# Does my spaceship accelerate forever?

1. Dec 16, 2004

### kawikdx225

Lets assume I create a spaceship that is powered by vacuum energy which gives the spaceship an unlimited fuel supply. I leave earth at full power and remain at full power forever. I have an accelerometer mounted to the dash just below the fuzzy dice. Will my accelerometer measure my ship accelerating forever?

I understand that my velocity measured with respect to any object will always be less than C but I am concerned only with acceleration.

My assumption is yes, it will accelerate forever, if not then why?

2. Dec 16, 2004

### Integral

Staff Emeritus
Yes you will continue to accelerate. However, after a period of time you will observe that Newtons laws do not properly predict your speed with respect to your starting position.

3. Dec 16, 2004

### pmb_phy

Yes. The speed will always be less than c and yet the ship will keep accelerating. For details please see example at
http://www.geocities.com/physics_world/sr/uniform_accel.htm

Pete

4. Dec 16, 2004

### Gamish

C

well, according to the traditional newton universe, yes, you will accelerate forever in a vacuum, unless an opposing force acts upon you. But will you acclerate forever? Well, if you keep on adding fuel to the ship, most certantly. You will never reach c, but you will tend to "Intntify closer to it". For instance, you acceslerate at 1, then as you approch c, it becomes .1, then .01, then .000001, then .00000000000000000000001, then 10^-100, and so forth. These are not mathematical proportions, but you get the idea, it is an expotental decrease in acceleration, but never a 100% decrease, hence, you will never reach c.

sorry for me spelling, I am in a rush.

Last edited: Dec 16, 2004
5. Dec 16, 2004

### kawikdx225

That's what I thought, thanks for the replies.

There were two things that Gamish said that were a little confusing.
Why only in the traditional Newton Universe? I assume this applies for the Einstein Universe as well?

Why would my acceleration rate decrease if there are no external forces acting upon the ship? I would assume my accelerometer would show a constant acceleration rate regardless my relative velocity.

For example, under full power my ship leaves our galaxy at 1m/s2. 100 trillion years later I should still be accelerating at 1m/s2 right?

6. Dec 16, 2004

### Grogs

Classically, that's correct. If you hop on a ship accelerating at x m/s2, you'll reach the speed of light in (v=at =>) t=c/a seconds. At 1G, this would take just under a year.

Relativity throws a monkey wrench in the works though. Consider two different points of view:

Observer A is a 'stationary' Earth observer watching the spaceship fly off. As the spaceship approaches the speed of light, A will observe that the mass of the spaceship increases (2.3 times more massive at .9c, 7 times as massive at .99c, etc.) Since F=ma => a=F/m => Acceleration appears to decrease given constant Force (thrust.)

Observer B is aboard the spaceship. He sees no increase in the ship's mass or the resulting decrease in acceleration observed by A. His shipboard clock; however, will run slower and slower (compared to A's) the closer he gets to the speed of light. He would come to the end (chronologically) of the Universe before he reached the speed of light. His shipboard clock (started at the beginning of the voyage) at that last instant, should read just under c/a seconds (the classical result.)

7. Dec 16, 2004

### mijoon

This is exactly correct, although I would word it differently to avoid the variable mass concept.

8. Dec 16, 2004

### pervect

Staff Emeritus
Yes - unless you run into something, you'll accelerate forever. Running into stuff will be a problem, though.

The sci.physics.faq on the relativistic rocket http://math.ucr.edu/home/baez/physics/Relativity/SR/rocket.html [Broken]

will give you your velocity, "gamma", and distance as a function of proper time (the time on your ship's clock).

Note that it won't be too many years before interstellar gas becomes a real hazzard. It will be coming at you at hyperrelativistic velocities. It will also appear to be more dense, because of Lorentz contraction. Eventually even commic microwave background radiation will become a problem - it will be blue shifted into an intense gamma ray source that is so intense it will easily be able to melt your spaceship. Shielding against that sort of thing is going to be a real trick.

Last edited by a moderator: May 1, 2017
9. Dec 16, 2004

### kawikdx225

Thanks, I should have specified deep space with no other objects within measurable distance and no other observer taking measurements. Only me, my ship and my accelerometer.

Most replies say yes and I agree but a few indicate this is only true in "classical physics". I will assume they misread my initial post.

CMBR a problem? If one can detect a frequency shift in the CMBR with a change in velocity then why can't we use this to determine our absolute velocity? I always thought that in deep space you couldn't determine your velocity but if what you said is true then I can always measure my velocity wrt the CMBR.

10. Dec 16, 2004

### pervect

Staff Emeritus
There's no problem with measuring relative velocities - and the CMBR is present even in deep space, so one can measure one's velocity relative to it. There will be only one frame where the CMBR is isotropic at any give point in space-time.

11. Dec 16, 2004

### Grogs

The relevant excerpt:

Last edited by a moderator: Apr 21, 2017
12. Dec 17, 2004

### Chronos

I totally disagree with that. Propose a single experimental test that will show the CMB photons do not obey GR. It is a convenient reference frame, not a 'special' reference frame.

Last edited by a moderator: May 1, 2017
13. Dec 17, 2004

### Gamish

Yes!`

1.YES, your space ship will accelerate forever in a
Einstein universe to, I guess I should says God's universe, lol. But, you have to consider, Einstein put a different face on the universe, he "twisted" the traditional newton way of thinking.

2.well, your ship will slow down its acceleration because as an object approaches c, the "mass" of that object will increase, and thus, more "energy" will be put towered moving that mass than the actual speeding up of the object. This is why your accleration rate would decrease. This is all within the bounds of Special Relativity.

Blah :tongue2:

14. Dec 17, 2004

### kawikdx225

Yes, a distant observer will observe my ship's mass increasing and my acceleration decreasing but this thread is about what the pilot of the spaceship will observe.

15. Dec 17, 2004

### mijoon

Let us remember that c is only a speed limit wrt the local continuum. You will be carried by the Hubble Flux and as you reach a great enough distance from the Earth, this will become significant. That is to say, you will approach c wrt your local enviroment, but eventually exceed c (:surprised ) wrt the Earth.

16. Mar 3, 2008

### nahkaimurrao

---"That is to say, you will approach c wrt your local enviroment, but eventually exceed c ( ) wrt the Earth."---

interesting, I have never heard this theory before, and don't understand how it fits with relativity

To the Original Poster:

you're accelerometer would read a constant acceleration. And in you're POV you would be traveling faster than the speed of light in the sense that it would take you less than a year to travel one light-year ( one light year is in the Earth's POV or Distant Star's POV or where ever you intend to journey to)

This does not defy relativity because though it seems like you are traveling faster than c, really it is due to time dilation or space contraction: space time is warping, the distance between you and the distant star is actually decreasing thus allowing you to get there faster.

But for all practical purposes, you can think of it as traveling faster than the speed of light.

What I mean is if you decide to accelerate at 1 G constantly from starting point until half way point and then decelerate at 1 G until destination this is what would happen:

To Travel 4 lyr's at 1-G would take 3.94 years in your POV and 4.88 years in Earth's POV

Likewise:

Distance------Time-----Max Velocity-------------------Time Max Velocity

20 lyr's--------8.81 yrs---4.54 c----------------------20.95 yrs---- .98 c
50 lyr's-------13.9 yrs----7.18 c----------------------50.96 yrs---- .99 c
100 lyr's------19.7 yrs----10.15 c--------------------100.97 yrs --- .999 c
500 lyr's------44.1 yrs----22.70 c--------------------500.97 yrs --- .9999 c
1000 lyr's-----62.31 yrs---32.10 c-------------------1000.97 yrs --- .99999 c

So it is interesting to note that at 1-G you could actually travel over 1000 light years in your life time (And even farther if you don't feel like decelerating before you get there), the only problem is that more than a 1000 years would pass for everyone else, But only 62 years would pass for you and who really cares what is happening on Earth if you are 1000 light years away.

Last edited: Mar 3, 2008
17. Mar 3, 2008

### nahkaimurrao

It may also be interesting to note that if you could somehow manage to achieve light speed, time would stop for you, and it would seem as if you were traveling instantaneously, even covering large distances in an instant.