Questions tagged [time]
Time is defined operationally to be that which is measured by clocks. The SI unit of time is the second, which is defined to be
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Time diffeomorphisms breaking in inflation
I am currently working on the topic of inflation.
It seems that at the stage of inflation, the universe can be described as a de Sitter space. In such a space, all spacetime diffeomorphisms are ...
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Why is my approach to the equation of time off by a constant?
I'm trying to better understand the causes for the equation of time by deriving an approximation from first principles.
My naive approach, $EOT_{NAIVE}$, is to take the difference between the right ...
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Correct statement of Birkhoff's theorem (spherically symmetric does not imply static?)
If I understand correctly, the appropriate statement of Birkhoff's theorem in general relativity is that
The Schwarzschild metric is the unique spherically symmetric vacuum
solution.
(Or we might ...
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Why are the propagators in old-fashioned QED oblique, while in modern QED they are horizontal (or vertical)?
In old-fashioned Quantum Electrodynamics, one can find diagrams such as these (probably Stückelberg was the first to use this notation, a kind of predecessor of Feynman diagrams):
In modern QED this ...
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In the context of condensed matter physics, what does it mean for time to have two dimensions?
In an online article that describes condensed matter physics for laypersons, the author describes various so-called "designer materials" that have exotic properties, including one in which ...
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What does the time reversibility of the laws of physics mean for causality?
Does the fact that the fundamental laws are symmetric with respect to direction of time show that causation does not exist? Since causality always requires the cause to precede the effect, but laws of ...
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Does electron have some intrinsic ~$10^{21}$ Hz oscillations (de Broglie's clock/Zitterbewegung)?
Louis De Broglie has postulated in 1924 that with electron's mass there comes some $\approx 10^{21}$Hz inner oscillation: $E=mc^2=h f=\hbar \omega$.
We would get such oscillation e.g. if using $E=mc^...
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Imaginary Hamiltonian
The Hamiltonian for nuclear spin independent parity violation in atoms is given by: $$H_{PV} = Q_w\frac{G_F}{\sqrt{8}}\gamma_5\rho(r)$$ Here $Q_w$ is the weak charge of the nucleus (which is a scalar),...
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Time-independent source and quantum field theory
Can anyone explain the fundamental reason of why time-independent sources cannot emit or absorb energy. Does it have to do with time-translation symmetry and Noether's theorem?
I was studying the ...
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What does the operator's explicit dependence or independence on time actually mean in Quantum mechanics?
Consider the equation of motion for the expectation value of an operator $A$
$$\frac{d\langle A\rangle}{dt} = \frac{1}{i\hbar}\langle [A,H]\rangle + \left \langle \frac{\partial A}{\partial t} \right \...
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Cases of various time symmetries
Is it possible to cook up three physically relevant examples where the Lagrangian has explicit time dependence but the system still has one of the following?
time-reversal invariance,
time ...
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How is time "homogeneous"?
My book$^1$ states:
Let's consider a clock moving freely over a curve such as:
\begin{equation}
\frac{dx^i}{dt}=\text{const} \tag{1.20}
\end{equation}
We define the proper time $\tau$ as the ...
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Equivalence of $d$ dimensional quantum system to $d+1$ dimension stats system
" There are close analogies between quantum field
theories in d dimensions and classical statistical mechanics in d + 1."
What does this statement imply and from where does this extra dimension ...
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Should we consider space and time as separate entity?
In general relativity, we think of space and time in spacetime framework. As some people say, metric tensor sign difference, along with our inability to go backward in time suggests that space and ...
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How to express Allan variance without neglecting clock drift
Allan variance, $\sigma^2[ \tau ]$, or its square root (Allan deviation, $\sigma[ \tau ]$) is a quantity (as function of parameter $\tau$) which is said to be a measure of (or related to) "stability ...
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Is time ordering defined for a single operator depending of two time variables?
The time ordering for the purpose of quantum mechanics is e.g. given by
$${\mathcal T} \left[A(x) B(y)\right] := \begin{matrix} A(x) B(y) & \textrm{ if } & x_0 > y_0 \\ \pm B(y)A(x) & \...
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Are there physics models that accurately handle the assumption of having solutions that achieve finite ending times?
Are there physics models that accurately handle the assumption of having solutions that achieve finite ending times?
Intro
Recently I learned on the answers and comments of this QUESTION that the ...
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Confusion between implicit and explicit dependence, and its interpretation of the Lagrangian
I just want someone to confirm if whatever I'm writing down is correct or wrong.
If the Lagrangian is given by $L(x,v,t)$, then we say that it explicitly depends on time.
Here, $x$ and $v$ are ...
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Time dissemination in Solar System IAU expression (apparently) not matching General Relativity general result
I have a question about time dissemination around Earth on in the Solar system.
A standard expression for an Earth satellite a proper time shift w.r.t. Earth centered coordinate time (TCG), derived ...
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$\partial F_2/dt$ part of a time dependent canonical transformation
Suppose we have a time-dependent canonical transformation - say generated by a function of the type $F_2(q,P,t)$. The resulting Kamiltonian picks up an extra partial $\partial F_2/\partial t$:
\...
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Uncertainty principle in relativistic quantum mechanics
In Walter Greiner book about relativistic quantum mechanics, he writes the uncertainty relations for 4-position and 4-momentum in a neat way as:
$$[p^\mu, x^\nu] = i\hbar \eta^{\mu\nu}{\bf 1}$$
with ...
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Is the Universe 11 billion years old?
This clip claims scientists found a star 200M years older than the Universe. However, I took another assertion more seriously: scientists estimated a faster expansion rate of the Universe, driving age ...
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Could two atomic clocks really be used to detect gravitational waves from a distant source? If so, how?
Three articles report on the recent paper in Phys Rev. D: Flanagan, Éanna É. et al. 2019 Persistent gravitational wave observables: General framework (also ArXiv):
Phys.org: Gravitational waves leave ...
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Time derivative in rotating frame
In Goldstein (2ed) sec 4.9 - Rate of change of a vector, why does he say that the instantaneous angular velocity $\omega$ is not a derivative of any vector?
$$ (d\textbf{G})_{space} = (d\textbf{G}...
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Is there any feature which distinguishes the Hamiltonian in the Poincare algebra?
The Poincare algebra is defined as
\begin{align*}
i[J^{\mu\nu},J^{\rho\sigma}]&=\eta^{\nu\rho}J^{\mu\sigma}-\eta^{\mu\rho}J^{\nu\sigma}+\eta^{\sigma\nu}J^{\rho\mu}-\eta^{\sigma\mu}J^{\rho\nu}\\
...
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Sakurai"s Comment Anti-particle in Klein-Gordon equation: Reversing momentum and Moving backward in time
In JJ Sakurai, p.492-493,
he made Comments on Anti-particle in Klein-Gordon equation. By analyzing the current EOM, he said that charge current density is the same for all particles, (regardless ...
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Is there a scheme for secure physical time-stamping?
Is there a physical phenomenon that could be used to record digital information in such a way that it has the following properties:
it relies on some immutable physical law and does not rely on any ...
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Why does the law of conservation of energy not hold true when the work-function $U$ depends explicitly on $t$?
[...] the infinitesimal work $\overline{\mathrm dw}$ comes out as a linear differential form of the variables $q_i$: $$\overline{\mathrm dw}= F_1~\mathrm dq_1 +F_2~\mathrm dq_2+ \ldots + F_n~\mathrm ...
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Can we derive the relation between proper time and the spacetime interval?
In GR, it's usually taken for granted - or as a definition - that the time measured by an observer's clock is related to the geometry in a very simple way, $d\tau^2 = |ds^2|$. This is easy enough to ...
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Radial quantization and time order
In CFT, one ususally begins quantization by defining radial ordering on the complex plane, with the notion of radial ordering being the equivalence of time ordering. This is often "motivated"...
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EM field in a strong gravitational field
Imagine simple solenoid 10cm in length with given magnetic field in a gravitational field with a large gradient, for example the clock near one pole of the solenoid is running 1 second faster, meaning ...
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Does shape dynamics introduce a temporal order on events separated by a space-like interval such that their simultaneity is not relative?
I've read some popular books and articles that reference shape dynamics (e.g., The Singular Universe and the Reality of Time, https://www.pbs.org/wgbh/nova/article/shape-dynamics/). I have also ...
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Time translational symmetry breaking
I have heard of time translational symmetry, which refers to the law of conservation of energy. Time crystals break time translational symmetry. I read on Wikipedia that it only breaks discrete-time ...
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Time dilation in 2+ dimensions. Relativity problem
I am a student and due to school closures, I am reading ahead in physics. I have been learning about special relativity and I made up a problem for myself. I've drawn a diagram below:
The diagram ...
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What was the rationale behind Stephen Hawking's "biggest mistake"?
Albert Einstein said he made his biggest blunder, while Stephen Hawking spoke of his "biggest mistake".
One can read this in this interesting book review (The Nature of Space and Time by Stephen ...
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Why is there a Moore's Law for atomic clocks?
From the NIST website:
If you add the more recent data points, like this one in 2019, which achieved $~10^{-17}$ fractional instability, the trendline continues.
Why should there be a Moore's law ...
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Time and Quantum Mechanics
my question is about the nature of time across classical/macro and quantum scales. I understand that the 2nd law of thermodynamics and entropy increase has a lot to do with our understanding of time ...
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Does our universe admit of a global time function?
My understanding of a global time function is this: a function whose value always increases as a body moves into its local future.
My confusion is this: I gather that the Gödel Universe is bizarre ...
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Time taken by an air bubble on the sea depth to reach sea level
There is an air bubble at a depth of s meters above sea level.
Suppose the air is an ideal gas and Temperature is constant.
I would like to calculate the time it takes for it to reach sea level.
...
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What is the difference between an ideal clock and a physical clock in relativity
A letter from Einstein's friend Besso mentioned what Einstein called his "original sin." Einstein's sin was that he defined a clock to be both a physical thing (an actual clock) and an ideal entity ...
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Gravitational time dilation and the pace of time
If we are in empty space far from a black hole, at rest relative to the hole, we would look at a clock and a light source inside the gravitational field of the hole, then we would, according to the ...
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Does the intensity of LED lights decrease after turning on?
LED lights come on immediately the power is supplied. This is different to the older compact fluorescent-tube lights. I am always impressed by the brightness of the LED lights when they come on. Later ...
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Causality in CPT symmetry analogue of free electron laser (stimulated absorbtion)?
While 2nd law of thermodynamics emphasizes past->future time direction, CPT theorem says that at least microscopic physics has some symmetry between past and future. For example the Feynman-...
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ADM decomposition and hyperbolicity
Given a spacetime $\mathcal M$ I am interested in the ADM decomposition of a metric $g_{\mu\nu}$
$$
ds^2 = - N_t^2 dt^2 + \gamma_{ij} (N^i dt + dx^i) (N^j dt + dx^j).
$$
By reading the literature I ...
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If microscopic dimensions were found in particle experiments, how do we determine whether it is spatial or temporal?
This is not a question asking why our universe is 1T+3D dimensional, and hence not about how the various models such as Itzhak Bars and F theory can incoporate multiple time into a model to describe ...
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Calculating relaxation time
When exploring the viscoelastic properties of glassy polymer like PMMA, there are usually two relaxation mechanism: alpha and beta.
Usually beta relaxation time varies with temperature following ...
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In KK theory, is proper time defined using the 5 dimensional or the 4 dimensional line element?
Let's consider five dimensional KK theory. This is Klein's metric
$\hat{g}_{AB}=
\begin{pmatrix}
g_{00}+A_{0}A_{0}&g_{01}+A_{0}A_{1}&g_{02}+A_{0}A_{2}&g_{03}+A_{0}A_{3}&A_ 0\\
g_{10}+...
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Expectation value for the time of a photon reflection
A photon is reflected by matter (by an electron in empty space). How long does the reflection take? (i.e. is there any infinitesimal time elapsing during the reflection process?), or more precisely, ...
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How to prove that a time-oriented spacetime possesses a nowhere vanishing timelike vector field?
Penrose gave a very brief proof to this question. Since the spacetime is paracompact, there exists a positive definite metric called $h_{ab}$. Then, the nowhere vanishing time-like vector field $V^a$ ...
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What's the connection between being homogeneous in energy and having a proper time scale?
Towards the end of page 8 of this scientific paper, I have found the following sentence:
...given the fact that the system is homogeneous in energy, or equivalently, that it has no proper time ...
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