Subjective FTL travel (relativity thread)

[Jarvitä]

Because the other relativity debates came close to making my head hurt and produced no agreeable conclusion, can a theoretical physicist please clear this up:

A starship headed for a star 100 ly distant accelerates up to a velocity of .9c relative to an Earth-based observer. At that velocity, the Lorentz factor is 2.294.

According to shipboard instruments, the voyage took [math]t=\frac{\frac{l}{v}}{{L_{F}}}=\frac{\frac{100ly}{0.9c}}{2.294}=48.43\ years[/math]
True/false? Why?

 

[xlns]

Because the other relativity debates came close to making my head hurt and produced no agreeable conclusion, can a theoretical physicist please clear this up:

A starship headed for a star 100 ly distant accelerates up to a velocity of .9c relative to an Earth-based observer. At that velocity, the Lorentz factor is 2.294.

According to shipboard instruments, the voyage took [math]t=\frac{\frac{l}{v}}{{L_{F}}}=\frac{\frac{100ly}{0.9c}}{2.294}=48.43\ years[/math]
True/false? Why?

True. People usually need some time to understand that apparent 2c speed of your ship is not in conflict with causality. Do note that apparent speed of ship can be as high as you want (if you got energy to push), BUT the price you pay for it is that from your perspective all process in outer universe speed up with same factor - let say that star of yours is about to go supernova in 50 years at the time you start the flight and you plan to make a closeup measurement - you will NOT make it in time for the show.

 

[jedidia]

True/false? Why?

True, but you still wouldn't perceive your speed as faster than light. Merely the distance would seem much shorter, because of the Lorentz contraction.

 

[hribek]

Yeah, the universe (everything you're counting your speed relative to) will contract in the direction of your travel. That's how it works.

Here's a flash application (English version) that might help you out. When you open it, flip the pages manually to "scene 12". There's a demo of 30 years for flight to Sirius B (you can change your speed using a simple slider in the +- 0.999c range).

http://utf.mff.cuni.cz/~jobdr/download/7xNO.rar

 

[xlns]

True, but you still wouldn't perceive your speed as faster than light. Merely the distance would seem much shorter, because of the Lorentz contraction.

I respectfully disagree. Perception of speed of the ship will be higher than speed of light. Reason this is so is because travelers would mix information from different coordinate systems; imagine that along the path you will pass near two stars: one at the 1/3 and second at 2/3 of the way. Aboard the ship, you start the clock right when you pass the first one and measure to see how much time passes until second star fly by - and exactly that is the perception of speed from the space ship. When you quantify your perception, what you do is divide the distance between the stars, which is known from Earth's(!) inertial system with the time on your clock, which is information from noninertial system of starship - and only because of that, speed comes up to be 2c. Sure, stars may look flattened along the velocity, but that doesn't change a fact that with enough energy, you could fly aside those stars in five heart beats - perception is about looking through window, not taking info from MFD and calculating exactly how much would those stars be flattened.

 

[hribek]

You have to keep in mind exactly that - you're mixing things up.

Because not only the stars would appear "flattened". So would the distance between them. And that distance will be shorter. So unless you deliberately combine the-distance-from-Earth-that-was and the-time-period-on-ship-that-is, you're not getting over the speed of light in your calculations or perceptions, ever.

 

[xlns]

You have to keep in mind exactly that - you're mixing things up.

Because not only the stars would appear "flattened". So would the distance between them. And that distance will be shorter...

My answer was directed at describing subjective perception of high gamma flights; you could board passengers at Earth and, as they see it, in a matter of hours land be at the other side of galaxy. To a average human traveler, a well known fact of galaxy diameter would combine with the time of travel to produce an intuitive FTL conclusion. Discarding this intuitive style of reasoning is the hardest part of learning relativity, but that is a perception of many c speed and it's real. Looking through a window of spaceship, you can't see empty space contracting.

 

[Jarvitä]

Looking through a window of spaceship, you can't see empty space contracting.

No, but you can see the stars becoming Doppler-shifted towards blue/red and eventually outside the visual wavelengths entirely.

 

[RisingFury]

You can get from one point in the universe to another in arbitrarily short time. But only in your own time frame...


The most energetic cosmic ray we ever detected had an energy of 50 J. That's huge for something that weighs on the range 10^-30 kg. That particle would travel from our Sun to the nearest star in microseconds.

 

[Jarvitä]

The most energetic cosmic ray we ever detected had an energy of 50 J. That's huge for something that weighs on the range 10^-30 kg. That particle would travel from our Sun to the nearest star in microseconds.

That would put its velocity within centimetres per second of c. But the subjective trip to alpha centauri would still take a half an hour, given its subjective velocity of 122000 times c.

 

[HarvesteR]

Hey, nice thread this one... I think I finally was able to visualize it.

Last week I found a very interesting article by Sean O'Neil, in which he details a method to render interplanetary scales on OpenGL, without loss of precision.

Now, OpenGL (and the video card's Z buffer) are limited to 32-bit precision floating point numbers... so that means that at 15000km distance from origin, you lose precision at the one milimeter level.... That caused planets on a sun-centered simulation to twitch and drop out of orbit due to these precision errors.

The solution he proposed was to, instead of actually placing objects at their real positions, to record these positions as double-precision numbers, and contract the scale of the universe depending on each object's distance from the observer.

This way, distances and sizes are scaled down, once the distance starts to reach the maximum threshold. This goes on up to infinity. So while planets will appear be very much farther away, they are just infinitesimaly close to this artificial outer border.

Why did I go through all this? Because it helps to visualize the effect. Only, instead of distances and sizes, you're talking about time and speed.

So, If I understand correctly, the closer one gets to C, the more your ship will seem to lose acceleration to the folks back at mission control.

To you and your crew, things around you will seem to speed up, and happen faster.

Actually, if the universe were a physics simulation (which some scientists say there is a good chance of being true ), this would be a neat way to prevent things like collision errors due to objects going too fast. :thumbup: :hmm:

Whoever coded the Matrix actually did a pretty good job then
(except for the occasional bug every now and then... but that we can blame on the marketers who hired him)

Cheers

 

[Jarvitä]

If the intention was only to produce more accurate results, they did it very poorly, because the optimisation method has profound effects on the simulated universe itself. :lol:

 

[hribek]

So, If I understand correctly, the closer one gets to C, the more your ship will seem to lose acceleration to the folks back at mission control.

Yes. From Earth POV the ship gets heavier and its clock runs slower, so with constant thrust the second (Earth time) derivative of (Earth reference) position will decrease if constant thrust is assumed.

To you and your crew, things around you will seem to speed up, and happen faster.

This is incorrect. To the crew, everything on ship is normal. In the Earth reference frame everything will happen slower as well from ship's perspective.
However, as mentioned in the flash app I linked, if there were clocks along your way that you saw as synchronized before you started moving, they would run slower (as I said above), but would get out of sync more and more as you speed up.

 

[Fizyk]

The answer is already given, it's true, and there is no travel at 2c because of Lorentz contraction. Everything is fine.

By the way, you can simulate this subjective FTL in the black hole simulator I wrote (http://orbiter-forum.com/showthread.php?t=20971). Turn on-board time on, ignore the black hole and just accelerate in some direction. When your velocity approaches c, the distance from the black hole will start to go crazy

Another funny effect is that when you travel at near-c speeds, objects in front of you visually appear to be further than normally, not closer (well, assuming you can see UV or X rays). It's because your field of view gets compressed to a narrow cone near the forward direction. Objects start to look smaller and therefore appear as if they were further, but if you were to measure the distance properly, the result would be that they are closer (Lorentz contraction again).

Also, another awesome program to visualize all this: http://realtimerelativity.org/

 

[jedidia]

you could fly aside those stars in five heart beats - perception is about looking through window, not taking info from MFD and calculating exactly how much would those stars be flattened.

I wasn't talking about subjective perception, which can be different for anyone. For example, I could as well perceive not travelling at the speed of light, because I can still see stars when I look out of the back window, so that light has to catch up somehow. Or I could hybernate for a two-milenia journey and perceive the trip as being instantaneous. It isn't helpfull.

In any case, no matter how ftl your perception was, reality will catch up with you when you get back to your point of origin. For all you can perceive, you might as well have slept a few years every night and noone on bord bothered to tell you.

I was talking about measurements, and measurments will tell you that you are advancing slower than light. And when you take it all and calculate it relative to any reference frame there is in the universe, it will ALWAYS be slower than light. That's just the way it is.

To you and your crew, things around you will seem to speed up, and happen faster.

Definitaley incorrect, but a common misconception. A second will always be a second. The best proof for that is that the atoms in your atomic clock will still have the same half-life. They don't suddenly start to decay sooner.

 

[HarvesteR]

Yes. From Earth POV the ship gets heavier and its clock runs slower, so with constant thrust the second (Earth time) derivative of (Earth reference) position will decrease if constant thrust is assumed.


This is incorrect. To the crew, everything on ship is normal. In the Earth reference frame everything will happen slower as well from ship's perspective.
However, as mentioned in the flash app I linked, if there were clocks along your way that you saw as synchronized before you started moving, they would run slower (as I said above), but would get out of sync more and more as you speed up.

Hmm, I think I get it... The crew's preception of time actually depends on the direction you're looking at, right?

If you're looking back at where you came from, time would seem to slow down as you approach c, provided you're still able to make sense of the hugely red-shifted light coming from behind...

Facing forwards, you're essentially fast-forwarding through the light feed coming from your destination, so it will start to catch up to it's present day state...

Hmm, it would be a huge bummer to try and reach a star some million light-years away, only to find out half way there that it went supernova a half-million years ago, but news of it hadn't reached you yet :uhh:

Hopefully I'm right this time

Cheers

 

[jedidia]

Hmm, I think I get it... The crew's preception of time actually depends on the direction you're looking at, right?

No, the crews perception of the speed will be the same no matter where they look. However, the speed of the ship will be different for different observers, depending where they're looking FROM (obviously the ship would apear to travel slower relative to another ship on its heels that also travels at a significant fraction of c than from earth, which travels at a totally insignifcant fraction of c).

The crew will only perceive the distance between origin and target to be much shorter than they're used to from earth, as it contracts (or, as seen from earth, the ship expands in the direction of travel).

both the distance as well as travelling time are subject to the Lorentz factor, which is a pretty simple formula and one of the most important when dealing with special relativity:

Lorentz-factor = 1 / sqr(1 - (v / c)) (sqr means square root, in case that is unclear. v is the velocity, c is the speed of light).

Both distance and time as perceived from an onboard observer are equal to the "real" time and distance divided by that Lorentz factor (hmmm... it's been a while, but I think thist statement should be correct?). It also shows why ftl is such a big fuss, at least in our current physical framework (which so far has held up to quite thourough experimentation, but still has to have some slight misconceptions somewhere as quantum mechanics have shown): if v > c, you get a value larger than one for (v /c), which means that 1 - (v / c) will come up negative. Take the root of a negative number on your calculator, and you'll see the problem... also, if v = c, you'll get a division by zero, which is just as bad...

 

[Jarvitä]

Take the root of a negative number on your calculator, and you'll see the problem...

So ftl is only possible on a complex time plane?

also, if v = c, you'll get a division by zero, which is just as bad...

And you have to jump from v < c to v > c without hitting c itself.

I'm getting ideas about cheesy handwavium already...

 

[HarvesteR]

I'm getting ideas about cheesy handwavium already...

I envision an entire Sci-fi show based around that premise :thumbup::lol:

Cheers

 

[Fizyk]

Hmm, I think I get it... The crew's preception of time actually depends on the direction you're looking at, right?

Depends on what you define as perception of time. There are two possibilities:

1. What the crew see (if they look at a clock, what time will they see).

2. What is happening where they look at the moment they look in their frame of reference (as in, what time there is on the clock now - with distance correction).

With definition 1, yes, it depends on the direction, the Doppler effect shows that pretty nicely (redshift behind, blueshift in front). With definition 2, it's independent of the direction.

It also shows why ftl is such a big fuss, at least in our current physical framework (which so far has held up to quite thourough experimentation, but still has to have some slight misconceptions somewhere as quantum mechanics have shown): if v > c, you get a value larger than one for (v /c), which means that 1 - (v / c) will come up negative. Take the root of a negative number on your calculator, and you'll see the problem... also, if v = c, you'll get a division by zero, which is just as bad...

Actually, that's the smallest problem. The main problem is that FTL travel breaks causality, which is widely believed to be true (although it's not proven to be true, we just believe it should work like that in a normal universe ).

So ftl is only possible on a complex time plane?

It's possible to redefine some values a bit and still have both FTL and real time, but as I wrote, it breaks causality. Actually, if you have FTL, you get time travel for free (although it's not true that going FTL makes you automatically travel back in time).