Special Relativity - its development, interpretation, and its role in physics

7/29/2019 Special Relativity - its development, interpretation, and its role in physics

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Special Relativity - its development, interpretation,

and its role in physicsDamian Boh

Tutorial Group 30Academic Tutors: Dr Yoshi Uchida, Dr Antonio Fernandez-Dominguez

Albert Einstein's special theory of relativity is no doubt one of the most supreme

achievements of the human intellect. It is commonly associated with science-fiction-like

concepts like time travelling and other bizarre behaviours of the fabric of space and time

itself. The main challenge in this theory lies in grasping its strange and counter-intuitive

concepts. Yet it is these concepts which make the subject so intellectually stimulating. After

all, the world would certainly be a boring place should physics be simply a mathematical

formulation of common sense. The occasional revolution in our understanding of the

universe, like that in relativity, serves to make physics a dynamic and exciting field. Hence it

is definitely well worth spending the extra effort to come to grips with the theory.

This article will therefore discuss about the framework and various interpretations of the

theory from a unique perspective not normally seen in textbooks. This is in the hope that the

reader will get a sense of what is actually happening to space and time as described by the

theory. I cannot emphasize enough that it is indeed possible to develop an intuitive feel for

the framework of relativity, bizarre though this may seem. We shall also find out that it is

ironic that a theory named relativity actually resulted from an absolute constant. Not only

that, it points towards an absolute entitythat of space-time. This leads to the next aspect of

the beauty of relativity from a scientific viewpointthat of unification, which will be further

discussed. Finally, apart from the intellectual fulfillment that its ideas provide, relativity has

an important role to play in physics as we shall see.

Concept of Relativity and Reference Frames

The concept of relativity

dates far before the

development of special

relativity in the form of

Galilean relativity. This was

studied by Galileo Galilei in

the 17th

century[1] and isfully consistent with

Newtonian mechanics and

with our intuitive notions

about reality. It is intuitively

obvious that Persons A, B, C

and D in Figure 1 will view each others speeds to be different. For example, Person B on the

train would measure As speed to be 1m/s, while a person C stationary on the ground would

measure As speed to be 51m/s. These people are in different inertial frames of reference.

The word inertial describes a non-accelerating reference frame in which Newtons first law

holds. Objects do not suddenly speed up, slow down or change their direction of motion in

such a frame.


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Clearly, measurements of velocities differ from frame to frame. Hence it is meaningless to

provide an absolute velocity of an object without referencing it to a frame. Each persons

views are also equally valid. In technical terms, the laws of mechanics have the same forms

in all inertial frames of reference in Galilean relativity.

Motivations behind Special Relativity

Like Galilean relativity, special relativity concerns

the measurements of physical quantities in different

inertial reference frames. It was proposed by Albert

Einstein in 1905 in his paper "On the

Electrodynamics of Moving Bodies"[3](Figure 2) as

an effort to reconcile the conflict between Maxwells

theory of electromagnetism and Galilean relativity in

Newtonian mechanics.

Conflict between electromagnetism and Galilean relativity

In Maxwells theory, light is viewed as a

propagating electromagnetic wave (Figure 3)

whose behaviour is described by Maxwells

equations. These equations predict an

absolute value for the speed of light c[4].

The fact that this is an absolute constant

presents a problem immediately. In Galilean

relativity and Newtonian mechanics, the

speed of something on its own is

meaningless unless it is being measured in

some reference frame. We are thus forced to

ask the question which frame of reference

is this absolute speed measured in?

Should such a reference frame exist, it would be unique as it is the only frame in which

Maxwells equations describing the speed of light holds. It should therefore be the absolute

frame against which all motion should be referenced. This idea contradicts the beautiful

symmetry of the equivalence of all inertial reference frames and forces us to conclude that

Galilean relativity breaks down. Einstein was not at all pleased with this as he embarked on a

quest to resolve this conflict.

Reconciling electromagnetism and Galilean relativity

It is tempting to believe that electromagnetism and Newtonian mechanics belong to 2

different realms in physics and hence Galilean relativity might not apply to both. Furthermore,

concepts like the aether were proposed as a medium for the propagation of light and hencethe absolute reference frame[6]. We should however realize that the laws of physics, be it in


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mechanics or electromagnetism, ultimately describe the same nature around us! They should

therefore be coherent.

In Einsteins second postulate in special relativity, the speed of light takes the same value in

all inertial frames of reference. This postulate is in addition to the postulate that the laws of

physics are of the same form in all inertial frames. In my opinion, the former postulate isredundant as it naturally follows from the latter. It is however interesting to note that all

Einstein did was to incorporate the constancy of the speed of light in all inertial frames in

addition to the physical laws. Yet this has led to so many ground-breaking concepts! This is

also the first instance of unification (between electromagnetism and classical relativity) being

involved in this theory.

Intuitive Feel for the Relativity of Time and Space

From here, textbooks often go on to describe various derivations of time dilation and length

contraction. I, however, feel that it is essential to develop in readers the intuitive feelfor the

relativity of space and time in different reference frames. I term this as the relativitists

intuition.

When we measure the speed of light, we are actually measuring the distance that light moves

over a unit time interval, both of which are measured in a particular frame A. Clearly,

following Galilean relativity, the speed of light would be different in any other frame B

moving with respect to frame A. In order for the speed of light to stay constant, the distances

and time periods we measure in frame B must somehow change. We are thus forced to make

the conceptual leap and propose that the size of space must be different and that time must

flow differently in different inertial frames of reference!

It is now apparent that such a counterintuitive concept can actually be proposed simply by

thinking more deeply into the factors involved in measuring speed. Many other

groundbreaking ideas in physics are hatched in similar ways. Of course, Einsteins brilliance

did not lie in coming up with the postulates of relativity but rather in proposing this concept

which totally defies every bit of our common sense as well as the state of physics at that time.

Relativity of Simultaneity

Thought experiments occur every

so often in relativity that its worthmentioning about one. To get a

feel for what the relativity of time

can lead to, lets consider this. A

classic example of the relativity of

simultaneity involves a person A

switching on a lamp (which shines

light equally in all directions) in

the centre of a moving train.

(Figures 4a and 4b)


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After some time A would observe that the light reaches both ends of the train simultaneously

as they are equidistant from A. B would, however, conclude that the light travelling at the

same speed creaches the back of the train first as the back of the train in Bs frame wouldhave moved forward to catch up with the light (Figure 4b). Thus, 2 events that are

simultaneous in one frame are not simultaneous in another frame. Both views are equally

valid as there is no preferred reference frame.

Time Dilation and Length Contraction

The effect of time dilation and length

contraction also follows naturally from the

constancy of the speed of light. Time

dilation describes the slowing down of time

flow in an inertial reference frame S which

is moving with respect to another frame S.

Every clock that a person B moving with Ssees will tick at a slower rate compared to

that in S (Figures 5a/b). B will also age

more slowly than A as the biological

processes in him will slow down as well.


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We can now see that time travelling is made possible. It is obvious that should person B stops

and moves back to person A, he would conclude that he has travelled 4 hours (5pm to 9pm)

into the future! It is vital to note that this time travelling does not occur instantly like that in

science fiction. Rather it is an accumulation of the slowing of time as B moves. Hence time

travelling is made possible simply by moving!

Similarly, length contraction describes the

contraction of space in moving frames. Figure 6

shows how the length of a rocket would differfor people travelling at different velocities (in

terms of c), hence in different frames of

reference, with respect to it. This relativity of

space in different frames is yet another bizarre

consequence of the constancy of the speed of

light.

The reason that the phenomena discussed are so unfamiliar to us results from the fact that

these only become obvious at speeds close to the immense speed of light smxc /100.3 8 .

This constant c occurs so often in the mathematical framework of relativity that if it falls

within our everyday speeds, time travelling and space contraction would be an apparent part

of everyday life!

The complete derivations of the formulas for the above phenomena can be found in most

textbooks with a section on modern physics. In this article, the intuitive feel for why space

and time should behave in this way will be discussed instead.


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Does Special Relativity Simplify or Complicate Matters?

Up till now, relativity may be seen as a complete mess which destroys our intuitive notions

about nature. Furthermore, it has complicated natures fundamental entities a little too much.

Wouldnt things be far simpler should space and time remain fixed and unchanging in every

reference frame? It is therefore tempting to dismiss such an inelegant theory. Contrary to

popular belief, nothing could be further from the truth! Though not obvious at first sight,

special relativity has in fact managed tosimplify things in nature!

Time dilation and length contraction can be interpreted as the constant efforts made by space

and time to completely compensate for an observers motion. No matter how we move and

behave, space and time always adjust themselves hand in hand to ensure that the speed of

light is constant for every observer in every reference frame! This effect is almost magical, as

though they can communicate with each other and coordinate their behaviour instantaneously.

This suggests an elegant underlying mechanism deep within these fundamental entities. A

unifying structure should exist beneath that of space and timeabsolute space-time.

For many centuries human beings have taken for granted that space and time exist

independently. Yet no one has ever questioned why our arena of reality should be divided

into 2 separate entities so different from each other! Special relativity elegantly simplifies

these two different fundamental entities into a single whole.

More about the Relativitists Intuition

We are now equipped with the essential concepts to develop the relativists intuition. In my

opinion this can be achieved simply by keeping 2 things in mind:

1. Motion through time is converted to motion through space in a single absolute entityspace-time, i.e. whenever we move through space, time flows more slowly as it

adjusts itself to compensate for our motion.

2. The speed of light c is an absolute constant which shows the extent to which motionthrough space is converted from motion through time as the conversion is such that c

is always kept constant.

The above 2 absolutes are the reasons why I particularly hate the name relativity given to

this theory. Such a name gives the false impression that everything is ultimately and

fundamentally relative. It masks the absolutes on which this theory is based.


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Space-time Loaf

A good way to visualize absolute space-time is that of a space- time loaf suggested by

Professor Brian Greene in his book[6]. This loaf has 2 dimensions of space and 1 of time. It

can be separated into parallel slices with each slice resembling that of a page in a flip-book.

Figure 7a shows a space-time loaf for a boxing duel between boxers A and B while Figure 7b

shows how it can be sliced up for an observer in Frame S1.

Each slice in Figure 7b corresponds to simultaneous events in space seen by the observer in

S1 at each instant. As time passes, each slice that he observes progresses to the next in the

direction of time flow. As shown in Figure 7b, the observer in frame S1 will see boxers A and

B in their stationary positions before they start to punch each other simultaneously (shown by

the darker coloured slice) and proceed to rest again. Observers in different frames moving

with respect to frame S1 will slice the space-time loaf in different ways (Figures 7c and 7d).

These slices are angled with respect to those in frame S1. The magnitude of angle isproportional to the speed at which the frames move with respect to S1. The direction of angle


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is different in frame S3 (Figure 7d) compared to S2 as frame S3 is moving in the opposite

direction compared to S2s motion relative to S1.

Clearly an observer in frame S2 moving with respect to S1 will conclude that boxer A starts

punching before B while the opposite is true for an observer in frame S3. It is important tonote that each way of slicing the space-time loaf is equally valid; there is no preferred way.

This illustrates the relativity of simultaneity as described before. Observers in different

frames do not agree on the simultaneous punches as observed by the observer in S1.

This is also a powerful model to visualise space-time as an absolute entity which exists out

there. Observations that we make are relative merely because we experience events in a

different way in the same space-time loaf depending on our motion. This also hints that

space-time is not merely a human abstraction; it exists as a physical entity[6]. We shall

further appreciate the beauty of such a concept in the next section.


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Unification

For centuries physicists have passionately sought to unify concepts and different phenomena

into a coherent framework. Special relativity has achieved way more than just that! Not only

does it unify the concept of relativity with electromagnetism, it provides the first instance of

the unification of 2 entities, space and time, that make up the fabric of reality itself!

Furthermore, we know space-time only exhibits this behaviour when we move through it.

This suggests that our perception of space-time is dependent on our activities and that we

(matter) are not entirely separated from our realitys arena! Many people are also aware of

the mass-energy equivalence resulting from this theory. This seems to hint that all the

fundamental entities of nature and reality (matter, energy, space and time) are somewhat

inherently linked to one another. Philosophically it is hard to imagine a concept more

fundamentally unifying than this!

In my opinion the science-fiction-like applications that could result from this theory pales in

comparison to such a fundamentally unifying principle. Sadly, too much attention has beengiven to these science-fiction-like aspects rather than the fundamental interpretation of reality

this theory has given us. Hence this article was written with a purpose to change this! Special

relativity is nota theory which complicates space and time to the extent that science fiction

becomes possible. Rather the true beauty of space-time is hidden away from our nave

intuitive notions!


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Special Relativitys Role in Physics


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Special relativity also provides a classic example of the process of development in physics

(Figure 8). Throughout the history of physics, the most ground-breaking discoveries are often

made when resolving conflicts between well-established theories[8]. This often results in

more conflicts leading to further mind-blowing discoveries. In our context, special relativity

was an effort to resolve the conflict between electromagnetism and classical relativity in the

Newtonian world. One of the consequences is that the speed of anything can never exceedthat of light[9].

This has led to another conflict as it contradicts the instantaneous transmission of gravity

across vast distances in Newtonians world. Einstein managed to resolve this in a more

general version of relativity which includes non-inertial (accelerating) frames. This theory

was far more revolutionary and revealing than special relativity. For example we now know

that space-time can be distorted simply by the presence of matter[8]. The conflict was

resolved in that the transmission of the gravity is through the speed-of-light propagation of

gravitational waves corresponding to ripples in the space-time fabric itself[10].

Yet the cycle continues; this has resulted in another conflict which remains unresolved atpresent. General relativity is one of the 2 modern pillars of physics and it describes the very

large and massive. Quantum mechanics is the other pillar which describes physics at

subatomic levels. The conflict happens between the probabilistic and discrete behaviour in

the microscopic world of quantum mechanics as opposed to the smooth and continuous

geometrical space-time in general relativity[11].

It is hard to imagine just what kind of revolution can result from the unification of general

relativity and quantum mechanics. Many physicists hope that it will ultimately result in the

Theory of Everything[12] which governs every behaviour of nature and reality itself. I

however secretly hope that the cycle of conflicts continues. In this way, every generation of

mankind will always be living in exciting times where important conflicts are resolved and

mind-blowing discoveries in physics made.


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References

1. Leo Sartori. Understanding Relativity: A Simplified Approach to Einsteins Theories.University of California Press. 1996

2. Einsteins 1905 paperOn the Electrodynamics of Moving Bodies. Digital image. Web.Available from:http://www.lonestar.edu/library/14915.htm[accesssed December

2012]

3. John S. Rigden.Einstein 1905: The Standard of Greatness. Harvard University Press.2005

4. Nicholas J. Giordano. College Physics Reasoning and Relationships. Brooks/ColeCengage Learning. 2010

5. Propagation of light. Digital image. Web. Available from:http://www.astarmathsandphysics.com/ib_physics_notes/Relativity/ib_physics_notes_

the_nature_of_light.html[accesssed December 2012]

6. Brian R. Greene. The Fabric of the Cosmos. Random House, Inc., New York. 20047. Different lengths of rocket due to length contraction. Digital image. Web. Available

from:http://www.ipodphysics.com/relativity-length-contraction.php[accesssed

December 2012]

8. Brian R. Greene. The Elegant Universe. Random House, Inc., New York. 19999. Michio Kaku. Einsteins Cosmos: How Albert Einsteins Vision Transformed Our

Understanding of Space and Time. The Orion Publishing Group Ltd. 2004

10.T. Padmanabhan. Gravitation Foundations and Frontiers. Cambridge UniversityPress. 2010

11.Anderthal Kord. The Third Piece: Unifying General Relativity, Quantum Mechanicsand Personal Identity. Mill City Press, Inc. 2010

12.Helen Buss Mitchell.Roots of Wisdom: A Tapestry of Philosophical Traditions.Wadsworth, Cengage Learning. 2005

Bibliography

Albert Einstein.Relativity: The Special and General Theory. (translated by Robert W.

Lawson) Methuen & Co. Ltd. English edition first published in 1920
http://www.lonestar.edu/library/14915.htmhttp://www.lonestar.edu/library/14915.htmhttp://www.lonestar.edu/library/14915.htmhttp://www.astarmathsandphysics.com/ib_physics_notes/Relativity/ib_physics_notes_the_nature_of_light.htmlhttp://www.astarmathsandphysics.com/ib_physics_notes/Relativity/ib_physics_notes_the_nature_of_light.htmlhttp://www.astarmathsandphysics.com/ib_physics_notes/Relativity/ib_physics_notes_the_nature_of_light.htmlhttp://www.ipodphysics.com/relativity-length-contraction.phphttp://www.ipodphysics.com/relativity-length-contraction.phphttp://www.ipodphysics.com/relativity-length-contraction.phphttp://www.ipodphysics.com/relativity-length-contraction.phphttp://www.astarmathsandphysics.com/ib_physics_notes/Relativity/ib_physics_notes_the_nature_of_light.htmlhttp://www.astarmathsandphysics.com/ib_physics_notes/Relativity/ib_physics_notes_the_nature_of_light.htmlhttp://www.lonestar.edu/library/14915.htm

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Special Relativity - its development, interpretation, and its role in physics