# 3 questions regarding velocity and the speed of light

1. May 31, 2013

### mpatryluk

Though i've always been familiar with the very (very) basic implications of relativity, I've only just now gone into the details in any way, and I'm experiencing the whole cliche of "having difficulty in wrapping my mind around the concepts". Maybe you who are more experienced than i could help shed some light on light for me.

A couple questions:

1. Correct me if I'm wrong, but my basic interpretation is that if i started travelling in the +x direction, and i wanted to catch a photon going in the +x direction, no matter how fast i went, i would never be any closer to catching it than if i were standing still?

-I derive this from the point that the speed of light is the same for any observer.
-I interpret this as happening because the faster i go, time slows down for me proportionally to my speed, thus the photon is in a non slowed state compared to me and is going at a speed of c when i observe it?

2. (assuming im not wrong on the above) If this is the case, does this mean that how much time slows for you compared to an inertial observer is directly proportional to the % of the speed of light you're travelling? (Where if you could hit the speed of light time would stop?) So at 10% of the speed of light would time pass for my frame of reference 10% slower?

3. Im so utterly confused as to when velocity counts and when it doesnt. I'll cite the spaceship example, where if i blasted off in a rocketship near the speed of light and came back later, time would have passed faster on earth. But if there's no absolute frame of reference or stillness in the universe, then wouldnt the earth be moving near the speed of light relative to me? Yet time passes more slowly for me than them. What are the terms that determine who is really moving at what speed, if it's all relative?

2. May 31, 2013

### Staff: Mentor

http://arxiv.org/abs/0902.2032

It may be a bit math intense but worth reading.

3. Jun 1, 2013

### mpatryluk

Thanks! It even specifically mentions one of the questions i asked. I'll give it a read.

4. Jun 1, 2013

### ghwellsjr

No, that's not right. If you were standing still and you want to consider yourself to be a rest in an Inertial Reference Frame (IRF) and you fired a photon away from you, then it will travel away from you at c so you always know where it is at any time thereafter. However, you will never be able to see or measure its progress since its speed is defined to be c in any IRF. Or to put it another way, we define time at remote locations along its progress to be such that its speed is c.

However, if after you fire the photon you start traveling toward the photon then you will certainly be closer at any particular Coordinate Time later than if you had remained stationary. Or to put it another way, if you left a brother behind, you would be closer to the photon than your brother. You have to keep in mind that when we are discussing issues like this, we have to state which IRF we are using. So the fact that your Proper Time is dilated, meaning that the Coordinate Time is progressing faster than your Proper Time, we still have to make the comparisons using the Coordinate Times and Coordinate Locations.

Now if you want, you can transform this scenario into one in which you are at rest after you started traveling. In this situation, your brother would be traveling in the opposite direction so you will still be closer to the photon than your brother which is where you would be if you had not started traveling.
Not any observer, just inertial observers. Since you started out at rest and then started traveling, you are not an inertial observer.
Your Proper Time does slow down compared to the Coordinate Time of an IRF in which you are defining your speed (but it's not simply proportional), however, how do you expect to observe the speed of a photon? You can't just shine a light on it like you could a high speed projectile and have reflected light to enable you to observe and measure its speed. So the only thing you can do is place a reflecting object such as a mirror some measured distance away but then you have the problem of knowing the speed of the light that is coming back toward you. SR's explanation is that the distance is contracted and, along with your dilated Proper Time, you will measure the round-trip speed of the light to average out to c even though the photon takes more time to go from you to the mirror than it takes for the reflected photon to get from the mirrror back to you.
It's not that simple. Look up the formula for gamma or the Lorentz Factor. Let's not consider hitting the speed of light, it's impossible. When you transform from a frame in which you are moving and the time on your clock is dilated to a frame in which you are at rest, then the Proper Time on your clock is no longer dilated.
I think your confusion is coming from trying to associate everything relative to an observer rather than to a single IRF. It's all relative to a particular IRF. So if you consider the IRF in which you and the rocketship started out at rest on the earth and you took off at a speed near that of light on a trip, your clock will be dilated during your whole trip compared to the Coordinate Time of the IRF. The clocks of the people who remained stationary on the earth will not be dilated at all since their speed remained at zero and so you will age less during your trip than the earthlings did. Is that so very hard to understand?

Last edited: Jun 1, 2013
5. Jun 1, 2013

### night_sky

I can see your confusion. First of all you must know that irrespective of observer's speed the light speed must be and will be measured to be constant every where,so if you are really travelling at the speed of light ,every observer will measure your speed to be constant(c).Yes ofcourse,the speed of earth relative to you will be c but only when you measure it, its not the same way if i am measuring the speed of earth from mars, the speed will be quite different,you must have realized now that light is constant every where,and hence it is measured to be constant everywhere. Speed of earth will be different if measured relative to different objects. Its all relative .I think this will clear your confusion.

6. Jun 1, 2013

### mpatryluk

Oops, silly of me, but i forgot that it only applied to constant velocity observers. I thought it was all observers at all times and i was struggling to comprehend how that reconciled.
So then if i started accelerating after the photon left, its perceived velocity relative to me would be lower than the speed of light, because i was a non inertial observer?

Oh ok that clarifies things!

I guess what I'm not understanding is the "stationary aspect". As in, let's say theoretically, i went and sat in my space ship just outside of the earth, and then instead of me blasting off, the earth and the entire galaxy accelerated to near light speed in the opposite direction. I would have undergone the same journey, and would wind up in the same spot, but since i was the inertial frame of reference, i would age much faster than the rest of the galaxy, and time would dilate for the rest of the galaxy instead of for me. Since the translation in space between the rocketship and the earth is identical either way, i cant tell why it should be one way and not the other. I guess the answer must lie in undergoing direct acceleration via a force?

Thanks for your clear and well thought out response, i found it very helpful in clarifying my misconceptions. Sorry i made so much work for you by being wrong about essentially everything :p

7. Jun 1, 2013

### ghwellsjr

No, the answer lies in specifying a scenario in terms of a single Inertial Reference Frame. You don't have to worry about accelerations or forces (which, of course are necessary factors but not relevant in an analysis according to Special Relativity).

And please don't buy into notions like "i was the inertial frame of reference". You are not an IRF. You and other things can be stationary or in motion at different locations in an IRF. You set up your scenario any way you want.

But what you can't do is set up one scenario like you did at first where you take a trip in your space ship and return younger than those that remain stationary and then say it is equivalent to your new scenario where you sit in your spaceship while the rest of the universe takes a trip. That is a different scenario with a different outcome and your "translation in space" is illegitimate because it does not follow the Lorentz Transformation. I posted an explanation of a Twin Paradox scenario with diagrams to show the IRF of the stay-home twin and then how it transforms into two other IRF's, one for the traveling twin on his way out and a second one for his trip back and finally a non-inertial frame for the traveling twin constructed using radar techniques. Check out this link and see if it helps: