Questions tagged [galilean-relativity]

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1answer
288 views

Why does galilean invariance imply that particles that start rest stay on the same line?

I'm reading Arnol'd for self study. I'm struggling with this question: "Show that any system of two particles will remain on the same line that connected them at the initial moment, if they started at ...
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5answers
3k views

Is it possible to stay up while riding a bike on a moving sidewalk without actually moving?

If I ride a bicycle on a moving sidewalk so that I am not in effect moving at all relative to the ground, will I fall over?
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2answers
166 views

Doppler shift and Galilean relativity

Doppler shift has different forms if the observer or the source are in motion. I consider Doppler shift in the case of sound. I tried to find an answer on the non symmetry of Doppler effect, ...
2
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1answer
690 views

Calculating relative velocity in three dimensional space

Given two points $\mathcal{A}$ and $\mathcal{B}$ in $\mathbb{R^3}$ whose position and velocity vectors are, respectively: $$\mathbf{r_A}=\begin{pmatrix}r_{A_{x}}\\r_{A_{y}}\\r_{A_{z}}\end{pmatrix}$$ $$...
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3answers
724 views

Frames of reference, relativity, and a ball thrown in the air

Ever since my high school physics days I found relativity fascinating but I don't think I have great insight even into special relativity. For example, in almost every lesson or video they give an ...
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1answer
451 views

Coordinate Transformation in Classical Mechanics

The coordinates in one inertial frame are represented by $(x,t)$. Under coordinate transformation, the coordinates in another inertial frame can be represented by $f(x(t),t)$. It can be shown that the ...
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0answers
52 views

Why rotating reference frames are not inertial? [duplicate]

Let's say I'm standing on the equator, and that there is no other reference point in the sky. If the planet is rotating, then I measure my weight to be lower than if it is not. But given that I have ...
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0answers
818 views

Galilean transformation of Schrodinger equation and momentum operator

Let $$ \left.\begin{aligned} t'&=t\\x'&=x-vt \end{aligned}\right\} \quad \Longrightarrow\quad \dot{x}'=\dot{x}-v $$ and therefore $p'=p-mv$. If $p'=-i\hbar\nabla' $, then $\nabla'=\nabla-iv/\...
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0answers
420 views

Derive Galilean transformation. (The meaning of the relativity)

In the book The meaning of the relativity Einstein says that in classic mechanics two postulates are previously supposed: 1.- The time is absolute. 2.- The longitude is absolute. And this implies ...
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2answers
145 views

Is it always possible for an observer to realize to be in a non-inertial frame?

Galilean relativity principle states that two frames moving with uniform linear motion cannot be distinguished. But is it always possible to realize to be in a non-inertial frame? In a rotating frame ...
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2answers
203 views

Rational for the Principle of Relativity [closed]

When Galileo postulated his principle of relativity, it seems like quite a logical assumption. After all, velocities combine cleanly, and everyday observation seems to show that the laws of physics on ...
-1
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1answer
198 views

While jumping in a high speed train why we fall on same place? [duplicate]

while we jump inside a high speed train why do we fall on the exact place? as train is in high speed and we are jumping so we should fall backside. but this doesn't happen why?
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1answer
219 views

Galilean relativity in QM

Intro I've been trying to show that the generator of boosts can be written in operator form as can be seen here, as: $$ B = \sum_i m_i x_i(t) - t \sum_i p_i $$ As a reminder the transformation ...
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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
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1answer
92 views

Can the use of a magnetic compass be inconsistent with Galileo's Relativity Hypothesis?

I just read Galileo's Relativity Hypothesis from this website: http://physics.ucr.edu/~wudka/Physics7/Notes_www/node47.html It states that - "any two observers moving at constant speed and direction ...
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1answer
80 views

How to prove that “all unaccelerated frames behave likely for all isolated bodies”? [closed]

Say in an unaccelerated frame "S" a "isolated body A" moves with constancy of velocity , can we predict mathematically that any other such body B will move with same velocity in that frame.... My ...
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2answers
696 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 ...
1
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3answers
767 views

Prove that the spacetime interval is not invariant under Galilean transformations [closed]

The spacetime interval $(\Delta s)^2 = (\Delta x)^2 + (\Delta y)^2 + (\Delta z)^2 - c^2(\Delta t)^2$ is invariant under the Lorentz transformation and this isn't the case for the Galilean ...
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1answer
1k views

Invariance of law of conservation of angular momentum under a Galilean transformation [closed]

Given a reference frame O' moving at a constant speed $\vec{V}$ in relation to another reference frame O, I want to prove that $\vec{r_{1B}} \times m_1\vec{v_{1B}} + \vec{r_{2B}} \times m_2\vec{v_{...
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2answers
110 views

Does it take less time to drop a ball than fire one horizontally (with $90^{\circ}$) [closed]

So I was arguing about this with my friend. If we take two balls and drop one from a certain height H and then fire another one with horizontally with some initial speed from the same height H, which ...
3
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4answers
12k views

Stone dropped from a moving train

This may look like a stupid question, but it is really getting to me. Imagine a train moving with an acceleration $a$, and a person drops a stone from the window. To an observer on the ground, the ...
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0answers
120 views

Mass, Spin, Internal Energy and 1-Particle States in Galilean Quantum Mechanics

I have been reading an article discussing the unitary representation of Galilean group and non-relativistic quantum mechanics. The link to the article is given below. http://arxiv.org/abs/1107.2442 ...
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1answer
253 views

Can Schroedinger equation be derived from the unitary representation of Galilean group?

I have been trying to understand quantum mechanics as a unitary representation of spacetime symmetries. My first question is: Can Schroedinger equation be derived from the unitary representation of ...
3
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2answers
565 views

Using the product rule to expand Newton's Second Law?

Newton's second law says that $$F=\frac{\text{d}p}{\text{d}t},$$ where $F$ is the net force on a body. My question is, why can't the product rule be used to yield $$F=v\frac{\text{d}m}{\text{d}t}+m\...
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2answers
435 views

Galilean relativity & the road to special relativity

Firstly, I just want to make sure that I've understood the notions of relative and absolute quantities correctly. Elementary analysis shows that position and velocity are relative quantities. Indeed, ...
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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 ...
2
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0answers
109 views

Why did Feynman tell “we cannot locate earth's angular position, but we can tell that it is changing”?

I was reading "Symmetry in physics" by Feynman, where he wrote: If we perform sufficiently delicate experiments, we can tell that the earth is rotating, but not that it had rotated. In other words, ...
2
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1answer
368 views

Does Doppler Effect violate Galilean relativity?

Apparent frequency when the source is moving away from the observer the relation between the frequencies is: $$f' = \frac{v}{v+ v_{s} } f$$ Apparent frequency when the observer is moving away from ...
4
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1answer
276 views

Can someone explain intuitively how, for a Galilean universe, $A^4$ is equivalent to $\Bbb{R} \times \Bbb{R}^3$?

I am reading Arnold's book on classical mechanics. Obviously, everyone who's studied basic physics feels comfortable with $\Bbb{R} \times \Bbb{R}^3$. This is just a pair $(t,\mathbf{x})$. There are ...
3
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2answers
825 views

Galilean Relativity is already included in Newton's Laws?

Usually I see an inertial reference frame being defined as a reference frame in which Newton's first and second laws holds. That means that if a particle is at rest, it stays at rest unless some ...
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2answers
285 views

Relationship bewtween the principle of Galilean Relativity and absolute time

The principle of Galilean Relativity is: The laws of Mechanics are invariant in every inertial frame of reference. I say "laws of Mechanics" specifically because I'm referring to the principle ...
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0answers
500 views

What are Galileons good for?

Lately I've seen many papers (for example "The galileon as a local modification of gravity"; 292 total hits on the arXiv) on types of field theories known as Galileons, and I'm wondering what the ...
5
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3answers
554 views

How can a Physical law not be invariant?

In Relativity, both the old Galilean theory or Einstein's Special Relativity, one of the most important things is the discussion of whether or not physical laws are invariant. Einstein's theory then ...
5
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1answer
652 views

Importance of the Galilean principle of relativity

The Galilean principle of relativity states that: The laws of mechanics are invariant in all inertial reference frames That means that if we have two inertial frames of reference $S$ and $S'$ then ...
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2answers
523 views

Why Galilean spacetime is not $\mathbb{E}^4$?

In Newtonian mechanics the physical spacetime is a Galilean spacetime with an affine surjection $\pi : \mathbb{A}^4\to \mathbb{E}^1$ from affine space $\mathbb{A}^4$ to Euclidean space $\mathbb{E}^1$. ...
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3answers
2k views

Why are forces independent from the frame of reference?

The following question occurred to me while reading a proof of the following statement: If K is an inertial frame of reference, then a K’ frame of reference, which is moving with a constant ...
3
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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
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1answer
820 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'=...
2
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1answer
229 views

Representations of Galilei group

Show that the operator $U(\alpha, \beta) = e^{i(\alpha \hat{x}^2 + \beta \hat{p}_{x}^2)}$ can represent the space reflection of the 1D Galilei group: $x \to -x; t \to t$. I don't really know anything ...
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1answer
969 views

Can one derive Galilean transformations from the harmonic oscillator equations of motion and the relativity principle?

I found myself puzzled with some very basic physical concepts and I hope to get enlightened with your help. Initially my confusion arose in connection with Maxwell's equations and Lorentz ...
6
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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 ...
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0answers
252 views

Question about Origins in Galilean transformation

I'm just learning about relativity, and every equation I see for a galilean transformation of frame $S'$ (moving with uniform velocity in the $x$-direction with respect to frame $S$) is $x'=x-vt$, $y'=...
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3answers
624 views

Is it possible to tell whether the space ship is moving or not?

Consider a space ship which is not under any force. Being inside the space ship, I will make a robotic fly from the platform to crawl inside using my remote. For simplicity assume that space ship will ...
6
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2answers
121 views

Possible mechanics based on the known symmetries in the nature (investigating rumor)

Somewhere I've heard about a relative new mathematical result regarding mechanics. Specifically, there is a list of the known symmetries of mechanics (both Newtonian and relativistic), i.e. different ...
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0answers
125 views

Galilean Transform

I tried to solve a problem using two different ways and I had some trouble, the problem is: We define a symmetry transform of the expected value of $\vec{P}$ like this: $$\langle \psi|\vec{P}|\psi \...
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62 views

Galilean group time interval

I have a question that arised by reading A Course in Modern Mathematical Physics by Peter Szekeres. He defines the galilean space $\mathbb{G}^{4}$ to be the space of events with a structure ...
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1answer
190 views

In space I am moving wrt to what?

Let us suppose I am running on a street. When my eyes are open, I can see many things moving backward, and thus it gives me an idea that I am moving wrt those things. Not even this, even if I close my ...
3
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1answer
440 views

Casimir Invariants of the Galilean group

I had studied a couple of things about Galilean and Poincare group. But in the Galilean group, there is not enough clarity on how to calculate generators for boosts ($B_i$), which if I do it seems I ...
6
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2answers
468 views

Time inversion for Euler equation in fluid dynamics

Consider Euler equation for continuum body: $$\frac{\partial u^i}{\partial t}+\mathbf u\cdot \nabla u^i=- \frac{1}{\rho} \frac{\partial p}{\partial x^i} $$ where $\rho$ is the mass density, $p$ is ...
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1answer
874 views

Generator of Velocity Transformations - Galilean Transformations

Under a Galilean transformation, the coordinates and momenta of any system transform as: $$ t \rightarrow t',\\ \vec r\:' = \vec r + \vec vt,\\ \vec p\:' = \vec p + m\vec v $$ where $\vec v$ is ...