# Speed of light/relativity question

I’m currently reading a book on relativity. Some of it I am grasping, some of it I am not. I have the following question to pose:

Can the approach speed of something be quicker than the speed of light? For example, the light from our sun being sent to the nearest star, and the light from the nearest star being sent to our sun. The “approach” speed of the two light sources must be double the speed of light, yes? (Assuming a neutral observer, who is “stationary” relative to the two light sources).

Now, if I was traveling along in a space ship, starting at the sun, and heading towards the nearest star, and this spaceship was traveling at the speed of light, would the approach speed of the oncoming light (from the other star) be twice the speed of light? Or is this where the famous “time slows down” stuff kicks in, and I would only perceive the oncoming light as approaching me at the speed of light?

Additionally, how would I perceive the light from the sun that I am traveling away from? Eg, would it be going past me at the speed of light?

Please keep answers as digestible as humanly possible! Thanks.

The core principle of relativity, both special (assuming a flat, unwarped space-time plenum) and general relativity), is that light moves the same speed in all reference frames, regardless of whether they are inertial (no external forces applied) or accelerated. What this means is that if you are going 0.8c, you still see a light coming from a source moving the same speed as an observer who is stationary with respect to the source. The thing that changes between you and the stationary observer is the frequency (or wavelength, which is proportional to frequency inverted); if you are moving toward the light source, the frequency becomes higher and the (visible) light becomes bluer, and vice versa if you are going away from the source.

This is counterintuitive because we don’t see these effects at “normal” speeds, but this has been seen both by theory and in experiment.

Stranger

Yes, the observer will observe light from both sources coming toward him at C (C = the speed of light).

First of all, it is impossible for a spaceship to accelerate to C (infinite energy would be required) so for these types of examples it’s better to say the spaceship is travelling at (for example) 0.9C. Anyway, you will still observe light from the star you are approaching to be travelling at C relative to you. This is where the strange time effects that you have heard about come into play.

Yes, you will always observe light to be travelling at C no matter what.
edit: or, what he said!

If you’re sitting in the middle and two light rays are moving towards you from opposite directions, you could say that, from your reference frame, their relative speed to each other is 2c, but that’s not really a relevant reference frame. If you’re in a ship going any speed, and a beam of light is moving in the opposite direction to you, its speed relative to you, in your reference frame, is exactly c.

What about in a collapsing Universe…one approaching a big crunch?

In any sort of universe at all, it is still true that light always moves at c relative to me, as measured in my reference frame.

When thinking of these types of questions it’s probably easier to ask yourself if any information is being transferred ftl. And the answer is clearly no.

Yes, but it would be redshifted (its frquency would be lower)

Light would still move at C. However it would be blue-shifted. As space contracts around it, its frequency increases.

Ok…help me out here

Let’s just say that we are alive and looking out at a universe approaching the big crunch…still a long ways off but the galaxies away from us are approaching us at, say, 4 times the speed of light because the space is contracting between us. would not the actual galaxy be much closer to us then the light indicates? If that is true, the galaxy would still be admitting light but THAT light would be radiated when the galaxy is closer so wouldn’t we see that light first? Wouldn’t the galaxy appear to be moving away but still be blueshifted?

Fight my ignorance!

Okay, so light always seems to move at C. But I think that other objects might seem to move faster than C.

Example: An object is ten light-years in front of me. I am moving towards it at 90% of the speed of light. I will reach it in about 11 years. But because time slows down, it doesn’t feel like 11 years. At 90% of the speed of light, time slows down by a factor of 2.294, so what was an 11-year trip to an outside observer is less that 5 years according to the clocks on my spaceship. I traveled 11 light years in less than 5 years! I seem to be going faster than light!

Where’s the error in the above paragraph?

You’re forgetting the Lorentz contraction:
http://en.wikipedia.org/wiki/Length_contraction
From your perspective, you are NOT traveling 10 lightyears.

I had thought that only the length of my spaceship contracts, not external things like the distance between me and my destination. But now you’ve made me realize that we could consider my spaceship to be at rest, and the universe moving towards me at 90% C, and that’s how the distance got shrunk.

Thanks! Ignorance has been vanquished!

Special relativity has always made my head hurt.

One really broad question I’ve never understood the answer to:
Why is the speed of light constant in all frames of reference? I understand how much of the rest follows from that premise (aka I can make the math work), but I’ve never gotten the “why” aspect.

No, because light itself is also carried along with the fabric of space as the universe contracts. If the contraction of the universe is pulling a distant object toward us at 4x the speed of light, then any photons emitted by that object will be swept along with contraction, moving at more than 4x the speed of light toward us as well. Older photons will still arrive first so the object will correctly look like it’s approaching.

Actually, you wouldn’t see a galaxy that was approaching at that speed at all, since the galaxy itself would get to you before the light from it would. Which would happen at the moment of the final singularity, so you’d have other things to worry about.

Have you ever had a two-year-old, at that stage where they’re always asking “why?”, and eventually you just have to say “Because that’s just the way it is”?

Well, the answer to your question is “Because that’s just the way it is”.

No, I don’t think this is true. Light is swept along with the expansion or contraction of space. The galaxy may be approaching at 4x the speed of light, but any photons it emits in our direction will still arrive before it does because the contraction affects them as well.

I tend to prefer giving the more honest and truthful answer, usually “I don’t know” or “that depends on what you mean” or “I’d rather not have to try and explain that right now”.

Telcontar said:

That seems to be a feature of the universe.

I call it a bug, but we’d need to see the original programming plan to be sure.

In some sense, in this case isn’t the “why” because otherwise the laws of causality would no longer hold?