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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Derivation of the de Broglie waves for a relativistic particle
Generally speaking I am looking for the derivation of the de Broglie waves for a relativistic particle. The particle is in electric field potential ($U$) which accelerates the particle as well.
Let's ...
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1answer
38 views
Speed of light dependent on source velocity in other medium [duplicate]
Does speed of light depends upon the velocity of source in a medium (like water) other than space? if yes, does the speed gets added up when the light source moves in direction of light?
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Spaceship A and Spaceship B move in opposite directions at half the speed of light, and A fires a laser at B, does the laser light reach Spaceship B?
This question has been bugging me for a week now!
I believe it would, but logically, I feel like I'm missing something.
Please give a full explanation.
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1answer
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Inertial frames with unknown past
Let's suppose two ships that cross in space at constant speed. We do not know their previous acceleration or velocity history. When they cross, they synchronize watches.
From that moment, if they ...
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Different prediction about the motion of a charge as observed by two different observers?
Suppose a charge is at rest in the laboratory frame. Also say two observers in two vehicles A and B are approaching towards it. Let A is accelerating towards it and B is moving uniformly towards it. ...
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Lorentz Transformation: sent before finish line
As she wins an interstellar race, Mavis has a
“hooray” message sent from the back of her 300m long ship as she crosses the finish line at v=0.6c. Stanley is at the finish line and at rest relative to ...
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How can direction of electric field due to a moving charge be from the present position of charge?
According to Maxwell's Equations, the electromagnetic waves in vacuum travel at the speed of light $c$. While solving Maxwell's equations using Lorenz gauge conditions (or basically evaluating scalar ...
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Is the potential energy of falling into a black hole already included into E=mc^2?
Each object in the Universe has a huge potential energy, because you can drop it into a black hole, accelerating it to nearly the speed of light.
Is this potential energy already included into ...
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What is the elapsed time at the centre of mass in the Twin Paradox scenario?
Do the twins age differently if you take away the Earth and the spaceship and the rest of the universe and tether them together with a bungee cord? I should hope not, unless one is fatter than the ...
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1answer
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Finding the mass of a relativistic particle resulting from decay
I'm studying relativistic kinematics for the first time. I’m working with a problem from a book but I’m stuck: A relativistic particle of rest mass $m_1$ decays at rest into a particle of rest mass $...
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2answers
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How to derive: $\frac{E^2}{c^4} = \frac{p^2}{c^2} + m_0^2$?
My teacher wrote the following equation on the board a few days ago: $$\frac{E^2}{c^4} = \frac{p^2}{c^2} + m_0^2$$ And I got no idea how this is derived especially since we already derived that: $$m^...
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Why in QFT what really matters is $\exp(\mathfrak{so}(1,3))$ instead of $O(1,3)$?
In QFT fields are classified according to representations of the Lorentz group $O(1,3)$.
Now, most books when getting into this say that in order to understand the representations of $O(1,3)$ we need ...
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1answer
64 views
Relativistic quantum mechanics ${}$
I am reading Weinberg's book "Quantum theory of field".
Сould you explain to me the following things? Vol.1, page 60:
How are we equating the coefficients? How we find the formula (2.4.8)?
2.3.10: ...
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1answer
65 views
Length contraction of an accelerating rod
Let us assume a rod of length, $4l$, initially at rest. The coordinates are defined s.t - (assuming uniform density)
$$X_{back-end}(0) = -2l$$
$$X_{front-end}(0) = +2l$$
$$X_{mid-point}(0) = 0$$
...
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Inner product axioms and Special Relativity
In Linear Algebra, an inner product is a function $(\cdot,\cdot): V \rightarrow F$ , where $V$ is a vector space over the field $F$. This function satisfies the usual three axioms (Conjugate symmetry, ...
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A (probably silly) doubt regarding motion of bar magnet
So my instructor was teaching electrodynamics the other day, and he analysed the electric and magnetic field of the bar magnet moving with velocity v in x direction, first from the ground frame and ...
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1answer
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Is Lorentz and Galilean invariance mutually exclusive?
I know that the classical mechanics stays valid under Galilean transformation. The same argument applies to relativistic equations and Lorentz transformation. My question is, can a set of equations ...
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2answers
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Special Relativity Confusion
Let's say there are 2 points X & Y and a spaceship is moving from X to Y at some very high speed. According to X & Y, let's say the spaceship takes 800 seconds to go from X to Y. According to ...
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1answer
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Indices in Special Relativity
I am studying special relativity and I can't figure out what is the difference between the matrix - index notation between:
$$ Λ_{α}{}^{β}, Λ^{α}{}_{β}, Λ^{αβ} ,Λ_{αβ} $$
Why do we introduce this ...
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1answer
66 views
How do you solve the twins Paradox? [duplicate]
I'm a beginner physics student only studying elementary AP-level physics and calculus, so when I came across the conceptual basis of the twins paradox I was, of course curious. People often explain ...
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1answer
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Is speed of light constant in every inertial reference frame, or does it just seems constant for observers? [closed]
Here is an hypothetical experiment. (I already used this experiment in previous question but the question was diferent) :
Let's call k the distance travelled by light in 1 second
We have two ...
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Why we get relativistic momentum without length contraction?
My last question was wrongly duplicated.
We've already known that "p=γmv" . v is particle's velocity depends on our rest frame and mass too.
But shouldn't we consider particle's momentum by its ...
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1answer
54 views
Light moving toward a moving observer's reference frame
The speed of light is supposed to be the same for all observers in an inertial frame, no matter the observer's speed. As a result, time slows down for observers moving quickly, and this explains why ...
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How can we write relativistic momentum without length length contraction? [duplicate]
We've already known that "p=γmv" . v is particle's velocity depends on our rest frame and mass too.
But shouldn't we observe particle's momentum by its displacement? for particle's view, displacement ...
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2answers
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How Maxwell theory of electromagnetism solved action at a distance problem?
According to wikipedia Maxwell's equations were an essential inspiration for Einstein's development of special relativity. Possibly the most important aspect was their denial of instantaneous action ...
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Is this a right approach to show that $\partial_{\mu} \phi \partial^{\mu} \phi $ is Lorentz Invariant?
When trying to convince myself that $\partial_{\mu} \phi \partial^{\mu} \phi $ is Lorentz Invariant, I stumbled upon this approach:
The last equation should read - $\partial_{i} \phi \partial^{i} \...
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2answers
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What exactly is the meaning of length contraction? [duplicate]
Let's say a train of length $L$ (wrt ground) is standing on rails which have markings for every femtometre (or even smaller units). Now if someone takes a photograph and measures the distance between ...
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stress energy tensor for a massless particle
I want to express stress energy tensor for a massless particle. I know that 4-momentum of a massless particle is $k = (E , EV_x , EV_y, EV_z)$ but I don't know how to use $k$ to construct the stress ...
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Hausdorff property in Minkowski spacetime
In the 4-dimensional Minkowski spacetime, for a given point $x = (x^0,x^1,x^2,x^3)$, its timelike future/past set is defined as,
$$ I^{\pm}(x) = \{y =(y^0,...,y^3) \in \mathbb{R}^4 : \eta_{\mu \nu}(y-...
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2answers
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Quantum Lorentz Transformations
Now I am reading a Weinberg's book "Quantum theory of field". Vol.1 page: 55
Сould you explain me the following things?
Einstein's principle of relativity states the equivalence of certain '...
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2answers
78 views
Length contraction between two objects
I have been thinking about how length contraction should work between two identical objects. Suppose object 1 is stationary relative to object 2, and as measured by object 1, object 2 is a distance of ...
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1answer
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Derivation of length contraction in Einstein, Relativity: The special and general theory
I was reading the book, "Relativity: The special and general theory" by Einstein. At some point it discusses the awkwardness of "relativity of simultaneity" with using universal time axis for all ...
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1answer
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Neutron decay discrepancy
I have been reading the article Neutron Lifetime Puzzle Deepens, but No Dark Matter Seen on the present methods of measuring the life span of neutrons The bottle method measures a mean lifespan which ...
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The chain rule and velocity transformation in relativity (2)
First of all, these answers (How to derive the law of velocity transformation using chain rule?, The chain rule and velocity transformation in relativity, and other from a quick search on this site.) ...
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1answer
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Time dilation derived from first principles vs. “width contraction”
Wikipedia describes the usual derivation of time dilation with a moving light clock:
In this and similar derivations nothing is ever said about a possible "width contraction" and why it does not ...
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3answers
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Confusion about the twin paradox in general relativity?
The twin paradox states that if you have one twin on earth and one twin is sent in a round trip journey to space in a rocket close to the speed of light, when the twin sent in the rocket returns to ...
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Calculating Time in different reference frames
Consider the following problem. A stick passes with speed v though a breadthless person whose(the stick) proper length is L. How does:
Stick See the time elapsed on my clock?
I see time elapsed on my ...
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What is the relativistic mass of Red Light? [duplicate]
After using all the equation and formula's I am getting Light has a certain mass, i.e. 3.157x10^-36 (approx) Kg. Then I have calculated the Energy by using the famous equation, i.e. the E=mC^2 (In ...
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Where does light get its speed from? [duplicate]
One source of light is, IIRC my high school physics, when an excited electron jumps back to its normal position. This jump generates a photon. How can an event like that shoot of a particle at the ...
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Constants of motion of an electron in a harmonic electromagnetic field in free space
I have encountered a question in Classical Electrodynamics, as below:
In free space, an electron, initially at rest at $z=0$, is subjected
to an intense laser field $\vec E=\hat x A \cos(\omega t-...
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Question about time and speed of light [closed]
Trying to understand how light can have constant speed in every inertial reference frame leaded me to the hypothetical experiment descibed bellow. My question is : "How two differents durations in one ...
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1answer
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Would a universe with special-relativistic gravity make sense?
Coulomb's law in electrostatics in analogous with Newtonian gravity. It's pretty clear neither of these can be used in a universe that obeys special relativity. They both must be modified to avoid ...
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1answer
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what is the physical meaning of the 4-vector inner product?
Given two 4-vectors, $P^\mu, Q_\mu$, what is the physical meaning of the inner product, $P^\mu Q_\mu = a$? Specifically I would like to know what it means when the vectors are orthogonal ($a=0$) with ...
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How we can prove that photons have no mass? [duplicate]
I am thinking nowadays that how its possible that a particle without mass, actually exists?
in the case of light its used to say that photons have no mass no weight but they have momentum.
can any ...
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What is the difference between LNRF and the LRF…?
I want to know what is the difference between local rest frame and local non-rotating rest frame, when we have no rotation, for example in the space-time of Schwarzschild, not Kerr?
Are there the ...
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Transformation to canonically conjugate coordinates in Special Relativity
Just like we can Fourier transform a field from $$x^\mu = (ct, x,y,z) \rightarrow p^\mu = (E/c, p_x, p_y, p_z)$$ via a Fourier transform, for spherical coordinates can we Fourier transform in the same ...
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Hyperbolic motion with non-zero initial velocity
The equations of hyperbolic motion in a single spatial direction with initial velocity of zero are pretty easy to find given a bit of googling, such as in this answer. And while I'm too rusty at ...
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1answer
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Rapidity in 4-vector Transformation
In Lorentz transformation we have a concept of rapidity as related to boost. Rapidity is defined as a hyperbolic angle α such that $$\tanh(α)=v/c .$$ This further defines a matrix for Lorentz ...
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Is the metric $ds^2=g_{\mu\nu}(x)dx^\mu dx^\nu$ Lorentz invariant?
Postulate of Special Relativity leads to the conclusion that the metric in flat Minkowski space $$ds^2=c^2t^2-\textbf{r}^2=\eta_{\mu\nu}dx^\mu dx^\nu\tag{1}$$ is Lorentz invariant. This follows as a ...
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Is this relativistic mass?
I have seen in a lot of places in here clearly stating that relativistic mass is outdated, that we can make do just fine with the concept of invariant mass,etc. But I've also seen people saying that a ...
