Questions tagged [galilean-relativity]

The tag has no usage guidance.

Filter by
Sorted by
Tagged with
18
votes
4answers
5k views

Galilean invariance of Lagrangian for non-relativistic free point particle?

In QFT, the Lagrangian density is explicitly constructed to be Lorentz-invariant from the beginning. However the Lagrangian $$L = \frac{1}{2} mv^2$$ for a non-relativistic free point particle is ...
13
votes
2answers
13k views

Galilean invariance of the Schrodinger equation

Is the Schrodinger equation invariant under Galilean transformations? I am only asking this question so that I can write an answer myself with the content found here: http://en.wikipedia.org/wiki/...
1
vote
1answer
137 views

How can I interpret or mathematically formalize Maxwellian, Leibnizian, and Machian space-times?

I've been reading the book, World Enough and Space-Time, and I came across a rough list of classical space-times with varying structural significance. Here is the same list, minus Machian Space-time,...
3
votes
6answers
5k views

Inertial Frames of Reference - Inertial vs. Accelerated Frames

According to Robert Resnick's book "Introduction to Special Relativity", a line states the following as the definition of an inertial frame of reference: "We define an inertial system as a frame of ...
6
votes
5answers
2k views

Special Relativity, 2nd Postulate — Why? [duplicate]

As a lowly physics undergrad who has been chewing on this 2nd postulate of special relativity for a year or more, I simply can't wrap my head around reasons why it is true or how Einstein might have ...
3
votes
1answer
1k views

How can the Gallilean transformations form a group?

In class my professor said the Galilean transformations form a group of order 10. $$ x'=x-vt\\ y'=y\\ z'=z\\ t'=t\\ $$ But how do these form a group? I don't see 10 things to interpret as elements. I ...
2
votes
2answers
324 views

Galilean spacetime interval?

Does it make sense to refer to a single Galilean Invariant spacetime interval? $$ds^2=dt^2+dr^2$$ Or is the proper approach to describe separate invariant interval for space (3D Euclidean distance) ...
0
votes
1answer
40 views

Frame uniformly moving to an inertial frame in Landau & Lifshitz mechanics

How to prove frame moving uniformly in straight line to an inertial frame is an inertial frame? (Assuming I do not know Galileo's relativity principle and Galileo's transformations and also taking an ...
16
votes
1answer
2k views

What does a Galilean transformation of Maxwell's equations look like?

In the 1860's Maxwell formulated what are now called Maxwell's equation, and he found that they lead to a remarkable conclusion: the existence of electromagnetic waves that propagate at a speed $c$, ...
37
votes
2answers
3k views

Isn't D'Alembert's wave equation enough to see that Galilean transformations are wrong?

The D'Alembert equation for mechanical waves was written in 1750: $$\frac{\partial^2u}{\partial x^2}=\dfrac{1}{v^2}\dfrac{\partial^2u}{\partial t^2}$$ (in 1D, $v$ being the propagation speed of the ...
6
votes
4answers
4k views

Are vectors truly independent of coordinate systems?

I have been told to think of vectors as existing independent of a coordinate system. This means that the magnitude of a vector should be independent of any coordinate system we choose. Galilean ...
9
votes
4answers
2k views

Are cause and effect the same as in our Universe in a non-relativistic, Newtonian Universe in which the speed of light is infinite? [closed]

Suppose the Universe was non-relativistic so time and space would be independent of each other. In other words, both of them separately would be absolute and independent of an observer's motion (...
7
votes
2answers
798 views

Why the Galileo transformation are written like this in Quantum Mechanics?

In Quantum Mechanics it is said that the Galileo transformation $$\mathbf{r}\mapsto \mathbf{r}-\mathbf{v}t\quad \text{and}\quad \mathbf{p}\mapsto \mathbf{p}-m\mathbf{v}\tag{1}$$ is given by the ...
6
votes
2answers
5k views

Galilean invariance of a subset of Maxwell equations

I read in Feynman's proof of Maxwell equations the statement that the subset of Maxwell equations comming from the Bianchi identity: $$ \nabla \cdot {\bf B} = 0, \quad \nabla \times {\bf E} + \frac{1}...
6
votes
2answers
491 views

Inonu-Wigner Group Contraction

I am trying to understand how one obtains the Galilean algebra from the Poincare algebra, specifically through the method of central extension. I'm doing this by imposing that the generators of the ...
4
votes
1answer
772 views

What is the Galilean transformation of the EM field?

Consider a reference frame $S$ and which we observe some electric field $\mathbf{E}$ and magnetic field $\mathbf{B}$. Let $S'$ be a reference frame moving at a constant velocity $\mathbf{u}$ with ...
3
votes
2answers
352 views

Does the density of a galaxy affect time?

Can denser galaxies appear blue shifted? Can galaxies with different densities then our own galaxy appear blue or red shifted from movement when in fact it could be from the time dilation from ...
1
vote
2answers
481 views

Mechanics Landau Galilean Principle

I started reading Landau's Mechanics book and was having some trouble understanding the Galilean Relativity Principle. What does Landau mean by saying space to be homogenous and isotropic and time is ...
4
votes
3answers
3k views

Maxwell equations invariant under Lorentz transformation but not Galilean transformations

Why Maxwell equations are not invariant under Galilean transformations, but invariant under Lorentz transformations? What is the deep physical meaning behind it?
2
votes
1answer
114 views

According to the Galileo Algebra, space translations commute with time translations. Does this mean that $[\vec P,H]=0$?

The Galileo Algebra is discussed in, for example, the wikipedia article Representation theory of the Galilean group. In that article, we can see that, for example, $$ [E,P^i]=0 $$ which means that ...
2
votes
1answer
805 views

Naive interpretation of Galilean invariance of the TDSE

I was told today by someone smarter than myself that the time-dependent Schroedinger equation in one dimension was invariant under a Galilean transformation of $(x,t)$, namely under $$\begin{cases}x'=...
1
vote
1answer
68 views

Galilei Invariance and Newton Third Law

Let's say we have a system of two point particles that can interact with each other by forces that are position and velocity dependent. The forces might or might not be derivable from a generalized ...
1
vote
2answers
694 views

Why will you float in free fall with 0 relative acceleration?

Imagine you are in an elevator that is falling freely to the surface of the earth. You begin to float. However you and the elevator have equal acceleration. Why is it that you begin to float with ...
2
votes
2answers
544 views

Confused on Newton's second law being invariant under relativity

I am a math student with some interests in physics. I picked up a book called "A First Course in General Relativity", and I am confused on the second page. I am assuming by notation or convention. ...
2
votes
2answers
780 views

Velocity of an object undergoing homogenous acceleration

So I was considering the following problem within the context of Special Relativity: Given an object O, with initial velocity v, undergoing constant acceleration at a rate of a, I want to express the ...
2
votes
2answers
298 views

Galilean Relativity and Electrodynamics

Consider the following: On the one hand, the principle of relativity, by Galileo, (totally applied to the Newtonian mechanics) says: There is no mechanical experiment that you could perform to ...
1
vote
1answer
151 views

Is this the reason why acceleration is said absolute?

I've seem sometimes people saying that although uniform motion on a straight line cannot be detected and hence it is not absolute, acceleration is indeed absolute in Classical Mechanics (I don't know ...
1
vote
1answer
321 views

Is there an “invariant” quantity for the classical Lagrangian?

$$ L = \sum _ { i = 1 } ^ { N } \frac { 1 } { 2 } m _ { i } \left| \dot { \vec { x } _ { i } } \right| ^ { 2 } - \sum _ { i < j } V \left( \vec { x } _ { i } - \vec { x } _ { j } \right) $$ This ...
0
votes
2answers
476 views

What does a Galilean transformation actually mean?

What does a Galilean transformation actually mean? I'm having trouble defining the equation for displacement shifts $x'=x-vt$. Does it mean that to any event $C$ the displacement in the primed ...
0
votes
1answer
90 views

Can we really not tell if we are moving?

It has been a while since I've thought about physics, however, I remember something about how if you are on a train with no windows that is going perfectly straight and is perfectly smooth, there is ...