All Questions
Tagged with galilean-relativity special-relativity
103 questions
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Resources to understand problems posed to Newtonian mechanics by Maxwell equations [closed]
Einstein undertook writing his paper on special relativity in response to the CRISIS that emerged in physics when trying to do mechanics for fast-moving bodies in the light (pun intended) of Maxwell's ...
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3
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94
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Is the surface of Earth a global inertial frame?
I understand that a reference frame attached to an observer standing on the surface of non-rotating Earth is not a locally inertial frame but I wonder it can taken as a globally inertial frame because ...
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Throwing a clock out of a white hole
If we look at a clock falling into a black hole (Schwarzschild metric), we will see its time slowing down further and further as it approaches the event horizon.
What would we see by looking, from far ...
- 1,231
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105
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$E=mc^2$ derivation using waves other than light
Can $E=mc^2$ be derived using waves other than light?
Einstein's derivation of his famous equation $E=mc^2$ relies on light waves (or photons). He considered a scenario with a light-emitting material ...
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217
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Is the definition of inertial reference frame circular?
In elementary physics classes, inertial reference frames are defined as a coordinate system which is in constant rectilinear motion (or at least that is how it was defined by my professor). How then ...
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Wave hits beach-example: Does sweeping crest constitute a Frame of Reference?
A long wave rolls in at 1 m/s and hits an almost parallel beach.
It's 900k km long, and hits the beach at .1 micro degrees.
Basic math tells us the crest of the wave rides down the beach at a speed of ...
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Analogy between Galilean relativity and thermal physics?
So I was thinking about an analogy, that could potentially be used for an explanation or at least to take a different perspective on thermodynamics as it is. But I don't want to abuse the analogy, so ...
- 2,987
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It seems as if Special Relativity breaks Galileo's principle of Relativity [closed]
simultaneity is redefined in special relativity because of the discovery that the speed of light is always constant. However, I think this violates Galileo's relativity, which states that you cannot ...
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3
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If an observer was trapped in a closed box with no way to interact with the external surroundings how will he know if he is moving or at rest [duplicate]
I am a high-school student. Recently we learned the concepts of relative motion and velocity. The idea that anything in motion can subsequently be at rest depending on the frame of reference ...
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The principle of relativity and why Inertial frames attribute the same velocity to one another
In introductory texts introducing relativity, it is always assumed that frames measure the same velocity for each other. For example if frame S' moves at velocity v with respect to respect, then S ...
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Galilean transformation vs boost matrices
I'm confused about the difference between a Galilean transformation and boost with reference to their matrices. I was given four statements (listed below) but I'm not sure what I should be looking for ...
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Is a Lorentz transformation allowing an infinite value $c$ still a proper Lorentz transformation?
Is it correct to say that inertial systems are related by Lorentz transformations even if we do not know if the "invariant speed" is finite or infinite? To me, this is incorrect because $c$ ...
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Schutz description of Galilean invariance of interval
In B. Schutz's textbook "A First Course in General Relativity", there is a sentence on page 172 discussing Galilean relativity and how the distance between events is invariant in coordinate ...
- 147
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Generalizing the Galilean law of addition of velocities using the Lorentz transformation [closed]
I am reading about how to generalize the Galilean law of addition of velocities using the Lorentz transformation, but I am confused about one step.
Here, I have the following equations for Lorentz ...
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Is there a general methodology for causal nets of observables regardless of kinematics?
The typical definition of a causal net of observables in quantum theory is to consider, for the case of a (globally hyperbolic) spacetime $M$, the category of open sets $O(M)$ ordered by inclusion, in ...
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Why is it "forbidden" to use EM waves as a way of detecting motion in two different inertial frames?
Constant motion can not be detected by neither particles (because of inertia) nor mechanical waves ( because they need a medium ). However when you consider light for example and assume it does not ...
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Why doesn't Galilean relativity lead to a contradiction in SR?
Two identical spaceships commanded by Alice and Bob are at rest next to each other in outer space. The clocks of the spaceships are synchronised; and when they are close by Alice can see Bob's clock ...
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D Alembert Wave Equation is not Gallean Invariant but Why y=Asin(wt-kx) is Gallean Invariant? [duplicate]
I just watched this video from MIT 8.04 Quantum Physics I by Barton Zwiebach, explaining Galilean transformation of y=Asin(wt-kx).
I have a confusion, are ordinary waves Galilean invariant or not? ...
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536
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Confusion regarding bundle structure of Galilean spacetime in Penrose's The Road to Reality
I am reading Roger Penrose's The Road to Reality. In section 17.3, I encounter the following passage. To give a context, Penrose was explaining that even though an Aristotelian spacetime can be ...
- 702
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Center of Mass and Systems of Particles in Galilean relativity
Consider a reference frame in which two particles move with constant velocities $\vec{v}_1 = v_1 \hat{i}$ and $\vec{v}_2 = -v_2 \hat{i}$. Their center of mass would be the vector $\vec{R} = \frac{(...
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What is metric (invariant) in Newton mechanics (equivalent to spacetime interval of Minkowski space)?
The answer might be obvious for those with much experience, but I could not get it via web search.
https://en.wikipedia.org/wiki/Minkowski_space
From the second postulate of special relativity, ...
- 151
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3
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Einsteinian principle of relativity in the limit of infinite propagation velocity
We can transform between inertial frames of reference using either the Lorentz transform in special relativity or the Galilean transform in the classical limit.
The Galilean transform gives: $$ x' = x ...
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Invariance over Galilean transformation [closed]
I want to prove that the Wave Equation is not invariant under Galilean Transformation. I'm having a little trouble with it but this is my attempt.
1. First of all, what does it mean by "not ...
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Why not define tensors under Galilean or Poincare transformations?
I have seen vectors (and tensors, in general) defined under rotations,
$$V^i=R^i_{~j}V^j$$
and under Lorentz transformations,
$$V^{\prime\mu}=\Lambda^\mu_{~~\nu}V^\nu$$
where $R,\Lambda$ are the ...
- 12.3k
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Aristotelian vs Galilean relativity in terms of bundles
In page-385 of Roger Penrose's Road to Reality, the following is written:
In our Aristotelian scheme, it is appropriate to think of spacetime as simply the product:
$$ \mathbb{A}= \mathbb{E}^1 \times ...
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How could any frame of reference be inertial?
The image below shows that a bystander watching the merry-go-round is in an inertial frame of reference. However, to nitpick, wouldn't the observer still be accelerating because it's on Earth?
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Galilean to Lorentz Transformation
I happened to come across a derivation of the Lorentz Transformation stemming from the Galilean Transformation. In two frames $S$ and $S'$ where the position and time coordinates for the frames are $(...
- 1,637
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88
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How can I show that the one-dimensional wave equation (with a constant propagation velocity $c$) is not invariant under Galilean transformation? [duplicate]
The one-dimensional wave equation is given by
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9
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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 ...
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What is the relationship between the Galilean group and the Poincaré group?
What is the relationship between the Galilean group and the Poincaré group?
Are they siblings within the Lie group? Or does the Poincaré group contain the Galilean group as a subgroup?
I'm not so much ...
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Why does the derivation for the Michelson & Morley time difference assume Earth moves in only one direction relative to the Aether?
In the Michelson and Morley experiment, we predict with Galilean relativity and the assumption of the existence of a luminiferous aether that there should be a time difference between the two beams of ...
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Assumptions in Galilean and Relativistic Frame Transformation
While deriving the frame transformation equations, either the Galilean Transformation or Lorentz transformation. I have seen almost all authors mentioning/assuming that if an inertial frame $\textbf{S}...
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How should this argument (about the non-validity of Special Relativity) be interpreted? [closed]
I have read the following (here) by Stephen J. Crothers:
Einstein’s Special Theory of Relativity requires systems of clock-synchronised stationary observers and the Lorentz Transformation. Without ...
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729
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Why is the phase of a matter wave not Galilean invariant? And what does this say about the Schrödinger equation? [duplicate]
Matter waves are not Galilean Invariant
Consider a non-relativistic freely-propagating matter wave in an inertial frame $\Sigma'$ moving along the $x'$-direction with kinetic energy $E'=1/2m_0v'^2$, ...
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Length measurement in Galilean relativity. Problem understanding a paragraph from Resnick's Relativity
The paragraph below is taken from the book An Introduction to Special Relativity by Robert Resnick.
Let A and B be the endpoints of a rod, for example, which is at rest in the S-frame. Then the ...
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What is the role of the mass Casimir invariant in Galilean and what it's actual role in special relativity? [closed]
What is the role of the (mass) Casimir invariant of the algebra of relativistic symmetries in Galilean and what it's actual role in special relativity?
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Galilean transform as limit of Lorentz one
Galilean transform:
$$\begin{pmatrix} ct' \\x' \end{pmatrix} = \begin{pmatrix} 1 & 0 \\-\beta & 1 \end{pmatrix}\begin{pmatrix} ct \\x \end{pmatrix}$$
Lorentz transform:
$$\begin{pmatrix} ct' \\...
- 1,158
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Effect of relative velocities in time dilation thought experiment
Related
Classical mechanics thought experiment:
We throw a ball upwards with a velocity of $10~m/s$ we know that the ball will fall on ground in 2 seconds.
We throw another ball now with a velocity ...
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102
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Prerelativity physics, Special Relativity, and General Relativity formalisms summary [closed]
In order this have a better understanding of "the big picture", a tried to do the following summary, but I can't really complete it for GR. This based on the introduction chapter of Wald's ...
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1
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251
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Understanding tensor and covariance
I'm really struggling to understand the use of tensors when we want to have a covariant equation.
From what I understand, if we write an equation using tensors only, then the physics behind it will be ...
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Mathematical model for Euclidean space in classical mechanics
Even knowing some basics of maths and physics I get puzzled when I try to systematise some concepts for better understanding. One is basically on how all the mathematical concepts comprise the model ...
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Time evolution of Galilean boost
I was introduced the generator of Galilean boost $K=mx-pt$.
I was given an Hamiltonian with several particles: $H=\sum_i \frac{p_i^2}{2m_i}+V(|x_i-x_j|)$ where the potential only depends on the ...
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Simultaneous Lorentz and Galilean invariance
The introduction of the Lorentz transformation is usually motivated by the Galilean failure when it comes to Maxwell's equations.
Are there physical systems that exhibit both Lorentz and Galileo ...
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Inertial frames in Newtonian mechanics and special relativity
In the literature I have seen the following definition of an inertial frame:
A frame is called inertial if any material point interacting with no other bodies or fields moves with constant velocity in ...
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9
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Suppose you are in a closed box which is in motion [duplicate]
Suppose you are inside a closed box which is moving with a constant speed with no acceleration whatsoever. You cannot see outside the box. If you are given all the instruments you need, what ...
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Why are Maxwell's equations correct and not Newton's laws of motion?
In many books, while introducing Special relativity it is shown that Maxwell's equations are not consistent with Galilean transformations. So either Galilean transformations (and consequently Newton's ...
- 1,108
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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}...
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Galilean boost on transverse momentum in infinite momentum frame
In the infinite momentum frame in $11$ dimensions, if we do a large boost along the $x^{11}$ direction, the total mass shell energy $E$ can be shown in a non relativistic approximation to be $ E - p_{...
- 1,105
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Absolute Space & Inertial Frames
When we solve the twin paradox we say something like the traveling twin has a Rindler Metric while the stationary twin has a Minkowski metric, or more plainly, the traveling twin experiences non-zero ...
- 879
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Inönü-Wigner contraction of Poincaré $\oplus$ $\mathfrak{u}$(1)
Metric = (-+++), complex $i$'s are ignored.
Using the following decompositions of the Poincaré generators,
I can write the Poincaré algebra as
I can get the Galilei algebra using the following ...
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