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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Question about dot product of four vectors?

I am looking back over some old notes and see that I have written $\bar{p}=\left(\overset{E}{\vec p}\right)$ and $\bar{x}=\left(\overset{t}{\vec x}\right)$ (using Plank units) And then $\bar{p} ...
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2answers
51 views

Is it possible to propagate a relativistic system of particles in time using Verlet?

The Verlet algorithm and its derivations are very popular methods to integrate Newton's equations of motion in time and obtain a trajectory for a system with $N$ particles. I work with classical ...
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3answers
64 views

Is it really possible to create some mass only from equivalent energy? [duplicate]

From Special theory of relativity we know that $E=m_0 c^2$, which says about mass energy equivalency. But my question : **Is there any real experiment where some mass is created purely from energy? ...
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Measuring speed of the moving train, if I'm inside it

So I am inside a coach in a train that is fully sealed (with no windows and a locked door). I have a torch, photo & time sensor and a scale with me. So, I place the sensor at one of the walls and ...
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25 views

$2\to3$ Phase space Integration

I have a $2\to3$ process ($P=p_1+p_2 \to p_3+p_4+p_5$) where all particles in the initial state and one of the particles in the final state ($p_3$) are massless. The other two ($p_4$ and $p_5$) have ...
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How does the Lorentz transformation $\Lambda^{\mu}{}_{\nu}$ transform?

For example the Four-velocity transforms as $$U^{a'}=\Lambda^{a'}{}_{\nu}U^{\nu},$$ the Faradaytensor as $$F^{a'b'}=\Lambda_{\,\,\mu}^{a'}\Lambda_{\,\,\nu}^{b'}F^{\mu\nu}$$ or in Matrixnotation: ...
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3answers
65 views

Circumference of a circle in a co-rotating frame of reference

According to Einstein it should be greater than $2 \pi R$ for a co-rotating observer, i.e. $L' = \gamma L$ where $L = 2 \pi R$ in a non-rotating frame and $\gamma$ is the usual Lorentz factor, which ...
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Does space between objects contract?

I had a question, let us assume a coordinate system where there is 2 objects moving at relativistic speeds (at same velocity) for the observer therefore the observer will observe the length ...
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3answers
131 views

Can length contraction really be derived from time dilation? Does speed equal speed?

I am referring to Wikipedia: "Length contraction can also be derived from time dilation." with the following proof which seems to be the result of a circular reasoning. The proof uses only one and ...
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112 views

How to describe arbitrary accelerations in special relativity

Describing acceleration in special relativity is in principle straightforward, and for simple cases the resulting transformations are simple. Examples include circular motion and constant acceleration ...
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67 views

A simple quantum mechanics question [closed]

Here is the problem: Find the energy of neutron, electron and electromagnetic waves of wavelength 0.1nm. English is my second language, so I am kind of confused about the meaning of problem ...
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Does a Michelson-Morley experiment uphold mass-energy equivalence and special relativity?

If there is an experiment that best supports $E=mc^2$, is it the Michelson-Morley experiment?
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80 views

Scalar operators In Quantum Field Theory

I am trying to learn Quantum Field Theory and I am stuck in a basic point. What is the definition of a scalar operator in QFT? That is, how does it transform under a Poincare transformation? Why do ...
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2answers
55 views

Tangent vector norm squared conservation in special relativity

I'm trying to analyse non-inertial motion in special relativity. First I'll start off with inertial motion. In my reference frame, my particle has coordinates $x^\mu = (t, x)$ And in the particle's ...
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1answer
95 views

If we could not see, would we think that nothing can go faster than sound?

And if so, then why does everybody keep asserting nothing can go faster than light speed (I'm implicitly assuming there could be something which we do not observe, which goes faster than light)?
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Can “uniform motion” (or “mutual rest”) be determined intrinsically, by members of Synge's “five-point curvature detector”?

In his description of a "five-point curvature detector" [1], J. L. Synge exhibits a Cayley-Menger determinant in terms of "optical distances" between five distinct participants; and he states that the ...
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4answers
815 views

Relativistic object impacts the earth

A familiar trope within science-fiction is that of a large relativistic object hitting a planet such as the earth. This is normally an interstellar spacecraft or a kinetic weapon with a mass in the ...
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Does mass increase at relativistic OUTSIDE of the mass's frame of reference? [duplicate]

There are other questions on here with responses saying that the mass does not change from its own frame of reference. But those answers were somewhat unclear if the mass changes to someone observing. ...
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Two clocks along different worldlines

I have been reading and watching videos about this subject for a while now. I just can not seem to grasp the idea. Let's say we have two clocks. I leave one at home and keep one in my pocket. Then, ...
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Is it OK to see time dilation and (relativistic) mass increase as phenomena that avoid $c$ being reached? And how about length contraction?

I think I have been exposed since years ago to this line of reasoning: if $ v\to c $, then $ \Delta t \to \infty $. As $\displaystyle v=\frac{\Delta s}{\Delta t} $, it's like a natural reaction to ...
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Stress Energy Tensor of EM Field

Stress energy tensor for electromagnetic field is given by $$T^{\mu\nu}=\frac1{4\pi}(F^{\mu\alpha}F^{\nu}{}_\alpha-\frac14 g^{\mu\nu} F_{\alpha\beta}F^{\alpha\beta}).$$ My textbook (unpublished ...
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1answer
48 views

Proof of equivalence of two different covariant notations of Maxwell's equations [closed]

My homework assignment is Prove that $$\partial_\beta F_{\gamma \delta} + \partial_\gamma F_{\delta \beta} + \partial_\delta F_{\beta \gamma} = 0$$ with the electromagnetic tensor ...
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1answer
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Effects of travel greater than speed of light [closed]

What will happen if a person with say weight of 100 kilograms, starts to travel with, a) equal to speed of light? b) greater than speed of light?
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2answers
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Is the explanation of special relativity in Stephen Hawking's “The Grand Design” flawed?

To explain special relativity (in chapter 5 titled "the theory of everything"), Hawking starts with an example involving a flying jet, its passenger (being an observer) and an observer on the earth. ...
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What is energy of light, as we know speed of light?

1.What is total energy of EM waves, as all got same speed? If two em waves has same energy, do they have same mass? If same mass and energy, do they have same frequency or wavelength still ...
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3answers
367 views

How does a single charge produce magnetic field?

I have studied in Introduction to electrodynamics (Griffiths) that magnetic field is actually due to effects of relativity unequal Lorentz contraction of the positive charge and negative lines, a ...
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27 views

Is it possible to measure relativistic mass of a body moving towards or from an observer?

It is clear there is no problem in measuring relativistic mass via magnetic field: “Suppose you know the strength of a uniform magnetic field B. Launch a charged particle, of magnitude charge q, ...
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5answers
256 views

How do we know that photons are exactly massless and travel exactly with speed $c$ in vacuum?

I know that this question may sound stupid, but what I mean is that photons have some energy and no mass, yet the mass and energy are said to be equivalent (or maybe I got that part wrong). In an ...
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1answer
54 views

Special Relativity: Four possible time spans between events?

I've got another question regarding time in special relativity. I'll start with the standard configuration: there are two observers O and O', their x-axis are aligned, in the rest frame of O observer ...
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873 views

Fundamental invariants of the electromagnetic field

It is a standard exercise in relativistic electrodynamics to show that the electromagnetic field tensor $F_{\mu\nu}$, whose components equal the electric $E^i=cF^{i0}$ and magnetic ...
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49 views

Hardy's paradox (see the article “Quantum Mechanics, Local Realistic Theories, and Lorentz-Invariant Realistic Theories”)

Does this thought-experiment (Phys. Rev. Lett., Vol. 68, No. 20, page 2981, year 1992) represent a proof against Bohm's interpretation of the quantum mechanics? The analysis of Hardy rules out local ...
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1answer
69 views

Spin statistics

I have a very intrinsic question about quantum field theory and even more general, why in 3+1-dimensional spacetime, we have only two statistics for particles to obey? Therefore why we have only two ...
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134 views

Does the passage of time effect a photons entanglement with another?

I recently read an article about "Delayed-choice entanglement swapping". Here is an excerpt from the article: Delayed-choice entanglement swapping consists of the following steps. (I use the ...
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1answer
101 views

Thought experiment: Tethered galaxies - to the extreme

If two rocks were tied together with a tight, absurdly long, non-elastic rope, and placed on planets at either end of Earth's observable universe - or beyond - What would happen? Is the structural ...
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31 views

Transverse doppler effect in light

In most books to explain transverse Doppler effect the following example is given: Consider a source that emits flashes at frequency f 0 (in its own frame), while moving across your field of vision ...
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2answers
67 views

Relativity and acceleration-acceleration

Presummary to save expert's time! (pls see below!) "In GR, is jerk relative?" As I understand it, "Special Relativity" (special meaning, specific limited situations) applies only for (in a word) ...
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1answer
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Is there a graphical representation of the Lorentz transformation equations?

I always loved theoretical physics as a kid and when I came upon this site while seeking computer advice via superuser I had to stick my silly little head into an oasis of intelligence. I have often ...
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1answer
617 views

Special relativity paradox and gravitation/acceleration equivalence

One of the features of the black hole complementarity is the following : According to an external observer, the infinite time dilation at the horizon itself makes it appear as if it takes an ...
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1answer
191 views

Reunion condition in the Twin Paradox

In the Twin Paradox two twins initially at rest in the same reference frame are separated and take different journeys through spacetime. Eventually they are reunited. What is the condition for the ...
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1answer
300 views

Interpretation of rank 2 spinors

While inspecting the $(\frac{1}{2},\frac{1}{2})$ representation of the Lorentz group and defining a right-handed spinor with upper dotted index and a left-handed spinor with lower undotted index and ...
2
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3answers
120 views

Problem with understanding time dilation (moving clocks can run faster?)

I ran into a serious problem with the Lorentz transformation and time dilation. In the standard configuration you have one observer S and another one S' with their x-axis aligned. I assume S to be at ...
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2answers
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Energy-Time Uncertainty Principle and Photons

Heisenberg's uncertainty principle states that: $$ \Delta E \cdot \Delta t \ge \frac{\hbar}{2} $$ It is clear that this has nothing to do with the accuracy of our measurements, but rather is a ...
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2answers
117 views

Does this proof for time dilation ignore length contraction?

A simple proof for time dilation can be found here http://en.wikipedia.org/wiki/Time_dilation#Simple_inference_of_time_dilation_due_to_relative_velocity What I am confused about is that when the ...
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4answers
582 views

Where's the energy in a boosted capacitor?

Suppose I look at a parallel plate capacitor in its rest frame and calculate the electrostatic energy, $E$. Next, I look at the same capacitor in a primed frame boosted in the direction perpendicular ...
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1answer
52 views

Relative velocity of two objects travelling at $c$ (or near $c$) [duplicate]

If two bodies are travelling at speed $0.9 \, c$ in opposite directions, what will be the speed of one, as observed by another? Newtonian mechanics won't apply at such speeds. As such, how will we ...
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1answer
30 views

Explicit Symmetry Breaking: Where do the additional d.o.f. come from?

Massless vector bosons have only two independent degrees of freedom, while massive ones have three. In spontaneous symmetry breaking, the massless vector belonging to the broken group becomes massive ...
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Is acceleration relative?

A while back in my Dynamics & Relativity lectures my lecturer mentioned that an object need not be accelerating relative to anything - he said it makes sense for an object to just be accelerating. ...
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4answers
356 views

Formal definition of an observer?

What is the formal definition of an observer in special relativity? I have seen a few: The actual coordinate system. The collection of synchronised clocks that cover the coordinate system. A well ...
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Moving coil contradiction of Faraday Induction

In Faraday's Induction Experiment, the e.m.f. induced in the induction coil becomes zero when the relative velocity of the coil and the magnet becomes zero. But one can also argue from a stationary ...
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Why does the existence of an aether go against Maxwell's equations

I am trying to determine why there is a conflict between Maxwell's equations and Galilean relativity. The standard way I have seen it explained is: The Galilean world model says velocities transform ...