers
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### Lense-Thirring effect: Revolution, precession, rotation … inside rotating shell?

This is a very basic and vague question (I don't know general relativity, nor much physics, but am interested in this question for idiosyncratic reasons). Consider a rotating spherical shell of mass ...
0answers
110 views

### A confusion between geocentric and heliocentric model [duplicate]

As per Ptolemy, he proposed firstly geocentric model and that model if one see with aspects of relativity he would find true. Here is an example how Suppose you are in a train which is moving and you ...
2answers
112 views

### Deriving special relativity free particle Lagrangian using infinitesimal boost?

At the very beginning of Landau and Lifshitz Mechanics they derive the form of the Lagrangian for a free particle in Newtonian mechanics. I want to see how to do the analogous derivation in special ...
1answer
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### Biological aging interval equals Proper Time interval?

In special relativity does proper time interval equal biological aging interval in every inertial reference frame?
3answers
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### Method to observe clocks on spaceships moving near $c$?

I have read the explanation for clocks slowing down on a spaceship moving relative to a stationary observer -- something like a beam of light between two mirrors taking longer for the observer to ...
2answers
67 views

### Relativity from a basic assumption

Is it possible to derive Lorentz transformations just by assuming that if two spaceships are moving away from each other with a constant speed, it is impossible for them to tell who is moving, even if ...
0answers
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### Equivalence in all inertial frames

Suppose there is a train moving to the right. and inside the train there is an observer, A. Outside the track, there is another observer B. When the train passes in front of B, right at the instant ...
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1answer
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### Proper time vs time

I'm reading about relativity and I thought I understood things clearly about proper time / coordinates until I read the analysis of the Doppler effect. A and B are 2 fixed points, there is a clock in ...
2answers
82 views

### $ct' = γ(ct − βx)$

I was reading a paper on S.R. saw this eq: $ct' = \gamma(ct − \beta x)$. However I am confused by the Minkowski's diagram: We know $\tan \theta = \frac{x}{ct}= \beta$. However, wouldn't it also mean \$...