Hypothetical question about time dialation

[Katt7777]

A spaceship has managed to accelerate to 86.6% of lightspeed. Focusing on special relativity would fuel consumption remain the same, better, or worse as opposed to traveling at non-relativistic velocities, what about breathable air?

I understand that the rate of fuel consumption would slowly receed as mass was lost through propellant usage, but I'm more interested in the captain's frame of reference and the effects of time dilation upon him and his ship. At .866c, 2 seconds would pass for an observer on Earth for every one that passed for the captain, since he needs less time to travel a set distance wouldn't he need less fuel, air, water, etc. too?

From his point of view, would nothing relativistic seem to be happening as far as maintaining acceleration, fuel consumption, and closing in on his destination. Would his instruments betray him, would his destination be closer than it should be for his rate of travel?

Thank you for your time.

 

[Naty1]

Hi Katt,
Some ideas you express, ok; some not so much...but some of this stuff is 'tricky'...

Focusing on special relativity would fuel consumption remain the same, better, or worse as opposed to traveling at non-relativistic velocities, what about breathable air?

once the ship reaches .866c the engines can be shut off and the ship will coast at that constant speed in the same direction. There is virtually no [air] friction to slow the ship down. With the engines shut off, no acceleration, those aboard will feel no force related to acceleration.

I understand that the rate of fuel consumption would slowly receed as mass was lost through propellant usage, but I'm more interested in the captain's frame of reference and the effects of time dilation upon him and his ship. At .866c, 2 seconds would pass for an observer on Earth for every one that passed for the captain, since he needs less time to travel a set distance wouldn't he need less fuel, air, water, etc. too?

His local time in the ship passes normally; his clock ticks normally; light continues to pass him at 'c' but will be color shifted; the distance he sees ahead towards his destination is foreshortened.

From his point of view, would nothing relativistic seem to be happening as far as maintaining acceleration, fuel consumption, and closing in on his destination. Would his instruments betray him, would his destination be closer than it should be for his rate of travel?

Inside the ship, nothing unusual happens. He would see a clock on earth, for example, tick more slowly relative to his own clock but should he return would find that his own elapsed time was less than than of the earthbound clock. As he nears speed 'c' more and more fuel usage will result in less and less velocity increase...his speed will be governed by 'rapidity' not classical velocity considerations.

Regarding the details of acceleration, I haven't looked into that aspect in any detail but wikipedia says this:

...the rapidity of an object in a given frame can be viewed simply as the velocity of that object as would be calculated non-relativistically by an inertial guidance system on board the object itself if it accelerated from rest in that frame to its given speed.

[That tricky wording relates to the spacetimes involved.]

http://en.wikipedia.org/wiki/Rapidity#In_one_spatial_dimension

Maybe an expert can comment: Aboard the ship if the acceleration continues, engines on at some fixed power, do those aboard feel a gradually reduced force from acceleration? Or do they feel a constant 'g' force? You might find this wikipedia illustration regarding a 1g rocketship acceleration trip of interest: http://en.wikipedia.org/wiki/Proper_acceleration#Acceleration_in_.281.2B1.29D

 

[Katt7777]

Thank you for your reply Naty1,

The links are nice especially the one about rapidity.

So you believe that in order to maintain a constant acceleration that more and more fuel will need to be used because of the increase in mass / kinetic energy of the spacecraft . Are you sure this wouldn't be mitigated in some way by time dilation?

What about breathable air, food, water, and radiation exposure? Would not they be greatly reduced by time dilation in this case?

 

[jartsa]

The captain of the spacecraft will say: "My spacecraft has exactly the same performance at all velocities"

"Always, when I burn 1 liter of rocket fuel, my velocity changes by 2 m/s. When my velocity changes by 2 m/s, my velocity changes by 1 m/s relative to things that are moving at speed 0.86 c relative to me"

... And the aforementioned "things" agree that the velocity of the spcecraft relative to the "things" changed by 1 m/s, but they say the change took twise the "normal" time.

They say the acceleration of the spaceship is reduced to one fourth of the normal, while its fuel burning rate is reduced to half of the normal.

 

[HallsofIvy]

Maybe an expert can comment: Aboard the ship if the acceleration continues, engines on at some fixed power, do those aboard feel a gradually reduced force from acceleration? Or do they feel a constant 'g' force?

Once again- motion is relative. A person moving with the rocket ship moving with the rocket ship will experience forces due to the acceleration but his speed relative to the rocket ship is always 0. He would feel the same thing whatever his, and the rocket ship's, speed relative to some external object.

 

[Katt7777]

Thanks for the replies,

Let's try a little different angle,

A captain and his spacecraft are moving at a velocity of .866c, which has a Lorenz factor approximating 2. His destination is .866 light years away, and he has only enough breathable air for a little over 6 months. Will he still be alive when he gets there?

From his perspective he has only been traveling 6 months so I would say, yes, but from a "stationary" observers perspective he has been traveling for a year.

What do you say and why?

 

[Nugatory]

Thanks for the replies,

Let's try a little different angle,

A captain and his spacecraft are moving at a velocity of .866c, which has a Lorenz factor approximating 2. His destination is .866 light years away, and he has only enough breathable air for a little over 6 months. Will he still be alive when he gets there?

From his perspective he has only been traveling 6 months so I would say, yes, but from a "stationary" observers perspective he has been traveling for a year.

What do you say and why?

Be precise:
- Captain measures .866 light-years to destination, or the observer who sees the spacecraft moving at .866c measures .886 light-years to destination? (note that I carefully avoided saying "stationary observer" as that's another imprecise concept - you may already know that, as you used scare-quotes around the word stationary - stationary with respect to the destination is what I'm assuming).
- Is the oxygen supply good for six months at the consumption rate that the captain measures, or the observer? They agree about the amount of oxygen consumed at each breath, have different clocks so measure the number of breaths per unit time and hence the rate of consumption differently.

If the captain uses his consumption rate and measured distance to destination, he'll come up with an answer; either he has enough oxygen or he doesn't. Whatever answer he comes up with, the observer will come up with the same answer, even though the observer sees a different consumption rate and distance to destination (and different speed to destination, if the observer is not at rest with respect to the destination).

 

[Katt7777]

Nugatory, please bear with me while I attempt to be more accurate.

The captain measures that he has a little over 6 months of breathable air left on his ship with instrumentation that is on his ship. The captain just past a space buoy that says his destination is .866 ly away. This distance was measured by the buoys instrumentation. The space buoy is moving at the same velocity as the captains target destination. The captain measures the difference in velocity between his ship and the space buoy at .866c, with the instrumentation on his ship.

One extra question, if the captain measured the distance between the buoy and his destination with instrumentation on his ship would this conflict with what the buoy was indicating?

I think it would but I'm not sure why except for the fact that it is being observed from a different frame of reference and relativistic "things" happen when an observer outside relativistic velocities observe relativistic things or vice-versa, but maybe this is the point.

Your input is appreciated and will help me verify or disprove my conjecture.

 

[Katt7777]

If someone could check my guess I'd be grateful.

 

[Nugatory]

One extra question, if the captain measured the distance between the buoy and his destination with instrumentation on his ship would this conflict with what the buoy was indicating?

I think it would but I'm not sure why except for the fact that it is being observed from a different frame of reference and relativistic "things" happen when an observer outside relativistic velocities observe relativistic things or vice-versa, but maybe this is the point.

Yes, the captain would measure a different distance to the planet. As far as he's concerned, there's a planet and a buoy rushing towards him at .866c while he's standing still. At the exact moment that the buoy passes him (it's important that he and the buoy are at the same point in space - otherwise the phrase "exact moment" would not be meaningful) he will see the planet to be .433 light-years away.

So the captain figures that he needs six months to reach the planet (well, actually for the planet to reach him, because he's at rest and the planet is rushing towards him) and because he has a six-month supply of oxygen he survives his journey.

Meanwhile, the guy on the planet (or on the buoy - planet and buoy are at rest relative to one another so are in the same frame) sees the spaceship rushing towards him at .866c. The buoy is .866 light years from the planet in their frame, so they'll see a full year pass before the ship reaches the planet. This would seem to make things look bad for the captain with his six-month air supply (did a little alarm bell go off in your mind when I said "his six-month"? I hope so). But because of time dilation, they also see the captain's clock run slow by a factor of two, so they see the rate of oxygen consumption to be lower by a factor of two, so once again, the captain survives.

It may be easier to think in terms of the number of breaths that the captain takes during his journey from buoy to planet. No matter how we're measuring time and distance, we all have to agree about the number of times he breathes and the amount of oxygen in his tanks... And either he has enough oxygen for that many breaths, or he doesn't.

 

[Katt7777]

Thanks Nugatory

I was hopeful that I didn't misunderstand some facet of special relativity. I was also thinking that the captain would perceive a .433 ly distance with his shipboard instruments. Thanks for the verification.

 

[ImaLooser]

Maybe an expert can comment: Aboard the ship if the acceleration continues, engines on at some fixed power, do those aboard feel a gradually reduced force from acceleration? Or do they feel a constant 'g' force?

Constant g force, of course.

 

[yuiop]

This article on the relativistic rocket http://math.ucr.edu/home/baez/physics/Relativity/SR/rocket.html might be useful, especially the part at the end about the fuel requirements for a relativistic trip.

 

[Naty1]

That baez article is great! I especially liked this last paragraph
[which doesn't even address how one avoids crashing into assorted large scale steller objects] :

One major problem you would have to solve is the need for shielding. As you approach the speed of light you will be heading into an increasingly energetic and intense bombardment of cosmic rays and other particles. After only a few years of 1g acceleration even the cosmic background radiation is Doppler shifted into a lethal heat bath hot enough to melt all known materials.

 

[Katt7777]

Yes, I agree very good article. Thank you for the link yuiop.

 

[Naty1]

Constant g force, of course.

That's not what I conclude from HallsofIvy post nor John Baez's article.

 

[yuiop]

Aboard the ship if the acceleration continues, engines on at some fixed power, do those aboard feel a gradually reduced force from acceleration? Or do they feel a constant 'g' force?

Constant g force, of course.

That's not what I conclude from HallsofIvy post nor John Baez's article.

I am not sure how you reach that conclusion. Here is what HallsofIvy actually said:

Once again- motion is relative. A person moving with the rocket ship moving with the rocket ship will experience forces due to the acceleration but his speed relative to the rocket ship is always 0. He would feel the same thing whatever his, and the rocket ship's, speed relative to some external object.

To me that means the accelerating observer on board the rocket feels constant proper acceleration over time no matter what the the velocity of the rocket is relative to some external inertial observer. It is only the the external inertial observer that considers the coordinate acceleration of the rocket to be slowing down over time for constant proper acceleration of the rocket.

The Baez article says: "First of all we need to be clear what we mean by continuous acceleration at 1g. The acceleration of the rocket must be measured at any given instant in a non-accelerating frame of reference traveling at the same instantaneous speed as the rocket (see relativity FAQ on accelerating clocks). "

In the Momentarily Co-moving Inertial Reference Frame the force and acceleration is essentially Newtonian, so F = ma and there are no relativistic factors and the acceleration is the same for any MCIRF for a given proper force felt on the rocket and does not vary with velocity. If we stick with a single arbitrary inertial reference frame, then the acceleration reduces over time by a factor of gamma cubed over time as the velocity of the rocket increases relative to that inertial frame, but the proper force measured on board the rocket remains constant.

Lets imagine we had a magnetic rocket and a very long linear accelerator. If we apply a constant force F to the accelerator, the occupants of the rockets will feel a constant proper force of F' as their velocity relative to the accelerator increases. The transformation is F=F'. The acceleration measured by the rocket occupants is a' and this is constant. The acceleration (a) measured by the inertial observers at rest with the accelerator is a=a'(γ^-3) and this reduces over time as the velocity of the rocket relative to the inertial frame increases. In the inertial launch frame the equation for force and acceleration is F = γ³ m₀ a.

In terms of the acceleration (a') measured in the MCIRF (or in the accelerating rocket by timing a released object) the above equation is F = γ³ m₀ a'(γ^-3) = m₀ a' = F'.

P.S. Many texts use confusing notation and quote the force transformation formula F = γ³ F' and qualify the statement with "per unit mass" and they are in fact talking about the acceleration transformation and not force.

 

[GeorgeDishman]

What someone on board feels depends on the way the question is phrased. If the assumption is that constant power is fed to the engines, we might also assume constant efficiency and hence constant fuel consumption and thrust. Since some material is being used as "reaction mass", the total mass of the craft is reducing so constant thrust implies rising acceleration.

Accelerating at a "constant 1g" conversely assumes that the thrust is being reduced to match the total remaining mass which also implies steadily reducing fuel consumption.

 

[Naty1]

I lost track of this discussion..
.
Yuiop, great observation, this seems clear enough:

...In the Momentarily Co-moving Inertial Reference Frame the force and acceleration is essentially Newtonian, so F = ma and there are no relativistic factors and the acceleration is the same for any MCIRF for a given proper force felt on the rocket and does not vary with velocity. If we stick with a single arbitrary inertial reference frame, then the acceleration reduces over time by a factor of gamma cubed over time as the velocity of the rocket increases relative to that inertial frame, but the proper force measured on board the rocket remains constant.

The Baez article says:

"First of all we need to be clear what we mean by continuous acceleration at 1g. The acceleration of the rocket must be measured at any given instant in a non-accelerating frame of reference traveling at the same instantaneous speed as the rocket (see relativity FAQ on accelerating clocks). "

I got stuck thinking about 'a' [single] inertial frame...and forget about proper behavior aboard.

I am still unsure what HallsofIvy statement means...but the above is clear enough.

Thanks Yuiop...