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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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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2answers
488 views

Why the generators of boosts transform like a vector under rotation?

$$\left[J_i,J_j \right]=i\epsilon_{ijk}J_k$$ $$\left[J_i,M_j \right]=i\epsilon_{ijk}M_k$$ $$\left[M_i,M_j \right]=-i\epsilon_{ijk}J_k$$ where $J_i$ is the generator of rotation of Lorentz group, $M_i$ ...
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182 views

What did Nobel laureate Smoot mean by “Modern Efforts to Find Violations of Special Relativity”?

In George Smoot's 2006 Nobel Lecture, having won the Nobel prize for his research on the Cosmic Microwave Background (CMB), he refers to the possibility of the CMB being a special frame stating ...
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3answers
815 views

Energy-Momentum Tensor under Lorentz Transformation

In relativity, the symmetric energy-momentum tensor is given by $$ T^{ij}, $$ where $T^{00}$ is the energy density and $\frac{1}{c}T^{10}$ is the momentum density. Thus: $$ \left(\frac{1}{c}T^{00}dV, ...
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797 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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3answers
246 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
565 views

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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2answers
197 views

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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1answer
140 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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222 views

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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1answer
142 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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1answer
644 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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2answers
167 views

The speed of light and unstable matter

Mr.E is on a luxury spaceship travelling about 1/2 the speed of light and finds a cubic lump of unstable matter(attached to a bomb) in his cabin. He of course is an expert with bombs but this device ...
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1answer
114 views

“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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1answer
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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2answers
1k views

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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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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1answer
73 views

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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0answers
101 views

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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2answers
177 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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What if photons are not the fastest particles?

Einstein originally thought that special relativity was about light and how it always travelled at the same speed. Nowadays, we think that special relativity is about the idea that there is some ...
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1answer
133 views

Concerning a previous possible tachyon observation? [duplicate]

A few years ago there was a story about the Large Hadron Collider where a possible tachyon was supposedly observed. It was later shown it didn't occur yet the incident made me think. If a large ...
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1answer
259 views

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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217 views

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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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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6answers
2k views

Minkowski Metric Signature

When I learned about the Minkowski Space and it's coordinates, it was explained such that the metric turns out to be $$ ds^{2} = -(cdx^{0})^{2} +(dx^{1})^{2} + (dx^{2})^{2} + (dx^{3})^{2} $$ where $ ...
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4answers
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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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6answers
450 views

Detecting absolute motion inside a box

This is not a contradiction and I know it is impossible but still consider a thought experiment by me and point out if something is wrong. See the following picture and then the explanation follows. ...
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2answers
301 views

How an accelerated object sees another accelerated body in special relativity?

Assume two objects are moving with a constant acceleration $a_1$ and $a_2$, which are the measured accelerations by respective object (or constant force being applied to each of the objects). My ...
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2answers
251 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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1answer
92 views

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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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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58 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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2answers
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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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1answer
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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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77 views

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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1answer
1k views

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 ...
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1answer
123 views

Electron distribution around atom when moving

I do not have much experience on this but if an atom has some electrons around nucleus and the atom itself it is moving at some speed does that affect the distribution of electrons around? I am ...
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5answers
343 views

How do we know that photons are exactly massless and travel exactly with speed $c$ in vacuum?

I know that this question may sound stupid, but what I mean is that photons have some energy and no mass, yet the mass and energy are said to be equivalent (or maybe I got that part wrong). In an ...
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1answer
104 views

Colliding particles at speeds aproaching c [closed]

(In natural units where $\hbar=c=1$.) Two particles are to be collided. Each of these particles has a rest mass of 0.9 GeV and they will be collided at equal but opposite speeds. What is the minimum ...
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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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4answers
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Is the existence of electromagnetic standing waves dependent on the observers reference frame?

If I take two plane EM waves travelling in opposite direction e.g. $E = E_0 \sin(kx-\omega t)$ and $E=E_0 \sin (kx + \omega t)$, they sum to give a standing wave with a time-averaged Poynting vector ...
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Is speed of light ( Sun-to-Earth ) related to the movement speed of solar system?

The speed of light has been measured to be 299 792 458 m/s. Now, the Solar System is traveling at an average speed of 828,000 km/h (230 000 m/s). Summing up the numbers we get close to 300 000 000 m/s ...
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1answer
52 views

Taking signal travel time into account in Special Relativity

I am having problems taking the time it takes for a light signal from an event to reach an observer into account: For instance, if we have two observers $A$ and $B$ who synchronize their clocks when ...
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203 views

Learning the stress-energy tensor

I am learning dynamics in special relativity and come across the stress-energy tensor. I have real trouble understanding it. I would love answers on How to motivate the definition of this tensor. ...
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2answers
165 views

Magnetism due to relativity?

So I have been reading in some books that magnetism does not have to be assumed a priori, but can be obtained from the electric field + special relativity. And I have seen how this leads to the common ...
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What happens when relativistic effects stop?

I'm currently learning special relativity in high school and we only primarily deal with what happens when an object is moving at constant relativistic speeds. But what if the object slowed back down ...
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1answer
255 views

Is there a graphical representation of the Lorentz transformation equations?

I always loved theoretical physics as a kid and when I came upon this site while seeking computer advice via superuser I had to stick my silly little head into an oasis of intelligence. I have often ...
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Are there 'special' cases for when special relativity can be applied for accelerating bodies?

I have the following theoretical situation: A space station modeled as a ring in free space is rotating about its centre point at a high speed. I am trying to work out where time flows slower. From ...
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3answers
418 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) ...