Specific Relativity/Light-Speed Question

[EWright]

Question: If you travel towards a light source that is 10-light days away, at .5c, how soon will you reach the light given off from that source at the time you began to move towards it? (please do not reaspond by stating the obvious fact that a person can't travel at .5c)

And similarly, how long will it take you to reach the actual source, which is 10 light days away.

[Erasmus00]

Originally Posted by EWright

Question: If you travel towards a light source that is 10-light days away, at .5c, how soon will you reach the light given off from that source at the time you began to move towards it? (please do not reaspond by stating the obvious fact that a person can't travel at .5c)

And similarly, how long will it take you to reach the actual source, which is 10 light days away.

It depends. Do you measure the light source as 10 light days away before or after you start moving toward it at .5c?
-Will

[EWright]

Originally Posted by Erasmus00

It depends. Do you measure the light source as 10 light days away before or after you start moving toward it at .5c?
-Will

?

Yes, how else would you measure it? (I don't mean that in a rude way, I really don't know how else). And don't include acceleration... our traveler accelerated before reaching the starting line.

[Erasmus00]

Originally Posted by EWright

?

Yes, how else would you measure it? (I don't mean that in a rude way, I really don't know how else). And don't include acceleration... our traveler accelerated before reaching the starting line.

I asked a "before or after" question, and you answered "yes." If I measure 10 light days between A and B, and then I accelerate to .5c, and measure the distance again, it'll be length contracted. As such, it means different things for you to measure 10 light days before you began the trip then it does to measure 10 light days right after you began the trip.
-Will

[EWright]

Originally Posted by Erasmus00

I asked a "before or after" question, and you answered "yes." If I measure 10 light days between A and B, and then I accelerate to .5c, and measure the distance again, it'll be length contracted. As such, it means different things for you to measure 10 light days before you began the trip then it does to measure 10 light days right after you began the trip.
-Will

Ah, my apologies; I misread the before or after question. My concept was that the space traveler is already traveling at .5c when he begins his trip by getting a 'running start' first, in order to avoid acceleration factors. So his time measurement would begin *as* he crossed the point precisely 10 light days from the source; as in the same time the source is releasing 'photon A' in his direction. At what point in time would he then encounter photon A, if everything is zeroed out as he crosses the starting line?

If this still does not after the before or after question, can you please answer for both situations, so I can better understand the difference?

Does no one else have an anwser for this???

[Erasmus00]

Alright, lets say right after he hits .5c he notices an object 10 light days away, and that light source spits out some light. The light gets to him in 10 light days, and he reaches the object in 20 light days.

Now, lets do a slightly different question. Lets say that there are two space stations 10 light days apart. Call them station A and B. A traveler takes off at .5c (assuming near instant acceleration) from A going toward B. Right as he takes off, B sends a light signal to A.

Now, as our traveler takes off, after he gets to .5c he would measure the distance between A and B as being 8.7 light days away. The traveler passes the light after he has been traveling for 8.7 days, and gets to the station in 17.4 days.

Now, an observer on A who is watching this would see our traveler as meeting the light at 6.67 light days, and he would see the traveler reach B in 20 light days. If the observer on A takes into account time dilation, he will believe that it took 17.4 days on the travelers clock.

But notice that simple time dilation won't explain the discrepancies between when the traveler met the light pulse. This is because the events happen at different coordinates in each observer's frame.
-Will

[EWright]

Originally Posted by Erasmus00

Alright, lets say right after he hits .5c he notices an object 10 light days away, and that light source spits out some light. The light gets to him in 10 light days, and he reaches the object in 20 light days.

Ok, say his starting point corresponds to a space station that he passes at the speed of .5c in this scenario. We agree that he should encounter photon-A, given off from a light sorce 10 light days away, in ten days. However, this same photon should reach is starting point and be measured at the space station at the ten day mark because it is traveling at the rate of c. This suggests the photon is at the traveler's location and being measured at his starting point at the exact same moment, which isn't possible given any dialations or contractions of time.

Now, lets do a slightly different question. Lets say that there are two space stations 10 light days apart. Call them station A and B. A traveler takes off at .5c (assuming near instant acceleration) from A going toward B. Right as he takes off, B sends a light signal to A.

Now, as our traveler takes off, after he gets to .5c he would measure the distance between A and B as being 8.7 light days away. The traveler passes the light after he has been traveling for 8.7 days, and gets to the station in 17.4 days.

Now, an observer on A who is watching this would see our traveler as meeting the light at 6.67 light days, and he would see the traveler reach B in 20 light days. If the observer on A takes into account time dilation, he will believe that it took 17.4 days on the travelers clock.

But notice that simple time dilation won't explain the discrepancies between when the traveler met the light pulse. This is because the events happen at different coordinates in each observer's frame.
-Will

Can you explain why this second scenario measures differently than the first one please?

[Erasmus00]

Originally Posted by EWright

Can you explain why this second scenario measures differently than the first one please?

I'm responding to your second question, because it helps address the first. The second scenario measures different then the first simply because they are different inertial frames. When an object is moving it measures different length and time scales then an object standing still. If an observer standing still measures 10 light years between two objects, then a person moving measures 10*(sqrt(1-v^2/c^2)) light years. This is what is meant by length contraction.
-Will

[EWright]

Originally Posted by Erasmus00

I'm responding to your second question, because it helps address the first. The second scenario measures different then the first simply because they are different inertial frames. When an object is moving it measures different length and time scales then an object standing still. If an observer standing still measures 10 light years between two objects, then a person moving measures 10*(sqrt(1-v^2/c^2)) light years. This is what is meant by length contraction.
-Will

But in the first scenario you say the traveler will reach the photon in 10 days. And the photo from the time it was given off would have to reach his starting point in 10 days. So given the different inertial frames of the traveler and his counterpart where he started, are you saying both will measure that photon at different points in space time, but at the same time of ten days? Are you saying that single photon can be in two places at once?

[Erasmus00]

Originally Posted by EWright

But in the first scenario you say the traveler will reach the photon in 10 days. And the photon from the time it was given off would have to reach his starting point in 10 days. So given the different inertial frames of the traveler and his counterpart where he started, are you saying both will measure that photon at different points in space time, but at the same time of ten days? Are you saying that single photon can be in two places at once?

No, I'm saying the "same place" corresponds to different labels depending on whose coordinate system you are in. Each observer only sees the photon pass the observer at one point, but different observers will disagree as to exactly where that point was. (just as they disagree as to exactly when it was). There isn't an absolute coordinate system you can use to label an event.
-Will