[Noxchi]

How fast are you really going?

One of the things I've thought about is relatively.

Consider a toddler strapped to his car seat in a luxurious BMW cocoon while his father speeds down the autobahn at 200km/h. He calmy drinks from his sippy cup.

You're in a passenger jet above him going 700km/hr. You're going 500km/hr faster than him.

But how fast are you really going?

Consider that the Earth is spinning around the sun at a rate of 1 billion kilometers per year or about 100,000 km/hr.

You're on Earth, so is your jet's true speed 100,700 km/hr?

Relative to the sun, yes, but everything that orbits our sun is considered our solar system which itself is orbiting our galaxy at a rate of 800,000 km/hr.

So if we add the 800k, 100k, and 700 km/hr your plane is moving, is it not fair to say you are traveling at almost a billion kilometers per hour?

I'm sure you can infer the galaxy itself is hurling through space at an ungodly speed.

I ask two questions:

1. When does this stop? What is the most supreme center in the universe?

2. Just as the child could roll down his window, and have instant access to the outside, is there a way we can do the same?

[RichardCA]

We generally give Albert Einstein credit for providing a definitive answer to this question, and we call it the Theory of Special Relativity.

Here, you might like this:

https://www.youtube.com/watch?v=feBT0Anpg4A

[gpawl]

It's still relative, though. You can't know your absolute speed, unless you are a photon and speed has no meaning to you at all.

[lomnakkus]

I think it's more that you have no absolute speed...? I.e. it's an ill-defined concept. Of course we often talk about speed as if it's absolute, but as you point out it's actually always relative to some assumed background, e.g. the ground.

(It's also impossible to measure speed without some sort of external reference.)

[TeMPOraL]

What about angular speed, though? My physics is very rusty where it comes to rotating things, and I don't recall dealing with rotation on relativity classes in school. Since you can derive momentary linear speed from angular speed and distance from centre of rotation, I assume there is no absolute angular speed either?

[tim333]

No, there is absolute angular speed. Which is kind of an odd thing that rotation is like that but linear motion is not. Take the Earth for example - you can't say how fast it's moving unless it's relative to something but you can say it's doing one rotation a day.

Another odd possibly related thing is linear momentum can be any amount but angular momentum is quantized which may be why we have particles. In Maxwell's equations you can have any amount of light but in practice it arrives in chunks with one unit of angular momentum each.

[raattgift]

> There is absolute angular speed.

Not really. If you have two bodies in hydrostatic equilibrium arranged so that you can extend the rotational axis of one such that it overlaps completely with the rotational axis of the other, how do you come up with "absolute rotation"?

You could consider the case where one is exactly spherical and the other is highly oblate. While you're free to choose a system of coordinates which keeps the highly oblate one non-rotating with respect to the coordinates, you have to appeal to fictitious forces to explain the oblateness of the coordinate-stationary body and the exact spherical symmetry of the coordinate-rotating body. Physics typically takes a simpler form if you decide the spherical body should be non-rotating against a set of coordinates that covers both bodies. (On the other hand, if these are large bodies -- planets, for example -- and you can put a lab on the surface of each, you get the Special Relativistic form of physics for practically all possible experiments wholly contained within each lab).

However, a more typical case is that neither body is exactly spherically symmetrical, in which case you might want to appeal to the view of the motions of deep sky objects observable on each body. One might be ultra-Machian and say that "absolute rotation is determined by the movement of fixed stars", but really you probably should be more interested about whether you need to resort to pseudotensors in your write-down of local physical behaviours, i.e., rely upon the principle of covariance instead, and ignore arguments motivated by less-formal arguments (sometimes only allegedly) related to any number of things Mach said.

The principle of covariance only allows a picking-out of "absolute rotation" in specific types of universe, and that picking-out is not very useful in a universe like ours.

> angular momentum is quantized

Spin is quantized in the Standard Model. Although one can call spin an intrinsic angular momentum, it's not the same thing as the angular momentum of a rotating macroscopic body like a planet. In particular, intrinsic spin survives changes of coordinates, whereas rotation does not (as discussed above).

There is a (very) technical and quite beautiful overview of the difference here:

http://www.askamathematician.com/2011/10/q-what-is-spin-in-p...

[lomnakkus]

My physics is also very rusty, but wouldn't any momentary linear speed derived from angular speed be relative to the center of the rotation?

Or am I not understanding you correctly?

[obastani]

A sibling post talked about special relativity, but you don't need special relativity to answer this question, just Galilean relativity. The answer is that you can measure velocity in any inertial reference frame you want. If you are in an inertial reference frame, you can say your own speed is 0 km/hr, or you can consider an inertial reference frame of the galaxy, which is some ungodly number, or you can measure your velocity relative to the cosmic microwave background. It's all the same -- only the relative velocity between you and another object has a real physical meaning.

[ingenuous2]

That is to say, everything is in an inertial reference frame, so there is no absolute center.

Just like we can only mark a distance traveled as from a starting point.

[plaguuuuuu]

Easiest way to think about it: Picture two satellites crashing into each other. It looks exactly the same if both satellites are doing 100 m/s, or one satellite is stationary and the other is doing 200 m/s.

>1. When does this stop? What is the most supreme center in the universe?

Is one of the above satellites the centre? The other? It doesn't change anything about the impact force. There's no physical difference. So we can choose either satellite to be the centre (0 km/h) or neither (100 + 100, 50 + 150, whatever)

>2. Just as the child could roll down his window, and have instant access to the outside, is there a way we can do the same?

The problem with the earth is that it's really big/heavy and gravity prevents stuff just sort of "hanging in the air" at human-height, relative to the rotation of the earth... speaking in practical terms, I mean.. so it's harder to visualise. But at the same time, sure. If you're on the earth, sitting in your chair, doing 0 m/s relative to the ground, and a satellite hanging around at head height that ISN'T rotating along with the earth hits you in the face, you just successfully accessed an intertial reference frame that's outside the earth :D

[fabatka]

Regarding the speed of galaxies, there is the astrophysical concept of comoving observers: https://en.wikipedia.org/wiki/Comoving_distance I stumbled upon this, when I searched for the question: is there any point in talking about the age of the Universe if there is no absolute reference frame? There is a good stackexchange page about this too: https://astronomy.stackexchange.com/questions/6525/age-of-th...

[kobeya]

> 1. When does this stop? What is the most supreme center in the universe?

There isn't one.

> 2. Just as the child could roll down his window, and have instant access to the outside, is there a way we can do the same?

No. See Michelson–Morley in 1887.

[posterboy]

I think the true answer is that the universe is so vast, we just don't know. The answer on quore etc. when searching for the center of the universe are not really satisfactory, a frequent answer is that the question is framed wrong, as per our lack of understanding. See, the geo in geometry means the planet earth, that's our frame of reference.

[platz]

there are no absolute reference frames. only relative ones! however, at least there is a fixed relationship between reference frames they all must obey with regards to the speed of light.

[xioxox]

There is the frame of the cosmic microwave background, which allows you to measure you speed with respect to the average expansion of the universe. It's not special in terms of physics, but it is a reference.

[tombh]

Just thinking out loud here. If the speed of light is absolute (it's not relative right? it doesn't change in any reference frame?), then could the speed of light be considered the base axis, or to continue the metaphor in the parent comment, that the speed of light is the 'outside the car'? Also, doesn't time 'stop' when you are at C, so that the whole idea of space (speed * time) sort of collapses?

[lmm]

> If the speed of light is absolute (it's not relative right? it doesn't change in any reference frame?), then could the speed of light be considered the base axis, or to continue the metaphor in the parent comment, that the speed of light is the 'outside the car'?

The speed of light is the same in any (inertial) reference frame. But you can't use it as a reference to compare other speeds against, because there are more degrees of freedom than you might think: a speed is calculated from both a distance and a time. So you and I could be looking at an asteroid and you say it's stationary and I say it's going half the speed of light, and we'd both be right, even though we both agreed what the speed of light was. Special relativity works like this.

> Also, doesn't time 'stop' when you are at C, so that the whole idea of space (speed * time) sort of collapses?

If you naively plug zeroes and infinities into the equations you won't get good answers, but if you're careful and work with limits then everything works right. What specifically were you asking about when going at C?

[jacobolus]

You should spend some time doing calculations in the “hypercomplex plane”. That is, something like the complex plane, but where you’ve taken the real number line and added a a new value u such that u² = 1 instead of the value i such that i² = –1.

Try to work out what perpendicular numbers look like in this space, what “circles” look like (hint: like hyperbolae), what the tangents to those circles look like, what kind of metrical relationships arbitrary triangles or other shapes have, and so on.

If you play with this simple 2-dimensional number system for a while, you’ll come to understand the nature of special relativity much better.

* * *

The displacement between two points in spacetime can be either “spacelike” in which case there is some inertial reference frame in which the two points are simultaneous, or it can be “timelike” in which case there is some inertial reference frame where the two points are at separate times, unmoving in space, or the displacement vector can be “lightlike”, which is a boundary between the two – the two points are always in every inertial reference frame separated by some speed-of-light separation.

[michaelscott]

It's consistently relative, because the unit of speed we use is relative to our subjective experience. Hell, if you were American you would've given these values in miles/hr, so localised is the subjectivity of distance. Hours too are a relative measure of time (consider an alien who could live for thousands of years and how they would measure time, or a being that could travel near the speed of light).

[booleandilemma]

Relevant quote:

"Speed has never killed anyone. Suddenly becoming stationary, that's what gets you". - Jeremy Clarkson

[baddox]

Even that wouldn't hurt you, if every part of you became stationary at the same time.