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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Would it be useful to our knowledge of time to have an electrical conductor with each end having a different rate of time passage? [closed]

I have not seen any recent experiments that could shed more information on the nature of time. It is possible to create a conductor (having access to both ends) that experiences time to flow at ...
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What is Lorentz transform purpose abcd [closed]

Lorentz transform was created for: (only one is correct) a) to ensure Maxwell equations are unchangeable b) to ensure time passes equally in all inertial frames of reference c) to ensure ...
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3 answers
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Chart transition maps in special relativity

To my understanding, Lorentz transformations are the chart transition maps between charts of different observers, but what would be the name of chart transition maps of a single observer? Naturally he ...
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2 votes
8 answers
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Is the frequency of photon invariant?

I saw a stackexchange answer that says the energy of photons is dependent on the reference frame. I did some digging and found that this is because the frequency of photons is dependent on the ...
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What is wrong with this derivation of the Special Relativity Doppler Shift formula?

I tried to use the Lorentz coordinate transformation between two inertial frames to generate the Doppler Shift formula, but I ended up with $\lambda$ over $\lambda'$ upside-down. I must have a ...
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What would be the angular momentum of one body (individually) in a two-body problem? Given that only masses and distance between them is known

Considering equation of motion: $$L = m r^2 \dot{\theta}$$ is constant angular momentum. Also see here. What would it be for two body problem?
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3 votes
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Abstract definition of four-vector

It is a long time that I am looking for an abstract definition of four-vectors. This is the definition that I have reach to so far: A four-vector is an element of the representation space of the ...
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2 answers
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Confusion regarding pseudo force

I have been taught that a pseudo force is a force that appears to act on a mass whose motion is being described using a non-inertial frame of reference I have also been taught that pseudo force = - (...
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Time transformation term in Lorentz transformation

In the lorentz tranformation, I have got the following equation for time: $$t' = \dfrac{t - \dfrac{ux}{c^2}}{\sqrt{1-\dfrac{u^2}{c}}}$$ The $S'$ system is moving relative to $S$ system with speed $u$, ...
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Velocity of one particle w.r.t. another

Let us say that two particles $p_1$ and $p_2$ are moving in an inertial frame fixed to some point on earth. Call this frame as world frame. The velocity of $p_1$ is $(v_{1x}, v_{1y})$ in $x-y $ ...
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Derivation of Force Transformation

There is a system $S$ where a particle is moving at speed $v$ to any system $S'$ which is moving relative to system $S$ at a speed $V$. With $\gamma$ defined using $V$, the complete transformation is :...
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Do vacuum solutions of Einstein's field equation violate Mach principle?

The Schwarzschild metric is mainly used to define the gravitational field on exterior region of an isolated, spherically symmetric body, but isolated bodies, according to Mach's Principle, are ...
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How time-like unit four-vector is tangent to the observer's world-line?

I just have started studying special relativity and moving to general relativity Special relativity only deals with inertial frame (non accelerated frame) but there are no inertial frame in the curved ...
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10 votes
2 answers
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On mathematical level, what exactly is time in Newtonian mechanics?

One easy answer would be that in practical purposes, it is a very special sort of parameter. This point comes up quite clearly when we do the derivation for the work-energy theorem: $$ W = \int\mathbf{...
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1 vote
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Lorentz transform of Levi-Civita Symbol

I was reading about Lorentz transformations and frequently I hear the notion of Lorentz transforming quantities like $\epsilon^{\mu \nu \rho \sigma}$. But I have never heard an explanation as to why ...
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Can I argue that the Earth's surface is an inertial reference to explain why we can't feel it's rotation? [duplicate]

Passengers on a plane cannot feel the plane move when it's at cruise speed. Can the same reasoning be extended to earth's rotation to explain why we cannot feel it rotate even though it's rotating at ...
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Galilean Symmetry of Newtonian Mechanics

So for the equations of motion to be symmetric about a transformation from $(t,x)$ to $(\tau, y)$, the following must be true (for Newtonian mechanics): $$m \frac{d^2 x}{dt^2} = f \left( x, \frac{dx}{...
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Why perpendicular axis are unaffected in special relativity?

In SR why are $y=y'$ and $z=z'$? I understand the examples they give to show physical contradictions if this was not the case, but it seems highly unsatisfactory as there is no physical basis for this ...
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6 answers
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"Moving" clocks

In regard to relativity of simultaneity, why are clocks in the "moving" frame of reference unsynchronized (i.e., in the direction of motion, they run behind toward the front and ahead toward ...
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Which will collide first to the imaginary line? (see the well drawn diagram)

So, we are having two similar blocks of mass $m$ each. Neglect the size of blocks and fixed pulley. For each block length between blocks and point of contact with pulley is $l$ initially. The block in ...
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-8 votes
3 answers
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Can one record a speed faster than $c$?

A ship goes to the moon at 0,5 c, the captain will record on his clock about 2 seconds and a half, right? Now he increases the speed to 0,999 c (or more), thanks to relativity he should record on his ...
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1 vote
1 answer
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Which of these is the beta factor in special relativity? [closed]

Obviously, $\beta=v/c$. But in this case, I'm not too sure what $v$ represents. I've mostly done 1-D special relativity and therefore it is pretty clear in those cases. However say there are two ...
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Observing attraction between parallel wires from two perspectives

Two parallel wires through which there flows a current in the same direction. While the electrons are moving, obviously the wires attract each other (the right hand rule for magnetism and electricity)....
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2 votes
2 answers
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Is there any clear and concrete proof that says the Earth is rotating and orbiting? [duplicate]

As the title states, I am wondering if there exists a clear and concrete proof that proves that the earth is revolving around the sun on an orbit, and proves that the sun is not revolving around the ...
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Special relativity book which describes concepts using linear algebra notions

It seems so every idea of special relativity can be formulated quite nicely in Linear algebra notions such as the inner product matrix and change of basis matrices. However, I can't find a single book ...
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1 answer
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Aristotelian vs Galilean relativity in terms of bundles

In page-385 of Roger Penrose's Road to Reality, the following is written: In our Aristotelian scheme, it is appropriate to think of spacetime as simply the product: $$ \mathbb{A}= \mathbb{E}^1 \times ...
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4 votes
5 answers
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Can't understand a statement about motion

From the book where I am studying motion, It says Motion is a combined property of the object under study and the observer. There is no meaning of rest or motion without the viewer. I know that, for ...
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1 vote
1 answer
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On general covariance

If newton's theory could be formulated in the language of differential geometry (symplectic manifolds), what do we really mean when we say that the theory is covariant under the Galilean group when it'...
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Drawing spacetime diagrams assuming absolute time (page-6,Section 1.5, Schutz)

Suppose an observer $O$ uses the coordinates $t,x$ as above, and that another observer $\tilde{O}$ with coordinates $\tilde{t}, \tilde{x}$ is moving with velocity $v$ in the $x$ direction relative to $...
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2 votes
3 answers
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Thought experiment in Mach's principle - Can a void universe be considered with special relativity?

Mach's principle is based on a thought experiment in which an astronaut floats in the middle of a space devoid of all matter and all landmarks. No star, no source of energy is present, whatever the ...
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Why does four-momentum have the same transformation matrix as spacetime coordinates?

I will outline my question in 1+1D for brevity. We can passively transform our coordinate system using a Lorentz boost; $\Lambda^{\bar{\nu}}_{\mu}x^{\mu}=x^{\bar{\nu}}$. I've seen that, by stipulating ...
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2 votes
3 answers
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What does size of an inertial frame mean?

It is the equivalence principle that provides the bridge between the ideal $SR$ model and the real world. According to it, we can find at each event a set of local inertial frames (LIFS), which may be ...
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19 votes
7 answers
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Why would black hole rip me apart?

According to my understanding of General Relativity, gravity is not a force and an observer which is falling freely under the influence of gravity should be considered inertial. Now, I have come ...
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2 votes
2 answers
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Are curvilinear coordinates inertial?

At 1:46:34 of this lecture by Frederic Schuller, Inertial coordinates are defined as ones which satisfy the following equation: I am confused by the above equation because it would imply any ...
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1 answer
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Does anybody know a physical explanation for the refractive index independence of the Sagnac Interferometer fringe shift?

It is generally accepted that the fringe shift produced in a fiber optic Sagnac interferometer is independent of the refractive index of the fiber. In fact, the waveguide aspect of the fiber is not ...
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6 votes
1 answer
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How could any frame of reference be inertial?

The image below shows that a bystander watching the merry-go-round is in an inertial frame of reference. However, to nitpick, wouldn't the observer still be accelerating because it's on Earth?
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1 answer
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How to represent a pair of inertial frames in relativity?

Can two Cartesian inertial frames, in general relative motion, be drawn parallel to each other? A picture in Wikipedia suggests this, but some answers on this site appear to differ. Consider observers ...
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2 votes
1 answer
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Dependence (or lack thereof) of forces on frames of reference

Consider a block A on top of block B with a coefficient of friction of say 0.3 in between them and the path providing zero resistance (no friction), with the bottom block moving such that its ...
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0 answers
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Invariant of time-order in lightlike interval

I'm trying to prove that the time order is invariant in a lightlike interval, I have this $$P_1=(X_1^0, X_1^1,0,0)$$ $$P_2=(X_2^0, X_2^1,0,0)$$ Two lightlike events in a inertial frame where $t_2>...
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0 votes
1 answer
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Riemann curvature tensor in an inertial frame

My understanding is that the mathematical definition of an inertial frame at $x_0$ is a choice of coordinates s.t: $g_{\mu\nu}(x_0) = \eta_{\mu\nu}(x_0)$ $\partial_\rho g_{\mu\nu}(x_0) = 0$ I've ...
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4 answers
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Simple resolution to the twin paradox?

There are a ton of videos that cover the twin paradox. They're all quite involved and don't really get to the heart of the matter, which is the fundamental asymmetry between the two observers (as ...
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-1 votes
1 answer
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Is gravity a direct result of Lorentz Contraction?

I am not a physicist. Curious to know if Gravity is a direct result or manifestation of the Lorentz Contraction between particles within a denser field of matter? Curious to know if anyone has tried ...
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2 answers
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Invariance of spacetime interval by Schutz

I am reading the book on General Relativity by Bernard Schutz. In it he proves the invariance of the interval in special relativity using the following argument. $S^2=0$ for all light-like paths. This ...
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2 votes
8 answers
313 views

Are Newton's laws just definitions?

I have read a bunch of articles online regarding my question but none have helped. Newton's Laws: In an inertial reference frame, an object's momentum doesn't change unless the object is acted upon ...
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2 votes
2 answers
98 views

Is angular momentum conservation Galilean invariant?

Suppose I have a system of particles with constant total angular momentum $\mathbf{L} = \sum_a m_a \mathbf{r_a \times v_a}$ in frame K. If frame K' moves with velocity $V$ with respect to K and their ...
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-5 votes
3 answers
145 views

FTL travel without time travel (again)

In discussions about FTL communication and time travel, there is a simple thought experiment: the relativistic duel which is used to demonstrate that FTL travel implies time travel (I know it has a ...
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1 vote
3 answers
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Relativity of simultaneity in special relativity

I’ve read a lot of article about the topic and I think I understood it : according to the theory, two observers in two different frames of reference can disagree on the order of two events. For ...
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3 answers
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Explanation for invariance of $c$ / Lorentz transformations? [closed]

First of all, I want to make it clear that I'm not proposing here that I have "discovered" something(I'm just trying to save myself here from accusations about being a relativity denier or ...
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0 answers
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Question from Einstein's original paper on special relativity

Just for fun, I started reading the original paper by Einstein on the special theory of relativity. Well, what do you know? I got stuck in a place because he jumped a few steps. See if anyone can help ...
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0 votes
1 answer
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Time derivative relation between two rotating frames

I know that the time derivative of some quantity $r(t)$ in a rotating frame which rotates with angular velocity $\Omega(t)$ is related to the derivative in a fixed (i.e. inertial) frame by $$ \Big(\...
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