Does time dilation automatically = super speed?

[Crossroads Inc.]

Ok, so to begin things, a Quick over view.
As well all know the faster you go, the more time distorts.
Eventually time "relatively speaking" becomes slower and slower.
But, does it follow the other way round?

Let us say you have a "Magic Stopwatch" that can slow time down when you use it.
And, for purposes of calculation, it will dilate time so that for every one Hour for the watch holder, will equal only one minute to the outside world.

If you use the watch, and then sit still for one hour... One minute passes for the rest of the world.
Obviously in that set up, you have travel no distance.
But...
What if you get in a car, and then activate the watch?
If you drive at a rate of 60miles and hour, travel for one hour, you move 60miles in what equates to one minute.
Calculating upwards, to the outside world you would be moving at a relative rate of 3600 mph!!

But... Does the relative speed effect the actual car?
Obviously if a car travelled at 3000+ mph, it would explode from Wind Resistance and friction.
Would such friction apply? or is even asking the question erroneous given a "magic" event like time dilation in the first place?

[Starglider]

To answer the question, more detail on the mechanism must be specified. For example, are you postulating a spherical field around the device that affects all particles inside a certain radius, or does it only affect matter 'in contact', or does it affect all particles inside the radius when the device is first activated. How is the kinetic energy and momentum of the particles altered etc.

[Feil]

As well all know the faster you go, the more time distorts.
Eventually time "relatively speaking" becomes slower and slower.
But, does it follow the other way round?

Yes, the math works both ways. For constant spacetime curvature,
t' = t*sqrt(1-v^2/c^2)
so
|v| =c*sqrt(1-(t'/t)^2)
If you had the ability to control the "time dilation" variable for an object (you) and you changed it to 1/60, you would cause the "relative velocity" variable of the object to increase to 0.9999c.

Likewise for constant velocity,
t'=t*sqrt(1-(2GM/r)/c^2)
so
M/r = (1/2G)c^2(1-(t'/t)^2)
If you had the ability to control the "time dilation" variable for an object (you) and you changed it to 1/60, you would cause the "distance to a supermass" variable of the object to increase to 6.7*10^26kg/m. A black hole the mass of the earth located in your belly button would do the trick.

Single Point of Departure answer: if you had a magic clock that dilated time, and didn't break any laws of physics, it would either create a supermass at your location or instantly accelerate you to near-c velocity, because space and time are the same thing and there's no way to change one without changing the other. Needless to say, both events would be instantly fatal for you and very bad for everyone else.

[Simon_Jester]

Let us say you have a "Magic Stopwatch" that can slow time down when you use it.
And, for purposes of calculation, it will dilate time so that for every one Hour for the watch holder, will equal only one minute to the outside world.

If you use the watch, and then sit still for one hour... One minute passes for the rest of the world.
Obviously in that set up, you have travel no distance.
But...
What if you get in a car, and then activate the watch?
If you drive at a rate of 60miles and hour, travel for one hour, you move 60miles in what equates to one minute.
Calculating upwards, to the outside world you would be moving at a relative rate of 3600 mph!!

But... Does the relative speed effect the actual car?
Obviously if a car travelled at 3000+ mph, it would explode from Wind Resistance and friction.
Would such friction apply? or is even asking the question erroneous given a "magic" event like time dilation in the first place?

Short answer:

The problem is that this is a magic stopwatch and has nothing to do with special relativity or the time dilation caused by special relativity.

[Incidentally, for purposes of special relativity, 3600 miles per hour is pretty close to "standing still." Interesting speeds in special relativity, that produce effects you could detect without very sensitive instruments, are measured in double digit percentages of the speed of light.]
______________________________

Long answer:

It depends on how the magic works. If all the magic does is somehow slow down time for you, but not for other objects your body interacts with, then you're unable to move objects out of your way. Breathing becomes difficult, or impossible, because extra air molecules aren't going into your mouth and nostrils fast enough to keep you supplied with oxygen. Air resistance becomes more and more noticeable.

Because this is magic, not real time dilation, there is a way around this. Consider this well-received scene from the movie Days of Future Past.

[youtube]https://www.youtube.com/watch?v=1NnyVc8r2SM[/youtube]

Quicksilver is a super-fast mutant and can act with incredible speed, which is how he's able to perform all the feats we see. Super-speed might logically have side effects, but we'll talk about those later.

However, we can imagine a person with magic time dilation power doing the same things, in a similar way. The catch is that to do the things Quicksilver does, his time dilation magic would have to magically affect things that he touches, but not things he doesn't touch. And to affect them only in the ways that he desires, not in other ways.

For instance, if Quicksilver wants to manipulate a guard's arm so that he hilariously punches himself in the face, he can, because he's fast and other people move at the Speed of Molasses compared to him.

But imagine if Time Dilation Man tries to do that, and touches the guard. He wants only the guard's arm to be time-accelerated, so he can manipulate it, without the rest of the guard being pulled into his time-acceleration effect. Because that would result in an ass-kicking for Time Dilation Man. But at the same time, he doesn't want there to be some kind of interface at the guard's shoulder between time-accelerated and non-accelerated flesh, because that would probably result in the guard's arm getting torn off or an outbreak of gangrene or something horrible.

Likewise, if Time Dilation Man wants to push bullets away from his friend's face, he can, but he wants to be able to touch the bullets as they crawl through the air, without them suddenly speeding up along with him as he touches them (in which case they'd be as fast to him as bullets are to a normal person, and all he'd have accomplished is making his friend get shot faster.

Now, Quicksilver as portrayed doesn't seem to have this problem, because he just moves faster than everything around him.

...

There are still other issues shared by both super-speed and time dilation. As noted above, either way you have a problem because the air is slow to move out of your way, and slow to move into your lungs, so that your movements become more and more labored and difficult, well before you reach "burn up on reentry" speeds of Mach 2.5 to Mach 3.

Almost by definition, Mach 1 is when you're moving so fast that air molecules don't have time to get out of your way at their natural pace, so unless your time compression or speed powers are affecting the air immediately around your body, you're going to be effectively unable to move at those speeds. Supersonic aircraft can do it- but they do it by having very specific, carefully designed aerodynamic shapes, which the human body doesn't. Things that aren't so aerodynamic just run into exponentially increasing amounts of air resistance until the sheer forces involved tear them apart, which is what happened to poorly designed aircraft that tried to break "the sound barrier" in the 1940s.

And if your power DOES somehow affect the stuff around you, not just your own body... you run back into the problem of being able to speed up only things you want to interact with, and only in the ways you want them to speed up.

Quicksilver's super-speed power seems to basically ignore this problem, acting in the "speed up things I touch, if I want them to speed up, but only if I want them to" way.

But then, this is magic we're talking about, not physics. So it isn't constrained by things like internal consistency.