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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Finding the velocity of a particle [duplicate]

How to find the velocity of a particle which has mass $m$ and energy $E$ considering the non-relativistic and the extreme relativistic limits?
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59 views

Photon has energy but no mass [duplicate]

The photons energy is defined as Plancks contant multiplied by the frequency of the light wawe it represents. However Einstein states that the total energy of a particle with rest mass $m$ is $m$ ...
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57 views

Lorentz contraction of object in circular motion

Apparently a bunch of people totally misunderstood my previous question and choose to ignore the clarifying comments. Let me change the conditions to remove all the confusion. A group of particles ...
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2answers
63 views

How does flying over synchronize clocks look like?

I have a relatively (pun intended) simple conceptual question that has me going in circles as I begin my course work into Modern Physics. The question is straight forward enough: You are gliding ...
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83 views

What happens to wheels of a car moving near speed of light? [duplicate]

Let's take a standard ACME Thought Experiment Division car with a max speed of a leisurely, constant 0.75c in a straight line. So, for an external observer, the body of the car behaves like a typical ...
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2answers
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Triplet paradox

The situation is: A stay at a station B,C board the same train that moving away from the station while the train moving away C start moving inside the train in the opposite direction as such A sees ...
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Can absolute speed of object be measured? [closed]

Let's say there are two objects in space - Station and huge non-transparent sphere. Sphere starts to move from station 5000 km/h. Inside the sphere, beam of light is produced in direction the sphere ...
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1answer
62 views

Is $E = p^0$ in non-inertial frames?

In special relativity the energy of a particle is the 0-component of the 4-momentum. However, is this still true in non-inertial frames, and in particular in non-freely-falling frames in general ...
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Performing Wick Rotation to get Euclidean action of scalar field

I'm working with the signature $(+,-,-,-)$ and with a Minkowski space-stime Lagrangian $$ \mathcal{L}_M = \Psi^\dagger\left(i\partial_0 + \frac{\nabla^2}{2m}\right)\Psi $$ The Minkowski action is $$ ...
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View of right-angled-triangle from a constant-velocity relative observer [closed]

Suppose I have a picture of a right angled triangle drawn in the X-Y plane, and a man whose velocity relative to the to picture is $0.4c\hat{x}-0.4c\hat{y}$. Will the angle $\theta$ that the man ...
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2answers
175 views

Does relativity violate uncertainty principle?

Let us say I sit on an electron. According to me the electron is at rest. Also, I will know the position of the electron accurately as I can take the electron as the origin. So, I know both position ...
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4answers
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if mass is dependent on velocity, and velocity is relative, how can we determine rest mass [closed]

If I'm not mistaken, $m=\gamma*m_0$ ($\gamma$ being the lorentz transformation) But $\gamma$ depends on velocity. How do we determine velocity if velocity is relative? If we are currently being flung ...
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How much is the maximum posible information travel speed in medium?

Light has slower speed in medium. Should we consider this when we use special relativity in atmosferic(or any other type of medium) motions? If we should use vacuum light speed, does it mean photons ...
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1answer
89 views

Relationship between locality, causality, and free theories

This text on QFT defines a free theory as that in which dynamics of the field for each degree of freedom evolves independently from all the other. In principle we have an infinite degrees of freedom, ...
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1answer
73 views

Constancy of speed of light in vacuum? [closed]

Have scientists tried their best to calculate speed of light in vacuum? It seems very absurd to me that light of all frequencies have same velocity in space. Can someone find in future if this speed ...
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62 views

Length contraction: Is it permanent? [closed]

Lorentz contraction problem: By Bertrand Boucquillon Components of the problem: - Bob (observer) - 2 identical rods that both measure 1 meter. Let's call them rod X and rod Y - Point A - Point B ...
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25answers
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Do we know why there is a speed limit in our universe?

This question is about why we have a universal speed limit (the speed of light in vacuum). Is there a more fundamental law that tells us why this is? I'm not asking why the speed limit is equal to ...
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23 views

Showing $\frac{d^3\underline{k}}{2\omega_{k}(2\pi)^3}$ is Lorentz invariant [duplicate]

Show $\frac{d^3\underline{k}}{2\omega_{k}(2\pi)^3}$ is Lorentz invariant. Hint: try to evaluate $\int dk_0\delta(k_0^2 - M^2)\theta(k_0)$ where $M^2 = \underline{k} + m^2$ My attempt is as ...
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Available energy in centre of mass system

The problem given is "A proton of total energy 3GeV makes a head-on collision with a 5GeV electron. Calculate the available energy in the centre-of-mass system to create any new additional particles ...
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Requesting explanation for why dark matter evidence is not explained by special relativity [duplicate]

Good afternoon. I'm doing research for a possible hard science fiction project and was looking up information on dark matter. Wikipedia--hardly an authoritative source, I know--mentions that the ...
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2answers
447 views

Lorentz invariance of the Minkowski metric

As far as I understand, one requires that in order for the scalar product between two vectors to be invariant under Lorentz transformations $x^{\mu}\rightarrow ...
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6answers
160 views

Light in mass moving at high velocity

Imagine if you will, a strand of fiber optic cable 186,000 miles long. A pulse of light is sent through the stationary cable: it takes 1 second for light to travel the entire length of the cable. Now ...
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3answers
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acceleration and its effect on the speed of light

One of Einstein's thought experiments involved a rocket and two light sensors inside the rocket, one at the top, and one at the bottom. When the rocket was at rest, a pulse of light from the bottom ...
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1answer
86 views

Does momentum space have a speed limit?

In ordinary $xyz$ space, the maximum velocity of propagation for mass-energy and/or information is $c$. So, my question: Is there also a maximum velocity of propagation in momentum ${p_x}{p_y}{p_z}$ ...
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2answers
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How do the postulates of relativity relate Lorentz transforms to their inverses?

This question is about one of the assumptions involved when one is deriving the Lorentz transformation, for example under "Principle of Relativity" in Wikipedia's page on the derivations. Let me ...
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1answer
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Acceleration of free particle in Minkowski space! [duplicate]

In Minkowski space, the equation of motion is $$a^c=\frac{d^2}{d\tau^2}x^c(\tau)=0.$$ How is this derived?
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Is mass directly or inversely proportional to time? [closed]

From a Newtonian perspective: F = ma F dx = ma dx E = m (dv/dt) dx m = (E dt) / (dv dx) Mass is directly proportional to time, if time slows down then mass goes down or decreases. From a ...
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Given a current velocity and a fixed input energy, how much faster will a relativistic particle be?

The relativistic kinetic energy of a particle with mass $m$ and velocity $v_0$ is $$m c^2 (\gamma_0 - 1) \textrm{ where } \gamma_0 = \frac{1}{\sqrt{1 - \frac{v_0^2}{c^2}}}$$ I would like to know how ...
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110 views

Is magnetic field due to an electric current a relativistic effect?

I was reading a paper of the same name by Oleg D. Jefimenko; here is the concerned text: [...] relativistic force transformation equations demand the presence of an electric field when the ...
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1answer
58 views

What is the physical significance of taking derivative with respect to proper time?

I would like to know if there is any physical significance associated with the derivative of a quantity with respect to proper time or is it just a mathematical trick. Since proper time is measured in ...
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2answers
123 views

What does diagonalization mean here?

In a gravity theory in spacetime, the metric has signature $− + +· · ·+$. Concretely this means that the metric tensor $g_{μν}$ may be diagonalized by an orthogonal transformation, i.e. ...
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45 views

Is the matrix representation of the Lorentz transform the same for all 4-vectors?

If I have a four vector of the form: $$ \left( \begin{array}{ccc} T\\ \vec{X}\end{array} \right) $$ where $T$ is the analogous time component (i.e. energy, angular frequency, scalar potential, charge ...
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What happens during mass-energy conversion?

A mass is another form of energy. When a mass ceases to exist as 'matter', it exists as energy - in the forms of energy we generally know (light, heat). But is this so simple? When a mass exists in ...
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1answer
106 views

Does the property of being “virtual” for a particle depend on the observer?

I've read at several places that a static magnetic (and electric for that matter) field can be thought of as made by virtual photons, at least that's what I understood. Now, in Special Relativity we ...
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70 views

Confusion regarding step in Einstein's 1905 paper on the electrodynamics of moving bodies

Could someone explain this step in Einstein's 1905 paper on the electrodynamics of moving bodies. I tried differentiating both sides of the first equation and still don't arrive at the second one, ...
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1answer
51 views

Minkowski metric: Why does it look like it does? [duplicate]

I have been searching for why would we even start with Minkowski spacetime metric as being written as: $$ds^2=-dt^2+dx^2+dy^2+dz^2.$$ No really, so why would we have a negative sign for temporal ...
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44 views

What Would One Observe of a Calendar on Earth, Given a Round Trip to Another Star and back?

I want to ask a clarifying series of questions on what I think is a relatively simple scenario. It's a long one but I've tried to word it as simply as I can manage while trying to do the question ...
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Equation of motion of a free particle

We know that the equation of motion of particle can be derived from the respective action. But in the book I am reading, the author is saying: ... timelike worldline of a massive particle is ...
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What's wrong with using the 4-current to find the potential of a moving particle?

According to Feynman (Lectures on Physics, Vol. II, 21–6), the potential of a moving point charge is: $$\phi = \gamma \cdot \frac q {4\pi\epsilon_0} \cdot \frac 1 {\sqrt{ \gamma^2 \left( x-vt ...
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1answer
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Lorentz covariant completeness relation

Let be $$ P^\mu |p> = p^\mu |p> $$ i.e. $|p>$ is the eigen-vector of the 4-momentum operator. Where does the following Lorentz-covariant completeness relation come from? $$ \int d^4p ...
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Relativistic Scattering

When we work out the relativistic general two-body scattering in the CM frame (like two elementary particles producing two other P1 +P2 -P3 -P4) , the cross section is proportional to absolute final ...
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The Ehrenfest Paradox and Euclidian Assumptions [duplicate]

As a result of the Ehrenfest Paradox, the geometry of a rotating disc is non-Euclidean. However, while reaching this conclusion, we assumed that "the radius doesn't undergo Lorentz contraction", ...
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Relativistic particle decay in ZMF [closed]

This is a problem that I feel is harder than I am making it but say you have: A particle at rest of mass $M$ decays into two smaller particles of masses $m_1, m_2$ where $m_1 \neq m_2$ and $M > ...
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1answer
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Time and velocity

Suppose two cars are traveling at a velocity of $c/2$ ($c$=speed of light) in two straight lines parallel to each other but in opposite direction in vacuum. Then what will a person sitting in one of ...
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2answers
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Why time slows only for moving object and not stationary observer? How the “stationary” & “moving” are decided? [duplicate]

Explanation for the questions in the title: According to the the (special theory of) Relativity, if an observer is stationary and sees a fast moving object then time runs faster for the observer ...
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Spin of a gauge field

I was wondering what is the simplest way to understand the reduction of the Wigner's little group from $SO(d-1)$ to $SO(d-2)$ when one considers massive and massless fields respectively (in a $d$ ...
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2answers
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Frustrated by the light clock special relativity thought experiment [closed]

Here is this age old thought experiment being told by a professor on Sixty Symbols: https://youtu.be/Cxqjyl74iu4 This explaination using the light clock is extremely frustrating. How can one use a ...
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Conservation of linear momentum (classical mechanics and special relativity)

How did Newton deduce the law of conservation of linear momentum? Can it be derived only by Newton's laws, or does it follow from practical experiments? If the law of conservation of linear momentum ...
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A doubt in special relativity

I read in the Feynman Lecs about muons. They are created in the upper atmosphere and hav a lifespan of about 2.2 micro seconds and if there was no relativity, they can travel as much as 600 metres ...
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66 views

Electron positron collision producing mesons

An electron of an energy 9 GeV and a positron of energy E collide to produce a $B^0$ and anti-$B^0$ meson, each with a mass of 5.3 GeV. What is the minimum positron energy required to produce the ...