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If a spacecraft were travelling at the speed of light (OK, forget the difficulties for now) relative to an observer on Earth then would it appear to an occupant on that ship that they had travelled instantly from one point to another?
Although a spacecraft cannot quite achieve the speed of light, it can, forgetting the difficulties, as you say, get as close to it as you want. So here is a formula that you can use to determine what speed you have to travel at to traverse any distance, d, in any time, t:If a spacecraft were travelling at the speed of light (OK, forget the difficulties for now) relative to an observer on Earth then would it appear to an occupant on that ship that they had travelled instantly from one point to another?
Once they are co-located and not moving fast relative to each other, they age at the same rate. If you ignore gravity (general relativity), you don't even need to worry about co-location, only relative speed. So yes, after disembarking, the traveler would age at the same rate as their earth twin - remaining 5 years younger (for example).Thank you for the replies. One further question please.
Does this mean that when our traveller disembarked at their destination, time for them would pass at the same rate as the observer on Earth? Let's not worry about stars moving apart or the universe expanding for now. Their twin would be 5 years older but they would now both age at the same rate.
Yes, they would now both age at the same rate and all frames will agree, but it is only in their common rest frame that we can say the traveling twin would be 5 years younger than the earth twin. Other frames would not agree. It is only when the traveling twin makes a quick return trip while the earth twin ages another 5 years that all frames will agree on their age difference.Thank you for the replies. One further question please.
Does this mean that when our traveller disembarked at their destination, time for them would pass at the same rate as the observer on Earth? Let's not worry about stars moving apart or the universe expanding for now. Their twin would be 5 years older but they would now both age at the same rate.
It mathematically proven that entanglement cannot be used to send messages.Thank you all. So now all we need is faster than light communications and we have a viable colony. Anyone invented a communication device using Quantum Entanglement yet?
Also, though relativity per se sets no limit on rocket speed, there are very strong reasons to doubt it will ever be achieved. For example, if you are traveling at a mere 90% of lightspeed (which is not enough for dramatic time dilation), hitting 1 gram particle will release energy greater than the Nagasaki atom bomb. It is really hart to see how effective shielding could exist for near light speed (where a speck of dust could be more dangerous than all the H-bombs in the world).Thank you all. So now all we need is faster than light communications and we have a viable colony. Anyone invented a communication device using Quantum Entanglement yet?
Speed of light limit and its consequences are experimentally established (to a high degree), not mathematical facts. OPERA result, if confirmed, would be new evidence requiring theory modification. Your question was asked in light of current theory and knowledge.Well the speed of light is also a mathematically proven fact but the OPERA experiment casts doubts on that.
Plus if the experiments prove that actions on one of a tangled pair affects the other then they must have observed the effect on the other. In other words they have passed on information. It's just a matter of encoding it surely?
Could you show the calculations or a reference?if you are traveling at a mere 90% of lightspeed (which is not enough for dramatic time dilation), hitting 1 gram particle will release energy greater than the Nagasaki atom bomb.
The calculation is simple. Using the relativistic KE formula, at around .86c the KE = mc^2 (that is, KE = rest energy). Then compare m c^2 in ergs (for example) to the Nagasaki bomb in ergs (available, for example, from wikipedia). I did it once when I was kid, and once in the last year to ensure I hadn't made a mistake. I remember this fact as as useful order of magnitude to keep in mind.Could you show the calculations or a reference?
I am sure it is, so why not work out this example, I am sure people will appreciate it. :)The calculation is simple.
This is really, really silly. I thoroughly outlined the computation. However, to humor a silly request:I am sure it is, so why not work out this example, I am sure people will appreciate it. :)