|MadSci Network: Physics|
Greetings, James: I have not seen that movie, and so don't know what the movie-rationale is, that supposedly would allow such Watches to exist. But I grew up on a diet of science fiction, and so the notion does not bother me, at least with respect to superficial willingness-to-suspend-disbelief. So, suppose we accept the face-value notion that Time itself is being modified for the Watchholders, and consider the consequences.... OK, if the rate at which Time passes is increased 100 times while someone is using a special Watch, then if that person keeps the Watch activated for an entire ordinary 24-hour day (as far as the rest of us are concerned), then that person would have to obtain 300 meals and sleep 100 times during that day, and would grow about 3 months (100 days) older. The trade-off, of course, is supposed to be the ability to move and do things undetectably fast. To some extent, the Physics seems reasonable (granting the existence of a special Watch, of course). For example, consider the ability to move your own arm. It possesses some mass, and to move it you must cause it to accelerate, which takes force. If you want to move it faster then you must accelerate it more intensely, and this takes rather more force. However, if you are living 100 times faster than normal, then the energy of 300 meals-per-day is available to "pay" for such efforts. It even seems reasonable to think that that energy is also available for moving other things, outside yourself. Also, since the human eye ordinarily takes about 24 images per second, if you could move across someone's viewpoint 100 times faster than normal ("between visual snapshots"), you could indeed manage to seem invisible. That is, average walking speed is about 5km/hr, so if you live 100 times faster than normal, you will be walking at 500km/hr! This is not invisibly fast, but someone WOULD have to know where to look, to see you coming! Is this not what you were Asking about? But now the nitty-gritty details start to get in the way. To STAY invisible, you have to KEEP moving. Holding still for any significant fraction of a second means that somebody will be able to see you, even if only momentarily. And, does an increase in the rate of the passage of Time affect the strength of the bones in your arm? If not, and you accelerate too fast, your own muscles could snap those bones! (Their mass is associated with "inertia", which is a kind of resistance to acceleration.) And if your own bones are actually OK, the bones of other people, whom you tried to move around, would not be OK. Then there is the matter of keeping cool: If you are burning calories at a rate of 300 meals per day, the ordinary processes of cooling airflow may prove to be inadequate, and your body will roast itself from the inside out. Finally, what about air-resistance? If you are walking along at 500km/hr, maybe you WILL be able to keep cool! But what about that WHOOOSHing sound, which doesn't help you stay unnoticed? Worse -- there is something like a Law to the effect that the amount of power it takes to double a velocity, against air resistance, goes up by 8 times. That is, suppose instead of walking 100 times faster than normal, you decided to walk only 64 times faster than normal, which is 6 doublings (2x2x2x2x2x2=64) of the normal rate (320km/hr is 64*5km/hr). The amount of effort it takes to go that fast should be something like 8x8x8x8x8x8=262,144 times the normal amount -- but your 300 meals per day is only yielding 100 times the normal amount of energy! (Even if I assumed that that Air Resistance Law only kicked in above some initial velocity, and ignored two of those 8s, well, 8x8x8x8=4096, and that is still about 41 times more effort than you have available, from eating 300 meals per day.) You will feel like you are trying to move through soup.... The preceding should more accurately answer your Question about what happens when interacting with the ordinary world, while living in the really-fast lane. ----------------------------- P.S. As it happens, there is an alternative trick that could accomplish many of the same effects as a Time-rate-modifying Watch. The science-fictional device needed for this trick is known as an "inertia damper", which if it could exist, and exist in compact form, might well be disguised as Watch. The thing that an inertia damper would do is lessen the resistance-to-acceleration of the things that it influences. That is, those bones in your arms would have the same mass and strength as normal, but their effective inertia might be reduced by 100 times, so that they could be accelerated AS IF they suddenly had only 1/100 their normal mass. Ordinary effort would yield 100 times the acceleration, just as if Time was passing 100 times faster! But there is no danger of bones breaking, because only ordinary forces are involved in accomplishing those accelerations. If an inertia damper affected your surroundings in a spherical way, say a little more than a meter all around the Watch (which you keep in a pants pocket), then the air you move through would likewise be influenced, and walking 500 km/hr would be no problem at all (even the WHOOSH may be subdued!). When you grab someone's arm, that arm is now within the influence inertia damper, so you can move it fast, and not break it in the process. All, in all, I think I'd rather have one of these.
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