What is a frame ?
February 5, 2007
I was looking around for something to post for JustScience.net. (I’ll come around to plasma physics as promised sometime later this week ) .
Jennifer (of Cocktail Party Physics) makes a list of “the Top Ten Things About Physics We Wish Everyone Knew” – Lo and behold, I find one of my favorite topics to ramble about –
3. Frames of reference. Yet another bit of jargon so common to scientists, they forget that the phrase might not hold any real meaning for John/Jane Q. Public, even though it’s a fairly simple concept. It’s still necessary to define the term. Chad touched on this in his post on forces, but it’s central enough that it bears repeating. For instance, it’s tough for a non scientist to grasp why scientists occasionally argue about centrifugal versus centripetal force without a solid grasp of frames of reference. It’s just as critical when considering the differences, physics-wise, between linear and rotational motion, and to understanding why Einstein’s theory of special relativity was such a revolutionary advance….
A frame of reference is basically a convention that is very useful in physics. Before going into what it actually is, let us look at a simpler but a related concept.
Consider the surface of the earth . On the earth, we find it very useful to name a specific direction as “North”. You can goto any place on earth(except the poles) and you have a reference direction which all of us have agreed to call as “North”. Similarly, we call a specific direction as “East”.
Now, why is this a useful thing ? It is useful because it gives a way for people to communicate with each other. Consider, for example, a person on a plane flying over the place marked P in the figure below. Now, if we want to tell the pilot to goto the place marked Q , one of the easiest ways to communicate the instruction is to ask him to go say 5 kilometres towards East.
Let me invent a shorthand and give an instruction – “Fly 5 E ”
Similarly, if you have a person at the place marked R , to goto Q , you just have to tell him to go 5 kilometres towards East and then 4 kilometres towards North. So, now the instruction is “Fly 5 E + 4 N“. So far so good.
Now, imagine that I intend to meet this pilot at the place Q some 10 hours after now. So, including the travel time, I want him to wait for 10 hours and be at Q after 10 hours. Now, how do I say that ?
Let’s assume the time taken for travel is very small. So, basically, I tell the pilot to fly 5 E + 4 N and then wait for 10 hours. Let us combine the two instructions into one and send him a single line instruction “Fly 5 E + 4 N + 10 T ” – of course, T represents waiting or “flying in time”.
Now, the question is this – Is my instruction unambiguous ? At the first sight, it does seem to be . But, I will insist that it is not !
To understand why, consider this possibility – say the pilot goes to the place Q and he is very tired after the journey. Since he has ten more hours, he decides to have a good sleep. So, he boards a good train going towards the place S and goes to sleep. He wakes up after ten hours to find himself at S. Having faithfully followed my instructions, he is angry that I am not there !
You might be saying – ” Come on, this is cheating. He didn’t just wait. He also traveled some more distance !” But, the pilot can insist that no-he didn’t go anywhere, that it was the stations which moved towards him as he slept. This might sound very philistine, but, technically, he is right !
What is mere waiting for one person can actually be waiting plus some additional motion for a second person, provided the first person is moving as seen by the second person. So, in a sense, what the first person calls waiting is actually what second person sees as waiting with flying.
So, the moral of the story is that it is not enough if I just say “Wait for ten hours”. It is like saying “Fly for five kilometres”. If I tell you “Fly for five kilometres”, you should ask me back – “Along which direction ? ” . Similarly, if I say “Wait for ten hours”, you should ask me according to whose definition of “waiting” – you see like “North” and “East” we also have to define a “way of waiting” so that our instructions are unambiguous.
So, you might be wondering, what has all this got to do with frame of reference ? The answer is simple – A frame of reference is basically a convention which decides ad hoc – what is “North”, what is “East”, What is “up” and what kind of “waiting” is a standard at each place and for all times.
The point about frames of reference is that one way of definition is as good as any other – sky is not going to fall if tomorrow everybody starts calling East as North and North as East. But, I am saying that and much more – heavens are not going to fall even if all of us change our convention of what it means to say that we are just “waiting” .
So, that in short, is what a frame of reference is . I’ve not addressed the other things that Jennifer mentioned – “centrifugal versus centripetal force”, “linear and rotational motion” and things like inertial and non-inertial frames of reference. I’ll probably take it up later in some other post.
 Actually I am cheating you. If you take the given figure to be a representation of earth, the distance shown would be about a thousand kilometres. If I had actually shown 5 km on that figure, it would be so small that you would have a hard time seeing what I’ve drawn.
 Of course, I am just repeating what I had already told before . The things I put in bold are basically vectors, and T is what physicists like to call a “Time-like vector”.