Matter-antimatter ship in GR clock paradox - fuel consumption

In summary, the conversation discusses the familiar round trip with acceleration g and the amount of matter-antimatter fuel needed for a 4-year trip with a 1000t ship. The participants are unsure about the calculation and ask for help in solving it within the framework of General Relativity. The response provides a link to a resource that covers the topic and states that 38 kg of fuel is needed for every 1 kg of payload.
  • #1
malin
1
0
hi,

recall the familiar round trip - it's more or less the same as in this arXiv article (http://arxiv.org/PS_cache/physics/pdf/0604/0604025v3.pdf) - round trip with acceleration g. me and my friends were wondering the following:
imagine that the passenger abroad the rocket travels for 4 years and the ship alone is 1000t. (or any other number, it doesn't matter)
how much matter-antimatter (100% efficiency, E=mc2) fuel would the ship need?

we don't even agree wheter m(t) is trivial from the boundary conditions, let alone m(x),
and we are working in GR framework...
can anyone tell me how to solve this one?


thanks!
 
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  • #2
Hi malin, welcome to PF,

The http://www.math.ucr.edu/home/baez/physics/Relativity/SR/rocket.html" [Broken] page covers all of this. For a 4.3 light-year trip stopping at the end you require 38 kg of fuel (at 100% efficiency) for every 1 kg of payload.
 
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  • #3


First of all, it's important to clarify that the concept of a matter-antimatter ship is purely hypothetical at this point, as we do not currently have the technology to create and contain large amounts of antimatter for propulsion purposes. However, let's explore this scenario from a theoretical standpoint.

In the context of the GR clock paradox, the fuel consumption of a matter-antimatter ship would depend on the specific trajectory and acceleration profile of the ship. The article you referenced provides an example of a round trip with constant acceleration, which can be used as a starting point for our calculations.

In this scenario, the ship travels for 4 years (proper time) and the ship alone has a mass of 1000t. We also assume 100% efficiency in converting matter to antimatter, according to the famous equation E=mc^2. This means that for every unit of mass converted, an equivalent amount of energy is produced.

To calculate the amount of fuel needed, we can use the equation E=mc^2, where E is the total energy required, m is the mass of the ship (including fuel) and c is the speed of light. We can also use the equation F=ma, where F is the force (thrust) required to accelerate the ship, m is the mass of the ship (excluding fuel) and a is the acceleration.

Using these equations, we can determine the amount of energy required to accelerate the ship to a certain velocity and maintain that velocity for the duration of the trip. This energy can then be converted to mass (fuel) using the equation E=mc^2.

However, as you mentioned, there may be some disagreement on the exact calculation of m(t) and m(x) in the context of GR. This is because GR takes into account the effects of gravity and the curvature of spacetime, which can affect the mass of an object. Therefore, the exact amount of fuel needed may vary depending on the specific calculations and assumptions used.

In conclusion, while we can make some theoretical calculations about the fuel consumption of a matter-antimatter ship in the context of the GR clock paradox, the exact amount needed would depend on various factors and may not have a definitive answer. It's an interesting thought experiment, but it's important to keep in mind that it is currently beyond our technological capabilities.
 

What is a matter-antimatter ship?

A matter-antimatter ship is a hypothetical spacecraft that is powered by the annihilation of matter and antimatter particles. Matter and antimatter are oppositely charged particles with the same mass, and when they come into contact, they annihilate each other, releasing a large amount of energy.

How does a matter-antimatter ship work in the GR clock paradox?

The GR clock paradox is a thought experiment in Einstein's theory of relativity, where two clocks moving at different speeds experience time dilation. In this scenario, a matter-antimatter ship would travel at near-light speed, experiencing time dilation. This would allow the crew to travel long distances in a shorter amount of time, according to their own perception of time.

What is the fuel consumption of a matter-antimatter ship in the GR clock paradox?

The fuel consumption of a matter-antimatter ship in the GR clock paradox would be extremely efficient. Since matter and antimatter annihilate each other completely, the only byproduct is energy. This means that a matter-antimatter ship would require a very small amount of fuel to power its journey.

Is a matter-antimatter ship in the GR clock paradox feasible?

Currently, the technology to build a matter-antimatter ship in the GR clock paradox does not exist. The production and storage of antimatter is extremely difficult and expensive. Additionally, the ship would need to be shielded from the high levels of radiation produced by the annihilation process. However, some scientists are researching ways to overcome these challenges and make this type of spacecraft a reality in the future.

What are the potential benefits of using a matter-antimatter ship in the GR clock paradox?

A matter-antimatter ship in the GR clock paradox could potentially allow for faster and more efficient space travel. This could open up opportunities for exploring distant parts of the universe and potentially even other galaxies. It could also have practical applications, such as delivering supplies and resources to other planets or aiding in the colonization of other worlds.

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