That would be very useful for Wikipedia. Would you agree that the view from Earth would show the spacecraft in the night sky for years, while the spacecraft's clock shows a minute for travelling through the solar system?
Here's where I get stuck: If gamma is 1,000, does that mean the spacecraft sees the luminosity of the planets and sun increase 1,000-fold, while Earth sees the spacecraft as dimmer by 1,000 fold?
That latter question affects panspermic spores at high velocity. By their own clock, they might go through a galaxy in a week, but they would get cooked from stars and cosmic rays.
Youvan, if I am reading the description under your question correctly, you have many points correct, but a slight and common misunderstanding of special relativity. This misunderstanding has led to such problems as the so-called "twins paradox." If two observers are relatively moving, each sees
- the other's clock as slow
- the other's length as contracted in the direction of motion
- and clocks in the other's reference frame skewed such that leading clocks lag.
The time measurements are deceptive, though, because they require time be measured by synchronized networks of clocks (reference frames), always using at least two clocks. For example observer A might use clocks A1 and A2 to measure a clock riding with B, B1.
However, to make an official Einstein measurement, B would use B1 and B2 clocks to measure one of the A clocks, say A1. So the clocks have been switched. And since each observer thinks the others' clocks are skewed, you can see how they get conflicting answers.
If both observers use the same clocks, say for example B compares his B1 clock against A1 and A2, then B will find time progressing faster in the A reference frame. This is a physical reality when measuring de Broglie waves (or frequency) which increases with velocity.
So the rocket and the Earth observers both see the other for only a very short time. At gamma of 1000, approximately the time for light to cross the solar system.
Your other conclusions are essentially correct. Any object going at near c, especially with a gamma of 1000, will encounter interstellar and/or interplanetary dust as cosmic radiation, and will be summarily destroyed. This is a severe problem with any concept of spaceflight at near lightspeed by conventional means. Even for a gamma in the low single digits astronauts would need a blast shield many meters thick. They might obtain this by using meteorite material without having to launch it from Earth.
Spores are more resilient, and only a few need to arrive undamaged. But I think you need to reduce your speed to a smaller gamma. Spores also probably do not care about elapsed time as much as humans. 70-80% c would get them pretty much anywhere they need to go, I would think. You going to colonize the galaxy?
Robert,
If we calculate the distance, d, the spacecraft travels, it seems like you are using the home-based clock (t) rather than the spacecraft's clock (t'), such that:
d=vt
rather than:
d=vt'
Correct?
Doug
P.S. Here is another question you might like:
http://community.wolfram.com/groups/-/m/t/321553?p_p_auth=8QzJotUd
Doug, good question as it sets up an important additional explanation. You must use measurements made in the same frame. In other words, there is a d and a d'. Only v will be the same in both frames (velocity is mutual). So you will have either:
d'=vt'
Or you will have
d=vt
In SR it is hard to tell what d is in the other frame sometimes. Often people talk about distances between us and them, which compares objects in different frames. You actually have to compare objects in the same frame, because the lack of synchronization of clocks makes anything else ambiguous. The distance to a moving object is a function of time, in particular time at a remote point which is constantly changing!
You have to measure distance to another point in your own frame which is at some instant near to the spaceship. You could for example notice when it passed the Pluto entering the solar system (Sorry, I grew up with Pluto being a planet, and the boundary of the solar system, and a God of the Underworld, and it's like a historical fact, there is no credibility in changing it!)
So this ship comes in at gamma=1000 past Pluto. Let's say it happens to be 6 billion km from Earth at that moment. Your outpost on Pluto notices the reading of the spaceship clock by looking through the window, and transmits that and his own clock reading. Your clocks have been previously synchronized.
His signal arrives 333.3 minutes later, and the spaceship arrives .3 minutes after that. You look through the window at the spaceship clock and you subtract your outpost reading from yours and find the occupants of the spaceship seem to have experienced only .3336 minutes time passage on their trip from Pluto.
However, you notice they also have a "distance traveled" indicator, and it reflects that they have only traveled 6 million km, not 6 billion, because of length contraction. Thus 6 million / .3336 minutes = 6 billion / 333.6 minutes = v, which you both agree on.
Robert,
My son, age 10, is upset by Pluto. It might continue one generation, like the influence the WWII veterans had on us.
You really should take a wack at Wikipedia's SR article on this ship coming through our solar system. The length contraction fooled me!
Doug
Wikipedia is a mess, with many articles on every subject, and all kinds of know-it-alls fighting over what is said. The winner is apparently the most persistent at deleting other people's edits. Send me a link to the exact article you are talking about and I'll see if there is anything simple I can do with it.
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