What Happens to Light Speed When Measured from a Fast-Moving Space Station?

[zoobyshoe]

I'm on a space station in deep space. I depart in a rocket and accelerate to .5 c then level off to that speed. No longer accelerating, I now define myself to be stationary. I define the speed of anything I percieve to be in motion as relative to my own stipulated-to-be-unmoving inertial frame

On board I have a Michelson-Morley (or better) apparatus for measuring the speed of light. However, I am not going to measure the speed of any light that originates on my own ship. I am going to measure the speed of a beam of light that comes from the space station I just left.

At a prearranged time the space station sends this beam of light in exactly the same direction I am traveling.

When it catches up to me I measure it to be going:

A. c?

B. .5 c?

c. other ?

 

[jcsd]

A. c

second postulate

 

[Nereid]

On board I have a Michelson-Morley (or better) apparatus for measuring the speed of light. However, I am not going to measure the speed of any light that originates on my own ship. I am going to measure the speed of a beam of light that comes from the space station I just left.

At a prearranged time the space station sends this beam of light in exactly the same direction I am traveling.

When it catches up to me I measure it to be going

How, exactly, do you measure the speed of light from the space station?

 

[zoobyshoe]

I assumed it could be done since people have measured the speed of light from stars.

You're saying it can't be done?

 

[Nereid]

There are several methods by which one could measure the speed of light. Many of those who find SR hard to understand (or accept) feel that part of the 'problem' is the actual method of measuring the (local) speed of light.

In the case of your hypothetical experiment, I was wondering if you were getting at something special about the space station you had left (or would any distant source do)?

 

[zoobyshoe]

Any source would do, actually.

 

[zoobyshoe]

Another Speed Of Light Question

In the above situation (space station, rocket ship) my speed away from the station is .5 c. The speed of the light departing the space station in my direction is c.

If I am, say, 300,000 km away from the station ( a distance selected for convenience) when the light is emitted from the station, what math do I use to determine 1.) how long it will take for the light from the station to catch up to me and 2.) How far away from the station I will be when it does catch up?

 

[Doc Al]

Assuming you are 300,000 km away from the station as measured in your frame, then:

(1) The light must travel 300,000 km to reach you, so T = D/c = 1 sec.
(2) During that 1 sec the station has traveled a distance D = VT = 0.5cT = 150,000 km. So when the light reaches you you'll be a total of 450,000 km from the station.​

 

[Janus]

In the above situation (space station, rocket ship) my speed away from the station is .5 c. The speed of the light departing the space station in my direction is c.

If I am, say, 300,000 km away from the station ( a distance selected for convenience) when the light is emitted from the station, what math do I use to determine 1.) how long it will take for the light from the station to catch up to me and 2.) How far away from the station I will be when it does catch up?

As measured by you or the space station? If measured by you, the light will reach you in one sec and the station will be 450,000 km away when it reaches you.

If measured by the space station, then the light will reach you in 2 sec and you will be 600,000 km away from the station.

 

[zoobyshoe]

Sorry I wasn't clear.

In the second question I meant to change my definition of myself as being motionless to being in motion at .5c relative to the source of the light - the space station.

So, If I am traveling at .5 c away from the station, and the beam of light is emitted from the station when I am a distance of 300,000 km away, how long will the light take to reach me, and how far away will I be from the station?

 

[Janus]

Sorry I wasn't clear.

In the second question I meant to change my definition of myself as being motionless to being in motion at .5c relative to the source of the light - the space station.

So, If I am traveling at .5 c away from the station, and the beam of light is emitted from the station when I am a distance of 300,000 km away, how long will the light take to reach me, and how far away will I be from the station?

Doc Al and I both gave you the answer already: 1 sec and 450,000 km, assuming that you are making the measurements.

 

[zoobyshoe]

Doc Al and I both gave you the answer already: 1 sec and 450,000 km, assuming that you are making the measurements.

OK, What math did you use to arrive at the 2 sec, 600,000 km figures?

 

[Janus]

OK, What math did you use to arrive at the 2 sec, 600,000 km figures?

From the space stations perpective, the relative speed between the light it emits and you is .5c. Since it the distance between you and the station is 1 light sec at the time of emission, it takes 2 sec for the light to close the distance. If the light travels for 2 secs, it travels 600,000 km.

 

[zoobyshoe]

OK the space station viewpoint makes sense to me, but I don't understand how there could be a difference from my perspective.

If the light is emitted from the station when I am 300,000 km away from it, it will take the light one second to reach that point. Once that second has elapsed and the light has reached that point, I will no longer be there. It will be one second later, and at .5c, I will be 150,000 km farther away, the light will not have caught up with me yet. In the half second it takes the light to reach that point 150,000km away, I will have traveled yet further, and won't be there when it arrives. And so on, such that I'm thoroughly confused as to why it isn't also 2 seconds 600,000 km viewed from my perspective as well.

 

[Doc Al]

view from the ship

If the light is emitted from the station when I am 300,000 km away from it, it will take the light one second to reach that point.

The light travels at speed c with respect to you. And, with respect to you, "that point" is you! The fact that you are also moving with respect to something else (the spaceship) is irrelevant. No matter what speed you are moving, if the light flashes when it's 300,000 km away from you, it will reach you in one second.

Once that second has elapsed and the light has reached that point, I will no longer be there.

In your frame, you don't move. (You are at rest in your own frame.) In the frame of the station you are moving, but that doesn't matter.

It will be one second later, and at .5c, I will be 150,000 km farther away, the light will not have caught up with me yet.

Yes, you will be 150,000 km further from the station. And yes the light will have caught up with you!

Just remember that in your frame light travels 300,000 km/sec with respect to you.

 

[GOD__AM]

Hi, I'm new so please excuse me if I'm butting in. This is all very interesting but I'd like to add another observer to the seudo experiment. Assuming what Doc Ai and Janus are saying is correct (as far as I understand they are) then we get the following senario.

Let's say there are 2 space stations 450,000k apart. The rocket leaves the first station (call it "a") as outlined already heading towards space station "b". The light is still turned on when the rocket is 300,000k from space station "a".

Now the observer in the rocket sees the light from space station "a" when he is right beside space station "b" . Space station "b" cannot see the light for another 1/2 second.

Now let's suppose that the observer in the rocket has a mirror set up that aligns the light source from space station "a" with our observer at space station "b" as it passes so that he sees the light reflected from the rocket nearly a 1/2 second before he sees the light from space station "a". :surprise:

Hope I didn't botch that up too bad. It makes perfect sense to me (the experiment not the results that is).

 

[zoobyshoe]

The light travels at speed c with respect to you.And, with respect to you, "that point" is you! The fact that you are also moving with respect to something else (the spaceship) is irrelevant.

The light is moving at c in its direction of propagation. That is: at any given time, the tip of the beam of light is propagating away from the point in space from which it was emitted, at speed c.

My speed in the same direction is relevant with respect to the tip of that beam of light. The light cannot reach me in one second, because I am moving away from its approaching tip. And: I cannot be aware of the beam of light to calculate anything about its time until it first catches up with me. Were I able, by magic, to see the tip of the beam of light, I would not see it closing the distance between us at c. The time it takes for the light to reach me from the time I was at 300,000 km from the station must be greater than 1 sec.

Just remember that in your frame light travels 300,000 km/sec with respect to you.

If, once the light has caught up with me, I measure its speed, I will clock it to be going at c regardless of my speed in any inertial frame. Jcsd confirmed this above, and I believe this is the agreed result. Einstein used this mysterious fact as his second postulate.

That, however, is a separate issue from the fact that the tip of a beam of light is limited to propagation at c from its point of origin. It is for this reason that the space station could determine that there was a difference of .5 c between my speed, and the speed of the beam of light as it is on its way toward me.

 

[Doc Al]

The light is moving at c in its direction of propagation.

The light is moving at speed c with respect to the observer.

That is: at any given time, the tip of the beam of light is propagating away from the point in space from which it was emitted, at speed c.

No. From the viewpoint of the spaceship, the separation distance between the tip of the light beam and the space station increases at only 0.5 c. (It is only from the view of the space station that the light travels at speed c with respect to the space station.)

My speed in the same direction is relevant with respect to the tip of that beam of light. The light cannot reach me in one second, because I am moving away from its approaching tip.

Not true. You are moving away from the space station, but the light is still moving towards you at speed c. This is what "invariant speed of light" means.

And: I cannot be aware of the beam of light to calculate anything about its time until it first catches up with me. Were I able, by magic, to see the tip of the beam of light, I would not see it closing the distance between us at c. The time it takes for the light to reach me from the time I was at 300,000 km from the station must be greater than 1 sec.

The only way to measure the speed at which the light got to you is to know when and where it started. You'll have to imagine an extended spaceship frame--or another spaceship moving along with yours but located next to the space station at the very moment the light is emitted. Your sister spaceship has its clock synchronized to yours, and it is 300,000 km away from you. When the light reaches you, you note the time. Later you compare notes with the other ship, which tells you the time the light flashed: you will find that the light took 1 second to reach you, according to the synchronized clocks in the two ships.

If, once the light has caught up with me, I measure its speed, I will clock it to be going at c regardless of my speed in any inertial frame. Jcsd confirmed this above, and I believe this is the agreed result. Einstein used this mysterious fact as his second postulate.

Exactly right. But in your frame, the light only traveled 300,000 km to get to you. So it took 1 second.

That, however, is a separate issue from the fact that the tip of a beam of light is limited to propagation at c from its point of origin. It is for this reason that the space station could determine that there was a difference of .5 c between my speed, and the speed of the beam of light as it is on its way toward me.

The speed of light will always be c with respect to whatever observer is making the measurement. That does not mean that from your point of view that light cannot separate from a moving object at some speed less than c. Of course it can.

 

[zoobyshoe]

Thanks for your patience, Doc Al. I have never explored this in such detail, and these answers are not what I expected.

If I reverse the direction of the rocket in the set up, then, to be headed toward the station, I take it that a beam of light emitted from the station when I am 300,000 km from the station will also reach me in one second, from my viewpoint, however: I will be only 150,000 km from the station when I detect it?

 

[plover]

If I reverse the direction of the rocket in the set up, then, to be headed toward the station, I take it that a beam of light emitted from the station when I am 300,000 km from the station will also reach me in one second, from my viewpoint, however: I will be only 150,000 km from the station when I detect it?

Linguistic point:
The phrasing used here (e.g. "headed toward the station") carries the connotation that the rocket is moving and the station is stationary, which is, of course, the familiar setup - vehicles move and destinations don't. However, part of the essence of special relativity is that describing events for a given observer must always presume that observer as being at rest.

Thus while the mindset of a person on the rocket might be "I am approaching the station at .5c", the necessary viewpoint for setting up any special relativistic calculations is "the rocket is at rest, the station is approaching the rocket at .5c".

Once that framework is established, it becomes easier to see that a photon emitted from a station 300k km away takes 1 second to reach the rocket (since the rocket is at rest) no matter the velocity of the station.

My point is that it's easy for intuitive descriptions of a situation to carry assumptions that conflict with the requirements of the formal model.

 

[zoobyshoe]

My point is that it's easy for intuitive descriptions of a situation to carry assumptions that conflict with the requirements of the formal model.

Point taken.

So, If I am at rest in my rocket with the station approaching me at .5 c and it emits a beam of light when it is 300,000 km away, I take it I will detect the light one second later, but the station will be 150,000 away at the moment I detect the light?

 

[plover]

Yes.

And you now have one second left to figure out how to avoid a collision...

 

[Olias]

Moral:
Dont try and signal the incoming station with some kind of " Morse-flashlight"!

Switch off all non essential onboard lighting, close one's eyes and hope that Shroedinger's Cat exists as a physical process!

 

[zoobyshoe]

Yes.

And you now have one second left to figure out how to avoid a collision...

Not sure it can be avoided:

The one second time for my reception of the light signal seems to me to be directly at odds with Einstein's understanding of the same situation as laid out in chapter IX of SR, The Relativity of Simultaneity

Here Einstein says:

"Are two events (e.g. the two strokes of lightning A and B) which are simultaneous with reference to the railway embankment also simultaneous relatively to the train.? We shall show directly that the answer must be in the negative.

When we say that the lightning strokes A and B are simultaneous with respect to the embankment, we mean: the rays of light emitted at the places A and B, where the lightning occurs, meet each other at the mid-point M of the length A ---->B of the embankment. But the events A and B also correspond to the positions A and B on the train. Let M' be the mid-point of the distance A---->B on the traveling train. Just when the flashes¹ of lightning occur, this point M' naturally coincides with the point M, but it moves toward the right in the diagram with the velocity v of the train. If an observer sitting in the position M' in the train did not possesses this velocity, then he would remain permanently at M, and the light rays emitted by the flashes of lightning A and B would reach him simultaneously, i.e. they would meet just where he is situated. Now in reality (considered with reference to the railway embankment) he is hastening toward the beam of light coming from B, whilst he is riding on ahead of the beam of light coming from A. Hence the observer will see the beam of light emitted from B earlier than he will see that emitted from A.

_{1 As judged from the embankment.}

If we substitute the situation where the space station is approaching me (from my perspective) for the situation where the observer on the train is approaching the flash of light from point B, you can see that Einstein would not reakon the time between the flash and when I detect it to be one second, rather, less than a second.

Likewise, if we substitute the situation where the station is moving away from me for the situation where the observer on the train is moving away from the flash of light at point A, you can see that Einstein would not reakon the time between the flash of light and when I detected it to be one second, but something greater than one second.

If, I detect the time of the light's travel to be one second coming or going, then Einstein has no basis on which to build his case for what he calls The Relativity of Simultaneity

Chapter 9. The Relativity of Simultaneity. Einstein, Albert. 1920. Relativity: The Special and General Theory
Address:http://www.bartleby.com/173/9.html

 

[plover]

The observer in the rocket is the equivalent of the person on the railway embankment who sees the flashes simultaneously.

It is often the case that effects in relativity can appear paradoxical if only some of the effects are accounted for. When the mathematical formalism is used, these problems tend to disappear.

I assume the situation presented by Einstein is thus:

Points A and B are two points on a perfectly straight rail track. Observer X is at the midpoint between A and B. The midpoint of a train which X would measure as having a length equal to the distance from A to B is passing X at .5c. At the same moment (as measured in the rest frame of X and the track) photons are emitted at A and B. Observer Y is positioned at the midpoint of the train.​

I will assume it is uncontroversial that these photons reach X simultaneously.

I will also assume that it is uncontroversial that the back of the train is at A when the photon is emitted at A, and that the front of the train is at B when the photon is emitted at B.

Now in order to see why these flashes do not reach Y simultaneously we first note that the train appears length contracted to X. Thus the length of the train at rest is actually longer than distance between A and B. Y, being at rest relative to the train, experiences the train as having that longer length. In addition, an observer on the train would measure the track as length contracted, so A and B are closer together for Y than for X.

So, according to Y, when the front of the train reaches B and the photon is emitted at B, the back end of the train is still (if I'm remembering my formulas right) 1/4 the length of the train away from A.

Thus, though Y would say that the photons traveled equal distances to reach the train's midpoint, Y would not say they were emitted at the same moment.

 

[zoobyshoe]

The observer in the rocket is the equivalent of the person on the railway embankment who sees the flashes simultaneously.

This is incorrect. The observer on the train is the counterpart to me in the rocket.

Please go to the link I edited in in my post above for the complete text of that chapter written by Einstein as well as the diagram referred to.

 

[plover]

The observer on the train is the counterpart to me in the rocket.

It is, of course, possible to construct an analogy where the observer on the train corresponds to the person in the rocket. In doing this, however, it is also necessary to state what the station(s) and any other relevant objects correspond to in the train scenario.

If you think the scenario I laid out in my previous post is somehow unfaithful to Einstein's thought experiment, could you explain?

I also note that the quote you give from the article describes what X predicts that Y will see (i.e. it is not a statement from the point of view of Y).

Chapters 10-12 of the Einstein article go over more about length contractions.

 

[Doc Al]

If I reverse the direction of the rocket in the set up, then, to be headed toward the station, I take it that a beam of light emitted from the station when I am 300,000 km from the station will also reach me in one second, from my viewpoint, however: I will be only 150,000 km from the station when I detect it?

That is absolutely correct. If the light flashes when it's 300,000 km from you, then it will reach you in 1 second regardless of your speed with respect to the light source. (Note that all measurements are made from your rocket frame.)

 

[Doc Al]

Einstein's train

If we substitute the situation where the space station is approaching me (from my perspective) for the situation where the observer on the train is approaching the flash of light from point B, you can see that Einstein would not reakon the time between the flash and when I detect it to be one second, rather, less than a second.

Right! As measured by observers on the space station, the light reaches you in less than a second.

Likewise, if we substitute the situation where the station is moving away from me for the situation where the observer on the train is moving away from the flash of light at point A, you can see that Einstein would not reakon the time between the flash of light and when I detected it to be one second, but something greater than one second.

Right again! As measured by observers on the space station, in this case the light takes more than a second to reach you.

If, I detect the time of the light's travel to be one second coming or going, then Einstein has no basis on which to build his case for what he calls The Relativity of Simultaneity

Not so fast. Einstein's train example had two events (lightning strikes) happening simultaneously when observed in one frame and he showed that they must happen at different times according to the other frame. Nothing in your example contradicts this.

Everything you've said so far agrees with Einstein. To see how simultaneity fits in, consider how you measured the time between when the light was emitted and when you detected it in your rocket: Remember that you needed a second rocket in your frame (moving at the same speed as you) that just happens to pass the station when the light flashes. That rocket measures the time when the light was emitted, and you find out that the light reaches you 1 second later. But what does the space station think about the clocks in your frame? For one thing, the station frame does not agree that your two clocks are synchronized! According to measurements made in the space station frame: (1) your rocket clocks are out of synch, (2) your rocket clocks are operating slowly compared to station clocks (time dilation), and (3) the distance that you think is 300,000 km is really smaller (length contraction).

To really understand how to compare measurements made in the different frames, you need to consider all of those relativistic effects operating together. But everything is perfectly consistent with the reasoning we used from the rocket frame in determining that the light took 1 second (rocket time) to get from the station to the rocket. We didn't need to take all that stuff into consideration because we assumed that all measurements were made by the rocket frame: the distance the light traveled (measured by rocket rulers), the time light traveled (measured by rocket clocks). Of course these better combine to get the proper speed of light--measured by the rocket!

 

[zoobyshoe]

That is absolutely correct. If the light flashes when it's 300,000 km from you, then it will reach you in 1 second regardless of your speed with respect to the light source. (Note that all measurements are made from your rocket frame.)

This seems to be at odds with what Einstein understood would happen, as I pointed out above.