8 votes
Accepted

Alpha particle moving faster than the speed of light

It can't. The fact that you're getting a speed that's larger than the speed of light is a sign something's gone wrong. Check your units. You should not get something larger than $c$ (I just checked ...
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  • 16.4k
5 votes

Can this experiment successfully be used to find out one-way speed of light?

No. "identical apparatus which can shoot a ball at the same speed [in opposite directions]" The same what now? The same speed in two directions? Sure, the apparatus looks like it works the ...
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  • 8,578
5 votes
Accepted

Time differential between two signals sent at two different near-relativistic speeds

This is a very interesting question. Indeed, as a one-way-speed-of-light (OWSOL) experiment the answer is a duplicate of all of the other myriad OWSOL questions: there is no possible experiment which ...
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  • 64.4k
4 votes

Can this experiment successfully be used to find out one-way speed of light?

Edited to add: The first four paragraphs below constitute my original answer. Below that is a new and better answer. Original Answer: Suppose the distance from A to C (and from B to C) is $s$. ...
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  • 12.4k
4 votes
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Poincare invariant Lagrangian?

You are not mistaken, but compared to Lorentz invariance, translation invariance is usually trivial because there are usually no fields with non-trivial behavior under translations - you have $\phi(x)\...
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  • 105k
3 votes

Alpha particle moving faster than the speed of light

Your calculations are incorrect, non-relativistic solution : $$v=\sqrt {\frac Em} = \sqrt \frac {20~MeV}{4 \times m_p} = \sqrt \frac {3.204 × 10^{−12} J}{4 \times 1.673 × 10^{−27} kg} = 2.188 × 10^7 ...
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3 votes
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How to make sense of the length of a rod in Special Relativity, using the mathematical framework of General Relativity?

Let $(\mathcal M,\eta)$ be Minkowski space, viewed as a lorentzian manifold. From only this data, we can rebuild the affine structure and therefore derive the formalism of special relativity from ...
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  • 3,514
3 votes

Units make speed of light dimensionless..?

It's a bit ill-posed but this is defining natural units (maybe look it up on wikipedia for more info), we just set the unit of speed as c (speed of light), so as the speed is unit 1 it means that ($[]$...
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2 votes
Accepted

For someone staying on Earth, what is the minimum possible time to send a spaceship to Alpha Centauri and have it back?

As the spaceship accelarates, at which point the time dilation added due to the incrase of speed starts to increase the total time of the journey measured on Earth? Never. If the ship can accelerate,...
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  • 33.7k
2 votes
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What does size of an inertial frame mean?

The Equivalence Principle (EP) is valid locally: if you perform a local experiment in an inertial frame of reference, you can't say if you're freefalling or not falling, you can't say if you're ...
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2 votes

What does size of an inertial frame mean?

I've never seen it phrased like that, but I understand it as the following. Strictly speaking, the frame is defined locally, on a point. So the further you move from that point, the less inertial the ...
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  • 682
2 votes

Why does four-momentum have the same transformation matrix as spacetime coordinates?

four-momentum is literally the first (proper) time derivative of position, multiplied by mass, so it is a vector with the same transformation rule.
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2 votes
Accepted

Does anything "break" in physics if you allow for instant (faster-than-light) communication?

Yes, it would allow Alice to send a message back in time to herself via Bob if they were moving relative to one another. This is because if they are moving they have different definitions of "...
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  • 5,883
2 votes
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How can any spatially extended object have 4-momentum assigned?

Consider a particular inertial reference frame with coordinates $\{t, x, y, z\}$, and let $t^a$, $x^a$, $y^a$, and $z^a$ be their corresponding orthonormal basis vectors. The set of events in ...
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1 vote
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How can we say potential or chemical energy is part of an object?

In a detailed microscopic model of a system of particles, we can distinguish energy of the microscopic EM field (EM energy), and the other energy (due to mass and kinetic energy of massive particles). ...
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1 vote

Does anything "break" in physics if you allow for instant (faster-than-light) communication?

For one, causality is now broken - in some frame, Alice will know that Bob wants her to jump before Bob has made that thought. This is clearly paradoxical.
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  • 2,031
1 vote
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Qualitative analysis of special relativity effects between moving planes (page-38 of Rindler)

You are overlooking the relativity of simultaneity. In the plane, the passengers at the front and the back see the flash at the same time. In the stationary frame, the passenger at the back sees the ...
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  • 18.3k
1 vote

Could there be some process or event that would make the universe to be Lorentz non-invariant?

It depends on what you mean by "could". "Could there be any process or event that would violate all these symmetries, based on what we know today?" NO, otherwise we wouldn't derive ...
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1 vote

What does size of an inertial frame mean?

I don't have the book but I think he means the following. At any point in spacetime you can assign an inertial frame, similar to how you can assign a tangent line to a point on a curve. The size of ...
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1 vote

Is CPT symmetry a direct consequence of Special Relativity?

Yes. Here is a sketch of how it works, although it can be proven under general assumptions. A Lorentz transformation takes the form \begin{bmatrix} \cosh{y} & 0 & 0 & \sinh{y} \\ 0 &...
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  • 845
1 vote

Can you resolve this special relativity paradox?

I think the question is: "Is it possible for the crate to slide through the window?" The answer is yes. The key is that the crate is not a cube, but a rhomboid. The length of the diagonal of ...
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1 vote
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Using invariant hyperbolas to calibrate between reference frames

In units where $c=1$, the Lorentz transformations are \begin{align} \bar{t}&=\frac{t-vx}{\sqrt{1-v^2}},\quad\bar{x}=\frac{x-vt}{\sqrt{1-v^2}}. \end{align} By following a similar process to what I ...
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  • 2,339
1 vote

Using invariant hyperbolas to calibrate between reference frames

Given the tickmarks on an inertial worldline, calibration is the establishment of the corresponding tickmarks along another inertial worldline using a hyperbola (akin to using a circle, as one might ...
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  • 8,028
1 vote
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Drawing spacetime diagrams assuming absolute time (page-6,Section 1.5, Schutz)

If you're considering a Newtonian/Galilean change of coordinates, the formulas are related as \begin{align} \bar{t}=t,\quad\bar{x}=x-vt. \end{align} This means take any point $p$ in the spacetime. It ...
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  • 2,339
1 vote

Drawing spacetime diagrams assuming absolute time (page-6,Section 1.5, Schutz)

On a Newtonian or Galilean Spacetime diagram (the PHY 101 position vs time graph), the circle is a horizontal line in your diagram. (In a Minkowski diagram, the circle is a hyperbola.) Lines of ...
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  • 8,028
1 vote

Thought experiment in Mach's principle - Can a void universe be considered with special relativity?

If reference frame is not an inertial one, this can be detected "from inside" as laws of physics are not invariant ones in non-inertial reference frames. In case system is rotating, it is ...
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1 vote

Are time and length independent or can one be derived from the other?

"Time" is not a quantity at all, it is a coordinate similar to "north", "east", or "up" (or "x", "y", "z"). What Rindler is saying ...
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  • 5,883
1 vote

Why does four-momentum have the same transformation matrix as spacetime coordinates?

$p^\mu$ has to transform as $p^\mu \to \Lambda^\mu_{~~\nu}p^\nu$ if you want quantities like $$x^\mu p_\mu$$ to be lorentz invariant. For example if you want to measure the mass of a particle you ...
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1 vote

Why does four-momentum have the same transformation matrix as spacetime coordinates?

Matematically, it is only the derivative at both sides with respect to the invariant parameter $\tau$, and multiplication by another scalar invariant $m$. As the Lorentz matrix is a constant, that is, ...
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1 vote

For someone staying on Earth, what is the minimum possible time to send a spaceship to Alpha Centauri and have it back?

The minimum time, as measured on Earth, for anything to travel to Alpha Centauri and back is 8.74 years or thereabouts, if the something was massless. For something massive like a spaceship the time ...
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