# 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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### Inelastic collisions in different frames of reference: regarding thermal energy loss

I am currently reading Introduction to Special Relativity by James H. Smith, and I am attempting to complete the exercise problems for chapter 1 before moving on. The 4th problem asks Show ...
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### Criteria on good inertial system approximation

I'm currently wrapping my head around Newton's First Law. I think I start to get a basic understanding on the meaning of this law in terms of "the existence of inertial system". Basically my ...
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### Goldstein Classical Mechanics exercise 5.17 (3ed) conceptual

I am having difficulty understanding a concept in the "Heavy symmetric top" type of problems. I will include all of my efforts as to hopefully have someone easily point out what it is that I'm missing....
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### Is the equivalence principle Machian?

There is a lot of discussion on the subject of Mach's principle, and whether it has any place in the theory of relativity. But it seems to me that one could argue that Mach's principle is at the heart ...
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### Does a mass gain inertia against movement in all directions as it approaches the speed of light?

If a mass moves along the x axis at near the speed of light, does it take as much energy to additionally accelerate the mass along the y axis as it does to accelerate it along the x axis by the same ...
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### Has this group something to do with the cone of light?

Consider the group $V=(-1,1)$ with addition $+_{rel}:V\times V\to V$ defined as: $$v+_{rel}w=\frac{v+w}{1+vw}$$ This group is analogous to the relativistic velocities where the speed of light equals ...
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### In Einstein's 1905 paper on electrodynamics, what he meant by energy of electromotive force?

In his 1905 paper, Einstein says that when the magnet is in motion and conductor stationary, changing magnetic field in space develops electric field "of certain definite energy", and this starts ...
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### How is time “homogeneous”?

My book$^1$ states: Let's consider a clock moving freely over a curve such as: $$\frac{dx^i}{dt}=\text{const} \tag{1.20}$$ We define the proper time $\tau$ as the ...
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### Electromagnetic field conversion in non-inertial frame

I found these equations for electromagnetic field conversion in inertial frame for non relativistic case. If I have permanent static magnetic field with 3 components $B_x, B_y, B_z$ and permanent ...
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### When do Lorentz transformations take straight field lines to straight field lines?

If you look at elementary examples, it seems like a Lorentz transformation takes a field pattern with a lot of straight field lines to another field pattern with a lot of straight lines. Examples: an ...
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### Different versions of Einstein's equivalence principle

As I understand it, there are two versions of Einstein's equivalence principle. The first states that "Locally, a frame in free-fall in a gravitational field is equivalent to an inertial frame in ...
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### Shape and even connectedness of accelerating components in SR is frame dependent?

In some inertial frame consider a disk of radius 1 lightyear at rest. Then along the edge of the disk there are some people in spacesuits at rest hovering right above the disk (which has negligible ...
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### Does relativistic glider violate principle of equivalence?

The relativistic glider proposed can slow down the fall of an object in gravitational field. Will this violate the principle of equivalence which says that one cannot distinguish between free falling ...
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### Inertial frames as in Landau & Lifshhitz mechanics 1st chapter

If we see inertial frames from a basic point of view (precisely more basic axiom from which I can at least derive the law of free body as in landau mechanics first chapter) that inertial frames are ...
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### To what extent is rotation relative (in GR and other theories)?

In Newtonian physics, rotary motion is absolute even though linear motion is not. More recently, there has been a hope that rotation can also be shown to be relative. Two definitions of relative A ...
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### Special relativity - loss of simultaneity - Is that real?

Below is normal example that is generally given for loss of simultaneity in relativity A person (A) is on platform. Another person (B) is travelling in train (moving left to right). When person A ...
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### About General Relativity and Reference Frames

So, I came up with this question which is intriguing me since a bit. Maybe it's stupid, but it's always better to ask. The question is about inertial reference frames (I'll name them IRF) We know ...
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### Space travel - communication of the arrival time

I have a particular passion for space travel and so, for fun, I'm trying to identify the possible problems in comunication systems for a spaceship that moves at sensible fraction of speed of light in ...
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### Quantum mechanical origin of pseudo forces

I am thinking about this from quite some time but could not come up with any satisfactory explanation. In a nutshell, how would one explain the pseudo forces felt by non-inertial observers given that ...
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### Is there an absolute accelerated frame of reference?

I know from special relativity and from a little common sense that there is no absolute inertial frame of reference; that is, physics acts the same no matter what velocity you go at. However, that ...
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### Schutz's geometrical proof that spacetime interval is invariant

I'm trying to understand the proof that spacetime interval is invariant under for any two inertial observers. I know it's easy to arrive at the result using Lorentz transformation but I'm trying to ...
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### Newton's first law and Inertial Systems

Newton's first law is part definition and part experimental. Isolated bodies move uniformly in inertial systems by virtue of the definition of an inertial system. In contrast, the assertion that ...
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### Do photons have absolute motion?

Absolute rest is not possible as the concept of motion is relative. But can we assert that photons have absolute motion as the observers in all the frames of reference would agree to the same value of ...
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### Different forces from different inertial frames?

I've been having trouble understanding this equation here derived in the picture given below. If I change reference frames to one which is moving at a velocity u with respect to the first frame, then ...
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### A concise definition of a frame of reference in Newtonian mechanics?

I've read Wikipedia's entry on frame of reference and also followed all of the references cited in the text (Salençon, Brillouin, Norton, etc) but I'm struggling to find any concise definition in all ...
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### Validity of Newton's second law in a non-inertial reference frame

Suppose two observers are mutually interact through gravitational force (assuming they are alone at space). If the reference frame is fixed in one of the observers could the observer in the reference ...
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### Colliding elastically in lab and CM frame

Two spherical bodies of mass $m_1$ and $m_2$ are placed in gravity free space as shown. Initially, the body with mass $m_2$ is at rest and the body with mass $m_1$ approaches the other body with a ...
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### Why can't we take space as universal frame of reference?

Suppose we have a ball filled half with water in space with nothing else around (nothing else in the whole space except the ball) and suddenly it accelerates for time t. obviously, there would be ...
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### Questions about an inertial frame

Can someone explain to me what I put in bold? Inertial frame definition: When the coordinate axes are stationary with respect to the mean position of the "fixed" stars or if they move with uniform ...
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### Is it possible to derive $2\times 2$ Lorentz transformation matrix from only eigenvectors?

As a preface, I am somewhat familiar with year 1 linear algebra but not too familiar with how one makes the connection to Lorentz transformation matrices so I apologize if the answer is obvious. One ...
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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 ...
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### What is the reasoning behind 1 step in Einstein's derivation of the Lorentz Transformation

In Einstein's book "Relativity" there is a wonderful derivation of the Lorentz transformation, requiring no more than high school algebra (pp. 117 - 121). It is quite clear but I do not understand ...
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### Difference betwee $(d\vec r/dt)_{fixed}$ and $(d\vec r/dt)_{not~fixed}$

$[![Picture ~from ~http://www.astro.uwo.ca/~houde/courses/PDF%20files/physics350/Noninertial_frames.pdf][1]][1]$ From the picture above, the set of coordinates $x_i$ are the ones that are not fixed ...
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### What direction would an engine spin in space?

I am working on a science project in school with a friend on artificial gravity in space. We are both wondering if we could use normal electric motors, to let the outer ring move. Since there's no ...
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### Relativistic equations are medium dependent?

Einstein proposed that light travels with a universal velocity from Maxwell's equations on electromagnetism. But light has different velocity in different mediums, so does this imply that the ...
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### Can an energy-momentum four vector include the quantities of all objects in a closed system?

Say I have a particle moving along the $x$-axis in the Earth's reference frame. It decays into an upsilon and a proton, each of which has an energy of 60 GeV. They are traveling in opposite ...
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### The absoluteness of time intervals in Newtonian mechanics: how is this input used?

One of the assumptions of Newtonian mechanics is that "time is absolute". Absolute, as I understand, implies that it is the same for all observers. But it's not quite true because if Tom's watch is ...
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### Is the change in kinetic energy of a system the same in all frames of reference in Newtonian Physics?

I learned in Grade 11 Physics that energy is conserved. That fact depends on the truth of the following fact. For any system of objects, if its mass and momentum remain unchanged in one frame of ...
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### Spinor Lorentz Transformation

Why should the transformation between the solutions of the Dirac equation for different inertial observers be linear?
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### Change in frequency of light clock due to to acceleration

The problem statement: A light-clock (a photon travelling between two mirrors) has proper length l and moves longitudinally through an inertial frame with proper acceleration $\alpha$ (ignore any ...
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### Interval Preserving in Minkowski Space

The squared line element in any spacetime is given as $$ds^{2}=g_{ab}dx^{a}dx^{b}.$$ The use of tensors helps us to infer that the line element in some other frame would be ds'^{2}=g'_{ab}dx'^{a}dx'^...
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### What happens to the light you see as a far away object approaches you with constant velocity?

A rocket ship 1000 light years away from me approaches me with a constant velocity. At first the light i see is 1000 years old and the ship is closer than it appears. Later the difference between the ...
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### Rotation of our Galaxy's inertial frame

Suppose in the universe, there are inertial frames in the vicinity of galaxies. Suppose also that these frames rotate slightly with respect to each other - that the universe is not quite a 'mill pond'....
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### What is the physical significance of locally Minkowskian but not necessarily geodesic coordinates?

Consider an event $P$ in spacetime and a coordinate system $x_\mu$ such that at $P$: $g_{\mu\nu}=\eta_{\mu\nu}$ $g_{\mu\nu,\sigma}=0$, or equivalently the Christoffel symbols vanish at $P$. $x_\mu$ ...
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### Help understanding the derivation of the reciprocity relation in Taylor's Classical Mechanics

When Taylor discusses length contraction, he defines two frames, $S$ and $S'$, in which $S'$ moves at speed $V$ relative to $S$. He then claims that the speed of $S$ relative to $S'$ is also $V$, ...
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### What would be the consequences of a preferred reference frame?

As I understand it, the conservation law associated with frame invariance via Noether's theorem is just the constancy of the center of mass at $t=0$, which is rather obvious, and therefore somewhat ...
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### Why is a world line's proper time the age of an observer moving along this world line?

We define "world line" in Minkowski Space to be a curve whose velocity is time-like. Then we define "proper time" to be its arc length (with respect to the metric). The given question is "why is ...
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### Can only inertial coordinate systems meet these requirements?

Sometimes people have underlying assumptions of how coordinates in a coordinate system should relate to measurements. My question is whether the following requirements would be so restrictive as to ...