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How could any frame of reference be inertial?

In newtonian mechanics, inertial frames are an equivalence class. They can be defined as frames where Newton's laws are valid. If you can find one inertial frame, then you automatically get an ...
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How to represent a pair of inertial frames in relativity?

In Special Relativity we couldn't say in general that the axes of two inertial frames $\:\rm S\:$ and $\:\rm S'\:$ in relative translational motion (boost) are parallel, see Figure-02, except of ...
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Dependence (or lack thereof) of forces on frames of reference

When you say "blocks A and B move with a relative acceleration of -3 m/s2" you are considering the motion of one block in the reference frame attached to the other block (block C). But the ...
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Galilean Transformations Derivation

Let's analyze the spacetime coordinate from the Greek perspective. The Greek will see that the Roman will approach him/her an meet at origin coordinate. Then the Greek perform some measurement at ...
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Recordings of journey traveling near speed of light

Each recorder shares proper time with its corresponding clock, so both sets record and show the same amount of time during playback. The clocks themselves though, after luminal travel, would show ...
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-2 votes

Simple resolution to the twin paradox?

Ronald Hatch proved to us (and it is re-proven every single day with GPS satellites) that the twin paradox simply does not exist. And it does not have anything to do with reversing course or an ...
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Riemann curvature tensor in an inertial frame

The fact that a function's first derivative vanishes at a point does not mean that its second derivative vanishes at that point. Note that for $f(x)=x^2$, $f'(0)=0$ but $f''(0)=2$.
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Simple resolution to the twin paradox?

From Alice's perspective, Bob accelerated, travelled far away and then returned. From Bob's perspective, it is Alice that accelerated, travelled far away then returned. No. For both Alice and Bob, it ...
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3 votes

Simple resolution to the twin paradox?

I'm sorry, Jacques, but as you suspected your explanation is incorrect. The twin paradox seems paradoxical because time dilation is entirely symmetrical, so both Bob and Alice might be expected to be ...
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Are Newton's laws just definitions?

Your statements starting with "in an inertial reference frame" are indeed trivially true, because of the definition of the inertial frame: inertial frame is a frame where the first and the ...
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Simple resolution to the twin paradox?

The calculation you performed clearly shows that distance depends on the observer. This does not resolve the twin paradox since if Alice does the math instead of Bob's perspective then you would get ...
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Invariance of spacetime interval by Schutz

I would suggest you read Landau & Lifshitz argument for invariance of $ds^2$, particularly the Wikipedia link because it states clearly the theorem which is being proved, and it fills in a few ...
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Invariance of spacetime interval by Schutz

The claim is that if the relationship between coordinates in the two inertial frames is linear and if $\Delta S^2 = 0$ necessarily implies that $\Delta S'^2 = 0$, then in general we must have that $\...
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Is gravity a direct result of Lorentz Contraction?

No. Special relativity on its own doesn't imply general relativity. It's not enough to have some invariance principles; you need to "turn on" mass-energy gravitating by specifying how they ...
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Are Newton's laws just definitions?

From a mathematical point of view, they are definitions: they relate mathematical abstractions. But from a physical point of view, they are not definitions: they capture real behavior of real physical ...
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Are Newton's laws just definitions?

Newton's first law is usually taken as the definition of an inertial frame. Hence it is not a special case of the second law, and resolves your concern of the second bullet point regarding the second ...
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Is angular momentum conservation Galilean invariant?

The answer is no. To begin with, a Galilean transformation in three dimensional Euclidean space(time) consists of space-time translation: $(t,\vec{x})\rightarrow(t+s,\vec{x}+\vec{a})$ spatial ...
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1 vote

Is angular momentum conservation Galilean invariant?

But this doesn't make sense to me because the rotational invariance of a system doesn't seem to change when I change to a new inertial reference frame. It can change. Torque depends on origin. As an ...
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FTL travel without time travel (again)

It seems to me we can change the thought experiment so that it is real FTL travel without time travel by slowing the FTL speed to less fast but still FTL speed I think this answer does a good job of ...
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FTL travel without time travel (again)

Is there some fundamental issue with this thought experiment? the first one (o1) shoots an FTL bullet at the other one (o2) This is a magic bullet from a physics point of view. If you start with an ...
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FTL travel without time travel (again)

You say "both bullets reached/missed their target at the same instant each duellist fired". You need to carefully clarify which reference frame you are using here. In special relativity, ...
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Relativity of simultaneity in special relativity

,You and I stand facing each other, looking for a coffee shop. I say, "Oh, there's the coffee shop --- it's about a half a block to the left''. Simultaneously, you say "Oh, there's the ...
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Relativity of simultaneity in special relativity

In the example of the Einstein train, if both the bystander and the train passengers know of the train movement, there is no reality relativity, there is an absolute state of the universe, right? Not ...
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Relativity of simultaneity in special relativity

In special relativity, the 'absolute state of the universe' is the Minkowski spacetime, where events are represented as points. In this spacetime, a point is four-dimensional, and there is no specific ...
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Explanation for invariance of $c$ / Lorentz transformations?

Explanation for invariance of c There is a semi-explanation in Maxwell theory. Basically, this theory says that the interaction between charged particles travels at certain speed. Of course, speed is ...
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Explanation for invariance of $c$ / Lorentz transformations?

Your example of the oscillator moving along a line normal to its axis is an exception, and your game would not show the correct relativistic effect in other cases. In particular, if you had two ...
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Explanation for invariance of $c$ / Lorentz transformations?

The modern view of special relativity is as a geometric theory, with time dilation and similar effects explained as a consequence of different observers having different directions in 4D spacetime as ...
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Why is it necessary that different observers agree on the value of the spacetime interval $ds^2$?

space intervals in Newtonian mechanics In Newtonian mechanics different observers can disagree on the position of events. As an example, let's say I am $100$ m to the left of you. An event, $A$, ...
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Why is it necessary that different observers agree on the value of the spacetime interval $ds^2$?

FIRST POSTULATE OF SPECIAL RELATIVITY The laws of physics are the same and can be stated in their simplest form in all inertial frames of reference. SECOND POSTULATE OF SPECIAL RELATIVITY The speed of ...
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What is the complete proof that the speed of light in vacuum is constant in relativistic mechanics?

There is no proof, because the constancy and invariance of the speed of light in space is an axiom. We took for granted that C is a constant and invariant speed (and also the speed limit in the ...
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Time derivative relation between two rotating frames

$$ (1) \Big(\frac{d}{dt}\Big)_{rot_1} r(t) = \Big(\frac{d}{dt}\Big)_{in}r(t) - \Omega_1(t) \times r(t) $$ where $rot_1$ denotes a coordinate system rotating at $\Omega_1(t)$ relative to the fixed ...
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Doesn't Lorentz transformation disprove aether?

Newton's mechanics assumed absolute space even though its rules obeyed Galilean relativity. The mathematics isn't physics: it's a story we tell about the physics. Einstein's story was clearer than ...
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Lorentz vs Einstein

Einstein came up with the correct set of postulates and framework (all inertial reference frames are indistinguishable, speed of light is invariant, two-way speed of light convention for measuring ...
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2 votes
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Show Energy-momentum operator transforms as a tensor under Lorentz transformations

In regards to your first question, that is, in fact, a definition. To appreciate it, let's recall what a representation is. Let $G$ be some group. A representation of $G$ is a pair $(V,D)$ where $V$ ...
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Problem with Inertial reference frames Rider on a merry-go-round

Ride 1 will just have centipedal force at a constant for the rider. Ride 2 In addition to centipedal force at a constant the rider will be accelerating and decelerating along the track. (Rigid body ...
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Problem with Inertial reference frames Rider on a merry-go-round

If the round-about is inside a train and protected from the breeze. Then the experience of the the rider will be independent of the constant speed of the train. (Consider your experience inside a ...
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2 votes
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Error in Derivation of Time Dilation Formula

The time dilation formula is a special case that applies only to the interval between two events that are in the same location in one frame and in two different locations in another. The example you ...
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Problem with Inertial reference frames Rider on a merry-go-round

You can see that the acceleration of the rider is not changed using polar coordinates. (@Dale used Cartesian coordinates.) See the figure below. This is as expected since there is no acceleration ...
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3 votes

Argument of a scalar function to be invariant under Lorentz transformations

A scalar Lorentz invariant function satisfies $$ f(k) = f(\Lambda k). $$ for all $\Lambda$ satisfying $\Lambda^T \eta \Lambda = \eta$. Let us look at the infinitesimal version of this equation. ...
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2 votes
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How is a locally inertial frame possible in Principle of Equivalence of General Relativity?

In the context of General Relativity, the "lab frame" is not inertial, because it is not freely falling. This is the point of Einstein's "elevator" thought experiments: a freely ...
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