# 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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### particle accelerator in space

I'm attempting to learn special relativity and i'm having trouble calculating velocity and momentum for each part of the system after interactions. I wanted to know how fast a linear accelerator and ...
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### Where might hertz per dioptre actually be useful?

I once came across the strange, artificial unit "hertz per dioptre", which is dimensionally equivalent to "metres per second". Could this unit, by some stretch of the imagination, be used in some ...
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### Graviton and photons interaction

If one believes in the theory of gravitons then by viewing a black hole you see gravitons affect photons. This in turn leads to the conclusion that force carrier's mass equivalences allow them to be ...
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### Special Relativity: Transforming Maxwell's equations

I'm working through Einstein's original 1905 paper*, and I'm having trouble with the section on the transformation of Maxwell's equations from rest to moving frame. The paper proceeds as follows: ...
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### What is the maximum time dilation between two objects, if one is standing still and the other is moving at $c$?

What is the maximum ratio in the rate of change in time in reference to object $A$ which is standing still and object $B$ which is moving at the speed of light?
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### Relativity exposition from the “naïve” viewpoint

A naïve observational viewpoint doesn't automatically try to correct for signal delays. In other words, the time co-ordinate is retarded. For example: In popular expositions of relativity you'll ...
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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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### What is 'past null infinity'?

For example, in the sentence "there is no incoming radiation at past null infinity".
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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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, $$\left(i\gamma^\mu( \partial_\mu +ie A_\mu)- m \right)\psi(x,t) = 0$$ We seek an equation where $e\rightarrow -e$ and which ...
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### 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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### 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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### 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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### 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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### 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 ...