Special relativity timebomb on distant planet 'paradox'?

[DarioC]

Reductionist time: First, what Alice perceives has no effect on what actually happens on the far planet. Next, get rid of the bomb. Have a light source that flashes every second on the far planet. It has been flashing forever (OK 50 years). In the time that it takes Alice to get to the planet it will have put out ten years worth of flashes. (in the far planets time). Alice will see these ten years of flashes spread over her time (3 years). She will see roughly 3 flashes per second.
Seems pretty simple to me.
DC

 

[PeterDonis]

In the time that it takes Alice to get to the planet

You have just confused the issue again, because this statement is frame-dependent. The ten years' worth of flashes are not emitted "in the time it takes Alice to get to the planet" in Alice's frame, only in the Earth-planet frame.

 

[DarioC]

Then you disagree with my concept that Alice will intercept each and everyone of these flashes while in transit to the far planet?
DC

 

[phinds]

Then you disagree with my concept that Alice will intercept each and everyone of these flashes while in transit to the far planet?
DC

You have misunderstood Peter's post. Read it again carefully.

 

[PeterDonis]

Then you disagree with my concept that Alice will intercept each and everyone of these flashes while in transit to the far planet?

I have said no such thing.

I strongly suggest that you work out the specific (t, x) coordinates (in the Earth/planet frame) at which each flash is emitted, and at which each flash intersects Alice's worldline. Then you can Lorentz transform those coordinates into Alice's frame. Hopefully that will help you to understand my previous post better.

 

[DarioC]

OK, I can see the phrase I used is not the way to express what I meant. Between the planets there is already a "string" of light pulses. When Alice passes through these pulses she will intercept them at much higher rate, according to her clock, than one pulse per her second--because her clock, along with everything else on her ship is slowed down. Those pulses can serve as a yardstick of distance that she will perceive as being much shorter than the speed of light for one second.
But none of her perceptions have any effect on what is actually happening on the far planet except for how she perceives it.

On consideration perhaps I should have said "during her trip to the far planet" the pulsing light on that planet will have emitted a number of pulses, according to the far planet clock, that is the number that you get when you calculate the number of seconds in 10 years. I see no reason why she would not intercept at least that number of pulses in route.

 

[PeterDonis]

Between the planets there is already a "string" of light pulses.

"Already" is still frame-dependent; "already" according to whose frame? "Already" has different meanings in different frames because of relativity of simultaneity.

On consideration perhaps I should have said "during her trip to the far planet" the pulsing light on that planet will have emitted a number of pulses, according to the far planet clock, that is the number that you get when you calculate the number of seconds in 10 years

"During" according to whose frame? Same comment as above.

Here is a frame-invariant statement that you might be groping towards: when Alice is just leaving Earth, some pulse from the far planet is just arriving. Call that pulse "pulse 0". When Alice is just arriving on the distant planet, some pulse is just being emitted; call that pulse "pulse N". Alice sees every pulse between pulse 0 and pulse N, in order, during her trip. (Note that "during" here has an invariant meaning because we are only talking about events on Alice's worldline--we don't care "when" they were emitted from the planet, we only care about their intersections with Alice's worldline.)

Now work out now much time passes, on the planet's clock, between the emission of pulse 0 and the emission of pulse N (which is also Alice's arrival). You will find it is not 10 years.

 

[PeterDonis]

When Alice passes through these pulses she will intercept them at much higher rate, according to her clock, than one pulse per her second--because her clock, along with everything else on her ship is slowed down.

This is also not quite right, because the rate at which Alice intercepts the pulses, according to her clock, is affected by the Doppler shift as well as time dilation. (Actually, if you look at the math, the relativistic Doppler shift formula by itself gives the correct answer.)

Those pulses can serve as a yardstick of distance

No, they can't, because Alice is moving relative to the source of the pulses.

 

[DarioC]

Well I guess that pretty much takes care of that. DarioC backs quietly out of the room, closing the door behind him.