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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Spacetime Diagrams

Suppose an observer $\mathcal{O}$ uses the coordinates $t$, $x$, and that another observer $\mathcal{O}'$, with coordinates $t'$, $x'$, is moving with velocity $\mathbb{v}$ in the $x$ ...
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microcausality and locality

There is this thing I got confused: Microcausality is the statement that spacelike separated local field variables commute so that we can specify field variables on a spatial slice as a complete ...
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While Space-man lives for 1 day, then how long does Earth-man live ? 1000 years or 1 second? [duplicate]

Acordding to Einstein's Relativity, while Space-man lives for 1 day(just a number for example , not an exact number calculated from the corresponding relative speed), Earth-man can live for 1000 ...
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3answers
380 views

Velocity measurement in relativistic perspectives

I understand the precepts of relativistic time dilation, but I'm looking to nail down the local perception of velocity in each frame. My question is threefold: Given two observers $A$ (rest frame) ...
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86 views

Relativity addition and signs

I have just covered a very brief module on special relativity as a part of my physics course. I have also done some extra reading mostly; Morrin's Classical Mechanics. While I found the book really ...
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Impulse from absorbing a photon? Is there an increase in rest mass?

I'm going through A P French's special relativity. In one chapter (6) the following is set up: Suppose that a stationary particle of mass $M_0$ is struck by a photon of energy $Q$, which is ...
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6
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Travel duration from Earth to a star at 9.8 m/s² acceleration

How much time would it take for a traveler (in traveler's perspective) to reach a star at distance $d$, if it accelerates at 9.8 m/s² (for a comfortable travel)? I understand that $V = V_0 + a\times ...
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25 views

Integral Over Hypersurface Simplification

How does one see it as obvious that $$\int_S \frac{\partial A_i}{\partial x^j} dS^{ji} = \int_S\frac{1}{2}(\frac{\partial A_j}{\partial x^i} - \frac{\partial A_i}{\partial x^j})dS^{ij}$$ where $d ...
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Hyperbolic Cosine and Sine in Terms of 3-D Velocity

Intuitively, why are $\cosh(\theta) = \frac{1}{\sqrt{1-(v/c)^2}}$ and $\sinh(\theta) = \frac{v/c}{\sqrt{1-(v/c)^2}}$ true in special relativity? Is there some picture I can draw in Minkowski space ...
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3answers
115 views

Does Contraction at High Speeds Happen in Any Dimension Besides Length?

I'm not sure if this is a duplicate. Whenever physics buffs talk about Einstein's relativity (I forget which kind) at high speeds, they always talk about "length contraction", or shortening of the ...
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$\tau$ pair production question

There's a question on my homework about the process $e^{-} e^{+} \rightarrow \tau^{+} \tau^{-}$. Specifically, it is claimed that the minimum energy required of the colliding positron and electron ...
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Help getting my head around frames of reference in special relativity

OK, so my textbook says that in time dilation and length contraction, the proper time and the proper length is "That which is in the frame of reference of the observer at rest relative to the event". ...
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What is the age of the Universe from the big-bang light perspective?

What is the age of the Universe from the big-bang light perspective? We all agree that the universe is around 14 billion years, from the perspective of a hypothetical observer moving in a galaxy, ...
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567 views

What are the eigenvalues of the Lorentz matrix?

The Lorentz matrix defines the transformation of a four-vector between different frames of reference, such that $$ p^{'\mu} = \Lambda^{\mu}_{\ \ \nu}p^{\nu} $$ where in this example $p^{\mu}$ is the ...
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How do particle scattering cross sections scale with energy in colliders?

How do particle scattering cross sections scale with energy in colliders? Particularly photons, electrons, protons, and gold or lead nucleii? (If necessary, break this into four separate questions.) ...
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678 views

Lorentz transformation of electromagnetic 4-potential

I'm looking for the exact correspondence between Lorentz transfer four vector and the four vector of scalar and vector potential $A^\mu = (\phi(t,\vec{x}),\vec{A}(t,\vec{x}))^{T}$. Does $ct=A(t), ...
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What's the purpose of the speed of light in $E = mc^2$?

Is $E=mc^2$ not just $E=m$. What does the speed of light have to do with this other than to give it a really big number so it looks cool? What spectrum of light is used? How can we test the speed of ...
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How much of Minkowski spacetime structure can be recovered from its causal structure?

A beginner's question: I have always understood that (four-dimensional) Minkowski spacetime can be recovered up to a constant factor—i.e. 'up to a dilation' or 'up to global scale'—from its causal ...
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237 views

Why don't we substitute for $p$ in $E = pc$?

See, the energy of a photon is given out by $E = pc = hv$ why don't we substitute for $p$ in $E ^2= p^2 c^2 + m^2 c^4$ by putting $p = \gamma mv$ and then get a value for $m$ (which will be $0$ for a ...
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2answers
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Uncertainty of permittivity of vacuum [duplicate]

Question: The value of permittivity of vacuum, $\epsilon_0$, is given with absolutely no uncertainty in NIST Why is this the case? More details: The permeability of vacuum can be given by ...
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1answer
134 views

Electric Magnetic potential and Lorentz transform [closed]

I have heard that the scalar potential and the magnetic vector potential in the electromagnetic four potential become the four vector by the Lorentz transform. Thereafter, the Lorentz transform leads ...
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1answer
136 views

Speed=mass=time? [closed]

I was wondering why objects gain mass with speed? How can we measure speed if there is no truly stationary point to measure from? And if an object comes to a stand still will it loose its mass? ...
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How does $E=mc^2$ put an upper limit to velocity of a body?

How does $E=mc^2$ put a upper limit to velocity of a body? I have read some articles on speed of light and they just tell me that it is the maximum velocity that can be acquired by any particle. How ...
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2answers
219 views

Apparent velocity of an approaching object

What would be the apparent velocity of an object approaching us at an actual velocity of $v$? I know $cv/c-v$ is a possible answer but here's another argument - shouldn't the velocity be the Doppler ...
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“Imaginary” Perfect Time

In the definition (in one spatial dimension) of $\Delta \tau$ there is the relation: $(\Delta \tau)^2 = (\Delta t)^2 - (\Delta x)^2$ which is invariant. If $(\Delta x)^2 > (\Delta t)^2$ then there ...
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What's the relationship between $SL(2,\mathbb{C})$, $SU(2)\times SU(2)$ and $SO(1,3)$?

I'm a beginner of QFT. Ref. 1 states that [...] The Lorentz group $SO(1,3)$ is then essentially $SU(2)\times SU(2)$. But how is it possible, because $SU(2)\times SU(2)$ is a compact Lie group ...
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Distance Between Two Photons Calculated in Different Inertial Frames

I am a self-studier. This is a question from a text I am studying: The distance between two photons traveling along the $x$-axis of an inertial frame, $S$, is always $l$. Show that in a second ...
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62 views

Electromagnetism and the principle of relativity

I'm reading the book "Fundamental Physics 2: Electromagnetism" by Alonso and Finn. I understand everything up to the point where everything is "unified". The following example is given in the book: ...
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Relativistic Transverse Doppler Effect

In Minkowski spacetime, two observers, A and B, are moving at uniform speeds u and v, respectively, along different trajectories, each parallel to the y-axis of some inertial frame S. Observer A emits ...
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What is the resolution to this apparent contradiction?

Momentum is defined as $$p = \gamma m_0 v$$ And here is another law $$E^2=(m_0c^2)^2+(pc)^2$$ And this website says the energy of a red photon is $1.9074 eV$. Also, light has a rest mass of $0$. The ...
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Reason why $F^{\mu\nu}F_{\mu\nu}$ and $\tilde{F}_{\mu\nu}F^{\mu\nu}$ are Lorentz invariant

I'm trying to think of an intuitive reasoning for why $F^{\mu\nu}F_{\mu\nu}$ and $\tilde{F}_{\mu\nu}F^{\mu\nu}$ are Lorentz invariant. By this I mean that I don't simply want to show that they remain ...
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Does decrease in temperature affect mass $E=mc^2$?

My understanding of Quantum physics and String Theory is very basic and I don't yet have a grasp on the maths, but in my research I have come up with a question. Does a decrease in temperature also ...
3
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2answers
172 views

Why do we set $x^0 = ct$ instead of $x^0 = t$?

When we deal with Special Relativity and we start considering spacetime instead of space and time each at once, we usually see books saying that we consider a space with four coordinate $x^\alpha$ ...
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About the speed of light

If Mr. E is aboard a spaceship traveling near the speed of light the usual reason for the spaceship not going faster than $c$ is the (relativistic) mass of the ship increases without bound, I think. ...
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Zero photon energy in moving frame

Suppose I have a photon with energy $E$ (in its rest frame) moving along the $z$ direction with momentum $\mathbf{p} = p_z\mathbf{\hat{z}}$: The Lorentz transform in the laboratory frame should be: ...
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Can one create mass from energy?

Due to $ E =m c^2 $, one can convert mass to energy. A classic example would be matter/anti-matter annihilation to produce energy (photons, etc.). Can one do the reverse? So could one do something to ...
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Relativistic addition of velocities of spaceships [duplicate]

If Spaceship 1 is traveling at speed $.5c$ relative to Earth, and Spaceship 2 is traveling at speed $.3c$ relative to Earth in the same direction, what does Spaceship 2 see Spaceship 1's speed as? I ...
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Time dilation in special relativity

Suppose a star ship is moving with some velocity. Two light pulses one in direction similar to star ship another opposite to it is shot towards the space ship. Then how time inside space ship adjust ...
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5answers
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What does a frame of reference mean in terms of manifolds?

Because of my mathematical background, I've been finding it hard to relate the physics-talk I've been reading, with mathematical objects. In (say special) relativity, we have a Lorentzian manifold, ...
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Breaking the speed of light relative to a moving object [duplicate]

You can't go faster than light, and light can't be additive (if you shine a light from a spaceship, the light is not going $c$+"speed of spaceship", it's just going like it always does). But what ...
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Is the “How to break the speed of light” minute physics video wrong?

I am referring to this video, on YouTube, by minutephysics, which has quite a lot of views. In the video it states that if you flick your wrist while pointing a laser that reaches the moon, that the ...
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1answer
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Why is $\phi$ constant in the hyperbolic Lorentz transforms?

If two spacetime events are separated by $(dx,dy,dz,dt),(dx',dy',dz',dt)$ in two reference frames $K,K'$ respectively, whose relative motion is purely along the $x$-axis, then, purely due to the ...
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2answers
107 views

State of constant motion

Why does an object remains in its state of constant motion if there are no forces acting on that object? My understanding is that all the energy of the motion will be kept inside and a change in the ...
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1answer
57 views

velocity in inertial and nontial frames

I got confused about the difference between the last term of both pictures. In the first one, we have w x r, but in the second we have w x r underlined. Does anyone have a better explanation? They ...
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Query into the cumulative velocity of mounted platforms

Consider throwing a stone at an object from rest, it travels at Vms-1. Now throw that stone whilst running at Ums-1. It seems in the latter scenario the total speed of stone is V + U. Now imagine ...
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Why is the Faraday Tensor derived from the Lorentz force?

If we start from the Lorentz force, $$\textbf{F}=q\textbf{E} +q\textbf{v}\times\textbf{B}$$ and use the four velocity u$^{\mu}$ and the four momentum p$^{\nu}$, then we get to ...
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The scissor paradox: can we pass the information faster than light? [duplicate]

click to view the image Before I start, I want to say that this is not a duplicate of "Is it possible for information to be transmitted faster than light by using a rigid pole?", Since point A is ...
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Are signal fronts in a beam not at rest to each other?

I'd like to investigate how the notion of "mutual rest" might be applied consistently, but distinctively, in the following thought experiment: Consider a light source ("$A$") which directs a beam ...
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Relativistic Elastic Collision

I am having trouble getting my head around the transfer of energy in a relativistic elastic collision. My understanding of a relativistic elastic collision is one in which the total rest mass on each ...