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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Metric signature conventions: minus sign for $x^a$ or $x_a$?

Say I use the metric signature $(-+++)$. Then $\partial_a=(\partial_0,\partial_i)=(-\partial^0,\partial^i)$, but $\partial^a=(\partial^0,\partial^i)=(-\partial_0,\partial_i)$. The same goes for $p^a$ ...
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Dingle vs. Bondi: Twin Paradox Debate on BBC radio?

Herbert Dingle and H. Bondi debated the twin paradox on BBC radio before 1971. Does anyone have a link to the audio of this debate? thanks
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80 views

Twin Paradox: Whose time is slow? [closed]

What I understand about the twin paradox is that if a person stays at rest with something lets say the earth and a traveller moves with a great velocity with respect to the firsy person, then the time ...
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294 views

$E=mc^2$ resembles kinetic energy formula?

The simplest equation expressing mass–energy equivalence is the famous $E=mc^2$ where $c$ represents the speed of light. Compare this with $E_K = \frac{1}{2}mv^2$. Since $E=mc^2$ can be applied to ...
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4answers
148 views

Relative Motion

I read the following: http://www.feynmanlectures.caltech.edu/I_15.html#Ch15-S4 "Now let us see what happens to the moving clock. Before the man took it aboard, he agreed that it was a nice, ...
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Twin Paradox: Still a Paradox?

Alright, so David Griffiths in his "Introduction to Electrodynamics" states that the Twin Paradox is not a paradox at all since the traveling twin returns to Earth. By returning to Earth, the twin had ...
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1answer
351 views

speed of the light emitted from a fast moving object [duplicate]

Would not speed of the light emitted from the front of the fast moving object be the speed of light + the speed of the fast moving object?
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2answers
279 views

Confused about the concept of time and time dilation [duplicate]

I am having a hard time understanding what is time. If scientists define time as a multiple of caesium frequency, then time itself is dependent on motion, so what if I have a number of particles that ...
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1answer
401 views

Minkowski metric — why does it follow from the constancy of the speed of light [duplicate]

In all the sources I’ve been able to find, the Minkowski metric appears ad hoc, or is defined analogously to the euclidean metric. I’d love to see an argument why this metric (time coordinates ...
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1answer
201 views

Do hot objects moving at relativistic speeds slow down as they emit radiation?

In an astrophysics class I learned about the Poynting-Robertson effect, by which grains of dust orbiting a star slow down and eventually fall into the star. Every source that I have been able to find ...
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2answers
679 views

How did Einstein come up with his postulates for Special Relativity using thought experiments on simultaneity?

In his popular book on relativity, in chapter IX, "The relativity of simultaneity", Einstein describes an experiment in which a flash happens simultaneously on A and B, as defined by the fact that an ...
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2k views

How to do calculation in relativity of simultaneity

I have great trouble in understanding simultaneity in special relativity. Let me illustrate it with a concrete example. Assuming there is a train, its two end points are $A$ and $B$, the length of ...
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5answers
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What is the cause of Special Relativity [closed]

Why does special relativity exist? Via studying the outcome(s) of such relativity, one can end up with all the equations involved in special relativity. Thus one runs into things such as contraction, ...
2
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1answer
193 views

Can I measure a journey time < 100 years on a 100 light year voyage? [duplicate]

So, I'm traveling to another star 100 light years away in my spaceship. This ship has a solar sail pushed by a laser beamed from my home star system, so can achieve a velocity close to c. It's also ...
4
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3answers
1k views

Chasing a photon [duplicate]

According to this article, the Theory of Special Relativity holds that if you were chasing a stream of light at half the speed of light, $c/2$, the light's speed relative to you would still be $c$. ...
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1answer
172 views

Red shift/blue shift: how would it appear to a fast-moving observer?

I've read sci-fi stories in which a spaceship crew, moving at some significant fraction of 'c', observes stars ahead as bluer, stars behind as redder, stars to port and starboard as...well, you get ...
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1answer
94 views

Distance and time measurement in the famous Superluminal Neutrinos Experiment

I tried to understand the technical aspects of the OPERA/CERN experiment, but apparently it takes some professional experience. Therefore I would like to ask someone better acquainted with such ...
2
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1answer
87 views

Pair Creation and Reference Frames

Ok, so I have a question about an example problem in my textbook (its long but not difficult to follow. My question is at the bottom after I outline the problem). Consider the situation below in frame ...
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4answers
2k views

Time dilation all messed up!

Okay! There is a problem with my logic and i cannot seem to point out where. There's a rocket ship travelling at close-to-c speed v without any acceleration (hypothetically), and there is an observer ...
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1answer
357 views

Question Regarding Lorentz Transformation

I have question regarding the following velocity transform formula: $$v_b = \frac{v_a - u}{1-uv_a/c^2}$$ $u$ here refers to the speed that one frame is moving relative to another. How do I decide ...
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0answers
83 views

Is the cross section of a relativistic water hose or string always a perfect circle?

Given is a very long tube, such as a water hose or a tubular string with finite thickness, that has a constant circular cross section of radius $r$ along the length and that is at rest in an inertial ...
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3answers
881 views

If a neutrino has a rest frame, why can't a photon have a rest frame as well?

Concerning Rest Frame Wikipedia states: For example, in the rest frame of a neutrino particle travelling from the Crab Nebula supernova to Earth the supernova occurred in the 11th Century AD ...
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3answers
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How does wind speed affect the velocity of light?

As you know, there is a maximum speed things can go called $c$, the "speed of light." Light in a vacuum goes $c$. Light in the atmosphere, however, goes a little less than $c$. My question is: what ...
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0answers
116 views

Deriving the relativistic Larmor equation

I have derived the Larmor equation as $$P = \frac{q^2}{6\pi \epsilon_0 c^3} |\ddot{r}|^2.$$ How do I make this relativistic? Apparently, I have to consider the acceleration parallel and ...
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1answer
79 views

Relativistic Dynamical System

I have read in a paper that: A relativistic dynamical system must be invariant under infinitesimal inhomogeneous Lorentz transformation. A dynamical system is characterized by the ten generators, $P^\...
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1answer
80 views

Is the presence of the phase velocity of De-Broglie wave in the Lorentz Transformations a mere coincidence?

We have the term $c^2/v$ in the lorentz transformation for time: $t' = \gamma (t - x v/c^2)$. Now, taking into account of the fact that $c^2/v$ is the phase velocity of the De-Broglie wave for a ...
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Can we glue femto-cameras to photons? [closed]

I know its not as easy as saying to glue nano-cameras to photons. Please consider the following extract (related to Heisenberg's Uncertainty principle) from the Modern's abc of Chemistry: ...to ...
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0answers
129 views

Paradox - Laws of physics are the same in all inertial reference frames vs Equivalence Principle (Pictures Added)

According to the equivalence principle, no experiment should exist that one can perform to determine whether one is in an accelerating elevator, or in a gravitational field. I will outline two ...
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2answers
519 views

Dropping a ball in a train moving close to the speed of light?

Suppose a train is moving very close to the speed of light, say 0.999c relative to a stationary observer on Earth. Now a stationary observer on Earth will observe clocks on the train to tick slower ...
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1answer
197 views

A simple question about special relativity [closed]

Assume that the table moves with the velocity $\vec{v} = v\hat{i}$. For the observer at $x=0$, the event at $(ct',x')=(0,k)$ is observed at $(t,x)=(k\gamma\beta, k\gamma)$ using Lorentz's ...
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5answers
169 views

Can the equivalence principle be shown to follow from special relativity?

Einstein showed in various papers that the energy content of a body was a measure of its inertial mass. If you increase the internal energy of a system while keeping the center of energy at rest, its ...
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185 views

Lorentz invariance?

What exactly is meant by Lorentz invariance? Is it just an experimental observation, or is there a theory that postulates it? What quantities do we expect to be Lorentz invariant? Charge? Charge ...
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1answer
386 views

Confusion about Length Contraction in special relativity [closed]

so I'm working on length contraction in relativity theory. I feel pretty confident time dilation and have not really gone over Lorentz Transformations that much. The question itself lies at the ...
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506 views

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 base....
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1answer
102 views

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 $x$ direction ...
3
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1answer
209 views

Does divergence of Taylor series for relativistic $E(p)$ for $p\ge m$ have any physical significance?

When one wants to include weak relativistic effects in classical equations, usually kinetic energy term is expanded into Taylor series about $p=0$. But the complete dispersion relation is $E=\sqrt{m^2+...
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Deriving formula for time dilation

Last week in class we derived the formula for time dilation using light clocks and got $$t=\gamma t_0\quad \gamma=\left(1+\left(\frac vc\right)^2\right)^{-1/2}$$ So far so good. However, after class I ...
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2answers
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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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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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Heat energy in special theory of relativity [duplicate]

Is heat energy invariant under Lorentz transformation? If so then how?
38
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1answer
15k views

How long would it take me to travel to a distant star?

Suppose I wanted to travel to one of the recently discovered potentially Earth-like planets such as Kepler 186f that is 490 light years away. Assuming I had a powerful rocket and enough fuel, how long ...
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3answers
853 views

Is there an upper limit to temperature in thermodynamics or statistical mechanics

In many presentations of statistical mechanics where we have a system of particles having mass, such as the molecules of an ideal gas, the temperature is often equated to the average relative velocity ...
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1answer
26 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 S^{...
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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 (...
2
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3answers
119 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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96 views

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, e.g....
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414 views

Problem in the Ladder paradox in relativity?

The ladder paradox consists of a ladder rushing towards a garage with two open doors. In the actual paradox, proper length of the ladder is greater than that of the garage, but in this case lets ...