The special theory of relativity describes the motion and dynamics of objects moving at significant fractions of the speed of light.

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Why cannot a perfect clock exist?

I have a question about the reason Feynman gives for why a perfect clock - a clock that remains in sync while in motion with a stationary clock, cannot exist. It is clear why the "light clock" (...
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Constant Jerk Relativistic Rocket [duplicate]

A quick google search will give many helpful pages and calculators regarding constant acceleration relativistic rockets, but my question is somewhat different. What if jerk is the parameter to be ...
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Is static gauge quantization of the particle equivalent to covariant quantization?

In the covariant quantization one is able to get directly (from the constraint $p^\mu_\mu+m^2=0$) the Klein-Gordon equation. But if one uses the parametrization $\tau=X^0$ then the Schrodinger ...
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Prove that the spacetime interval is not invariant under Galilean transformations [closed]

The spacetime interval $(\Delta s)^2 = (\Delta x)^2 + (\Delta y)^2 + (\Delta z)^2 - c^2(\Delta t)^2$ is invariant under the Lorentz transformation and this isn't the case for the Galilean ...
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Is the double slit experiment valid in all inertial frames?

In a double slit experiment done with particles having mass (say electrons), the results are inferred as being caused by probability waves. The wavelength of these waves is dependent upon the velocity ...
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Is there a geometric interpretation of the spacetime interval?

In Euclidean space, the invariant $s^2 = x^2+ y^2+ z^2$ is equal to the length square of the position vector $r$. This is easily understood and can be represented geometrically in a graph. On the ...
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Potential energy in $E_f^2=(mc^2)^2+(pc)^2$?

Let's consider $$E_f^2=(mc^2)^2+(pc)^2$$ where the $mc^2$ is the rest energy due to the rest mass -- in Finnish "lepomassa". $$ \sqrt{(mc^2)^2+(pc)^2} - mc^2~=~(\gamma-1)mc^2$$ is the kinetic ...
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Boosting massless particles

How does one calculate the boost matrix to go from a photon of (standard) four-momentum $k^\mu = (k,0,0,k)$ to $p^\mu = (p,0,0,p)$? (in terms of $|p|/|k|$) Weinberg in his Quantum Field Theory Vol.1 ...
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1answer
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What is a Lagrangian of a photon? [duplicate]

In sense of classical mechanics+special relativity what is lagrangian of a photon? Lagrangian of a relativistic massive particle is as follows: $$ L_{massive}= -mc\sqrt{c^2-v^2} $$ So is it a zero?
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Does constant acceleration (from starship crew pov) to relativistic speeds look newtonian?

The last 25 years I thought that time dilation, mass increase and length contraction is "scaled" that way that on the first glance the crew of an accelerating starship could think everything is ...
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Potential energy in Special Relativity

In Special Relativity, the energy of a free particle is $E^2=p^2c^2+m^2c^4$. But what would be the energy when there is potential energy? If it's something like $E=\sqrt{p^2c^2+m^2c^4}+U$, what ...
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Time dilation derivation of special relativity

In almost all of the derivations using the postulates of special relativity (SR), we use experiments involving light signals. For example, we make a clock using a light signal or measure lengths using ...
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Light-cone coordinates

The light-cone coordinates are defined as $$x^{\pm} ~=~\frac{x^0 \pm x^3}{\sqrt{2}}.$$ Then in the light cone coordinates the position 4-vector becomes: $(x^+, x^-, x^1, x^2)$ . Zwiebach, in his A ...
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How should I interpret relativistic mass? [duplicate]

If I have a mass that gets accelerated to a near the speed of light, before it gets I would think its relativistic mass would expand its Schwarzschild radius enough to turn it into a black hole. I ...
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Is spacetime absolute?

As I understand it Newton's Laws imply that space is relative, as the laws of physics are the same in all inertial frames and as such there is no way, even in principle, to distinguish a frame that is ...
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183 views

Special Relativity and Gravity

As Einstein was seeking a relativistic theory of gravity, he thought that special relativity should be upgraded to general relativity thus promoting the Minkowski space to curved pseudo-Riemannian (...
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2answers
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What do physicists mean when they say “speed of light”?

Does it make sense to say, "The speed of light varies?" Some may say right off the bat "Yes, it changes as a wave passes through a different medium." However, I'd like to say no, because when I hear ...
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Theoretically if you passed the speed of light in a medium, would there be a sonic boom equivalent?

I know that it is technically impossible to reach the speed of light in vacuum since the mass of the object travelling would reach infinity. However in a medium, would there be some sort of ...
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Does quantum mechanics allow faster than light (FTL) travel?

Let's suppose I initially have a particle with a nice and narrow wave function[1] (I will leave these unnormed): $$e^{-\frac{x^2}{a}}$$ where $a$ is some small number (to make it narrow). Let's also ...
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Physics behind this neutrino-related joke

In the comment section of a newspaper article reporting on the 2015 Nobel Prize for Physics, which was awarded for work on neutrino oscillation, I found the following joke: "I'm sorry, we do not ...
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Does my interstellar pole thought experiment violate casualty? [duplicate]

I have heard that it is impossible to send a signal faster than light. However, what if I had a long (4.5 light years) pole and placed one end on Earth and the another end around Proxima Centauri. If ...
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How can length contraction result in electron circular motion in a magnetic field?

If you ask around about magnetic fields, you will read seemingly-authoritative articles which say magnetism is a consequence of length contraction. This is widely taught and is repeated in answers ...
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Why does gravity affect time?

So Special Relativity states that for all non-accelerating objects of matter the laws of physics are the same. I'm confused on why this law of physic applies to objects in acceleration and gravity ...
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Could this be a valid reason for why the universe could be infinite?

So, special relativity says that every frame is as good as any other frame, and there is no absolute frame of reference. All good. Suppose there is a finite universe (let's just assume the universe ...
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Minkowski spacetime: Is there a signature (+,+,+,+)?

In history there was an attempt to reach (+, +, +, +) by replacing "ct" with "ict", still employed today in form of the "Wick rotation". Wick rotation supposes that time is imaginary. I wonder if ...
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Observing light speed

Consider an observer B is moving with speed $0.8c$ relative to another observer A in standard-configuration (I think it is called that in english: that the system B is only moving along the $x$-axis ...
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The origin of the value of speed of light in vacuum

Meaning, why is it the exact number that it is? Why not 2x10^8 m/s instead of 3? Does it have something to do with the mass, size or behavior of a photon? To be clear, I'm not asking "how we ...
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How can relativistic effects be the cause of magnetic forces when the normal speeds of carrier charges are so low?

I had read here that magnetism arises from a current because of the special relativistic effect associated with the speed of the moving charges in that current. However that speed is only on the ...
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What is the physical significance of Rapidity in Relativistic kinematics?

Recently I have came across a new term called rapidity in relativistic kinematics. We are using it in relativistic kinematics due to its additivity whereas velocity is not a additive quantity in ...
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Why must the speed of the aether wind be so small compared to the speed of light?

I was doing some reading on the Michelson-Morley Experiment. One of the principle equations for the equations is this one. $$\frac { 2w }{ c } \times \frac { 1 }{ 1-\frac { { v }^{ 2 } }{ { c }^{ 2 }...
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Deduce time dilation from a Minkowski diagram?

Is it possible to deduce the phenomena of time dilation from a carefully constructed Minkowski diagram? For example, consider the image below. Here, Let us say the Euclidean distance between the ...
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Determining the velocity of an inertial frame of reference

Back in grade 12 I was told by my physics teacher that one would have no way of determining the velocity of an inertial frame of reference without comparing it to another (e.g. if a person was in a ...
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Why is light in vacuum so slow? [duplicate]

Accepting the speed of light in vacuum and infinite mass and all that, I wonder why light does not have infinite speed? I know light does not have rest mass, but people use the term infinite mass ...
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1answer
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What speed does a proton have with the energy 7 TeV?

So this is a question from the 2014 admission test for Chalmers University of Technology, Gothenburg. To clarify some rules (cited and translated from the test): Calculators and physics ...
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Lorentz transformation of Gamma matrices $\gamma^{\mu}$

From my understanding, gamma matrices transforms under Lorentz transformation $\Lambda$ as \begin{equation} \gamma^{\mu} \rightarrow S[\Lambda]\gamma^{\mu}S[\Lambda]^{-1} = \Lambda^{\mu}_{\nu}\gamma^{\...
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What experiments have been done that confirm $E=mc^2$?

What experiments have been done that confirm $E=mc^2$? Are there experimental results that contradict $E=mc^2$? Or are experimental results consistently showing this famous formula to be true?
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In a nuclear reaction, where does the energy go?

Lets say two hydrogen fuse together, where does the energy released go? Is it carried away as momentum imparted on the helium atom? Is it carried away in neutrinos? Is it carried away as gamma rays? ...
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Phase space volume and relativity

Much of statistical mechanics is derived from Liouville's theorem, which can be stated as "the phase space volume occupied by an ensemble of isolated systems is conserved over time." (I'm mostly ...
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Michelson-Morley expression for relative phase

I am trying to find the relative phase when ether is propagating vertically versus when ether is propagating horizontally. The question is written below When the light (of wavelength) is split at the ...
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How is viscosity related to the forces in fluid?

I think it was that the forces are only perpendicular but do not know how this is related and from where it comes from. EDIT: I am asking for the difference between viscous and non-viscous fluid in ...
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If changing inertial reference changes velocity/energy, shouldn't that produce conflicting observations of gravity?

A particle $X$ has mass $m$ and passes above observer $A$ with an apparent horizontal velocity $v$. Colinear with these is another observer $B$ moving with apparent horizontal velocity $u$. Colinear ...
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Calibration of a clock [duplicate]

I was inspired by this interesting question on this forum: How do I measure an earth year without a clock? Say you're stranded on an alien planet without any significant tools. How would you ...
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1answer
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Why does photon have to travel in sideways to hit the light clock?

From this article, Let’s say Alice is holding a light clock, and Bob is watching her run by, while holding it, with speed V. Alice is standing still (according to Alice), and the time,$ \tau$, ...
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Finding the momentum of a muon in $\pi\to\mu\nu_\mu$ [closed]

The $\pi$-meson's mass is 139.57 MeV, and it decays into a muon and a neutrino. The muon has a mass of 105.4 5MeV, and a proper lifetime of $2.197 \times 10^{-6}$. The neutrino can be treated as ...
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Given the intervals of a punctured flat spacetime how to reconstruct the intervals of the complete flat spacetime?

A set $\mathcal S$ of events can be characterized as a flat unbounded spacetime through a function $s^2 : \mathcal S \times \mathcal S \rightarrow \mathbb R$ which assigns spacetime interval values to ...
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Tensor as outer product

This is a problem I am trying to solve and need help with. Given a $ \left( \begin{array}{} 0 \\ 2 \end{array} \right)$ tensor h such that h$(\quad ;A)=\alpha $h$(\quad ;B)$ for any two vectors $...
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Does relative velocity time dilation occur at any relative velocity?

The reason I ask this question is due to the fact that every example I've found is presented such that the relative velocity is "near the speed if light", or that it happens as the object " approaches ...
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Relativistic spaceships moving towards each other

There are two spaceships, A and B, moving towards each other, such that they will eventually pass each other. At a point equidistant from both ships, their velocities are both 0.5c towards that point. ...