# Tag Info

21

Yes, you are right. We don't only see the Sun 8 minutes in the past, we actually see the past of everything in space. We even see our closest companion, the Moon, 1 second in the past. The further an object is from us the longer its light takes to reach us since the speed of light is finite and distance in space are really big.

19

(I will assume a Schwarzschild black hole for simplicity, but much of the following is morally the same for other black holes.) If you were to fall into a black hole, my understanding is that from your reference point, time would speed up (looking out to the rest of the universe), approaching infinity when approaching the event horizon. In Schwarzschild ...

19

The answer is sort of trivial. If you travel 1000 ly so fast that in your own reference frame it takes one year, then you will have aged by one year in your own reference frame. To do so, you will need a speed of almost the speed of light, so in the reference frame of Earth, you will have spent just a tad more that 1000 yr to travel 1000 ly. In general, the ...

18

The answer is yes time dilation does affect how much time an observer experiences since the big bang until the present (cosmological) time. However there is a certain set of special observers called comoving observers, these are the observers to which the Universe appears isotropic to. For example we can tell the Earth is moving at about 350 km/s relative ...

13

Gravity doesn't affect the speed of light. It affects the space-time geometry and hence the paths of light. However, this can have a similar effect. Light emitted at source $S$ to pass a massive object $M$ that is very close on the otherwise (if M weren't there) straight path to an observer $O$ has to "go around" $M$, which takes longer than following the ...

12

As Walter says, gravity doesn't bend light. Light travels along null geodesics, a particular type of straight path. Since (affine) geodesics don't change direction by definition, geometrically light trajectories are straight. Moreover, the speed of light in vacuum is $c$ in every inertial frame, regardless of whether or not spacetime is curved, although a ...

10

And that is why you don't do the calculations in a frame that is moving at lightspeed. If you have two observers that are moving relative to each other you can use the Lorentz transformation to change between their frames of reference. But if one of the observers is a photon the lorentz transformation becomes singular, because $\gamma$ is infinite. Simply, ...

9

Yes. The velocities you list (X, Y, …) are all velocities with respect to some reference frame. But all reference frames are arbitrary, and you can always define a reference frame where the velocity of some object is exactly zero, as long as it's not accelerating. For instance, Earth's velocity in the Sun's reference frame is X, but in its own reference ...

9

There is no contradiction between special relativity and quantum mechanics. Quantum field theory fully merges special relativity and quantum mechanics to describe relativistic electrons and protons (quantum electrodynamics) and quarks (quantum chromodynamics). The problems lie with merging general relativity and quantum mechanics.

9

You have neglected length contraction in your analysis. You see the initial distance of the star contracted by the same factor that the elapsed time is shortened. So, from the perspective of the Earth, you take 1.0101 years to travel a distance of 1 light year at a speed of $0.99c$. From your perspective, the destination comes to you. It arrives after 0.1425 ...

8

In the standard model, the universe looks the same for all locations moving in the local rest frame. This includes its apparent age. You can tell if you are in the local rest frame if the expansion of galaxies around you is symmetric in all directions and the microwave background also is the same in all directions. Simply put, any civilization on any ...

8

Jonathan's answer is essentially correct, but as Rob Jeffries comments, he doesn't take into account that the Universe is expanding during the journey. The edge of the observable Universe is 47 billion lightyears (Gly) away. Even if you are a lightbeam, you cannot reach that point. The farthest you can go if departing today is roughly 5 Gpc, or 17 Gly, but ...

8

Suppose there was a magic gun that fired a bullet at ten times the speed of light relative to the firer. If I have the only such gun, and I don't move then there is no paradox. But now suppose these guns are generally available. At time zero, an observer flies past me at velocity 0.5 c and I give them one of these guns. 7 years later, I fire the gun ...

8

First, let's clear up a few misconceptions: The Hubble sphere The speed of light as an upper limit is valid in special relativity (SR). In general relativity (GR), which must be used to describe the expansion of the Universe, although locally (i.e. where SR is a good approximation) you cannot exceed the speed of light, there is no limit to the relative ...

7

Accounting for the transverse Doppler effect (and other relativistic effects) is essential in modelling the X-ray spectral emission lines from the accretion discs around black holes (e.g. Cadaz & Calvani 2005). In this case the transverse Doppler effect is "mixed up" with gravitational redshift and it is treated holistically in the Schwarzschild or Kerr ...

7

You are essentially asking the following: if someone falls from the Earth from some way beyond the event horizon of a black hole, how long after they have left can an observer on Earth still signal to them with a light beam? The answer of course depends on exactly how far the Earth is from the black hole. It is also often forgotten that it is not just light ...

6

Note that for cosmic expansion, special relativity only applies when the spacetime region in question is approximately flat, which in our case happens when it is small. As the M31 galaxy is moving toward us at great speed it's "depth" should appear slightly flattened for us. A sphere moving toward us at the speed of light will appear "pancaked" in lack of ...

6

Sort of. The Lorentz factor is $$\gamma = \frac{1}{\sqrt{1-\frac{v^2}{c^2}}}$$ whereupon a stationary object in the stationary reference frame of length $L$ has a length of $L' = \frac{L}{\gamma} = L\sqrt{1-\frac{v^2}{c^2}}$ in the moving reference frame. As the velocity $v$ increases toward $c$, we get  \lim_{v \to c} L' = L \lim_{v \to c} \sqrt{1-\...

6

The cosmic "now" is well-defined: It is the time for an observer that has always been at rest in the Universe's comoving coordinates, i.e. the coordinates that expand along with the Universe. Although this reference frame is no more special than any other frame, it makes sense to use this. For instance, it is the only frame in which the cosmic microwave ...

6

The faster you move, the slower does time feel No. The faster someone else you are observing moves relative to you, the more time (as observed by you in their frame) slows down relative to the passage of time in your local frame. Put another way, your local time is the fastest rate at which time changes. Any measurement you make of time passing in ...

5

Yes - quite a few isolated neutron stars have been observed, where any magnetospheric emission or accretion-related emission is either negligible or has been otherwise separated. As you suspect, this emission is thermal in nature. Neutron stars are roughly approximated by black bodies but, like "normal" stars, they do have atmospheres and strong magnetic ...

4

Would an object with mass traveling the speed of light destroy the whole universe because it would have infinite energy / mass? If we understand the question as a limiting process, which is the only way it makes any sense, the answer is no. For illustrative simplicity, take a spherically symmetric isolated body, so that its exterior gravitational field is ...

4

First off, if Earth were point B, and you were an observer at point A looking at it with the most magnificent telescope ever imagined, you would still not see the Earth, because it didn't exist 13 billion years ago. I assume you picked 13 billion years because it is roughly the age of the universe, so you'd see the universe as it existed then, but that ...

4

The way that you have specified the question, the answer is as far as you like. You simply put your spaceship into any orbit around the black hole and wait. A more sensible question is what is the largest time dilation factor that can be accomplished - i.e. that maximises your travel time into the future for a given amount of proper time experienced on the ...

4

I think it is referring to the speed and Lorentz factor $(\beta = v/c$ and $\gamma = [1-\beta^2]^{-1/2})$ of the gas as a whole. Within the gas, there could be particles moving with a variety of velocities. So if you pick up a ball of gas at 10,000 K (ouch) and throw it at 100 m/s then the bulk speed is 100 m/s, but obviously the particles in the gas have ...

4

Time is kind of funny when you look at such distances. Let's imagine that you are running away from a person throwing a ball at you. The ball will travel further to hit you, based on your speed, than the distance that was present when you started to run. The universe is expanding. The early Universe expanded very quickly, giving large deviations from the ...

4

Chris, you are actually on the verge of understanding how special relativity works. You're very close. You only need to take one extra step. to state that all speed is relative to an object is to essentially say, "speed does not exist, but is only relative to an observer" This is correct. Absolute space, as in newtonian physics, does not exist. Same for ...

4

The effect is small, but not negligible. It is not accounted for in astronomical catalogues. Let's work it out. We can start with the visible stars. Most of these are closer than 1000 light years; let's say 100 light years. The typical velocity of these stars with respect to the Sun is tens of km per second; let's take an extreme example of 100 km/s in a ...

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