# Slow motion movement in SR

1. Nov 10, 2014

### alackofcolor

This is something I've wondered for a long time. In discussing time dilation in SR, you often hear something along the lines of, "If you looked into a spaceship traveling near the speed of light, you'd see the astronaut inside moving in slow motion, the hands on their watch ticking slowly..." etc. My question is, does the motion of the spaceship also appear slow like its contents? That is, would I be observing a very slowly moving spaceship?

2. Nov 10, 2014

### Staff: Mentor

No. The spaceship is traveling near the speed of light. The "slowing down" due to time dilation refers to periodic processes taking place in objects that are inside the spaceship, being carried along with it.

Also, the "slowing down" due to time dilation is not what you would directly observe if you looked at the ship through a telescope. What you would directly observe would depend on the ship's direction of motion relative to you, as well as its speed, because of the relativistic Doppler effect.

3. Nov 15, 2014

### alackofcolor

Here is a passage from Elegant Universe concerning two astronauts passing each other in spacesuits in space with some relative velocity:

“From George's perspective, he is stationary while Gracie with her flashing green light and large digital clock appears in the distance and then passes him in the blackness of empty space. He notices that Gracie's clock is running slow in comparison to his (with the rate of slowdown depending on how fast they pass one another). Were he a bit more astute, he would also note that in addition to the passage of time on her clock, everything about Gracie—the way she waves as she passes, the speed with which she blinks her eyes, and so on—is occurring in slow motion. From Gracie's perspective, exactly the same observations apply to George."

I guess I don't understand the relation between time dilation and slow motion movement, in particular why it only applies to movement other than the velocity of the object(s) in motion.

4. Nov 15, 2014

### Staff: Mentor

Read the passage you quoted again. Does it say anywhere that Gracie's ship itself is in "slow motion", as opposed to things inside the ship?

Now consider it logically: we start with the assumption that Gracie's ship is moving at near the speed of light relative to George. We deduce from this that things inside Gracie's ship appear to George to be in slow motion. But if we apply that same deduction to the ship itself, we contradict our initial assumption, that Gracie's ship is moving at near the speed of light. Also, if the ship itself is moving slowly relative to George, then we no longer deduce that Gracie's clock runs slow, or that her waves or eyeblinks appear in slow motion to George. So applying the "slow motion" deduction to the ship, instead of just to things inside the ship, leads to an infinite logical loop, so to speak--we never reach a consistent picture of what's happening. The way to avoid that is to hold the speed of the ship itself, relative to George, as a constant, and only apply the "slow motion due to time dilation" effect to objects inside the ship.

(There are other issues lurking beneath the apparently innocuous phrasing in the passage you quoted, but I won't go into those until we've got the main point taken care of. As a general rule, you should not use pop science presentations as a source if you actually want to understand the underlying physics.)

5. Nov 15, 2014

### alackofcolor

I didn't mean to imply that the passage was stating that her spaceship was moving slowly (even though the example posted is just two astronauts in space without ships, but that's really beside the point). I only posted the passage to serve as the source of my confusion: how dilated time results in slow motion movement of astronauts. I recognize that there's not much sense in viewing the spaceship as moving slowly as well, because then how could you be saying that it's moving at the speed of light, as you said. That said, I don't under how anything would appear to be moving in slow motion.

6. Nov 15, 2014

### jartsa

Let's consider the effect of spaceship engines on spaceship parts, when spaceship is accelerating towards star X:

Effect1: Spaceship engines accelerate all the spaceship parts so that all the parts will arrive to star X almost at the same time.

Effect2: Spaceship engines curb any relative motion between parts. (This helps all parts to arrive to star X at the same time)

Last edited: Nov 15, 2014
7. Nov 15, 2014

### George Jones

Staff Emeritus
This only true if the spaceship is moving away from you. If the spaceship is moving towards you, you would see the hands on the astronaut's watch ticking fast.

8. Nov 16, 2014

### Staff: Mentor

I guess we'll have to go into those other issues that I said were lurking. George Jones already brought up the main one: if the word "appear" means "what each astronaut would actually see with his eyes, or with a telescope", then while the astronauts are moving towards each other, they would each see the other's clock ticking faster than their own, not slower (and similarly for other things happening inside the other's ship). Furthermore, when the astronauts are moving away from each other, while they will see each other's clock ticking slower than their own, the difference in rates actually seen will not be what you would calculate from the standard time dilation formula. The difference actually seen is given by the relativistic Doppler formula. The time dilation formula gives what each astronaut would calculate the rate of the other's clock to be, after correcting what he actually sees (with his eyes or a telescope) for light travel time.

Furthermore, the whole "appear to be moving in slow motion" thing glosses over a key distinction, which I'll illustrate as follows. Suppose one astronaut starts bouncing a light beam from one end of his ship to the other. And suppose, for definiteness, he is moving away from the other astronaut as he does this. The light beam will be traveling at the speed of light according to both astronauts; so if we just consider one "leg" of the beam's motion (back end of ship to front, or front end to back), the light beam is certainly not moving "in slow motion".

So where does the "slow motion" thing come from? Consider the time it takes, according to the other astronaut (the one in the other ship, watching the first ship and the beam bouncing inside it), for the beam to make one round trip, compared to the time it takes according to the astronaut in the same ship as the ball. The former time (according to the other astronaut) will be longer than the latter. Why? Because, from the standpoint of the other ship, the beam, starting from the rear of its own ship, has to "catch up" with the front end of the ship in order to bounce (since, from the standpoint of the other ship, the front end of the ship is moving too). This lengthens the time the beam takes to reach the front end of its ship and bounce. Some of this time lag gets made up on the return leg, because now the rear end of the ship is catching up to the beam; but if you work out the math, the total time for the beam's round trip will still be longer from the standpoint of the other ship. This difference is time dilation (work out the math and you will see that the ratio of the two times is just the standard time dilation factor--in fact this is just the standard "light clock" thought experiment).

So to understand where the "slow motion" comes from, it's important to draw a distinction between the speed at which something is moving, and the time it takes for a particular process (such as the beam making one round trip) to complete. The latter is where the "slow motion" comes in.