# Light speed spaceship time travel conundrum

1. Nov 28, 2009

### Jebus HChrist

Let’s say we have a space ship capable of travelling at the speed of light, and a planet we can visit 50 light years away. From earth’s perspective if we can track the ship we would be able to see it was travelling at the speed of light and we would also see it has taken 50 years to complete the journey.

From the travellers perspective time will slow down, so let’s say to them the time only lasts 1Year. Doesn’t this mean that they would experience the journey as if they travelling 50 times the speed of light? If they have instruments on board showing speed what will these instrument show, speed of light or 50 times speed of light?

I’m not a student I’m old and love this stuff hence maybe some young whippersnapper can answer this question for me.

JHC

2. Nov 28, 2009

### Staff: Mentor

The speed of the space ship with respect to the earth/planet frame (0.99c, say) will equal the speed of the earth/planet with respect to the ship (0.99c again). But to the space ship the distance to the planet is much less than 50 light years.

3. Nov 28, 2009

### Staff: Mentor

You need to be careful about saying things like "traveling at the speed of light" because no object with mass can travel at the speed of light with respect to any other object.

Then the ship isn't traveling at the speed of light. It's actually traveling at 0.99980 times the speed of light, and from the Earth's perspective it takes 50.01 years to complete the journey.

Using distances and times measured in their own reference frame (in which they themselves are stationary), they would observe the earth receding behind them at a rate of 0.99980 times the speed of light, and their destination approaching them at the rate or 0.99980 times the speed of light. The distance between the earth and their destination would be length-contracted to 0.99980 light-year, so the elapsed time comes out right: t = d / v = (0.99980 light-year) / (0.99980 light-year per year) = 1 year.

4. Nov 28, 2009

### edpell

But of course the folks on the ship traveling 0.99980c are not fools. They know before they start that the distance is 50 light years and they know when they arrive that the distance traveled was 50 light years. And yes they only age one year so for them it is exactly as if they had traveled about 50 light years per one year of body aging. So I would say their bodily processes had slowed down. But time remains unaffected as they and we who stayed behind are both able to figure out that when they arrive 50.001 years have gone by.

Last edited: Nov 28, 2009
5. Nov 29, 2009

### HallsofIvy

"They and we who stayed behind" are both able to figure out that when they arrive 50.001 years have gone by in earth's frame of reference. It makes no sense to talk about "time gone by" without specifying the frame of reference nor does it make any sense to say "time remains unaffected".

6. Nov 29, 2009

### DrGreg

As has been pointed out above, when you calculate speed as distance / time, the distance and time both must be measured in the same frame.

In fact, there is a name for what you get when you divide the earth-measured distance by the ship-measured time. It is called celerity (or proper velocity, a name I don't like). In this example the celerity of the ship is 50 times the speed of light, but you have to compare like with like. The celerity of light is infinite.

7. Nov 29, 2009

### edpell

I agree both in the same frame. When the travelers arrive 50 light years away they can calculate in the earth reference frame that they have gone 50 light years of distance and that about 50.001 years have gone by in the earth frame so a velocity of 0.9998c. They can also look at their bodily aging and say that is great we only aged one year.

8. Nov 29, 2009

### edpell

HallsofIvy by the phrase "time remains unaffected" I mean on arrival (and stopping) both the Travels and the Earthers can measure and agree that the Travels have moved 50.001 years into the future just as the Earthers have moved 50.001 years into the future. No surprise there the surprise is that the bodies of the Travels have only aged one year. So do we want to say time changed for the Travels or do we want to say physical processes went slower for the Travels? We are agreed on the facts this is a question of interpretation, meaning, wording.

9. Nov 30, 2009

### Jebus HChrist

I’m still with you all so far and understand technicalities like the max speed would have to be 0.999 the speed of light etc. Ed I don’t think the travellers experience the 50 years in real time and yet their bodies only age 1 year. If time slows down the closer light speed is reached then the travellers experience must to them appear like a one year journey.
Doc Al you say “But to the space ship the distance to the planet is much less than 50 light years”. So for arguments sake would you agree that the travellers could experience the journey as though it were 1 year, and that it would therefore appear from their perspective that they were travelling 50 times the speed of light. My original question still stands.

JHC

10. Nov 30, 2009

### Nabeshin

In the space ship's frame, the distance between them and the planet is lorentz contracted, so 50ly looks like 1ly to these travelers. Then they see the planet approaching them at .9998c ~ 1c, and so the journey takes only one year. That is how things look from the traveler's reference frame. They arrive on the planet and say "Gee, one year has passed for us", the folks on earth say "Gee, over fifty years for us". The critical part is "for us". Without that, any measurement of time is completely useless. The observers will no doubt agree on what the others experienced, however. I.e, those on Earth will say "Yeah, you really did only experience one year", and those on the ship say "yup, 50 years passed back on Earth."

Make sense?

11. Nov 30, 2009

### Staff: Mentor

Yes.
From their perspective, using their own standards of length and time, they are moving at close to the speed of light, not at 50 times the speed of light--but distances are squashed. But you are correct that they can travel 50 earth-light years in only 1 space ship year. See DrGreg's comment about celerity.

If you don't use consistent measurements--made in the same frame--you'll get tied up in knots thinking that things are moving faster than light. Only in the mixed-frame sense of celerity.

12. Dec 14, 2009

### edpell

I am not disagreeing with anyone here. The travelers observe one year of travel over a distance of one light year. The stay behinds observe 50 light years of travel in 50 years (approx. - a little longer). But consistent. Both no faster than light speed. All fine. But after the trip is over A and B both agree to transmit how much bodily aging they have each experienced. A transmits 50 years of aging observed between your departure and your arrival. B reports one year of bodily aging observed between departure and arrival. What do we, A and B who are now both in the same inertial frame, want to say? Time went slower for A or A's physical processes went slower? Or are these both the same statement? To me it does not seem that these are both the same statement. Because if the trip started at the beginning of the year x and ended the beginning of the year x+50 in A's frame which both A and B are now in I think we have to say they both traveled 50 years into the future in frame A. Yet the physical process of body aging progressed only one year for B. In frame A, B has aged one year but "moved" 50 years into the future. For me that would best be described as B's physical process slowed by a factor of gamma. How would you feel it is best to describe the events? After the trip is over and both A and B share the same inertial frame.

13. Dec 14, 2009

### ZikZak

Time is not slowed down for the spaceship in an absolute sense. There is no such thing as "real time," only time as measured in particular frames of reference. There is no universal clock ticking off "real seconds," and if the spaceship travelers experience a 1-year yourney, then it IS a one-year journey to them, no "appearances." Time dilation is not an illusion.

Earth observes clocks on the spacecraft to run slow, this is true, but the spacecraft is at rest relative to the pilot, while the Earth is traveling backwards at nearly c. So the pilot observes the spacecrafts clock running normally and the Earth's clock running slow. Which clock is running slow depends on whose reference frame you are in. Time dilation never happens to you. It always happens to other objects moving relative to you.

No, in their reference frame they are at rest and the Earth and destination are traveling at nearly c. the reason the destination reaches them in 1 year rather than 50 is that the distance between earth and the destination is 1 light-year, not 50 light years. The distance between Earth and Destination is not "really" 50 light-years. There is no absolute answer to how separated the two planets are. The distance between them depends on reference frame.

14. Dec 14, 2009

### DaveC426913

What the OP is struggling with is that the spaceship occupants know that "the distance between their lift-off planet and Earth is 50 light years", yet they made the trip in 1 year.

Yes, they know this when measuring from their planet. But once they accelereate to .999c they will see the distance between their planet and Earth shrink to one light year. The universe along the axis of their travel will flatten by fifty times.

15. Dec 15, 2009

### Al68

The only reason SR predicts less aging is as a result of less elapsed time. If there were not less elapsed time for the traveler, why would he age less?

16. Dec 15, 2009

### Ich

As the difference between proper time and coordinate time.
Don't start with physical processes slowing. Since every conceivable process has to "slow down" consistently, there cannot be an operationally defined intrinsic time relative to which physical processes are slower than normal.
It is common (and mandatory in SR) therefore to call any suitable operationally defined intrinsic time "time" or, specifically, "proper time". Under constraint, one may speak of time slowing down, but not processes.
Ideally, one would avoid these phrases and give instead a precie definition between which events which time has elapsed.

17. Dec 21, 2009

### edpell

What sets the time scale for all physical processes is inertia. The inertia of the travelers increased which set a different time scale for the travelers. This is how I read Einstein's 1905 paper "Does the Inertia of a Body Depend Upon its Energy-Content?".

18. Dec 30, 2009

### otas

If I am on such space ship. After accelaration I see that earths clock is running slow. After a (my) year I get on that planet and ask my friends in earth how much time have passed.
Would they say 50 years or less then a year?

Last edited: Dec 30, 2009
19. Dec 30, 2009

### Al68

50 years, after the ship decelerates. When the ship reaches the planet, earth's clock reads less than a year before the ship decelerates, and 50 years after the ship decelerates.

Relative to the ship clock, earth's clock "jumps ahead" or runs fast during the deceleration.

20. Dec 30, 2009

### otas

if my deceleration takes 1 day. Does that mean if I observe earths clock during deceleration it goes 49 years in one day (approx. 49x365 faster)?