Home, Science, Science Concepts

Reference Frames

Hi guys,

In my previous post about Newton’s First Law of motion:

When viewed in an inertial reference frame, an object either is at rest or moves at a constant velocity, unless acted upon by an external force.

I did not explain reference frames which may have confused some of you. So i shall be explaining reference frames in this post.

Essentially, reference frames are frames which can be used to describe a location of an event(something that occurs at a very specific point and does not include things that occurs in an area).

To further explain what is an event, imagine you are in a science fair (preferably one with lots of amazing science experiments being carried out (but it doesn’t really matter)) to you the science fair may seem like an event, however in terms of reference frames, the science fair is not  an event (because it occurs over an area).

So you may be thinking right now: What in the world is an event since practically everything has a volume and takes up space? Well classically nothing can physically be an event, reference frames are just used to describe things based upon (non-existent) events or “events” (objects which still take up space) in classical physics.

However in quantum physics, events do physically exist in the form of elementary particles in the standard model of particle physics. Examples of such particles include: Electrons, quarks, muons and all three types of neutrinos (electron neutrino, muon neutrino and tau neutrino). These particles supposedly do not take up any space/volume however they do have mass. (This is where classical physics and quantum physics clashes. Since these particles posses a certain amount of mass but no volume, they posses an infinite density and in classical physics they would be black holes/singularities) i may do an in depth post about the standard model of particle physics in the future.

So how do these reference frames look like? They have a x, y and z axis which each represent a dimensions in our 3 dimensional world. However in the context of physics, there is a fourth dimension of time which is represented as t not within the reference frame.

Reference frames

Fig 1.1: two reference frames with the origins being O and O’

Notice that any point in space can be described using coordinates taken with reference to the origin of the reference frames hence the name “Reference frames”

NOTE: Coordinates can also hold a negative value so events behind the origin can still be described by using a reference frame.

In the above example, observer O is ‘stationary’ and observer O’ is ‘moving’. You may wonder why i use inverted commas to describe their motion. That is due to the fact that there is no such thing as an object that is absolutely moving or absolutely stationary (although there was once an ‘ether’ which was an absolute reference frame, however it was later dismissed through a ‘ether wind’ experiment)

Now I shall move on to Galilean and Lorentz Transformations.

So what are these? Galilean and Lorentz transformations are a set of formulas which can be used to calculate the velocity, location and time that is relative to one observer by using values obtained from the other observer and the first observer him/herself.

What is the difference between Galilean and Lorentz Transformations? Galilean Transformations reflect Galilean Relativity which is based upon common sense. While Lorentz Transformations reflect Einstein’s Theory of Special Relativity which is based upon the idea that the speed of light is constant in any reference frame.

Do remember the following points:

  1. x=Length
  2. y=Height
  3. z=Breadth
  4. t=Time
  5. c=Speed of Light (3.0 x 10^8)

Points 1-4 are the four dimensions of reference frames that you should take note of. Do note that there is also a velocity transformation which has the values u and v which are the velocities of the two observers.

Allow me to reuse Figure 1.1 as an example to describe the Galilean Transformations.

Reference frames

In Figure 1.1, there are 2 observers: Observer O and Observer O’

Observer O’ is moving forward at a velocity of v relative to Observer O who is moving at a velocity of u.

Galilean Transformations are as follows:

x’=x-vt

y’=y

z’=z

t’=t

u’=u-v

After transforming the values, you will get a different value, which is what observer O observes. An example will be if observer O was moving at a speed of 3m/s and observer O’ was moving at 5m/s, observer O will see observer O’ moving forward at a velocity of 2m/s relative to him. In this case what is the true velocity of observer O’? It is both 5m/s and 2m/s, this is due to the fact that these 2 velocities are observed in different reference frames, and are thus both correct.

Lorentz transformations are different from Galilean transformations as they take into account the change in time and space due to the velocity of the observers (aka Special Relativity). I/Jackson will explain this phenomenon in a later post.

The Lorentz Transformations are as follow:

x’=((x-vt))/√(1-v^2/c^2 )

y’=y

z’=z

t’=(t-(vx/c^2))/√(1-v^2/c^2)

The Lorentz Velocity Transformations are a little difficult to understand due to the definitions of u, v and u’ and will be explained in the Special relativity post.

As previously mentioned in the post, an ‘Ether’ Reference Frame was proposed.

This was to resolve the conflict between the Galilean Relativity and Maxwell’s Theory. Maxwell’s Theory is essentially the idea of which Special Relativity was based upon. They are based on 4 equations (The 4 Maxwell’s Equations) which are named after James Clerk Maxwell, the publisher of the early form of the equations which are the foundation of classical electrodynamics. Maxwell’s equations prove that the Speed of Light-c is a constant. and this is in direct conflict of Galilean Relativity which show that if you move a t a sufficiently high velocity, you will be able to see light moving.

Therefore to solve this conflict, the ‘Ether’ Reference Frame was proposed. This reference frame is an absolute reference frame, meaning objects which are stationary relative to this reference frame are truly at rest and objects which are in motion relative to this reference frame are truly in motion.

However this was dismissed due to the Michelson-Morley Experiment which tested for ‘Ether Wind’.

Capture

Fig 1.2: The Michelson-Morley experiment. On the left is a directed light source. The beam of light is directed at a beam splitter which splits the beam of light and directs them in 2 directions toward 2 mirrors of equal distance. The mirrors bounce the light back which then is sent to a light detector.

How does this experiment prove the ‘Ether’ Reference Frame wrong? This experiment was conducted on Planet Earth of course. During that period, it was already known that Earth rotates around an axis. thus the setup of the experiment would be rotating together with the Earth. This would mean that should the ‘Ether’ Reference Frame be present and correct, the light going toward the mirror on the right would take shorter/longer (depending on whether the experiment was set-up facing the east or the west) as compared to the light hitting the top mirror. However the detector detected that the light was hitting together at the same time, thus dismissing the idea of the ‘Ether’ Reference Frame. This also prompted the development of Einstein’s Theory of Special Relativity.

Reference Frames are key in the understanding of both Classical and Quantum Physics as they are useful in the understanding of many experiments and theories.

And with that i end this post on Reference Frames.

Should you spot any mistakes or have any questions, please leave a comment to benefit the other readers and of course myself! We will be posting the second part to Newton’s Laws of Motion and another post on Black Holes by my new co-writer Jackson! Lastly, we will be blogging about new upcoming projects in the series ‘The Power Surge’ (For reals this time). If you have any ideas for more projects, please feel free to comment/contact me in the contact form.

Thank you For Reading and I hope to see you soon!

Clyde Lhui 🙂

 

P.s: An Inertial Reference Frame is a reference frame that either is stationary or moving at a constant speed.

References:

Special Thanks to Mr Damian Boh for his explanation of the topic to me which greatly aided me in the writing of the content of this blog post.

Advertisements

2 thoughts on “Reference Frames”

  1. But the first Michelson-Morley Experiment, which is the one shown here was rejected?

    Wikipedia:
    However, Alfred Potier (and later Hendrik Lorentz) pointed out to Michelson that he had made an error of calculation, and that the expected fringe shift should have been only 0.02 fringes. Michelson’s apparatus was subject to experimental errors far too large to say anything conclusive about the aether wind. For a definitive measurement of the aether wind, a much more accurate and tightly controlled experiment would have to be carried out. Nevertheless the prototype was successful in demonstrating that the basic method was feasible.

    But, their second one succeeded:

    Wikipedia:
    As shown in Fig. 5, the light was repeatedly reflected back and forth along the arms of the interferometer, increasing the path length to 11 m. At this length, the drift would be about 0.4 fringes. To make that easily detectable, the apparatus was assembled in a closed room in the basement of the heavy stone dormitory, eliminating most thermal and vibrational effects. Vibrations were further reduced by building the apparatus on top of a large block of sandstone (Fig. 1), about a foot thick and five feet square, which was then floated in an annular trough of mercury. They estimated that effects of about 1/100 of a fringe would be detectable….The mercury pool allowed the device to be easily turned, so that given a single steady push, it would slowly rotate inertially through the entire range of possible angles to the “aether wind”, while measurements were continuously observed by looking through the eyepiece. Even over a period of minutes, it was presumed that some sort of effect would be noticed, since one of the arms would inevitably turn into the direction of the wind and the other away……. “since the displacement is proportional to the square of the velocity” they concluded that the measured velocity was “probably less than one-sixth” of the expected velocity of the Earth’s motion in orbit and “certainly less than one-fourth.”[1] Although this small “velocity” was measured, it was considered far too small to be used as evidence of speed relative to the aether, and it was understood to be within the range of an experimental error that would allow the speed to actually be zero.[A 1] (Afterward, Michelson and Morley ceased their aether drift measurements and started to use their newly developed technique to establish the wavelength of light as a standard of length.)

    Fig 5:

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s