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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what is use of relativistic action?

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!?
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Proof for $p=\gamma_Pmu$

As I'm reading about Relativistic Momentum, my book states the following: $$p=m \frac{\Delta x}{\Delta t}=m\frac{\Delta x}{\sqrt{(1-u^2/c^2)}\Delta t}=\frac{mu}{\sqrt{1-u^2/c^2}}=\gamma_Pmu$$ ...
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239 views

Does the mass of a falling body decrease?

Let's say a body with m=2kg falls from 100 meters. Obviously it's speed would be far lower than the speed of light so the change in mass (if it exists) would be very tiny. However, I know that if the ...
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74 views

Single electron non-perturbing detector

I am designing an experiment where I need to trigger the release of an electron by a radioactive source (Sr-90). The easy way to do it is to use a thin scintillator right after the source collimator. ...
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60 views

Speed of light and lorentzian factors [duplicate]

Possible Duplicate: How can a photon have no mass and still travel at the speed of light? If light travels at the speed of light, and anything with rest mass will experience relativistic ...
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453 views

where the proper time is invariant why $d\tau$ is not zero?

where the proper time is invariant why change (differential) in proper time $d\tau$ is not zero? $\Delta \tau=\tau_f-\tau_i$ as i know. $d(invariant)=0$ note to comment: action $S=-m_oc^2\int_C d\tau$ ...
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132 views

Can the zeroth-component of a 4-velocity be negative?

Is it allowed to have the zeroth-component of a four-velocity be negative? I presume the answer is yes, but I just want to make sure. Many thanks. This is referring to $V^0$ for a curved space ...
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Does the increase of (relativistic) mass, while flying near speed of light, has any impact on astronauts? [duplicate]

Possible Duplicate: Would travelling at relativistic speeds have any impact on human biology? I am asking myself this question for a few day. What is the answer on: Does the increase of ...
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106 views

Why does isotropy principle require existence of inertial transformation when axes are reversed?

Assuming one spatial and one termporal dimension, let's assume an intertial transformation $A(v)$ as follows: $$ \begin{pmatrix} t' \\ x' \\ \end{pmatrix} = A(v) \begin{pmatrix} t \\ x \\ ...
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Does quantum mechanics allow faster than light (FTL) travel?

Let's suppose I initially have a particle with a nice and narrow wave function[1] (I will leave these unnormed): $$e^{-\frac{x^2}{a}}$$ where $a$ is some small number (to make it narrow). Let's also ...
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Is there any uncertainty between mass and proper length or time?

I was trying to naively draw a parallel between special relativity and the Heisenberg uncertainty principle. I try to understand uncertainty principle as a consequence of 4-position and 4-momentum ...
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552 views

What is 'past null infinity'?

For example, in the sentence "there is no incoming radiation at past null infinity".
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310 views

Can the overall sign of the Minkowski metric be changed?

If we take the Minkowski metric, $\eta_{\mu\nu}=(1,-1,-1,-1)$, instead of the usual $(-1,1,1,1)$, does this change the form of the Lorentz Transform? I think the standard Lorentz Transform looks like: ...
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520 views

What are the consequences of relativistic angular velocities?

If I take a rod of some radius $r$ and length $L$, and I spin this rod with angular velocity $\omega$. How would the geometry of the rod appear to an observer as one converges to $c$? What are the ...
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5answers
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How a spacecraft travelling near light speed avoid asteroids?

How would a spacecraft traveling near light speed avoid a (relatively dense group of) asteroids? Or suppose such spacecraft is designed, how would the physics work for steering it inside such a ...
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How is the speed of light constant in all directions for all observers?

Please imagine the following thought-experiment: Order of Events: Pulse - A single pulse of light is emitted from the light towards the mirror Reflect - The pulse hits the mirror and is ...
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2answers
673 views

D'Alembert operator and special relativity

We are currently covering special relativity in the theoretical physics lectures where we defined: $$ \mathrm ds^2 := \mathrm dt^2 - \mathrm dx^2 - \mathrm dy^2 - \mathrm dz^2 $$ In Road to Reality, ...
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532 views

Why does weak equivalence principle say gravity is equivalent to acceleration?

I am told that the weak equivalent principle, that $m_i=m_g$ (inertial and gravitational masses are equivalent) is equivalent to the statement that in a small system you can't tell whether you are in ...
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Speed astronauts measure moving at the speed of light

Lets suppose a spaceship travels with v = 0.9c relative to the Earth. The time inside the spaceship would pass slower than on Earth. Would the astronauts measure a different speed (that means, a ...
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174 views

Does photon possesses no time to cover any arbitrary distance?

Photon travel 8 minutes (with speed $c$) from the sun to reach the earth. Any particle (or space-ship) with velocity $0.99 c$ covers the same distance (93 millions km) within less than 2 minutes ...
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170 views

What's wrong with this reactionless drive?

I think this is analogues for the Woodward effect, but macroscopic: We assume a spacecraft consisting of a broomstick, a donut and lots of gear for storing and transfering mechanical energy. Take the ...
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6answers
312 views

What can $E=mc^2$ do? [closed]

In the famous equation $E=mc^2$, the variables stand for: $E$ is energy, $m$ is mass, and $c$ is the speed of light (in vacuum). And I understand the equation fairly but limited in knowing in ...
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Would travelling at relativistic speeds have any impact on human biology?

If a person was sitting on a craft that has accelerated to near light speed speed from Earth (e.g. 99.999% of light speed) would there be any impact on his or her human biology due to relativistic ...
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859 views

Potential energy in $E_f^2=(mc^2)^2+(pc)^2$?

Let's consider $$E_f^2=(mc^2)^2+(pc)^2$$ where the $mc^2$ is the rest energy due to the rest mass -- in Finnish "lepomassa". $$ \sqrt{(mc^2)^2+(pc)^2} - mc^2~=~(\gamma-1)mc^2$$ is the kinetic ...
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Matrix manipulation for Dirac matrices

From the Dirac equation in gamma matrices, we know that $$\gamma^i=\begin{pmatrix} 0 & \sigma^i \\ -\sigma^i & 0 \end{pmatrix}$$ and $$\gamma^0=\begin{pmatrix} I & 0 \\ 0 & -I ...
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If airplanes' highest speed depends directly on the air it is moving through and not the ground,

If airplanes' highest speed depends directly on the air it is moving through and not the ground, does it mean we can build a time machine if only the air moves near the speed of light?
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Extended Rigid Bodies in Special Relativity

I was reading Landau & Lifshitz's Classical Theory of Fields and I noticed that they mention that an extended rigid body isn't "relativistically correct". For example, if you consider a rigid ...
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Charge conjugation in Dirac equation

According to Dirac equation we can write, \begin{equation} \left(i\gamma^\mu( \partial_\mu +ie A_\mu)- m \right)\psi(x,t) = 0 \end{equation} We seek an equation where $e\rightarrow -e $ and which ...
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361 views

Why geometrically four acceleration is a curvature vector of a world line? And what is proper acceleration?

Why geometrically four acceleration is a curvature vector of a world line? Geometrically, four-acceleration is a curvature vector of a world line. Therefore, the magnitude of the ...
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Is the “How to break the speed of light” minute physics video wrong?

I am referring to this video, on YouTube, by minutephysics, which has quite a lot of views. In the video it states that if you flick your wrist while pointing a laser that reaches the moon, that the ...
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Intervals as infinitesimals of same order (Landau & Lifshitz)

I don't understand the following statement in Landau & Lifshitz, Classical Theory of Fields, p.5: $ds$ and $ds'$ are infinitesimals of same order. [...] It follows that $ds^2$ and $ds'^2$ must ...
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190 views

Can time dilation be explained by limitations on computing power?

Are there any ideas of explaining the time dilatation as limits in "computing power"? What I mean is basically that the greater is a concentrated mass, the harder is to "compute" what happens in such ...
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I need to understand the Lorentz transformation [closed]

Two observers A and B, in different initial system describe the same physical event with their particular, different space time coordinates . Let the coordinate of the event be $x^\mu$ for observer A ...
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2answers
358 views

Matrix operation in dirac matrices

If we define $\alpha_i$ and $\beta$ as Dirac matrices which satisfy all of the conditions of spin 1/2 particles , p defines the momentum of the particle, then how can we get the matrix form ? ...
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645 views

How is quantum mechanics compatible with the speed of light limit?

Consider a free electron in space. Let us suppose we measure its position to be at point A with a high degree of accuracy at time 0. If I recall my QM correctly, as time passes the wave function ...
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Empirical meaning of relativity in the context of QM

In special relativity an event E is mapped to coordinates (x,t) in one inertial frame, and to coordinates (x',t') in another, and SR provides the relation between (x,t) and (x',t'). What is the ...
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The definition of an inertial reference frame in Einstein's relativity

I'm reading Sean Carroll's book on general relativity, and I have a question about the definition of an inertial reference frame. In the first chapter that's dedicated to special relativity, the ...
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2answers
219 views

Photons and Relativity

Consider a Photon from Sun and travels with a velocity $c$. Now think we are that photon. For us, it looks like Sun is moving away from us with a velocity $c$. So, why don't we get attracted back ...
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What do massive photons have to do with superconductivity?

I keep reading that the idea of massive photons leads to an explanation of the Meissner effect but I fail to see how photons are involved with the repulsion of fields inside a superconductor. How ...
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172 views

Scattering Amplitudes in Centre of Mass Frame

I'm reviewing page 59 of the QFT notes here and am a little confused by a reference frame argument. You can compute the second order probability amplitude term for nucleon-nucleon scattering to be ...
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Calculating the speed of an object moving relative to another moving Object (Frame of reference) [duplicate]

Possible Duplicate: How to deduce the theorem of addition of velocities? Let's say that you are in a rocket speeding at 90% the speed of light away from Earth. Now fire a bullet inside the ...
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2answers
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Lorentz invariance of the integration measure

This is regards to the lorentz invariance of a classical scalar field theory. We assume that the action which is $S= \int d^4 x \mathcal{L}$, is invariant under a Lorentz transformation. How do you ...
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Why do many people say vector fields describe spin-1 particle but omit the spin-0 part?

We know a vector field is a $(\frac{1}{2},\frac{1}{2})$ representation of Lorentz group, which should describe both spin-1 and spin-0 particles. However many of the articles(mostly lecture notes) I've ...
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Why do Maxwell's equations contain each of a scalar, vector, pseudovector and pseudoscalar equation?

Maxwell's equations, in differential form, are $$\left\{\begin{align} \vec\nabla\cdot\vec{E}&=~\rho/\epsilon_0,\\ \vec\nabla\times\vec B~&=~\mu_0\vec J+\epsilon_0\mu_0\frac{\partial\vec ...
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305 views

Lorentz Invariant Equation of Motion for Scalar Field

I'm trying to understand why you can't write down a first order equation of motion for a scalar field in special relativity. Suppose $\phi(x)$ a scalar field, $v^{\mu}$ a 4-vector. According to my ...
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Does Bernoulli's principle hold in moving reference frames? [duplicate]

Possible Duplicate: Bernoulli’s equation and reference frames Sometimes in train, when setting behind opening window, I can feel strong gale blowing in. The closer to the window the ...
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153 views

Mass-Energy Equivalency

We call $E=mc^2$ the Mass-Energy Equivalency because it equates mass and energy together. But, by that same logic, shouldn't we call $E=\frac{1}{2}(mv^2)$, the equation of kinetic energy in Newtonian ...
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Limitations on how far one can travel in the universe

Someone once incorrectly told me that, given the speed of light is the speed limit of the universe, aliens would have to live for hundreds of years if they are to travel distances of hundreds of light ...
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What does a sphere moving close to the speed of light look like?

What shape does the viewer in a reference frame with $v=0$ perceive? I suppose that since the sphere moves in one direction only (oX only, not oY) its section would change into an ellipse, where the ...
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Classical vs. Quantum use of the spin 4-vector

I have a few basic questions about the Pauli-Lubanski spin 4-vector S. I've used it in quantum mechanical calculations as an operator, that is to say each of the components of S is a matrix operator ...