Relativity Question

[CodBall]

Hi all, 23 year old here new to the forum after watching an episode about Time on "Through the Wormhole"

 

I couldn't quite bend my head around the concepts in the video and thought perhaps some of you could help out, I only hold a GCSE in Physics but I'm constantly intruiged and amazed with the field and find myself watching and reading things about it.

 

My question is as follows:

 

Understanding that time is relative to the speed of an object or the gravity surrounding an object and that time will appear normal to an observer stood in the moment looking at his surroundings even on the event horizon of a black hole, the documentary said that if a spaceship were to travel at the speed of light to a planet say 10 light years away and back, that when the ship returned the crew would have experienced for 20 light years of time however during that time Earth would have experienced a thousand years.

 

But...if the speed is constant and the distance remains the same when the spaceship arrives back at Earth won't they both have experienced (and aged) 20 years?

I guess from the perspective of Earth it would look like the ship is taking longer to get to the planet but on it's way back the trip would only look as if it takes half as long, would that be right?

 

Excuse if it's a stupid question, just something I'm trying to wrap my head around.

[Janus]

To start off, your spaceship could not travel at the speed of light, as material objects are restricted to travel at speeds less than c.

 

I'm not sure that you are quoting the documentary quite right. If the spaceship travels to a planet 10 ly away (as measured by the Earth), then if it is traveling at almost the speed of light, it will take ~20 yrs to make the round trip as measured by the Earth. The occupants of the ship will however measure a much shorter trip, aging very little.

 

From the Earth's perspective, this is because time on the ship ran slow during the trip.

For the ship this is true because, for it, the distance between Earth and the planet is much shorter than 10 ly.

 

Clocks and rulers moving relative to each other measure time and distance differently. This is why I prefaced the above statement of the distance to the planet with "as measured by the Earth", as the distance between the two i is different as measured from the spaceship.

 

Now the documentary could have meant that the planet was 10 ly from Earth as measured by the Ship, in which case, the distance could have been ~500 ly as measured from the Earth, making the ship trip duration 20 yrs and the Earth trip duration 1000 yrs, however, I doubt it. Doing so, without being very clear about it and making mention of the difference in the distance as measured by Earth and Ship would have been unnecessarily confusing.

 

The effect you allude to when talking about the outbound trip being long and the inbound one being short is due to the Doppler effect, which is separate form the Relativistic effect of time dilation which the example is discussing. The time dilation effect is what is left over after you account for the Doppler effect. Most times when discussing Relativity, when someone says something along the lines of " the Earth Sees, or from the perspective of the Earth, etc. They mean after any Doppler effect has been accounted for.

Edited May 2, 2012 by Janus

[IM Egdall]

Understanding that time is relative to the speed of an object or the gravity surrounding an object and that time will appear normal to an observer stood in the moment looking at his surroundings even on the event horizon of a black hole, the documentary said that if a spaceship were to travel at the speed of light to a planet say 10 light years away and back, that when the ship returned the crew would have experienced for 20 light years of time however during that time Earth would have experienced a thousand years.

 

Say the rocket took off into outer space and returned to Earth 1000 years later, as measured on Earth. This is 1000 years Earth-time for the round-trip.

 

If the rocket traveled at 99.98 percent the speed of light, then only 20 years will have elapsed for people on the rocket for the same trip. This is 20 years rocket-time.

 

The rocket's speed relative to Earth is what determines how much time slows down in rocket time versus Earth time. This is given by the time dilation factor:

 

square root ( 1 - v^2 ) where v is a percentage of the speed of light.

 

Here v = 0.9998 which gives a time dilation factor of 0.02, and 1000 years times 0.02 equals 20 years.

 

(Gravity effects on time are ignored, as they are a small effect here.)

 

I hope this helps.

[elfmotat]

But...if the speed is constant and the distance remains the same when the spaceship arrives back at Earth won't they both have experienced (and aged) 20 years?

I guess from the perspective of Earth it would look like the ship is taking longer to get to the planet but on it's way back the trip would only look as if it takes half as long, would that be right?

 

This sounds vaguely like the twin paradox. Basically, the ship needs to accelerate to turn around, so both observers agree that the ship has aged less.

[mindless]

It is best to point you to a book that explains this fully: http://en.wikibooks.org/wiki/Special_Relativity/Simultaneity,_time_dilation_and_length_contraction

 

Relativity is a theory that proposes that the world is a four dimensional place. Each point has its own time. When you travel, you travel in four dimensional spacetime. When you travel in four dimensional spacetime you go from a point at a particular location and time to another point at another location in space and time. Remember, in 4D you are travelling in both space and time whenever you travel. I would recommend reading the book from the beginning to understand special relativity fully.

 

A quote from "Special Relativity":

 

"The term "time dilation" is applied to the way that observers who are moving relative to you record fewer clock ticks between events than you. In special relativity this is not due to properties of the clocks, such as their mechanisms getting heavier. Indeed, it should not even be said that the clocks tick faster or slower because what is truly occurring is that the clocks record shorter or longer elapsed times and this recording of elapsed time is independent of the mechanism of the clocks. The differences between clock readings are due to the clocks traversing shorter or longer distances between events along an observer's path through spacetime."

 

The Twin Paradox is also discussed in the book. Basically one twin goes to a different place at a time in the other twin's future then turns round and does it again.

http://en.wikibooks.org/wiki/Special_Relativity/Simultaneity,_time_dilation_and_length_contraction