If I were traveling at near the speed of light, would I be able to "think" normally?

If I were traveling at near the speed of light (enough to significantly slow time), would I be able to “think” normally? Would I be able to tell that time is slowing down?

Short Answer: As long as you were moving at a constant velocity, then nothing would appear “strange” to you. A key point of special relativity is that the laws of physics work the same in any (i.e. non-accelerating) inertial frame of reference. So yes, if you have a spaceship that is moving relative to a planet, then the clock on the spaceship would tick more slowly than a clock on the planet due to time dilation. But for the people on the spaceship, nothing would change, they would perceive time as passing normally.

Long Answer: One of the consequences of the fact that the speed of light must be equal in all frames of reference is that the very notion of simultaneity is relative. In other words, the idea that two distant events happen at the “same time” is not an absolute, but depends on our frame of reference. This is the key to understanding one of the apparent paradoxes of physics, namely the so-called twin paradox. In the most general terms, the “paradox” is that if you have two objects say A and B, which are moving relative to each other, then from the perspective of an observer on A, it is B that is moving, and hence time on B should run slower due to time dilation, but by the same token for an observer on B, it is the time on A that is moving more slowly. The fact that both perspectives are equally valid physically goes goes to the heart of special relativity and to the idea that there are no “privileged frames of reference.”

Let’s go back to the classical example of a person leaving the Earth on a spaceship and making a roundtrip and to the question of who would be older, a person on the ship or a person left on Earth. If the spacecraft is moving close to the speed of light, for an observer on Earth events on the spaceship would be unfolding in “slow motion” due to time dilation while life on Earth would continue at a normal pace. On the other hand, for a person on the spacecraft, it would appear as though things on on the ship would unravel at a normal pace, while it would be events on Earth that were happening more slowly! The resolution to this apparent contradiction is that once again, simultaneity is relative. It is not until the traveler would switch reference frames first by changing direction to return back to Earth and then again when stopping that a person on the spacecraft and a “stationary” observer on Earth could agree on the time. In that case they would find that it was the person on the spacecraft that would actually be younger than the one on Earth. Switching reference frames effectively creates discrete jumps in the apparent time.

How about if there was a video camera filming the people going near light speed?

So you have two scenarios:

• Camera is with the people going near light speed (as if they were taking a selfie). The camera will simply take a normal video of these people. Why? Because the camera is travelling at the same speed as these people, they are in the same reference frame, and light will bounce between the person and the camera eye at the speed of light.
• Somebody else is holding the camera and watching the people go by at near lightspeed: this camera will see the people moving slowly.

A constant and comfortable 1g acceleration will get you to 0.97c in two years. Not only would you continue thinking normally, but you’d find that journey times become drastically shortened.

Accelerating at 1g for half the journey and decelerating at 1g for the rest would get you to the Andromeda galaxy in less than 30 years subjective time – while more than two million years would have passed on Earth.

You would certainly notice relativistic effects, and you’d probably get cooked by Unruh radiation. But that aside, as a thought experiment there’s no reason why you wouldn’t be able to travel across a huge part of the visible universe in a constantly accelerating ship – although it would be ageing visibly around you as travelled.