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Context

According to relativity law, it is possible to travel into the future approaching the speed of light. For the 2nd Newton's Law of motion, in absence of friction (or opposite force), we can accelerate every object indefinitely if we apply a continuous constant force. Today the biggest obstacle to achieve an high speed is the friction on earth or the impossibility to apply an indefinitely force in the space. But the friction can be easily bypassed with a vacuum tube, today we are already able to accelerate particle almost at of light in accelerators like LHC. Accelerate a macroscopic object is much more difficult, because it require lots of energy, but I think it's technologically possible.

Vactrain is an emerging technology, developed to transport people using a maglev train in a vacuum tube. A first project that uses that technology (HyperLoop One) will be develop to connect Dubai to Abu Dhabi (~130 km) in only 12 minutes with maximum speed of 1200 km/h. Assuming 6 minutes of acceleration and 6 of declaration, we are able to achieve a speed of 1200 km/h in only 6 minutes.

Idea

  1. So I had an idea, if instead of 6 minutes, we accelerate the train with a constant force for 1 month with a constant acceleration, we are able to approach the speed of light?
  2. If no, assuming a tolerable acceleration of 1G (9.8 m/s²), how much time will be required to approach the 99.9% of light speed ?

With the question 1, I am asking to apply the relativity law to calculate if is feasible to approach the speed of light (I assume 99.9% as arbitrary value).
Remember that when we approach the speed of light, the acceleration is no more constant, because the force will increase the mass instead to increase the speed.    

  

Question 2 , to answer only if you answer to question 1 that is impossible to approach the speed of light in only one month of acceleration with a constant force
With question 2 I am asking to calculate the time necessary to approach the speed of light with a tolerable acceleration.
I assume 99.9 % of light speed and 1 G as arbitrary values.

  1. Furthermore, because it's impossible to achieve that speed on a straight path, we need to create a circular vacuum tube.
    The defect, of this solution is the Centrifugal force, so we need to create a very large circle, and the question is how much large should be the circle to maintain a tolerable force of 1G with the speed of light?

With question 3 I ask to calculate the centrifugal force function with a speed similar to light speed (I don't think that 100% or 99.9% affect the calculation)
And then I ask to optimize that function to achieve a maximum force of 1G, I'm expecting that you provide the diameter of circle in km as optimized value.

  1. Then if we build this system, with a speed of 99.9% of speed of light, how much time will be required to travel of 100 years into the future?

With question 4 I ask to apply the relativity law to calculate how long should be the trip to send a human into 100 years into the future.
The time is related to passenger, since for observer is equivalent to 100 years.

  1. Probably today if this project might be technologically possible, is not economically, also the only one that can take benefit is the passenger, anyone else should wait 100 years to have a feedback.
    But according to this in the 2039 will be the first trillionaire, and if we think that today lots of people entrust their lives cryogenesis in the hope of a better life, probably someone can built this machine for personal interests.
    Today cryogenics has lots of limits, especially ethical, we have no proof that a human frozen can be revived, and for that reason we can freeze only death people.
    But a death people, probably not even be resurrected, so a true time travel can be the only option to see the far future.

5 is not a question, but I express my opinion about the idea.

  1. Do you think that a vactrain time machine can be ever be built? and do you think that can be a valid alternative to cryogenics for very rich people?

With 6 I ask your option about this project, in particular feasibility and use case.
Alternative to cryogenics is an example of use case that I proposed.

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  • $\begingroup$ It's not really clear what you're asking - you ask "how much time will be required to accelerate" and "how large would the loop be" and "how much time will be required to travel" and "can it be built" and "will it replace cryogenics" ----- consider breaking this into separate questions or this may be closed. $\endgroup$
    – Zxyrra
    Nov 24, 2016 at 23:57
  • $\begingroup$ Thanks @Zxyrra for edit, I speak bad English. About the questions they are related, practically I am asking the feasibility of this idea. The first questions are only physics calculations (calculate the time to approach the speed of light the relativity law), then I asked an opinion about this idea. I'll try to edit the post to improve readability... $\endgroup$
    – Stefano Balzarotti
    Nov 25, 2016 at 0:04
  • $\begingroup$ I would suggest your questions are better suited to the Physics Stack Exchange. Perhaps you should ask a moderator to migrate your questions there on your behalf. $\endgroup$
    – a4android
    Nov 25, 2016 at 1:05
  • $\begingroup$ @a4android I was undecided about where to open this post, but because I don't need accurate physics calculation, but an opinion about feasibility of this futuristic project, I think this site is better. $\endgroup$
    – Stefano Balzarotti
    Nov 25, 2016 at 12:53
  • $\begingroup$ Four out of six of your questions require calculations for answers, so Physics SE seemed like a better choice. Ultimately, you're one who knows what you want answered. The choice is yours. $\endgroup$
    – a4android
    Nov 26, 2016 at 7:42

3 Answers 3

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Your train can't be built.

To save some math, consider a satellite in very low Earth orbit. Its period is about 80 minutes. That's a reasonable approximation of what it would be on the surface, also.

You build your train around the equator, if it goes around its track in 80 minutes you have 1g outward force balancing the 1g from Earth, the passengers are in free fall. That's only 8km/sec.

Obviously, we aren't building this on Earth.

Remove the Earth, put our train in space. 1g outward force—acceptable. Let's scale it up:

×10,000. Our train is now moving at 26% of lightspeed but we have a track 127,000,000 km across—nearly a big as Earth's orbit.

×4. Yes, we are supposedly moving 104% of lightspeed and our track is 508,000,000 km across—it's out there between the asteroids and Jupiter.

Note that this is purely Newtonian, I'm out of my depth in trying to figure what's going to happen when we apply Einsteinian math to this.

And another point—boosting at 1g it takes about a year to get close to lightspeed, not a month.

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  • $\begingroup$ And don’t forget the amount of energy it would consume! $\endgroup$
    – JDługosz
    Nov 25, 2016 at 7:22
  • $\begingroup$ Thanks, now I understand that technology is not feasible in the near future, maybe in a very far future we can build a train around the asteroid belt ☺. But I think in the space a tube is no necessary, since the space is already empty... $\endgroup$
    – Stefano Balzarotti
    Nov 25, 2016 at 10:09
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    $\begingroup$ @StefanoBalzarotti Actually, at those velocities you need the tube to protect it against what little is out there. The tube need not be strong, though. The track has to be, though--and needs stationkeeping systems to keep it in orbit. Left to it's own devices a ring falls out of orbit. $\endgroup$
    – Loren Pechtel
    Nov 25, 2016 at 11:07
  • $\begingroup$ @Loren Pechtel, true but probably is easier to accelerate a space ship into interstellar space and turn back using an antimatter engine... Anyway these are only speculations, because this technology is too futuristic to make a prevision. $\endgroup$
    – Stefano Balzarotti
    Nov 25, 2016 at 12:57
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Yes, a vacuum train doesn't have to deal with air resistance. But if it's a circular track, you still have to deal with centrifugal force. If you're moving at speeds close to light speed, that's a huge amount of energy.

And by the way, you can't pump literally 100% of the air out of your vacuum train tube. You can pump out enough so that for a train travelling at several hundred miles per hour, it's close enough to a vacuum that the small amount of air makes negligible difference. But at near-lightspeed, you'd be hitting billions of air molecules every second at incredible speeds, releasing incredible amounts of energy. Barring some sort of advanced technology -- force fields or whatever -- your train would be vaporized in seconds.

And bear in mind that this is only "sort of" time travel. The people on board will experience time moving more slowly for them than it does for the people around them. But the vacuum tube is not moving at near lightspeed, so it's still experiencing time normally. So while a person on the train might perceive himself as travelling 100 years into the future while he only lives 1 year, someone has to be maintaining that vacuum tube for them to travel in for 100 years. Someone has to be supplying power to the train over that whole time, etc. If at any time during the trip there's a breakdown, we could have a train travelling at near lightspeed running off the track. This would seem like a bad thing.

I haven't worked out any of the numbers, but I suspect the technology to do anything like this is very, very far away.

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  • $\begingroup$ I don't think that some few particles can cause issue, because we don't put directly the train at light speed. The train increases its speed gradually, and if encounter a particle, the particle acquires the speed of train. After one year of continuous acceleration, the train and all particles they moves at same speed. The only issue is that is necessary more energy to accelerate the train and the few particles of air. $\endgroup$
    – Stefano Balzarotti
    Nov 25, 2016 at 12:45
  • $\begingroup$ @StefanoBalzarotti That assumes that no new particles of air (or dust or whatever) can enter the tunnel during its trip. I doubt that its possible to build a tunnel on the Earth that is really 100% air tight. Also that any particle that strikes the train is carried with the train indefinitely. I suppose we'd have to know more details of how the train and tunnel are constructed to be definitive about that. $\endgroup$
    – Jay
    Nov 28, 2016 at 14:11
  • $\begingroup$ How do you think accelerator like LHC works? The pressure is 1.013 × 10^-10 mbar, but they are able to accelerate hadrons without interferences. However as @Loren Pechtel said, it's impossible to build that machine on earth, the centrifugal force is too high... This construct can only be built in the space with a diameter of ~ 500,000,000 km $\endgroup$
    – Stefano Balzarotti
    Nov 28, 2016 at 16:47
  • $\begingroup$ They don't run trains through colliders! They run a small number of subatomic particles. The probability that a subatomic particle will hit a random oxygen molecule is pretty low. The probability that a train will hit a random oxygen molecule is very high. I don't know enough about the number of particles being accelerated or the density of atmospheric molecules to calculate the probabilities. Do they sometimes have such collisions? I'd guess they do, but I don't know. I'd be happy to hear from anyone on here who knows more. $\endgroup$
    – Jay
    Nov 29, 2016 at 14:22
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Q2. It will take approximately one year at a constant acceleration of one gravity to attain a sufficiently large fraction of lightspeed. Allowing for special relativity, this will mean an external observer we see the vehicle at constant one gravity acceleration taking about thirteen to fourteen months to reach, say, 0.99 c.

Q1. In one month your vactrain accelerating at a constant one gravity will only attain one-twelfth of lightspeed.

An acceleration track or tube to accelerate an object to almost lightspeed also needs to be about half a light year long. An equivalent circular system must deal with incredibly strong forces to keep the vehicle on track.

Devices like this are only plausible as hypothetical constructs.

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