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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“Vectors” (i.e. 1-tensors) their definition and motivation for relativity

I'm reading Einstein Gravity in a Nutshell (by Zee) and here he defines a vector as an object which is invariant under coordinate representation; concretely, if in one coordinate representation, $V$, ...
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1answer
66 views

How much time passed for the passenger traveling with at speed-of-light spaceship? [duplicate]

Let's suppose we have a spaceship with the exact speed of light. If a traveller takes this spaceship to go to proxima centauri (approximately 4 years light away from Earth) and come back, we (as ...
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2answers
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Is it ok to have two events $A$ and $B$ so that for one person $A$ occurs before $B$ but for another $B$ preceds $A$

Imagine two laser beams A and B are released at the same moment to bounce between two mirrors, A was moving and B was at rest, doing the calculations I found that for a person at rest B would reach ...
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One question about derivation of Maxwell equations

I saw the following way of derivation of Maxwell equations: author starts from Lorentz transformations for the 3-vector of force, then he applies them for the Coulomb law, after that gets the Lorentz ...
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what about doing the laser beam in a moving reference frame but with a ball

I realize the situation where a laser beam moves vertically in a moving vehicle but what if the laser beam was a normal ball If we do the same steps of the proof considering that the velocity of the ...
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Is it possible to derive Lorentz transformation equation without Einstein's postulates?

Overview Einstein's proof for the Lorentz transformation is given here: From $O$'s view point, $x^2+y^2+z^2 = (ct)^2$. Form $O'$'s view point, $x'^2+y'^2+z'^2 = (ct')^2$. We find that Einstein ...
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Relativity and the Higgs field

We know very well that as the velocity of an object increases, its relativistic mass also increases because of an increase in its energy which is directly equivalent to mass. We also know that the ...
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123 views

Dragon Ball Z: Hyperbolic Time Chamber *(also increased gravity training) [closed]

Firstly, I am sorry if this seems like a joke. It is not. I have always loved the Dragon Ball series, so this question has been on my mind for a while. Can ...
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2answers
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Why does the light intensity increase as I approach a distance light source?

Analogy: assume that I have constant rain fall and I have a water bucket to collect this rain. If I am rest relative to the earth, I will catch a certain amount of rain. However, if I now move towards ...
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Energy carried by photon not conserved?

In an imaginary frame of reference traveling with a photon, the length of the path traveled is 0. If the length of the path is 0, isn't it similar to say that the photon is either at the source or at ...
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1answer
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What invariant counting process derives the Minkowski metric?

Starting with Euclidean space, suppose I make a number of copies of a coordinate system all coincident at the origin, together with copies of a standard unit length. For any space interval common to ...
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Understanding the “$\pi$” of a rotating disk

Let us say you are in an inertial reference frame with a circular planar disk. If you take your meter measuring rods (or perhaps tape measure) you can find the diameter and circumference of the disk. ...
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Would infinite time elapse relative to an outside observer if an object was completely at rest?

Here's my reasoning... time dilation due to velocity: t'=t√(1-v^2) v expressed as a % of the speed of light. If you are moving through distance at the speed of light, to an observer at rest relative ...
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1answer
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Lorentz transformation via light clocks in parallel direction

In order to derive the Lorentz transformation one can use the picture of a light clock. A Photons bounces back and forth between two mirrors. This is then observed in two different inertial systems. ...
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2answers
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Binding energy and invisible mass

The gravitational binding energy of a sphere is: $U=\frac{3GM^2}{5r}$, the mass defect is $\Delta E=\Delta m c^2$. Putting: $M=\frac{4}{3}\rho\pi r^3$, we get: $$U=\frac{16}{15}G\rho^2\pi^2 r^5$$. Now ...
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Why doesn't time change in the non-relativistic limit of Lorentz transformations?

A simple boost in the $x$ direction is given by: $$ \Lambda = \begin{pmatrix} \cosh(\rho) & \sinh(\rho) & 0 & 0 \\ \sinh(\rho) & \cosh(\rho) & 0 & 0 \\ 0 & 0 & 1 & ...
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Special relativity and imaginary coefficient of the time coordinate

I read somewhere that part of Minkowski's inspiration for his formulation of Minkowski space was Poincare's observation that time could be understood as a fourth spatial dimension with an imaginary ...
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1answer
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Relativity Question Fireworks explosion

A firecracker explodes at the origin of an inertial reference frame. Then, 2.0 microseconds later, a second firecracker explodes 300m away. Astronauts in a passing rocket measure the distance between ...
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Why is the speed of light arbitrarily the limit? [duplicate]

I know Einstein was great and all. Why is it that exactly at the speed of light is where infinite energy is required to accelerate any object with mass? Is it simply because the math of relativity ...
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1answer
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NASA Theoretical Faster Than Light Space Travel (IXS-Enterprise)

I was recently reading about NASA Faster than Light proposed spaceship, it supposedly will bend spacetime behind the spacecraft, so technically instead of bringing the ship to the destination, "it ...
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1answer
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Why does time dilation cause you to age slower? And is time considered relative to the observer?

I understand that the higher your velocity the slower light will move. But how does time itself slow down while you are moving faster?
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1answer
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Can you calculate unix timestamps (universal clock) from any planet?

Given the definition of unix timestamp as the number of seconds elapsed since January 1st, 1970 as GMT+0, without leap seconds, is it possible to create a universal clock that will generate the ...
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Is the total cross section a Lorentz Invariant?

In Peskin and Schroeder's book (P&S), on the botton of page 106, the authors say that the total cross section transforms as its only non-invariant factor, namely: $$ {1 \over E_{A} E_{B} |v_A - ...
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1answer
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How to get the accurate relativistic momentum form for photons? [duplicate]

I have studied from Griffiths, the relativistic form of momentum is $$p = \frac{1}{\sqrt{1-\frac{v^2}{c^2}}} m_0v$$ Now when I evaluate the momentum for photon, I just insert $v=c$ and $m_0=0$ and I ...
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A Subtle Connection Between Time Dilation in SR and GR - Why is this so?

I've been reading a book on General Relativity lately (Gravitation and Cosmology, Weinberg), and I was reading about the weak field approximation. It derived the time dilation in a weak gravitational ...
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Why should photons obey the rules of causality? [on hold]

This may have a quick answer, but it has been on my mind so here it goes: why, if according to special relativity, do photons obey the rules of causality, if they are inherently timeless. According to ...
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thrust-bursting towards a destination in space

<--burst of thrust------|ME in a ship>----->>--<<--laser radar--<<---->>---||destination In the above, I imagine myself in a ship, marking my speed to a far off destination with laser ...
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1answer
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Finding the total energy in centre of mass frame

I'm working through a problem in a special relativity textbook (Woodhouse) and I'm having some difficulty. I have to show that if I have a particle of rest mass $M$, total energy $E$ colliding with a ...
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1answer
87 views

Exeeding the speed of light by adding velocities [duplicate]

Well you know how it's said that things can't travel at or past the speed of light? However, can't they move at speeds greater than the speed of light relative to another object? For example: What ...
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472 views

Why isn't there a limit for a Euclidean rotation, as for a Minkowski rotation?

From invariance of the Minkowski scalar product, we get the Lorentz transformations. In addition, we get a constant $c$ preventing space-like and time-like intervals being rotated into one another. ...
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Clocks in special relativity

One book on special relativity says: Any observer at rest relative to his own timepiece will see that other clocks moving with respect to him run fast - the greater their speed, the faster they ...
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Most natural tensor structure for a quantum field

A quantum field is described by a Hilbert space. In many instances, the chosen tensor structure on this Hilbert space corresponds to that of space-like separated regions of space-time. The ...
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Where did the energy of the charge go?

Suppose there is a positron and an electron, and they both collide, and we get $E=2mc^2$ of energy from the collision. Now, the charge also got vanished. Now suppose, I create neutrinos from the ...
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Time and the principle of relativity

We know that every moving clock with respect to some clock A, is running slower than A. My question is simple - why it does not contradict the principle of relativity? Why can't we say that the clock ...
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How do I actually calculate the Lorentz transformation of a field strength tensor

Say now I have an arbitrary field strength tensor $F$, and I want to boost it according to a Lorentz transformation matrix $(\Lambda)$ The transformation is given by $$ F^{'\mu \nu} = ...
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1answer
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Will we feel the gravity of a star 10 light years away for the next 10 years if, somehow, it vanishes today from its position? [duplicate]

I was watching a relativity video, and although I am not sure, I felt that it was trying to tell that the effect of gravitation of a body is instantaneous, in the sense that a sudden change in the ...
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4-acceleration of rotating frame

Consider the 3-dimensional Minkowski space $$ ds^2=dt'^2-dr'^2-r'^2d\phi'^2 $$ Now we transform it into a rotating frame: $$ t'=t,r'=r,\phi'=\phi+\omega t $$ Then the metric becomes $$ ...
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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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5answers
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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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2answers
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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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1answer
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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 ...