27
The light that we see from the Andromeda galaxy was emitted 2.5 million years ago. During those 2.5 million years the Andromeda galaxy may have moved one or two thousand light years closer to us. However, the uncertainty in the 2.5 million light year distance estimate is of the order of 100 thousand light years (just because measuring the distance to other ...
14
This is a more complicated question than you might think because in relativity there is no unique definition of time and therefore no unique definition of now. You have probably heard of time dilation, and this arises because different observers will in general define time in different ways.
However there is a natural choice for the time coordinate known as ...
6
When we look at the Andromeda galaxy, we see it as it was $2.5 \times 10^6$ years in the past, because the light from there was emitted $2.5 \times 10^6$ years ago. In that time, the galaxy may have changed its distance, but probably not by a significant amount.
Distances to cosmic objects are obtained by astronomers using the cosmic distance ladder methods. ...
6
No.
The Feynman-Wheeler interpretation of antiparticles as particles going backwards in time is a heuristic description of how antiparticles propagate. It is not possible, in actuality, to disentangle the interactions of electrons and positrons entirely, in much that same way that it is not possible to distinguish the effects of one electron from another; ...
5
In special relativity, is the time light travels to the observer already included in time intervals?
The time that the light takes to travel to the observer is not included. The time an event happens in a reference frame is defined as the time that a clock at the location of the event would show. To tell time in a reference frame, Special Relativity imagines clocks at all relevant locations, and all those clocks properly synchronised within the reference ...
4
It is a very common mistake to assume that moving watches slow down, one that is no doubt due to the ambiguous phrase 'moving clocks run slow.' What time dilation actually means is that the time interval between two events occurring in the same place in one frame is shorter than the time interval between the same two events in any other moving frame. Let me ...
3
In special relativity, is the time light travels to the observer already included in time intervals?
You are confusing time dilation with the Doppler effect.
In SR, time dilation refers to the fact that the time between two events that occur at the same place in one frame is always less than the time between the same events in another inertial frame moving relative to them. In your example, Bob passing the planet and Bob arriving at Earth are two events ...
3
In special relativity, is the time light travels to the observer already included in time intervals?
When we talk about Alice's or Bob's frame, that includes all the spacetime. So, when Bob passes the planet at $t_0$ in Alice's frame, we can postulate there a synchronized clock with Alice's one. Alice herself will receive the information 10 years later. But this planet, that is in her (A) frame receives the information at $t_0$.
The time travel according to ...
3
In an observer's rest frame their four-velocity is always $(1, 0, 0, 0)$, so in a time $\tau$ recorded by their clock the length of their trajectory is just $\tau$.
3
About $168,000$ years ago, a supernova occurred that was observed in $1987$. We called it SN 1987A. Except when the distance to a star is known to within at most a few light months, which is the case for only the nearest stars, one couldn't compute the calendar year in which it really happened. Indeed, trying to impose a human calendar onto events across the ...
3
You have this the wrong way around. Time changes because the speed of light is constant. Consider this simple thought experiment, bearing in mind that the speed of light is always 299 792 458 metres per second...
You and I stand together and flash a light to the east and west at t=0. At t=1, the light is exactly 299 792 458 metres away from us in each ...
3
As a supplement to Marco Ocram's excellent answer: we are all moving not only in space, but also in time. We have no choice about that: even if we think we are "at rest" in space, we'll be moving forward through time. But different observers may be moving in different directions in spacetime. If we assign $(x, t)$ coordinates to the path of a watch,...
2
The gravitational time dilation and length contraction are analogues to that in special relativity theory (SR). For example, in static spherically spacetime the first one is related to square root of metric component $g_{00}$ and the second, to square root of metric component $g_{rr}$, i.e.
\begin{equation}
d\tau=\sqrt{g_{00}}~dt<dt,~~~~~dl=\sqrt{g_{rr}}~...
2
In his book "Cycles of Time" (it can also be found in "Road to Reality") from Roger Penrose he states that the universe already started in a macrostate with maximal number microstates (if gravitation is neglected).
How is this possible ?
The best picture we can get from the start of the universe (also called Big Bang) is the cosmic ...
2
It is just a time of reference. You can consider time zero being the beginning of the universe or the appearance of humankind. It will just shift your system but not alter the dynamics
2
Let,
$l=$ length of pendulum
$x=$ amount of pendulum bob displaced
$g=$ acceleration due to gravity
$θ=$ angle subtended by the pendulum with the vertical
So as we know that the general equation for SHM
$$A=-\omega^2x\tag1$$
So, here we have to break the force vector in its components.
So, from the diagram we get to know that the horizontal component of ...
2
The equation of motion describing a pendulum is given by:
$$\frac{d^2\theta}{dt^2} = -\frac{g}{L}\sin(\theta)$$
For small angles, one can approximate:
$$\frac{d^2\theta}{dt^2} \approx -\frac{g}{L}\theta$$
Solving this equation, one finds the general solution to be:
$$\theta(t) = A\sin\left(\sqrt{\frac gL}t\right) + B\cos\left(\sqrt{\frac gL}t\right)$$
With $...
1
This comes from the physics lore that quantum field theory (QFT) in Minkowski spacetime can be analytically continued (Wick rotated $\beta=iT$) to statistical physics (SP) in Euclidean spacetime.
The upshot is that QFT in Minkowski spacetime should be regularized with the Feynman $i\epsilon$ prescription.
In SP the ground state dominates at low temperature $\...
1
It depends on one's perspective.
We never start in an eigenstate
If we are solving a Schrödinger equation for the eigenmodes, the solutions will already contain the particle on the two sides of the barrier or a photon simultaneously emitted and non-existent (with the atom in the excited state). Note that I am talking here not about superpositions, but about ...
1
The average delay before a decay or emission event is known as its "lifetime" (or, with a factor of $\ln 2$, its "half-life"). Quantum states with the same quantum numbers are indistinguishable. There is no difference between a system which happens to be on the cusp of a decay versus a system which happens to end up not decaying for many ...
1
We generally mean "is now", because the word "is" means present.
The problem is that where we see it now, is where it really was 2.5 million years ago, because the light from Andromeda which we are seeing now, has taken 2.5 million years to reach us.
So Andromeda has of course moved since then.
But the galaxy moves much slower than the ...
1
Since the relative speed between the Miliky Way and the Andromeda system is much smaller than the speed of light the difference is in this relatively very small.
1
There are a couple of tricky things in this question. Firstly, notice that we do not mean time is a spatial dimension. It is a fourth dimension, but it does behave differently than the spatial dimensions. More specifically, you shouldn't ask where is $t=0$, but rather when is $t=0$. The idea is that fixing $t$ to a constant value will provide you a snapshot ...
1
Yes, the length does change as well. This is called "length contraction". Space and time are linked, so any changes to how we measure one will also affect the other. The exact formula for how they are linked is called the Lorentz transformation and actually predates Einstein's special relativity.
Only top voted, non community-wiki answers of a minimum length are eligible