Galilean Definition and 158 Threads

As the title says, is energy Galilean invariant? I'm fairly sure it isn't, since if one considers the simple case of a free particle, such that its energy is ##E=\frac{p^{2}}{2m}##, then under a Galilean boost, it follows that ##E'=...

I'm getting quite stuck on this problem here. Galileo said that Xb = Xa - V*Ta. (This follows from dv = dx/t --> Xa - Xb = t*dv --> the above formula) Thus, it is concluded Xa = Xb + V*Ta, but why? In my thought experiment the objects are moving relative to each other, thus if A is moving away...

Homework Statement Two bodies are moving on the same line. When they move away from each other the distance between them changes for 16m in a time interval of 3 s (Δd1 = 16 m ; Δt1 = 3 s). When they move towards each other the distance between them changes for 3 m in a time interval of 3 s (Δd2...

In Galilean Relativity, laws of mechanics are invariant across frames. In all the frames they are the same. So, in Dynamics and Relativity by W.D.McComb, it is written that this implies you cannot perform any experiment in an inertial frame that can tell whether an inertial frame is moving or...

The Galilean equivalence principle (or weak equivalence principle) is the statement of the universality of free-fall under gravity. For example, according to Wikipedia, it can be stated as follows My question regards the limitation of the principle to point masses. Does universality of...

The Galilean transforms for rotations, boosts and translations in 2D are the follows: Rotations: x' = xcosθ + ysinθ y' = -xsinθ + ycosθ Boosts: x' = x - vxt y' = y - vyt Translations: x' = x - dx y' = y - dx I wanted to combine these into a single pair of equations, so my first thought was...

How do we get (5.381)? The term involving ##V## in (5.378) is ##V(r' + vt, t)\ \Psi(r' + vt, t)##. After dividing on both sides of (5.378) by the exponential term ##e^{[i(mv.r' + mv^2t/2)/\hbar]}## [which appears in (5.379)], the term becomes ##V(r' + vt, t)\ \Psi(r', t)##. But the term as...

I thought of explaining galilean relativity to a layman like this: "A person is heavily drunk and he revolves, revolves and revolves. He shouts," The world is revolving around me". You are bystander and u say," you drankard, the world is not revolving, but you are the one who is going in rounds...

klotza submitted a new PF Insights post The Speed of Light and Galilean Relativity Continue reading the Original PF Insights Post.

Homework Statement Two particles are created in a high-energy particle accelerator and move off in opposite directions. The speed of one particle, as measured in the laboratory, is 0.650 c, and the speed of each particle relative to the other is 0.950 c, where c = 3 × 108 m/s is the speed of...

Galilean creation is one of a number of proposed alternatives to inflationary cosmology. This paper; http://arxiv.org/abs/1504.05710, Galilean Creation of the Inflationary Universe, takes the idea a step further by showing how it can transit smoothly to the single field inflationary model...

I was trying to get a couple of quick handheld shots of the waxing crescent moon with Venus with my Nex-5N last night, when just for fun I thought I'd snap Jupiter and see if the moons showed up with the Sony 200mm zoom. Much to my surprise I was able to see a couple of the moons with just a...

I'm a little bit confused about the relationship between Galileo's Principle of Relativity and Newton's Laws. Indeed, as I understand, the Galilean Principle of Relativity is what Galileo presented with Salviatti's ship discussion. The discussion seems to lead to a simple idea: "if one performs...

Homework Statement Consider Newton’s force law for two particles interact through a central force F12(r1',r2',u1,u2), where by Newton’s third law F12 = -F21. m1(d^2r1/dt^2) = F12(r1,r2,u1,u2) m2(d^2r2/dt^2) = F21(r1,r2,u1,u2) A. Show that Newtonian mechanics is form invariant with respect to...

r\rightarrow r-2qz and \psi\rightarrow\psi+q\cdot(r-qz), I don't know how to derive it, anybody know? This question results from the book "Optical Solitons: From Fibers to Photonic Crystals [1 ed.]" section 6.5

How would one find the reference frame in which an object [which undergoes a perfectly inelastic collision with a second object] experiences no change in its kinetic energy?

This is a follow-up to a question I asked earlier. We have the following exercise: We have two parallel mirrors, which are located at y=0 and y=l in the (x,y) plane. A photon is traveling between the mirrors, up and down along the y-axis. Consider an observer O at rest w.r.t. the mirrors...

We have two parallel mirrors, which are located at y=0 and y=l in the (x,y) plane. A photon is traveling between the mirrors, up and down along the y-axis. Consider an observer O at rest w.r.t. the mirrors. What's the time (Δt) measure by O for the photon to make a full period. Consider an...

I just start to read Mathematical Methods of Classical Mechanics by Arnold. And I am sort of very puzzled by all the notion. Firstly, if the universe is seen as a 4D affine space, why is time a mapping from R^4→R? I mean this kind of 4D contains time, right? Secondly, I thought the kernel of...

Homework Statement A girl is riding a bicycle along a straight road at constant speed, and passes a friend standing at a bus stop (event #1). At a time of 60 s later the friend catches a bus (event #2) If the distance separating the events is 126 m in the frame of the girl on the bicycle...

I am a little confused about the Galilean transforms. If I have t'=\gammat Is t ALWAYS the frame of reference that we are in? i.e. If a spacecraft is moving away from Earth, and I wanted to measure the time taken on the spacecraft to reach some distance, would t be the variable I...

Homework Statement At what speed v will the Galilean and Lorentz expressions for x differ by 0,10 percent? Homework Equations xL= (x'+vt')/√(1-(v/c)²) (Lorentz Transformation) xG=x'+vt' (Galilean Tranformation) The Attempt at a Solution I've tried: xG/xL = √(1-(v/c)²) =...

Galilean principle of relativity is for sure not absolutely true, isn't it? Say one has a pool full of water within a spaceship, if the spaceship is accelerated and then acceleration stops, one can look at the ripples in the pool, analyze their form and then tell, up to a certain degree of...

βI solved this problem but I do not know if it is correct becasue there is no way to check it: Imagine that we define the rear end of a train 120 m long to long to define the origin X'=0 in the train frame and we define a certain track signal light to define the origin X=0 in the track frame...

May you help me with finding the angle, and what is "line of sight"?(the final answer is 15°) Thank you in advance

A Galilean transformation is defined as a transformation that preserves the structure of Galilean space, namely: 1. time intervals; 2. spatial distances between any two simultaneous events; 3. rectilinear motions. Can anyone give a short argument for the fact that only measuring the...

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...

It is my understanding that a Galilean telescope has a smaller field of view (FOV) than a Keplerian. Doing some "pencil" ray tracing on a sheet of paper I don't seem to get this result. Can anyone suggest a source that works the math for the FOV of both types? thanks Fritz

Homework Statement I came across this problem in a worksheet and I am completely lost as to where to start; can someone help? The question is: Two trains are heading at the same speed, relative to the Earth, in opposite directions. A bomb explodes on each train, but not at the same times...

Help please. I can't find what am I missing. The solution is in the attachment. Thanks in advance.

seems to be a "paradox" in galilean relativity Hello I'm having a little bit of trouble with so-called rest frames. I will distinguish two cases. consider frame S, and a particle moving along the x-axis at speed v. Case I: consider the rest frame S' traveling along with x at speed v...

Homework Statement Prove that the electromagnetic wave equation:  (d^2ψ)/(dx^2) + (d^2ψ)/dy^2) + (d^2ψ)/(dz^2) − (1/c^2) * [(d^2ψ)/(dt^2)]= 0 is NOT invariant under Galilean transformation. (i.e., the equation does NOT have the same form for a moving observer moving at speed of...

Homework Statement If there is a change of variables: (\vec x(t),t)\to (\vec u=\vec x+\vec a(t),\,\,\,v=t+b) where b is a constant. Suppose I wish to write the following expression in terms of a gradient in (\vec u, v) \nabla_\vec x f(\vec x,t)+{d^2\vec a\over dt^2} How do I do that? Homework...

Hello all. I'm a long time reader and a first time poster. I should start by saying that I am not a physicists or a physics student and am studying it merely out of curiosity so please forgive any ambiguous terms I may use that are not standard. I came up with a sort of thought experiment to do...

Here is a question, that is so many levels above my analytical, logical, mathematical and physics skills (which sum up, in my case, to no more than popular science and science fiction reading), so the only reason that i am still asking this question, is that, not asking a question, seems to me...

Hello, I've been spending a lot of time trying to solve this problem but I can't figure out a good solution. I have to show that the action of a non-relativistic particle ( Schrodinger density Lagrangian ) is invariant under Galilean boost with the form...

I was told in another thread that saying that the Galilean relativity of Newtonian and classical mechanics could be thought of as light speed having the possibility of being infinite was nonsense. Since it was true that a discussion there of these points was off-topic, I use this new thread to...

Homework Statement You are piloting a small airplane in which you want to reach a destination that is 750 km due north of your starting location. Once you are airborne, you find that (due to a strong but steady wind) to maintain a northerly course you must point the nose of the plane at an...

Dear Forum, I am familiar with the formulas between inertial frames of reference that move at a constant speed between each other. The observed object move at a constant speed or at a constant acceleration. It can be shown that while the positions and velocities are different in the two...

I just purchased a book on the introduction of special relativity and I seem to be stuck on a simple mathematical step. For some reason I just can't see this! This is what it says: Gotta love getting stuck on something when the book says its "Easy to see." Confidence -1.

So I keep hearing that the maxwell equations are variant under Galilean transform. Tired of simply accepting it without seeing the maths, I decided to do the transformation on my own. To make things easy, I only tried Gauss' law, furthermore I constricted the field to the x-axis only. So I have...

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...

I need to diagram a galilean teliscope for a project at school using a ray diagram. I know how to do the ray diagram for the first convex lens, but how does it work with the second concave lens. It always makes the image smaller for me. Does anyone know how to do this? Pictures would be great!

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...

Homework Statement Suppose you have two bodies (assume a unit mass) approaching one another at the same speed, i.e., the velocities, v, have the same magnitude but are in opposite directions. Presumably the center of mass is half way between them, and it is not moving. It appears that the...

I posted several questions on Galilean and Minkowskian spacetime on this forum lately, but I just don't seem to be able to get a real grip on things. I noticed that the core of my problems mostly arise from the definition of world lines. Therefore I tried formulating a definition of them in both...

A Galilean transformation consists of a rotation (in space), a boost (in space) and a translation (in space and time). This can be represented for homogeneous coordinates as \left[\begin{matrix}t'\\x'\\y'\\z'\\1\end{matrix}\right]= \left[\begin{matrix} 1&0&0&0&t_{t}\\...

To talk about differentiable vector fields in Galilean space-time, one needs to define convergence. Galilean space-time is an affine space and its associated vector space is a real 4-dimensional vector space which has a 3-dimensional subspace isomorphic to Euclidean vector space. There is no...

How can I see that the generators of the Galilean group correspond to energy, momentum, etc.? References which cover the Galilean group and algebra as well as their realization in phase space are appreciated, especially if they are not too sophisticated. Thanks kith

I'm still having trouble with the basic foundations of relativity so I am taking a look here at the Galilean transformation. I know the only thing that changes is x' = x-vt Now can someone explain what each variable stands for and can show me how you would do an actual example with...