Posted: Mon Dec 03, 2007 8:14 pm Post subject: Hiro and Inertia
So, let's say Hiro is on a plane that is going down. If he stops time just prior to impact, opens the emergency door, unloads everyone to a safe distance away and then restarts time, are those people still falling at a terminal velocity and feel the same impact they would in the plane now on the ground where they are sitting, or does that go away? Also, let's say Hiro is falling out of a plane and teleports himself to the ground; does he continue to carry that same speed, or does it go away?
Sorry, my flight was delayed about 2.5 hours yesterday and it gave me a lot of time to sit and think.
considering he moved from Japan to New York... which would have nearly opposite radial velocities... and he went from standing still to standing still..
Inertia and conservation of momentum do not apply.
considering he moved from Japan to New York... which would have nearly opposite radial velocities... and he went from standing still to standing still..
Only in relation to the center of the Earth, not to Hiro. His velocity (if standing still) would be zero. The rotational speed of the Earth is the same in Japan as it is in New York.
I think back to the start of season 2 when Hiro is flung backwards when he appears in feudal Japan, the byproduct of his being thrown by Sylar prior to his teleportation. It seems teleportation and straight-up time travel would be more consistent with a conservation of inertia, but what about the stopping and restarting of time?
rotational speed isn't identical...
1) velocity is a vector with a directional component. Japan say in the evening has a velocity away from the sun, New York at the same time (morning) has its velocity towards the sun.
2) I'm not sure of the exact latitude of each city, but the closer to the equator the greater to scale of the vector, would also come into play.
3) season. Only at the equinox would both vectors be parallel in the solar plane. Summer would incline the Japan vector and decline the New York one.
Time is part of the fundamental forces of the universe. It beats -- hands down -- INERTIA, anytime Hiro uses it.
So in your scenario, he can do what he has to do, and not worry about physical effects. Time "tramps" inertia.
Right. So, when time is stopped, inertia does not come into play, as t=0. There is no gravity, no velocity, no acceleration. However, when he restarts time, all those things go back into play, and the acceleration, velocity and momentum that were in play prior to his stopping time are back. Since time stopped and then restarted, they never really went away.
For example, if someone shot a gun and Hiro stopped time, the bullet would be frozen in space, as there is no gravy (gravity is an acceleration, which depends on time, squared) and no horizontal velocity (again, time dependent). If Hiro restarts time, the bullet will continue as it had gone prior to his stopping time. What if he moved the bullet 2 inches lower and then restarted time? Would the bullet simply fall, or would it continue on it's previous trajectory, only 2 inches lower? The way you explain it, the bullet would fall, as Hiro's manipulating it destroyed it of it's horizontal velocity. I'd argue the bullet would continue on its previous path only 2 inches lower, as when time is restarted it will pick up both velocities where they left off.
Therefore, I think the inertia/momentum of people saved from a crashing plane will still carry them into the ground at whatever velocity they had prior to his removing them from the plane.
If he "unloads" the plane, as you termed it, then in his plane (or frame) of reference those people are stopped. Let's say he stops the plane 5 feet before it hits the ground. That gives him the ability to get them out of the plane and to safe distance while time is frozen.
Now, after every passenger has been removed and time is restarted, that doesn't mean that those passengers have re-acquired the momentum of the plane when it was falling. He basically moved them from the airplane's frame of reference to Hiro's frame of reference. So, the airplane, WITH ALL OF IT'S original momentum SMUCKS into the ground exploding and doing all sorts of fireballs and what have you damage. But, no one is on board. And none of those people have that momentum.
Does that make sense?
Same with the bullet!
IF Hiro was to push the bullet, while it is frozen in time, it no longer responds just to forces imparted on it by it's original frame (or plane) of reference, but also by Hiro's new (HIGHER) frame of reference. His frame of reference which adds the dimension of time, therefore TRAMPS any INERTIA that original frame of reference might have imparted on the system.
rotational speed isn't identical...
1) velocity is a vector with a directional component. Japan say in the evening has a velocity away from the sun, New York at the same time (morning) has its velocity towards the sun.
2) I'm not sure of the exact latitude of each city, but the closer to the equator the greater to scale of the vector, would also come into play.
3) season. Only at the equinox would both vectors be parallel in the solar plane. Summer would incline the Japan vector and decline the New York one.
But the vector of origin isn't the sun, it is the core of the Earth. I'd say Tokyo and New York are both under 100 ft in elevation. That means, their vector from the center of the earth is nearly identical. The rotational speed of the Earth is constant no matter where you stand. The Earth is a sphere, so the vector from the core to each city would be the same.
If you are talking about Kelper's 2nd law of planetary motion and talking about his velocity in relation to the universe, the vector from the sun to the planet goes to the planet's center to explain velocities. The difference between the speed on one side of the planet as compared to the other is negligible in such a large system. In fact, Newton's law of gravitation says that "every object in the universe attracts every other object along a line of the centers of the objects, proportional to each object's mass, and inversely proportional to the square of the distance between the objects," again suggesting the velocity at the surface is negligible.
If he "unloads" the plane, as you termed it, then in his plane (or frame) of reference those people are stopped. Let's say he stops the plane 5 feet before it hits the ground. That gives him the ability to get them out of the plane and to safe distance while time is frozen.
Now, after every passenger has been removed and time is restarted, that doesn't mean that those passengers have re-acquired the momentum of the plane when it was falling. He basically moved them from the airplane's frame of reference to Hiro's frame of reference. So, the airplane, WITH ALL OF IT'S original momentum SMUCKS into the ground exploding and doing all sorts of fireballs and what have you damage. But, no one is on board. And none of those people have that momentum.
Does that make sense?
Same with the bullet!
IF Hiro was to push the bullet, while it is frozen in time, it no longer responds just to forces imparted on it by it's original frame (or plane) of reference, but also by Hiro's new (HIGHER) frame of reference. His frame of reference which adds the dimension of time, therefore TRAMPS any INERTIA that original frame of reference might have imparted on the system.
So what would the bullet do? Would it fall or would it continue on? If you say it would continue on, then so would those people in the plane, even if they were removed, as they had a velocity (that of the plane) prior to his moving them. I don't think he has imparted a new vector into the equation, because his t=0, so there is no velocity, it is just a change in position. When time restarts, the velocity starts and the people still have the same velocity towards the Earth that they had while in the plane.
Sami-
I have no idea what would happen if he turned the bullet. I'd be inclined to say it would continue in the original direction, as it would have a velocity vector pointing it that way and I feel that is independent of which end is front and which is back (I'm basing this solely on the fact that the old, round lead bullets used to spin while in flight, yet kept the same horizontal velocity vector). Good question!
The rotational speed of the Earth is constant no matter where you stand.
incorrect. the rotational speed at the poles is zero, at the equator its max ~= 1000 miles/hour and varies as you travel between.
but your point about universal frame is well made vs. the solar system frame.
oh and as per what the bullet would do... I think Hiro is allowed to choose if he "resets" the object to his frame or lets it retain it's own when he unfreezes time.
incorrect. the rotational speed at the poles is zero, at the equator its max ~= 1000 miles/hour and varies as you travel between.
Dang it, I confused myself by trying to debate on two different fronts. You are absolutely correct; in polar coordinate velocities, the rotational speed at the poles is zero. In relation to rotation around the sun, though, they are (basically) the same anywhere on the planet.
At any rate, Tokyo is about 35 degrees S lat and NYC is about 40 degrees N lat. I can't do the math in my head so I don't know how different they would be, but it seems it should be enough to make him at least stumble when he arrived in NYC.
If he "unloads" the plane, as you termed it, then in his plane (or frame) of reference those people are stopped. Let's say he stops the plane 5 feet before it hits the ground. That gives him the ability to get them out of the plane and to safe distance while time is frozen.
Now, after every passenger has been removed and time is restarted, that doesn't mean that those passengers have re-acquired the momentum of the plane when it was falling. He basically moved them from the airplane's frame of reference to Hiro's frame of reference. So, the airplane, WITH ALL OF IT'S original momentum SMUCKS into the ground exploding and doing all sorts of fireballs and what have you damage. But, no one is on board. And none of those people have that momentum.
Does that make sense?
Same with the bullet!
IF Hiro was to push the bullet, while it is frozen in time, it no longer responds just to forces imparted on it by it's original frame (or plane) of reference, but also by Hiro's new (HIGHER) frame of reference. His frame of reference which adds the dimension of time, therefore TRAMPS any INERTIA that original frame of reference might have imparted on the system.
So what would the bullet do? Would it fall or would it continue on? If you say it would continue on, then so would those people in the plane, even if they were removed, as they had a velocity (that of the plane) prior to his moving them. I don't think he has imparted a new vector into the equation, because his t=0, so there is no velocity, it is just a change in position. When time restarts, the velocity starts and the people still have the same velocity towards the Earth that they had while in the plane.
Sami-
I have no idea what would happen if he turned the bullet. I'd be inclined to say it would continue in the original direction, as it would have a velocity vector pointing it that way and I feel that is independent of which end is front and which is back (I'm basing this solely on the fact that the old, round lead bullets used to spin while in flight, yet kept the same horizontal velocity vector). Good question!
Ok, here's the point I was trying to make without listing mind-numbing equations:
Hiro is what Special Relativity and Relational Quantum Mechanics calls a "Privileged Observer". That means that his "Frame of reference" is always "superior" to what he's observing/changing when he stops time.
So, yes, the bullet will respond/act according to the momentum he imparts on it.
And yes, the passengers will have ZERO VELOCITY when he removes them from the plane. Now, does that mean there is no penalty? Nay! There are massive amounts of energy expenditure involved. That's why no one has figured out how to do it yet! So, all the energy that Hiro is expanding with his Time Jumps all over the place are causing some sort of energy to do something somewhere else across the Universe.
AND.... if you want to get metaphysical about it, Quantum Mechanics says that there are a series of Observers, SO, does that mean there is an all encompassing entity watching our Universe (our whole existence) from outside our Universe?
I think it's safe to say that once he interferes with an object, its prior inertia is moot
But yes, I did wander for a while, ever since he teleported in S1 to save himself from Sylar's throw. I know he fell when he appeared in ancient Japan, but I think he just messed up his re-entry.
He touched the arrows that were headed for what he thought was Takezo Kensei, and afterwards they embedded themselves in the ground just like the ones he didn't touch. I know that the writers have not quite thought about it like this, so what happens in the show is not a great indicator, but it is true that we have seen it both ways on the show. Also, other heroes are able to (probably) just pull tons of energy out of nowhere like TK, Electro K, Radio K, Pyro K, etc. The law of conservation of energy is not really applied. About Hiro's time traveling: he can't really just say,"this very same place, five years in the future, go!" because the entire universe has shifted in that time, as in revolution of cities around earth around sun around galaxy, and expansion of space. Even if he is able to get the time right (because the space-time continuum doesn't know what a year is) he would land in the vacuum of space, or if he is extremely lucky land on a planet with 70 degree temperatures , a breathable atmosphere, and a surface to stand on (near impossible, I know.) He must have some sort of crazy accurate subconscious homing system or something.
