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**Physics, Astronomy & Cosmology / The speed of light relation: 0.71 approximately ! **

« **on:**18/06/2007 23:16:59 »

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!

[]

thanks.

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!

[]

thanks.