General Relativity Question

[Gestahl]

You guys probably get a lot of these: sorry if this has been posted before many times.

I thought I understood General Relativity, until I read a question posted by RussDill a while ago. Now he has got me confused again...

Scenario:

A ship is 100 meters long (at rest w.r.t. the barn), and traveling at 5/6 the speed of light, relative to and in the direction of a barn on a planet. The barn is 60 meters long. We of course have a barn-owning physicist and a ship owning physicist who are bored with lots of equipment. Assume the barn has two doors, North and South, with the ship traveling northwards.

The barn-physicist will see the ship squashed to approx. 50 meters (rounding here), and will appear to him to fit inside the barn. Remember, from his prespective he is not moving, and the ship is at high speed.

Meanwhile, the ship physicist will see the barn squashed to only 30 meters(!). Remember, from his perspective, he is not moving, and the barn is moving towards him at high speed.

Now the barn physicist gets and idea... he says: I will throw a wrench in this relative-frame idea. He rigs a system whereby as soon as the tail of the ship passes by the South doorway an intense laser will activate which can cut through the ship, in the plane perpendicular to the path of the ship.

Now, we know that the ship does not "fit" inside the barn from the perspective of the ship, or from the perspective of an observer with the ship at rest w.r.t. the barn.

What happens when our intrepid ship-physicist tries to go through the barn? Will the laser cut off his ship? If it does, how much of the ship will it cutoff, as observed from rest w.r.t. to the barn afterwards? 70 meters, as the astronaut would expect, or 40 meters, as an observer of the two together at rest w.r.t. each other would expect, or none at all, the ship fits in the barn, as the barn-owner would expect. Ignore that the laser beam is finite in speed and all, imagine its instantaeous.

My attempt to answer below in ROT-13, feed it into this translator to see it.

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Another little thought: If we could view the universe from the POV of a photon, we would see the entire universe as a singularity (i.e. single point), and time would consist of a single instant, and nothing would ever change. However, you would get to whereever you wanted instantly.

 

[QuarkChild]

I think you mean Special Relativity.

 

[cbish]

yeah, this is Special Relativity. Isn't General warping of space time? (gravity)

 

[Gestahl]

I think you mean Special Relativity.

My conception was that SR {subsetof} GR, but I may be mistaken. I though General Relativity implies SR as a specific case.

 

[Martin]

Meh. I'm not doing all the work for you. Here's a hint, though: two events which are simultaneous in one reference frame will typically not be in another.

 

[Martin]

My conception was that SR {subsetof} GR, but I may be mistaken. I though General Relativity implies SR as a specific case.

Correct. SR is the weak-gravitation limit of GR.

 

[QuarkChild]

My conception was that SR {subsetof} GR, but I may be mistaken. I though General Relativity implies SR as a specific case.

Well, technically, newtonian mechanics is a special case of quantum theory, but if someone was asking a question about Hooke's Law, it would be a little misleading to call it a quantum mechanics question!

But anyway, yes, GR reduces to SR in flat space.

 

[Hamish]

A couple of things to help you get an answer.

First, just to clarify, the laser chops off anything at the NORTH end of the barn, correct?

But the sensor is at the SOUTH end. Information cannot be transmitted instantaneously from one end to the other. In fact it takes 60/c seconds for the information to be transmitted from the point of view of the barn physicist.

The answer of a 40m cut off section is meaningless since no observer sees the ship at rest w.r.t the barn.

 

[TillEulenspiegel]

The answer is....maybe neither . The cut through the ship would be an ellipse or diagonal from the entry of the laser ( lets say cutting top to bottom)at the top to the exit at bottom because of the forward motion of the ship. Even if the cutting action is @LS.

You don't put any constraints on the position of the laser so just to demonstrate we will place the laser at the middle of the barn.

Let's say that light speed ( the upper limit of the system ) is 60 MPH, that means that the ship is traveling at 50 mph, the differential of the two systems is Dv/Dt = 10mph, so the laser is traveling @ 10 mph from top to bottom. The ship is still going forward. If the ship was a perfect square then the cut will be a diagonal, if the ship is "ship shaped " ( hahaha I made a funny ) it will be elliptical..

The only magic here is due to NLS travel meaning Lorenz contraction, aside from that its simple math, make the ship a box and regardless of dimensions the proportion of ship separation remains the same. You will have a right angle pyramid on top of a box. Do a little geometry and you have your answer.

Actually that's not quite true the will be a differential between the entry point of the laser on the side that it projects from and the opposite side of the ship so there will be a slope, bleh, but in the interest of brevity...

sides I don't think the cows in the barn would like all that racket!
Caveat this is a four Guinness post ..weeee!

 

[Gestahl]

The answer is....maybe neither . The cut through the ship would be an ellipse or diagonal from the entry of the laser ( lets say cutting top to bottom)at the top to the exit at bottom because of the forward motion of the ship. Even if the cutting action is @LS.

You don't put any constraints on the position of the laser so just to demonstrate we will place the laser at the middle of the barn.

Fair enough. I was conceptualizing the laser being at the North door. Imagine the door is just wide enough for a ship, so the laser start cutting nearly instantaneously. Where does the cut start when measured as the ship is at rest w.r.t. the barn?

 

[Gestahl]

A couple of things to help you get an answer.

First, just to clarify, the laser chops off anything at the NORTH end of the barn, correct?

Yes. Looking back I realize that I did not say that, but from the information at the end is it implied... my bad.

But the sensor is at the SOUTH end. Information cannot be transmitted instantaneously from one end to the other. In fact it takes 60/c seconds for the information to be transmitted from the point of view of the barn physicist.

Light travels at c no matter what in a vacuum, from *any* observer ( I did not state this was in a vacuum, but assume it). The signal will reach the north end before the ship, no? From the perspective of the ship-physicist, it would be almost instantaneous, right? (Though red shifted).

In any event, the signal will reach the north end at some point before the ship. If the ship is 100m long in its perspective, and the barn is 30m, the signal will appear to still happen at the speed of light, and take no time at all to go from end to end, and the front of the ship is getting cutoff. From the barn-physcists POV, the ship is 50m and the barn is 60m, so in the time it takes the signal to go the 60 meters, the ship will go 50m, and the last 10m will be cut off (or that is when the cut will start).

The answer of a 40m cut off section is meaningless since no observer sees the ship at rest w.r.t the barn.

They will when the ship stops ;-). Space ships don't work too well when they are sliced up.

 

[Gestahl]

Meh. I'm not doing all the work for you. Here's a hint, though: two events which are simultaneous in one reference frame will typically not be in another.

Seeing as I have not been able to *do* the work (obviously), I need someone to help me (thus my posting here). If you don't wanna help, it does not require your derision.

I am aware of that simultanaity (is that even a word?) is not a given, due to a lack of an absolute reference frame. However, see my post above.

I understand the concept of non-simultaneous actions because of the speed of information travel. However, when you are dealing with things this close together, my mind reels again.

 

[Dancing David]

What the high minded and stuck up wonks here are not telling you is something that Russ Dill pointed out to me in a LifeGazer thread.(All I can say is that LifeGazer is at least willing to be nice to people at first, something lacking from some people in this thread.)

The compression effect is a relative effect, as the ship approaches the speed of light the barn observer will observe the compression of the space ship. So guess what (this is the point I forgot and Russ reminded me of), the barn is also moving close to the speed of light compared (relative) to the ship. Soo, what happens to the barn from the relative perspective of the ship?

I say that the Capn of the ship will refuse to enter the barn.

 

[Hamish]

Light travels at c no matter what in a vacuum, from *any* observer ( I did not state this was in a vacuum, but assume it). The signal will reach the north end before the ship, no? From the perspective of the ship-physicist, it would be almost instantaneous, right? (Though red shifted).

Almost instantaneous? No.

In any event, the signal will reach the north end at some point before the ship. If the ship is 100m long in its perspective, and the barn is 30m, the signal will appear to still happen at the speed of light, and take no time at all to go from end to end, and the front of the ship is getting cutoff. From the barn-physcists POV, the ship is 50m and the barn is 60m, so in the time it takes the signal to go the 60 meters, the ship will go 50m, and the last 10m will be cut off (or that is when the cut will start).

10 m (from the point of view of the barn physicist which includes length contraction of the moving ship pieces) is correct. Your reasoning on the ship physicist's view is wrong though. You need to take into account both the time taken for the signal to get from the sensor to the laser AND the fact that the barn (and hence sensor and laser) appears to be moving at 5c/6. I get the same answer for both frames. The answer is that, in the rest frame of the ship, 18.1 metres are sliced from the end of the ship (assuming, for the sake of the problem, instantaneous magic slicing lasers).

They will when the ship stops ;-). Space ships don't work too well when they are sliced up.

Well, the bits won't actually slow down just because they've been sliced up.

 

[TillEulenspiegel]

Gestahl,

The people here have an ...shall we say acerbic wit? If You had approached the question from a different direction rather then a challenge wrapped in a riddle , and asked for help. There are world class specialists that subscribe to this board and they would have been happy to help. There are also other boards that help with homework like http://www.physicsforums.com/index.php?. The hints and scenarios that people have stated here are BTW correct information.

 

[Martin]

Seeing as I have not been able to *do* the work (obviously), I need someone to help me (thus my posting here). If you don't wanna help, it does not require your derision

What, giving hints isn't helping? I had thought you might like to work through it yourself with guidance from us. Suit yourself.

 

[69dodge]

If the laser at the front of the barn fires at the same time that the ship's tail enters the barn (same time in the barn's reference frame, that is), it won't cut the ship, because the ship hasn't reached the front of the barn yet. In the ship's reference frame, the laser fires before the ship's tail enters the barn, so the ship still doesn't get cut.

If the laser firing is delayed by a time interval (in the barn's reference frame) of 60 meters / c, because, for example, it is triggered by a light-speed signal from a sensor at the other end of the barn, then the ship will move 50 meters in that time and the laser will cut off the last 10 meters of the 55-meter ship. In the ship's reference frame, the front of the 33-meter barn is moving backward at a speed of (5/6)c, so it meets the c-speed forward-moving signal from the back of the barn after a time delay of only 33 / [(1 + 5/6)c] = 18 / c. In this time, the barn moves back 15 meters, and so the laser cuts off the last 33 - 15 = 18 meters of the 100-meter ship. Like Hamish said.

Notice that this is the same, percentagewise, as the 10 meters of the 55-meter ship in the barn's reference frame (allowing for rounding to the nearest meter, as I've done).

 

[Ziggurat]

You guys probably get a lot of these: sorry if this has been posted before many times.

I thought I understood General Relativity, until I read a question posted by RussDill a while ago. Now he has got me confused again...

Scenario:

A ship is 100 meters long (at rest w.r.t. the barn), and traveling at 5/6 the speed of light, relative to and in the direction of a barn on a planet. The barn is 60 meters long. We of course have a barn-owning physicist and a ship owning physicist who are bored with lots of equipment. Assume the barn has two doors, North and South, with the ship traveling northwards.

The barn-physicist will see the ship squashed to approx. 50 meters (rounding here), and will appear to him to fit inside the barn. Remember, from his prespective he is not moving, and the ship is at high speed.

There's a better version of this problem, which is basically the same up to this point. Instead of lasers, though, the question becomes, can you close the barn doors to trap the ship inside, and then stop the ship as soon as it's inside? No synchronicity required here (you need to decide in which reference frame the two events, the back end of the ship going through the barn and the laser beam triggering, are simultaneous), just keep the back door closed and close the front door as soon as the ship is inside.

It turns out you can't do it, the ship will collide with the back barn door and one or the other will break, again because of the problem of simultaneity. But it also brings up an issue that most people don't tend to think about: in special relativity, the speed of sound in a material cannot exceed c either, meaning that you cannot have an infinitely rigid body. The space ship will necessarily stretch/compress as you accelerate/decelerate it.

Another little thought: If we could view the universe from the POV of a photon, we would see the entire universe as a singularity (i.e. single point), and time would consist of a single instant, and nothing would ever change. However, you would get to whereever you wanted instantly.

A photon isn't a valid inertial reference frame. Not to say you're wrong, more that it's just not really relevant to anything.

 

[Gestahl]

Almost instantaneous? No.



10 m (from the point of view of the barn physicist which includes length contraction of the moving ship pieces) is correct. Your reasoning on the ship physicist's view is wrong though. You need to take into account both the time taken for the signal to get from the sensor to the laser AND the fact that the barn (and hence sensor and laser) appears to be moving at 5c/6. I get the same answer for both frames. The answer is that, in the rest frame of the ship, 18.1 metres are sliced from the end of the ship (assuming, for the sake of the problem, instantaneous magic slicing lasers).



Well, the bits won't actually slow down just because they've been sliced up.

Thanks! I was forgetting to take that into account. It is hard to keep track of all the modifications you need to make to the frames when you have not done it mathematically. Thanks again.

 

[Skeptic]

What we have here is a vivid example of the problem of thinking in relativistic terms. (I'm not dissing you--we ALL have this problem; our brain didn't evolve to deal with a relativistic world.)

Your question, with the pyrotechnics taken out of it, is: "if A sees B's length become shorter and B sees A's length become shorter, which one of them REALLY became shorter?". It's the same idea as "If A sees B's time slow down and B sees A's time slow down, which one's time REALLY slowed down?", or "If A sees B gain mass and B sees A gain mass, which one of them REALLY gained mass?"

The question is in a deep sense meaningless, since the whole point of relativity is that there is no such thing as the "real" answer (e.g., a "real", or preferred, reference frame in which to make the length, time, or mass measurement.)

To answer your question, though, note that the closing of the barn's doors, which are simulatanous from the barn's frame of reference (e.g., occur "at the same time") need not be so from the ship's point of view. Here is a detailed answer (usually given as the "pole in a barn paradox"):

http://www.phys.unsw.edu.au/~jw/pole.html