Twin Paradox, Paradox?

[EWright]

Since I apparently offended some people by proposing a possible paradox that included a reference to the age of the Universe (apparently there are too many posts per week on that subject so be sure to never reference it or they won't address your actual question) I'll pose another scenario instead.

 

We're all familiar with the Twin Paradox, in which one twin travels into space at a significanty fraction of the speed of light and when he returns he has aged much less than his twin back on earth.

 

Now consider that the same twin leaves earth is a space ship but does not travel distantly. Instead he assumes a high-earth orbit, but still at a significant fraction of the speed of light. Relativity tells us that he should still age less than his twin on earth because of the speed at which he is traveling. But consider that during his entire trip he is receiving a light speed signal in the form of a microwave television signal from the north pole or a satellite that is traveling at earth's same speed. The twin on the spaceship can view this signal in a monitor. Now, althought time should slow for the twin in the space ship, causing him to age less, the electromagnetic signal he is receiving should travel at a constant speed of c along its entire path of travel. And because he is traveling in a high earth orbit rather than far from earth, the signal does not need the significant time to reach him that it would if he traveled far from earth, so there should be no significant delay in it reaching him. Therefore, the twin in the spaceship should receive the signal at the same rate that it is transmited because the light-speed signal muyst remain CONSTANT between the two points at all times. If the signal, visible in his monitor, is of constant events on earth and has a visible time code to the frame (30 frames per second), how does the traveling twin perceive the image and time coded relationship in relation to his own clock?

 

(disclaimer: I am posing this as a thought experiment, not a proof of anything.)

[Tormod]

Could you please do as I suggested and visit our astronomy and cosmology forum? This topic has been discussed many times over there.

 

You could also try to search for "twin paradox" in our search field.

 

And no, you are not offending anyone - you are simply ignoring common courtesy which is to find out what is already being discussed before you post.

[EWright]

I am proposing an altered scenario to the twins paradox. Are you telling me that my exact scenario has been proposed already?

[Tormod]

I am telling you that your scenario is similar to others that are being discussed, yes. It would be tremendously better for the site if you would join in those discussion rather than start new threads on topics that are already being discussed.

[EWright]

So much for trying to introduce new concepts using old analogies.

[Erasmus00]

So much for trying to introduce new concepts using old analogies.

 

Please actually pay attention to what Tormod said. You are free to discuss your ideas, simply roll on over the Astronomy section, find the thread where they are discussing the twin paradox, and post there. That way, all the talk of the twin paradox and variations there of are in one area. You are still free to discuss your ideas.

-Will

[Tormod]

Now consider that the same twin leaves earth in a space ship but does not travel distantly. Instead he assumes a high-earth orbit, but still at a significant fraction of the speed of light.

 

It is actually impossible to orbit the Earth at a significant fraction of the speed of light and still stay within a distance where relativistic effects would not be perceived.

 

A "high-earth" orbit cannot be higher than a geostationary orbit, at 35,800 kilometers, because at this height the speed of the orbit perfectly matches the rotation of the Earth, so that any satellite placed in this orbit always hovers above the same spot on the Earth.

 

Now, the escape velocity for Earth is 11200 meters per second, or about 25,000 miles per hour. The escape velocity of the Solar System is about 1,000 kilometers per second. That is 1/300th of the speed of light. So even at 1/299th of the speed of light, your space craft would never return.

 

In order for an object to be in a similar orbit at higher speed you would need constant maneuvering, which would actually mean that A) you are not in an orbit, and ;) you would need to draw an immense circle in space to be able to follow a path all the way around without increasing the distance from Earth.

 

The amount of fuel needed for maneuvers is another issue completely.

 

I have not calculated what distances you would need to be at but I think you'd have to be far, far outside of our solar system. And, importanly, you would no longer orbit the Earth but the entire solar system.

 

The time for transmissions from Earth to this spacecraft would be immense.

 

So this thought experiment cannot work in real life.

[EWright]

It is actually impossible to orbit the Earth at a significant fraction of the speed of light and still stay within a distance where relativistic effects would not be perceived.

 

A "high-earth" orbit cannot be higher than a geostationary orbit, at 35,800 kilometers, because at this height the speed of the orbit perfectly matches the rotation of the Earth, so that any satellite placed in this orbit always hovers above the same spot on the Earth.

 

Now, the escape velocity for Earth is 11200 meters per second, or about 25,000 miles per hour. The escape velocity of the Solar System is about 1,000 kilometers per second. That is 1/300th of the speed of light. So even at 1/299th of the speed of light, your space craft would never return.

 

In order for an object to be in a similar orbit at higher speed you would need constant maneuvering, which would actually mean that A) you are not in an orbit, and :) you would need to draw an immense circle in space to be able to follow a path all the way around without increasing the distance from Earth.

 

The amount of fuel needed for maneuvers is another issue completely.

 

I have not calculated what distances you would need to be at but I think you'd have to be far, far outside of our solar system. And, importanly, you would no longer orbit the Earth but the entire solar system.

 

The time for transmissions from Earth to this spacecraft would be immense.

 

So this thought experiment cannot work in real life.

 

Nice of you to side step the actual, tho hypothetical, question. Whether you could stay in orbit or not is not the issue here. The usual "Twins Paradox" scenario is just as impossible to pull off because it still requires reaching an impossible speed. So put a nuclear powered latteral side booster on the space ship to keep it in orbit if you must. Why can we remove all objects from the universe to "prove" hypothetic SR theories, but I can't propose a space ship engineered to orbit the earth at a significant fraction of light speed? The question at hand is how would the light-speed signal be perceived by the twin on the ship if it must be constant for both those on earth and the person on the ship, yet time must slow for the person in orbit?

[Erasmus00]

Your orbit isn't inertial, and so handling the problem is a bit subtle. I suggest a treatment along the lines of what is traditionally done for the Sagnac effect. Calculate the interval from the earth's frame, which will give you a proper time measurement for your orbiting frame.

-Will

[Boerseun]

EWright:

 

I see what you're trying to say. If you can actually rig up a system like this, the time signal would come from Earth, which is standing still for all practical purposes, and hit the spaceship perpendicular to its direction of flight say, once every second.

 

The spaceship will see the timesignal coming from Earth, and everything on Earth will appear (from the spaceship's point of view) to be moving at a hectic rate, including radiosignals beamed off the planet. So, as time slows down relativistically on the spaceship, it should seem as if the signal speeds up. The crux of your story seem to be the fact that the signal is hitting the spaceship perpendicular to its motion - but keep in mind that the spaceship is flying at a right angle to the direction the radio waves are travelling, and intercepts the wave in an ever-increasing sweep as the spaceship's speed increases.

[EWright]

EWright:

 

I see what you're trying to say. If you can actually rig up a system like this, the time signal would come from Earth, which is standing still for all practical purposes, and hit the spaceship perpendicular to its direction of flight say, once every second.

 

The spaceship will see the timesignal coming from Earth, and everything on Earth will appear (from the spaceship's point of view) to be moving at a hectic rate, including radiosignals beamed off the planet. So, as time slows down relativistically on the spaceship, it should seem as if the signal speeds up. The crux of your story seem to be the fact that the signal is hitting the spaceship perpendicular to its motion - but keep in mind that the spaceship is flying at a right angle to the direction the radio waves are travelling, and intercepts the wave in an ever-increasing sweep as the spaceship's speed increases.

 

FINALLY!!! Someone addresses the question at hand!!! Yes, SR dictates that everything on earth should appear to speed up to the observer in the spaceship. However, how can the microwave signal that has a timecode synched to real-time on earth, be different on the spaceship if light travels at a constant speed? If SR is correct, the video signal being beamed from eath should appaer to speed up as well. But it is being sent at light speed and SR says that can't vary, so how could it possibly appear to speed up? (Which it must if it is synched with earth-time and SR is right.)

[Erasmus00]

But your rather simple SR anaylsis, and the time dilation equation you wish to apply, only hold in inertial frames. Circular orbits are non-intertial. Non-intertial systems can be treated with SR, but it is a much more subtle thing. The easiest way is probably to start with the minkowski metric, and coordinate change into the rotating system (like you would for Sagnac effect). Having done this, calculating space-time intervals (and hence proper time) isn't really too difficult.

-Will

[EWright]

But your rather simple SR anaylsis, and the time dilation equation you wish to apply, only hold in inertial frames. Circular orbits are non-intertial. Non-intertial systems can be treated with SR, but it is a much more subtle thing. The easiest way is probably to start with the minkowski metric, and coordinate change into the rotating system (like you would for Sagnac effect). Having done this, calculating space-time intervals (and hence proper time) isn't really too difficult.

-Will

 

Then by all means, clarify it for us.

[Tormod]

Nice of you to side step the actual, tho hypothetical, question. Whether you could stay in orbit or not is not the issue here.

 

Sorry for considering your post with a serious reply. You did actually open your statement with "Instead he assumes a high-earth orbit, but still at a significant fraction of the speed of light."

 

...which I simply pointed out is impossible, and I backed up that statement.

 

The usual "Twins Paradox" scenario is just as impossible to pull off because it still requires reaching an impossible speed.

 

No, it is not impossible at all. Atomic clocks flown on jet planes in the 1970s proved time dilation actually happens.

 

Why can we remove all objects from the universe to "prove" hypothetic SR theories, but I can't propose a space ship engineered to orbit the earth at a significant fraction of light speed?

 

Why resort to examples that cannot exist? GPS satellites use both general and special relativity in order to calculate extremely precise timecodes.

 

http://www-astronomy.mps.ohio-state.edu/~pogge/Ast162/Unit5/gps.html

 

The twin paradox is only a paradox because it appears to be one. It is however a very real feature of our universe.

[EWright]

Sorry for considering your post with a serious reply. You did actually open your statement with "Instead he assumes a high-earth orbit, but still at a significant fraction of the speed of light."

 

...which I simply pointed out is impossible, and I backed up that statement.

 

 

 

No, it is not impossible at all. Atomic clocks flown on jet planes in the 1970s proved time dilation actually happens.

 

 

 

Why resort to examples that cannot exist? GPS satellites use both general and special relativity in order to calculate extremely precise timecodes.

 

http://www-astronomy.mps.ohio-state.edu/~pogge/Ast162/Unit5/gps.html

 

The twin paradox is only a paradox because it appears to be one. It is however a very real feature of our universe.

 

:shrug:

Why resort to examples that cannot exist? [/Quote]

Because this is exactly what relativity does in its examples that remove every reference frame in the blank-stinkin universe to show the relativity of two objects' inertial frames. Show me a universe with just two objects moving in relative motion with no force that put either one in motion and I'll agree relativity is the perfect description of that universe.

 

I know you're tired of my "my theory" references, but mine does account for the time fluctuations in the atomic clock tests. My reference to the regular twins paradox scenario was about the speed usually referenced by the traveling twin, which is a significant fraction of the speed of light; one which we cannot achieve.

 

AND YOU STILL HAVEN'T ANSWERED HOW MY LIGHT SOURCE WOULD BE VIEWED BY THE ORBITING TWIN. THAT IS THE QUESTION AT HAND. :wave: IT HAS NOTHING TO DO WITH ORBITING OR ANGLES. ITS THE FACT THAT HE'S CLOSE ENOUGH FOR THE LIGHT SPEED SIGNAL TO HIT HIM WITHOUT HAVING TO "CATCH UP" AND HOW IT COULD VARY BETWEEN THE ORBITING TWIN AND THOSE ON EARTH IF THE LIGHT SPEED SIGNAL MUST REMAIN CONSTANT!?!? :)

[Tormod]

Resorting to angry rants and yelling gets you nowhere.

 

You seem to be missing my points.

 

The point of explaining the impossibility of a high-speed orbit was twofold - one, it means no acceleration, and two it means an extremely low orbit. So drop the term "orbit" and it might be possible to answer your query. "Circling around" is a more correct term, but my explanation still stands - it is impossible to stay in such close proximity to a planet that a light signal will not be time dilated in any way, while maintaining an acceleration. This is orbital mechanics 101.

 

The point of showing you that the GPS satellites need to adjust for SR and GR shows that the observer (in whatever position he is to Earth) cannot be reached instantly by the light. The light takes time to reach the observer, however small the distance is.

 

It does not matter what the twin's relative position to Earth is, really - what matters is his acceleration. If he does not accelerate relative to Earth then the signal will appear perfectly fine, only delayed by the distance it has to travel, plus the difference in the gravitational field. His replies to Earth will likewise only be shifted by the same.

 

This is exactly what happens when we receive signals from satellites orbiting Mars, for example. The difference in gravity on Mars and Earth does however mean that clocks tick slightly different around Mars than around the Earth.

 

If he is accelerating, the signal he receives will be time dilated, so the harder he accelerates the more time dilation will be observed. His clocks will be ticking at different rates than those on Earth. Simple as that. No need to incorporate systems of bodies with "no force that put either in motion" - a force is what causes a body to move.

[EWright]

Resorting to angry rants and yelling gets you nowhere.

 

You seem to be missing my points.

 

The point of explaining the impossibility of a high-speed orbit was twofold - one, it means no acceleration, and two it means an extremely low orbit. So drop the term "orbit" and it might be possible to answer your query. "Circling around" is a more correct term, but my explanation still stands - it is impossible to stay in such close proximity to a planet that a light signal will not be time dilated in any way, while maintaining an acceleration. This is orbital mechanics 101.

 

The point of showing you that the GPS satellites need to adjust for SR and GR shows that the observer (in whatever position he is to Earth) cannot be reached instantly by the light. The light takes time to reach the observer, however small the distance is.

 

It does not matter what the twin's relative position to Earth is, really - what matters is his acceleration. If he does not accelerate relative to Earth then the signal will appear perfectly fine, only delayed by the distance it has to travel, plus the difference in the gravitational field. His replies to Earth will likewise only be shifted by the same.

 

This is exactly what happens when we receive signals from satellites orbiting Mars, for example. The difference in gravity on Mars and Earth does however mean that clocks tick slightly different around Mars than around the Earth.

 

If he is accelerating, the signal he receives will be time dilated, so the harder he accelerates the more time dilation will be observed. His clocks will be ticking at different rates than those on Earth. Simple as that. No need to incorporate systems of bodies with "no force that put either in motion" - a force is what causes a body to move.

 

 

:) :wave: :) I'll rant if I want to rant :shrug: :D :)

 

So should I also explain that it's impossible to remove everything from the universe except for two spaceships in relative motion? Whether it is possible or not doesn't dismiss the question of the physics involved. And I'm not missing your points, I'm just ignoring those points that are irrelevant to the question had hand.

 

I work with signals sent via satellites and am well aware of the delay in the signal, thank you. However, the signal that is sent and the one that are received still share the same rate of speed (ie, 30 frames per second for a microwave video signal). We can allow for the delay of a second in my question to make up for the time the signal from earth takes to reach the ship; that is not an issue. The issue is that the orbiting twin's overall clock should be running faster than that of the twin on earth. So aside from the one second DELAY, I want to know how the twin on the ship will perceive a visual time coded signal if relativity demands that time is running faster for him. When we receive a signal sent from earth to a satellite that is then returned to earth, there is also a delay, but the signal remains at 30 frames per second. Relativity says this can not happen for the orbiting/circling twin because his clock must run faster than ours on earth if he's traveling at a significant fraction of c even at a constant speed (ie, no acceleration... granted he had to accelerate for an instant to gain speed, but assume we began the signal after that moment and he traveled at a constant rate thereafter). But relativity also says the light signal must travel at a constant rate, so how can he view it as moving faster or slower than what is being sent, minus the one second delay. SO, WILL HIS FRAMES PER SECOND THEN READ FASTER, SLOWER OR THE SAME???