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Old 2011-01-29, 05:22   #1
retina
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Question Does the photon ever reach the spaceship?

One of my minions came to me with this.

A spaceship is accelerating in a straight line at a constant 1g (local time frame within the ship) in a vacuum in flat space.

At t=0 the position of the spaceship is x=0 and the velocity of the spaceship is v=0. The ship immediately starts accelerating at 1g at t=0.

Some time tp>0 later a photon is sent directly towards the spaceship from point x=0.

Assuming GR and SR are true then ...

1) The photon reaches the spacecraft:
(a) Never. Photons a wussies and can't catch me.
(b) Depends upon the value of tp. Did someone say "dilation"?
(c) Always. Photons are crazy fast dude.

2) Show your working to prove either (a), (b) or (c) is true.

[size=1]Yes, the answer is available with a search engine. Yes, you are cheating if you use a search engine.[/size]
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Old 2011-01-29, 13:09   #2
Mini-Geek
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1) (c)
2) I have no actual work or proof to show, I just guessed based on the fact that you can never go faster than c, so you shouldn't be able to outrun a photon. I'd like to see the real answer though. :) I googled to no avail.

Last fiddled with by Mini-Geek on 2011-01-29 at 13:09
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Old 2011-01-29, 15:27   #3
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Quote:
Originally Posted by Mini-Geek View Post
2) I have no actual work or proof to show, I just guessed based on the fact that you can never go faster than c, so you shouldn't be able to outrun a photon. I'd like to see the real answer though. :) I googled to no avail.
Your reasoning is wrong.. Suppose the spaceship kept a distance 1/t ahead of the trailing photon emitted at the origin at t=0. Because 1/t is always positive, the photon never catches up. Moreover, the spaceship's position at time t is given by ct + t[sup]-1[/sup]. differentiate wrt t to get the speed: c - t[sup]-2[/sup] which is less than c at all times.

This doesn't suffice to demonstrate that a spaceship could do this while maintaining constant (local) acceleration, but I'm pretty certain it could.
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Old 2011-01-29, 15:51   #4
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My reasoning:
The spaceship can never accelerate to c. The photon always approaches the spacecraft at c. Therefore (c). If the ship was, say, 1 light year away when the photon was released then it would take 1 year to catch up, from the point of view of the pilot. Despite the ship's acceleration.
Of course, I'm bound to be wrong!
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Old 2011-01-29, 16:19   #5
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Quote:
Originally Posted by retina View Post
One of my minions came to me with this.

A spaceship is accelerating in a straight line at a constant 1g (local time frame within the ship) in a vacuum in flat space.

At t=0 the position of the spaceship is x=0 and the velocity of the spaceship is v=0. The ship immediately starts accelerating at 1g at t=0.

Some time tp>0 later a photon is sent directly towards the spaceship from point x=0.

Assuming GR and SR are true then ...

1) The photon reaches the spacecraft:
(a) Never. Photons a wussies and can't catch me.
(b) Depends upon the value of tp. Did someone say "dilation"?
(c) Always. Photons are crazy fast dude.

2) Show your working to prove either (a), (b) or (c) is true.

[SIZE=1]Yes, the answer is available with a search engine. Yes, you are cheating if you use a search engine.[/SIZE]
This is an old favourite and I've already set Retina a PM to that effect.

I won't reveal an answer but will hint that, as in so many cases in relativity, drawing a spacetime diagram will probably be very helpful.


Paul
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Old 2011-01-29, 16:29   #6
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Quote:
Originally Posted by xilman View Post
... I've already set Retina a PM to that effect.
I don't have PMs enabled. Methinks your PM has probably gone into never never land.
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Old 2011-01-29, 16:42   #7
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Quote:
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I don't have PMs enabled. Methinks your PM has probably gone into never never land.
Strange. I'll send email.

Paul
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Old 2011-01-29, 16:50   #8
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Quote:
Originally Posted by xilman View Post
Strange. I'll send email.
I am interested to see what happens. I also disabled emails.
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Old 2011-01-30, 15:11   #9
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Quote:
Originally Posted by Flatlander View Post
The spaceship can never accelerate to c. The photon always approaches the spacecraft at c. Therefore (c). If the ship was, say, 1 light year away when the photon was released then it would take 1 year to catch up, from the point of view of the pilot. Despite the ship's acceleration.
Quote:
Originally Posted by Mr. P-1 View Post
Your reasoning is wrong.. Suppose the spaceship kept a distance 1/t ahead of the trailing photon emitted at the origin at t=0. Because 1/t is always positive, the photon never catches up. Moreover, the spaceship's position at time t is given by ct + t[sup]-1[/sup]. differentiate wrt t to get the speed: c - t[sup]-2[/sup] which is less than c at all times.

This doesn't suffice to demonstrate that a spaceship could do this while maintaining constant (local) acceleration, but I'm pretty certain it could.
Two competing ideas. Which is correct? Maybe both are correct? Maybe neither is correct?
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Old 2011-01-30, 15:45   #10
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Zenone

c the speed you can not put the "arrow" ( Light arrow )

btw, ... lane change without signaling it is rude uncivilized ...
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Old 2011-01-30, 16:30   #11
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Since the Universe is expanding, after some time t[sub]z[/sub] the photon cannot reach the spaceship. The value of this t[sub]z[/sub] is an exercise for the reader.

Last fiddled with by alpertron on 2011-01-30 at 16:32
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