Are some frames of reference more equal than others?

[Slaihne]

Hi there,

 

Here's another question i asked in the Introductions forum. Again, it was suggested i post it here.

 

The second conundrum i’ve been puzzling with is the situation when you have two objects heading directly away from each other at relativistic speeds, say 0.6 the speed of light.

 

Newton would have us believe that the relative speed of the two objects is 1.2C, but i can, sort of, get my head round the fact that time dilation effects could make this appear to not be the case for observers on each of the objects.

 

The problem i face here is that both objects, let’s call them rockets with the capability to immediately accelerate to 0.6C and then, later decelerate to a standstill, can be set so that they stop exactly at a known marker. Clocks can be shuffled over to these markers in advance and the time noted when the objects stopped. The results from these clocks can be shuffled back to the central point where both objects originally set out from.

 

Now, the central observer may only have seen each object heading away from him at 0.6C but after the results came in from the clocks and the math was done it would be an unavoidable conclusion that the objects were travelling at 1.2C relative to each other.

 

I just can’t get my head round this problem. If the clocks shuffled back and the math was done and it ended up showing that the two objects were not travelling faster than the speed of light relative to each other then what does that mean?

 

Or is it invalid to consider either of them as valid frame of reference. And why can’t we?

 

rgds

 

David

[Janus]

Hi there,

 

Here's another question i asked in the Introductions forum. Again, it was suggested i post it here.

 

The second conundrum i’ve been puzzling with is the situation when you have two objects heading directly away from each other at relativistic speeds, say 0.6 the speed of light.

 

Newton would have us believe that the relative speed of the two objects is 1.2C, but i can, sort of, get my head round the fact that time dilation effects could make this appear to not be the case for observers on each of the objects.

 

The problem i face here is that both objects, let’s call them rockets with the capability to immediately accelerate to 0.6C and then, later decelerate to a standstill, can be set so that they stop exactly at a known marker. Clocks can be shuffled over to these markers in advance and the time noted when the objects stopped. The results from these clocks can be shuffled back to the central point where both objects originally set out from.

 

Now, the central observer may only have seen each object heading away from him at 0.6C but after the results came in from the clocks and the math was done it would be an unavoidable conclusion that the objects were travelling at 1.2C relative to each other.

 

I just can’t get my head round this problem. If the clocks shuffled back and the math was done and it ended up showing that the two objects were not travelling faster than the speed of light relative to each other then what does that mean?

 

Or is it invalid to consider either of them as valid frame of reference. And why can’t we?

 

rgds

 

David

 

 

Okay, one problem is that you are butting up against is the Relativity of Simultaneity. The problem is that neither rocket ship will determine that the other ship stopped at the same time as it did. Each will determine that it reaches its marker and stops before the other ship does.

 

For example, assuming that the markers are 1.2 light years apart as measured by the ships. So ship 1 by his reckoning takes 1 year to reach his marker. The other ship (ship 2) is receding at 0.882c relative to ship 1 as measured by ship 1. The other marker is receding at 0.6c from ship 1. Since the starting distance between ship 2 and its marker is 0.6 ly, according to ship 1, after one year, ship 2 will still be 0.318 ly short of reaching its marker.

 

You are also not taking into account length contraction or the effects that the acceleration of stopping the ships has on its observations. (For instance, when ship 1 stops at his marker, the act of stopping will, from his perspective, cause a clock at marker 1 to jump forward in time.)

 

IOW, just because clocks in the same frame say that the difference in velocities between the two ships was 1.2c, this is only true in that frame. In the frame of either ship while moving, they never exceeded a relative speed of 0.882c (though the other ship kept traveling after they stopped), and neither frame is more right than the other.

[modest]

The following site also explains the same thought experiment,

 

Naively the relativistic formula for adding velocities does not seem to make sense. This is due to a misunderstanding of the question which can easily be confused with the following one: Suppose the object B above is an experimenter who has set up a reference frame consisting of a marked ruler with clocks positioned at measured intervals along it. He has synchronised the clocks carefully by sending light signals along the line taking into account the time taken for the signals to travel the measured distances. He now observes the objects A and C which he sees coming towards him from opposite directions. By watching the times they pass the clocks at measured distances he can calculate the speeds they are moving towards him. Sure enough he finds that A is moving at a speed v and C is moving at speed u. What will B observe as the speed at which the two objects are coming together? It is not difficult to see that the answer must be u+v whether or not the problem is treated relativistically. In this sense velocities add according to ordinary vector addition.

 

But that was a different question from the one asked before. Originally we wanted to know the speed of C as measured relative to A not the speed at which B observes them moving together. This is different because the rulers and clocks set up by B do not measure distances and times correctly in the reference from of A where the clocks do not even show the same time. To go from the reference frame of A to the reference frame of B you need to apply a Lorentz transformation on co-ordinates as follows (taking the x-axis parallel to the direction of travel)...

 

Relativistic Velocities

 

~modest

[Slaihne]

Hi Modest,

 

That was great link. It was fairly simple to follow, leading to the concept that you can’t add relativistic speeds together to attain a velocity of more than c.

 

But, unfortunately, i have a couple of problems with it. Consider two objects placed 0.6 light years from the central observer along with clocks synchronised to the central observer; this journey is carried out symmetrically and at low velocity. They immediately accelerate to 0.6c heading towards the observer and the clocks are stopped, remaining at the points the objects started from. When they collide at the observers point he stops his clock. When the 3 clocks are brought together would they show that the two clocks that were originally sent out with the objects had been stopped at the same time? Would they show that the two distant clocks had been stopped a year prior to the stopping of the observer’s clock? Have the two objects closed a distance of 1.2 light years in a year relative to the observer? Does this result in a net speed of 1.2c?

 

I’m trying to get my head round this, I really am. Would something happen to the clocks even though they are travelling at low speeds back and forward? Would the time difference be more than a year, resulting in a net speed of less than c? From the Lorentz Transformation it would seem that each object would perceive the other as travelling at 0.882353c. That i can accept for the moment since the observation is dependent on light itself and i can accept that unusual things happen when you start to encroach on the limit of you measuring tool. But, here, i’m not referring to the relative speed of each object to each other, i’m referring to an ‘after the fact’ analysis of what happened, not perceptions during the experiment. If the clocks were stopped a year apart then surely, in reality, the objects travelled towards each other at a net speed of 1.2c?

 

The second problem i immediately had with the Lorentz Transformation was the introduction of c. My immediate reaction was, “well of course it’s gonna be a limiting factor, since it’s right there set up to be one!” But i had a read of the Wikipedia entry for it and discovered that apparently these transformations were introduced between 1887 and 1904, prior to Einstein’s theory of relativity (1905). From what i can quickly read in the wiki entry i get the impression that they were a natural good match for each other. You need one for the other to work, or one can be derived from the other. I still can’t see why the c term was introduced apart from it needs to be there to work. It’s something that doesn’t just sit right (hehe), but i’ll have to do some reading on my own to figure out why.

 

But again, thanks for the link and taking the time to comment.

 

Rgds

 

 

David

[Slaihne]

Hi Janus,

 

Cheers for the reply, I like the Uncle Clive avatar btw

 

I can get on board with the fact that the relative velocity of each object to each other appears to be 0.882c. Actually, the word ‘appears’ there is maybe my main stumbling block. Are the objects moving apart at a rate faster than the speed of light? I haven’t asked if they appear to be moving faster than the speed of light; i’m more interested in the reality of the situation.

Is that a stupid thing to say? I would have thought that from the central observer’s reference point that they are, after all they are travelling at 0.6c directly away from each other.

 

I seem to be getting more brain melted by the minute.

 

Rgds

 

David

[modest]

Hi Modest,

 

That was great link. It was fairly simple to follow, leading to the concept that you can’t add relativistic speeds together to attain a velocity of more than c.

 

But, unfortunately, i have a couple of problems with it. Consider two objects placed 0.6 light years from the central observer along with clocks synchronised to the central observer; this journey is carried out symmetrically and at low velocity. They immediately accelerate to 0.6c heading towards the observer and the clocks are stopped, remaining at the points the objects started from. When they collide at the observers point he stops his clock. When the 3 clocks are brought together would they show that the two clocks that were originally sent out with the objects had been stopped at the same time? Would they show that the two distant clocks had been stopped a year prior to the stopping of the observer’s clock? Have the two objects closed a distance of 1.2 light years in a year relative to the observer? Does this result in a net speed of 1.2c?

Yes. This is correct. In the reference frame of the center observer (and any other clocks or observers in that frame) the two ships will travel a collective distance of 1.2 lightyears per year. If the two ships start the journey simultaneously in the center observer's frame then both clocks (which are set to be simultaneous in that frame) will 'stop' at the same time.

 

As Janis says, you cannot transpose these times, distances, or ideas of simultaneity to the ship's reference frame. As soon as the ships accelerate they have new ideas of those things. Their frame is just as real even though their clocks and distances disagree.

 

That i can accept for the moment since the observation is dependent on light itself and i can accept that unusual things happen when you start to encroach on the limit of you measuring tool. But, here, i’m not referring to the relative speed of each object to each other, i’m referring to an ‘after the fact’ analysis of what happened, not perceptions during the experiment. If the clocks were stopped a year apart then surely, in reality, the objects travelled towards each other at a net speed of 1.2c?

Yes, again, in the frame of the center observer (according to those clocks and rulers) the ships did really travel a net distance of 1.2c. You are considering the "analysis of what happened" from that frame.

 

If you do an analysis of what happened from the reference frame of one of the ships then you'll get a different after-action report with different times and distances (using the ship's clocks and rulers). Neither is any more real than the other, but they are different because of,

time dilation

length contraction and,

relativity of simultaneity

 

~modest

[Slaihne]

Thanks Modest,

 

I think i’ve cracked it now.

 

The theory of relativity explains how things appear rather than how they are in reality. We can do an after the fact analysis and validly conclude that the two objects were moving at 1.2c relative to each other. But, and it’s a big but, at no stage during the scenario could anyone have detected anyone else moving at a speed greater than c. Each moving observer would have seen the other observer retreating at 0.88c and change, and from this they can infer that they are actually travelling at a speed of 1.2c relative to each other?

 

Einstein crafted a theory that describes how this movement appears and from this we can infer things. We live in a universe where stuff is constantly happening and the luxury of an after the fact analysis is not always available, so we need to observe while the events in question are taking place. This observation comes at the cost of not actually seeing what is happening, we see the appearance of what is happening.

 

Basically, there IS no spoon? :singer:

 

Rgds

 

David

[modest]

The theory of relativity explains how things appear rather than how they are in reality.

 

It is not the usual scientific approach to say relativistic effects show how things appear rather than how they really are. For example, time dilation doesn’t just appear to happen to a moving clock because of a difference in perception. If you synchronize two clocks then send one of them around you in circles quickly before reuniting them you’ll find they are no longer synchronized. The clock that got spun around didn’t *just* appear to run slow—the effect was real. The spinning clock really did run slow from the center clock's perspective.

 

We can do an after the fact analysis and validly conclude that the two objects were moving at 1.2c relative to each other. But, and it’s a big but, at no stage during the scenario could anyone have detected anyone else moving at a speed greater than c. Each moving observer would have seen the other observer retreating at 0.88c and change, and from this they can infer that they are actually travelling at a speed of 1.2c relative to each other?

 

I'm not sure you're looking at this quite right. When the ships are moving away from each other with an observer in the center there are 3 inertial reference frames:

The two questions you’re asking are:

1. What is the velocity of C relative to A (i.e. the distance AC increases per second) in frame A?
   
2. What is the velocity of C relative to A (i.e. the distance AC increases per second) in frame B?
   

These will give different answers as we’ve established. The first gives 0.882c and the second gives 1.2c. This is because clocks and rulers work differently in frame A and B. But, neither frame is any more or less real than the other. From A's perspective, C really is receding at .882 lightyears per year according to A's clocks and measures of distance. From B's perspective, A and C really are putting 1.2 lightyears between them each year according to B's clocks and measures of distance.

 

Have you checked out the twin paradox?

 

~modest