# Traveling at the speed of light and time dilation

1. Aug 16, 2013

### DHF

hey guys,

I need some tech support for a spaceship in a story that is currently in the works :)
Assuming the characters could get their ship up to the speed up light in real space (no hyper drive or warp drives) What would the effects of time dilation be on the crew? Time slows down as you approach the speed of light but what happens when you actually reach that barrier? does time stop for the crew? A trip to Alpha Centuri would take 4 years to the outside world but to the crew how much time will have passed?

Thanks for the help

2. Aug 16, 2013

### phinds

You don't reach it.

3. Aug 16, 2013

### Ryan_m_b

Staff Emeritus
It's impossible for objects with mass to attain the speed of light. You're question is therefore unanswerable because it essentially asks "if we ignore the laws of physics what do the laws of physical say?"

4. Aug 16, 2013

### micromass

You can't go the speed of light or faster.
That said, you can get to Alpha Centauri arbitrarily fast if you go close enough to the speed of light. So if you go fast enough, then you can get there in just a minute or less. Of course, to people on earth, it will have taken years.

5. Aug 16, 2013

### Fieldwaveflow

The best books

You may want to stick with some of the science fiction I've read. Ships (and the people in them) have an almost instant trip time (t1) while traversing the distance of 4 light years (d) as they move 4 years (t2) into the future.

Hard to comprehend. It's not a standard way of thinking.

6. Aug 16, 2013

### DHF

ok good to know. so reaching the speed of light would never happen but the crew could reach 99.99% the speed of light, in which case from their perspective they would only be in transit for a few minutes.

7. Aug 16, 2013

### Bandersnatch

8. Aug 16, 2013

### Ryan_m_b

Staff Emeritus
I first encountered this in Ken MacLeod's Engines of Light trilogy. Ships essentially have a jump drive but rather than being instant like most other science fiction universes it takes exactly 1 second to jump 1 lightsecond but is instant from the perspective of the crew.

Actually at 99.99% 4 lightyears would take about 3 weeks. Many science fiction worlds use near-light speed travel but you have to consider things like how these speeds are achieved (try plugging in 0.99c into the relativistic rocket equation and you'll quickly realise how unrealistic the fuel requirements are), what protects the crew from radiation (which gets worse and worse the faster you go) etc etc.

9. Aug 16, 2013

### cyberdiver

If you DID (somehow) reach the speed of light, γ = ∞, which means your mass would be m*∞, the light in coming toward you would be blueshifted by a factor of ∞, the shipboard time would be slowed by a factor of ∞...you get the idea (everything changes by a factor of ∞ relative to whatever you choose to call stationary.)
This website should explain why it's impossible for any matter object to reach the speed of light: http://www.pitt.edu/~jdnorton/teaching/HPS_0410/chapters/Special_relativity_adding/index.html

10. Aug 16, 2013

### DHF

yeah that might not be so cool. I wanted to give them a method of travel without warp bubbles or any of the other classic sci-Fi devices but as you all pointed out, traveling in real space would be packed with obsticals. not just the radiation but I imagine the sadness they would have if they passed through a dust cloud.

thanks for the info and calculators. I will try to figure an alternate method of travel for my intrepid crew.

11. Aug 16, 2013

### cyberdiver

Relativistic travel can be quite fun. For example, there's Stephen Baxter's short story Pilot available in the public domain here which explores the real extremes of relativistic travel.

Edit: The dust problem can be solved with a dust shield, but a dust shield can only erode so much.

12. Aug 16, 2013

### Ryan_m_b

Staff Emeritus
What's the general plot of the story? Perhaps we can help come up with a suitably scientific plot device. For example; if the story takes place in another system you could have them getting there very slowly (i.e. in a ship that's only boosted up to 1% light speed) whilst travelling in some form of suspended animation.

13. Aug 16, 2013

### DHF

the plot of the story is about the first manned flight to Alpha Centuri. I haven't set a date for the tale yet but I figured it was several hundred years from now. The story will center around the characters's reactions to being separated from their native time. the concept of only a few days passing for them yet years or decades have escaped their notice on Earth. I didn't want warp drives or other magical forms of tech because I didn't feel we would be there yet. I wanted to give Earth advanced tech by our standard but still grounded by our current understanding of physics. That being said, thanks to the Calculator Bandersnatch provided (thanks man you are always helpful) I realize the utterly absurd amounts of energy required, so unless the crew has a ship powered by their own personal sun, I don't think my original idea will work.

Two possibilities I can think of involve :
- pushing the ship into an alternate dimension during travel where it would not be subjected to the laws of physics.
- Wrapping the ship in some some sort of energy field that gives the ship 0 mass during the acceleration period.

Both of those ideas however dance happily into the realm of magical technology so I wanted to avoid that.
Taking your advice Ryan_m_b I could put them in suspended animation and move them at 2% of c. that would get them there in about 400 years. it would require a near sentient computer system to pilot the ship on such a long journey but I think that is a lot more feasible then getting a ship to the speed of light.
Although if I go that route I would have to figure if the government of the time would be willing to spend the money and resources for a venture that would not benefit their nation for centuries. Of course it also opens the door for the crew to spend 400 years in stasis and when they wake up, Humanity is already their, having invented faster means of travel while the astronauts slept.

possibilities.

14. Aug 17, 2013

### cyberdiver

Perhaps the government could be motivated by some threat in Sol, and so start throwing together colony ships to spread humans around.

15. Aug 17, 2013

### Fieldwaveflow

dust cloud

dust... The ship would sort of be in a time bubble. Anyone looking at the ship might see it as a small, fast moving black hole. Maybe since the ship is near light speed the ship density would be altered to allow it to plow through anything non-relativistic. Or maybe it would just be a very quick trip into oblivion. I'd like to see how a ship near c would decompose on impacting an object. May just look like what happens in atom smasher, not just vaporized but decomposed to destabilized particles of energy. How would you ever turn with that much momentum? What power source could possibly produce the energy needed? You'd have to carry tons of extra mass as fuel even if you could get every last proton of the material to convert to energy. You couldn't see anything, let alone dust, because most of the visible light would be reduced to a little point in the front of the ship from lensing.

16. Aug 19, 2013

### DHF

that's an interesting idea, The ship moving at near light speed would have near infinite mass but does mass translate into density? and the dust and particles they plowed through,seeing as how they would be impacting the hull at near light speed relative to the ship, would those particles impact them with the same amount of energy as they were spending to move forward?

17. Aug 19, 2013

### cyberdiver

The ship would have 'near-infinite' mass relative to a stationary observer. About the particles, probably not (1 hydrogen atom/cm^3).

18. Aug 19, 2013

### Karden

If they are successful at someday building this "warp drive": [http://www.newscientist.com/article...ising-a-starship-warp-drive.html#.UhLUIWT70pc ], wouldn't this counteract the effect of time dilation to some extent? I've always thought of time dilation as related to the reduction of space-time density as speeds increase, but since this drive would compress space-time in front of the ship, seems like it would reduce the time dilation effect to some extent.

That would seem to modify the amount of information in the universe during the duration of the flight (for reasons that are too complicated for me to go into, but if you get it, you get it), so seems like there's some special circumstance math that would have to be included in order to calculate time dilation effects for this type of spacecraft.

Another thing that bugs me about the idea of warp drives like this are that the density of space-time is correlated with mass. If they are compressing space-time in front of the ship, are they circumventing the "infinite mass" problem?

Last edited: Aug 19, 2013
19. Aug 19, 2013

### Karden

If it compresses space-time in "front" of the ship, and decompresses "behind" the ship, I think this would actually propel the ship *backwards*. Not only does nature abhor a vacuum, but so does space-time. It demonstrates this by propagating the information that represents coherent structures (like spaceships and atoms) from denser regions of space-time to less dense regions, across vast distances. This attribute of information propagation through the switching fabric of space-time is often referred to as Gravity.

20. Sep 3, 2013

### DHF

Thanks CyberDriver,

That was a good read. It did a good job of trying to stick to realistic concepts. One of the weak spots I noticed however was fuel. The author accounts for this by noting that the fugitives are cannibalizing their planet for fuel but the missile on the other hand has no such fuel source so how does it continue to pursue them?

The other inconsistency I noted was their acceleration. They say the missile is using an Earth made drive which limits it to 1 G acceleration. the missile later updates itself to 2Gs, we can accept this because the dialog suggests the missile is reinventing itself beyond its original limits. but then our fugitive heroes casually accelerate to 2 Gs to match the missile, later there is talk that they are traveling at 1000 Gs acceleration. You might say that they can afford such acceleration because they have massive amounts of fuel but that leads me back to my question about how the missile can keep up.

Last edited: Sep 3, 2013
21. Sep 3, 2013

### cyberdiver

Exactly. It illustrates relativistic effects well, but it just surpasses my willing suspension of disbelief threshold by several orders of magnitude. When they mention accelerating at 1000 Gs, I forgot to drop my jaw as well.

22. Sep 3, 2013

### DHF

Yeah 1000Gs was pretty ridiculous, he could have played the same story at 1G, with the Missile increasing by small increments. 1.1G would still allow the missile to catch them, so with much effort they manage to go 1.15, and the missile eventually moves just a little faster ect.

At 1000Gs time looses all meaning for the crew. The main character speaks of the chase lasting years and I assume she means outside time because relatively the entire journey would only last a few days. The trip all the way to Andromeda would only take 15 days or so. at that speed time bogs down so much that going to the next galaxy or going a hundred billion light years would only be a matter of days to their reckoning.

Yet at the end of the story then mention the journey to Andromeda taking 2 months, that wouldn't be correct if they were still accelerating at 1000Gs and by the end they are going several magnitudes faster then that because of the black hole.

...
really, the solution was there from the beginning. when they noticed that the missile was accelerating towards them at 1G they could have just tossed a chunk of ice directly in their path. it sounded like neither the missile nor the dwarf planet had any real maneuverability so if they chucked a bolder behind them as they were going .25G, the missile, traveling at 1G would have smashed into the bolder and likely been destroyed.

my story would have been over very quickly. I suppose his way was a lot more interesting :)

Last edited: Sep 3, 2013
23. Sep 3, 2013

### Fieldwaveflow

I'm wondering

To an observer; what would be the apparent size of the relativistic ship? Aside from not being able to see the spaceship due to high energy concentration space-time. The place where it is would be would appear very small from length contraction.
From the missile's perspective...well, the sensors would need to correct for the light warping effects when traveling near the external c by using some de-lensing algorithms for the onboard computer and sensors. Then it might see a faint dark spot in a bright back ground to go after. You may need to take into account how much light is coming out of the back of the ship from propulsion.

That is cool. The idea of a missile trying to catch up to something near light. The missile would need to put out more energy to the point of going faster in time to catch the ship. And of course the ship would need to be traveling to a far distant destination to allow the missile time for it's faster rate of time to catch up to the ship before it reached the destination...The ship would have to decelerate at some point. That would mean doom. Unless they had enough fuel to outrun the missile or maybe alter course to put an asteroid between the ship and the missile. I wonder if the missile stayed at near c when it got to a planet destination if it wouldn't just pass through the planet since it would be so small and the density of a planets mass would be like a gas compared to the missile. The missile might see itself just zip right through a planet while those on the planet saw a black hole headed their way for hundreds of years.
Sorry, hard not to think of the other implications of a missile doing 1000g while trying to catch a ship near c.

24. Sep 3, 2013

### DHF

Fuel is something that the story does not take into consideration at all. The protagonists's ship is a dwarf planet and they are using the mass of the planet itself to fuel their acceleration. there is no mention of what the missile is using for fuel but it is mentioned that it is using the same type of engine so the dialog clearly indicates that large amount of mass have to be fed into the drive to continue accelerating. by the end of the story the main character describes her world as having been reduced to a splinter after years of feeding the engine. yet the missile is never mentioned as having any sort of unlimited fuel.

This story does bring up another interesting question though. If a ship is traveling to Andromeda at just under the speed of light, in actuality it would take 2 million years to get there. Relatively however it would take days. Would the ship need 2 million years worth of fuel to feed the engines or would they only need to keep the engines fueled for 15 or so days, assuming you could accelerate to and survive the 1000Gs proposed in the story.

25. Sep 4, 2013

### Drakkith

Staff Emeritus
Fifteen days seeing as how the trip lasted that long for the ship. And that assumes the engines are constantly being fed the same amount of fuel. If not, then you cannot measure the fuel in "days".