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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What is the relationship between the “mass” of QFT and that of Newtonian mechanics?

In QFT we work with Lagrangians which contain terms $m$ such that the relativistic relation $E^2 = p^2 + m^2$ is satisfied. By classical analogy $m$ is called the 'mass'. We note that due to the ...
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Relativistic momentum (Lorentz boost) low velocity expansion

If I have a momenta $p^{\mu}=(E, p_x, p_y, p_z)$ and transform it via lorentz boost in x-direction with velocity v I'll get for the new 0th component $E'=\gamma E + \gamma v p_x$ why is this in the ...
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Do all moving object appear contracted?

In the derivation of Lorentz contraction my prof considered a rod moving away from you with speed $v$. In this case the rod appears shrunk by a factor gamma. But now let's consider a rod moving ...
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How can we say that difference in energy between 99.99% and 100% of speed of light is infinite? [duplicate]

How is it not possible for a particle to attain 100% speed of light and what will happen if it attains the speed of light?
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1answer
63 views

Spacelike interval and length contraction

I am having a serious trouble finding an agreement between the two facts in Special Relativity: (1) given two events $A$ and $B$ in spacetime separeted by a spacelike interval $s$, the distance in ...
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What is the physical meaning of $\alpha$ in this disintegration problem?

I am taking a course where I have to solve the following problem related to the disintegration of a baryon in a proton and a pion $(\Lambda \to p^+ + \pi^-)$: Assume that a $\Lambda$ particle with ...
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1answer
140 views

Behavior of the Electric- and Magnetic-field under time reversal and parity

The behavior of the electric- $\mathbf{E}$ and the magnetic-field $\mathbf{B}$ und time reversal and parity can be calculated in different ways. My first solution is to study the transformation ...
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Kinematic equations of a cascading particle decay

This paper discusses different measurable quantities that can be used to search for unknown particles at particle accelartors. For the following decay it introduces the invariant mass $m_{XY}$: It ...
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How to obtain Thomas Precession from lie algebra of the Lorentz group? [closed]

it seems to be possible that you can get the Thomas Precession just through the commutation relations of the Lorentz group. With Thomas Precession i mean, that in general the product of two boosts is ...
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Speed of an antimuon in a pi meson decay [closed]

I'm trying to confirm the speed of an antimuon in the $ \pi^+ \rightarrow \mu^+ \nu_{\mu}$ decay through the laws of conservation but it doesn't add up. I'm using $m_{\pi} = 139.6 \ \frac{MeV}{c^2}$, ...
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Simple special relativity problem [closed]

A body at rest in a frame of reference $S$ disintegrates into two pieces moving in opposite directions. The masses of each fragment are $3.0 \ kg$ and $4.0 \ kg$ and their velocities $0.8 \ c$ ...
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Why is $V=(1/2) m^2 \phi^2$ for a free relativistic scalar field of mass $m$?

Bit of a basic question here but how come for a free relativistic scalar field of mass $m$ such as Klein Gordon theory, we take the potential to be $$V=\frac{1}{2} m^2 \phi^2$$ Is the mass term ...
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Is presuming that any linear uniform motion is transformed into another one sufficient to assume that Lorentz transformation must be linear?

I've read this condition in a script: The Lorentz transformation must be linear because any uniform motion must be a uniform motion in any inertial frame. All other proofs that I've read so far need ...
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1answer
56 views

Metric of an accelerated reference frame (without gravitation)

If we look at a flat Minkowski space-time (without any gravitation) an choose an accelerated frame of reference, what happens to the metric tensor is it still in Minkowski coordinates or will he be ...
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51 views

A Magnetic Vortex in a Magnetic Vortex

This is not to scale. Can a magnetic vortex be compressed into a flat disk using magnetic entrapment? Can a magnetic vortex happen inside another magnetic vortex?
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4answers
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What if a light clock travels perpendicular to mirrors that make up the clock?

I'm guessing you're all familiar with the classic intuitive way of explaining time dilation: with a light clock traveling at velocity v directed at a parallel direction to the mirrors that make up the ...
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Magnetic field of a circular particle accelerator

Suppose there's a $500 \ GeV$ proton beam ($q=1.6 \times 10^{-19} C$) inside a circular particle accelerator, what would be the magnetic field intensity $B$ in Teslas required to keep it stable at a ...
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1answer
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Why does an electromagnet attract iron according to Special Relativity?

I saw a video of Veritasium on "How Special Relativity Makes Magnets Work" and came up with a question. So please watch the video first before answering my question as it is related to the video. 1) ...
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1answer
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Take advantage of time dilation or create a warp drive? [closed]

It is my understanding that time dilation slows down perceived time relative to the outside of a given vessel as it approaches the speed of light. Does that not mean that the inhabitants of said ...
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Why is special relativity still in use, if general relativity is more broad?

I always thought special relativity is only there because it is the building block for "The General theory of Relativity", until recently I encountered a text from my course book given below. A ...
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Einstein's famous equation $E = mc^2$

A fellow engineering student told me many years ago, that $E = mc^2$ means is that as an object of mass $m$ approaches $c$, the speed of light, it's mass increases and, at the speed of light, becomes ...
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If electric fields can't pass through a grounded shield, how can a magnetic force be generated on moving charges outside a wire? [duplicate]

Say an electron outside a wire is moving with the same velocity as the electrons inside, then due to Lorentz contraction, an electric field would be generated in the outside electron's frame of ...
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Speed of a point on a concentric disk setup

I have been really solving this question that my friend and I had thought of while discussing about speed of light. Imagine there is a set-up where there is a light source that is surrounded by a ...
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“Warp-drive” thought experiment

Why wouldn't this "warp-drive" work? Assuming we can build a flywheel that can survive near light speed and have an onboard power storage or beamed energy that can spin it up to that speed and back ...
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What the common examples of $E=mc^2$? [duplicate]

this theory say's mass convert into energy and energy convert in to mass Whats he example of energy convert into mass?
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Twin paradox in special relativity [duplicate]

The Twin Paradox involves 2 observers, usually twins. Let them be named A and B. A remains at rest in the same reference frame as Earth while B is in a separate reference frame moving at velocity v, ...
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Coordinate Time and Proper Time/Simultaneity [closed]

At close to the speed of light, clock A is running slower than "stationary" clock B. Does clock A enter the future time reference of clock B as it slows down? Trying to understand where the forward ...
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Relativity: easy spaceship scenario. easy questions [duplicate]

Your spaceship is traveling at 1/2*c and you approach Bob's spaceship going -1/2*c in the opposite direction. Relative to you, Bob is going the speed of light, and of course he has a giant ticking ...
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Derivation of $E=pc$ for a massless particle?

In classical mechanics, massless particles don't exist because for $m=0$, $p=0$. The relativistic relation between energy, mass and spatial momentum is: $E^2= (pc)^2 + (mc^2)^2$ . So it is said that ...
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How can parity be meaningful in an affine space?

I've recently begun a course in QFT (within a Physics Master's), and despite (admittedly limited) reading I can't get my head round the idea of parity. Here's what I think I understand: the Minkowski ...
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What is the correct relativistic distribution function?

General Statement and Questions I am trying to figure out the proper way to model a velocity/momentum distribution function that is correct in the relativistic limit. I would like to determine/know ...
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1answer
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Range of a mediating particle

My book describes the derivation of the formula $R\approx\hbar/2mc$ by: $$(\Delta E)(\Delta t)\geq\hbar/2$$ The violation of energy conservation is $\Delta E=mc^2$ to create the particle’s mass. Also, ...
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Why light moves sideways?

Greatings! I'm trying to understand special relativity and have one question bugging me. In almost every book or video about the subject there is a thought experiment with moving light clock. I hope ...
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1answer
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Special relativity, calculate velocity

Lets assume that a spaceship travels to a star 8 light-years away, in a time its crew considers to be 8 years. How do we calculate the speed of the ship? Is at as simple as saying: since the star is 8 ...
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45 views

Integral Represation of Four Current with proper time

I have a question about the four current in covariant representation. the four current is defined as $$ J^{\alpha} = \binom{c\rho}{\vec{j}} $$ and i'm having a point charge, ...
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87 views

How can magnetic fields pass through a grounded shield?

Suppose an electron outside a wire is moving with the same velocity as the electrons inside, then due to length contraction, there would be excess positive charges per unit area causing attraction of ...
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1answer
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How to spatially rotate the frame of reference Faraday Tensor? Special Relativity and Galilei Transforms

Hey I'm currently just starting out doing special relativity and I stumbled upon following problem: If I have the faraday antisymmetric tensor $F^{\alpha \beta}$ and I perform a spatial rotation of ...
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What makes energy content of a body harder to accelerate it?

There was this video http://www.youtube.com/watch?v=Xo232kyTsO0 where the host explains the "Real meaning of $E=mc^2 $" by saying that even at the most microscopic level even the fundamental particles ...
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Will my mass increase in my perspective while approaching near the speed of light?

Suppose I start my journey by a spaceship accelerate the velocity to 0.7c from Earth. Now the question arises that- Will my mass increase gradually as I'm going to a speed of .7c in my perspective and ...
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How does this incorrect model of a wire give the correct result for B-field produced?

I see in Griffith's book Introduction to Electrodynamics, 4th edition, the following model (paraphrased). Consider a wire (infinitely-long) with positive linear charge-density $\lambda$ moving to ...
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Why does inter-electron distance in wire grow with acceleration?

When you have an electrically neutral wire, and apply a voltage across it, free electrons (provided by source) flow through the wire and thus an electric current is created. Assuming an ideal ...
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Space time diagrams and world lines

When you draw a space-time diagram and the associated world line for an object moving through space-time, the diagram will be dependent upon the reference frame you are observing from, right? Like for ...
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What if an object had enough speed that from another perspective it was enough to form a blackhole? [duplicate]

Suppose a baseball is traveling through a vaccum towards another object extremely fast. If it's travelling fast enough then shouldn't its kinetic energy give it enough mass that the observer thinks it ...
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1answer
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Quantum Mechanics and Causality

Causality coupled with special relativity states that no particle can travel faster than light. Interpreting in terms of quantum mechanics, it means that dirac delta wave-function at x=a, can't ...
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1answer
108 views

An apparent contradiction to $m = m_0/\sqrt{1-v^2/c^2}$ [duplicate]

Using theoretical framework of the special relativity, we can show that the quantity that we classically regard as energy does have a property of inertia. And particularly, if the total energy of a ...
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Deriving proper time invariance from first principles

I'm trying to learn special relativity right now, and for various reasons I'd like to start by getting the invariance of proper time, rather than starting with the Lorentz transformations - if you can ...
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Confusion in Special Relativity: Rotating frame of reference

Suppose we are observing a rotating frame from an inertial frame, free from gravity, and try to measure the circumference of a circle drawn in the rotating frame. Since our measuring rod would be ...
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Why is it that when I do some substitution, I get $p=1$ for a photon? [closed]

I know that this is wrong, but where did i make a mistake? I just use a few equations and substitutions and I get that the momentum of a photon is one. Here is my math: $p=h/λ$ $p=hf/c$ (substituted ...
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What is the meaning of the square of the four-velocity?

The square (or dotproduct) of the four-velocity u is -1 or 1 (depending on the metric convention and with c=1, I think (in flat spacetime)). What does this physically mean? It sounds like "my speed" ...
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1answer
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Why a motionless proton doesn't feel any force in a magnetic field according to special relativity?

In this ( https://www.youtube.com/watch?v=1TKSfAkWWN0 ) specific video uploaded by Veritasium on YOUTUBE , we come to know about how special relativity makes magnets work. We observe that when a ...