Questions tagged [galilean-relativity]

This tag is for questions related to the Newtonian Era idea that space and time are the same for everyone while speed adds up in the straightforward direction (if you are going 50 mph and throw something 20 mph it is going 70 mph) DO NOT use this tag for questions related solely to General Relativity.

429 questions
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What does a Galilean transformation of Maxwell's equations look like?

In the 1860's Maxwell formulated what are now called Maxwell's equation, and he found that they lead to a remarkable conclusion: the existence of electromagnetic waves that propagate at a speed $c$, which turns out to be the speed of light, implying…
41
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Isn't D'Alembert's wave equation enough to see that Galilean transformations are wrong?

The D'Alembert equation for mechanical waves was written in 1750: $$\frac{\partial^2u}{\partial x^2}=\dfrac{1}{v^2}\dfrac{\partial^2u}{\partial t^2}$$ (in 1D, $v$ being the propagation speed of the wave) It is not invariant under a Galilean…
38
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8 answers

What determines which frames are inertial frames?

I understand that you can (in principle) measure whether "free particles" (no forces) experience accelerations in order to tell whether a frame is inertial. But fundamentally, what determines which frames are inertial (i.e. what principle selects in…
38
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Deriving the Lagrangian for a free particle

I'm a newbie in physics. Sorry, if the following questions are dumb. I began reading "Mechanics" by Landau and Lifshitz recently and hit a few roadblocks right away. Proving that a free particle moves with a constant velocity in an inertial frame…
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Galilean invariance of Lagrangian for non-relativistic free point particle?

In QFT, the Lagrangian density is explicitly constructed to be Lorentz-invariant from the beginning. However the Lagrangian $$L = \frac{1}{2} mv^2$$ for a non-relativistic free point particle is not invariant under Galilean transformation. This…
29
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Galilean covariance of the Schrodinger equation

Is the Schrodinger equation covariant under Galilean transformations? I am only asking this question so that I can write an answer myself with the content found here: http://en.wikipedia.org/wiki/User:Likebox/Schrodinger#Galilean_invariance and…
22
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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?
21
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9 answers

What is the connection between mechanics and electrodynamics that makes it necessary for both of these to obey the same principle of relativity?

Mechanics obeyed Newtonian relativity (faithful to Galilean transformations) before Einstein. Einstein formulated Special relativity (faithful to Lorentz transformations), and Maxwell's equations became invariant under Special relativity. So,…
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Relativity without constancy of light speed

Using homogeneity of space, isotropy of space and the principle of relativity (without the constancy of light speed), one can derive: $$x' = \frac{x-vt}{\sqrt{1+\kappa v^2}}$$ $$t' = \frac{t+\kappa vx}{\sqrt{1+\kappa v^2}}$$ $\kappa = 0$ denotes…
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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 speed of light must be the same in all reference…
18
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4 answers

How is Newton's first law of motion different from Galileo's law of inertia? If the two are the same, then why is the first law named after Newton?

Galileo's law of inertia (at least what I've learned) is "A body moving with constant velocity will continue to move in this path in the absence of external forces". And Newton's first law says "A body moving with constant velocity will continue…
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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 absolute velocity of the frame of reference These two…
18
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Why are there only $1+3+3=7$ Additive Integrals of Motion?

1. I was reading Landau & Lifschitz's book on Mechanics, and came across this sentence on p.19: "There are no other additive integrals of the motion. Thus every closed system has seven such integrals: energy, three components of momentum, and three…
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3 answers

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 absolute time, existing independently from anything…
14
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Why the Galileo transformation are written like this in Quantum Mechanics?

In Quantum Mechanics it is said that the Galileo transformation $$\hat{\mathbf{r}}\mapsto \hat{\mathbf{r}}-\mathbf{v}t\quad \text{and}\quad \hat{\mathbf{p}}\mapsto \hat{\mathbf{p}}-m\mathbf{v}\tag{1}$$ is given by the…
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