# Tagged Questions

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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Einstein's wonder equation $E=m c^2$,if we take energy is proportional to the mass, we can put single constant to make that equivalent equation. We all know that $\mathrm{constant}\cdot\mathrm{... 2answers 1k views ### Why are the proper time and the proper length not defined in the same frame of reference? I've just read this interesting Wikipedia article about time dilation and length contraction in special relativity. . Derivation of time dilation Applying the above postulates, consider the ... 2answers 70 views ### Relativity asymmetry? If you have two bodies that move towards each other at a constant velocity, each body will observe the other body experience time faster. This does not make sense to me because if you had a person ... 2answers 99 views ### What is the difference between these two equation dealing with time dilation? In my textbook, the time dilation equation is presented as$\Delta t' = \gamma \Delta t,$where$ \gamma = 1/ \sqrt{1 - v^2/c^2} $. My understanding of this equation is as follows (correct me if I'm ... 0answers 54 views ### Relativistic doppler effect in three dimensions Consider a sphere that travels through space with a velocity$v$. I wish to investigate the relative intensities of the CMB on all points on the sphere. For the microwaves approaching from the direct ... 1answer 106 views ### How to motivate this approach on Special Relativity? One of the most common approaches to Special Relativity is that based on the two Einstein's postulates: The laws of Physics are invariant in every inertial reference frame The speed of light ... 1answer 43 views ### Perception at relatavistic speeds If one were to be traveling at near the speed of light, their mass would be$m_{rel}= m_0 / \sqrt{1 - \frac{v^2}{c^2}}$. For the mass to double the speed would have to be$86.6\%c$ To better ... 2answers 84 views ### About Lorentz Group In definition of orthogonal matrices we say that the a matrix$A$is orthogonal if$A^TA = I$, while for Lorentz Group it is written as$\Lambda^Tg\Lambda = g $. And we say that Lorentz transformation ... 3answers 321 views ### Is a nuclear bomb in some sense a bullet travelling at the speed of light, but along time rather than along space? Apologies if this is a silly or perhaps obvious question, but$E=mc^2$just looks so much like classical kinetic energy (except for the factor of 2). So I'm thinking of the to-be-fissioned-away ... 2answers 247 views ### Sign convention for the Minkowski metric$\eta_{\mu\nu}$In special relativity, one is confronted with a quadratic form called proper time, which is$c^2t^2-(x^2+y^2+z^2)$,$t$being time and$x,y,z$being the space coordinates. One usually introduces a ... 1answer 65 views ### Boyles law & relativity In relativity when an object approaches the speed of light,$c$,its volume decreases due to length contraction. As a thought experiment, consider a rectangular metal box travelling at a relativistic ... 3answers 2k views ### Why collide a moving particle with a particle at rest, rather than two moving particles? I was just reading some lecture notes about relativistic and quantum mechanics, and in the later part of this page the author demonstrates that any relativistic particle collision in the "lab" ... 4answers 1k views ### Is there a formula that gives the position of an object depending on the time, but which doesn't allow the object to surpass the speed of light? I have found these two formulas:$v = at + v_0x = \frac{1}{2}at^2 + v_0t + x_0$a is the acceleration v is the velocity x is the position t is the time$v_0$is the initial velocity$x_0$is ... 1answer 307 views ### Proving the conservation of 4-momentum for a particle collision$A+B\to C+D$Let me say that particle A hits particle B and two particles come out - C and D; In system S I can write: $$p_A^μ+p_B^μ=p_C^μ+p_D^μ;\tag{1}$$ here$p_N^μ$is the 4-momentum. Using the Lorentz ... 1answer 509 views ### Gravity's Rainbow What is it? I've seen it in context of a few research papers such as Absence of black holes at LHC due to gravity's rainbow and Thermodynamics of black holes in gravity’s rainbow formalisms My best ... 1answer 91 views ### Special relativity and Lorentz transformation I recently learned about special relativity and different reference frames. The conversion from two inertial reference frames is given by Lorentz transformations: $$x' = \frac{x-ut}{\sqrt{1-\frac{u^2}... 3answers 103 views ### How does an electromagnetic field oscillate if time does not pass for the speed of light? As far as I'm aware, traveling at c will prevent time passing due to time dilation. Electromagnetic waves rely upon oscillations to propagate. Since oscillations rely upon the passing of time, how ... 6answers 1k views ### why is the magnetic field circular According to relativity, If magnetic field is just an electric field viewed from a different frame of reference, why is the magnetic field around the wire is circular? 0answers 53 views ### Are reversible and irreversible processes frame dependent? since it is all about time. If I have a look at an irreversible process from a frame where time runs really slow. is there a possibility of considering that process reversible from that frame? 2answers 79 views ### Rigorous computation of four-velocity In Special Relativity we can consider spacetime to be the Minkowsky space \mathbb{R}^{1,3} which is just \mathbb{R}^4 together with the non degenerate symmetric bilinear form g that in some ... 3answers 407 views ### How can one motivate the relativistic momentum? Motivating the classical momentum \mathbf{p} = m\mathbf{v} is quite easy: it is meant to represent the quantity of motion of the particle, and since the mass is one measure of quantity of matter it ... 1answer 137 views ### How to visualize the world while travelling near the speed of light? [closed] I have been having some trouble with this for a while. I think in terms of vivid , moving images and i haven't been able to visualize this completely. I wondered if a person, like the Flash from the ... 1answer 119 views ### How does the Lorentz boost change if we introduce transformation to the minkowski metric Let's say we have the Lorentz boost given by the \Lambda^\mu_\nu in the Minkowski metric diag\{1,-1,-1,-1\}. Now if I do a transformation on the Minkowski metric such that the new metric is diag\... 2answers 86 views ### Time Dilation: One observer at rest, two observers in motion I am currently taking a course in Modern Physics mainly focused on Special Relativity and came up with the following problem: Let O_1 be an observer at rest. A second observer O_2 is moving to ... 1answer 51 views ### Double-slit experiment [closed] Given the following wavelength: \lambda = 1.75 \cdot 10^{-12}\ m This leads to the velocity of the electron (matter wave). First approach: p = \dfrac{h}{\lambda}=m(v)v=m_e\gamma v [...] v =... 2answers 247 views ### Off-diagonal terms in metric for 4D space-time [closed] Consider a delta between two events in 4D space-time written as a 4-vector, x^\mu=(dt, dR). The time dt is a scalar difference in time. The 3-vector dR points some direction in space. One ... 3answers 652 views ### Faster than light signals and the price to be paid if we accept them : a very simple protocol Some physicists currently understand entanglement as transferring information instantaneously, yet not violating causality. Is this really a satisfactory explanation, or should be look for something ... 2answers 109 views ### Deriving the equations for a moving inertial reference frame [closed] I assume c=1 in the following derivation: In order to derive the equations for a moving inertial reference frame, I immediately wrote down the following:$$ x'=Ax+Bt, \tag{1}t'= Dx+Et. \tag{... 2answers 117 views ### Can a point in empty space be motionless with respect to light? Being that the speed of light is constant throughout the universe, can a point in empty space be motionless with respect to light? 1answer 59 views ### Parity transformation is proper orthochronous? In 3+1 dimensional spacetime the parity transformation is $$P^\mu_{\;\,\nu}=\begin{pmatrix}+1&&&\\&-1&&\\&&-1&\\&&&-1\end{pmatrix}.$$ This is ... 1answer 343 views ### Biot-Savart law from relativity Few days ago I came by a derivation of STR from Bio-Savart law. Since then I have been trying to derive Bio-Savart law from STR. The derivation mentioned previously used two parallel current-carrying ... 4answers 143 views ### What is the mass of a sphere? A solid sphere of mass M is rotating along an axis. We can consider it as a collection of large number of point masses, every point mass is moving with respect to center of mass with velocity which ... 0answers 39 views ### Does the algebraic number field used to define spacetime always have to be the real numbers? When we talk about Minkowski space, do we assume the field$K$we are using is the real numbers? Why couldn't spacetime be made up of the rational numbers or something? Also, I was reading Arnold and ... 1answer 248 views ### Physical interpretation of distances Suppose we have a universe with only two distinguishable particles, neglecting gravitation. These particles start off next to each-other, ostensibly "touching" each-other and at rest. If it takes ... 3answers 266 views ### How can a Physical law not be invariant? In Relativity, both the old Galilean theory or Einstein's Special Relativity, one of the most important things is the discussion of whether or not physical laws are invariant. Einstein's theory then ... 3answers 2k views ### Can quaternion math be used to model spacetime? Quaternions are commonly used to model 4 dimensional systems where the quaternion consists of a real 3 dimensional vector and an imaginary scalar. So on the surface Quaternions seem well suited to ... 1answer 51 views ### Why do we restrict the maximal supercharge to 32? Many supersymmetry textbook state that the maximal supersymmetry in any dimension has 32 hermitian supercharges. (Actually for lowest number of supersymmetry$N=1$the highest dimension is$D=11$) I ... 2answers 122 views ### Is there any theory in physics that might support the existence of tachyons? According to Einstein, we all know that light is the fastest thing and it's impossible to beat it's speed. But isn't there a way to go around this? I read somewhere that tachyons gain speed per the ... 4answers 6k views ### What spacelike, timelike and lightlike really mean? Suppose we have two events$(x_1,y_1,z_1,t_1)$and$(x_2,y_2,z_2,t_2)$, then we can define $$\Delta s^2 = -(c\Delta t)^2 + \Delta x^2 + \Delta y^2 + \Delta z^2$$ which is called the spacetime ... 2answers 90 views ### Through relativity could a person be dead and alive at the same time? For the purposes of the question ignore the fact that radiation and several other things would kill humans long before this. You and another person are jumping into a black hole and the other person ... 0answers 59 views ### Two spaceships are accelerating equally, uniformly on exactly parallel tracks. Does a rope suspended between them eventually rip? This question is a variant of "Bell's spaceships problem". Rather than one spaceship following the other "on the same track", let the two spaceships accelerate "side by side", on exactly parallel ... 0answers 63 views ### Rest masses, binding energy - mechanism for negative mass Let us have an two objects (in a box) both of mass$m_0$far from each other. They attract each other and at some moment their distance is close and they have substantial kinetic energy. Something ... 2answers 123 views ### Is FTL communication compatible with Lorentz ether theory? I have come to understand, that faster-than-light communication is problematic with special relativity, because it leads to the possibility of sending signals into the past. I also read about the ... 2answers 90 views ###$V_{\rm ball}=V_{\rm train}+V_{\rm ball}\$?

30 years after reading Einstein's books I'm having another go at understanding astrophysics, but one thing I didn't understand back then still doesn't make sense to me. It is the example of a ball ...
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### Travelling at the speed of light [closed]

more of a philosophical questions normally if you are travelling at some speed and you bump into some object, you generally would get slowed down and the force from your acceleration would be ...
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### Phase velocity greater then the speed of light?

It is my understanding the the phase velocity of a wave can be greater then the speed of light. So imagine we had a wave packet consisting of a single sinusoidal wave; $$y=\sin(\omega t-kx)$$ Then ...
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### Can we change a photon's frequency in mid-air?

Can we have a light source emitting photons in the infrared range and after, lets say, 5 meters, these photons become a photon in the x-ray range? The only way I know we can change a photon's ...