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 ...
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.
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
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, ...
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
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 ...
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 ...
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 ...
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 ...
5
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 ...
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
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
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
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
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 ...
3
Since the collision is perfectly elastic, the ball's velocity goes from -80
km/h from the train's reference point (negative being towards the train) to
+80 km/h from the train's reference point, a speed increase of 160 km/h.
For a stationery observer, therefore, the velocity goes from -30 km/h
(towards the train) to 130 km/h, an increase of 160 km/h.
...
3
The question itself is wrong, actually.
There is no such thing as absolute velocity, which is what you're assuming in your question. Velocity is always relative to a frame of reference.
Your speed relative to your chair is zero, but it's not zero relative to the airplanes flying over your house.
When you say "a point in space where nothing is moving and ...
3
As MBurke said, the star in each galaxy will hardly be perturbed. Moreover, the chance for any two stars to collide is miniscule (there is about 1 star per pc$^3$ in the denser part of a galaxy, so the star fill about $10^{-30}$ of the volume).
However, most galaxies are also filled with gas in various phases (the so-called ISM -- inter-stellar medium and ...
3
Have 2 people stand in opposite corners of a large empty room each with a jar of marbles. Have them roll these at each other all at once as fast as they can, and you will get a pretty good answer to your question.
97% (or thereabouts) of a given galaxy is empty space. Most of one is going to pass harmlessly through the other, though you are likely to get ...
3
I will answer all of your points with zero tact and/or precision in order to fit them all in.
1) It will take you about a "split second" given you stated that it only takes your brother a split second to travel from Earth to the point 13Bly away and back again. He will be exactly said split second older and no more, because as he is traveling faster than ...
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