Questions tagged [special-relativity]
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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Can you resolve this special relativity paradox?
I've devised a thought experiment called the "Killer Crate Paradox" to further improve my understanding of Lorentz Transformations. This is not a paradox I am able to resolve, so please read ...
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Circular motion of proton in special relativity
Consider a proton in uniform circular motion in a plane perpendicular to a magnetic field. The Lorentz force acts as the required centripetal force.
At a low speed, we have $\frac{m\cdot v^2}{r}=B\...
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Using invariant hyperbolas to calibrate between reference frames
We can now calibrate the axes of $\tilde{O}$. In fig 1.11.
The axes of $O$ and $\tilde{O}$ are drawn, along with an invariant hyperbola of time like interval $-1$ from the origin. Event $A$ is on the ...
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Drawing spacetime diagrams assuming absolute time (page-6,Section 1.5, Schutz)
Suppose an observer $O$ uses the coordinates $t,x$ as above, and that another observer $\tilde{O}$ with coordinates $\tilde{t}, \tilde{x}$ is moving with velocity $v$ in the $x$ direction relative to $...
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Thought experiment in Mach's principle - Can a void universe be considered with special relativity?
Mach's principle is based on a thought experiment in which an astronaut floats in the middle of a space devoid of all matter and all landmarks. No star, no source of energy is present, whatever the ...
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Are time and length independent or can one be derived from the other?
In particular, the time coordinate $t$ can be choosen so that the mathematical expression of the physical laws reflects their inherent symmetries. Already Newton's first law then fixes the time rate ...
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Why does four-momentum have the same transformation matrix as spacetime coordinates?
I will outline my question in 1+1D for brevity. We can passively transform our coordinate system using a Lorentz boost; $\Lambda^{\bar{\nu}}_{\mu}x^{\mu}=x^{\bar{\nu}}$. I've seen that, by stipulating ...
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Experiment vs manipulation (Rindler Page-41)
As just another application of the midframe lemma, we end this section with a proof of the obvious-seeming 'reciprocity theorem' which asserts of any pair $S$ and $S'$ of inertial frames, using ...
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Qualitative analysis of special relativity effects between moving planes (page-38 of Rindler)
Suppose we are in an IF(inertial frame) and a fast air plane flying overhead constitutes a second IF; let it be the top plane in Fig. 2.3(a). Suppose that a flash bulb goes off in the exact middle of ...
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Could there be some process or event that would make the universe to be Lorentz non-invariant?
As far as we know the universe is invariant under the Lorentz symmetry and does have many other fundamental symmetries from which we derive the fundamental laws of physics.
But could there be any ...
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What does size of an inertial frame mean?
It is the equivalence principle that provides the bridge between the ideal $SR$ model and the real world. According to it, we can find at each event a set of local inertial frames (LIFS), which may be ...
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Angular-momentum of the Dirac spinor theory
The standard Dirac action
$$
S = \int d^4 x \bar \psi (i \gamma^\mu \partial_\mu - m) \psi
$$
is invariant under Lorentz transformation.
In David Tong's lecture note, eq (4.96) lists that the ...
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Time differential between two signals sent at two different near-relativistic speeds
There is something I don't quite get about relativistic velocities, which I am hoping to clarify with this question.
Suppose you have an emitter and receiver both located somewhere far away from one ...
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For someone staying on Earth, what is the minimum possible time to send a spaceship to Alpha Centauri and have it back?
Suppose we want to send a spaceship to Alpha Centauri and calculate the minimum possible time it will take for us here on Earth to have the spaceship back. We are not interested in how fast the time ...
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What is the correct derivation for particle concentration from one frame to another?
I. The simplest derivation I can think about is based on conservation of the number of particles and length contraction. In frame S, say we have a volume V (surface S, length l) of particles of ...
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Units make speed of light dimensionless..?
We shall now adopt a new unit for time, the meter. One meter of time is the time it takes for light to travel one meter ... (page-4, Bernhard Schutz's A first course in relativity)
I am confused, how ...
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How to calculate the relativistic final velocity? What's the formula?
Assume we have an object of 1 kg, at rest and we invest 100 Joules of energy to accelerate it. The resultant velocity can be calculated by
$$ v = \sqrt{\frac{2K_{e}}{m}} $$
so, $$ \sqrt{\frac{2 (100)}...
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Why the proper time of photon is zero? [duplicate]
I'm currently taking classes on General Relativity, and whilst working on Geodesis equation:
Find out that for mass particle q is equivalent to proper time but in case of photon the proper time of ...
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Time taken to travel by light a minimum or maximum?
Im stuck on the following.
We know that the path taken by light to travel between 2 points A and B corresponds to the path which minimises time elapsed.
However, from relativity we also know light ...
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Can this experiment successfully be used to find out one-way speed of light? [duplicate]
As with almost every question on this topic, this question is also inspired by the Vertiasium video Why No One Has Measured The Speed Of Light.
This experiment tries to measure the one way speed of ...
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How to make sense of the length of a rod in Special Relativity, using the mathematical framework of General Relativity? [duplicate]
This question asks how exactly Special Relativity (SR) emerges mathematically as a special case of General Relativity (GR).
In GR, spacetime is modeled as a pseudo-Riemannian manifold with generally ...
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The momentum delivered to completely absorbing surface by an oscillating electron through electromagnetic waves is not ENERGY/$c$. Am I right?
As far as I understood, electron's rest mass is not equal to zero (unlike photons) and hence the momentum associated with oscillating electron != Energy/$c$. So, The momentum delivered to completely ...
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Tachyon velocity in relation to light speed [duplicate]
tachyonic particle are merely hypothetical particle that always travels faster than light., But if real, how fast would they be?
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Does anybody know a physical explanation for the refractive index independence of the Sagnac Interferometer fringe shift?
It is generally accepted that the fringe shift produced in a fiber optic Sagnac interferometer is independent of the refractive index of the fiber. In fact, the waveguide aspect of the fiber is not ...
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How could any frame of reference be inertial?
The image below shows that a bystander watching the merry-go-round is in an inertial frame of reference. However, to nitpick, wouldn't the observer still be accelerating because it's on Earth?
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A question about relativity and time dilation from a lay-person
Observer A is in a spacecraft flying toward earth
Observer B is standing on earth
A is traveling at near light-speed and will reach the earth in 1 week.
When B looks at A's clock, he sees it moving ...
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Relativistic Euler-Lagrange equations for a four-vector (or one-form) field
I think the best way to ask my question is by considering the maxwell-Lagrangian,
$$\mathcal{L}=-\frac{1}{4}F^{\mu \nu}F_{\mu \nu}=-\frac{1}{2}(\partial^{\mu}A^{\nu}\partial_{\mu}A_{\nu}-\partial^{\mu}...
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Why is some mass converted into energy when neutrons and protons combine to form nucleus?
So some of the mass is converted into energy when neutrons and protons combine to form nucleus. Why? And how? And then why do we need to supply the same amount of energy to separate them?
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Where/ how does light propagate? [duplicate]
The Michelson–Morley experiment proved there is no aether, but we (used to) know that a wave needs a medium in order to propagate. Einstein showed the invariance of speed but assigned no properties to ...
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How would a rigid disk rotating near speed of light behave? [duplicate]
Say you had a perfectly rigid disk so that you can't morph it or bend it. If you were to spin near the center of the disk at near speed of light, the edge of disk would have to be faster but of course ...
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Does this relativistic generalization of the Schrodinger equation make sense? [duplicate]
So I'm aware that the correct relativistic approach to quantum mechanics is through quantum fields, but I'm still interested in the question that follows.
We know the Schrodinger equation in free ...
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Is there a way to assign 4-momentum vectors to spatially extended mass distributions in a covariant manner?
We know that the 4-momentum of a point particle is of the form $p^{\mu} = (E/c, p^{i})$, whose transformations across different inertial reference frames are given by Lorentz transformations. If we ...
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Why does the trajectory of a relativistic particle "minimises its Minkowski distance"?
The action of a relativistic free particle is
$$\mathcal{S}=\int^{t_{1}}_{t_{0}} L dt\tag{1},$$
for
$$L=-\frac{mc^{2}}{\gamma}.\tag{2}$$
I understand that a particle will follow the trajectory of ...
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How do massless particles have the same chirality and helicity when they are different properties?
I read this article about chirality and helicity. At some point it says
For massless particles, chirality is the same as helicity.
But as far as I know, helicity takes form in numbers, $(-1/2, +1/2)...
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Minkowski's equation of motion
I'm trying to prove $f^{\mu}U_{\mu}=0$ for four-force $f^{\mu}=c\frac{dP^{\mu}}{ds}$ and four-velocity $U_{\mu}$. I start by using the chain rule, $f^{\mu}=c\frac{dP^{\mu}}{dt}\frac{dt}{ds}=\gamma\...
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Vacuum Transitions and Lorentz Symmetry Breaking
There are many "bumblebee" models 1, 2 where Lorentz invariance is violated usually resulting from a local vector or tensor field acquiring a nonzero vacuum expectation value
We do not know ...
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Relativistic doppler redshift
From Wikipedia I can only find "longitudinal" and " closest approach" redshift.
I was wondering what resources I can use to find the redshift (and resulting energy change) of ...
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How does a ring magnet rotating in-place lose K.E. when it does work on an external charge using its curl-free/irrotational/conservative $E$-field?
Consider a ring magnet that is rotating in-place. By rotating in-place, I mean that the ring magnet is symmetrical about an axis and is rotating about that axis.
Such a ring magnet produces an ...
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How to represent a pair of inertial frames in relativity?
Can two Cartesian inertial frames, in general relative motion, be drawn parallel to each other? A picture in Wikipedia suggests this, but some answers on this site appear to differ.
Consider observers ...
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Test for Lorentz invariance of scalar function
This is a simplification of a previous question. I have a function of two 4-vectors and two factors. One factor is on-shell, that is $q_0=\sqrt{M^2+q^2}$. The other factor is off-shell, that is the ...
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Is there a limit to how close faraway objects can get due to the conservation of angular momentum?
Say a 1kg object is going 1 meter/sec tangentially to a point 600,000,000 meters away, its angular momentum is $$1kg*1m/s*600,000,000 meters$$ If it were to decrease its radius to the point similar to ...
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Why aren't all photons black holes?
According to Special Relativity, there is no preferred inertial reference frame. And shifting reference frames can cause blue shifting or red shifting of photons.
And according to General Relativity, ...
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Distance contraction and acceleration
I'm trying to understand length contraction. I've created a diagram with three examples. I'm wondering if my diagram is correct. According to this diagram, when you accelerate towards an object, the ...
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Could the speed of causality be (significantly) faster than $c$?
The other day my son (13) asked me whether it was possible that light went very slightly slower than our best measured $c$, and at the same time had a very tiny mass, but we aren't able to measure ...
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Can "relativistic mass increase" be explained in terms of time dilation? [duplicate]
If, for example, the body is moving at a speed close to the speed of light, the rest mass will of course remain the same, but many people argue that the relativistic mass increases. But if we take ...
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Paradox with muons decay [closed]
I wonder what would happen if muons or something similar would travel at 99.999999999% of light speed. Also, can anyone please shine some light on what happens to the sunlight (photons) and the ...
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Relativistic angular momentum confusing definition
After reading Wikipedia, I'm confused by the relativistic angular momentum definition. OK for the 4-angular momentum tensor. But does it mean that the following more intuitive "angular momentum&...
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A synchronous clock problem in a rigid frame with constant proper acceleration
I am a beginner of general relativity. I read and follow the notation in Andrew Steane's book, Relativity Made Relatively Easy, chap 9.2. Suppose there is an rigid accelerating frame with constant ...
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Length contraction and acceleration in opposite directions
If you accelerate in a direction, objects in front and behind you get closer relative to you. If you then accelerate again in the opposite direction, the same thing happens, which leads to a ...
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Prove dot product between two timelike vectors in Minkowski spacetimw [closed]
In the Minkowski 4-dimensional space-time $(\mathbb{M}^4,\eta)$ the dot product is:
$a\cdot b = -a^0b^0 + a^1b^1 + a^2b^2 + a^3b^3 ~\qquad~ a = (a^0,a^1,a^2,a^3) ~~,~~ b = (b^0,b^1,b^2,b^3)$
Now ...