# Weight vs time

1. Oct 22, 2006

if you could freeze time, and you could walk around, you know like that guy from the show heroes, and say you wanted to pick up an airplane, could you do it? i mean, wouldnt frozen time mean weightlessness?

2. Oct 22, 2006

### JesseM

Last edited: Oct 22, 2006
3. Oct 22, 2006

but if F=ma then wouldnt a=0 and so therefore everything will be weightless?

Last edited: Oct 22, 2006
4. Oct 22, 2006

### JesseM

Again, I don't think it's meaningful to imagine infinitely fast movement (especially not if you take relativity into account), but you can imagine all your movements being sped up by any finite factor, from twice as fast to a million times as fast. In this case, as seen by normal un-sped-up observers (whose time coordinate you're assumed to be using when you write physical equations like F=ma), the velocity of all your movements would increase by whatever the speedup factor was...so since acceleration is change in velocity over time, does that mean the acceleration would increase by the speedup factor squared? Now I'm confused. Ok, for the sake of the argument let's say that an un-sped-up observer's arm muscle contraction would accelerate his hand according to a function like x(t) = (a/2)*t^2 during the period of the contraction, in which case the velocity of his hand would be given by v(t) = a*t and the acceleration of his hand would be a constant a(t) = a. This means, for example, that if his hand is at x=0 with v=0 at t=0, and the twitch lasts for 1 second, then at the end of the twitch his hand would be at position x=(a/2) and the velocity of his hand would be a. If we speed this up by a factor of 5, then the function would be x(t) = (a/2)*(5t)^2 (meaning that since the twitch now lasts only 1/5 of a second, at the end of the twitch his hand would again be at x=(a/2)). So in this case, the velocity as a function of time would be v(t) = 25a*t (so when the twitch ends after 1/5 of a second, the velocity of his hand would be 5a), and the acceleration would be a constant 25a. So yes, it seems that the force a given muscle contraction would apply would increase as the square of the speedup factor, meaning that from your perspective it'd be as if the inertia of objects around you had decreased by the square of the speedup factor.

Last edited: Oct 22, 2006
5. Oct 23, 2006

### TDS

I am confussed?

Would one you fine folks please explain to this layman how the way that Time is monitored and the Weight of an object are related. Where in General Relativity or Special Relativity is this discussed?:uhh:

6. Oct 23, 2006

### DaveC426913

He's talking about inertia. I think what he's trying to grasp is this:

If you had one of those watch-thingies that stopped time (bing! fantasy - no science here, move to GD), and tried to save someone about to be hit by a truck, by picking them up and moving them, there would be a paradox.

From the hapless victim's PoV, they would have instantly moved ten feet.

Or would they?

Would it not be more like something shoved her so hard, she was pushed ten feet almost instantly? From the victim's PoV, she was just hit by a human moving at very high speed. She'd suffer broken bones.

There's more thinking to this. Consider the effect it would have to non-rigid components like her hair, her purse or her necklace. Are they frozen? Or do they swing? When he picks her up, does she act like a statue?

My take on the matter is that the rescuer would experience the victim as if she weighed a ton. She would be VERY difficult to move, and once moving, very difficult to stop. Also, my take on the matter is that stopping time would be impossible (since all mass would be inifinite, inclduing the air molecules), the best you could hope to acheive is slowing time. If you slowed it by 100x, then the victim would appear to have a mass of 12,000lbs.

Last edited: Oct 23, 2006
7. Oct 23, 2006

### TDS

@DaveC426913

To paraphrase the original question, if time was reduced to 0 would the weight of an object also be reduced to 0?

As for your response. We have all seen it in the movies & TV shows and you have describe it perfectly. But how does this answer the original question?

If I had the little "watch-thingy" that you mentioned, and I saw a person or a thing that weighed 50 lbs that is about to be hit by a moving object and I activated the "watch-thingy" and all movement stopped except for me. I walk to the 50 lb object and picked it up and moved it out of the way, I would notice the weight of the object being what I said it was. Time has no bearing on the weight of the object. At least in my opinion anyway.

In response to your paradox, she should respond like a mannequin that can be posed in any position that you want. When the device has been turned off, the only thing that she would be aware of is that she has moved from where she was to where she is but not having a clue as to how she got there. Also, if you are the one that has control of the "watch-thingy", why would you need to run if everything around you has stopped moving? You would literally have all the time in the world, and that would eliminate the damage that you have spoken of.

8. Oct 23, 2006

### JesseM

I think the best way to analyze the "slowing time" situation is from the perspective of someone in normal time, since it is their definition of time-intervals that is assumed when you write down equations for the laws of physics, and I'm assuming that it is only the rate of perception and the movements of the person which have sped up, the laws of physics governing his body haven't changed. Do you agree that from a normal person's perspectives, if all the movements of the guy were sped up by a factor of N, and his mass remained unchanged, then the force he would apply with a given movement would increase by a factor of N^2? So by speeding him up enough (again, as seen by normal un-sped-up bystanders), he could easily move huge objects with movements of his body whose normal-speed analogue would not provide nearly enough force to move those objects?

9. Oct 23, 2006

### DaveC426913

I postulate that there is no plausible way time could be "reduced to zero"; that "arbitrarily close to zero" is the best you can hope for.

Not weight, inertia. (The experiment works perfectly fine in deep space, where the object has no weight.)

And realize, we are not talking about an actual amount, as it were, so much as we are talking about a human perception - which is affected by time.

If I push on an object (on a frictionless surface) with all my might for one minute, and I barely start it moving, then for all intents and purposes, that object is perceived as having a very large mass/inertia.

10. Oct 23, 2006

### MeJennifer

I understand that this is an hypothetical question but even then it does not make any sense. It is simply impossible to freeze local time.

Local time always goes at the same speed.

The closest thing to "frozen time" is when you make remote measurements of strong gravitational fields or objects in fast relative motion. For these situations it appears that time goes slower than locally.

11. Oct 23, 2006

### TDS

Okay. Everybody that has reponded to Quadruple Bypass's question has handled the Time issue expertly but the second part of the question is still pending. Even if you were able to get time "arbitrarily close to zero"; would it affect the weight of an object on this planet? Could an idividual do what has been described in the original question posed by Quadruple Bypass? I say no.

12. Oct 23, 2006

### JesseM

Well, if all your movements were sped up by a factor of N, then your initial upwards velocity when jumping should increase by a factor of N as well, so you'd go a lot higher...in general, if you jump upwards with initial velocity $$v_0$$, your initial kinetic energy is $$(1/2)mv_0^2$$, and your potential energy as you go upwards is given by mhg, with $$mhg = (1/2)mv_0^2$$ at maximum height, giving a height of $$h = (1/2g)v_0^2$$. So, if you increase $$v_0$$ by N then h will increase by N^2, meaning height you are able to jump also increases by the square of the speedup factor. And note that this equations says that if you went to a planet where the gravitational acceleration g was decreased by a factor of N^2, this would also increase the height you could jump by a factor of N^2.

Likewise, if you increase your rate of perception by a factor of N it obviously takes a falling object N times as long to fall the same distance...so we might ask, is it also true that if you go to a planet where the gravitational acceleration is decreased by a factor of N^2, while your rate of perception remains unchanged, then on this planet it takes a falling object N times as long to fall a given distance? Well, if an object is falling with acceleration g from a state of rest, its velocity as a function of time is v(t) = gt and its position (measured downward from its starting points) as a function of time is x(t) = (g/2)*t^2, so if you decrease g by factor of N^2, you must indeed increase t by a factor of N in order for the object to fall the same distance x. So, it seems like an observer whose perceptions are sped up by a factor of N will see gravitational phenomena work exactly the same way as if he had not been sped up but if gravity had decreased by a factor of N^2 (this is ignoring changes unrelated to gravity, like the apparent decrease in inertial mass of objects around the sped-up observer that I discussed earlier).

13. Oct 23, 2006

### TDS

@JesseM,

Is the term "inertial mass of objects" the same as saying the "weight" of an object?

14. Oct 23, 2006

### gijeqkeij

Well "freeze time" is a) not well defined, b) impossible to test... so the answer can be "yes" or "no" and you can't verify if is right or not. So no dense.

gijeqkeij

15. Oct 23, 2006

### JesseM

No, inertial mass is the same regardless of gravity, you could define it in terms of the force it takes to accelerate the object a given amount (it would still take more force to accelerate a more massive object than a less massive one in zero-G, for example). Weight could be defined in terms of the reading on a scale that the object is sitting on, which depends on the gravitational force pulling down on the object.

16. Oct 23, 2006

### TDS

@JesseM,

Thanks for clearing that up for me!

17. Oct 23, 2006

### myoho.renge.kyo

for what interval of time are you going to keep time frozen?

you cannot freeze time and walk around. how many swings of your arm did it take for you to walk from one point to another?

the non-existence of time means the non-existence of all things.

there is no way that we can experience the non-existence of all things. as an analogy, there is no way that those who believe in God can experience God. the best they have is a holy interval of time (a sign between God and them).

Last edited: Oct 23, 2006
18. Oct 23, 2006

### Staff: Mentor

I don't know that this is a useful question, but I'd just like to point out that you have to be careful to differentiate between weight and mass (which it seems a lot of people are not doing). Ie, if you encountered a 1kg mass in a gravitational field 1000 times earth's, you wouldn't be able to lift it, but you'd still be able to push it laterally exactly as if you were on earth (minus friction, of course).

So being able to lift something and being able to move something are not the same question/issue. So if what you are fiddling with affects acceleration, that's inertia (mass) you're talking about. If it affects gravitation, that's weight. And in fantasy situations, the two don't necessarily need to be related.

Last edited: Oct 23, 2006
19. Oct 23, 2006

### JesseM

I agree with you about the importance of differentiating these issues, but I think if your perceptions and movements were sped up by a factor of N, then for you it would be as if the inertial mass of objects around you decreased by N^2 and as if the strength of the gravitational field had decreased by N^2 as well--see my earlier posts #4 and #12 for separate discussions of these two issues. (edit: Actually, if you decrease both the inertial mass m of an object and the strength of gravitational field g by N^2, I guess that would mean the weight of objects would decrease by N^4, since the gravitational force is proportional to mg...does this mean it would be even easier for the sped-up-guy to lift things than to move them sideways? Equivalently, if you were trying to move a 3-kg object on a planet with 1/10 the gravity of Earth, would it be ten times as easy to move it sideways as it would be to move a 30-kg object sideways in Earth's gravity, but one hundred times as easy to move it upwards as it would be to move a 30-kg object upwards in Earth's gravity? That can't be right, because even in zero-G it should be just as hard to move something "upwards" as it is to move it "sideways", because of inertial mass. I guess I would need to define what I meany by "easy to move", maybe in terms of the amount of force you'd need to apply in a given time-interval to accelerate it by a given amount in that time...in this case the "easiness" of moving something upwards is not just proportional to its weight, I think the force needed to accelerate something upwards would just be equal to the force needed in zero-G plus its weight in the gravitational field you're in, in which case the sped-up-guy would still always find it harder to lift things than move them sideways, but the amount of extra difficulty in lifting things up as opposed to moving them sideways would decrease by N^4, while the total difficulty in moving them sideways would decrease by N^2.)

Of course there is also the issue that everything around you would appear much more "fragile" to you, since it would be easier for you to tear apart/pulverize/vaporize objects with your hands (although unless the material properties of your body were changed to correspond to the factor you were sped up by, your movements would more easily tear apart/pulverize/vaporize your own hands and body as well), but I don't know enough about materials science to do a quantitative analysis of this.

Last edited: Oct 23, 2006
20. Oct 23, 2006