# Light moving toward a moving observer's reference frame

The speed of light is supposed to be the same for all observers in an inertial frame, no matter the observer's speed. As a result, time slows down for observers moving quickly, and this explains why light always seems to move away at the same speed. However, what if light moves toward a person in an inertial frame traveling at, say, half the speed of light? Without time dilation, the speed of light would appear to be be moving at a speed greater than the speed of light, in the observer's frame. The only way to fix this problem is for time dilation to occur; HOWEVER, to fix this problem, time should speed up for the observer, not slow down. And yet, for observers moving quickly, time slows down (which solves the problem of light moving away from an observer). Where is my misunderstanding in all of this/ what is going on here?

• If you want to know what an inertial observer sees, and what times & distances they measure, you need to remember that an inertial observer is always at rest in their own frame. Apr 18, 2019 at 2:54
• Yea, so if the inertial frame is moving at half the speed of light, and light is moving toward the frame at the speed of light, wouldn't the observer see the light traveling at 1.5 times the speed of light w/o dilatation? Wouldn't we need to observer's time to speed up in order for them to really see the light move at the speed of light? Apr 18, 2019 at 3:38
• You appear to have completely ignored the comment of @PM2Ring . Him: "An inertial observer is always at rest in his own frame." You: "So if the inertial frame is moving at half the speed of light..." ..... Apr 18, 2019 at 3:54
• Can't an inertial observer be at rest in his own frame even though his frame is moving? Ie if I'm on a train, isn't my inertial frame moving? I considered this problem as follows: I am on a non acceralerating spaceship (inertial frame) that moves toward some light at speed c/2. W/O S.R., I would see the light move at 3/2 C. With special relativity, time changes so that I always see light move at speed c. Thus, I reasoned that if my ship moves forward some distance in some time, and light moves toward me, time must change so that it seems as tho I the light moves at speed c. Apr 18, 2019 at 4:42
• And here is your other misconception: " time should speed up for the observer, not slow down" . Time does not speed up or slow down; I don't even know what this would mean. If we are in motion relative to each other, then your clocks run normally in your frame and slow in my frame, while my clocks run normally in my frame and slow in your frame. There is no frame in which any clock runs faster than normal (unless the clock is broken!!). Apr 18, 2019 at 5:18

What you are thinking about is that time dilation is relative.

Let's say that in your case there is an observer moving at the c/2. OK, but compared to what? There has to be a observer at rest. So the observer moving at c/2 is moving relative to the observer at rest.

Now the observer at rest has a clock, and this observer at rest will see its own clock tick normally. But if he compares his clock to the clock of the observer that is moving at c/2, he will see that the clock of the observer at rest is moving faster then the clock of the observer moving at c/2.

The observer moving at c/2 sees its own clock tick normally. But when he compares it to the other's clock, he will see that the clock of the observer who is moving at c/2 is ticking slower then the clock if the observer at rest.

This is due to time dilation.

Now as per SR, all observers will see light moving at speed c (when measured locally, in vacuum), regardless of the speed of the observers or their direction.

In your case, it does not matter whether the light is coming toward the observer or moving away from the observer, and it does not matter whether the observer is moving toward the light or away from the light. The observer moving at c/2 will always see light moving at speed c.

• This helped, but I'm not sure it answered my question. Lets say theres a guy standing still in an inertial frame (as above). A spaceship moves away from him at c/2. Light moves toward the spaceship and the guy. (lets say this is all in one d). As you said, by SR, both observers will see light moving at speed c. However, by my reasoning, I think this would imply that the clock of the observer traveling speeds up, not that it slows down. Can you go through how this shows that the clock of the traveler slows down? Apr 18, 2019 at 4:31
• I understand the case where light moves away from the traveling observer better. (When the light moves away, using the same speeds as above, without dilation the apparent speed would be c/2. If time is dilated s.t. it slows down by a factor of two, however, things work out, because the observer sees the light move at speed c. [Don't know if this is the right reasoning, but that's how I've been thinking about it] ). Apr 18, 2019 at 4:35
• "Philosophy [i.e., physics] is written in this grand book - I mean the universe - which stands continually open to our gaze, but it cannot be understood unless one first learns to comprehend the language and interpret the characters in which it is written. It is written in the language of mathematics, and its characters are triangles, circles, and other geometrical figures, without which it is humanly impossible to understand a single word of it; without these, one is wandering around in a dark labyrinth." Galileo Galilei, Il Saggiatore (The Assayer, 1623). Apr 18, 2019 at 12:30
• @MarcelMazur ok so in your case the spaceship moves at c/2 away from the guy standing still. Light moves toward them. Both will see light coming at c. Why? You are right, time dilation causes the spaceship to slow down in time. In the time dimension, light moves at 0. The spaceship moves in the time dimension with c/2. The guy standing still moves in the time dimension with speed c. Now you need to read about the four vector. The four vector is built u so and the universre is built up so that its magnitude needs to be c always. Apr 18, 2019 at 15:47
• @MarcelMazur So, light moves in the spatial dimensions woth speed c, and in the time dimension with speed 0. The spaceship moves in the spatial dimensions with speed c/2 and in the time dimension with speed c/2. The guy standing still moves in the spatial dimenaions with speed 0 and in the time dimension with speed c. All of them move in spacetime with speed c. Their four vector's magnitude is all c. If the spaceship moves at c/2 in space, it has to slow down in time to c/2. As it closes to the speed of light, it slows down in time more. Apr 18, 2019 at 15:50