What is Galilean invariance: Definition and 18 Discussions

Galilean invariance or Galilean relativity states that the laws of motion are the same in all inertial frames. Galileo Galilei first described this principle in 1632 in his Dialogue Concerning the Two Chief World Systems using the example of a ship travelling at constant velocity, without rocking, on a smooth sea; any observer below the deck would not be able to tell whether the ship was moving or stationary.
The young Albert Einstein "was engrossed in analyzing Galileo's principle of inertia (Galilean relativity)".

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1. B Energy as a non relativistic scalar and Galilean invariance

Summary: Why is there no contradiction between energy as a non relativistic scalar and Galilean invariance? If energy is a non relativistic scalar, doesn't it mean that there is a contradiction with Galilean invariance? What i mean is that if i try to accelerate an object within the Galilean...
2. I Galilean Invariance and constraints on Forces.

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 potential. Assuming Isotropy of space and homogeneity of space and time, what are the constraints...
3. I ##F=\dot{p}=\dot{m}v+m\dot{v}## and Galilean invariance

Hi. In Newtonian physics, total mass is conserved, but open systems can obviously gain or lose mass, such as a rocket. But how can the term ##\dot{m}v## be Galilean invariant?
4. System of two particles: Prove motion along connecting line

Homework Statement Given an isolated system of 2 particles in space, we can express the motion of both particles as follows: $$m_1\ddot{\vec{x_1}}=-\frac\partial{\partial \vec{x_{1}}} V(\vec{x_1},\vec{x_2})\\ m_2\ddot{\vec{x_2}}=-\frac\partial{\partial \vec{x_2}} V(\vec{x_1},\vec{x_2}),$$ where...
5. Galilean Relativity (Invariance) Problem

Homework Statement Imagine two inertial frames, S and S'. Inertial frame S' moves with velocity v0 = 5 m = s in the upward (positive y) direction as seen by an observer in frame S. Now imagine that a person at rest in frame S throws a ball with mass m straight up into the air with initial...
6. Galilean invariance: Newton's 2nd Law of motion

Consider a frame S' moving with speed u along +ve x direction with respect to another frame S. Consider a body moving with speed v along +ve x direction with respect to frame S . Both frame are inertials. here,force acting in S frame on the body is $$F\hat x=\frac {dp} {dt}\hat x,$$...
7. Galilean invariance and kinetic energy

I tried to look this up on the internet. I know there is a book about it but I forgot its title. I know that you can prove that the kinetic energy should be proportional to velocity squared by saying that this is the only Galilean invariant definition of kinetic energy. Can someone help me...
8. How to prove Galilean invariance

I'm having problems showing that Newton's second law of motion stays invariant (has the same form) under a Galilean transformation. If we write the general Galilean transformation as t=t'+t_{t} \bar{x}=R\bar{x}'+\bar{u}t'+\bar{t}_{\bar{x}} where R an orthogonal transformation, then velocity...
9. Galilean Invariance and the Special Principle of Relativity

To what extent is the PoR an extension of the galilean PoI? A stated consequence of the Galilean PoI is that inertial observers cannot determine by experiment if they are "in motion" or "at rest", with a similar consequence being mentioned for the PoR - to what extent to these differ, does...
10. Galilean invariance of Maxwell equation

always say us Maxwell equations are not covariance under Galilean Transformation They say merely this because of constant speed of light that the result of Maxwell Equations But there arent any excitability prove for Non-Ggalilean invariance of Maxwell equation I Decided try to show...
11. Galilean invariance verification (kinetic energy and momentum)

Hi all, First of all, sorry for not using the template, but I think in this situation it's better to explain my problem right away: I'm studying for a physics test, but I think I don't really understand Galilean invariance. In my textbook there is an example in which they proof that if you...
12. Verifying Galilean Invariance of the KdV Equation

Homework Statement Show that the KdV has Galilean invariance. That is ut + 6uux + uxxx = 0 is invariant under the transformation xi = x - ct, tau = t, psi = phi - c/6 Homework Equations The Attempt at a Solution Do we use the chain rule on these and plug into the KdV?
13. Galilean Invariance: Determining Invariant Quantities in Newtonian Mechanics

Homework Statement Explain which of the following quantities are invariant in Newtonian mechanics. Position Distance between two points Velocity Acceleration Momentum Kinetic Energy Potential Energy (I presume gravitational) Homework Equations N/A The Attempt at a Solution I understand...
14. Galilean invariance question

Hi, I've been reading Vic. Stenger's book "The comprehensible Cosmos" and have a question about the example he gives for Galilean invariance. In his example, Galileo drops a weight from the tower of Pisa and to a person standing near the tower (and thus in the same inertial? frame of the tower)...
15. Galilean invariance and conserved quantities

Hi I have a simple question what is the conserved quantity corresponding to the symmetry of galilean invariance? and Lorentz invariance? cheers M
16. Tensors: Lorentz vs Galilean invariance

What is the physical significance of tensors? Occasionally, motivating statements are made roughly along the lines of "if an equation can be expressed purely in terms of tensors, then it is true for all observers". But that doesn't seem quite complete because different tensor-users would have...
17. Galilean invariance (and Maxwell's equations)

Right or wrong? Specifically, an equation is said to be Galilean invariant if a substitution x \rightarrow x \pm v_x t y \rightarrow y \pm v_y t z \rightarrow z \pm v_z t t \rightarrow t doesn't change the equation. If right, would simply showing that x \rightarrow x \pm vt y...
18. Schroedinger Equation - Galilean Invariance

Hi All, I'm new to this forum. I'm a third-year undergrad Physics Major in Australia, about to go on to Honours, very exciting project in Helium atom detection. To the point. My 3rd year Special Rel project is an investigation of the development of relativistic QM (RQM). I have to...