Superluminal (a question)

[RickyVernio]

I'm rather slow at times, so please be patient.

The Theory of Relativity states, in no uncertain terms, that:

1. Nothing can travel faster than light
2. ANYTHING AT ALL can be viewed as a motionless reference point.

The Earth rotates and revolves, so let's set it aside.

Let's select a point anywhere on Earth's orbit except where the Earth actually is. Let's elect it The Reference Point of the Day.

Alpha Proxima (and all the rest of the stars in the galaxy except the Sun) do actually rotate around this point at speeds that exceed the speed of light.

What gives?

[Da6onet]

I'm rather slow at times, so please be patient.

The Theory of Relativity states, in no uncertain terms, that:

1. Nothing can travel faster than light
2. ANYTHING AT ALL can be viewed as a motionless reference point.

The Earth rotates and revolves, so let's set it aside.

Let's select a point anywhere on Earth's orbit except where the Earth actually is. Let's elect it The Reference Point of the Day.

Alpha Proxima (and all the rest of the stars in the galaxy except the Sun) do actually rotate around this point at speeds that exceed the speed of light.

What gives?

Simplified postulates of special relativity:
1. The laws of physics are the same in all inertial frames of reference.
2. The speed of light in free space has the same value c in all inertial frames of reference.

The stars in the galaxy are not actually rotating about this point's inertial frame of reference and have very small velocities compared to the speed of light. The inertial frame you're describing is analogous to putting a stick in a stream and measuring how fast the current flows past. What you would see is the stars in the plane of the galaxy (either looking toward the center or toward the outer edge) passing by you at around 200-300km/s.

The confusion may be because you're thinking of what the point "sees" as it would orbit. However, you have to remember that there is literally a constant stream of photons that the observer on Earth, or in orbit, or anywhere, is running into. Every photon you're seeing was emitted  from their star 4.3 years ago (alpha centauri a/b and proxima) to ~100,000 years ago (rough diameter of galactic disk) but obviously you can't perceive the time difference now. If I were unaware that I was turning, I could look to the west, then look to the east, then say, half the universe just rotated around me!

The real question you should ask is why the speed is roughly constant throughout the disk of the galaxy regardless of radius from the center!

[RickyVernio]

Okay, so you're saying that nothing can move faster than light WITHIN an inertial frame of reference, and by "inertial frame of reference" you mean a section of space where ... hmm ... the curvature of space is negligible, while gravity is not - if I understand correctly.

You've made a great point about looking to the west, and then to the east. Dancers make Pluto exceed the speed of light every time they do a pirouette - but that "doesn't count," because the force of gravity between them and Pluto is negligible.

So - correct me if I'm wrong - Relativity is similar to Euclid's geometry in that it only works within certain parameters and does not apply to the entire Universe or even galaxy.

[Da6onet]

Okay, so you're saying that nothing can move faster than light WITHIN an inertial frame of reference, and by "inertial frame of reference" you mean a section of space where ... hmm ... the curvature of space is negligible, while gravity is not - if I understand correctly.

You've made a great point about looking to the west, and then to the east. Dancers make Pluto exceed the speed of light every time they do a pirouette - but that "doesn't count," because the force of gravity between them and Pluto is negligible.

So - correct me if I'm wrong - Relativity is similar to Euclid's geometry in that it only works within certain parameters and does not apply to the entire Universe or even galaxy.

More like, within what we would consider normal or 3D space, like an ant moving across graph paper, special relativity works like a charm (length contraction, time dilation). In that sense the rules are the same everywhere in the observable universe including galaxies (at least outside of the Schwarzschild radius of black holes). General relativity steps in to explain situations such as gravitational lensing - which was used to prove that space isn't really Euclidean

Another way to think of special relativity is that the two observers must agree on an event happening. In the dancer scenario, an observer on Pluto would observe a spinning dancer with a very small angular displacement. The dancer's view of Pluto rapidly passing him/her by every turn doesn't match the same angular displacement, so they aren't observing the same event. Remember the dancer is actually just viewing streams of photons. If the dancer were spinning at same rate as the photons (speed of light), they would see Pluto nearly stationary with a very small angular displacement.

[RickyVernio]

Thanks! Lots of food for thought.

Two things I'm not quite clear on:

1. The whole photon thing. I mean, YES, we know that any star one can see may not even exist anymore. In the case of Alpha Proxima the proof will arrive four years from now; on some other starts, we'll have to wait a whole lot longer. So what? I mean, if the photons traveled a thousand times slower, what difference would it make in determining the velocity of an object relative of another object?

2. If the dancer were spinning at same rate as the photons (speed of light), they would see Pluto nearly stationary with a very small angular displacement.

Uh ... why? Uh ... Is the distance between one photon and the next similar or greater than the circumference of the spin? Or what?

[Da6onet]

Thanks! Lots of food for thought.

Two things I'm not quite clear on:

1. ...what difference would it make in determining the velocity of an object relative of another object?

2. If the dancer were spinning at same rate as the photons (speed of light), they would see Pluto nearly stationary with a very small angular displacement.

Uh ... why? Uh ... Is the distance between one photon and the next similar or greater than the circumference of the spin? Or what?

1. Light from an object can be look redder or bluer depending on it's radial velocity. Light from Andromeda is blue shifted because it's head straight for us! Of course we're talking nanometer range shifts, but they are measurable to a high degree of accuracy.

2.
Sorry I was trying to pick an extreme example to show how the dancer and Pluto are observing the same event. Light behaves as both a particle and a wave. The waveform of light has a period (meaning there is a delta t between photons). If the dancer were spinning at the speed of light her period wouldn't match all the incoming light, so she wouldn't see a continuous rotating sky anymore, she could only see light when the multiple of her period matched up with the multiple of a period of incoming light. I was implying the assumption that the dancer's period exactly matches the light coming off Pluto, then all she would see (for the most part) is darkness and a blinking Pluto -- she couldn't perceive any rotation. So from her point of view Pluto is the only object in the sky and appears not to move much each time it is observed. Just as the observer on Pluto only sees the light from the dancer's eyes each period. Slowing this back down to normal speeds, this matching still works, just now the dancer perceives continuous light from all around her (because it's so much faster than her rotational period) but should only measure Pluto's apparent position each time she sees it (pretend she's closing her eyes between each full rotation) -- measuring the change in position compared to difference in time between each observation (she's counting seconds between each observation). delta x/delta t = Pluto's actual speed

[Tbone]

*joins the conversation*
*nods a few times*
*awkwardly backs out of the conversation*

[Broin]

Would this be a good time and place to talk about the varying speed of light in relationship to time and gravitational influences.

[RickyVernio]

Light from an object can be look redder or bluer depending on it's radial velocity. Light from Andromeda is blue shifted because it's head straight for us! Of course we're talking nanometer range shifts, but they are measurable to a high degree of accuracy.

Noted. The Doppler effect never sleeps. Pardon my slowness, I still don't see the connection. Correct me if I'm wrong: Depending on our relative positions on our respective orbits, Pluto gets nearer us sometimes, and tries to distance itself from our petty affairs at other times; it's like a drunken girl who can't make up her mind whether she should get into the guy's car and get it over with already, or go back to the bar and have a few more. However, neither action is fast enough to involve Herr Doppler.

2. Regarding your (both informative and entertaining) point 2: do we see APPARENT and ACTUAL movement as two separate phenomena? In other words, as far as the relative velocities of two objects within one inertial frame of reference are concerned, is Relativity in any way affected by the fact that PERCEIVED motion (light playing tricks on us) and ACTUAL motion are different? ... Cause (yeah, you guessed it) I still don't get it.

I mean, I believe (again, correct me if I'm wrong) it's a KNOWN and MEASURABLE fact that Pluto's gravity does affect Earth, and vice versa. So in some degree we ARE looking at a single ... uh ... indivisible ... inertial frame of reference. Or what? ...

Broin: Would this be a good time and place to talk about the varying speed of light in relationship to time and gravitational influences.

Not yet. Yes, absolutely, but not yet. I'm the slowest ship in the fleet here, apparently, and I'd like to get some things straight first. Pleeeease? ... I beseech you!

[Da6onet]

Noted. The Doppler effect never sleeps. Pardon my slowness, I still don't see the connection. Correct me if I'm wrong: Depending on our relative positions on our respective orbits, Pluto gets nearer us sometimes, and tries to distance itself from our petty affairs at other times; it's like a drunken girl who can't make up her mind whether she should get into the guy's car and get it over with already, or go back to the bar and have a few more. However, neither action is fast enough to involve Herr Doppler.

True the radial velocity is slow enough that the Doppler effect is tiny (but it is still there). I was answering your question about how we can measure velocities of cosmic objects. with a dwarf planet like pluto, it's easier to just measure it's angular velocity since we can determine the radius with a higher degree of accuracy.

2. Regarding your (both informative and entertaining) point 2: do we see APPARENT and ACTUAL movement as two separate phenomena? In other words, as far as the relative velocities of two objects within one inertial frame of reference are concerned, is Relativity in any way affected by the fact that PERCEIVED motion (light playing tricks on us) and ACTUAL motion are different? ... Cause (yeah, you guessed it) I still don't get it.

I mean, I believe (again, correct me if I'm wrong) it's a KNOWN and MEASURABLE fact that Pluto's gravity does affect Earth, and vice versa. So in some degree we ARE looking at a single ... uh ... indivisible ... inertial frame of reference. Or what? ...

Yes there is mutual attraction between Earth and Pluto, however, like the Doppler effect, it is negligible. Yes apparent and actual motion are two different phenomena. A perfect example of this are blobs ejected by active galactic nuclei. The blobs are already ejected at near the speed of light (.8c up to .99c!), and so at angles less than 45 degrees (angle between AGN and path of blob if straight line drawn between Earth and AGN), we see blobs moving with a transverse speed of much greater than c. I'm not at home at the moment or I would just copy the math derivation I had to do on this topic of why apparent and actual are different things without getting gravity/general relativity involved, which if you're into that would explain it more rigorously.

I'll address Broin's topic once we move on from special relativity (and I get some more sleep).