“Because time compresses as a result of traveling > 0? Does it in fact go to 0 at c?”
Yes, at c, time dilation is infinite. However, the time dilation and length contraction are just expressions of the same phenomenon. So, you can say that the photon sees no time passing between leaving and arriving. Or, you can say that, to the photon, the outside world is flattened to 2 dimensions, perpendicular to the direction it is traveling. From that perspective, the photon traveling instantly is a given, since there exists no distance between any two points along the axis it is traveling.
“So what’s to say that in the instant the photon knew it was traveling some vast distance it raised its hand and waved. Would you not observe the hand wave at the fraction of the instant amidst the distance traveled?”
I think the problem with that is that the photon would never have any opportunity to wave at you. It can’t be aware of anything while it is moving at c, since time is basically frozen.
The way I like to look at it is to imagine that time really is a “fourth dimension” we can’t see. The rule seems to be that the total velocity of anything in ALL directions can’t exceed c, include your velocity through time. When you are at rest, you must be moving near the speed of light, but only in the direction of the time axis. When you start accelerating in the other directions, you must slow down in the direction of time, in order to stay under the maximum total velocity. If you reach the maximum velocity in any other direction, then your velocity through time must stop.
Now, the upshot of looking at things like that is you realize that, just like the physical direction the photon is traveling gets compressed to a single plane, it stands to reason that, if we are normally moving close to c in the time direction, then our perception of time would be very narrow too, because that dimension is compressed from our perspective. And that is exactly what we perceive, since we can only “see” a single moment, or point of time, and can’t look ahead or behind us.
“This is the result of not being able to propel something behind you at c+1 in order to fully reach c. Thus I believe it’s not impossible to go faster than c, it’s simply that we haven’t figured out a way to do it yet.”
Well, that’s a physical impediment but it’s not the root cause. Even if we used another system, like magnetic acceleration, we still couldn’t reach c, because matter just can’t achieve that velocity, only energy can. Even something with a very small mass, like an electron, just can’t reach c, no matter how energetic it gets.
“If you could harness the vacuum of space in front of your vehicle in order to pull yourself ahead, since space is always in front of you, this I believe would allow you to exceed c.”
I haven’t heard of that, but it sounds almost like a “warp drive”, which I think is the only feasible way, besides maybe wormholes, that we could travel faster than light. But, in either of those cases, we would never actually achieve the velocity of light, we’d just be shortening our distance of travel.
Thank you for the lengthy response; I like discussing and doing the mental exercises that topics like this require.
However, your explanation (and to date, the argument of those in the field) is based around the premise that “at c, time dilation is infinite”.
While this is shown mathematically, I can’t see how this makes sense in reality (which as you eluded to is a 2-dimensional view of the universe but wow let’s not go there today).
As far as I’m aware this premise can’t be proven empirically, so we’re left with the math - at which point I kinda wave my hands and step away. One because the math is beyond me, but also because they’ve discovered time and again that the math is incomplete at best and entirely misguided at worst.