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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Conditions that the coordinate must satisfy in order to become local inertial

Consider the coordinate transformation $$ \tilde x^a=x^a+\frac{1}{2}\Gamma^a_{bc}x^bx^c $$ I have shown that at the origin $O=(0,0,0,0)$, $$ \frac{\partial\tilde g_{ab}}{\partial\tilde x^c}=0 $$ ...
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(Special Relativity) Points that can be seen by an observer

Let the metric be $$ ds^2=(1+gz)^2dt^2-dx^2-dy^2-dz^2 $$ where $g$ is a positive constant. Let an observer be stationary at $x=y=0$ on the surface $z=0$ and look upwards at an angle $\theta$, how ...
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Acceleration or Deacceleration. Can either be identified?

An accelerated clock will measure a smaller elapsed time between two events than that measured by a non-accelerated (inertial) clock between the same two events. . Experiment #1 Imagine that ...
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Space distance between observers and Lorentz transformation

I'm not a specialist of Lorentz transformation. I would like to know if the Lorentz transformation from one observer to another preserves the space distance between these two observers. Example ...
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1answer
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Hyperbolic geometry in SR

I'm having trouble understanding just what the hyperbolas on a space-time diagram actually signify. From what I understand, these hyperbolas trace out the equation $S^2=x^2-(ct)^2$, which is the ...
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Does the general topology of Minkowski space-time change under a Lorentz transformation?

Does the general topology of Minkowski space-time change under a Lorentz transformation? Open balls in $\mathbb{R}^{4}$ (with the standard topology) are not invariant under Lorentz transformations. ...
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Is proper time a vector?

Proper time is identical with the spacetime interval of a timelike movement. A spacetime interval is the dot product of two vectors and thus a scalar. Proper time however is always pointing exactly ...
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Is Michelson-Morley experiment an axiom?

Sorry for my ignorance, but does the result of Michelson-Morley experiment have some explanation? Is there some reason why light speed in vacuum is maximum or we just find it by experiments?
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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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Is there an orthogonal time dimension in Minkowski spacetime?

Space dimensions are orthogonal one to each other. But what about time in the Minkowski diagram? At first sight, time seems to be orthogonal to space. But we have to consider that each Minkowski ...
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Photons have no mass. So, why does $E = pc$ hold? [duplicate]

It's a somewhat theoretical question. In special relativity, The energy of a photon is given by $E = pc$. But, my argument is that, since photons have no mass, how can they have a momentum $p$? The ...
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68 views

Relative speed when approaching the speed of light [duplicate]

According to this chart of the Lorentz factor as a function of speed: If a spacecraft neared (roughly) 0.85c, would it appear to be traveling at 1.7x the speed of light from the perspective of ...
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Exercise Lorentz Transformations

I have 2 inertial frames, both are in relative motion along the x axis moving with constant velocity $v_x$. It is called with Standard figuration where the Lorentz transformations relate the ...
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1answer
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Bi-vector in Minkowski space

I have a problem, I have a bi-vector that define like: $\omega^{\mu \nu}=a^{\mu}b^{\nu}-a^{\nu}b^{\mu}$ where, $a^{\mu}=(a^0,a^1,a^2,a^3)$ and $b^{\nu}=(b^0,b^1,b^2,b^3)$ I need show that ...
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53 views

Complete Energy Equation for Non-Zero Masses

The most simplified version of the energy equation (which is also the most known) is $E=mc^2$ However, I understand that this only applies to objects with non-zero mass and zero velocity. I also read ...
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Does Light Experience Length Contraction?

Lorentz length contractions states that the length of any moving object gets divided by the Lorentz factor equal to the Lorentz factor for that object (always $\geq 1$), equal to $$ ...
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The speed limit is with respect to what?

As I understand, an object with mass cannot reach the speed of light because its (relativistic) mass increases "exponentially" as it approaches light speed. So there is a relation between mass and ...
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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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Problem understanding sign of volume integral in Minkowski space

My professor told me that a 4-dimensional Minkowski - Space Integral I was working on can be written as the product of a metric tensor and a scalar: $\int d^4 k \frac{k^\mu ...
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Why is the ratio of velocity to the speed of light squared in the Lorentz factor?

Why is the ratio of velocity to the speed of light squared in the Lorentz factor? $${\left( {{v \over c}} \right)^2}$$ My only guess is the value must be positive.
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Help with Special Relativity velocity addition formula

While looking for question about speed of light I saw this Physics.SE question where I found this: $$v_\text{rel} = \frac{v_1 - v_2}{1 - \frac{v_1v_2}{c^2}}.\tag1$$ But in another answer there was ...
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Infinitesimal transformations for a relativistic particle

The action of a free relativistic particles can be given by $$S=\frac{1}{2}\int d\tau \left(e^{-1}(\tau)g_{\mu\nu}(X)X^\mu(\tau)X^\nu(\tau)-e(\tau)m^2\right).$$ If we then make an infinitesimal ...
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Tensor decomposition of $\partial_\mu A_\nu$

In the decomposition of a rank-2 Minkowski tensor into irreducible representations, I expect the 16 components of the tensor product $M_\mu N_\nu$ to reduce to the sum of a scalar (1), a rank-2 ...
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Is there always a frame in which spatially separated events are simultaneous?

In relativity, if two events are simultaneous in a specified frame, they cannot be simultaneous in any other frame. My question is this: given any two events, is there always a frame in which these ...
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How is time not a constant?

I am a visual person, so it's hard to imagine the information I keep getting, but shouldn't time be a constant? If you were traveling at the speed of light and your able to cover $299{,}792{,}458$ ...
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Quantum entanglement and special relativity PARADOX

imagine two entangled atomic clocks , we entangle them and then measure the time , it has to be the same , right ? now lets suppose that we entangle them , but don't measure them, then we plant one ...
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Frequency of cosmic microwave background

Some people refer to cosmic microwave background's (CMB) frame of reference as an absolute one. If I understand correctly, we can measure 'absolute' velocity in this frame by using the Doppler effect. ...
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What is the speed of light relative to?

Consider the scenario where you measure the time it takes for light to travel to the left 10 meters and to the right 10 meters. Both measurements will take the same time, even though we are moving ...
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What does $\frac{1}{\sqrt{1 - \frac{v^2}{c^2}}}$ mean with respect to special relativity?

What does the following mean with respect to special relativity? $$\frac{1}{\sqrt{1 - \frac{v^2}{c^2}}}$$
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Time travel outside of light cone without causality violation

If one is able to travel into the past but at a spatial distance that puts him outside of his own past light cone would this be considered a causality violating trip? Looking at a Minkoski diagram, it ...
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How would one compute the angle of deflection, in a relativistic collision - underspecified system?

Consider the simplistic case of two identical mass particles colliding elastically with the second particle initially stationary and the first particle travelling with energy $E$. By conservation of ...
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Field interaction betweeen two point charges?

[SOLVED] Consider two particles A and B having equal charges and placed at some distance. The particle A is slightly displaced towards B.So, Does the EM force on B increase(+/-) as soon as the ...
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Possible mechanics based on the known symmetries in the nature (investigating rumor)

Somewhere I've heard about a relative new mathematical result regarding mechanics. Specifically, there is a list of the known symmetries of mechanics (both Newtonian and relativistic), i.e. different ...
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How do you determine who is moving “faster” in relativity? [duplicate]

I suspect this question has a simple answer, but I can't get my head around it. The classic example of a person in orbit around the Earth at high speed experiencing a slower passage of time than the ...
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What is the relative speed of two near-light speed particles headed towards each other?

I understand that nothing can move faster than light due to time dilation. I want to build upon my understanding of Einstein's theory of Special Relativity, so I came up with this hypothetical problem ...
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Velocity in frame $S$ and $S'$

If I take the Lorentz position transforms between two inertial frames, $S$ and $S'$ moving with relative velocity $u$ along a common axis (say $x-x'$), then: $$x'=\gamma(x- ut)$$ $$y'=y$$ $$z'=z$$ ...
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Why does Minkowski space provide an accurate description of flat spacetime?

What is the chain of reasoning (beginning, of course, from observations about the universe) that leads one to predict that Minkowski space provides an accurate description of space-time in the ...
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Confused about time dilation/length contraction [duplicate]

I have a following problem: A meson is generated $h$ meters above the earth's surface and begins to move towards the earth with velocity $v$. Its (proper) lifetime is $t_m$. What is $v$ if the meson ...
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Proof that 4-potential exists from Gauss-Faraday field equation

This is a problem concerning covariant formulation of electromagnetism. Given $$\partial^{[\alpha} F^{\beta\gamma]}= 0 $$ how does one prove that $F$ can be obtained from a 4-potential $A$ such ...
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4-velocity and 4-acceleration in instantaneous rest frames

I am trying to solve this problem: Consider a rocket moving relative to an inertial frame $\mathcal{F}$ , such that its worldline is given by ...
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Person in a special relativistic frame observes light refract on a passing ship

The speed of light is the same in all frames of reference. But imagine a scenario in which you passed by a ship which had (B=.78), while your ship had (B=.94). While somehow being able to look through ...
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Electric field generated by a point charge moving at the speed of light

As you see, this is the electric field generated by a point charge moving at constant speed v. I know that when $v$ -> 0, $E$ is just the Coloumb Law. But how do you interpret $E$ when $v$ -> $c$ ? ...
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Difference between “Lorentz transformation” and “proper orthochronous”

I'm doing an assignment and I've been given a list of $4 \times 4$ matrices and asked: Which of the following are Lorentz transformation matrices? Which are proper and orthochronous? But, as ...
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What will I see in this scenario? Will this be faster than the speed of light?

Let say there's a particle that is travelling very near the speed of light. Lets say I have a camera capable of filming this high velocity particle and I film the particle on my camera then I fast ...
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Derivation of proper acceleration in terms of rapidity

In the Wikipedia page for proper acceleration, an equation for proper acceleration in terms of rapidity is given as $\alpha = \frac{\Delta \eta}{\Delta \tau}$, where $\eta$ is the rapidity of the ...
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Special Relativity Problem [closed]

I am having trouble with the following problem: Fry travels in a rocket ship towards Leela, at constant relative speed $v$: Fry is delivering a pizza, which in its rest frame stays hot for ...
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Speed of light as a universal speed limit

It follows from special relativity that nothing can travel faster than light. Einstein believed this would have to hold so generally that he assumed the Einstein-Podolsky-Rosen paradox to indicate a ...
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Everything is a Photon

If we accept $E=\hbar \omega$, $p=\hbar k$, and $E^2-(pc)^2=(m_0 c^2)^2$, then we find $$(m_0 c^2)^2 = (\hbar \omega)^2-(\hbar kc)^2 = \hbar (\omega^2 - (kc)^2)=0$$i.e. the rest mass of any particle ...
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Construction of Observer Coordinates in General Relativity

In A First Course in General Relativity, Second Edition, by Bernard Schutz, on the bottom of Page 8, he is expanding on the spacetime diagrams in Figure 1.5. He states "[...] the four angles are ...
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The wave equation in general relativity, special relativity, and Cartesian coordinates

The relativistic wave equation is $$\square\varphi=\rho$$ where $\varphi$ is the field, $\rho$ is the source, and $\square$ is the D'Alembert operator, defined by ...