Galilean Definition and 159 Threads

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 am wondering if anyone is able to help me understand applying the transformation. I can see what...

My question is why the direction of gravitational field doesn't change relative to moving observer take for example gravitational field in the y direction relative to stationary observer but relative to an observer moving with velocity v in the x direction the field should have x component

how to think of translations and Galilean boosts commuting intuitively

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I am reading "A First Course in General Relativity" by Bernard Schutz. In Chapter1 on Special Relativity Shutz writes: "... the principle of relativity is not at all a modern concept: it goes back all the way to Galileo's hypothesis that a body in a state of uniform motion remains in that...

I have encountered a problem related to the Galilean Transformation. Let's consider two observers who will be referred to as ##O## and ##O^{'}##, with their corresponding coordinates ##(t,x,y,z)## and ##(t^{′},x^{′},y^{′},z^{'})## respectively. They are initially at the same location, at time...

In a classical example, for a system consisting of a mass attached to a spring mounted on a massless carriage which moves with uniform velocity U, as in the image below, the Hamiltonian, using coordinate q, has two terms with U in it. But if we use coordinate Q, ##Q=q−Ut##, which moves with the...

In Problem 3.7, Ballentine says: The unitary operator ##U(v) = exp(iv·G)## describes the instantaneous ##(t = 0)## effect of a transformation to a frame of reference moving at the velocity ##v## with respect to the original reference frame. Its effects on the velocity and position operators are...

I refer to the video of this page, where there is a description of Galilean relativity that is meant to be an introduction to SR, making the comprehension of the latter easier as a smooth evolution from the former. All the series is in my opinion excellent, but I think that this aspect is...

From my limited understanding the Galilean transform has 2 frames but 4 four perspectives. For example x is the stationary frame when using ## ∆x = ∆x′ + v ∆t ## and x' is moving. When using ## ∆x' = ∆x - v ∆t ## and x' is stationary and x is moving. Now lets use the example of ## ∆x = ∆x′ + v...

In https://www.physicsforums.com/threads/what-assumptions-underly-the-lorentz-transformation.1015982/post-6657920 a discussion evolved from the basic assumptions of the Lorentz transformations, to a paper M. LeBellac, J. M. Levy-Leblond, Galilean electromagnetism, Nuovo Cim. 14B, 217 (1973)...

I have a quick question about the Galilean transform. If I have Alice running and Bob stationary. The Galilean transform will tell me the position of Alice from Bob's stationary position. Also if I have Alice's position which is moving it will tell me Bob's stationary position. If I want Bob...

In the frame of Observer C standing by the side of the road, the speed of Car A with respect to Car B = v1 + v2. (Galilean Transformation). In the frame of Car A, the speed of Car B < v1 + v2 (Lorentz Transformation). Please tell me if this understanding is correct.

It's frequently discussed Galilean transformation brings one inertial frame to another inertial frame, and such a transformation leaves Newton's second law invariant (of the same form). I wonder what happens for non-inertial frame? If we start with a non-inertial frame, and Galilean transform...

I know we can prove that a Galilean transformation sends one inertial frame to another inertial frame, by proving ##\frac{d^2 f(\vec{r})}{d(f(t))^2} = \frac{d^2 \vec{r}}{dt^2}##, but can we prove the reverse? Can we prove that if the acceleration seen in two frames are the same, then the...

I got a bit confused, and hoped someone could clarify a few things. As far as I am aware, a change of basis is an identity transformation ##I_V## on the vector space (pg. 113) and we can write the relationship between the components of some vector ##v## in the different bases ##\beta## and...

I'm reading the article https://www.researchgate.net/publication/267938119_ON_THE_GALILEAN_COVARIANCE_OF_CLASSICAL_MECHANICS (pdf link here), in which the authors want to establish the transformation rule for momentum, assuming only that ##\vec{F}=d\vec{p}/dt## and notwithstanding the relation...

I'm reading a section in a textbook on the explanation of covariance of Newton's 2nd law under Galilean boosts. It's explained that ##\mathbf{a}=\mathbf{a'}## (where we're considering two frames ##S## and ##S'## moving inertially w.r.t. each other). Mass is assumed to not vary across the frames...

Without assuming a universal speed that is constant in all inertial reference frames, is it a necessary consequence of Galilean symmetry that interactions are instantaneous? If this is the case how can we prove this?

The equations of motions for a closed system consisting of ##N## particles are: $$m_i \vec x_i'' = \sum_{j \neq i}^N \vec F(\vec x_i, \vec x_i', \vec x_j, \vec x_j')$$ $$ i = 1,..., N$$ Now if we impose the requirement that this closed system be symmetric under Galilean transformations, do we...

Hi, reading the book "The Road to Reality" by Roger Penrose I was a bit confused about the notion of Galilean spacetime as fiber bundle (section 17.2). As explained there, each fiber over absolute time ##t## is a copy of ##\mathbf E^3## (an instance of it over each ##t##), there exist no...

Shouldn't the equation be x' = x + (v')(t) instead of x' = x + (v)(t)?

Hi everyone, We've just started special relativity and I'm just wondering if you'd mind clarifying something for me. The transformation is described as x'=x-vt, where x' is moving relative to x. However, in the diagram I've attached, x' is ahead of x ; so why is the transformation described...

What about if the speed parameter in a Lorentz boost were in fact related nontrivially to a Galilean speed ? More formally ##L(v_L)=G(v)\circ F## where L is a Lorentz boost with Lorentz speed ##v_L##, G is a Galileo transformation with speed ##v## and ##F## is still an unknown linear...

Hi, I'm looking for books with a really good explanation on Galilean Transformations. I find the books and/or sections where only the theory of how to convert from one to another inertial system is mentioned, but nothing with concrete examples and additional exercises. Any suggestions are...

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...

I'm studying how derivatives and partial derivatives transform under a Galilean transformation. On this page: http://www.physics.princeton.edu/~mcdonald/examples/wave_velocity.pdf Equation (16) relies on ##\frac{\partial t'}{\partial x}=0## but ##\frac{\partial x'}{\partial t}=-v## But this...

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...

It seems that there is a difference between Galilean transformations and (the transformations of the) Galilean group, for one thing: rotations. The former is usually defined as the transformations ##\{\vec{x'} = \vec x - \vec v t, \ t' = t \}##, where ##\vec v## is the primed frame velocity...

Homework Statement I am having a issue relating part of this question to the Galilean transformation. Question Relative to the laboratory, a rod of rest length ##l_0## moves in its own line with velocity u. A particle moves in the same line with equal and opposite velocity . How long dose it...

Homework Statement Using the chain rule, find a, b, c, and d: $$\frac{\partial}{\partial x'} = a\frac{\partial}{\partial x} + b\frac{\partial}{\partial t}$$ $$\frac{\partial}{\partial t'} = c\frac{\partial}{\partial x} + d\frac{\partial}{\partial t}$$ Homework Equations Chain rule...

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?

I want the proof for a general wavefunction Ψ(x,t).

Homework Statement Mary and Frank are each in their own rocket ships moving along the x-axis. Mary's ship passes Frank's ship at t0=t0'=0 with a speed "v" to the right. When t=t1 in Frank's frame, Frank shoots a missile with a speed "u" where u>v in the direction of Mary. At time t=t2 in...

Homework Statement P and M are each riding Ents while playing catch with two rings. P throws his gold ring with a speed relative himself that is twice the speed that M throws his silver ring relative to himself. P and M start off going with the same speed and direction, 30m apart with M in...

Homework Statement Given for one-dimensional Galilean symmetry the generators ##K, P,## and ##H##, with the following commutation relations: $$[K, H] = iP$$ $$[H,P] = 0$$ $$[P,K] = 0$$ Homework Equations Show that the Lie algebra for the generators ##K, P,## and ##H## is isomorphic to the...

The Galilean transformations are simple. x'=x-vt y'=y z'=z t'=t. Then why is there so much jargon and complication involved in proving that Galilean transformations satisfy the four group properties (Closure, Associative, Identity, Inverse)? Why talk of 10 generators? Why talk of rotation as...

Homework Statement Assume two masses m1' and m2' are moving in the positive x-direction with velocities v1' and v2' as measured by an observer in S' before a collision. After the collision, the two masses stick together and move with velocity v' in S'. Show that if an observer in S' finds...

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...

Is the attached solution complete? In particular, do we need to prove that ##V'(r_{12}')=V(r_{12})##, where ##V'(r_{12}')## is the potential energy function in the reference frame ##S'##, moving at a uniform velocity with respect to the reference frame ##S##, and ##r_{12}'## is the distance...

For using Galilean transformation, I have to assume that speed of light w.r.t. ether frame is c. W.r.t. ether frame, E = E0 eik(x-ct) W.r.t. S' frame which is moving with speed v along the direction of propagation of light, E' = E0 eik(x'-c't') Under Galilean transformation, x' = x-vt, t' = t...

Homework Statement 1. The common form of the heat-diffusion equation governing the temperature distribution $$\rho C_p \frac{\partial T}{\partial t}=k\nabla^2T$$ Is this equation valid in any inertial frame of reference? (i.e. does it have the property of Galilean invariance?) If not, can it...

Hello everyone, I am confused with the minus sign of x'=x-vt. When there are 2 references frames called K and K' which K is at rest and K' moves to right with velocity V with respect to K. Let there is another frame which is my frame of reference called O. The vector sum of the displacement...

Homework Statement Write the Galilean coordinate transformation equations for the case of an arbitrary direction for the relative velocity v of one frame with respect to the other. Assume that the corresponding axes of the two frames remain parallel. (Hint: let v have componentsvx, vy, vz.)...

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 $$ F\hat x=\frac {dp} {dt}\hat x,$$...

Homework Statement 2. The attempt at a solution 3. Relevant equations In the first problems of that book i was using the Galilean transformations where V1 = V2 + V But if i use that then V1 = 0.945 - 0.6 V1 = 0.345 Is not the same result, so I am confused. In this new problems we are...

The D'Alembert equation for the mechanical waves was written in 1750. It is not invariant under a Galilean transformation. Why nobody was shocked about this at the time? Why we had to wait more than a hundred years (Maxwell's equations) to discover that Galilean transformations are wrong...

I was reading my textbook for my elementary modern class and the author said that a pulse of light from a light bulb would be spherical and could be expressed as x2 + y2 + z2 = c2t2 and x'2 + y'2 + z'2 = c2t'2. Then the author goes on to say that this cannot happen for both reference frames in a...

Homework Statement I am asked to draw the ray diagram for an incident plane wave whose rays are at an angle α with respect to the optical axis of the telescope. I have done this, but I need to find an expression for the angle between the outgoing rays and the optical axis, in terms of f1, f2...

Homework Statement Professor C. Rank claims that a charge at (r_1, t_1) will contribute to the air pressure at (r_2, t_2) by an amount B \sin[C(|r_2 − r_1|^2− c^2|t_2 − t_1|^2)] , where B and C are constants. (A) Is this effect Galilean invariant? (B) Is this effect Lorentz invariant...