portal question/weirdness/random wondering

[Tomlidich]

so i had this idea a while back while playing portal. lets ignore all the physics behind the portals themselves, and just go with the newtonian ones.

lets say you have a bowling ball, and two portals, one on the ceiling, and one on the floor. the floor and the ceiling are exactly level with each other and the earths gravity. it is a closed room, so there are no winds or fans.

you drop the bowling ball exactly in the middle of the bottom portal. naturally, it goes into infinite loop at this point.

now here is the weird bit: you leave it there.

it continually picks up speed. normally a falling object would hit terminal velocity, but the bowling ball is now drafting itself, breaking the wind friction.

eventually it attains a small column around itself of perfect vacuum due to the amount of speed it has achieved.
within this vacuum the ball cannot break up due to wind friction heating it up.

at some point, it gains enough speed to fall within the theory of relativity, transporting the ball to a time when the portal was not on the floor. due to its immense speed, it smashes a crater in the floor. of course, this prevents a portal from being there, causing a paradox because it could not attain that high speed without the portal being there.

now, i know this can be a little hard to folow, and my logic is probably insane, but what do you guys think?
also, would said paradox destroy space time?

[gmalivuk]

at some point, it gains enough speed to fall within the theory of relativity, transporting the ball to a time when the portal was not on the floor.

No, this will never happen, because traveling at relativistic speeds is not the same as traveling back in time.

[Tomlidich]

at some point, it gains enough speed to fall within the theory of relativity, transporting the ball to a time when the portal was not on the floor.

No, this will never happen, because traveling at relativistic speeds is not the same as traveling back in time.

aha ok.

i knew there had to be a flaw in there somewhere.

i personally only have a rough knowledge of these things soo

[idobox]

Also the fact that the portals seem to create energy (the kinetic energy given to the ball comes form?), makes it easy to get absurd results.

[AvatarIII]

i do wonder, personally, what stops an object from surpassing the speed of light if the force supplying acceleration is gravity for example,

on earth an object will accelerate at 9.81ms^-2, now in normal circumstances, the exertion of gravity wouldn't have effects on an object for long enough to build up relativistic speeds, but in the portal scenario it would have infinite time.
i was under the impression that things could not accelerate above the speed of light because whilst within the time frame of an object it would be accelerating constantly, from an outside time frame it would be reducing in acceleration due to relativistic effects, but if the cause of the acceleration was not under these effects, would the bowling ball constantly feel 9.81ms^-2, or would earth gravity in the normal time frame continue to accelerate the ball at 9.81ms^-2?

[gmalivuk]

It's pointless to wonder about what relativity says in a magical system where we have a constant infinite gravitational field.

[Izawwlgood]

This is sort of a useless comment given I can't remember the name of the webcomic, but I recall a gag wherein the protagonists stumble across a hole in the ground, and when they drop something into it (a shovel, I think?) it falls from the sky and back into the hole. It gains speed until it's basically just a giant beam of light, which vaporizes the hand of one of the protagonists (they were kind of dumb) when he touches it. Then some other weird stuff happens.

The comic was about two guys who wake up in a world devoid of any reference frames or stuff, and then gradually go on a rather non-sequitor adventure.

[AvatarIII]

It's pointless to wonder about what relativity says in a magical system where we have a constant infinite gravitational field.

True I suppose, but we are in the fictional science area, so there's no harm in speculation.

[Soralin]

i do wonder, personally, what stops an object from surpassing the speed of light if the force supplying acceleration is gravity for example,

on earth an object will accelerate at 9.81ms^-2, now in normal circumstances, the exertion of gravity wouldn't have effects on an object for long enough to build up relativistic speeds, but in the portal scenario it would have infinite time.
i was under the impression that things could not accelerate above the speed of light because whilst within the time frame of an object it would be accelerating constantly, from an outside time frame it would be reducing in acceleration due to relativistic effects, but if the cause of the acceleration was not under these effects, would the bowling ball constantly feel 9.81ms^-2, or would earth gravity in the normal time frame continue to accelerate the ball at 9.81ms^-2?

Well one main thing that stops it is that 1 + 1 =/= 2. At least when it comes to velocities. Velocities don't actually add together linearly, see: http://en.wikipedia.org/wiki/Velocity-addition_formula

So, the actual way velocities add is like so: s = (v+u)/(1+ vu/c²) (if you have velocities in terms of c=1, it simply becomes (v+u)/(1+ v*u)). So if you're moving at 0.8c away from me, and someone is moving at 0.8c away from you in the same direction, that person is moving away from me at 0.9756c The same holds true for lower velocities as well, just adding the two numbers together is only an approximation, although a pretty good approximation for low differences in velocity.

So yes, you can keep adding 9.81m/s every second, but you can't just sum the two velocities together, reality is an unusual place, and doesn't actually work like that.

[PM 2Ring]

We can use the Relativistic Rocket equations on this problem.

First of all we need to be clear what we mean by continuous acceleration at 1g. The acceleration of the rocket must be measured at any given instant in a non-accelerating frame of reference travelling at the same instantaneous speed as the rocket (see relativity FAQ on accelerating clocks).
This acceleration will be denoted by a.
The proper time as measured by the crew of the rocket (i.e. how much they age) will be denoted by T, and the time as measured in the non-accelerating frame of reference in which they started (e.g. Earth) will be denoted by t. We assume that the stars are essentially at rest in this frame.
The distance covered as measured in this frame of reference will be denoted by d and the final speed v.
The time dilation or length contraction factor at any instant is the gamma factor γ.

The relativistic equations for a rocket with constant positive acceleration a > 0 are the following. First, define the hyperbolic trigonometric functions sh, ch, and th (also known as sinh, cosh, and tanh):

sh x = (e^x - e-^x)/2
ch x = (e^x + e-^x)/2
th x = sh x/ch x

Using these, the rocket equations are

t = (c/a) sh(aT/c) = sqrt[(d/c)² + 2d/a]

d = (c²/a) [ch(aT/c) - 1] = (c²/a) (sqrt[1 + (at/c)²] - 1)

v = c th(aT/c) = at / sqrt[1 + (at/c)²]

T = (c/a) sh-1(at/c) = (c/a) ch-1 [ad/c² + 1]

γ = ch(aT/c) = sqrt[1 + (at/c)²] = ad/c² + 1

These equations are valid in any consistent system of units such as seconds for time, metres for distance, metres per second for speeds and metres per second squared for accelerations. In these units c = 3 × 10⁸ m/s (approx). To do some example calculations it is easier to use units of years for time and light years for distance. Then c = 1 lyr/yr and g = 1.03 lyr/yr². Here are some typical answers for a = 1g.

Code: Select all

    T          t         d          v                γ
    1 year    1.19 yrs  0.56 lyrs  0.77c                 1.58 
    2         3.75      2.90       0.97                  3.99
    5        83.7      82.7        0.99993              86.2
    8     1,840     1,839          0.9999998         1,895
   12   113,243   113,242          0.99999999996   116,641


Of course, these equations don't take air resistance into account, or the fact that the acceleration is very slightly lower at ceiling level than it is at floor level. The air resistance will depend on whether or not the room is sealed because the friction will heat up the air. If the room is sealed, then the air pressure will rise in proportion to the temperature. If it's not sealed, then most of the air will eventually be driven out of the room, assuming that the ball itself is indestructible. If it's not, then I suspect that it will have been completely vaporized before its speed gets to a significant fraction of c.

[MHD]

The comic is called Blank It. The joke is that the shovel is seemingly not affected by areodynamic friction, yet suddenly creates a sheath of plasma similar to athmospheric reentry.

"It can't be both affected and not affected at the same time!"

Also, portals break the law that the order of the factors is irrelevant.
x * y is the area of an x by y rectangle. Or to put it another way, you walk x steps to the right and y steps foreward to reach a destination (sort of iffy, but I don't know the exact terminology and my technical english is less than perfect...)
With portals, walking x steps to the right can bring you to a point further to the left than when you started.

I am pretty sure that the law of conservation of energy includes a product somewhere, so there you go.

Portals break multiplication and therefore conservation of energy.

----------------

Also I have this theory of a portal based thing...

Two portals, stationary compared to one another, and a rod of ferrimagnetic metal fused in a closed loop between them.
The system is in vacuum and the rod is suspended by electromagnets

Code: Select all

/\     oooo     /\
|================|
\/     oooo     \/

Then you apply current to accelerate the rod, thus providing a net force on the coils.

Reactionless drive (although with a limited delta-v if you don't want a relativistic rod of metal in your ship).

[KrO2]

That's clever. You can get around the limited delta-v by placing another portal on the outside of the ship, assuming you can switch which one it comes out of without timing problems, so there might be an upper limit on how fast the rod can move. But once the rod gets moving to wherever you're not comfortable accelerating it any more, you can just have it railgun out the back of your ship (or whatever direction you want, if you want to hit something with it) and just start again with another rod.

[BlackHatSupport]

Yiou have yet to understand how the portal affects momentum, or, more accurately, how it does not.

In layman's terms, speedy thing goes in, speedy thing comes out.

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[KrO2]

If you're talking about MHD's reactionless drive, that's kind of the point. You can accelerate the rod backward (and thus, yourself forward) as much as you want while using the portals to keep it in approximately the same position relative to you. If you meant my comment about ejecting the rod once you don't want it in your ship any more, I know that's not going to affect your ship's momentum; it was just a way to get rid of the thing.

[Tomlidich]

That's clever. You can get around the limited delta-v by placing another portal on the outside of the ship, assuming you can switch which one it comes out of without timing problems, so there might be an upper limit on how fast the rod can move. But once the rod gets moving to wherever you're not comfortable accelerating it any more, you can just have it railgun out the back of your ship (or whatever direction you want, if you want to hit something with it) and just start again with another rod.

but wait.... tell me if i am wrong here, but to create this rod, you just feed a piece of steel, (like a pipe or something) through one, out the other, and weld it to itself.

wouldn't that mean it is impossible to close either of the portals without first stopping this peice of metal and cutting it with a lance or something?
im not sure how the portal physics work there. or maybe you can close it but you would end up fusing the rod to your wall, causing a catostrophic failure of that section of wall since it is a very fast peice of moving metal.

[gmalivuk]

If you don't have artificial gravity pulling it in some direction other than toward the other portal, there's actually no need for it to be a continuous rod. Hell, you could just use a stream of metal pellets or something.

This is a cool idea for a "reactionless" drive, though I feel like the portals are a more tongue-in-cheek way of doing it than just handwaving it away, so it'd be better for Douglas Adams style SF than for hard SF.

[Tomlidich]

excuse a noobish question, but what is handwaving? google has turned up nothing.

[Xanthir]

"handwaving" means "ignoring all the details, and assuming everything works out", or something similar depending on context.

[idobox]

For example, if you FTL ships in your fictionnal universe, and you don't want to bother with all the paradoxes, you just say I have a drive with a fancy name, that allows you to travel faster than light without violating causality. Tadaa! You just handwaved.

[eSOANEM]

Also the fact that the portals seem to create energy (the kinetic energy given to the ball comes form?), makes it easy to get absurd results.

Portals can be made to conserve energy (and, in certain senses, momentum), you just need to allow it to steal energy from its surroundings when it is giving an object extra energy and dump gamma rays (which portals are known to emit) when it is losing energy. As for momentum, you just take the area immediately local to the portals, join them up (remembering that portals have a specific orientation) and then conserving momentum in this portal-space.

Of course, this makes portals very powerful weapons; not only can they easily accelerate relativistic kill vehicles or other projectiles, they can also be used to dump gamma rays by portalling a surface inside a black hole and the other one near your enemy.

[Tomlidich]

Also the fact that the portals seem to create energy (the kinetic energy given to the ball comes form?), makes it easy to get absurd results.

Portals can be made to conserve energy (and, in certain senses, momentum), you just need to allow it to steal energy from its surroundings when it is giving an object extra energy and dump gamma rays (which portals are known to emit) when it is losing energy. As for momentum, you just take the area immediately local to the portals, join them up (remembering that portals have a specific orientation) and then conserving momentum in this portal-space.

Of course, this makes portals very powerful weapons; not only can they easily accelerate relativistic kill vehicles or other projectiles, they can also be used to dump gamma rays by portalling a surface inside a black hole and the other one near your enemy.

death by radiation poisoning.
loads of fun.

[gmalivuk]

Yeah, I think it's the stepping disks in Larry Niven's Known Space that can only handle up to a certain limited momentum difference, and get really hot and have to cool down if there's a lot of extra energy that needs bleeding off.

[Tomlidich]

Yeah, I think it's the stepping disks in Larry Niven's Known Space that can only handle up to a certain limited momentum difference, and get really hot and have to cool down if there's a lot of extra energy that needs bleeding off.

of course there must be some useful purpose for that extra energy.....
damnit sorry the engineer in me wont shut up. tom, its theoretical physics, stop trying to improve it.
but.... NO! gaghaghagggggahhhhhhhhhh