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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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Speed of light as the maximum speed and movement course

Assuming we have 3 objects d,e,f moving on the same line while e is stationary, d is moving to the left at 'almost speed of light' and f is moving to the right at 'almost speed of light'. What is the ...
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55 views

Journey away and back at close to the speed of light $c$

If a person drives away from a clock tower at a speed close to $c$ for one whole day, and then drives back to it at the same speed (for another day), what would he see during each of the journeys? I ...
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85 views

How does acceleration affect time dilation and length contraction?

I just studied SR and I understand how velocity affects time and length; how do they evolve during the process of reaching a certain velocity?
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Question about terrell rotations and measured lengths

I was studying terrell rotations and high speed imaging. From what I've gathered, things moving close to the speed of light look like they have rotated, but when you measure them, you find that their ...
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55 views

Isometry in two dimensions

Let A be an isometry, then $g^{ij}=A^i{}_{k}A^j{}_l\,g^{kl}$ (1) First, consider an infinitesimal transformation $A=\exp(\epsilon \lambda )$ Then express A by its power series to the first ...
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If a photon doesn't experience time, how can it have a frequency? [duplicate]

It is said that photons, moving at c, do not experience time. But then, if a photon doesn't experience time, how can it have a frequency?
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Why is the magnitude of a photons 4 momentum vector 0 if it has momentum?

I've just started studying 4 vectors. I understand because a photon has 0 rest mass and travels at c, you can not define a 4 velocity for it, and as momentum 4 vector = mass x velocity 4 vector, it ...
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How much energy is required to perform the Saitama's moon-jump?

I have no real knowledge of physics beyond the very basics of classic Newtonian mechanics, but as far as I understand, when a particle moves closer to the speed of light, its "relativistic mass" ...
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61 views

Expression of proper time with light perturbation on Minkowski metric

In my lecture on General relativity, it is said that, by taking the following metric : $$g_{\mu\nu}(x)=\eta_{\mu\nu}+h_{\mu\nu}(x),~ {\rm with}\ h_{\mu\nu}\ll1$$ one has the definition below of ...
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Light's direction in a spinning emitter

A stick of length x accelerates in a circular path around an axis. At its end is an emitter that radiates photons in a path parallel to the stick when at rest. How much would the stick have to be ...
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Time dilation misunderstanding

There is a person at rest and a train in motion with velocity $v$. Inside the train, there is a dog running with velocity $u$ respect to the train. The problem states the person inside the train has ...
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1answer
61 views

Is length contraction and time dilation symmetrical between non-accelerating reference frames?

You awaken on a deep space observing station. You do not know its acceleration history but right now there is no gravity and you are billions of light years from the nearest other molecules. A light-...
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Keeping Time constant instead of speed of light in “Special Theory of Relativity” [closed]

I was reading special theory of relativity and I figured out that, basically this whole theory is revolving around three main factors. Motion(speed) Time Space (length) The result of Michelson–...
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140 views

About the mass of the particles

Studying Higgs mechanism in EW theory and QCD I have a couple of questions that I would like to clarify: 1) The quark mass term in QCD Lagrangian should come from Higgs mechanism in EW sector of SM. ...
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71 views

$E = mc^2$ and Binding Energy Confusion [closed]

I have been introduced to $E =mc^2$ and binding energy recently while studying nuclear physics and I have a hard time understanding the following: Mass-Energy what does $E=mc^2$ really mean, as I ...
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42 views

Special relativity, question about the transformation of EM field

We have defined the electromagnetic tensor field as always as : $ F^{u \nu} = \partial^u A^{\nu} - \partial^{\nu} A^u$ Then to see how the fields transform we have applied: $ F'^{u \nu} = \Lambda^...
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Particle decay and momentum

Studying particle physics I had a doubt that I can't seem to find a solution: Is possibile in a particle decay to produce some particles with no momentum? As an example: take the following decay ...
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84 views

Questions about special relativity, index in the Lorentz matrix

I'm studying special relativity I have read this: We have $ x^u = (ct, x^1,x^2,x^3) $. If we apply Lorentz transformation we can write: $x'^u = \Lambda^{u}_{\hspace{0,2 cm}\nu} x^{\nu} $ $x'_u =...
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Rindler's trap door experiment with a rod (or a tank, or a pile of fragile matter) of finite hight

About 60 years ago a thought experiment was proposed which is widely referenced, e.g. as "Man falling into grate variation" of "The ladder paradox" or, perhaps more poignantly, "The tank paradox": ...
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Query about a variation of the ladder paradox

I am learning about special relativity on brilliant.org, they have a problem where a space ship is trying to escape a laser beam that is shot at them by hiding behind an asteroid of length 1. The ship ...
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106 views

Intuitive explanation for the Lorentz transformation for time

I've recently started learning SR, and while the Lorentz transformation for space is pretty obvious, just the Galilean transformation combined with space contraction, I can't figure out the ...
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154 views

Does general relativity reduce to special relativity for free falling objects?

The following was stated in a general relativity lecture series: "Full space is needed in GR. Minkowski space is sufficient for SR. However, Minkowski space is sufficient to compute properties of free ...
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The Electromagetic Tensor and Minkowski Metric Sign Convention

I am trying to figure out how to switch between Minkowski metric tensor sign conventions of (+, -, -, -) to (-, +, +, +) for the electromagnetic tensor $F^{\alpha \beta}$. For the convention of (+, -,...
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Increased mass of compressed springs [closed]

Based on the idea that mass is an emergent property of fundamental particles with potential energy bound in a restricted space, I want to make a macroscopic analogy. I want to put compressed springs ...
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3answers
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Can the Pauli equation be used to derive the usual $\mathbf L\cdot \mathbf S$ spin-orbit coupling? If not, what's the simplest way?

Can the Pauli equation, $$ \left[{\frac {1}{2m}}({\boldsymbol {\sigma }}\cdot (\mathbf {p} -q\mathbf {A} ))^{2}+q\phi \right]|\psi \rangle =i\hbar {\frac {\partial }{\partial t}}|\psi \rangle, $$ be ...
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Upper limits for jerk and higher derivatives in physics

Is there an upper limit for jerk in physics? What about higher derivatives? A consequence of special relativity is that no material body can reach or exceed the speed of light in vacuum (due to ...
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Error with generators of Lorentz group (basis of Lorentz Lie algebra) [closed]

Can someone help me figure out why my $J_y$ is incorrect? :/ It's supposed to be \begin{pmatrix} 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 1 \\ 0 & 0 & 0 & 0 \\ 0 & -...
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Understanding the reasoning of answer

This is exercise from Morin's book of classical mechanics(Q-12.14 in screenshot 2). He asks to calculate force in 2 different frames. I got the answer and it matches with the solution provided(...
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2answers
216 views

A simple proof covariance of Maxwell equations

I read that Maxwell equations are covariant under Lorentz transformations, but I can't find a proof. Or at least a proof understandable by someone that doesn't know higher mathematics (please don't ...
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Is magnetism caused by effect of relativity on interaction between moving charges?

I have heard that cause of magnetism is easily amswered by relativity ? Is it true ? If then how can we explain cause of Fleming's left and right hand rules ?
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Thought experiment: if an observer can travel at the speed of light [closed]

What would the observer see if he could travel at the speed of light and shot a photon beam at the same time?
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Why are fields which do not transform in a certain way not fundamental?

When I was first exposed to Math physics textbooks and textbooks on vector calculus, I found: Temperature distribution in a room $T(x,y,z,t)$ or the density variation in a fluid $\rho(x,y,z,t)$ etc ...
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Time in Lorentz transformations

I have a question about the meaning of time in Lorentz transformations. When we say that event A for S' occurs at t', I understand that this ct' is a distance, but I wonder exactly what does it ...
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Speed of light dependent on source velocity in other medium [duplicate]

Does speed of light depends upon the velocity of source in a medium (like water) other than space? if yes, does the speed gets added up when the light source moves in direction of light?
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Spaceship A and Spaceship B move in opposite directions at half the speed of light, and A fires a laser at B, does the laser light reach Spaceship B? [closed]

This question has been bugging me for a week now! I believe it would, but logically, I feel like I'm missing something. Please give a full explanation.
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Inertial frames with unknown past

Let's suppose two ships that cross in space at constant speed. We do not know their previous acceleration or velocity history. When they cross, they synchronize watches. From that moment, if they ...
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Different prediction about the motion of a charge as observed by two different observers?

Suppose a charge is at rest in the laboratory frame. Also, say two observers in two vehicles A and B are approaching towards it. Let A be accelerating towards it and B be moving uniformly towards it. ...
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Lorentz Transformation: Message sent before finish line

As she wins an interstellar race, Mavis has a “hooray” message sent from the back of her 300m long ship as she crosses the finish line at v=0.6c. Stanley is at the finish line and at rest relative to ...
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1answer
118 views

How can direction of electric field due to a moving charge be from the present position of charge?

According to Maxwell's Equations, the electromagnetic waves in vacuum travel at the speed of light $c$. While solving Maxwell's equations using Lorenz gauge conditions (or basically evaluating scalar ...
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Is the potential energy of falling into a black hole already included into E=mc^2?

Each object in the Universe has a huge potential energy, because you can drop it into a black hole, accelerating it to nearly the speed of light. Is this potential energy already included into ...
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What is the elapsed time at the centre of mass in the Twin Paradox scenario? [closed]

Do the twins age differently if you take away the Earth and the spaceship and the rest of the universe and tether them together with a bungee cord? I should hope not, unless one is fatter than the ...
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Finding the mass of a relativistic particle resulting from decay

I'm studying relativistic kinematics for the first time. I’m working with a problem from a book but I’m stuck: A relativistic particle of rest mass $m_1$ decays at rest into a particle of rest mass $...
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2answers
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How to derive: $\frac{E^2}{c^4} = \frac{p^2}{c^2} + m_0^2$?

My teacher wrote the following equation on the board a few days ago: $$\frac{E^2}{c^4} = \frac{p^2}{c^2} + m_0^2$$ And I got no idea how this is derived especially since we already derived that: $$m^...
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4answers
212 views

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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1answer
74 views

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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1answer
78 views

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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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
84 views

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 ...