Can the universe contract to less the size of your spaceship?

[gib65]

I'm in a discussion on another forum. The topic is relativity and length contraction. I'm trying to explain to someone that anyone who measures something moving will also measure length contraction. This was meant to correct a common misconception about relativity - that since certain measurable quantities dilate as one's speed increases (time slows down, length contracts, mass increases), those quantities would have to seem to dilate in the opposite direction from the point of view of the one moving. In the case of this discussion, my interlocuter assumed that if someone traveling in a spaceship close to the speed of light undergoes length contraction, then relative to him the entire universe would have to seem to undergo length 'extension'. I tried to correct this by saying that relative to him, the universe also would undergo length contraction because it would be moving relative to him.

 

Then he stumped me: it should therefore be theoretically possible to arrive at a speed sufficiently close to c such that the entire universe seems to contract to shorter than the length of his spaceship. The front end would essentially have shot passed his destination and the back end would essentially have regressed behind his point of origin. How does one resolve this paradox?

[md65536]

Then he stumped me: it should therefore be theoretically possible to arrive at a speed sufficiently close to c such that the entire universe seems to contract to shorter than the length of his spaceship. The front end would essentially have shot passed his destination and the back end would essentially have regressed behind his point of origin. How does one resolve this paradox?

With these extremes you can't treat the spaceship as one unit. You have to take relativity of simultaneity into account. Different parts of the ship would experience the situation and its timing differently.

 

To simplify the situation, we can consider the viewpoint only from the back of the ship (to begin with, at least).

Let us set up the timing such that from this viewpoint, the observer never moves relative to the front of the ship. We can make the ship very long (a lightsecond, say) if it helps.

To simplify, rather than considering the entire universe we could consider only some distant "destination" point, for the front of the ship to reach.

Let's assume instant acceleration and deceleration.

 

I think the paradox resolves as follows:

With extreme enough velocity, the destination would indeed contract to a length less than the length of the ship.

However, the travel time (according to the observer's clocks) to reach the destination would be shorter than the time that it takes light to travel from the front of the ship to the back (someone please correct me if that's not certain).

 

When the ship instantly accelerates, it experiences an "update to simultaneity" relative to the destination.

Before the observer can observe anything happening at the front of the ship, the ship has reached its destination, and the observer experiences another "update", and at no point has the observer observed the front of the ship being farther ahead than the destination.

 

 

If the ship instead passes the "destination point" and keeps going, the observer simply observes it all happening with different timing than the front of the ship would.

If the front of the ship crashes into the destination while the observer continues moving forward, the length of the ship would be decreased to the length between observer and destination before the observer could witness anything impossible happening.

 

 

 

I have a feeling this explanation is missing something in the details though...

Edited July 4, 2011 by md65536

[J.C.MacSwell]

I'm in a discussion on another forum. The topic is relativity and length contraction. I'm trying to explain to someone that anyone who measures something moving will also measure length contraction. This was meant to correct a common misconception about relativity - that since certain measurable quantities dilate as one's speed increases (time slows down, length contracts, mass increases), those quantities would have to seem to dilate in the opposite direction from the point of view of the one moving. In the case of this discussion, my interlocuter assumed that if someone traveling in a spaceship close to the speed of light undergoes length contraction, then relative to him the entire universe would have to seem to undergo length 'extension'. I tried to correct this by saying that relative to him, the universe also would undergo length contraction because it would be moving relative to him.

 

Then he stumped me: it should therefore be theoretically possible to arrive at a speed sufficiently close to c such that the entire universe seems to contract to shorter than the length of his spaceship. The front end would essentially have shot passed his destination and the back end would essentially have regressed behind his point of origin. How does one resolve this paradox?

 

No. (obviously, though great question)

 

My take:

 

First of all if n the universe is infinite in size (we don't know) then it would require infinite energy for infinitely long to still not succeed.

 

If the universe is finite then it would require more energy than the universe has to accelerate the spaceship to the "necessary approaching light speed" to accomplish this.

 

In each case, the faster you go...the faster you are displaced toward an area of the universe that has most of it's mass that is at rest in your new inertial frame (due to the expansion)...so the behinder you get.

 

Again great question. Sometimes looking at things from extremes brings up a lot of interesting ideas.

[gib65]

In each case, the faster you go...the faster you are displaced toward an area of the universe that has most of it's mass that is at rest in your new inertial frame (due to the expansion)...so the behinder you get.

 

What do you mean by this? How is "most of its mass" at rest at any point in the spaceship's travels? And how does this solve the paradox?

[md65536]

I couldn't help thinking some more about this problem.

 

 

Let's simplify the problem further.

Suppose we have an observer at the back of the ship, and the front of the ship is one unit away (1 LY say). We'll consider the front and back of the ship as 2 separate entities, with nothing in between; we'll ignore the rest of the ship so we don't have to worry about how it behaves.

Suppose one unit beyond the front of the ship is a destination.

 

The destination is 2 units away from the observer. Length contraction of gamma = 2 will bring the destination to the same distance as the front of the ship; any higher gamma and the destination will be closer than the front of the ship.

 

 

The ship can't start moving as a single unit at a single time according to all observers. At best the start time can be synchronized according to some location. This can be done by sending a signal to start, to both the front and back of the ship. Suppose this is done from the middle of the ship. From that perspective, equidistant to front and back, both start at the same time. But according to the observer at the back, she gets the signal to start before she observes the front of the ship starting.

 

Another alternative is that the front of the ship sends the signal to start. Then, the observer at the back observes the signal to start at the same time that she observes the front of the ship also starting. In this case, the observer sees the ship starting as a single unit.

 

Using this synchronization method, it's clear that there are only 2 cases: The observer will begin moving before observing the front of the ship starting to move, or at the same time as observing the front of the ship starting to move.

 

Case 1: Observer begins moving first.

Until the observer sees the front of the ship moving, the front of the ship will be in the same inertial frame as the destination.

The length of the ship will contract by a factor of gamma, the same ratio that the distance to the destination contracts. The front of the ship will never be seen to be beyond the destination.

 

... Then there are a bunch of details I don't want to try to figure out and am skipping, in the timing of this.

 

Case 2: Observer begins moving at the same time as the front.

With gamma=2, what the observer sees is that the distance to the destination contracts to half its length, and the front of the ship appears to have instantly reached the destination, at which point it stops and becomes part of the destination's inertial frame (thus again, now length-contracting by the same amount with the front never appearing to be beyond the destination).

 

This is consistent with what other observers would see: From another perspective, the front appears to have a head start, the ship stretches, and the front of the ship reaches the destination early.

 

 

Again there's a bunch of details that can be worked out, but this is enough to resolve the paradox:

Unless the front of the ship passes the destination (according to all observers), then an observer elsewhere on the ship will necessarily see her own ship length-contract (for at least part of the duration) along with the destination, such that she never observes the front of the ship passing the destination.

 

 

 

---------

Edit: I think I got this at least partly wrong. It should be possible to set this up so that the rear observer never observes any change in the length of the ship.

I think I was forgetting about the travel time of light.

 

Dammit complicated relativity, you are ruining me.

Note: the following turned into a huge mess when I tried to correct errors in the original.

 

 

Alright say for example the ship is 1 LY long, and the front travels a further 1 LY to reach its destination, at v=0.866c with gamma = 2.

The time it takes, according to an observer in the destination's frame, is 1 LY /0.866c = 1.15 years.

According to the front of the ship, it has to travel a length-contracted distance of 0.5 LY at 0.866c, taking half as long or 0.577 years local rocket time.

 

If the front of the ship gets a 1.15 year (destination frame time) head start, the length of the ship becomes 1.15 year * 0.866c = 1 LY longer according to the rear, but the distance is length-contracted by a factor of gamma=2 before the rear starts moving, to a distance of 1 LY. Sorry... confused...

If the front of the ship gets a 0.5 year (destination frame time) head start, the length of the ship contracts by a factor of 2 to 0.5 LY, so it takes 0.5 years for observations of this to reach the rear. But if the rear observer begins moving at the same time as this observation reaches her, she is now at rest relative to the front and observes herself moving in sync with the front, keeping an observed ship length of 1 LY.

In the destination's frame, the rocket is 1 LY + 0.5 year * 0.866c = 1.433 LY long. If the front stops while the rear is still moving, their distance according to the rear will contract to half that, 0.7165 LY. (Ugh, sorry these calculations got a lot more complicated than I expected..) Now if the front stops by a time of t earlier than the rear, then the rear will continue to move forward at 0.866c while the observation of the front having stopped travels backward at c... we want (1+0.866)*t = 0.7165 LY. t = 0.3839 years... If the front stops 0.3839 years before the rear, then the rear will observe this after 0.3839 years... at which time it stops. Having traveled 0.3839 years*0.866c = .332 LY, the rocket is now 1.433 LY - 0.332 LY = 1.10 LY long.

SO! I don't know if I've just thoroughly confused myself and everyone trying to read that,

or if I've demonstrated that if the scenario is set up so that the rear observer observes being in sync with the front (and thus never experiencing extreme length contraction relative to the front), then the rear cannot remain at 1 LY away from the front (ie. it's impossible to keep the ship always appearing to be 1 LY long).

I'll try to figure out the rest of the details sometime later. I'm probably still wrong here so far, somewhere. Feel free to correct me!

Edited July 6, 2011 by md65536

[md65536]

Continued...

 

In this example the ship is 1 LY from Rear to Front, and there is a travel distance of 1 LY from Front to Destination. v = 0.866c; gamma = 2.

Assume negligible acceleration time.

 

 

Okay so if we let the Front get a half??? 1.15??? year start (according to Rear), and stop one year some time in advance (again according to Rear but this time in a different frame), Rear never sees the length of the ship change ???????, although it is certainly affected by length contraction.

 

So if the distance to Destination contracts to 1 LY according to Rear, but the ship also remains at least 1 LY long, then what gives?

 

 

Okay so after the Front's head start, Rear travels at 0.866c for 0.577 years local time, covering 1 LY of rest distance in the Destination's frame (ie. the total distance of the trip).

At the start of its trip, the distance to the Destination (rest distance 2 LY) contracts by gamma = 2 to 1 LY, and continues to decrease as the rocket approaches. In other words, it contracts to closer than the front of the ship. BUT the observations of this still take 1 LY to reach Rear.

 

Before Rear can observe the Destination contracted to closer than the Front, after 0.577 years rocket time it stops, undergoing a frame shift, and changing its simultaneity relative to Destination. Any observations of the Destination being closer than the Front are unobservable, because they happen too far away to be seen in the time that Rear remains in its moving frame. The frame shift essentially changes what has not yet been observed.

This brings up an interesting consequence of SR: If an event is predicted to happen, but then becomes unobservable due to an update to simultaneity, then that event didn't happen. Only observable events actually happened.

 

So in conclusion: The ship will also be affected by length contraction (relative to the observer on the ship), BUT if the front is ever calculated to be beyond the destination, it will only happen for a short enough duration to make it unobservable, which means it never actually happens.

 

 

 

If you read all that... sorry...

Edited July 6, 2011 by md65536

[quantumstrides]

you cannot think of the universe and the ship as the same system without accelerating both uniformly and simoultaneously. there is no physical contraction to the universe, and no paradox.