Is travel at almost infinite speed (FTL) actually possible?

[eohjelle]

Relativity is a truly fascinating and interesting subject that I don't fully understand. I'm currently in the process of studying it and this idea popped up in my head. This is just pure speculation from my side, which I expect to be wrong.

I'll now try to explain the foundation for my outrageous idea. Please point any errors and mistakes in my reasoning.

What's the speed of light relative too?
It is a well known fact that nothing can travel at the speed of light. But in order to know what this means - we must know more about the speed of light. The real paradox here is that the speed of light is the same relative to all observers. So our place and velocity relative to other objects is independent of the speed of light. All observers measure the speed of light as the defined value c in their own frame of reference.

Coming from this I reasoned that it is actually possible to travel faster than the speed of light relative to other objects. I'll make an example to illustrate this. Let's say our friend George has only one task, and that task is to stand still. In our frame of reference, he's not moving at all. George is our observant. In addition to George there's a blind horse and there's Usain Bolt, and they're both in the exact same spot as George. When George makes the signal Usain Bolt and the blind horse are going to race. As George makes the signal, Usain Bolt runs east, while the blind horse (being a blind horse and all) runs directly west. They both run at 0.60c, or in other words 60% of the speed of light.

Judging by my logic, Usain Bolt and the blind horse should, in relation to each other, actually move faster than the speed of light. As I write this I have a feeling that this is wrong. In Usain Bolt's frame of reference, does the blind horse travel faster than c? That would be impossible, because nothing can travel faster than c. If Usain Bolt turns his head and looks in the direction that the blind horse went, what does he see? I really don't know - please enlighten me.

The speed of light in its own frame of reference
I read something a while back (I don't remember where) that while we measure the speed of light as c, if we let an actual photon be our observer, the photon itself actually experiences that it travels through the entire span of the universe in an instant. I don't have a source for this but I believe it to be true.

Does this mean that faster than light travel is actually possible?
Because c is the same for all observers, even as we move faster in a spaceship relative to earth, we still measure c to be the same relative to ourselves. So as our speed increases - so does our c compared to the c of an observer standing still in space. And if we keep increasing our speed to impossibly fast, we still measure c to be the same. Until we can travel the span of the universe in almost an instant.

Again, the paradox here is that while we don't travel faster than c in our frame of reference, isn't it also so that Earth can't move away from us faster than c? Because nothing can?

My head is about to explode right now. I stand in awe to our magnificent, incomprehensible universe.

 

[mathman]

http://en.wikipedia.org/wiki/Special_relativity

See section - composition of velocities. They don't simply add as you described.

 

[Nabeshin]

The speed of light in its own frame of reference
I read something a while back (I don't remember where) that while we measure the speed of light as c, if we let an actual photon be our observer, the photon itself actually experiences that it travels through the entire span of the universe in an instant. I don't have a source for this but I believe it to be true.

Whoever wrote this was being sloppy. Simply put, light does not HAVE a frame of reference -- i.e. one in which it is at rest. So to talk about what it is like to be an observer on a photon, such a statement is meaningless. You can of course talk about an observer who moves infinitesimally close to the speed of light in some reference frame, in which case time dilation becomes arbitrarily large.

 

[John232]

Whoever wrote this was being sloppy. Simply put, light does not HAVE a frame of reference -- i.e. one in which it is at rest. So to talk about what it is like to be an observer on a photon, such a statement is meaningless. You can of course talk about an observer who moves infinitesimally close to the speed of light in some reference frame, in which case time dilation becomes arbitrarily large.

Isn't one of the postulates of relativity say that all objects in constant motion can assume that it is at rest? Light travels at a constant speed all the time, so why would it not be included in the postulate? I wouldn't say time dilation would become large, that would be misleading. Say for instance you moved the gamma factor of the lorentz to the other side of the equation, you would in turn find that the amount of time the photon experiences is zero. It doesn't decay, and can travel an infinite distance, and the amount of time dilation experienced by other particles can show how long they will live and when they will decay, like the muon. I think the stability of the photon can show that it does not experience time.

 

[Nabeshin]

Isn't one of the postulates of relativity say that all objects in constant motion can assume that it is at rest? Light travels at a constant speed all the time, so why would it not be included in the postulate? I wouldn't say time dilation would become large, that would be misleading. Say for instance you moved the gamma factor of the lorentz to the other side of the equation, you would in turn find that the amount of time the photon experiences is zero. It doesn't decay, and can travel an infinite distance, and the amount of time dilation experienced by other particles can show how long they will live and when they will decay, like the muon. I think the stability of the photon can show that it does not experience time.

No, it is not a postulate of SR (or any relativity). If you take an object moving at a speed v(=! c), the theory tells you how to transform into a frame in which the object is at rest (a lorentz boost, in this case). But you can't boost into a frame with v=c. If you really must posit a frame of reference for the photon, it exists outside the set of all frames attainable through lorentz transformations (It's not in the lorentz group). At any rate, this puts it firmly outside special relativity.

Time dilation becoming large/small is, as you say, a matter of which side you put the gamma on, and precisely which interval it is you're discussing. My point is that the lorentz factor becomes arbitrarily large, but regardless of which side of the equation you put it on, it never gives an answer of zero (for any time interval).

The stability of the photon is another issue, one I must admit I'd never thought of. But this is something rooted in field theory, not pure relativity. Someone who knows more will comment on why a photon cannot decay into anything.

Edit: First link on google to a discussion a few years back here on PF re: photon decay: https://www.physicsforums.com/showthread.php?t=165262

 

[John232]

The fact that photons do not decay was a point I read in a book once. It mentioned that Einstein didn't believe in particle physics and when they had these issues they came to the conclusion that particles do not have a frame of reference so they no longer continued working on it this way. But with more recent discoveries in muon behaivor and particle decay, they have found that particles do act as though they experience different amounts of time. So I would say that you hold a more Einstein approuch but I think it is out of date. This is the only reason I know of that anyone would say why a photon doesn't decay. I don't think another explenantion exist. The reason why they say it is undefined at v=c is that gamma is in the denominator of the equation that would give a value of zero. If it was moved to the other side of the equation gamma would no longer be in the denominator. I never heard of a phyical law changing because of what side a value was on an equation. Every law could have a value put into a denominator that would give a value of zero. Another thing that postulate is from Galilean relativity, before Einstein used it. But, Einstein used the same concepts to form his theory. It states that all the fundamental laws of physics are the same in all inertial frames. I don't think anyone has proved him wrong yet...