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Questions tagged [special-relativity]

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 in QFT what really matters is $\exp(\mathfrak{so}(1,3))$ instead of $O(1,3)$?

In QFT fields are classified according to representations of the Lorentz group $O(1,3)$. Now, most books when getting into this say that in order to understand the representations of $O(1,3)$ we need ...
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Time dilation caused by gravity and special relativistic velocity [closed]

I am working on an exercise for my Relativity class. The exercise is: Two atomic clocks are transported in two aeroplanes once around the Earth in either eastern or western direction. For ...
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Length contraction of an accelerating rod

Let us assume a rod of length, $4l$, initially at rest. The coordinates are defined s.t - (assuming uniform density) $$X_{back-end}(0) = -2l$$ $$X_{front-end}(0) = +2l$$ $$X_{mid-point}(0) = 0$$ ...
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1answer
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Relativistic quantum mechanics ${}$

I am reading Weinberg's book "Quantum theory of field". Сould you explain to me the following things? Vol.1, page 60: How are we equating the coefficients? How we find the formula (2.4.8)? 2.3.10: ...
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Inner product axioms and Special Relativity

In Linear Algebra, an inner product is a function $(\cdot,\cdot): V \rightarrow F$ , where $V$ is a vector space over the field $F$. This function satisfies the usual three axioms (Conjugate symmetry, ...
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A (probably silly) doubt regarding motion of bar magnet

So my instructor was teaching electrodynamics the other day, and he analysed the electric and magnetic field of the bar magnet moving with velocity v in x direction, first from the ground frame and ...
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1answer
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Is Lorentz and Galilean invariance mutually exclusive?

I know that the classical mechanics stays valid under Galilean transformation. The same argument applies to relativistic equations and Lorentz transformation. My question is, can a set of equations ...
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2answers
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Special Relativity Confusion

Let's say there are 2 points X & Y and a spaceship is moving from X to Y at some very high speed. According to X & Y, let's say the spaceship takes 800 seconds to go from X to Y. According to ...
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Deriving Doppler effect in observer's frame

I am attempting to find the Doppler factor from the frame of the observer. In the frame of the observer, the source is moving at velocity $v$ towards the observer. Since the source emits at time ...
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1answer
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Indices in Special Relativity

I am studying special relativity and I can't figure out what is the difference between the matrix - index notation between: $$ Λ_{α}{}^{β}, Λ^{α}{}_{β}, Λ^{αβ} ,Λ_{αβ} $$ Why do we introduce this ...
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Why is the space-time interval squared?

The space-time interval equation is this: $$\Delta s^2=\Delta x^2+\Delta y^2+\Delta z^2-(c\Delta t)^2$$ Where, $\Delta x, \Delta y, \Delta z$ and $\Delta t$ represent the distances along various ...
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How do you solve the twins Paradox? [duplicate]

I'm a beginner physics student only studying elementary AP-level physics and calculus, so when I came across the conceptual basis of the twins paradox I was, of course curious. People often explain ...
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Is speed of light constant in every inertial reference frame, or does it just seems constant for observers? [on hold]

Here is an hypothetical experiment. (I already used this experiment in previous question but the question was diferent) : Let's call k the distance travelled by light in 1 second We have two ...
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Why we get relativistic momentum without length contraction?

My last question was wrongly duplicated. We've already known that "p=γmv" . v is particle's velocity depends on our rest frame and mass too. But shouldn't we consider particle's momentum by its ...
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1answer
125 views

Experimental proof of light speed isotropy

Where is the experimental proof that observers travelling toward or away from a light source, will always find that light from that source measures the same speed, regardless of their own speed?
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Light moving toward a moving observer's reference frame

The speed of light is supposed to be the same for all observers in an inertial frame, no matter the observer's speed. As a result, time slows down for observers moving quickly, and this explains why ...
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Length contraction between two objects

I have been thinking about how length contraction should work between two identical objects. Suppose object 1 is stationary relative to object 2, and as measured by object 1, object 2 is a distance of ...
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0answers
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How can we write relativistic momentum without length length contraction? [duplicate]

We've already known that "p=γmv" . v is particle's velocity depends on our rest frame and mass too. But shouldn't we observe particle's momentum by its displacement? for particle's view, displacement ...
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2answers
80 views

How Maxwell theory of electromagnetism solved action at a distance problem?

According to wikipedia Maxwell's equations were an essential inspiration for Einstein's development of special relativity. Possibly the most important aspect was their denial of instantaneous action ...
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Question about time and speed of light [closed]

Trying to understand how light can have constant speed in every inertial reference frame leaded me to the hypothetical experiment descibed bellow. My question is : "How two differents durations in one ...
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1answer
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Is this a right approach to show that $\partial_{\mu} \phi \partial^{\mu} \phi $ is Lorentz Invariant?

When trying to convince myself that $\partial_{\mu} \phi \partial^{\mu} \phi $ is Lorentz Invariant, I stumbled upon this approach: The last equation should read - $\partial_{i} \phi \partial^{i} \...
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1answer
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Neutron decay discrepancy

I have been reading the article Neutron Lifetime Puzzle Deepens, but No Dark Matter Seen on the present methods of measuring the life span of neutrons The bottle method measures a mean lifespan which ...
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What exactly is the meaning of length contraction? [duplicate]

Let's say a train of length $L$ (wrt ground) is standing on rails which have markings for every femtometre (or even smaller units). Now if someone takes a photograph and measures the distance between ...
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General Lorentz boost for a spinor in Hyperbolic form with Pauli matrices

I am having trouble deriving the general Lorentz boost for a spinor with rapidity $\rho $ using the hyperbolic functions. I know that the matrix: $$\exp [-\rho/2 \mathbf{n}\cdot \mathbf{\sigma }]=\...
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stress energy tensor for a massless particle

I want to express stress energy tensor for a massless particle. I know that 4-momentum of a massless particle is $k = (E , EV_x , EV_y, EV_z)$ but I don't know how to use $k$ to construct the stress ...
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Quantum Lorentz Transformations

Now I am reading a Weinberg's book "Quantum theory of field". Vol.1 page: 55 Сould you explain me the following things? Einstein's principle of relativity states the equivalence of certain '...
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Hausdorff property in Minkowski spacetime

In the 4-dimensional Minkowski spacetime, for a given point $x = (x^0,x^1,x^2,x^3)$, its timelike future/past set is defined as, $$ I^{\pm}(x) = \{y =(y^0,...,y^3) \in \mathbb{R}^4 : \eta_{\mu \nu}(y-...
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1answer
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Derivation of length contraction in Einstein, Relativity: The special and general theory

I was reading the book, "Relativity: The special and general theory" by Einstein. At some point it discusses the awkwardness of "relativity of simultaneity" with using universal time axis for all ...
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Postulates of Special Relativity

I have two questions about SR postulates. So first question, I heard two formulations of first postulate: "If a system of coordinates K is chosen so that, in relation to it, physical laws hold ...
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What happens when a photon hits a mirror?

When a photon of light hits a mirror does the exact same photon of light bounce back or is it absorbed then one with the same properties emitted? If the same one is bounced back does it's velocity ...
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The chain rule and velocity transformation in relativity (2)

First of all, these answers (How to derive the law of velocity transformation using chain rule?, The chain rule and velocity transformation in relativity, and other from a quick search on this site.) ...
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3answers
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Confusion about the twin paradox in general relativity?

The twin paradox states that if you have one twin on earth and one twin is sent in a round trip journey to space in a rocket close to the speed of light, when the twin sent in the rocket returns to ...
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Schutz's geometrical proof that spacetime interval is invariant

I'm trying to understand the proof that spacetime interval is invariant under for any two inertial observers. I know it's easy to arrive at the result using Lorentz transformation but I'm trying to ...
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The value of $c$ in $E=mc^2$

In Einstein’s formula $E = m c^2$, $c$ is the speed of light. However the speed of light is not a unique number. It can be expressed in kilometres per second or miles per second for example, which ...
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Time dilation derived from first principles vs. “width contraction”

Wikipedia describes the usual derivation of time dilation with a moving light clock: In this and similar derivations nothing is ever said about a possible "width contraction" and why it does not ...
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The Meaning of Newton's Second Law of Motion Being Invariant Under Certain Transformations

What do we mean when we say that Newton's Second Law of Motion is invariant under Galilean transformations? Does it mean that the value of a force measured in one reference frame is the same when ...
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Calculating Time in different reference frames

Consider the following problem. A stick passes with speed v though a breadthless person whose(the stick) proper length is L. How does: Stick See the time elapsed on my clock? I see time elapsed on my ...
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Does aether not exist or is it simply superfluous?

My question is motivated from studying the null result of the Michelson Morley experiment. Does the experiment prove that the aether does not exist? Wikipedia says that it was more broadly ...
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Proving the validity of the relativistic version of Newton's second equation

I want to verify the relativistic version of Newton's second equation $ F^\mu = m_0 A^\mu $ is true. My idea is that I expand both sides and compare the components. Left $$ F^\mu = \frac{dP^\mu}{d\...
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What is the relativistic mass of Red Light? [duplicate]

After using all the equation and formula's I am getting Light has a certain mass, i.e. 3.157x10^-36 (approx) Kg. Then I have calculated the Energy by using the famous equation, i.e. the E=mC^2 (In ...
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Where does light get its speed from? [duplicate]

One source of light is, IIRC my high school physics, when an excited electron jumps back to its normal position. This jump generates a photon. How can an event like that shoot of a particle at the ...
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What if you recorded the point of view of someone traveling at the speed of light? [closed]

According to the theory of relativity, the rate at which time passes is relative in accordance with speed. They say for example that if your twin gets in a rocket and flies to another planet at close ...
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Constants of motion of an electron in a harmonic electromagnetic field in free space

I have encountered a question in Classical Electrodynamics, as below: In free space, an electron, initially at rest at $z=0$, is subjected to an intense laser field $\vec E=\hat x A \cos(\omega t-...
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Special relativity conceptual doubt [closed]

Suppose a beam of light is fired from an object to a planet while the object is moving away from the planet. Will an observer on the object measure the time taken for the light to reach the planet ...
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1answer
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Can a spaceship accelerate at $1g$ forever?

Let's say a spaceship is designed to accelerate continuously at 9.8m/s/s, and thereby create an earth-like environment on one surface for its inhabitants to live. From the perspective of the ...
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2answers
78 views

Spacetime diagrams and their interpretation

Recently started an introductory course of relativity, and started learning about space time diagrams. I couldn’t figure out what are the uses of a spacetime diagram as an alternative to Lorentz ...
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1answer
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Would a universe with special-relativistic gravity make sense?

Coulomb's law in electrostatics in analogous with Newtonian gravity. It's pretty clear neither of these can be used in a universe that obeys special relativity. They both must be modified to avoid ...
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what is the physical meaning of the 4-vector inner product?

Given two 4-vectors, $P^\mu, Q_\mu$, what is the physical meaning of the inner product, $P^\mu Q_\mu = a$? Specifically I would like to know what it means when the vectors are orthogonal ($a=0$) with ...
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How we can prove that photons have no mass? [duplicate]

I am thinking nowadays that how its possible that a particle without mass, actually exists? in the case of light its used to say that photons have no mass no weight but they have momentum. can any ...
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