Help me understand Reference Frame

Factual Questions
21

It is important to remember, up until recently, people were able to be absolutely still, and anyone else who was absolutely still had exactly the same frame of reference as they did. All of their observations on distance, motion, and acceleration would be identical.

Then Ugh started throwing rocks AT us, and we had to move away. Now, Ugh’s observations were less troublesome, as long as we were in a frame of reference moving away from Ugh.

I know that sounds like a lame assed joke, but the facts of physics are not far removed from it. When you are measuring time in Days, and distances in visual horizons, the differences due to the motions of observers are far less than the ability to measure. By the time of Michelson, and Morley, that had all changed. A flash of light far away could be shown to occur earlier to one observer than another. Different frames of reference, different observation. It had been proven that the Earth itself moved very rapidly indeed around the sun, and the surface very rapidly with respect to the surface at the antipodes. All these facts were known, and over a fairly short period of time (Within the span of some single professional careers of scientists, in fact) it was known that almost every observation made was variable with different frames of reference. All of them in fact except one. Light moved the same speed in all frames of reference.

It was a real pisser.

Tris

22

This is pretty much it, except in addition to “at the moment”, a reference frame usually defines these quantities for all times (i.e. it is possible to talk about a reference frame that is stationary for 10 min then accelerates at 20km/s/s NNE for six years, then moves at a constant speed of 12cm/year towards proxima centauri for a century, all the while rotating around an axis pointing towards Sirius at a rate of 5 radians/year, &c.)

Of course, in order to define terms used to describe the motion of the reference frame like “stationary”, “12cm/year”, and in the context of relativity “10 min”, &c, you need to use another reference frame. Part of the stuff of physics is how the laws of physics in these reference frames relate to each other.

23

nm

24

The concept of a “Frame of Reference” gained relevance and prominence with the understanding of the implications of Einstein’s Theory of Special Relativity. Prior to that time, there was a consensus among physicists that there was a preferred frame of reference which was at “Absolute Rest.” In principal, all measurements taken could, in theory, be related to the frame at rest. They knew that the surface of the Earth was rotating once per day, and the Earth, itself, was orbiting the Sun, and the Sun was moving around the Galaxy, and so forth. But all these motions could be mathematically reduced by considering Absolute Rest as the frame of reference.

Or so they thought.

All that came crashing to the ground in 1887 with the spectacular failure of the Michelson–Morley experiment.

Their experiment was designed to measure the Earth’s motion with respect to the frame of absolute rest, and had the necessary precision to accomplish this. The continued failure, after many attempts, and by other researchers, to measure any motion was a thorn in the collective side of classical physicists of the day.

Einstein’s contribution to the resolution of this puzzle was to collect theoretical concepts which had been developed to explain the negative result, and draw them out to their full conclusion. Several researchers had given rigorous mathematical treatment to the transformations under which Maxwell’s equations were invariant. Many physicists, including George FitzGerald, Joseph Larmor, Hendrik Lorentz and Woldemar Voigt, had been discussing the physics behind these equations since 1887.

In particular, Einstein was able to derive the Lorentz Transformation equations from his Theory of Special Relativity.

This involves a term usually labeled [SIZE=2]γ ( the lower-case Greek letter “Gamma”.)[/SIZE]


         1
γ =    ______
[SIZE=2]    √1-*v[sup]2[/sup]/c[sup]2[/sup]*
[/SIZE]

(read “gamma equals 1 divided by the square root of the quantity 1 minus velocity squared divided by c (speed of light) squared.”)

This term is essentially one (1) for velocities up to about 10% the speed of light in a vacuum.

It turns out that using this mathematical treatment resolves many discrepancies in the real world, and its value and significance has been tested and confirmed in many experiments.

A shorthand thought experiment would be:

Imagine you are flying past my position in a ship going a significant fraction of c. As you pass, in your moving frame of reference (from my point of view) you measure the length of your ship, while I, at relative rest, measure your ship from my frame of reference.

I will have measured a length (L[sub]me[/sub]) of your ship that differs from the length you measure (L[sub]you[/sub]), by an amount given by

L[sub]me[/sub] = L[sub]you[/sub] / [SIZE=2]γ[/SIZE]

[SIZE=2]that is, if, for example, you were moving at half the speed of light (c/2), the length I measure would be 86.6% of the length you measure on board your ship.

[/SIZE]The question “How long is the ship really?” is not relevant in this context. We each, in our own frame of reference, measure a length which is the “real” length from our point of view. This, in a nutshell, is the answer to your question about [capital “O”] Objectivity. There may be some objective reality “out there,” but the best we can do, any of us, is to describe it from our own frame of reference.

25

Thank you all for your insights and explanations. I think I have overcome a least few misconceptions and I understand the idea much much better.

I can’t claim to have a handle on it, but reading the various articles is making much, much more sense.

26

Only in the weakest sense. Usually “subjectivity” implies that what a person sees is a product of a person’s belief system and personal history. The fan of one team sees a bad call by a ref; the fan of the other team sees the other team’s coach cynically challenging an obviously good call - that’s usually what people mean by subjectivity. A New Yorker seeing the sunrise over the Atlantic, and an Irishman seeing the sunset over the Atlantic doesn’t seem like the same thing at all - when the New Yorker visits Ireland, he sees the sunset in the Atlantic.

27

That is what I was trying to get at by borrowing the capital ‘B’ Blank approach. As far as I know there isn’t really a capital ‘S’ subjectivity.

I can put on a beret and slather oil paint on a canvas and call it art, but the Mona Lisa is capital ‘A’ Art.

If it helps to clarify my thinking (definitely lower case ‘t’)…:
Imagine a scenario with two people driving in a car and a policeman with a radar gun somewhere along their route.

The driver may say: “I’m not going too fast.” She has a speedometer, controls the speed of the car, and presumably knows the speed limit. But her observation is based in part on her desire to get to the destination and her beliefs about appropriate speed. I might even suggest it is based on her belief that she might be observed.

The passenger may ask: “Are you going too fast?” She can’t directly control the car, doesn’t know the actual speed, doesn’t know the speed limit (or isn’t considered responsible for knowing it) and her desires and beliefs don’t affect anything but her speech.

The policeman has a radar gun and measures the speed of the car at 73.

The policeman with the radar gun represents objectivity. Any vehicle traveling at the same velocity will been measured the same.

The driver represents subjectivity: beliefs, desires and views affect her observations as much as objective criteria.

The passenger represents (emphasis: represents) SUBJECTIVITY (tee-tee-tee).

Her beliefs, views and desires don’t immediately affect the scenario. She can ask for objective details, and she is affected by those details; but ultimately she is just another object in the scenario.

So, a human can be subjective, but the Moon cannot. However, the Moon could be capital ‘S’ Subjective–in that it can be abstracted into a positional perspective (one might say: “From the point-of-view of the Moon…”).

I recognize that that is not any kind of dictionary definition and that you are correct that the usual sense of the term is as you describe it.

I am also starting to realize that the arguments I referred to in the OP are playing a similar game. Using the concept of a physical reference frame as a way of saying that objectivity (in the sense of a person trying to look past their own capricious whims in decision-making) is limited to a specific reference frame, and as such is not really objective at all.
If I am understanding this thread correctly, a physical reference frame is really only specified by the needs of the moment and isn’t actually defined, itself, physically.

The Earth, for example, isn’t a reference frame unless it is the simplest focus for a given observation. Likewise with North America or the constellation Cygnus.

A physical reference frame imparts objectivity by defining the variance in subjective observations, based on known physical qualities.

Of course, if I’m not understanding this thread that might be only my own belief based on a desire to understand.

28

Reference frame is really just a way of specifying the context of a measurement.

Extending the concept beyond physics into a general notion of objectivity vs. subjectivity is of questionable value.

29

Not only do I agree with you, I am beginning to agree more and more keenly.

Of course, that doesn’t change the fact that it is indeed extended. In some cases, it seems appropriate (e.g. in some debates about evolution -v creationism). In other cases, the idea seems decidedly overstretched.

It might just be my own selective perception, but I have noticed an increase in the number of arguments that seem to invoke the idea of reference frame and I want to understand it better; both in the physics context and in the more rhetorical context.

ETA:

Likewise, I would like to be able to argue from my own understanding just why that is so.

30

Think of it this way:

In maths, if you change the coordinate system describing something or other then nothing ‘mathematically’ changes only the particualr labels you use to describe whatever it is you’re describing. Simlairly if you change your reference frame in physics nothing ‘physically’ changes only theparticualr labels. The difference being in physics these ‘labels’ generally correspond to how a particualr person/thing ‘experinces’ the physical situation which you wish to describe.

Infact in physics there often isn’t any distinction between a coorindtae system and a reference frame, the only differences being that quite often we like to call sets of coordinate systems that have something in common and call that set a frame of reference (also technically you can’t call a frame of reference a cooridnate system in non-relatvistic physics due to the lack of requiste space-time structure).

31

Let me see if I understand you. If I have a simple X,Y graph and a point at (1,-1) and I change the labels such that I now have a point at (-1,1), the point itself doesn’t change.

And if I connect that point by a line from another point at (1,-1) and then switch the labels back, the line isn’t changed, just the way it is described.

Something like that?

32

Yes, if you take a standard Cartesian cooridinate system,then rotated the axes 180 degrees the point labelled (1,-1) is given the new label (-1,1).

The labels of the set of points which make up the line segment you descirbe change, but ‘mathemtically speaking’ it is still the same line segment.

33

Very much like that.

To throw the discussion into sharper focus, consider the equation for a circle in Cartesian (X,Y) coordinates.

X[sup]2[/sup] + Y[sup]2[/sup] = R[sup]2[/sup]
(X-coordinate squared plus Y-coordinate squared equals Radius squared.)

The mapping of the points comprising the circle are well-defined by this equation, and the locus of the circle is unique.

If, instead, you were to describe the locus of the circle using Polar coordinates:

r(θ) = a
(Radial distance (r) as a function of Angle of Rotation (lower-case Greek letter “Theta”) equals a constant, a)

the mathematics will be different, but the actual values remain identical.

In many cases, circular motion equations which are complex to resolve in Cartesian coordinates are trivial in Polar coordinates. Of course, YMMV, and “complex” and “trivial” may be “Subjective.”

The point to take away from this thread is, there are many different ways to look at, and measure, events in the real world. Which set of observations are most appropriate and useful are the only relevant criteria.

If you were driving to work, and wanted to calculate your total travel time and average speed, including stop-and-go traffic in the city, the fact that the Earth is spinning at about 1,000 mph at the equator (and orbiting the sun at about 67,000 mph, and moving, with the rest of the Solar System, at about 550,000 mph around the center of the Milky Way galaxy, and so forth,) is not really relevant to your calculations. It is perfectly acceptable to adopt a “Frame of Reference” where the surface of the Earth is at rest for the purposes of your calculations.

34

The band Stewed Mulligan claimed to have the only dance tune written about Albert Einstein. An excerpt:

*Had a frame of reference,
Set it on a fence.
Showed it Relativity,
Ain’t seen the damn thing since.

Albert, dance around,
Albert, be profound,
Albert, let your hair stick out,
And your socks fall down.*

35

So, is it safe to say that a relevant criterion might very likely be accounting for any discrepancy between observations?

36

…is that a No?