The speed of light relation: 0.71 approximately !

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Offline felixtheferret

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Hi Gurus.
  I still have this firm suspicion that even some of the most highly respected physicists do not understand, fundamentally, special relativity.  The reason for this is that if you read several layman's books on the subject, the respected authors all seem to take the Lorentz equations, plug arbitrary numbers in and draw completely different conclusions from the results!

For example, the worst authors ignore SR completely and say that because the speed of light is absolute, It would take 4.1 years even at just under light speed to reach our nearest star.  Of course, they fail to mention that that is 4.1 years as measured by the astronomer on Earth. For the astronaut, time has slowed down so by his watch is very much younger that 4.1 years older when he reaches there!

In another book, the respected author claimed you could go 'anywhere in the universe, in theory, in about 4 years.'  This claim was based on the idea that with a reasonably comfortable acceleration of 1G, using Newton's equations as a rough guide, it would take 2 years to reach just under light speed (ignoring the issue of energy required for the time being!) At this point, just under light speed, distance would shrink (as per the Lorentz equations) to almost nothing, and our would-be spaceman would blat across vast tracts of space in just seconds. At the convenient point, he would decide to decelerate by 1G, taking then a further 2 years to get back to rest, making a total journey time of 4 years.

In another book, I think it was the Physics of Star Trek or the sequel, the author  uses a similar idea but takes energetics into account, and tries to work out what practical speeds you could reach using antimatter for fuel, and then calculating the time-dilation via the Lorentz equations, and coming up with a different end figure for the 'local time' required to reach such-or-such a star.

Now, the logic in me tells me that as the interpretations are all different, they can't all be right!

So for a bit of fun I decided to calculate my own offering.
The question I posed myself was:

"At what percentage of the speed of light would an astronaut need to travel at to arrive at a destination, say the nearest star, in an equivalent LOCAL TIME as what the astronomer back on Earth is measuring ?"

If you do the simultaneous equations, I think it comes out to about 0.71 % of the speed of light, any mathematicians out there feel free to correct me.  Here's how it works.

A spaceship has been fueled and is set up to fly to our nearest star, about 4.1 light-years away. The spaceship sets off and soon reaches its maximum speed of 0.71 % of c.  Back on Earth, the spaceship is measured to take 5.78 years
to reach the star, as 4.1 / 0.71  equals 5.78.   However,  on board the spaceship, the spaceman's 'year watch'  has ticked over exactly 4.1 years,  because at 0.71 % of the speed of light,  time and distance dilation has become quite significant, significant to the point that for ALL INTENTS AND PURPOSES, the spaceship, relative to itself, is covering a distance at LIGHT SPEED IGNORING RELATIVISTIC EFFECTS.  Mr. Spaceman knows the star is 4.1 light years from Earth,  his watch says 4.1 years therefore he has been traveling at the speed of light. Of course, in reality, time and distance have changed relative to him so in reality he has only been doing 0.71 % of the speed of light. 

But for all practical intents and purposes, he has only aged 4.1 years.

- - - - -

And then you have to stop and ask yourself - although speed can be made constant for all observers very very easily IN MATHEMATICS by allowing distance and time to vary (as speed = distance / time ) what is the REAL INTERPRETATION of these variations from a physical perspective?

I suspect that these two central pillars of SR/GR are in fact poorly understood.  I don't understand them, and I'm certain our scientists have only a vague idea as well - simply because their conclusions come out all different in the layman's books that they write .  As Einstein said - if you can't explain something to your grandmother, you haven't really understood it.  And in failing to reach consensus in their layman's (read grandmother's) guides, our scientists have shown that they too, haven't really understood it!  What chance the future of physics ?

comments please!

It's the clocks that are slowing down, not time !!!


Offline JP

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The speed of light relation: 0.71 approximately !
« Reply #1 on: 19/06/2007 02:39:57 »
The clock sitting on earth can be assumed to be the stationary clock (nothing is truly stationary in relativity, merely relative, but you can assume that in the 2-body system here that the earth is stationary and the spaceship is moving).  In this case, the clock on earth ticks out an interval of 4.1/0.71~5.78 years.

The spaceman whose clock has been synchronized with the clock on earth would see it measure:
5.87/g, where g=1/Sqrt[1-v^2/c^2], which is the Lorentz contraction factor.  The mathematics works out to g~1.42 in this case.  So the spaceman measures just about 5/1.42~4.07 years passing.  The spaceman's clock appears to be moving slower than earth. (It would not tick off exactly 4.1 years as you indicated--indeed, if he were going AT the speed of light, which is impossible for any object with mass, it would tick off no time at all!)

If the spaceman and the earth both had meter sticks that matched up before he left, and they measure the distance to the star, the earth observer measures 4.1 light years.  The spaceman's ruler would now be shorter when compared with the earth's ruler would measure 4.1/g~2.89 light years. 

The speed the spaceman measures for himself is:
2.89 lyears/4.07 years=0.71x the speed of light.  The speed the earth measures is 4.1 lyears/5.87 years = 0.71x the speed of light.  They both agree on the speed, but the spaceman thinks its because he's moving over a shorter distance in a shorter time, and the earth thinks its because he's moving over the 4.1 light years at 0.71 c.
In other words, length contracts for a moving observer, and the time needed to make the trip get shorter by the same factor, so in any reference frame, distance/time=speed=constant.  This is why

So there's no real contradiction. 

If someone's an expert on this than me, check my math.  I think its right, but I haven't done special relativity in a few years.



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The speed of light relation: 0.71 approximately !
« Reply #2 on: 20/06/2007 11:46:27 »
Your math checks out. Alas,  [:-'(] Einstein made a good SF story or space opera impossible. So we writers took our revenge and invented FTL, warp speed, loopholes through space, hyperspace and what ever else we needed to keep the pace going.
If you can lay your hands on it, "Tau zero" by Poul Anderson is a good read on the subject. It includes all the formulas (formulae?) too.



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The speed of light relation: 0.71 approximately !
« Reply #3 on: 27/06/2007 11:27:39 »
All this deep space travel is all very well but  the  people in the ship would be launching themselves into a completely isolated existence - isolated in space, of course, but, more importantly, in time. After a very short while (in their experience) the people who sent them off would be dead and buried.  There would be no returning 'to base' after a successful mission. Earth civilisation would long since have gone down the pan or the Sun would be a red giant.
The travelers would be on their own for the rest of time.

The same applies to  contacting distant civilisations;  communications with anyone more than a few light years away is, essentially, a  transmit-only process. You'd be long dead by the time a reply arrived.  There is a sort of 'relevance horizon' around us which kicks in at, perhaps, ten light years (that's a couple of parliaments worth of time). It would be just possible to have a 'conversation' with that sort of delay. A sphere of that radius is not very likely to contain many life forms at the same stage of development as us (I suggest).
I guess there is always the possibility (did you see A for Andromeda in the 60s?) where we get a communication from a distant, malign, civilisation which consists of the instructions to build a super computer /life form which will take us over.  Or we could get a message from some  distant, benign source which gives us the secret of eternal something or other.

And what about the poor creatures, 50LY distant, who are just starting to get all our rubbish TV programmes? That's not very benign of us Earthlings, is it?


Offline syhprum

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The speed of light relation: 0.71 approximately !
« Reply #4 on: 27/06/2007 11:43:19 »
I sent an e.mail to S.E.T.I explaining that I thought their activities were rather futile because of the long time delay communicating with any conceivable civilisations, they were very polite and said what a wonderful scientific achievement it would be if they located other beings 1000 LY away but it all leaves me rather cold.



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The speed of light relation: 0.71 approximately !
« Reply #5 on: 27/06/2007 12:14:00 »
Well - it's nice to know I'm not the only cynic!.
I guess we could learn something from a long distance communication but the information would have to be treated with an awful lot of caution.