Another what if Question concerning gravity

[mcjosep]

Another "what if" Question concerning gravity

Lets assume that we can have an object fall into a wormhole only to come out the other side above the wormhole it just fell into, making a loop. Now let's put this loop in a Jar and make a vacuum inside it eliminating all air resistance. Now we drop a marshmallow into this loop and watch it constantly accelerate at 9.8 meters per second (not loosing any speed by going to the upper wormhole) just constantly accelerating because of gravity. What would happen? would this marshmallow accelerate to the speed of light, or past the speed of light? 9.8 can only go into the speed of light so many times before it matches or passes it. I am curious as to what would happen. Please enlighten me.

 

[vandegg]

I always had a problem with wormholes just because of stuff like this. Anytime you open a hole in space and go somewhere else you bring a lot of problems with you. You break all kinds of fundamental and thermodynamic laws, and this suggests to me that such travel is impossible.

 

[DaveC426913]

Lets assume that we can have an object fall into a wormhole only to come out the other side above the wormhole it just fell into, making a loop. Now let's put this loop in a Jar and make a vacuum inside it eliminating all air resistance. Now we drop a marshmallow into this loop and watch it constantly accelerate at 9.8 meters per second (not loosing any speed by going to the upper wormhole) just constantly accelerating because of gravity. What would happen? would this marshmallow accelerate to the speed of light, or past the speed of light? 9.8 can only go into the speed of light so many times before it matches or passes it. I am curious as to what would happen. Please enlighten me.

It will accelerate like any other object under constant acceleration - whether by gravity or by propulsion. This is very easy to duplicate without resorting to any hypothetical wormhole setup.

An objects's increase in velocity near relativistic speeds is calculated using the Lorentz Transform - it is asymptotic with c - it will get closer and closer but never reach it.

In an extremely simplified and rounded nutshell:
Say it got to .9c via a constant acceleration A for time T.
Another constant acceleration of A for the same time T will get it to .99c,
and another constant acceleration factor will get it to .999c, etc.

 

[DaveC426913]

I always had a problem with wormholes just because of stuff like this. Anytime you open a hole in space and go somewhere else you bring a lot of problems with you. You break all kinds of fundamental and thermodynamic laws, and this suggests to me that such travel is impossible.

The wormhole is nothing but a red herring, making the issue seem more mysterious than it is. Remove it.

It is quite easy to set up an experiment where an object is under constant acceleration.

A rocket under constant propulsion will result in the same experimental setup (gravity and acceleration are indistinguishable, as per the Equivalence Principle).
Alterenately, we postulate a black hole large enough (galaxy-sized) that an object can fall into it for an arbitarily long time. With a big enough black hole, the gravitational gradient over the object's fall will be arbitrarily small.

 

[vandegg]

The wormhole as i understand it is creating problems because it is imparting free energy and therefore mass on the object falling through it, which is increasing the acceleration due to gravity. Free energy in and of itself is a problem but the extra mass that the object experiences doesn't jive with the results of relativistic motion under constant acceleration.

Edit: by the mass thing i meant that the acceleration would increase over time. I guess that this is a similar situation to something falling into a huge black hole over an arbitrary amount of time but the problem for me is that this wormhole process is creating energy where as in the black hole situation it is not, and also the arbitrary time involved is theoretical for the black hole and is real for the wormhole.

 

[K^2]

You've played too much Portal. That's not how wormholes work. There is space within a wormhole. Within that space, there are fields. In particular, there are gravitational fields.

Of course, wormhole itself is a result of gravity, but you can usually break it up into a major source of gravity that gives you the curvature you need for the wormhole, and the minor sources that just add a classical gravitational field within that curved space. Think of it as perturbation theory for gravity.

When you break the problem apart this way, you'll immediately notice that there is going to be a compensating gravitational field within the wormhole. So unless you have enough kinetic energy going into the wormhole to compensate for the potential energy change at the wormhole's mouth, you aren't going through.

Even in a crazy curvature, as long as it is a proper solution to Einstein's Equations, the gravitational potential is purely a function of location. It's not path-dependent. So you'll never see something ending up at the point it started with more energy than before. If it made a loop without some external source of force, it will be traveling just as fast as the first time through that point.

No paradoxes here.

 

[vandegg]

You've played too much Portal. That's not how wormholes work. There is space within a wormhole. Within that space, there are fields. In particular, there are gravitational fields.

Of course, wormhole itself is a result of gravity, but you can usually break it up into a major source of gravity that gives you the curvature you need for the wormhole, and the minor sources that just add a classical gravitational field within that curved space.

When you break the problem apart this way, you'll immediately notice that there is going to be a compensating gravitational field within the wormhole. So unless you have enough kinetic energy going into the wormhole to compensate for the potential energy change at the wormhole's mouth, you aren't going through.

Even in a crazy curvature, as long as it is a proper solution to Einstein's Equations, the gravitational potential is purely a function of location. It's not path-dependent. So you'll never see something ending up at the point it started with more energy than before. If it made a loop without some external source of force, it will be traveling just as fast as the first time through that point.

No paradoxes here.

Oh, and the only Red Herring in the wormholes is the negative energy density required to make a traversable one.

Well that is good to know then. I do not know the math behind wormholes, but i do hear them thrown around a lot by the media and physics teachers and such, and honestly the question the original poster asked is always running through my head whenever someone brings it up. I'm glad that they are in reality paradox free, even if they are still just theoretical.

 

[Antiphon]

Even in a crazy curvature, as long as it is a proper solution to Einstein's Equations, the gravitational potential is purely a function of location. It's not path-dependent. So you'll never see something ending up at the point it started with more energy than before. If it made a loop without some external source of force, it will be traveling just as fast as the first time through that point.
No paradoxes here.

This is really only true in the case of static solutions. For accelerating matter there are closed paths where the potential increases on going around the loop. Here's a simple one: a massive rotating cylinder which is accelerating. A small test mass orbiting the cylinder will accelerate one way and another orbiting in the direction will decerate. This goes by the name of frame dragging by I prefer the non-standard terminology of gravitational induction. It makes the frame dragging mechanism easier to understand by analogy with a solenoid. If you put a test charge outside of a solenoid which carries a current I=t, the charge will be accelerated around the solenoid by a non-potential (but steady-state) electric field.

 

[K^2]

This is really only true in the case of static solutions.

Yes, that's true. If you have a time-dependent metric, the energy is not even generally conserved. Of course, that happens in classical mechanics too when potentials are time-dependent.

Of course, if you make motion of all particles agree with the metric and other forces present, total energy should still be conserved, but it may be passed from one body to another in some unexpected ways.