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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Noether's theorem and energy in four-momentum
In Newtonian physics, momentum and energy are often treated as distinct entities, which happen to be separately conserved. In relativity, energy is regarded as the "time" component of the ...
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Linearity of Lorentz Transformations from Principle of Relativity
Many derivations of the Lorentz transformations assume they must be linear maps on $\mathbb R^4$, where we identify the components of $\mathbb R^4$ with orthogonal coordinate systems associated to ...
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What if the Twin Paradox use the "day time" and "night time" on earth as their age reference?
I've searched this site, I found a similar question here but not exactly like mine.
So I can't understand the Twin Paradox when I use the "day" (bright time) and "night" (dark time)...
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Can a massless particle travel along a timelike path [duplicate]
It seems to be generally accepted that massless particles always travel at the speed of light, but I have never seen any explanation for why that needs to be the case. What in our theories prevents ...
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Lorentz-invariant Lagrangian for spinor field
Schwartz book on QFT (page 167), Zee book on group (page 461) and Maggiore book on QFT (page 55), prove that $\psi_R^{\dagger}\sigma^{\mu}\psi_R$ is a 4-vector, where $\psi_R$ is a right-handed spinor ...
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Artificial gravity and forces in non-inertial frame
If we have a rotating space station. In a inertial frame we have $$\sum F = ma = F_c = ma_c$$
Thus, in a non-inertial frame of reference inside the space station for instance.
We have $$\sum F = F_c - ...
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If kinetic and potential energy are relative, how do they exert a gravitational force? [duplicate]
I am imagining two bodies flying through empty space near the speed of light relative to their (distant) surroundings. Let’s say they are a bowling ball and a tennis ball. They are not moving with ...
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How are spatial coordinate systems in physics defined?
Grothendieck once asked "What is a meter?" (https://golem.ph.utexas.edu/category/2006/08/letter_from_grothendieck.html). This innocent sounding question, made me to think about how ...
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Do $LC$ tank oscillators violate the conservation of linear momentum?
General setup
Consider the following thought experiment: A capacitor $C$ and an inductor $L$ are mounted with fixed joints on a plate in outer space at say $1$ meter apart. They are connected in the $...
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Mass-Energy equivalence - speed of light?
According to Einstein, $E=mc^2$.
Is $c$ always the speed of light in vacuum in this equation?
And for the relativistic mass: $m=\frac{m_0}{\sqrt{1-(v/c)^2}}$ does the same hold for $c$ here?
So if I ...
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How can an observer establish a coordinate system in curved spacetime only with GR?
Consider the theory only posseses GR.
If an observer lives in a curved spacetime, how can he measure the metric of the spacetime without knowing the matter distribution? Suppose he can establish a ...
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Project Hail Mary - Does relativity cause us to need more fuel or less fuel for interstellar travel?
In the book, project Hail Mary, Eridians were not aware of relativity. It is claimed that, due to this, they calculated that they would need much more fuel than actually needed for interstellar travel....
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Can we measure the one-way speed of anything at all? [duplicate]
I know the one-way speed of light question has been exhausted, and I'm sorry for the naive question, but I would like to understand one thing. Can we measure the one-way speed of anything at all? If ...
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Indices in QFT help
I am going over an example regarding the Lorentz group. The indices do not make sense to me, can you please explain the following result to me in terms of matrices?
$(M^{12})^{\mu}_{\ \ \ \nu} = - \...
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Lorentz boosting orthogonal to the direction of a photon's momentum- what's going on here?
So while solving a special relativity problem, the following problem came to my mind, which seems to admit two inconsistent methods of resolution. I'd like to know which is incorrect, where the ...
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Can the one-way speed of light be different in different direction? [duplicate]
Can speed of light be different in different direction?
Due to clock synchronization issue for time dilatation scientists used to measure speed of light with mirror. Does it mean that, it is never ...
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Confusion about the Lorentz transfornation of position
In my frame, I see a traveler moving at a constant speed in the $x$ direction. An event occurs. I then measure the position he would assign to that event, assuming we are living in the $x$ axis, to be ...
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Please solve the integral . OR You can solve the below path integral [closed]
The integral arises during calculation of commutator of two bosonic fields for a spacelike interval.The answer will come in terms of spherical bessel functions and hankel function.The answer you will ...
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Can an object theoretically reach, or exceed the speed of light? [duplicate]
I'm sorry if this is a naïve question, but it's been bugging me for a bit. If a spacecraft were traveling in a perfect space with unlimited fuel, could it not, assuming it is not influenced by other ...
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How to prove the helicity operator is a Casimir operator for massless particles?
I am reading the classification of irreducible unitary Poincaré group representations. It seems that for massless particles, the momentum operator and the Pauli-Lubanski operator get aligned so the ...
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Linus Pauling, General Chemistry 1-2 - Does Light has mass?
Linus Pauling, General Chemistry 1-2:
"...it was pointed out by Einstein that energy also has a mass, and
that light is accordingly attracted to matter by gravitation."
Isn't that wrong? ...
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Is the First Postulate of Special Relativity Redundant?
For what I understand, in order to develop special relativity we follow this reasoning:
Definition: an inertial frame is a frame in which an object not
subjected to a force moves with uniform ...
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Mass: a form of energy [closed]
Einstein's $E=mc^2$ and law of conservation of energy implies that mass is a form of energy, but if it is a form of energy then why can we freely interact with mass while the other forms of energy are ...
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What are the physical reasons for considering the Maxwell invariant ${\cal G}=E.B$ in the action?
As I know, the Maxwell invariant ${\cal G}=E.B$ is the fundamental invariant such as ${\cal F}=\frac{1}{2}\left( {{{\bf{B}}^2} - {{\bf{E}}^2}} \right)$ that can be used to construct all possible ...
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Infinite-dimensional representation of Lorentz algebra
In QFT, we need to use infinite-dimensional representations of the Lorentz algebra, because all the non-trivial finite-dimension al representations are not unitary, and we need unitary ...
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Interrupted Laser propulsion and relativity
I have seen concerns that in order for a laser sail ship to work, the laser on Earth has to continue operating for centuries, which there is no gurantee of.
If the laser stopped operating after 300 ...
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Special Orthogonal Group in Euclidian and Minkowski spacetimes
I apologize if my question seems a little half-baked. I was wondering if while working with a QFT, one can make transitions from imaginary time to real time and thereby changing the underlying ...
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Can force change mass in a system?
My physics teacher defined force as "an agent that may change the shape, state of motion, size, or mass of an object" but I disagreed with him about "mass" being changed in any ...
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In the presence of a stationary electron, a high energy photon can produce an electronpositron pair via the reaction [closed]
The equation is
photon + electron ---> positron + electron + electron.
What is the minimum energy of the photon for this reaction to go through...
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Why would it break Lorentz invariance if $\rho_{\text{vac}} $was not equal to $-p_{\text{vac}} $?
Using $\Lambda$ in the field equations, one can derive that then $p_{\text{vac}} =-\rho_{\text{vac}} $. The energy density of the vacuum is the same (with opposite sign) as the pressure of the vacuum.
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What is the connection between the relativistic explanation for magnetic fields and the phenomenon of natural magnets existing?
How does the concept of the relativistic explanation for magnetism— that is, the explanation that considers the reference frame of a moving charge in cooperation with length contraction— overlap with ...
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Doesn't Veritasium's Recent Video About Circuits Violate The Speed Of Light?
A recent Veritasium video discusses the following circuit:
...
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Usage of Velocity = Displacement/Time to get the time interval at relativistic speed
Say I am in a spaceship. Another ship moves relative to me along a direction directly away from me, with a relative velocity(comparable to c) which I determine by measuring the doppler effect. My ...
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Does relativity and frame of reference contradict each other?
so relativity states that nature doesnt depend on how we look at things, and a physical process is the same no matter what perspective we choose to think about it in, and frame of reference is a set ...
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Is it possible for the one-way speed of light to be infinite? And how does it relate to the geometrics of the universe?
I probably get bashed for asking this question, sooo... I ask anyway, sorry in advance.
As any physics laymen I came from the Veraterasium Video and was left a bit puzzeled. Specifically about how ...
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Motion of electric charge as seen from non inertial frame of reference [closed]
Consider a charge Q resting at point A . If the observer watch the charge from non inertial frame of reference, will that charge acquire kinetic charge from the perspective of the non inertial ...
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Lorentz transformation of operator
I am reading the Zee book on group and at pg.442 when explaining the Poincare' algebra an the infinity dimensional representation, it states that since $P_{\mu}P^{\mu}$ is a Lorentz invariant then it ...
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Lorentz Transformation - Representation for Rotations, the Scalar Product and Kronecker Delta
I'm currently reading this article about the Dirac Fermion by Yehonatan Viernik. In section 3.3 (looking at Lorentz transformations), we define matrices $S
^{ij}$ to be representations for rotations. ...
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Relation between kinetic energy and momentum in relativity
In a recent discussion a friend of mine claimed that kinetic energy ($K$) an momentum ($p$) in relativity can me expressed by
$$K=\frac{p^2}{(1+\gamma)m} \tag{1}$$
This equation if holds, has some ...
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1answer
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The General Lorentz Transformation in 3+1D
In the following link https://en.wikipedia.org/wiki/Lorentz_transformation#/media/File:Lorentz_boost_any_direction_standard_configuration.svg ,
we have: $\ \mathbf{r}'=\mathbf{r}_{\bot} +\gamma( \...
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Paradox of quantum entanglement
in quantum entanglement, it is said that two opposite spins are if entangled with each other we can determine state of a spin if one of them is known to us.
But my question is, why is it even a ...
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1answer
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Space-time metric in tensor form
In space time metric in tensor form:
The distance is given by $$ds^2=c^2dt-dx^2-dy^2-dz^2$$
Which in tensor form is: $$ds^2=\sum_{\alpha \beta}g_{\alpha \beta}dx^\alpha dx^\beta$$
Using Einstein ...
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A photon cannot exist if it travels at speed lower than $\mathrm{c}$ in a vacuum, why?
This is known in physics that photons travel only at fixed speed $\mathrm{c}$ in vacuum but also inside a medium going from one atom to the next and taking advantage of the vacuum that exists between ...
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Ideal Gas Mixing and Galilean Relativity
This is a conceptual question more than anything else.
Assume you have a container with two ideal gases separated by a partition. The container is somewhere out in empty space and is not influenced by ...
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Kinetic energy of an electron inside the sun [closed]
I have to tell if an average proton or electron at 15 million degrees kelvin be treated by relativistic mechanics. The criterion is that the kinetic energy differ from the classical kinetic energy by ...
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How is electromagnetic induction analogous to gravitational frame dragging?
This wiki says: https://en.wikipedia.org/wiki/Frame-dragging
Qualitatively, frame-dragging can be viewed as the gravitational
analog of electromagnetic induction.
I was wondering what exactly this ...
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The acceleration of a particle moving at fixed Rindler coordinate $X=\frac{1}{g}$ [closed]
Let us define the transformation from the Minkowski coordinates $x^\alpha=(t,x)$ to the Rindler coordinates $x^{\bar\alpha}(T,X)$ by
$$t=X\sinh T,\\
x=X\cosh T.$$
If an object is moving at fixed ...
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Does any time dilation take place within an electrical conductor when electricity is flowing through it?
I am curious to know if any time dilation takes place within an electrical conductor when electricity is flowing through it.
It is my understanding that an electrical current (electromagnetic waves) ...
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1answer
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Would stellar engines cause their planets to experience time dilation? [duplicate]
For instance, if the stellar engine is moving the solar system at relativistic speeds, would, say, a 5,000 light year voyage be shorter for the inhabitants of a planet, or would the trip still take 5,...
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About general covariance
\begin{equation} u^{\mu}=\frac{d}{d\tau}x^{\mu} \end{equation}
\begin{equation} \partial_{\lambda}(u_{\nu} u^{\nu}) = (\partial_{\lambda}u_{\nu}) u^{\nu} + u_{\nu}(\partial_{\lambda}u^{\nu}) = 0 \end{...
