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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General electromagnetic equation from Coulomb's law
Can we define the differential charge as the sum of (current × infinitesimal time) and (charge density × differential volume) where current is the partial derivative of charge w.r.t time and charge ...
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Energy to produce particles in different frames
I am a fourth year undergraduate student taking a course in Nuclear and Particle physics.
When asked nuclear related questions like "how much energy is produced [in the LAB frame] in the decay $X ...
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What is the meaning of universal speed limit?
When it is said that no object can exceed the speed of light $c$ in vacuum, I have some misunderstanding about this statement. Does exceeding the speed of light mean exceeding the speed of light ...
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Is Schwarzschild spacetime in Eddington-Finklestein coordinates flat at Schwarzschild radius?
Schwarzschild metric in Eddington-Finklestein coordinates reads
$$ds^2=-\left(1-\frac{2M}{r}\right)dv^2+2dvdr+r^2d\Omega^2$$
My professor claimed that at $r=2M$, this metric becomes Minkowski metric. ...
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How do different observers decide if they are looking at the same thing?
Note: I added some more descriptions, so that anyone who reads can benefit possibly more. I suspect this question become somewhat popular, because there may be many people confused with SR, but how ...
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Order of events is invariant in timelike intervals
I thought that the order of events could be something that changes with a boost. But recently, I read in a book that for time-like separated events, the order of events is invariant.
If I think about ...
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Find a "paradox" in QFT where you can identify an absolute frame of reference, please point out errors in my reasoning
I'm not an amateur and I learned QFT systematically. This paradox just occurred to me out of nowhere.
The principle of SR tells us that the law of physics should look the same in all inertial frame. ...
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Limit of relative speed [duplicate]
Let us suppose that two rockets travel in opposite directions from the earth. The speed of each is more than half the speed of light. My question is whether the two rockets will travel at more than ...
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How to prove that events A and B are the same as C and D (A=C, B=D) in two different systems if their spacetime intervals are equal? [closed]
Consider two spacetime intervals that are equal in two different intertial systems 1 and 2: $$s_1^2=s_2^2$$
Let events A and B happen in system 1 and have coordinates: $$A(T_a,X_a,Y_a,Z_a)$$ $$B(T_b,...
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Galilean boost operator for quantum multi-particle system
If I have a two particle system with with a potential of form $V(x_1,x_2)$, is it possible to apply the galilean boost operator to only a single coordinate? Essentially, is it possible to move only a ...
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Work done in an electric field, when both the charges are moving
We know the work done on a charge by another charge when one is fixed and other is moving but what if the other charge is not fixed? Both the charges can move, what will the work be when the ...
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Is the Lorentz-contracted length of an object its true length in the stationary frame?
Let's consider an iron rod, weighing $55.8\,\text{g}$ ($6\times 10^{23}\,\text{atoms}$) and having a cross section of $1 \,\text{cm}^2$. Its volume (one mole) is $7.1 \,\text{cm}^3$. Its proper length ...
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Why can coefficient $a$ between spacetime intervals depend on absolute relative velocity between the systems?
I read Landau & Lifshitz' Classical Theory of Fields book (page 14-15) (see pic below) and I was confused when I saw in proof that coefficient $a$ between spacetime intervals $(ds)^2$ and $(ds')^2$...
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Does speed affect gravitational force according to special relativity? [duplicate]
According to the special relativity, when the speed of an object increases, its mass also increases. Does it mean that objects moving at speeds close to the speed of light exert higher gravitational ...
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Does Lorentz transformation affect mass density, pressure or temperature of a physical object?
A cylinder filled with gas and moving along its axis would be Lorentz contracted, diminishing its volume. Viewed from stationary frame, would the pressure of the gas be higher than in the co-moving ...
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Cherenkov radiation in the frame of a moving observer
Imagine a medium in which an electron is moving at speeds faster than the speed of light in the medium. Within the same medium an observer moves at the same speed with the electron. Will the observer ...
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Does a clock at the rear end of a train is ticking faster than a clock at the front end of a train?
When a train zooms past us, we observe a clock at the rear end of the train ahead of a clock at the front of the train. I wonder if it implies that the clock at the rear end is ticking faster than the ...
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Is my understanding of the "existence statement" interpretation of the 1st Law of Newton correct?
It is often questioned by people who have begun learning physics why the 1st Law of Newton is necessary, since the 2nd Law seems to imply it anyways. A modern interpretation of the first law that ...
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A Computer Moving Close to the Speed of Light
I'm a computer science student with a limited physics background and was recently introduced to special relativity. I have a question I haven’t been able to answer, and I would appreciate your help.
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Galilean boost and translation in field theory
I am reading some literature which is considering translations and boosts in field theory. The reference is Construction of Lagrangians continuum theories, Markus Scholle, 2004, The Royal Society. I ...
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Generators and Lorentz transformations (LT)
I have been trying to understand how $SO^+(1,3)$ generators are related to LT elements.
I am confused as I don't know how many types of generators are considered.
If we consider the following ...
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Why is the First Law of Motion a physical law?
I'm learning physics on my own and this question I searched for answers but couldn't really find any discussions of this math/physics distinction.
The First law of motion is essentially
if $$\tag 1 \...
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Regarding motion [closed]
I am conducting a thoughtful experiment
involving a train that accelerates at 10 m/s^2
. The train has a long passage of
12 m, and I am standing in that passage. If I jump up straight and remain in ...
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Could someone explain this leap in the Feynman lectures that 'derives' the fourth Lorentz transformation equation
So suppose that two coordinate systems are in uniform relative motion. Then the Lorentz transformation is:
$$x' =\frac{x-ut}{\sqrt{1-u^2/c^2}}$$
$$y' = y$$
$$z' = z$$
$$t' = \frac{t- ux/c^2}{\sqrt{1-u^...
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Can I ignore the negative time value in this space-time coordinate transformation with $v = 0$?
When transforming a space-time event $P = (ct, x, y, z)$ from the inertial frame $I$ to the inertial frame $I'$ and $I'$ has the relative speed $v = 0$ observed from $I$, I want to check whether $t = ...
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Incorrect proof that four-current $J^\mu$ is a four-vector
This question is inspired by this answer to a question about proving that $J^\mu$ is a four-vector.
The answer uses the continuity equation $\partial_\mu J^\mu = 0$ and the experimental fact that ...
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Regarding Motion
Suppose there is a train that travels from point A to point B, and some distance vertically from point A, there stands an observer, let's name them O1. Beside O1, there is another observer, O2, who is ...
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A relativistic fly flies at $0.7c$ in the same direction as a car traveling at $0.8c$. What will the speed of the fly be according to the driver? [closed]
A relativistic fly flies at 0.7c in the same direction as a car traveling at 0.8c. According to the driver of the car, how quickly will the fly approach the car?
To solve this problem, I applied the ...
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Examples of global and local inertial frames
I am still struggling to grasp the difference between local and global inertial frames in special and general relativity and I would appreciate some concrete examples for
Global but not local ...
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Reversed effective force and d'Alembert's Principle
Reading some answers on this forum on "reversed effective force" and from my class lectures I came to the conclusion that the reversed effective force is just the pseudo force from the rest ...
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Hitting a target moving at light speed [closed]
Initially a target and a person with a laser aiming at the target were 1 meter apart.
Somehow the target was accelerated to light speed in an instant and the laser was switched on.
(Considering the ...
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How is Newton's First Law equivalent to the postulate that inertial systems exist?
Some of the modern mechanics textbooks provide further comments on Newton's laws and aim to refine them. To understand these modern interpretations, I'm referring to "Introduction to Mechanics&...
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Is the surface of Earth a global inertial frame?
I understand that a reference frame attached to an observer standing on the surface of non-rotating Earth is not a locally inertial frame but I wonder it can taken as a globally inertial frame because ...
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Is a frame of free falling observer inertial in Newtonian mechanics?
It seems to me that a frame of an observer undergoing free fall on Earth (before entering its exosphere) is not inertial in Newtonian mechanics, even though it is inertial in special and general ...
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Time reversal operation on $\gamma$-matrices
I know that time reversal is realized as an anti-linear operator. Nevertheless I am quite bewildered by the realization of the $T$ reversal on $\gamma$-matrices.
We assume here a Minkowski metric $\...
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Can the time period between simultaneous events be made arbitrarily long? [closed]
(not a prank question. We know simultaneous events may be non-simultaneous to moving observers)
The question comes from the classic "train struck by lightning twice" scenario: https://en....
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Principle of relativity and Lorentz invariance and their mathematical description
From wikipedia
In physics, the principle of relativity is the requirement that the equations describing the laws of physics have the same form in all admissible frames of reference.
I don't ...
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How can moving observer explain non-simultaneity?
This question comes from the classic "passing train" scenario you see in almost all textbooks on relativity.
Summary: A guy on a train passes a guy on a platform. The moment they pass two ...
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About relativistic momentum and energy
So we differentiate displacement (from our frame of reference) with respect to proper time of the moving object $\dfrac{dx}{d\tau}$ to get to the momentum equation: $$p=\gamma mv$$
But when we derive ...
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Does the object's motion trajectory have to be along the inclined plane?
let’s say we have a frictionless inclined plane The angle between it and the frictionless Horizontal desktop is “$θ$”.
And we have a very small object that can be considered as a mass point which has ...
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Minkowski's interpretation of Increase of relativistic mass for moving object
Minkowski's spacetime gives an easy interpretation of space and time contraction as the projection of space and time for the (hyperbolic) rotated reference frame of the moving object on the observer's ...
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Explanation for Rigid Body Dynamics Formula: Understanding the Role and Composition of Matrices $M$ and $C(ω)$
I'm working on understanding the dynamics of a rigid body, and I've come across a formula that I'm trying to make sense of. The formula is:
Where M is:
and C(w) is
The Parameters used in these ...
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Is the definition of inertial reference frame circular?
In elementary physics classes, inertial reference frames are defined as a coordinate system which is in constant rectilinear motion (or at least that is how it was defined by my professor). How then ...
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Proving that the Lagrangian of a free particle depends only on $|\boldsymbol{v}|^2$
The question is NOT answered by
Deriving the Lagrangian for a free particle,
as the answers therein assume the quadratic dependence, which is what
I am trying to prove. Additionally, while one of the ...
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How does conservation of energy work with time dilation?
According to special relativity time will appear to have slowed down for an observer $B$ travelling at a uniform speed when observed by an observer $A$ (say 1s for $B$ equals 2s for A). If that is ...
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Does special relativity also imply that speed of sound is constant for all observers irrespective of their relative motion?
I am reading lec15 The Special Theory of Relativity from the Feynman lectures.
Poincaré made the following statement of the principle of relativity: “According to the principle of relativity, the ...
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If $\Delta t_0 < \Delta t$ then does it mean that first light signal will reach receiver faster or earlier than second light signal?
Let we have light clock.
Light signal transmits from point A to point B (receiver).
In moving inertial frame we see first light signal. Clock shows $\Delta t_0$
In stationary inertial frame we see ...
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On JD Jackson's derivation of Matrix Representations of Lorentz Tranformations
Jackson derives the ordinary rotation matrix for a rotation through angle $ \omega$ about the $z$ axis (eq.11.96) via the exponential map of the Lorentz group:
$$A=e^{-\vec{\omega}\cdot\vec S-\vec \...
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Understand the Lorentz transformation in QFT
I am a beginner in QFT,so let me introduce my question by the problem in MIT8.323 (2023 spring,by Hong Liu) pset 1
.
All steps seem clear, the measure is invariant because the Jacobian is 1 and the ...
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Is there a general solution to all spherical triangles as described by Arnold Sommerfeld?
Arnold Sommerfeld has demonstrated that it is legal to use spherical trigonometry in solving relative velocity compositions. In this work,
https://en.wikisource.org/wiki/Translation:...
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