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special relativity | Doppler redshift in special relativity | https://physics.stackexchange.com/questions/68132/doppler-redshift-in-special-relativity | <p>I came across this exercise in Elementary General Relativity by Alan MacDonald:</p>
<p>A source of light pulses moves with speed v directly away from an observer at rest in an inertial frame. Let $ \Delta t_e $ be the time between the emission of pulses, and $ \Delta t_o $ be the time between their reception at the... | <p>Your answer is right assuming $\Delta t_e$ is the interval between emission <em>as measured by the emitting source itself</em>. The given answer is right assuming $\Delta t_e$ is the time between emission <em>as measured by the observer</em>. It seems as though this problem is aiming at a lower level than your curre... | 400 |
special relativity | Relativistic corrections to classical physics formulae | https://physics.stackexchange.com/questions/71943/relativistic-corrections-to-classical-physics-formulae | <p>How are classical formulas in physics (such as p = mv, or kinetic energy, or maxwell distribution of speeds) treated with the appropriate relativistic correction/modification? Is it done by using the Lorentz transformation equations? Could anyone give me a few examples of relativistic corrections to classical formul... | <p>Alfred Centauri's wiki link certainly gives you a nice list of such things, but that entry doesn't exactly show you how such quantities reduce to their non-relativistic counterparts. </p>
<p>In particular, in the context of classical mechanics, one can generically show that relativistic expressions reduce to their... | 401 |
special relativity | Minkowski Metric | https://physics.stackexchange.com/questions/76134/minkowski-metric | <p>Hi all I'm a little confused </p>
<p>So I have that in special relativity time is included as a coordinate so that in 1 spatial dimension we have 2 space time coordinates. The most basic metric is the Minkowski metric given by $\left[ {\begin{array}{*{20}{c}}
{ - 1}&0 \\
0&1
\end{array}} \right]$ ... | <p>We assume that we are working in units where the speed of light $c=1$. Given a vector with time and space components $A=(A^t, A^x)$, the Minkowski square of the vector is
\begin{align}
A^2 = -(A^t)^2+(A^x)^2
\end{align}
We can classify the vector $A$ according to the sign of its square length. In particular, in... | 402 |
special relativity | Is it possible to derive the invariant spacetime interval from Einstein's two postulates for SR? | https://physics.stackexchange.com/questions/76716/is-it-possible-to-derive-the-invariant-spacetime-interval-from-einsteins-two-po | <p>In many textbooks, the interval</p>
<p>$$
I = -(c\Delta t)^2 + (\Delta x)^2 + (\Delta y)^2 + (\Delta z)^2
$$</p>
<p>is taken for granted as the same for two events in any reference frame.</p>
<p>Is it possible to derive this just from the two postulates,</p>
<ol>
<li>That the laws of physics are the same in all ... | 403 | |
special relativity | Time dilation apeears in the both frame: Where is the problem? | https://physics.stackexchange.com/questions/83841/time-dilation-apeears-in-the-both-frame-where-is-the-problem | <p>Let we consider time in stationary frmae t, and respect the to stationary frame moving frame time $t^ \prime $ .</p>
<p>According to lorentz transformation,</p>
<p>$$t^\prime= \frac{t-\frac{vx}{c^2}}{\sqrt{1-\frac{v^2}{c^2}}}$$ and according to inverse Lorentz transformation, $$t= \frac{t^\prime +\frac{vx^\prime... | <p>For defining time dilation you first need to understand 'proper time interval'.
Proper time(denoted $\Delta t_0$) is time taken in an inertial frame in which two events occur at same position. This proper time interval is dilated in all other frames of reference. </p>
<p>Let two events occur at $(x_1,t_1)$ & $... | 404 |
special relativity | Special Relativity and current in wire | https://physics.stackexchange.com/questions/83908/special-relativity-and-current-in-wire | <p>If I am a stationary observer and the electrons are moving relative to me,then shouldn't its density increase according to special relativity and thereby create an altogether negative net charge.</p>
| <p>Increase in density doesn't mean that it creates negative net charge. The charge is preserved. </p>
| 405 |
special relativity | Speed of Light and Special Relativity | https://physics.stackexchange.com/questions/91344/speed-of-light-and-special-relativity | <p>If light is travelling vertically upwards and I am travelling horizontally and perpendicular to light, the velocity of light in the vertical direction will get reduced. How does this happen? How does motion in x-direction cause a reduction in speed of light in y-direction ?</p>
<p>Also, in Lorentz Transformation, s... | <p>You're asking so many questions that the only way to answer satisfactorily would be to completely rejustify special relativity. I suggest you take a look at a book like <a href="http://rads.stackoverflow.com/amzn/click/0393097935" rel="nofollow">Special Relativity</a> which does such a thing!</p>
<p>I'll try to ans... | 406 |
special relativity | How is length contraction reconciled with other objects occupying space? | https://physics.stackexchange.com/questions/91084/how-is-length-contraction-reconciled-with-other-objects-occupying-space | <p>Say I have a ball at 0.999999% the speed of light going past the Sun toward Earth. Now from the ball's reference frame, the distance between Earth and Sun is the same length as the ball's diameter. Why is the ball occupying the entire space between the Earth and Sun? What happened if a comet was between the Earth an... | <p>You should check out the barn paradox! It's about the same thing.</p>
<p>The problem is that there's an extra effect in relativity you haven't accounted for: observers don't agree on the order of events. For example, in the earth frame, we may have the ordering</p>
<ol>
<li>Back of ball at sun</li>
<li>Something p... | 407 |
special relativity | Synchronisation of clocks | https://physics.stackexchange.com/questions/93463/synchronisation-of-clocks | <p>How can two clocks be synchronised with each other at some instant without being at the same place and same time $?$ considering that simultaneity is a relative concept .</p>
| <p>Here's the standard way in flat spacetime. Let's say you want to produce a synchronized pair of clocks that are a spatial distance $d$ away from one another, then perform the following steps:</p>
<ol>
<li><p>Construct two identical clocks such that they start ticking when they receive a special light signal. Call... | 408 |
special relativity | Moving Clocks Time Problem | https://physics.stackexchange.com/questions/93675/moving-clocks-time-problem | <p><a href="http://www.pitt.edu/~jdnorton/teaching/HPS_0410/chapters/Special_relativity_rel_sim/index.html" rel="nofollow">http://www.pitt.edu/~jdnorton/teaching/HPS_0410/chapters/Special_relativity_rel_sim/index.html</a></p>
<p>Talking about the situation of clocks shown on this page. Clocks A&B. Now suppose cloc... | 409 | |
special relativity | Relativity and speed of light again - two opposite light sources | https://physics.stackexchange.com/questions/94492/relativity-and-speed-of-light-again-two-opposite-light-sources | <p>Two light sources emit light at the same moment but in opposite directions. At what speed the distance between two light fronts is increasing? <strong>c</strong> or <strong>c</strong> * 2?</p>
<p>Note, that there is only one coordinate system here - a system, where these two light sources are placed and they don't ... | <p>I think you are asking: If I turn on a lightbulb, I can imagine a sphere of light spreading radially outward from the bulb at the speed of light. How fast is the diameter of the sphere increasing in the lightbulb's frame? The answer is 2*c.</p>
| 410 |
special relativity | Inner product of four-vectors in special relativity | https://physics.stackexchange.com/questions/32762/inner-product-of-four-vectors-in-special-relativity | <p>Reference) "Feynman lectures on Physics Vol.3 , p.7-4 ."</p>
<p>With four vectors $x_{\mu} = (t,x,y,z)\ , \ p_{\mu} = (E,p_{x},p_{y},p_{z})$</p>
<p>the inner product of these two four vectors is scalar invariant and equals to $Et - \overrightarrow{p} \overrightarrow{x}$ . Alright.</p>
<p>But I cannot understand w... | <p>The value of $xp=x^\mu p_\mu=\eta^{\mu\nu}x_\mu p_\nu$ (with the sum over repreted indices) is invariant, i.e. if $A$ and $A'$ denote two frames, then the number given by the product $xy$ is the same as $x'y'$. </p>
<p>In one frame $A$, the expression $xp$ might evaluate to $Et-\vec x \vec p$, in another frame $A'$... | 411 |
special relativity | Airplane example of special relativity | https://physics.stackexchange.com/questions/43258/airplane-example-of-special-relativity | <p>I'm struggling with an introductory example of special relativity. We haven't done the math yet so I would like an explanation based only on the fact that the speed of light is the same in every inertial frame.</p>
<p>An airplane travels east with a certain speed. There is a "clock" at both ends of the airplane. If... | <p>You started by sentences that indicated that you realize that the speed of light is $c$ regardless of the speed of the source and the observer. However, you quickly wrote another sentence that indicated that the conclusion about knowledge in the previous sentence was an illusion:</p>
<blockquote>
<p>The light's s... | 412 |
special relativity | Special Relativity | https://physics.stackexchange.com/questions/45308/special-relativity | <p>Could someone explain to me how <a href="http://en.wikipedia.org/wiki/Special_relativity" rel="nofollow">special relativity</a> works?</p>
<p>I know there are thousands of sources and databases of knowledge out there, but I find it difficult to understand, even after reading up on those sources.</p>
<p>(Note: if y... | <p>I think I could give some intuitive look on SR. It is not very hard to understand the basic overview of SR. There are only <a href="http://en.wikipedia.org/wiki/Postulates_of_special_relativity" rel="nofollow noreferrer">two postulates</a> and not more that that..! But, there are many sites which provide a bit <em>w... | 413 |
special relativity | what is use of relativistic action? | https://physics.stackexchange.com/questions/52122/what-is-use-of-relativistic-action | <p>this is relativistic action:
$$S=\int_C \mathcal {L}dt$$
where the $\mathcal{L}$ is $-m_oc^2\gamma^{-1}$
what is use of relativistic action!?</p>
| <p>The use of an action is do derive all the dynamical equations of a theory from the least-action principle, $\delta S=0$ (action is minimized along the right path). Quantum mechanically, the use of an action is to derive the transition amplitudes from an initial state to the final state by summing over histories weig... | 414 |
special relativity | Why does 'proper length' exist as a notion? | https://physics.stackexchange.com/questions/52912/why-does-proper-length-exist-as-a-notion | <p>$$\text{proper time}= \tau= \sqrt{dt^2-d\mathbf{s}^2}$$</p>
<p>$$\text{proper length}= L= \sqrt{-dt^2+d\mathbf{s}^2}$$</p>
<p>What tangible benefit is brought about by calling $i \tau$ 'proper length' (applying when $\Im(L)=0$ (the spacetime intervals are spacelike))?</p>
<p>Could one extend the notion of the int... | <p>This isn't complex analysis. There is no reason to complexify anything. These notions do not both exist for a single pair of events. Either two events are timelike separated from one another, and there is a proper time between them that all observers agree on, or the two events are spacelike separated, and there ... | 415 |
special relativity | What are the uses of proper length as a parameter? | https://physics.stackexchange.com/questions/55007/what-are-the-uses-of-proper-length-as-a-parameter | <p>Proper time is used to parameterize the world line of a moving particle in a way which is Lorentz invariant, which is elegant and powerful. Since space and time are usually treated on the same footing, I'd expect proper length to be a powerful parameter of some sort, yet I've never come across it being used in this ... | <p>Proper distance and proper time are both really the calculation of the metric disitance between two events. In general relativity the infinitesimal metric is:</p>
<p>$ds^2 = g_{\mu\nu}dx^\mu dx^\nu$</p>
<p>In special relativity (with units where $c=1$ ), space-time is flat so the Cartesian Minkowski metric betwee... | 416 |
special relativity | Does an accelerating spaceship move backwards due to length contraction? | https://physics.stackexchange.com/questions/62008/does-an-accelerating-spaceship-move-backwards-due-to-length-contraction | <p>Let's assume I have a spaceship in front of me let's say at 1000000km distance. Now let's assume I have also a stationary wall just behind the spaceship at 999999km. Initially the spaceship's speed is 0.</p>
<p>Now let's accelerate the spaceship rapidly to relativistic speeds.</p>
<p>Due to the length contraction ... | <p>The paradox of your situation lies in which frame of reference you're using. In reality, there is no paradox. It seems as though you have a decent grasp on relativistic effects, so I'll spare you the gory details. However, you problem is that in your and the wall's frame, the distance between you and the spaceship... | 417 |
special relativity | Faraday tensor, antisymmetric electromagnetic tensor | https://physics.stackexchange.com/questions/62309/faraday-tensor-antisymmetric-electromagnetic-tensor | <p>I want to write $F^{\mu \nu}F_{\mu \nu}$ in terms of $F_{\mu \nu}F^{\mu \nu}$. How to do it?</p>
| <p>The two expressions you wrote down are the same because for each pair $(\mu,\nu)$, the quantities $F^{\mu\nu}$ and $F_{\mu\nu}$ are real numbers and can be commuted past one another.</p>
| 418 |
special relativity | Doppler shift of radio signals to an accelerating observer | https://physics.stackexchange.com/questions/62851/doppler-shift-of-radio-signals-to-an-accelerating-observer | <p>Suppose a man leaves from Earth to a star which is 1000 light years away. He accelerates to a velocity such that the entire trip lasts a year, from the reference frame of the rocket.</p>
<p>Now lets pretend the person in the rocket wants to have a transmission of the radio to him.</p>
<p>Due to time dilation, when... | <p>You are <em>not quite</em> correct (see edits). Except I wouldn't say that "in reality it takes just slightly over 1000 years" - the rocket frame is no less real than the Earth's frame. As far as the actual numbers go: at one gee acceleration it takes about a year in the rocket frame to accelerate, and a year again ... | 419 |
special relativity | Speed of Light and Information | https://physics.stackexchange.com/questions/64419/speed-of-light-and-information | <p>Einstein in his thought experiment(?) for the constancy of speed of light in vacuum in all frames reasoned , that if speed of light of vacuum isn't constant than you'll be able to perceive effect before action .</p>
<p>But then this must happen in all mediums , but it doesn't ,that means if you live in a medium wit... | <blockquote>
<p>Einstein in his thought experiment(?) for the constancy of speed of light in vacuum in all frames reasoned , that if speed of light of vacuum isn't constant than you'll be able to perceive effect before action .</p>
</blockquote>
<p>Hm, as far as I know his reason for saying that the speed of light i... | 420 |
special relativity | A video conference between earth and a space shuttle | https://physics.stackexchange.com/questions/8539/a-video-conference-between-earth-and-a-space-shuttle | <p>I have just started looking into special relativity and I have come up with an intriguing <em>gedanke</em>, as Einstein himself called such theoretical thought experiments.</p>
<p>Imagine a space shuttle traveling through space at a constant velocity close to $c$. As the shuttle passes earth, a previously set-up ca... | <p>The astronaut will not have received 50 years worth of transmissions at the time you specify. </p>
<p>Let's start by stating precisely what time dilation means in this instance. Consider two "events": </p>
<ol>
<li>The people on Earth have a party to celebrate 50 years of radio broadcasting.</li>
<li>The astronaut... | 421 |
special relativity | Physical interpretation of equation for relativistic aberration | https://physics.stackexchange.com/questions/9507/physical-interpretation-of-equation-for-relativistic-aberration | <p>I'm working in a book on relativity. The author states that if $u$ and $u'$ are a velocity referred to two inertial frames with relative velocity $v$ confined to the $x$ axis, then the quantities $l$, $m$, $n$ defined by </p>
<p>$$
(l, m, n) = \frac{1}{|u|}(u_x, u_y, u_z)
$$</p>
<p>and</p>
<p>$$
(l... | <p>The last form avoids any usage of $u'$ as well as $u_x$ which may be considered derived or non-covariant quantities, respectively, so the last form may be superior in many contexts. Moreover, it makes it much easier to imagine how far the result is from one - because it resembles a Taylor expansion of a sort.</p... | 422 |
special relativity | How is energy conserved when a moving charge has false ideas about positions of other charges | https://physics.stackexchange.com/questions/11075/how-is-energy-conserved-when-a-moving-charge-has-false-ideas-about-positions-of | <p>An electron is shot towards a target that is negatively charged. While the electron is traveling, the target makes an abrupt move towards the electron. While the information that the target moved is traveling from the target to the electron, the electron behaves like an electron that is moving towards a target that ... | <p>Moving the target requires energy.</p>
<p>Suppose the target is an infinite plane with constant charge density $\sigma$. It will not radiate when you move it because the electric field is constant everywhere. Suppose the test charge $q$ is small enough that its radiation is negligible.</p>
<p>The electric field ... | 423 |
special relativity | Non-interchangeability of time-like intervals | https://physics.stackexchange.com/questions/12265/non-interchangeability-of-time-like-intervals | <p>I am reading Landau's Volume 2 of the course of theoretical physics. I have a doubt after reading the first few pages of it which I explain below.</p>
<p>Landau first defines intervals and on pages 5 and 6 shows that two events having time like interval between them can never occur simultaneously in any reference s... | <p>If you believe that (a) timelike separated events cannot be simultaneous in any reference frame, <em>and</em> (b) the set of inertial frames is (in some appropriate sense) a continuous set, then L&L's conclusion follows. After all, if there were two frames in which the order of two timelike separated events diff... | 424 |
special relativity | Looking for specific Relativity example | https://physics.stackexchange.com/questions/14958/looking-for-specific-relativity-example | <p>Many years ago (in the '70s I think) I read an explanation of the meaninglessness of simultaneity at large distances. The example had to do with two people walking along a sidewalk in opposite directions, and an alien race on a planet millions of light-years away planning an invasion of the Solar System. The examp... | <p>I think you are talking about the <a href="http://en.wikipedia.org/wiki/Rietdijk%E2%80%93Putnam_argument" rel="nofollow">Rietdjik-Putnam argument</a>.</p>
| 425 |
special relativity | Relative Synchronicity | https://physics.stackexchange.com/questions/15906/relative-synchronicity | <p>Einstein said that the synchronization of two clocks is dependant on the velocity of the observer. But I feel a conceptual contradiction can be made:</p>
<p>There are two observers A and B. Observer 'A' faces direction X, and will be labeled "stationary." Another observer B faces direction X and is travelling ra... | <p>I don't think you're missing anything. If the two clocks are not separated in the dimension of the velocity of the systems (say this is the x dimension), then they are synchronized with respect to both systems. Try thinking about light clocks held this way. In both systems, light takes the same time to go from B ... | 426 |
special relativity | why evaluate at lambda = 0 | https://physics.stackexchange.com/questions/16432/why-evaluate-at-lambda-0 | <p>I am trying to understand Herbert Goldstein's introduction to 4-vectors. He describes a 1-D curve in spacetime $ P_(\lambda) $ then he says a 4 vector is defined as the tangent vector to this curve $$ v = \biggr ( \frac {dP} {d\lambda}\biggr)_{\lambda =0} $$ </p>
<p>why is $ \lambda $=0? what does that have to ... | <blockquote>
<p>he says a 4 vector is defined as the tangent vector to this curve</p>
</blockquote>
<p>That is <em>not</em> true in general. A four-vector is not always defined as the tangent vector to a curve. In the book they are computing a tangent vector to a curve in 3+1D spacetime; the tangent vector is just <... | 427 |
special relativity | Lorentz Transformation via Geometry | https://physics.stackexchange.com/questions/16845/lorentz-transformation-via-geometry | <p>Today, I was tutoring and explained the space-time. I explained how one can convert North-South into West-East by rotating, and how you can convert time into space with velocity.</p>
<p>Below the Energy-Momentum stuff the book had some problems. One was the following:</p>
<blockquote>
<p>Given an event at (1 Lig... | <p>I'm going to take $c=1$. The top orange line, which is the $t'$ axis in your drawing, is drawn with a slope of $1/0.6$; this follows from the definition of velocity. The bottom orange line, which is the $x'$ axis, has a slope of 0.6.</p>
<p>What's a little harder is to get the scale on the orange axes. The scale fo... | 428 |
special relativity | A possible absolute reference system | https://physics.stackexchange.com/questions/17055/a-possible-absolute-reference-system | <p>What about considering the microwave background radiation (2.7K if I remember well) as a reference system with some absolute character? Please explains if this question make sense and possible answers.
Thank you.</p>
| <p>No more absolute than using the position of distant Quasars</p>
| 429 |
special relativity | What would an observer see if he/she flew toward a clock at relativistic speeds? | https://physics.stackexchange.com/questions/19370/what-would-an-observer-see-if-he-she-flew-toward-a-clock-at-relativistic-speeds | <p>If an observer approaches a clock at a significant fraction of the speed of light, would they see the clock's hands moving at a faster or slower than usual rate?</p>
<p>I figure there are two competing effects at play - time dilation and diminishing distance.</p>
| <p>You can see this as an example of the relativistic Doppler shift (for equations, see eg: <a href="http://en.wikipedia.org/wiki/Relativistic_Doppler_effect">http://en.wikipedia.org/wiki/Relativistic_Doppler_effect</a> ).</p>
<p>The hands of the clock are moving with some angular frequency and you are moving with a v... | 430 |
special relativity | Einstein's Famous Thought Experiment Contradiction | https://physics.stackexchange.com/questions/20532/einsteins-famous-thought-experiment-contradiction | <p>Putting Special Relativity into the General Relativity category as is current practices submerges important aspects of Einstein's 1905 paper, which I recently read in a 1952 Dover paperback (The Principle of Relativity). That paper is totally unlike the modern presentations in texts. I noticed a marked discrepancy o... | <p>You are confused because you are not taking the relativity of simultaneity into account in your analysis. When you have two mirrors moving to the right with velocity v, you are thinking that it takes light a long time to go to the right, but a very short time to go to the left, because in one direction, the mirror i... | 431 |
special relativity | Is radiation pressure constant in this experiment, and does force of a spring change? | https://physics.stackexchange.com/questions/21419/is-radiation-pressure-constant-in-this-experiment-and-does-force-of-a-spring-ch | <p>Let's say a light clock consists of two parallel mirrors, some photons bouncing between the mirrors, and a spring that pulls the mirrors together with the same force that the photons push them apart.</p>
<p>Now we start accelerating the mirrors and the spring, in the direction parallel to the mirrors. Whenever a ph... | <p>The way I understand your description, the motion of the light and the spring tension are perpendicular to the direction of acceleration. Consider the problem in the (instantaneous) rest frame of the mirrors and spring.</p>
<p>Let's use coordinates where x is the direction of the photon's motion (in the unmoving re... | 432 |
special relativity | Pushing with a lorentz contracting stick | https://physics.stackexchange.com/questions/21919/pushing-with-a-lorentz-contracting-stick | <p>If I use a stick to push and accelerate an object, my hand pushes one end of the stick distance $x$, while the other end of the stick pushes the object distance $y$.</p>
<p>Distance $y$ is smaller than distance $x$, because of Lorentz contraction of the stick. </p>
<p>My hand does work $Fx$.</p>
<p>Work $Fy$ is d... | <p>$y=x$</p>
<p>For a constant pushing velocity, lorentz contraction is constant. It's just a smaller, rigid rod, solve classically.</p>
<p>V2:</p>
<p>The missing energy went into accelerating the stick, of course. I'm not sure if you even are allowed to use an accelerating situation in SR.</p>
| 433 |
special relativity | Factor 2 and equations for the weak gravitational field | https://physics.stackexchange.com/questions/24188/factor-2-and-equations-for-the-weak-gravitational-field | <p>By using some axioms people derives equation for Lorentz force and, then, Maxwell's equations from the Coulomb's law and Lorentz transformations. When I used analogical methodology for Newton's law of universal gravitation, I derived some equations like gravitomagnetic equations deriving from the GR equations in the... | <p>What's going on here is that the relativistic force is</p>
<p>$$ {d^2x^\mu \over d\tau^2} = - \Gamma^\mu_{\alpha\beta} \dot{x}^\alpha\dot{x}^\beta$$</p>
<p>Where the Christoffel symbol is</p>
<p>$$ \Gamma^\mu_{\alpha\beta} = -{1\over 2}g^{\mu\nu}(g_{\alpha\nu,\beta} + g_{\beta\nu,\alpha} - g_{\alpha\beta,\nu} ) $... | 434 |
special relativity | What are the increasingly sophisticated ways to perform a Lorentz transformation? | https://physics.stackexchange.com/questions/29387/what-are-the-increasingly-sophisticated-ways-to-perform-a-lorentz-transformation | <p>Since Einstein first derived the Lorentz transformations, their generalisation and execution has changed over the century. So starting with those first derived by Einstein: </p>
<p>What are the main, increasingly sophisticated ways, of carrying out a Lorentz transformation today? What are their advantages/disadvant... | <p>"Since Einstein first derived the Lorentz transformations...", that's priceless. </p>
<p>The Lorentz transformations, motivated as specific linear transformations of in a vector space (i.e. matrices) have not and will never change. What changes is notation. If by "...execution has changed over the century" you mean... | 435 |
special relativity | The temperature in space | https://physics.stackexchange.com/questions/29418/the-temperature-in-space | <ol>
<li><p>We know that cosmic microwave background temperature is about 2.7K. But what temperature we will measure in space using a simple Kelvin thermometer in the shadow? Can it be lower than 2.7K?</p></li>
<li><p>Suppose a space ship is flying in our solar system with a speed of 0.99c relative to earth. Will it me... | <p>Re question 1: It's relatively simple to calculate temperatures in space because since there is no air, there is no heat conduction or convection. A body in space can only absorb heat by absorbing radiation, and can only lose heat by radiating.</p>
<p>The CMB behaves like a black body with a temperature 2.725K, so ... | 436 |
special relativity | Computing inverse Lorentz transformations in matrix form | https://physics.stackexchange.com/questions/408382/computing-inverse-lorentz-transformations-in-matrix-form | <p>I have a question about finding inverse Lorentz transformations explicitly, in matrix form:</p>
<p>Suppose I have a Lorentz transformation $\Lambda^\mu_{\;\nu}$, with matrix representation $\underline{\underline{\Lambda}}$. The inverse Lorentz transformation $(\Lambda^{-1})^\mu_{\;\nu}=\Lambda_\nu^{\;\mu}$ can be f... | 437 | |
special relativity | Time dilation formula question | https://physics.stackexchange.com/questions/408604/time-dilation-formula-question | <p>I understand that the formula for time dilation is given as</p>
<p>$$T = T_0\gamma = \frac{T_0}{\sqrt{1-v^2/c^2}}$$</p>
<p>Where T is moving with velocity <em>v</em> seen from $T_0$. Though, this is when an event is occuring, since the value for $T$ would in any case of $v>0$ be greater than $T_0$, meaning that... | <p>In your case when the twin on the spaceship travels with constant speed, the twins will see each other age at the same rate. Both of them could say that the other one is traveling relative to him, so the other one should age slower.
But they age at the same rate in this case. This is because speed is simmetrically r... | 438 |
special relativity | Paradox of the twins in time dilation | https://physics.stackexchange.com/questions/411161/paradox-of-the-twins-in-time-dilation | <p>In the twin paradox from what I understand both observer see each other's time dilated so they always believe that the other frame is younger. Finally because the space ship frame has to make many accelerations it results that he will be younger. However, what if the frame in the space ship doesn't have to make any ... | <p>The traveling twin will be younger, because the paths are not symmetric.</p>
<p>When considering paths in these spaces, you have to consider homotopy classes. Two paths are in the same homotopy class if they can be continuous deformed into one and other.</p>
<p>It the standard twin paradox, the traveling twin's pa... | 439 |
special relativity | Proof that an observer cannot be in two places at once | https://physics.stackexchange.com/questions/422405/proof-that-an-observer-cannot-be-in-two-places-at-once | <p>If you went at light speed, you would literally and instantly teleport from the sun to the Earth. Any slower would create the perception of time. In other words, we appear frozen to the light (or observer going at c).</p>
<p>Still, the light can never appear frozen to us. Its speed is always the same, so that if we... | <p>No object with rest mass can travel at c. Everything is relative to c, the speed of light in vacuum (when measured locally).</p>
<p>For an observer on Earth, it takes 8 minutes for a photon to reach Earth. That is why an observer on Earth (observer who has rest mass) experiences time.</p>
<p>A photon does not have... | 440 |
special relativity | what is the behavior of an electronic oscillator at relativistic speeds? | https://physics.stackexchange.com/questions/433230/what-is-the-behavior-of-an-electronic-oscillator-at-relativistic-speeds | <p>Imagine an LC circuit in which the capacitor consists of two metal discs of area <span class="math-container">$A$</span> and spacing <span class="math-container">$D_0$</span> which is connected to a solenoid coil which for convenience has length <span class="math-container">$D_0$</span>, cross-sectional area <span c... | <p>Interesting question, unfortunately circuit theory is non relativistic. Circuits that satisfy the assumptions of circuit theory in their rest frame do not satisfy them in other frames. For example, one of the assumptions of circuit theory is that all of the components of a circuit have no net charge (Nilsson and Rie... | 441 |
special relativity | Car-garage paradox with just one door | https://physics.stackexchange.com/questions/436396/car-garage-paradox-with-just-one-door | <p>Special relativity implies the possibility of some apparently paradoxical situations, which can ususally be made sense of if one applies the theory rigorously. One of these is the car-garage paradox: a car speeds towards a garage which, at rest, is slightly shorter than the car. From the reference frame of the garag... | <blockquote>
<p>it is still longer than the garage (neglect shortening due to the accident)</p>
</blockquote>
<p>You cannot neglect the shortening. The rear of the car is moving forward. The front of the car is having a collision.</p>
<p>The crucial point is that information about this collision cannot reach the ... | 442 |
special relativity | Rest mass of electron-positron would be the same as their energy in annihilation? | https://physics.stackexchange.com/questions/442709/rest-mass-of-electron-positron-would-be-the-same-as-their-energy-in-annihilation | <p>If the combined mass of an electron and a positron was approximately <span class="math-container">$1$</span> MeV/<span class="math-container">$c^2$</span>, then would the total energy of their annihilation be equal to <span class="math-container">$9 \times 10^{16}$</span> MeV? Why do we not multiply the rest mass by... | <p>We do multiply the mass by <span class="math-container">$c^2$</span> to get the energy. The mass is roughly <span class="math-container">$1$</span> MeV/<span class="math-container">$c^2$</span> and when we multiply this by <span class="math-container">$c^2$</span> we get <span class="math-container">$1~c^2$</span> M... | 443 |
special relativity | Length Contraction Scenario | https://physics.stackexchange.com/questions/460049/length-contraction-scenario | <p>Suppose a space ship is traveling from star A to star B at some significant fraction of the speed of light. In the frame of the ship, the distance A to B is less than the distance in A and B's rest frame. Is it possible for the ship to quickly increase its speed so that in its frame the ship is then closer to A comp... | <p>This is an interesting puzzle and I don't think I agree with the previous answer.</p>
<p>Suppose the ship is stationary, halfway between A and B, which are <span class="math-container">$L$</span> apart. In a very short (negligible) time it accelerates towards B at high speed. A and B are now <span class="math-cont... | 444 |
special relativity | Question regarding Lorentz Transformation formula | https://physics.stackexchange.com/questions/466211/question-regarding-lorentz-transformation-formula | <p>So the Lorentz Transformation formation equation are
<span class="math-container">$$x′=\gamma(x−vt),$$</span></p>
<ol>
<li>Does <span class="math-container">$x′$</span> and t represent time and position at one event(one instance) or do they represent two events- meaning is <span class="math-container">$x'$</span> a... | <p>The equation you've given is not the full Lorentz transformation. There is also a transformation giving t'.</p>
<blockquote>
<p>Does x' and t represent time and position at one event(one instance) or do they represent two events- meaning is x′ actually x2−x1</p>
</blockquote>
<p>It works for either purpose.</p>
... | 445 |
special relativity | 3 variations of the Twin Paradox | https://physics.stackexchange.com/questions/467099/3-variations-of-the-twin-paradox | <p>Here I state and try to answer three variations of the twin paradox</p>
<p><strong>1) "Classical" problem, no acceleration, no turn around</strong></p>
<p>Consider the case where there's a stationary planet, and a moving spaceship moving at close to the speed of light, starting at the left going right at c... | <p>The question is not stupid. So in the normal twin paradox, the traveling twin's path includes acceleration, and hence can be distinguished from the "stationary" twin.</p>
<p>In the toroidal version, both twins are inertial, but the traveling twin's path cannot be continuously deformed to a point. As explained in <a... | 446 |
special relativity | Is length contraction and time dilation symmetrical between non-accelerating reference frames? | https://physics.stackexchange.com/questions/477472/is-length-contraction-and-time-dilation-symmetrical-between-non-accelerating-ref | <p>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-year-long series of high speed, high resolution video cameras stretches out left to right as viewed from your observat... | <blockquote>
<p>I am confused, because it seems asymmetrical.</p>
</blockquote>
<p>It is asymmetrical because the vehicles are asymmetrical. The length of the 40m craft really has no bearing on the time of the interaction. So for you, the length contraction doesn't matter.</p>
<p>The length of the light-year-long... | 447 |
special relativity | What does Ethan Siegel mean by "The fact that there are no stationary, oscillating in-phase electric and magnetic fields led to Special Relativity." | https://physics.stackexchange.com/questions/496197/what-does-ethan-siegel-mean-by-the-fact-that-there-are-no-stationary-oscillati | <p>In <a href="https://medium.com/starts-with-a-bang/this-one-anomaly-is-driving-physicists-to-search-for-light-dark-matter-774ec0eb7023" rel="nofollow noreferrer">This One ‘Anomaly’ Is Driving Physicists To Search For Light Dark Matter</a>, what does Ethan Siegel mean by "The fact that there are no stationary, oscilla... | <p>In a traveling wave, the magnitude of the magnetic field is proportional to the magnitude of the electric field at each point in space (they can't be equal because they have different units, but they are related by <span class="math-container">$|E| = c|B|$</span>). This means the <em>nodes</em> and <em>antinodes</em... | 448 |
special relativity | How can two different inertial frames observe two different events? | https://physics.stackexchange.com/questions/509553/how-can-two-different-inertial-frames-observe-two-different-events | <p>Consider an apparatus similar to that used in Michelson-Morley experiment kept in a frame (S') moving with a constant speed (v) to the right of an inertial frame (S).</p>
<p>The apparatus consists of a light source, a partially silvered glass (B) in front of the source and two mirrors facing B (at a length L from B... | <p>If the arrival of the photons at a specific point (B) is simultaneous from the viewpoint of one inertial observer, it will be simultaneous from the viewpoint of any other inertial observers.</p>
<p><a href="https://i.sstatic.net/G6D1o.gif" rel="nofollow noreferrer"><img src="https://i.sstatic.net/G6D1o.gif" alt="Fi... | 449 |
special relativity | Special Relativity - Perpendicular Boosts Equaling to a Rotation after a Boost | https://physics.stackexchange.com/questions/515663/special-relativity-perpendicular-boosts-equaling-to-a-rotation-after-a-boost | <p><strong>[Question]</strong>
I recently read that two perpendicular Lorentz boosts equal to a rotation after a boost. Can anyone here show me an example of this happening? Thank you for your time and assistance!</p>
<p><em>Source: None - (not a homework question)</em></p>
| <p>Here is an explicit example. The matrix rows and columns are in the usual order <span class="math-container">$t,x,y,z$</span>.</p>
<p><span class="math-container">$$
\left(
\begin{array}{cccc}
\frac{2}{\sqrt{3}} & 0 & -\frac{1}{\sqrt{3}} & 0 \\
0 & 1 & 0 & 0 \\
-\frac{1}{\sqrt{3}} & 0... | 450 |
special relativity | How will the length of a moving rod change for an observer 'seeing' it? | https://physics.stackexchange.com/questions/516209/how-will-the-length-of-a-moving-rod-change-for-an-observer-seeing-it | <p>I was studying length contraction and it considered the following scenario.</p>
<p>A rod is moving at a velocity <span class="math-container">$v$</span> with respect to a frame <span class="math-container">$S$</span>. A frame <span class="math-container">$S'$</span> observes the rod stationary and thus measures pro... | <p>There are two separate effects which should not be confused, one being length contraction and the other being Terrell rotation. </p>
<p>Length contraction is the reduction in the measured length of an object when it is measured in a frame moving relative to it.</p>
<p>Terrell rotation is a change to the apparent l... | 451 |
special relativity | How does a photon decide what to hit along it's path? | https://physics.stackexchange.com/questions/531552/how-does-a-photon-decide-what-to-hit-along-its-path | <p>In general, let us have a light emitting point A and two light absorbing points B and C, such that the three points fall on a straight line and B is somewhere between A and C. For simplicity, let us consider all photons emitting from A to travel along this same line in the direction of the points B and C. Also, let ... | 452 | |
special relativity | Analogue to special relativity in other physical systems | https://physics.stackexchange.com/questions/541139/analogue-to-special-relativity-in-other-physical-systems | <p>It's hard to get an intuitive grasp of the Lorentz transformations; I was wondering if the same mathematical formulas – hyperbolic rotation – appear under disguise in other physical systems. Note: I doubt there's a direct <em>mechanical analogy</em>, with a speed limit much lower than <span class="math-container">$c... | <p>Here are two related abstracts that might be of interest to you.
(I have not read the papers to comment.)</p>
<ul>
<li><p>Geometrical interpretation of optical absorption<BR>
J. J. Monzón, A. G. Barriuso, L. L. Sánchez-Soto, and J. M. Montesinos-Amilibia<BR>
Phys. Rev. A 84, 023830 – Published 17 August 2011<BR>
<a... | 453 |
special relativity | Simultaneity and special relativity | https://physics.stackexchange.com/questions/554156/simultaneity-and-special-relativity | <p>Suppose, in inertial reference frame <span class="math-container">$F_1$</span>, observers A and B are at rest, each having torch, and are separated by some distance and we have put machine M at middle of A and B.</p>
<p>Machine M has light bulbs on both sides ,right and left, so that if it catches light from A whic... | <p>The machine M responds to events right there at the machine---the events of light arriving from left, light arriving from right. So the machine is reporting that the <em>light arrival</em> events are simultaneous at M. This is fine; all reference frames will agree that two things happening at the same place and time... | 454 |
special relativity | Can different observers observe different realities? | https://physics.stackexchange.com/questions/569274/can-different-observers-observe-different-realities | <p>The question is extention of thought experiment proposed by Einstein of light pulses in a train cart called <a href="https://en.m.wikipedia.org/wiki/Relativity_of_simultaneity#:%7E:text=Einstein%27s%20thought%20experiments-,Einstein%27s%20train,to%20strike%20at%20different%20times." rel="nofollow noreferrer">Einstei... | <p>You're assuming that events that are simultaneous in one frame will be simultaneous in another frame too which is not the case. That is the whole point of the Einstein's train thought experiment. If in the train's frame, the light pulses are emitted at the same time from the ends, then to an observer in the train th... | 455 |
special relativity | Why does Feynman say “That is all there is to the theory of relativity – it just changes Newton’s law by introducing a correction factor to the mass” | https://physics.stackexchange.com/questions/594901/why-does-feynman-say-that-is-all-there-is-to-the-theory-of-relativity-it-just | <p>In the Feynman Lectures, he lays out how in special relativity, the mass is adjusted by a factor of <span class="math-container">$\sqrt{1 - v^2 / c^2}$</span> and then writes:</p>
<blockquote>
<p>For those who want to learn just enough about it so they can solve problems, that is all there is to the theory of relati... | <p>The claim is wrong because Newton's second law does <em>not</em> become <span class="math-container">$F=m \gamma a$</span>.</p>
| 456 |
special relativity | Energy of a $n$-particle system in special relativity | https://physics.stackexchange.com/questions/621603/energy-of-a-n-particle-system-in-special-relativity | <p>Consider an inertial frame <span class="math-container">$S'$</span>. With respect to this frame of reference consider a system of <span class="math-container">$n$</span> particles. The <span class="math-container">$k$</span>-th particle has rest mass <span class="math-container">$m_{0,k}$</span> and it moves with sp... | <p><span class="math-container">$\sum\gamma_k m_k c^2$</span> is called the "total relativistic energy" <span class="math-container">$E_{rel,tot}$</span>.
<BR>
Although some have called <span class="math-container">$\frac{1}{c^2}E_{rel,tot}=\sum\gamma_k m_k$</span> the "relativistic mass",
because o... | 457 |
special relativity | How does Lorentz transforming forwards, then backwards, stay consistent? | https://physics.stackexchange.com/questions/635048/how-does-lorentz-transforming-forwards-then-backwards-stay-consistent | <p>Let me take you through the logic in my head...</p>
<ul>
<li>In frame S, you have coordinate <span class="math-container">$x$</span></li>
<li>Transform to frame S' with velocity <span class="math-container">$v$</span> so the coordinate is now <span class="math-container">$x' = \gamma x$</span></li>
<li>Now treat the... | <p>The Lorentz transformation always transfoms not only coordinates but also time. In fact you can consider it as a sort of a "rotation" in <span class="math-container">$(t,x)$</span> "plane".</p>
<p>Whe you start with an event <span class="math-container">$(0,x)$</span> in the new frame it will hav... | 458 |
special relativity | How can a twin travelling astronaut paradox be resolved? | https://physics.stackexchange.com/questions/657975/how-can-a-twin-travelling-astronaut-paradox-be-resolved | <p>This is a variant of the twin paradox. But having each of the twin astronauts take off in opposite directions and returning to meet such that all aspects of acceleration and velocity are the same. Both should observe the other’s clock being slow for the whole trip but when they meet they should have aged equally. Ho... | <p>The mistake you are making is that you are forgetting about the relativity of simultaneity. Although each twin's clock will seem to tick slowly compared with clocks stationary in the other twin's reference frame, those other clocks will appear to be out of synch to the twin who is moving relative to them. Over the c... | 459 |
special relativity | What is the meaning of "clocks and rods" in special relativity? | https://physics.stackexchange.com/questions/662666/what-is-the-meaning-of-clocks-and-rods-in-special-relativity | <p>In my introductory text about special relativity, I am told to consider the whole coordinate system as consisting of meter sticks (rods) joined by clocks. I am told to consider a light pulse which is used to synchronize the clocks, with each clock stopping when it receives the pulse and correcting for the time taken... | <p>It looks to me like the <em>way</em> the "clocks and rods" idea has been introduced to you is more complicated than necessary, and this has caused you to have trouble understanding it. It is in fact very simple and down to earth, although it can be <em>used</em> for some subtle purposes.</p>
<p>It's sad to... | 460 |
special relativity | How does Wigner rotation manifest itself in 3-forces? | https://physics.stackexchange.com/questions/687497/how-does-wigner-rotation-manifest-itself-in-3-forces | <p>There is no gravity. Two lasers, one in <span class="math-container">$(x, 0, 0)$</span> and the other in <span class="math-container">$(-x, 0, 0)$</span>, are motionless. Both of them are pointing upward (in z direction) toward circumference of a motionless disk. The disk will start moving upward in z direction, if ... | 461 | |
special relativity | Understand result of Lorentz transform | https://physics.stackexchange.com/questions/689301/understand-result-of-lorentz-transform | <p>Assume an event that happens at P=(ct:2,x:4) in some inertial frame of reference S. Assume a second inertial frame S' in standard configuration and <span class="math-container">$\beta=4/5$</span> (<span class="math-container">$\gamma=5/3$</span>). The Lorentz transform is:</p>
<p><span class="math-container">$$ P'=\... | <p>Information can never travel faster than light. You can draw a light cone eminating from the origin and the point <span class="math-container">$P$</span>, both before and after the transform. Since <span class="math-container">$P$</span> is outside the lightcone of the origin it can't communicate anything with the o... | 462 |
special relativity | How does the principle of relativity imply that photon clocks and mechanical clocks experience time dilation the same way? | https://physics.stackexchange.com/questions/699949/how-does-the-principle-of-relativity-imply-that-photon-clocks-and-mechanical-clo | <p><strong>Context for this question:</strong> There is a famous thought experiment used to explain time dilation that uses two mirrors and a photon to set up a clock. The two mirrors are placed parallel to one another, and a photon is sent travelling perpendicular to the planes of the mirror, bouncing back and forth. ... | <p>You seem to think that Robphy uses the principle of relativity as a kind of self-evident universal truth (like 1+1=2), which you could come up by yourself if you think hard enough. He then seems to deduce something even more obvious from it (equivalence of light clocks and everyday clocks). But you believe in neithe... | 463 |
special relativity | Relativistic inelastic collisions | https://physics.stackexchange.com/questions/731793/relativistic-inelastic-collisions | <p>Suppose a clay ball of mass <span class="math-container">$m$</span>, travelling at speed <span class="math-container">$v=\sqrt{3}c/2$</span>, collides with an identical clay ball that is at rest. They undergo a perfectly inelastic collision.</p>
<p>After performing the relevant calculations (using two separate metho... | 464 | |
special relativity | How can I read articles by famous scientists for free? | https://physics.stackexchange.com/questions/729882/how-can-i-read-articles-by-famous-scientists-for-free | <p>I am high school student. I want to read the articles of famous scientists. These articles must be in their original language and not edited in any way. For example, I want to read Special Relativity, which was published by Einstein in 1905. In the German language and with an exact copy from 1905. Where can i find t... | <p>Einstein published in German Annalen der Physik, look this up in wiki
<a href="https://en.wikipedia.org/wiki/Annalen_der_Physik" rel="nofollow noreferrer">https://en.wikipedia.org/wiki/Annalen_der_Physik</a> and you find most of his german work free to download. for other authors go to there name in wiki and look up... | 465 |
special relativity | Spacetime diagram in Rindler coordinates | https://physics.stackexchange.com/questions/440400/spacetime-diagram-in-rindler-coordinates | <p>I am currently studying the <a href="https://en.wikipedia.org/wiki/Rindler_coordinates" rel="nofollow noreferrer">Rindler coordinates</a> </p>
<p><span class="math-container">$$T = x \sinh(a t) , \, X = x \cosh(at).$$</span></p>
<p>I am trying to understand the connection between the Rindler coordinates and their ... | <p>Start with the coordinate system <span class="math-container">$(T,X)$</span>, so that every point in two-dimensional spacetime is labeled by a pair of numbers <span class="math-container">$(T,X)$</span>. Define <span class="math-container">$t$</span> and <span class="math-container">$x$</span> implicitly by
<span cl... | 466 |
special relativity | Symmetrical twin paradox without changing direction | https://physics.stackexchange.com/questions/201700/symmetrical-twin-paradox-without-changing-direction | <p>If I understood well, in the special relativity </p>
<p>1- A stationary observer sees other moving observer's clock works more slowly than the stationary clock. </p>
<p>2- Motion is relative, the moving observer thinks the stationary observer is moving.</p>
<p>I cannot understand how it is possible then. Because ... | <blockquote>
<p>It is like to have two numbers each smaller than the other, it is not
possible.</p>
</blockquote>
<p>It's not like that at all. Consider the following true statement:</p>
<ul>
<li>B observes A's clock to run slowly while A observes B's clock to
run slowly.</li>
</ul>
<p>This is not a contradicti... | 467 |
special relativity | Regarding synchronization of clocks in special relativity | https://physics.stackexchange.com/questions/203920/regarding-synchronization-of-clocks-in-special-relativity | <p>I am trying to read of synchronization of two clocks in same inertial frame in special relativity. Suppose we have two synchronized clocks in an inertial frame placed at positions $x_1$ and $x_2$ in that frame. Suppose two observers at $x_1$ and and $x_2$ try to measure speed of some object moving in between $x_1$ a... | <p>There is a fundamental flaw in your setup. While the actual times the entrance signals may reach clocks 1 and 2 could be different, $t_1'-t_1$ will be the same as $t_2'-t_2$, because the clocks are at rest with respect to each other.</p>
<p>In fact, consider there are two events: entrance and exit. SR says that $$c... | 468 |
special relativity | Why do objects traveling faster appear shortened rather than elongated? | https://physics.stackexchange.com/questions/220921/why-do-objects-traveling-faster-appear-shortened-rather-than-elongated | <p>I'm sure this seems like a stupid question but I hope someone can try to explain it as if to a child...</p>
<p>This relates to Lorentz contraction. Why do objects in motion relative to the observer not get <em>longer</em>?</p>
<p>In the train example. A stationary observer is at the middle of a train car which is ... | <p>Actually your perception is correct in regards to the events you consider, but the conclusion does not contradict the concept of length contraction. </p>
<blockquote>
<p>In short, what you are looking at are <em>simultaneous events in the train's rest frame</em>. These do measure the length of the train in the re... | 469 |
special relativity | Lorentz contraction of object in circular motion | https://physics.stackexchange.com/questions/231614/lorentz-contraction-of-object-in-circular-motion | <p>Apparently a bunch of people totally misunderstood my <a href="https://physics.stackexchange.com/questions/231505/what-happens-to-wheels-of-a-car-moving-near-speed-of-light">previous question</a> and choose to ignore the clarifying comments. Let me change the conditions to remove all the confusion.</p>
<p><a href="... | <p>I tried to put it into a figure the results from reasoning in the framework of Special Theory of Relativity, this is what the observer would see:</p>
<p><a href="https://i.sstatic.net/asKtf.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/asKtf.png" alt="enter image description here"></a></p>
<p>Wher... | 470 |
special relativity | Feynman Lectures on Physics, Michelson Morley question about angle of light | https://physics.stackexchange.com/questions/238535/feynman-lectures-on-physics-michelson-morley-question-about-angle-of-light | <p>My question is similar, if not identical, to <a href="https://physics.stackexchange.com/questions/214247/feynman-lectures-on-physics-the-michelson-morley-experiment">this one</a>, but I don't find the answer satisfying, given the context of experiment.</p>
<p>First, here is an outline my understanding of the motiva... | <p>I may be wrong, but I think the effect of the ether would just be to alter the alignment of the mirrors slightly. It is kind of analogous to hitting a golf ball or kicking a football in the wind. If the wind is blowing one way, you have to aim a little the other way to correct for the wind.</p>
<p>For example, in t... | 471 |
special relativity | Does light still slow down in the direction of motion? | https://physics.stackexchange.com/questions/240143/does-light-still-slow-down-in-the-direction-of-motion | <p>This is quite a naive question however I hope to learn from this - I had always learnt a light clock in a space ship is placed like so :</p>
<p><a href="https://i.sstatic.net/YK2wc.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/YK2wc.png" alt="enter image description here"></a></p>
<p>That said as ... | <p>Let's calculate it then to gain some intuition. For a stationary horizontal light clock, the time for one tick will be given by $$t=\dfrac{2l}{c}$$ where $l$ is the distance between its two ends.</p>
<p>What about the moving one? First, as you pointed out $l$ will be length contracted by a factor of $\gamma=\dfrac{... | 472 |
special relativity | Direction of the lightbeam in SRT thought experiments | https://physics.stackexchange.com/questions/244701/direction-of-the-lightbeam-in-srt-thought-experiments | <p>Extending on the <a href="https://physics.stackexchange.com/questions/241792/time-dilation-diagram-on-wikipedia">question about the time dilation on Wikipedia</a>, namely this diagram in the <a href="https://physics.stackexchange.com/a/241807/56376">accepted answer</a>:</p>
<p><a href="https://i.sstatic.net/Ue5Xi.gi... | <p>Forthcoming answers will, I'm sure, invoke equivalency and other Relativity theory to explain the observed: here I intend to begin with observables and derive the theory.</p>
<p>A photon emitted from a particle is emitted in no preferred direction: it has an equal chance of going any direction in space. In order to... | 473 |
special relativity | Relativity paradox with mirrors and light pulses | https://physics.stackexchange.com/questions/259199/relativity-paradox-with-mirrors-and-light-pulses | <p><a href="https://i.sstatic.net/1tQFG.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/1tQFG.png" alt="Experiment seen from two different inertial frames."></a></p>
<p>Consider two very short light pulses emitted from the centre (C) of two mirrors A and B (as shown in the diagram).
From the point of vi... | <p>If $t_{CA}$ refers to the time it takes in the lab frame for the light to reach C from A, and the same with $t_{AC}$, $t_{CB}$ and $t_{BC}$ then we have:</p>
<p>$t_{CA}=\frac{L/2+v t_{CA}}{c}$</p>
<p>$t_{AC}=\frac{L/2-v t_{AC}}{c}$</p>
<p>$t_{CB}=\frac{L/2-v t_{CB}}{c}$</p>
<p>$t_{BC}=\frac{L/2+v t_{BC}}{c}$</p>... | 474 |
special relativity | Special relativity: is this a known paradox, or one at all? | https://physics.stackexchange.com/questions/262076/special-relativity-is-this-a-known-paradox-or-one-at-all | <p>Two ships of the same proper length $L$ move towards each other, as in the diagram below (which shows it in the reference frame where the ship at the left is at rest). The fronts (noses) are pointing to each other.</p>
<p><a href="https://i.sstatic.net/Dw0QB.jpg" rel="nofollow noreferrer"><img src="https://i.sstati... | <p>I said this in comments already, but I suppose it should be an answer.</p>
<p>Everything depends on where the clocks are. If they're at the front of the ships, then they get synchronized when the fronts pass, and both pilots agree that it's noon. An hour later (according to each of them), the backs of the ships p... | 475 |
special relativity | Special Relativity with no short cuts | https://physics.stackexchange.com/questions/277520/special-relativity-with-no-short-cuts | <p>I am currently a 3rd year undergraduate electronic engineering student. I have completed a course in dynamics, calculus I, calculus II and calculus III. I have decided to self study a basic introduction to special relativity as it was not part of my physics syllabus and is not included in any of my other modules. Th... | <p>First set up space and time origins for each frame. Say the spatial origin of Sally's frame is right in point A, and her time origin is right when Sam's point B passes by her. For Sam, say his space origin is in point B and his time origin is also when his point B passes Sally at her point A.</p>
<p>Now write down ... | 476 |
special relativity | Relativity of Simultaneity - Issue with the train car example | https://physics.stackexchange.com/questions/285760/relativity-of-simultaneity-issue-with-the-train-car-example | <p>One of the classic examples to describe that simultaneity is relative is the following:</p>
<p>"Imagine a freight car, traveling at a constant speed along a smooth, straight track. In the very center of the car there hangs a light bulb. When someone switches it on, the light spreads out in all directions at speed c... | <blockquote>
<p>but the rate that the distance between the back wall and the light beam decreases can't be greater than c, because nothing can move faster than the speed of light</p>
</blockquote>
<p>You are mistaken. Yes, nothing can move faster than light in a sense that physical motion is fundamentally bounded fr... | 477 |
special relativity | A question about the relativity of simultaneity | https://physics.stackexchange.com/questions/286536/a-question-about-the-relativity-of-simultaneity | <p><a href="https://i.sstatic.net/GULKM.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/GULKM.png" alt="enter image description here"></a></p>
<p>In the above figure Observer A is detecting the events P and Q by sending and receiving lights to the continuous paths. Observer B is also trying to locate th... | <p>The figure is a <a href="https://en.wikipedia.org/wiki/Minkowski_diagram" rel="nofollow">Minkowski diagram</a>, where light rays always are lines with a 45 degrees slope. The diagram also shows only one space dimension. Wordlines of observers with different speeds are represented by differently inclined lines all pa... | 478 |
special relativity | Bell's spaceship paradox - Special relativity | https://physics.stackexchange.com/questions/287428/bells-spaceship-paradox-special-relativity | <p>I will refer to this wikipedia page: <a href="https://en.wikipedia.org/wiki/Bell%27s_spaceship_paradox" rel="nofollow noreferrer">https://en.wikipedia.org/wiki/Bell%27s_spaceship_paradox</a>
and especially this diagram:</p>
<p><a href="https://i.sstatic.net/8KZdj.png" rel="nofollow noreferrer"><img src="https://i.s... | <p>From a frame S point of view, one has to compare to what the accelerating rope profile would look like in that diagram and would realize that it would look smaller in frame S. Therefore frame S would conclude that rope should snap.
That information is not in the diagram as it is.</p>
<p>If we were used to look at r... | 479 |
special relativity | Is a photon going through a center of mass affected by time dilation more then another going around? | https://physics.stackexchange.com/questions/289234/is-a-photon-going-through-a-center-of-mass-affected-by-time-dilation-more-then-a | <p>Please don't mark as duplicate. My specific question was not answered in other posts. And this question here <a href="https://physics.stackexchange.com/questions/289025/which-photon-would-win-the-race">Which Photon would win the race?</a></p>
<p>is also about neutrinos, electrons. </p>
<p>My question now is only a... | <p>You would think that a particle moving in the centre of mass experiences the same time as moving through space wthout any mass in it. In both cases no gravity is felt, so you would think time proceeds at it's fastest rate. The pace of time is nevertheless dependent on the gravitational potential, which is different ... | 480 |
special relativity | Analysis of simultaneity in Special Theory of Relativity | https://physics.stackexchange.com/questions/299459/analysis-of-simultaneity-in-special-theory-of-relativity | <p>Set up: A moving train with two flash lights on the wall, a person in the middle of the train. A mid point on the tracks where second person/observer stands. Flash lights flash a light when mid-point on the tracks and of the train have the same coordinate in both frames of reference. Suppose 1D problem plus time of ... | <p>It should be clarified, what means “an observer sees”. To make proper conclusion, at what time certain event took place in certain coordinate of reference frame, you have to have clock in that place. Procedure for every observer looks like this thought experiment. An observer in a train and observer on the platform ... | 481 |
special relativity | With quad spaceship setup, will RF time periods between all ships remain the same? | https://physics.stackexchange.com/questions/310673/with-quad-spaceship-setup-will-rf-time-periods-between-all-ships-remain-the-sam | <p>The red dots shown below, are RF transmitters.<br>
Clocks are located nearby each of these RF transmitters.<br>
All spaceships are identical and thus have identical rocket engines.</p>
<p><a href="https://i.sstatic.net/nb4Sn.gif" rel="nofollow noreferrer"><img src="https://i.sstatic.net/nb4Sn.gif" alt="http://www.o... | <p>After the engines are shut off, they will still be at rest relative to each other, so it will look exactly the same as before. Even before they fired their engines, they were traveling at great speed relative to other galaxies and this is no different. Stuff that is at rest relative to each other and not too distant... | 482 |
special relativity | Relativity and a Rotating Rod | https://physics.stackexchange.com/questions/318013/relativity-and-a-rotating-rod | <p>I was doing a problem on relativity and I was thinking about the problem in terms of the postulates of Special Relativity. Special Relativity only considers motion in inertial reference frames and I was doing this problem over here; </p>
<p>Essentially, if I have a rod which is tilted at an angle (theta)0, with res... | <p><strong>interpretation of your result</strong></p>
<p>You should not interpret this is a rotation of the angle. It is merely a result of there only being length contraction along the motion of the observer.</p>
<p>The y length of the rod changes but it's x length will change due to length contraction (as you corre... | 483 |
special relativity | Time lines of observers meeting each other - doubts about their graphical representation | https://physics.stackexchange.com/questions/320581/time-lines-of-observers-meeting-each-other-doubts-about-their-graphical-repres | <p>I am trying to make sense of Fig. 2.12, page 23 of Introducing Einstein's Relativity (D'Inverno, Oxford University Press). There it goes:</p>
<p><a href="https://i.sstatic.net/wiLWO.jpg" rel="nofollow noreferrer"><img src="https://i.sstatic.net/wiLWO.jpg" alt="fIG.2.12, PAGE 23"></a></p>
<p>The book picture is in ... | <p>The complete diagram from d'Inverno (p. 23) is shown below.
It appears that observer-A has performed radar experiments on events P and Q. Observer-A assigns time-coordinates to events as the halfway time between emission and reception of the radar signal. So, Observer-A assigns P and Q the same time coordinate---to ... | 484 |
special relativity | Rotation matrix and referencials in relativity | https://physics.stackexchange.com/questions/594933/rotation-matrix-and-referencials-in-relativity | <p>I am reading the book "Gravity in a nutshell" in which the author talks about rotation in a plane and different frames, one rotated with respect to the other. The rotated frame is denoted with a prime. We are trying to find the matrix relating the differences of coordinates in both frame. It is strange, he... | 485 | |
special relativity | In relativity, if units of length contracts and time dilates then does unit of velocity or speed also change? | https://physics.stackexchange.com/questions/574856/in-relativity-if-units-of-length-contracts-and-time-dilates-then-does-unit-of-v | <p>I'm just starting to learn special relativity, and I'm having trouble with the following concept:</p>
<p>In relativity, units of length and time of moving frame are related to that of stationary one through <span class="math-container">$$x’=\frac{x}{\gamma}\quad \quad \text{ and }\quad \quad t’=t\times \gamma$$</spa... | <p>No. Velocities do transform in a non-intuitive way in special relativity, but not in the way you're describing. This is sadly a very common misunderstanding due to the fact that Relativity is usually first introduced using time-dilation and length contraction, without actually explaining under which conditions they ... | 486 |
special relativity | How can I resolve this version of the twin paradox in special relativity? | https://physics.stackexchange.com/questions/603880/how-can-i-resolve-this-version-of-the-twin-paradox-in-special-relativity | <p>I have a version of the twin paradox which I am completely stumped by. There is a similar question on the forum but this particular version is unanswered. I really hope someone a lot better at physics than me is able to solve it!</p>
<p>Imagine two twins (Max and Tony) which are accelerated at birth in two opposite ... | <blockquote>
<p>they stop accelerating and are both travelling at constant velocity in an inertial (non-accelerating) reference frame (special relativity now applies).</p>
</blockquote>
<p>Special relativity applies to the whole problem, including the accelerating parts, since there's no gravity.</p>
<blockquote>
<p>Ma... | 487 |
special relativity | If an object is orbiting another body, don't both the orbiting object and an observer "know" that the orbiting object is moving? | https://physics.stackexchange.com/questions/611376/if-an-object-is-orbiting-another-body-dont-both-the-orbiting-object-and-an-obs | <p>In many relativity illustrations, it is mentioned that someone in a spaceship believes he is standing still and the observers are moving and vice versa. The example of a light-beam clock slowing down for an observer but not for the passenger of the ship is often how relativity is explained.</p>
<p>But if the ship is... | <p>Well Yes, but actually no. You know that Earth is orbiting the Sun, because you can observe relative motion of Sun to the other (fixed) stars on the sky. But let Say now, that we don't have any other Stars or reference objects. And let's introduce 2D polar coordinates. Let say, that we are on the Sun, and we believe... | 488 |
special relativity | Why do we take measurments of the end points of a rod at the same time in an inertial frame moving with uniform velocity? | https://physics.stackexchange.com/questions/612498/why-do-we-take-measurments-of-the-end-points-of-a-rod-at-the-same-time-in-an-ine | <p>I have a question regarding the concept of length contraction.
Consider a rod of rest length <span class="math-container">$L_o=x_2-x_1$</span> in frame <span class="math-container">$S$</span>. Now if we want to measure the length of the rod in <span class="math-container">$S^{'}$</span> i.e <span class="math-contain... | <p>Consider a rod of length 1 metre, aligned with and on the X axis, moving at 10 m/s in the +X direction. Clearly, this speed is non-relativistic, so the length contraction is negligible.</p>
<p>At time <span class="math-container">$t=0 s$</span>, we measure that the back of the rod is at <span class="math-container"... | 489 |
special relativity | Don't twin paradox explanations imply universal velocity/time? | https://physics.stackexchange.com/questions/573254/dont-twin-paradox-explanations-imply-universal-velocity-time | <p>On the Wikipedia page for the Twin Paradox, the example lays out the perspective of each twin in turn. Both twins are portrayed as understanding the ship's velocity as v, and the travelling twin's sense of time is then explained by saying that the earth-distant star system, being in effect one giant object, undergoe... | <p>Suppose the stationary twin occupies the origin of our coordinates, <span class="math-container">$x=0$</span>, and observes that the velocity of the traveling twin is <span class="math-container">$v$</span>, in their frame. In other words, suppose that the traveling twin covers a certain distance <span class="math-c... | 490 |
special relativity | Lorentz transformation of a trajectory | https://physics.stackexchange.com/questions/578953/lorentz-transformation-of-a-trajectory | <p>I am having trouble understanding how to apply the Lorentz transformation to a particle trajectory.</p>
<p>Suppose we have a body moving in one dimension in one frame where the position is given by <span class="math-container">$x(t) = f(t)$</span>. Then if we apply a Lorentz transformation with velocity <span class=... | <p>Yes, your explanation is right. Moreover, the function you call <span class="math-container">$g$</span> always exists because of the implicit function theorem. You can easily see that <span class="math-container">$t'=F(t)$</span> satisfies <span class="math-container">$F'(t)\neq 0$</span>. Here <span class="math-con... | 491 |
special relativity | What happens with the number of protons inside a wire in movement? | https://physics.stackexchange.com/questions/581380/what-happens-with-the-number-of-protons-inside-a-wire-in-movement | <p>In Special Relativity we solve the problem of the moving wire with an electrical current saying the protons inside the wire have a higher density: hence the wire is not neutral anymore (and we exchange a force caused by a B field with a force caused by an E field):</p>
<p><a href="https://phys.libretexts.org/Bookshe... | <p>Normally this idea is presented in the case of a wire that is infinitely long. That gives the problem a translational symmetry and makes everything simpler. For an infinite wire, the number of protons is infinite. If you change to a different frame, the number is still infinite, but with a different density. This is... | 492 |
special relativity | Compute the vertical motion of the Rindler's length contraction paradox | https://physics.stackexchange.com/questions/584984/compute-the-vertical-motion-of-the-rindlers-length-contraction-paradox | <p>Suppose a rod with length <span class="math-container">$L$</span> moving toward a hole whose radius is <span class="math-container">$L$</span>. The paradox is, from the ground frame, the length of the rod is contracted hence rod will fall into the hole. However, from the rod's frame, it is the length of the hole con... | <p>I am afraid that your second equation belongs not only to the front end of the rod but also to any point on the rod at a distance <span class="math-container">$x'$</span> from the observer located at the hind end of the rod. For the front end, you had better substitute <span class="math-container">$x'=L'$</span>, an... | 493 |
special relativity | Confusion about Lorentz Coordinate Transformation | https://physics.stackexchange.com/questions/584040/confusion-about-lorentz-coordinate-transformation | <p>A normal Lorentz coordinate problem might say:</p>
<p>At <span class="math-container">$t=t'=0$</span>, two coordinate systems <span class="math-container">$S$</span> and <span class="math-container">$S'$</span> have their origins coincide with the <span class="math-container">$S'$</span> system moving with speed <sp... | <p>Consider Einstein's train thought experiment that demonstrates non-simultaneity. Let's say the train moves left to right. The lightning strikes at the front and back of the train occur simultaneously for the platform observer (S frame) but for the train observer (S' frame) the strike at the front of the train occurr... | 494 |
special relativity | About relativity and train | https://physics.stackexchange.com/questions/590415/about-relativity-and-train | <p>Imagine a train moving with velocity v wrt a reference frame S, there is a clock in the rear and in the front of the train, and them are synchronized in the train reference, let's call this reference frame S'.
If you, the reference frame S, take a look simultaneously wrt your reference on the clocks, how will the ti... | <p>You are comparing things in different coordinates, which always causes problems in relativity, and you do it twice:</p>
<p>(1) The train is not <span class="math-container">$L$</span> in <span class="math-container">$S$</span>, it is <span class="math-container">$L/\gamma$</span>, which brings your formula to:</p>
<... | 495 |
special relativity | Lorentz transformation and rotation matrix | https://physics.stackexchange.com/questions/590829/lorentz-transformation-and-rotation-matrix | <p><span class="math-container">$$\begin{pmatrix}
1& 0 & 0 & 0\\
0& \cos\theta & \sin\theta &0 \\
0& -\sin\theta & \cos\theta &0 \\
0 & 0 & 0 &1
\end{pmatrix}$$</span></p>
<p>See this matrix, it represents a rotation in the xy plane for the Lorentz transformati... | <p>The rotation in the opposite direction (with <span class="math-container">$-\theta$</span>) is also a Lorentz transformation. Conventions about which one to use as an example have no physical significance.</p>
<p>This is similar to asking why we use a right-hand rule rather than a left-hand rule to define a cross pr... | 496 |
special relativity | Light perpendicular to spaceship constant relativistic speed - different points where it hits the wall as seen inside and from outside? | https://physics.stackexchange.com/questions/591364/light-perpendicular-to-spaceship-constant-relativistic-speed-different-points | <p>I googled that question and found this answer:</p>
<p><a href="https://www.quora.com/If-I-had-a-laserpoint-inside-a-very-fast-moving-spaceship-and-I-point-at-the-wall-in-front-of-me-normal-to-the-direction-of-motion-will-the-light-hit-a-bit-lower-due-to-the-speed" rel="nofollow noreferrer">https://www.quora.com/If-I... | <p>For the laser being inside the spaceship, the answer to the question , <em>"will the light hit a bit lower due to the speed"</em>, the correct answer is, "What speed?". The spaceship isn't moving, so a horizontal laser moves across the capsule at a constant height above the floor.</p>
<p>If the l... | 497 |
special relativity | Two light sources are a distance D apart. Show that in an inertial frame O' the photons are separated by a constant distance | https://physics.stackexchange.com/questions/590998/two-light-sources-are-a-distance-d-apart-show-that-in-an-inertial-frame-o-the | <p>Two light sources are at rest and at a distance D apart on the x-axis of some inertial frame, O. They emit photons simultaneously in that frame in the positive x-direction. Show that in an inertial frame, O', in which the sources have a velocity v along the x-axis, the photons are separated by a constant distance <s... | <p>Note that in <span class="math-container">$O$</span>, if the photons have wavelength <span class="math-container">$\lambda$</span>, then the number of cycles (of phase) between the two photons is:</p>
<p><span class="math-container">$$ N = D/\lambda $$</span></p>
<p>Since <span class="math-container">$N$</span> is a... | 498 |
special relativity | Does clock really run slow inside a high velocity rocket ship? | https://physics.stackexchange.com/questions/592924/does-clock-really-run-slow-inside-a-high-velocity-rocket-ship | <p>In time dilation, does clock really run slow when it’s in high speed? Is that means the mechanical parts of the clock run slow?
Or , It’s just the other inertial observer who thinks that the other one’s clock is running slow.(because the successive light signal is taking more time to reach the destination)</p>
<p>An... | <p>At high speeds, time really does slow down as you get close to the speed of light. All processes (not just mechanical clocks) slow down, including things like radioactive decay as well as everything biological going on inside your body. This means you yourself do not notice your clocks running slow inside the spaces... | 499 |
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