Twin paradox question..

[rudeonline]

Well, I like to keep it simple.

 

If I would stay on planet earth and a traveller would make a trip trough space it would be possible that I will be 10 years older and he only became 1sec older when he returns to earth.

 

My question is..

 

If the traveller only became 1sec older and I became 10 years older. How is it possible that he travelled more through space than I.

 

I moved during 10 years with 30km/sec ( 1800km/h! ) arround the sun, the traveler never could travel more then 300.000km because he became only 1sec older.

 

How do you explain this?

[Janus]

Well, I like to keep it simple.

 

If I would stay on planet earth and a traveller would make a trip trough space it would be possible that I will be 10 years older and he only became 1sec older when he returns to earth.

 

My question is..

 

If the traveller only became 1sec older and I became 10 years older. How is it possible that he travelled more through space than I.

 

I moved during 10 years with 30km/sec ( 1800km/h! ) arround the sun, the traveler never could travel more then 300.000km because he became only 1sec older.

 

How do you explain this?

 

By your measurement, the traveler traveled just under 10 lightyears. By his measurement he traveled just under 300,000 km. But, due to length contraction, That same distance that you measured as 10 lightyears, he will measure as only 300,000km.

 

For instance, a planet 10 light years from Earth (as measured from the Earth) will only be 300,000km from Earth for him while he is traveling at near the speed of light. For you, it took 10 years for him to travel 10 lightyears at near light speed, but he only ages 1sec because he aged very slowly during that time. For him it took him 1sec to travel 300,000km at near light speed, aging at a normal rate. Both he and you will agree that he reached the planet and that he aged 1 sec in doing so.

[rudeonline]

Okay, bit if his second was lasting 10 years and he was measuring the speed of light during his trip, was the speed of light in this case then 300.000km/ 10 years?

[Tormod]

No, the speed of light in a vacuum is always c, or 300,000 km/s.

[CraigD]

If I would stay on planet earth and a traveller would make a trip trough space it would be possible that I will be 10 years older and he only became 1sec older when he returns to earth.

…

If the traveller only became 1sec older and I became 10 years older. How is it possible that he travelled more through space than I.

An interesting question. In my brief career teaching an introductory science class that included the subject, where I thought I’d heard nearly every basic variation of question about relativity, I don’t recall encountering it!

 

Janus’s and Tormod’s answers are, to the best of my understanding, correct. However, I’ll try to provide a more brief, less technical answer to the original question:

 

It is possible that the traveler traveled through more space than you because, as perceived by him, he did not.

 

The essence of relativity is that neither time, distance, nor mass appear the same to observers with different velocities relative to each other of any frame of reference. The geometric and mathematical details can be found in many places, and should be mastered by people wanting a sound understanding to the theory of relativity, but the essence of the theory of special relativity is simply that.

 

:) It’s amusing and educational to calculate some specific values for at a given example. In the case of a 10 LY trip that appears to the traveler to take 1 sec, his speed would have to be about

[math]\sqrt{1 - \left ( \frac1{315576000} \right )^2} \dot= .999999999999999995 c[/math] (315576000 is the approximate number of seconds in 10 year).

Assuming the traveler and all the (super-high-tech) equipment required to make the trip massed about what an ordinary person on an overnight trip does, about 100 kg, his trip would require about [math]100 \, \mathrm{kg} \cdot 315576000 \cdot c^2 \dot= 10^{28} \, \mathrm{J}[/math]. This is about the amount of energy

• all of the worlds current manmade machines use in 180 million years
  
• the Sun produces in 30 seconds
  
• that would be released by the complete annihilation of 1.3 million tons (1.3*10^9 kg) of matter and antimatter (by comparison, the Great Pyramid of Giza masses about 6 million tons)
  

This energy would have to be delivered, and converted with perfect efficiency into velocity in a way that didn’t rip the traveler into subatomic particles, in sub-microsecond intervals of time at the beginning, middle, and end of the trip, while at the same time, measures are taken to avoid reducing the traveler to a burst of gamma radiation from a collision with so much as a speck of interstellar dust. :eek_big: Quite an engineering challenge!

[rudeonline]

Thank you for this answer. The big question I have is as follow..

 

I understand that you would need a lot of energy to speed a mass up to 9.99%c. What I try to explain is that you would need thids energy not speed a mass up to a speed, but you will need this energy to put the mass in a complete rest. There is a lot of gravity in space what make mass speeding up akll the time. The velocity off the sun arround the centre of the milkyway is about 900.000km/h. How much enrgy would you need to make a mass slow down from 900.000km/h till zero? The point I mean isthat the speed of light also could been seen as the zeropoint of movement. If you really can stop a mass moving in space and time, this mass will become the middle of the universe. All other mass will finaly be atracted to this mass.

 

If a mass becomes infinity by the speed of light, this mass will be the middle of the universe. To be the absolute middle of the universe you need a infinitive amound of energy. You could stop the whole universe moving if you really coyuld stand stil in space and time.

[sanctus]

You can stop about any mass in space-time, just pick the right referential.

 

You are right if you speed up to 0.99c using x Joules, then you need the same energy to slow down.Just choose the referential so that you are at rest and then slow down in the old referential (which now travels at 0.99c) is equivalent to accelerate to 0.99c in the new referential. So you need the same enrgy to slow down.

[rudeonline]

You can stop about any mass in space-time, just pick the right referential.

 

You are right if you speed up to 0.99c using x Joules, then you need the same energy to slow down.Just choose the referential so that you are at rest and then slow down in the old referential (which now travels at 0.99c) is equivalent to accelerate to 0.99c in the new referential. So you need the same enrgy to slow down.

 

 

How do you stop a mass in time?

[sanctus]

ok, you got a point there...

[CraigD]

There is a lot of gravity in space what make mass speeding up akll the time.

Gravity increasing the speed of objects moving toward one another. It reduces the speed of objects moving away from each other. For the many objects orbiting a common center, gravity has no long term net effect on their speed.

 

On a cosmic scale, gravity is very weak compared to the total kinetic energy of the universe. Although very important in creating structures - planets, stars, galaxies, and galaxy clusters and superclusters - it doesn't dramatically effect the speed at which objects move.

The velocity off the sun arround the centre of the milkyway is about 900.000km/h.

250000 m/s (900000 km/h, or about .0008 c) is a bit higher than the usual figure of 217000 m/s (781200 km/h), but not enough for concern.

How much enrgy would you need to make a mass slow down from 900.000km/h till zero?

The same amount of energy you'd need to increase its speed from zero to 900000 km/h. It depends on the mass of the object being accelerated.

 

Because 250000 m/s is a small fraction of the speed of light, the calculation works out about the same using classical or relativistic mechanics:

[math]E_k = \frac{(250000 \mbox{ m/s})^2 M}2 \dot= M \left ( \frac1{\sqrt{1-\left ( \frac{v}c\right )^2}} -1 \right )c^2 \dot= 3.125 \times 10^{10} \mbox{ J/kg}[/math]. This is the minimum energy required to accelerate the object, assuming 100% mechanical efficiency. Propulsion systems tend to be very inefficient, typically by a factor of greater than 100000, so this calculation is of little practical use.

If you really can stop a mass moving in space and time, this mass will become the middle of the universe. All other mass will finaly be atracted to this mass.

As predicted by any accepted physics, this isn't true. Decreasing the speed of any object relative to any point in space has almost no effect on that object's gravitation attraction to other objects. What slight effect it does have is to slightly reduce the objects relativistic mass, slightly decreasing the gravitational force it exerts on other objects.

If a mass becomes infinity by the speed of light, this mass will be the middle of the universe. To be the absolute middle of the universe you need a infinitive amound of energy. You could stop the whole universe moving if you really coyuld stand stil in space and time.

Rudeonline, you appear to be equating a relative velocity of c with one of zero. Worse, you appear to be assuming the existence of some absolute, privileged frame of reference that would allow us to determine that some object is at “absolute rest”. The whole of modern physics refutes these claims.

 

Velocity (and its scalar magnitude, speed) is relative. Physics permits us to assign a velocity to any object relative to any frame of reference, so any object can be said to be at rest. This choice doesn't make the object the center of the universe, or effect how it interacts with other objects in any way.

How do you stop a mass in time?

The usual meaning of “stop” is “accelerate to a speed of zero”. Speed is change in distance divided by change in time. So a mass is considered to be stopped in space-time when it is not changing position in space, regardless of its change in position in time.

 

:Exclamati This thread seems to have strayed far from its original question about the twins paradox. Unless claims like

If a mass becomes infinity by the speed of light, this mass will be the middle of the universe.

can be explained in scientific terms, it will be necessary to move this thread to the strange claims forum. :Exclamati

[rudeonline]

On a cosmic scale, gravity is very weak compared to the total kinetic energy of the universe.

 

Weak? Do you know that the sun is under influence of the gravity in the middle of the milkyway? You can not call this gravity a weak force..

[sanctus]

When you jump down from the first floor gravity pulls you down, but the forces between the atoms and molecules on the ground stop you easily. That should exemplify the weakness of gravity.

 

Gravity is a weak force compared to the other forces, if the universe weren't overall electrically neutral (what seems to be the case so far), then gravity would be negligible.

 

For example, a fun calculation shows that if the electron and proton were not charged but tied together only by gravity then the Bohr radius (= something like average distance) would be about 10^13 lightyears which is even more than the obsrvable universe (about 1.5 * 10^10 light years), comparing to the Bohr radius in the normal case (i.e electrically charged) which is about 0.5*10^(-10), you easily see why one says gravitation is weak.

[ronthepon]

Indeed, even the constants of proportionality in the inverse square laws that help describe these forces have an enormous difference in magnitude.

 

The gravitational force between two electrons if around forty five orders of magnitude less than the electrostatic force.

[rudeonline]

When you jump down from the first floor gravity pulls you down, but the forces between the atoms and molecules on the ground stop you easily. That should exemplify the weakness of gravity.

 

And this force is not "gravity"?

[sanctus]

No it is not gravity, it is mainly the EM-force which holds the molecules together (for example exchange an electron etc. all this things seen in the basic chemistry courses many years ago :lol: ).

Also if you read and understood my example (if you don't get it right away, it is worth spending some on it because I think it is really astonishing!) of an hydrogen atom hold together by gravitational forces you would see it is impossible that this forces which stop you are gravitational.

[CraigD]

As many of us in this thread will attest, an appreciation of the tremendous difference in the relative strengths and long-distance behavior of the fundamental interactions, and at least a high-level understanding of their roles in everyday mechanical phenomena (eg: a ball dropped from hand to ground) is essential to having a basic understanding of physics.

 

Tables listing the 4 fundamental interactions (occasionally, one sees tables that include a 5th interaction, the Higgs mechanism, but this is both still hypothetical and more complicated than called for by the current discussion) can succinctly illustrate their relative strengths and long-distance behavior (The wikipedia article “Fundimental interaction” contains such a table).

 

A high-level understanding requires a more detailed study of the step-by-step order, distances, and strengths of the interactions, but can be found outlined in many physical science text books, and some online texts (though I’m unable to find a very clear one with a brief web search).