[watsisname]

I am a tachyon.

[General Battuta]

The resolution lies in the definition of an inertial reference frame vs. non-inertial reference frame.

There is no frame from which the Herc can be seen as stationary that is itself not undergoing acceleration. Any observer in such a frame would feel fictitious forces due to said acceleration.  Thus the frame is said to be non-inertial.

Therefore all the weird stuff like the Twin Paradox applies to the Herc, but not the ship containing the Herc.

Yeah, this is my understanding.

[Herra Tohtori]

Twin paradox is only a paradox because it presents a situation where special relativity does not work.

Special relativity can only be applied when everything moves at constant velocity. As soon as accelerations come into play, it means that the accelerating observer is no longer contained to the same inertial frame.

And before you ask, even though constant velocities are relative, accelerations are absolute (although the amount of acceleration is relative - if you accelerated at 9,80665 m s^-2 for infinite time, you would feel the same acceleration for the whole time but static observers would note that your velocity approaces c and acceleration approaches zero).

Rest assured though that when the crane moves Herc, both the Orion and Herc experience accelerations (conservation of momentum, shift of common centre of gravity and all that) but due to Orion's immensely larger mass, it can in almost all practical applications of physics be considered as static object while the Herc moves within the inertial coordinates fixed at the Orion. Errors using this method would likely be about the same order as (Herc's mass)/(Orion's mass) which I would estimate at, say, something close to 10^-9 magnitude just from the top of my head. Or even less.

..actually, what the heck.

* Herra Tohtori goes check the mass values from the model files

From sparky_fs2.vp:
Retail HercI: mass 302.460114 units
Retail Orion: mass 1646203.000000 units

...which results as about 2x10^-5

Which is actually a lot more than I would have expected, to be honest, but still very, very much.

It means that if Herc moves a metre, Orion moves about 20 micrometres to opposing direction. Not exactly an observable amount in most situations.


Plus I don't know if these units of mass make any sense whatsoever. Which actually brought up an interesting topic in irc - are the mass and MOI values of ships preserved comparative to retail values in MediaVP's?

[General Battuta]

Twin paradox is only a paradox because it presents a situation where special relativity does not work.

Incorrect, to my knowledge. The twin paradox can be resolved entirely inside SR.

[Herra Tohtori]

Twin paradox is only a paradox because it presents a situation where special relativity does not work.

Incorrect, to my knowledge. The twin paradox can be resolved entirely inside SR.

Yes, it is, as long as you assume that all changes of velocity are instantaneous and then handle each phase of the trip as an idealized component.

What I meant is that it's only a "paradox" when people look at it assuming that same stuff that applies to constant-speed inertial frames applies into switched inertial frames. My wording was poor; what I should have said is that the simplest example of Special Relativity does not apply to more complex situations (where velocity is NOT a constant).

And properly solving it still requires handling accelerations which are synonymous to gravity fields in General Relativity so, you probably would end up needing to use GR anyway if you wanted anything but idealized solutions.


The simplest way to un-paradox the twin paradox is to make both twins emit EM pulses at standard intervals and calculate the amount of pulses that both twins receive from the other, taking pulse travel time into account...


That said...

* Herra Tohtori sees Newton and Einstein and raises Schrödinger and Dirac

[Mongoose]

That should clear things up.

[watsisname]

Rest assured though that when the crane moves Herc, both the Orion and Herc experience accelerations (conservation of momentum, shift of common centre of gravity and all that) but due to Orion's immensely larger mass, it can in almost all practical applications of physics be considered as static object while the Herc moves within the inertial coordinates fixed at the Orion.  [etc]

Haha, that's a good point -- I don't think any of us had thought of that.


Edit:  On the note of xkcd discussing physics, I always loved this one, too:
http://xkcd.com/669/

[Astronomiya]

...which results as about 2x10^-5

Which is actually a lot more than I would have expected, to be honest, but still very, very much.

If you assume the mass ratio to be somewhat similar to that between a Nimitz carrier and one of its fighter complement, this makes some sense.  A Nimitz class CVN displaces about 100,000 tonnes, while the loaded mass of one of its F/A-18 fighter complement is about 17 tonnes (10 tonnes empty), for a ratio of about 1E-4, an order of magnitude greater than that between Herc and Orion.  Of course, the Orion is a much, much larger ship than a Nimitz, to the tune of being almost ten times as long, and something like three to five times wider as well as "taller," while a Herc isn't all that much larger than the Hornet, IIRC.  Assuming a similar density between the Orion and the Nimitz, I get that an Orion is about 100-250 times more massive than a Nimitz, while a Herc might conceivably be several times heavier than a Hornet or similar modern fighter.

* Herra Tohtori sees Newton and Einstein and raises Schrödinger and Dirac

What the hell does QM have to do with all this?

[Herra Tohtori]

Well, in case we have to solve the interactions of a very small Herc and a very small Orion...

[Flipside]

Newton wins, he is the deadliest son of a ***** in Space, after all