Nothing can travel faster than light

[Dauden]

A question has been in my head for some time and I have yet to find an answer when I researched it.

I know that nothing can travel faster than light, but WHY?

All observers, no matter what speed they are traveling to or from the source of light, see the light as coming at them at 670 million miles per hour. My mind is boggled by this. I made a scenario in my head that made me want to find this answer out.

It might seem difficult to picture, it might not, I don't know but here it is.

Say a light source is at point A. A stationary person #1 is at point B which is 670 million miles away (the light will take an hour to reach B from A). Say person #2 is running past point B going 100 million mile per hour (theoretically) away from the light source. Person #3 is running the exact same speed as the #2 but running toward the light source. If they all reach point B the exact time the beam of light hits point B from A, according to the principle of GR, they all see the light going 670 million miles per hour. If this is true, wouldn't the light reach point B at different times for each?

Person #2 would see the light hit point B before the others because, to his perspective, the light is traveling 670 million miles per hour. If Person #1 saw the light going at the same rate at which person #2 saw, because person #1 is stationary, he would see it as going 770 million miles per hour. But this is not possible since light travels 670 million miles per hour.

So, the light would reach point B faster for person #2 than #1 and #3.

I don't know if this is understandable. It is a complex situation that I had to rethink to get a grasp of and I still don't know if I understand the scenario fully.

 

[K.J.Healey]

It seems like the primary problem with people who just start to get into Special Relativity is they take for granted the "If they all reach point B the exact time the beam of light hits point B from A" question for granted.
Who is measuring this "Reach point B", what do you mean by "exact time", who's reference frame? You have to chose one, and for SR it CANNOT STOP, velocities can't change even when you're measuring.
It all depends on who is the observer. They will all witness different things, in a different order, and they won't agree on when things happen.

 

[Dauden]

Is there anyone answer to why you cannot go faster than light?

 

[neutrino]

I haven't read through the entire scenario, but to answer the question...

So, the light would reach point B faster for person #2 than #1 and #3.

No, it won't. All events in spacetime are the same for all observers.

Observers in relative motion will disagree on the distance light travelled, the time it took for it travel that distance, but they will all agree on what happened. You must realize that in this case, this ratio of distance traveled by light to the time taken is a constant, viz., c.

 

[neutrino]

Is there anyone answer to why you cannot go faster than light?

Here's one...the velocity combination rule.
http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/einvel.html#c1

 

[pervect]

I think the issue here is probably the "relativity of simultaneity".

See for instance http://en.wikipedia.org/w/index.php?title=Relativity_of_simultaneity&oldid=138735828

As far as visualizing things, a diagram would help. Here's one I drew from your problem description:

Time axis runs up and down (this isn't necessary, but is traditional). If the time axis went left-right, the diagram would be more like a graph of position vs time.

We can see the slanted light beam has the greatest velocity, making a 45 degree angle, while the moving observers, traveling at less than c, labelled 1 and 3, have worldlines that are more vertical.

What happens is that #1 #2 and #3 have different notions of simultaneity. See the diagrams in the Wikipedia article in the section on space-time diagrams for a very similar problem.

The diagram I just drew is getting a bit cluttered, I've added a pink line for the concept of the simultaneity of the stationary observer, so that you can see that event A and event B on the diagram occur "at the same time" according to the stationary observer.

I picked observer #2 for the second line of simultaneity, the green one. You can see that event C is the event on the worldline of observer #2 that happens "at the same time" as event A according to observer 2.

The point is that simultaneity is relative.

You might also like to look at the simpler space-time diagrams such as those in the wikipedia article, in particular http://en.wikipedia.org/wiki/Image:Relativity_of_simultaneity.png

 

[Dauden]

Alright, thank you for the replies. It seemed to have solved the problem but I think I was actually asking the wrong thing.

Why is c the same for all observers no matter how fast they move to or from the source?

 

[pervect]

Science can tell you that that's what we measure - that the speed of light is constant for all observers. In general there isn't any answer as to "why" - sometimes, in special cases, there is a cause and effect relationship that allows us to answer "why" questions scientifically. But there is no obvious "cause" that "made" light travel at a constant velocity, it's just something that we observe that happens. So this isn't one of the cases in which we have a scientific answer as to "why".

 

[Fra]

Is there anyone answer to why you cannot go faster than light?

It can be argued to follow to a high degree of plausibility from other things, but these things can in turn be questioned, so the questions is when are we happy.

Relativity is based largely on an assumption that there is a maximum possible signal speed that all observers agree upon. The speed of light. From this SR predicts by various fairly plausible consistency arguments that you can't accelerate something faster than light.

But this generates the next why: why is there this apparent invariant upper bound of information transfer, that everyone agrees upon?

Consistency of current models, and current experimental experiences
supports this.

I personally think there may also some other ways to argue why this is plausible in a deeper way, using a relational thinking of time in information theoretic terms, outside of relativity (ie not assuming it). The basic idea is that time can be thought of as a relative change, and information about a moving object is also change, internal consistency implies a relation between information of the clock device and the information about the _most probably_ change of the object. I haven't bothered doing it properly yet but a lineout in my head suggests that this implies an upper bound of the subjectively measured relative "change" per "change". Anything else contradicts that the change was probable. So at least this suggest that violation of the upper bound is "unlikely", but not strictly impossible. Exactly how unlikely may depend on the information distributions. Classically I think the peaking is sharp enough so it's fair to consider it impossible for all effective purposes. There's probalby a proof somewhere the idea is in principle simple. I've postponed trying to "prove" it until later, while trying to develop more important points. This is however formally speculative and I'm not sure if it was the wrong type of answer you wanted.

But I think nothing foolproof. Nothing is foolproof.

So one "why" is that our scientific knowledge suggest this as a pretty good assumption at least.

The other possible "why" is, wether we can "invent" a cause, consistent with our knowledge that appears to "imply" this. but I think the first version is better.

/Fredrik