Speed in Space: Relative Motion & Time Effects

[W3pcq]

Nothing can be said about an objects speed in space unless it is compared to the motion of another object.

1. Can an object travel faster than the speed of light relative to another object ie. our sun relative to the furthest star in the universe?

2. How is it that time can be affected by speed when nothing can be said about an objects speed in absolute space alone? Is it the speed relative to our local electro magnetic fields that create the effect? What is speed considered relative to when determining how much its time rate will be affected?

 

[JesseM]

1. Can an object travel faster than the speed of light relative to another object ie. our sun relative to the furthest star in the universe?

In general relativity where space can expand, in the most common cosmological coordinate system, distant objects can move faster than c relative to us. But the speed of light limit really is only supposed to apply to inertial coordinate systems in the flat spacetime of special relativity (where spacetime is not curved and space is not expanding), and if you zoom in on any arbitrarily small region of spacetime in general relativity it should look arbitrarily close to the the flat spacetime of special relativity.

2. How is it that time can be affected by speed when nothing can be said about an objects speed in absolute space alone? Is it the speed relative to our local electro magnetic fields that create the effect? What is speed considered relative to when determining how much its time rate will be affected?

Time isn't affected by speed in any objective way; if you and I are moving inertially relative to one another, in my frame your clocks are slowed down, but in your frame my clocks are slowed down, there isn't any objective truth about whose time is "really" running slow (at least no objective truth that can be determined by any possible experiment). If you're interested, I gave an illustration of how this symmetry works a long time ago in this thread.

 

[W3pcq]

Lets say I were in a spaceship facing one way and you were in a spaceship pointed the opposite way. Let's say an observer with a clock stayed in location of the starting point. We leave at the same time and same speed at a relative speed of 1/2 C. Then turn around and head back to the starting location. During the time in motion my spaceship by coincidence is in a positive direction with respect to the largest bodies of motion. Your spaceship happens to be going upstream, and ultimately my relative speed is greater than your relative speed overall. All three clocks end up in the same place and are checked. Both of our ships were calibrated to move at the exact same velocity with respect to each other. Which clocks say what? Will mine be slower than yours because I was going upstream and you downstream?

 

[JesseM]

Lets say I were in a spaceship facing one way and you were in a spaceship pointed the opposite way. Let's say an observer with a clock stayed in location of the starting point. We leave at the same time and same speed at a relative speed of 1/2 C. Then turn around and head back to the starting location. During the time in motion my spaceship by coincidence is in a positive direction with respect to the largest bodies of motion. Your spaceship happens to be going upstream, and ultimately my relative speed is greater than your relative speed overall. All three clocks end up in the same place and are checked. Both of our ships were calibrated to move at the exact same velocity with respect to each other. Which clocks say what? Will mine be slower than yours because I was going upstream and you downstream?

No, external bodies are irrelevant (unless their gravity curves spacetime significantly), if the observer in the middle was moving inertially (not accelerating), and in that observer's frame our speeds at all moments were identical, then in that observer's frame our time dilation factors will also have been identical at all moments, so we will be exactly the same age when we meet (younger than the central observer though).

 

[W3pcq]

Does this mean that space itself is dragged around by mass?

 

[JesseM]

Does this mean that space itself is dragged around by mass?

Which comment of mine are you referring to when you say "does this mean"? Spacetime is curved by mass/energy in general relativity.

 

[W3pcq]

My point is how can you even say that me or you or the observer is even moving or at rest. I am moving away from you, but closer to some other object. You are moving away from me and away from other object. How is my speed determined. You could say I am moving 2x relative to you, or x relative the other object. You could be moving 2x, or x relative to the other object. I don't see how speed in space can in any way be ponderable unless there is an absolute background reference that all objects are moving through. For my clock to be behind the guy at "rest"'s clock you need to assume I was moving faster than him. How can you claim that, when nothing can be said in any true was as to how fast either of us are going.

You could pick any object in space and say how fast we move relative to it, but that leaves any speed possible depending on which way you decide to measure.

I thought that if space was somehow dragged around by mass, then a background could be in place for determining speed and the effects of time dilation.

Lets say me and you are in space ships facing opposite directions and you accelerate but I do not. We are still traveling at equal relative speeds. Why would your clock read younger than mine when returned to point A?

 

[JesseM]

My point is how can you even say that me or you or the observer is even moving or at rest.

Who is saying that? Certainly not relativity, which rules out the idea of absolute motion or absolute rest, and says that motion and rest can only be defined relative to a particular frame of reference.

I am moving away from you, but closer to some other object. You are moving away from me and away from other object. How is my speed determined.

Relativity gives no objective "speed" for anything, only speed in one frame of reference or another. If we are moving at 0.8c relative to one another, then in my rest frame I am at rest while your speed is 0.8c, and in your rest frame you are at rest while I am moving at 0.8c. Both frames are equally valid as far as relativity is concerned.

You could pick any object in space and say how fast we move relative to it, but that leaves any speed possible depending on which way you decide to measure.

Yes, that's exactly the point. Why is this a problem?

I thought that if space was somehow dragged around by mass, then a background could be in place for determining speed and the effects of time dilation.

No.

Lets say me and you are in space ships facing opposite directions and you accelerate but I do not. We are still traveling at equal relative speeds. Why would your clock read younger than mine when returned to point A?

Why? Because we will make that prediction no matter what inertial frame we choose (the rules of SR such as time dilation only work in inertial frames, meaning the frames of observers who don't accelerate). We could pick a frame where you or at rest, or we could pick the frame of an observer who sees you moving at 0.99c, and the two frames would disagree on what my speed was on both the inbound and outbound leg of the trip, but they'd end up calculating the same value for how much I aged using the time dilation equation. You can see an example on this thread; if you want to try analyzing it with some different numbers, just give the velocities and times for both the inbound and outbound leg of the trip in one frame, tell me how fast you want the second frame to be moving relative to the first, and I can show how the second frame will make the same prediction about aging in spite of seeing the speeds differently.

 

[W3pcq]

Who is to judge who is accelerating and who is at rest?

 

[JesseM]

Who is to judge who is accelerating and who is at rest?

Did you read what I just wrote? In relativity there is no objective truth about who is at rest and who is moving at constant velocity, each inertial observer defines themselves to be at rest in their own inertial rest frame, and every inertial frame is equally valid in SR. On the other hand, there is an objective truth about acceleration (changes in velocity), I'll just repeat my comments from post #3 of this thread:

But there is no question about which one accelerates--that twin will feel G-forces during the acceleration. Of course, even if you ignore G-forces you could also define an inertial path through flat SR spacetime as the one that causes a clock to elapse the maximal time when it traverses it. Or you could define it as one in which the laws of Maxwell's laws of electromagnetism are observed to work consistently (an observer on an accelerating ship doing electromagnetic experiments on board would find that they didn't match the predictions of Maxwell's laws). The important thing to note is that acceleration is absolute in SR, even though velocity is not.

 

[W3pcq]

Why can't a spaceship fly faster than the speed of light relative to the earth? Once you accelerate then you keep your momentum right? With enough fuel couldn't a spaceship gradually move faster and faster relative to Earth and reach distant galaxies. I mean, you accelerate in space and the energy is conserved and turned into momentum right? As long as you don't accelerate faster than light, then you can move faster than it does right? Sort of?

 

[JesseM]

Why can't a spaceship fly faster than the speed of light relative to the earth? Once you accelerate then you keep your momentum right? With enough fuel couldn't a spaceship gradually move faster and faster relative to Earth and reach distant galaxies. I mean, you accelerate in space and the energy is conserved and turned into momentum right? As long as you don't accelerate faster than light, then you can move faster than it does right? Sort of?

If you accelerate at a constant rate as felt on the ship--constant thrust, constant G-force experienced by the passengers--your velocity as seen in some fixed inertial frame does not increase at a constant rate as it would in Newtonian physics, instead the rate of velocity increase in the observer's frame continually slows down as you approach the speed of light in that frame. This is somewhat related to the fact that velocities don't add in relativity the same way they do in Newtonian physics (see this page)--if I shoot a torpedo from my ship at 0.4c relative to me, and my ship is moving at 0.5c in the same direction relative to an observer on Earth, the observer on Earth does not measure the torpedo to be moving at 0.4c + 0.5c = 0.9c, but instead measures it to move at (0.4c + 0.5c)/(1 + 0.4*0.5) = 0.9c/1.2 = 0.75c. Keep in mind that each observer measures speed in their frame using rulers and clocks at rest relative to themselves to find distance/time, but each observer measures that other observer's rulers are shrunk and other observer's clocks are slowed down and out-of-sync, so in a way it shouldn't be surprising that velocity wouldn't add the same way as in Newtonian physics where you don't have such issues.

Anyway, the upshot is that no matter how long I accelerate I'll never reach c in any inertial frame, assuming I always accelerate at a finite rate. For more on acceleration in relativity, see the http://math.ucr.edu/home/baez/physics/Relativity/SR/rocket.html page.

 

[W3pcq]

That is true that you cannot reach C in any inertial frame because in any inertial frame there is no objective velocity. So in a sense you can never move any velocity in an inertial frame right?

Lets say you are leaving Earth and headed for the center of the Milky Way. You begin by accelerating up to 20,000 miles per hour relative to both the Earth and the center of the milky way. Once you reach 20,000 miles per hour you shut off engines and there is no more g force. Now your relative speed is at 20,000 mph relative to Earth and your inertial frame velocity is back to 0?

 

[JesseM]

That is true that you cannot reach C in any inertial frame because in any inertial frame there is no objective velocity. So in a sense you can never move any velocity in an inertial frame right?

In any particular choice of inertial frame there is a definite truth about your velocity, it's just that different inertial frames assign you different velocities, and all inertial frames are equally valid as far as relativity is concerned.

Lets say you are leaving Earth and headed for the center of the Milky Way. You begin by accelerating up to 20,000 miles per hour relative to both the Earth and the center of the milky way. Once you reach 20,000 miles per hour you shut off engines and there is no more g force. Now your relative speed is at 20,000 mph relative to Earth and your inertial frame velocity is back to 0?

In the inertial rest frame of Earth, your speed is 20,000 mph. In the inertial rest frame of your ship, your speed is 0 (and in this frame the speed of the Earth is 20,000 mph).

 

[W3pcq]

Lets say that I developed a photon thruster that required nothing as fuel except EM radiation. I Gradually accelerate until my speed relative to Earth is 25C. In my inertial frame my speed is o, but I am headed for the center of the galaxy at 25c relative to it. I pass an observer at rest relative to the Earth and pass them at 25c. The shine a laser at the center of the galaxy which turns on at the instant I am passing it. Who reaches the center of the galaxy first?

 

[JesseM]

Lets say that I developed a photon thruster that required nothing as fuel except EM radiation. I Gradually accelerate until my speed relative to Earth is 25C. In my inertial frame my speed is o, but I am headed for the center of the galaxy at 25c relative to it. I pass an observer at rest relative to the Earth and pass them at 25c. The shine a laser at the center of the galaxy which turns on at the instant I am passing it. Who reaches the center of the galaxy first?

Again, you can't accelerate from sublight speeds to FTL speeds in relativity. We could consider your problem where a light is emitted from a given location at the same time as a tachyon which always moves at 25c in the frame of the Earth, but this tachyon does not have an inertial rest frame of its own, so it's not true that "in its inertial frame its speed is 0", nor is it true that the photon moves at c in its frame. The tachyon would reach the center of the galaxy 25 times quicker than the photon in the Earth's frame, though, that's just what it means to travel at 25c.