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21 views

Inertial frame definition in Rindler Introduction to STR vs Landau' & Lifshitz Mechanics

Juxtaposing Rindler's Introduction to STR (page 7) vs Landau's Mechanics (page 5) inertial frame definition,I get that rindler assumes frame moving uniformly w.r.t inertial frame as an inertial frame ...
2
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2answers
71 views

Inertial frames as in Landau & Lifshhitz mechanics 1st chapter

If we see inertial frames from a basic point of view (precisely more basic axiom from which I can at least derive the law of free body as in landau mechanics first chapter) that inertial frames are ...
0
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1answer
35 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 ...
3
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0answers
55 views

In Einstein's 1905 paper on electrodynamics, what he meant by energy of electromotive force?

In his 1905 paper, Einstein says that when the magnet is in motion and conductor stationary, changing magnetic field in space develops electric field "of certain definite energy", and this starts ...
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3answers
40 views

Defining what it means for a reference frame to move with a velocity $\mathbf{u}$ with respect to another

In describing a Galilean transformation, for example, one might say that if a reference frame $S'$ is moving at a velocity $\mathbf{u}$ with respect to $S$, then an object traveling at a velocity $\...
1
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1answer
33 views

Galilean transformation and differentiation

Given $x=x’-vt$ and $t=t’$, why is $\frac{\partial t}{\partial x’}=0$ instead of $1/v$? $t$ seems to depend on $x’$ because if $t$ changes, $x’$ changes. Also, in this problem, $dx=dx’$ as well, but I ...
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1answer
76 views

What was Newton's idea of absolute space and time?

When one says that Newton believed in the concept of "absolute space" and "absolute time" does it simply mean that the length interval between two points in space and time interval between two events ...
0
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1answer
34 views

Question on force invariance under the Galilean Transformations (GT)

By the Galilean transformations, one can easily derive that two different inertial observers 1,2 always measure the same forces. That is: $$ \vec{F_1} \ \left(\vec{r_1}, \frac{d\vec{r_1}}{dt_1},t_1\...
2
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1answer
464 views

Newton's theory of gravity is covariant under Galilean transformations

We know from classical mechanics that the gravitational field equation for the scalar potential takes the form $$\nabla^2\phi=4\pi \rho,$$ where $\rho$ is mass density (which, can depend on time and ...
0
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1answer
136 views

How length is an invariant in Euclidean space?

The special theory of relativity shows that intervals are invariant under Lorentz transform in the Minkowski space -time. But how can we prove (any postulates or theory) that the length is an ...
8
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1answer
182 views

How would General Relativity be different if we assumed Galilean instead of Lorentz transformations?

If we assume a universe where Galilean transformations are the correct transformations between inertial reference frames, would GR be any different ? Gravitational and inertial mass would still be ...
1
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1answer
69 views

The absoluteness of time intervals in Newtonian mechanics: how is this input used?

One of the assumptions of Newtonian mechanics is that "time is absolute". Absolute, as I understand, implies that it is the same for all observers. But it's not quite true because if Tom's watch is ...
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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 ...
2
votes
2answers
154 views

Galilean transformations of velocity

If I perform a Galilean boost $$x' = x - vt \\ t'=t$$ between two frames $S$ and $S'$, observers in each frame would disagree on the velocity of a particle because $$ \frac{dx'}{dt'} = \frac{dx}{dt} -...
0
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2answers
84 views

Can we deduce the principle of relativity from some more basic principles?

I was reading "Relativity" by Albert Einstein. In chapter 5 page 14, it is written that If K is a Galilean co-ordinate system, then every other co-ordinate system K' is a Galileian one, when, in ...
2
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4answers
561 views

Velocity of light in Galilean transformation

What is the velocity of light in Galilean transformation? Is it infinity?
0
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1answer
161 views

Galilean Transformation

The transformation between inertial systems are given by affine transformations of $\mathbb{R}^{1+3}$. These are given by $t'=\lambda t+\vec{c}^\top \vec{x} +a$ and $\vec{x}'=\vec{v}t+M\vec{x}+\vec{b}$...
1
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1answer
155 views

Transformation of the operators $\mathbf\nabla$ and $\partial/\partial t$ under Galilean transformation

I'm want to know how are the transformations of the operators $\mathbf\nabla$ and $\partial/\partial and $\partial/\partial t$ when the transformation of the Galilean relativity is applied. This is ...
18
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1answer
1k views

How do we know that the laws of physics are invariant in all inertial frames?

Einstein's Special Relativity theory is based on the assumption that the laws of physics are invariant in all inertial frames, and from there - according to Maxwell's equations - it derives that the ...
2
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2answers
295 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 ...
2
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2answers
206 views

Is relativity of simultaneity just a convention?

Lorentz transformations are well known to imply time dilation, length contraction, and relativity of simultaneity. This is prominently featured in any course on Special Relativity (SR), e.g. in ...
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5answers
426 views

How do we mathematically know for sure that absolute time is abandoned in relativity?

It is an often mentioned assumption in physics that in going from classical to relativistic spacetime the main difference is that the absolute time postulate holding in the former is "relaxed" or ...
2
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2answers
364 views

Kinetic Energy in different reference frames

Good morning, I've got a strange little paradox I thought of that I just can't figure out. Imagine that you are building a machine that lets a ball fall in vertical direction from a height h, and ...
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1answer
202 views

Angular momentum conservation under Galileo transformation

I was trying to see when angular momentum is independent of choice of origin, but then it seems angular momentum no longer conserved under Galileo transformation to me : Given a point mass is doing ...
1
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0answers
108 views

Galilean invariance of the free schroedinger equation [duplicate]

My question follows this question: Naive interpretation of Galilean invariance of the TDSE Essentially, I'm not sure how to proceed mathematically. We have the transformations: $$\begin{cases}x'=x-...
1
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1answer
107 views

Shouldn't work be the same in all coordinates?

We know that the work done by a force $\mathbf{F}$, along a path $\mathbf{x}$, is given by: \begin{equation} W = \mathbf{F}^T \cdot \mathbf{x} \end{equation} However, suppose that i apply some change ...
4
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1answer
806 views

Does force definition depend on frame of reference?

Let’s assume we have 2 different observers. Observer 1 sits in space and observer 2 sits in a space lab which is in a free fall state toward the Earth. We further assume that observer 2 in the space ...
-2
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1answer
132 views

Symmetry properties of time and space in non-inertial frames

Are symmetry properties of time and space true for non-inertial frames? If yes, how? If no, why not? Please, can you explain? We already know that an important feature of inertial frames is the ...
14
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2answers
1k views

How can Newton's idea of absolute space be reconciled with Galilean relativity?

I wasn't sure if this might be better suited to History of Science and Mathematics SE, but I suppose it is a bit more 'science-y' than historical. Apparently Newton believed in absolute space and ...
6
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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 ...
4
votes
1answer
744 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 ...
0
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2answers
460 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 ...
2
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0answers
128 views

Observer Watching a Ball Thrown Up on A Train [closed]

Let's suppose I'm on a train, moving with constant speed V1. At a time T1 I throw a ball up in the air, the ball do not accelerate but has constant velocity V2, and, in this hypotetical scenario, no ...
1
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1answer
97 views

Simultaneity in Newtonian mechanics

How would Newtonian mechanics answer the train and moving light question? The setup is: A train is moving in the positive x_axis with speed c/2. A person stands in the middle of the train. There ...
5
votes
2answers
177 views

Why position and velocity are symmetries and acceleration is not?

Position and velocity are symmetries. The law of physics do not change if the observer changes his position or velocity. But acceleration which is just a derivative of velocity is not a symmetry. In ...
3
votes
1answer
261 views

Is the Euclidean metric the only one invariant under Galilean Transformations?

Is $$ds^2=dx^2+dy^2+dz^2$$ the only metric that is invariant under Galilean transformations? And if yes how do you prove it?
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2answers
559 views

The Meaning of Newton's Second Law of Motion Being Invariant Under Certain Transformations

What do we mean when we say that Newton's Second Law of Motion is invariant under Galilean transformations? Does it mean that the value of a force measured in one reference frame is the same when ...
1
vote
2answers
149 views

How does the existence of aether allow for the Galilean transformation?

I was reading this and it said that the aether was proposed as a fix to accommodate the Galilean transform because the Laws of Electromagnetism did not remain constant under the Galilean transform. ...
0
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0answers
250 views

Galileo principle (from Landau Lifshitz to derive free particle Lagrangian)

I am reading the Landau & Lifshitz on mechanics to understand how we find the free particle Lagrangian, and there are some things that I don't understand. First, he defines an inertial frame as ...
1
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2answers
494 views

Confusion about momentum in an inertial reference frame?

In my notes, it says that the total change in momentum of an inertial reference frame is zero. Please see the picture below This has confused be because I nnderstand that the inertial reference ...
1
vote
2answers
227 views

Expansion in $\epsilon$ and $v^2$ dependence of the Lagrangian - Landau & Lifshitz's Mechanics [duplicate]

On page 4 of Landau & Lifshitz's Mechanics they say $$L\left({v^\prime}^2\right) = L\left(v^2 + 2\bf{v \cdot} \bf{\epsilon} + \epsilon^2\right).$$ Expanding this expression in powers of $\...
3
votes
2answers
292 views

(SR) Lorentz low speed approximations

In Special Relativity, the standard Lorentz transformations are: $t' = \gamma (t - \frac{vx}{c^2}) \\ x' = \gamma (x - vt) \\ y' = y \\ z' = z$ However, if we make a low speed approximation where $v ...
12
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5answers
4k views

How did Maxwell's theory of electrodynamics contradict the Galilean principle of relativity? (Pre-special relativity)

The Galilean principle of relativity: The laws of classical mechanics apply in all inertial reference systems OR No experiment carried out in an inertial frame of reference can determine the ...
21
votes
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?
1
vote
1answer
430 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 ...
4
votes
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 ...
1
vote
0answers
810 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/\...
1
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0answers
409 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 ...
1
vote
2answers
142 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 ...
-1
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1answer
193 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?