CONCLUSION (for lazy readers): Calculations by laws of physics show that traveling by rocket ship, the traveling twin cannot return even 5 years younger than his “stay at home brother.” As the time traveler could age a maximum of 7.36 years while his staying home twin ages 1.57x7.36 = 11.55 years.
To even do that, if a standard D/T fusion reaction is used, the fuel mass ONLY at launch is 837 times greater than the mass of Earth!
To show the extremely difficult actually doing only slowing aging by a factor of (7.14/4.5) = 1.57 via a rocket ship, I post physics from this link: http://www.astro.cornell.edu/pdfs/relrocketderiv.pdf
{Most equations are omitted and text in these “curly brackets” was inserted in the quotes by Billy T.}
“.. Consider a rocket that accelerates uniformly. This means that the acceleration is fixed in the rocket rest frame; let the acceleration be a. Now suppose we wish to go a total distance D in the Earth frame going out halfway at a uniform acceleration, a, and then the rest of the way at uniform {reversed} acceleration -a so that we arrive at our destination with zero speed.”
{Note their analysis is for a “one way” trip and in later numerical results, D = 4.5 light years as the destination is Alpha Centaurus. Also the acceleration assumed for the trip is acceleration of Earth's gravity. I. e. a = g = 980 cm /sec^2 ≈ 1.03c / year. They define m as the mass of the rocket when it has attained speed v {max speed at the half way point} and m(0) is the much larger mass at launch. We can assume when half way the crew yaws their space craft 180 degrees so it ends up back on Earth, instead of near Alpha Centaurus.}
“Note that the astronauts age less than 4.5 years, {getting to full stop near Alpha Centaurus} a reflection of their relativistic motion and time dilation.” {While their twins on earth age 6.14 years} “The amount of fuel consumed during the journey depends critically on the value of v0.” {Speed of the exhaust relative to the rocket, a constant if the fuel never changes. Speeds are “normalized” by the speed of light c.}
{The best conceptually possible exhaust is only gamma rays - no real mass is discarded. It is 100% converted to energy. However only way to make them is particle / anti-partial annihilation and then the gammas go in opposite uncontrollable directions.} “In this case, m(0)/m ≈ 42. But this is a lower bound on this ratio. For more realistic rocket fuel, the requirements are more stringent. Nuclear energy derived from H fusion, {assuming that can be done}, is a more practical source of fuel, would have v0 ≈ 0.122, and in this case we would have m(0)/m ≈ 2 × 10^13. {I. e. Gamma ray exhaust is fantastically more “mass efficient,” However, even if that were possible, the intensity required for 1 g acceleration is so great that the heavy thick lead shield for the traveler(s) would be glowing red hot even with huge internal cooling coil flows and that refrigerator's needs would dominated the power requirements*}
“For nuclear fuel, a practical limitation on the maximum distance that can be traveled may be derived from assuming that at most all of the H in the solar system could be packed along as fuel. That amounts to something like 10^30 kg of H. Even with the most Spartan design, it seems hardly possible for a spaceship to weigh less than a ton, or about 1000 kg. Thus, a practical limitation would be m(0)/m 10^27.”
{I. e. You need for reactor's fuel more than half the mass of Jupiter, the largest planet, inside your fuel tank, at lift off from Earth! (even if it is only hydrogen, not a 50/50 mix of D/T.)
Also total empty space craft weight of only 1000 kg with that m(0)/m ratio is ridiculously optimistic – you can not hold more than half the weight of Jupiter in 10^6 gram tank! But I'll continue using their numbers.}
“For such a spacecraft, the distance traveled cannot exceed about 41.06/(a/g) light years! Longer trips can be made at lower accelerations, since the distance traveled is inversely proportional to the acceleration given m(0)/m, but the biological effects of protracted living at sub-g gravity may be prohibitive. The astronauts would age about 7.36/(a/g) years during this longest possible nuclear powered journey.”
{Please note I try to spread physics facts, not BS - this thread is "saturated" with repeated copies of same BS and inane short posts already.}
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Now consider making a worm hole humans could travel thru, although that is almost certainly impossible to do. I. e. probably is not possible, but if it is, doing so takes more mass energy in “exotic mass” than is known to exist. Also most of space time is so nearly “flat” that which way it curves, if it does, is not certain; yet some section of that space time must be “bent” approximately U-shaped in central cross section so the time required for traveling around normal surface of the bent U is greater than traveling to cross between the tops of the U, if and when they are connected via a worm hole, which of course needs to be made (and stabilized against its strong tendency to collapse – to again cease to exist.)
At the start this essentially impossible construction task the Space Bending Machine, SBM, needs some where to “stand” as it starts making just a small “dimple” in the flat space time. Then it needs to orbit the depression it is producing to avoid simply falling in due to the new gravity (curved space) it is making.
Also the “dimple” is much more like a long trough. Somewhat like the start of a bend in a flat sheet of paper. - An elongated “trough dimple” shape is very hard to “orbit” but I will continue, for want of a better word, to say the SBM “orbits” around the initial elongated depression it is making in space time.
Thus to “deepen the long trough dimple” the SBM must “de-orbit” some more “exotic mater” so it can fall into the beginning of the depression in space time. Not at all clear, even in principle, how this exotic material can be “slowed from orbit” to fall without some normal matter touching it – big explosion etc.
More ill defined procedures needed as this is just the start of worm hole making. - AFAIK, no one discusses how one could be made or stabilized against collapse, if it could be made, so I certainly will not venture any guesses. – I just wanted to note that the process starts by making a slight elongated “trough dimple” in flat space-time by using (negative gravity?) “exotic mater,” which probably needs to be created there by unknown processes (but requiring at least the energy E = Mc^2 of it and accelerators to collide normal mater to produce it. Last time I looked, any such accelerator cost billion dollar or more and weighed more than 10,000 tons. That SBM will be something to take you children to see.).
To even do that, if a standard D/T fusion reaction is used, the fuel mass ONLY at launch is 837 times greater than the mass of Earth!
To show the extremely difficult actually doing only slowing aging by a factor of (7.14/4.5) = 1.57 via a rocket ship, I post physics from this link: http://www.astro.cornell.edu/pdfs/relrocketderiv.pdf
{Most equations are omitted and text in these “curly brackets” was inserted in the quotes by Billy T.}
“.. Consider a rocket that accelerates uniformly. This means that the acceleration is fixed in the rocket rest frame; let the acceleration be a. Now suppose we wish to go a total distance D in the Earth frame going out halfway at a uniform acceleration, a, and then the rest of the way at uniform {reversed} acceleration -a so that we arrive at our destination with zero speed.”
{Note their analysis is for a “one way” trip and in later numerical results, D = 4.5 light years as the destination is Alpha Centaurus. Also the acceleration assumed for the trip is acceleration of Earth's gravity. I. e. a = g = 980 cm /sec^2 ≈ 1.03c / year. They define m as the mass of the rocket when it has attained speed v {max speed at the half way point} and m(0) is the much larger mass at launch. We can assume when half way the crew yaws their space craft 180 degrees so it ends up back on Earth, instead of near Alpha Centaurus.}
“Note that the astronauts age less than 4.5 years, {getting to full stop near Alpha Centaurus} a reflection of their relativistic motion and time dilation.” {While their twins on earth age 6.14 years} “The amount of fuel consumed during the journey depends critically on the value of v0.” {Speed of the exhaust relative to the rocket, a constant if the fuel never changes. Speeds are “normalized” by the speed of light c.}
{The best conceptually possible exhaust is only gamma rays - no real mass is discarded. It is 100% converted to energy. However only way to make them is particle / anti-partial annihilation and then the gammas go in opposite uncontrollable directions.} “In this case, m(0)/m ≈ 42. But this is a lower bound on this ratio. For more realistic rocket fuel, the requirements are more stringent. Nuclear energy derived from H fusion, {assuming that can be done}, is a more practical source of fuel, would have v0 ≈ 0.122, and in this case we would have m(0)/m ≈ 2 × 10^13. {I. e. Gamma ray exhaust is fantastically more “mass efficient,” However, even if that were possible, the intensity required for 1 g acceleration is so great that the heavy thick lead shield for the traveler(s) would be glowing red hot even with huge internal cooling coil flows and that refrigerator's needs would dominated the power requirements*}
“For nuclear fuel, a practical limitation on the maximum distance that can be traveled may be derived from assuming that at most all of the H in the solar system could be packed along as fuel. That amounts to something like 10^30 kg of H. Even with the most Spartan design, it seems hardly possible for a spaceship to weigh less than a ton, or about 1000 kg. Thus, a practical limitation would be m(0)/m 10^27.”
{I. e. You need for reactor's fuel more than half the mass of Jupiter, the largest planet, inside your fuel tank, at lift off from Earth! (even if it is only hydrogen, not a 50/50 mix of D/T.)
Also total empty space craft weight of only 1000 kg with that m(0)/m ratio is ridiculously optimistic – you can not hold more than half the weight of Jupiter in 10^6 gram tank! But I'll continue using their numbers.}
“For such a spacecraft, the distance traveled cannot exceed about 41.06/(a/g) light years! Longer trips can be made at lower accelerations, since the distance traveled is inversely proportional to the acceleration given m(0)/m, but the biological effects of protracted living at sub-g gravity may be prohibitive. The astronauts would age about 7.36/(a/g) years during this longest possible nuclear powered journey.”
{Please note I try to spread physics facts, not BS - this thread is "saturated" with repeated copies of same BS and inane short posts already.}
---------------------
Now consider making a worm hole humans could travel thru, although that is almost certainly impossible to do. I. e. probably is not possible, but if it is, doing so takes more mass energy in “exotic mass” than is known to exist. Also most of space time is so nearly “flat” that which way it curves, if it does, is not certain; yet some section of that space time must be “bent” approximately U-shaped in central cross section so the time required for traveling around normal surface of the bent U is greater than traveling to cross between the tops of the U, if and when they are connected via a worm hole, which of course needs to be made (and stabilized against its strong tendency to collapse – to again cease to exist.)
At the start this essentially impossible construction task the Space Bending Machine, SBM, needs some where to “stand” as it starts making just a small “dimple” in the flat space time. Then it needs to orbit the depression it is producing to avoid simply falling in due to the new gravity (curved space) it is making.
Also the “dimple” is much more like a long trough. Somewhat like the start of a bend in a flat sheet of paper. - An elongated “trough dimple” shape is very hard to “orbit” but I will continue, for want of a better word, to say the SBM “orbits” around the initial elongated depression it is making in space time.
Thus to “deepen the long trough dimple” the SBM must “de-orbit” some more “exotic mater” so it can fall into the beginning of the depression in space time. Not at all clear, even in principle, how this exotic material can be “slowed from orbit” to fall without some normal matter touching it – big explosion etc.
More ill defined procedures needed as this is just the start of worm hole making. - AFAIK, no one discusses how one could be made or stabilized against collapse, if it could be made, so I certainly will not venture any guesses. – I just wanted to note that the process starts by making a slight elongated “trough dimple” in flat space-time by using (negative gravity?) “exotic mater,” which probably needs to be created there by unknown processes (but requiring at least the energy E = Mc^2 of it and accelerators to collide normal mater to produce it. Last time I looked, any such accelerator cost billion dollar or more and weighed more than 10,000 tons. That SBM will be something to take you children to see.).
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