Looking for complete explanation of logic behind relativity

[fuzzy127]

Hello,
My name is Joe and I am a junior in high school. I am taking AP Calculus right now along with a basic physics class. I am very, very interested in the special and general theories of relativity, but I want to know the exact logic behind it. Right now, I don't really understand any of it. I am looking for a source that will start from scratch and explain everything. I have done a lot of research on my own so I know what the theories are but I can't find an explanation that starts at my level of understanding. I know the special theory of relativity is a way that the principle of relativity and the fact that the speed of light is a constant velocity no matter the velocity of the observer do not contradict each other. But in order to truly understand this I need to start by understanding why the speed of light is constant no matter the velocity of the observer. I read somewhere that no one really knows why this is but I would at least like to know where this idea came about and what evidence there is that supports this. There is obviously logic behind this fact. I don't want to assume anything without fully understanding it.

If my level of mathematical background is not sufficient then I want to know what the next step is in truly understanding relativity. I am in the middle of a calculus course right now, and I understand all math up to this level extremely well.

If someone has any suggestions for me I really appreciate any advice at all. Thanks in advance!

 

[m00npirate]

Einsteins book on the subject isn't too complicated, and I found it very helpful. I personally can't stand to read long things online, so I bought the book, but you can find it here online: http://www.bartleby.com/173/

 

[Integral]

You do not need to understand why the speed of light is constant to understand Special Relativity. SR is what follows, given that the speed of light is constant.

Now, why is the speed of light constant?
technically Physics does not address such questions, all we can talk about is the evidence which shows that to be true.

Mathematically Maxwell derived the value of the speed of light in 1867. This derivation started what was known as "The Schism" in classical physics. It seemed that light obeyed different rules then massive objects. The problem existed until Einstein published SR, showing that all objects obeyed the same rules as light.

Have you tried reading Einstein's original work, his initial development of SR is short not that hard to follow.

You do not yet have the math to understand Maxwell's equations, and that is where the underpinnings of the constancy of c lies. For now accept that c is constant and continue working on Special Relativity.

 

[D H]

As a junior in high school taking AP calculus and basic physics, special relativity is within your grasp. However, the mathematics of general relativity are well beyond it. I would stick with special relativity for now.

The idea that the speed of light is the same to all observers comes from two places, experiment and theory. The famous Michelson-Morley experiment in 1887 failed to measure a difference in the speed of two beams of light moving in different directions. Whether Einstein knew of this experiment is arguable.

What Einstein certainly did know about were Maxwell's equations (Maxwell, 1861 and Heaviside, 1884). Maxwell's equations describe electromagnetic phenomenon. One very funny thing about them: The speed of electromagnetic waves falls out of Maxwell's equations, and this speed doesn't depend on the either speed of the transmitter or the receiver. It is the same for all observers. There was a big disconnect at the end of the 19th century between the newly developed electromagnetic theory and the long standing Newtonian mechanics.EDIT:

Integral, you type too fast.

 

[yogi]

At the turn of the century, science was having great difficulty explaining why the MMX experiments failed to detect the Earth's motion through the supposed ether. It didn't make sense, and many attempts were made to rationalise the null results - what Einstein did was turn the problem into a postulate - if the speed of light is always measured as locally equal to c, then these over and back type of experiments could be explained because time and space are not measured the same in relatively moving reference frames.

 

[robphy]

Here are some starting points:

"The principle of relativity; original papers by A. Einstein and H. Minkowski"
http://www.archive.org/details/theprincipleofre00einsuoft

"What is the experimental basis of Special Relativity?"
http://math.ucr.edu/home/baez/physics/Relativity/SR/experiments.html"

"Special Relativity: A Centenary Perspective" - Clifford M. Will
http://arxiv.org/abs/gr-qc/0504085
(published: Einstein, 1905-2005: Poincare Seminar 2005, ed. T. Damour, O. Darrigol, B. Duplantier and V. Rivasseau (Birkhauser, Basel 2006), pp. 33-58)

The constancy of the speed of light postulate could be regarded as a simple way to suggest that the principle of relativity be extended from merely mechanical laws to include electromagnetic laws as well. There do exist symmetry arguments that lead to various "derivations of special relativity without the speed of light postulate", leaving a free constant parameter with units of velocity... whose physical character is either finite or infinite (to be consistent with possible causality conditions)... and whose numerical value is determined by experiment.

 

[Count Iblis]

Special Relativity is more fundamental than electromagnetism. Many modern textbooks on electromagnetism start with Coulomb's law and then, by requiring the theory to be covariant under Lorentz transformaton, derive the Maxwell equations. Electromagnetism is much easier to understand when it is taught this way.

 

[robphy]

Special Relativity is more fundamental than electromagnetism. Many modern textbooks on electromagnetism start with Coulomb's law and then, by requiring the theory to be covariant under Lorentz transformaton, derive the Maxwell equations. Electromagnetism is much easier to understand when it is taught this way.

Yes, SR is certainly more fundamental than classical EM. Historically, it was used as a motivator to uncover the underlying SR-invariance since the structure of Galilean kinematics and Newtonian dynamics did not reveal it [and experiment had not advanced far enough to note their disagreements with phenomena correctly predicted by SR].

The relativistic approach to teaching EM does make its structure easier to understand... although that approach might not help an introductory student understand its practical phenomena. So, that approach is probably better suited to a second course in EM.

Additionally, with the current curricula, it may be difficult to sufficiently motivate to an introductory student the appreciation of relativistic invariance. So, a revision of the curricula along the lines of

"If Maxwell had worked between Ampère and Faraday: An historical fable with a pedagogical moral" - by Max Jammer and John Stachel
http://link.aip.org/link/?AJPIAS/48/5/1

might help.

 

[Mentz114]

DH:

The famous Michelson-Morley experiment in 1887 failed to measure a difference in the speed of two beams of light moving in different directions.

The MM experiment nothing to do with SR2. Please stop quoting this as experimental evidence for SR2. It only shows that there is no classical luminiferous aether.

 

[robphy]

DH:

The MM experiment nothing to do with SR2. Please stop quoting this as experimental evidence for SR2. It only shows that there is no classical luminiferous aether.

What is SR2?

 

[Daverz]

What is SR2?

I think he means Einstein's second postulate, the constancy of the speed of light, though I don't think we need an obscure acronym for that. I think DH was merely being descriptive, and I don't understand Mentz's objection.

 

[Mentz114]

SR2 is postulate 2 of SR. I don't know how accepted this is but, from Wiki

Postulates of special relativity
1. First postulate (principle of relativity)

Observation of physical phenomena by more than one inertial observer must result in agreement between the observers as to the nature of reality.
Or, the nature of the universe must not change for an observer if their inertial state changes.
Or, every physical theory should look the same mathematically to every inertial observer.
Or, the laws of the universe are the same regardless of inertial frame of reference.
2. Second postulate (invariance of c)

Light is always propagated in empty space with a definite velocity c that is independent of the state of motion of the emitting body.

I think he means Einstein's second postulate, the constancy of the speed of light, though I don't think we need an obscure acronym for that.

Don't use it then. It's a lot quicker than writing it out in full.

 

[Daverz]

I am very, very interested in the special and general theories of relativity, but I want to know the exact logic behind it. Right now, I don't really understand any of it. I am looking for a source that will start from scratch and explain everything.

Look for one of N. David Mermin's books, either About Time or Space and Time In Special Relativity (the former is a revised and slightly simplified version of the latter.)
He does an excellent job of working out the logic of relativity from first principles, and you shouldn't have any problems with the math.

 

[D H]

The famous Michelson-Morley experiment in 1887 failed to measure a difference in the speed of two beams of light moving in different directions.

The MM experiment nothing to do with SR2. Please stop quoting this as experimental evidence for SR2. It only shows that there is no classical luminiferous aether.

Mentz, please stop quoting out of context. Continuing with the omitted part of my post,

Whether Einstein knew of this experiment is arguable.

While Einstein may or may not have known about the Michelson-Morley experiment before developing his theory of special relativity, there can be no doubt that the MMX and follow-on experiments did contribute to the very rapid acceptance of the theory. The MMX has everything to do with special relativity, after the fact. It disproved the classical luminiferous aether. If not SRT, then what? Lorentz Ether Theory? While LET and SRT are indistinguishable in terms of results, they most certainly are distinguishable in terms of axioms. SRT stands well above LET in terms of elegance and simplicity.

 

[Mentz114]

DH, from your original post :

The famous Michelson-Morley experiment in 1887 failed to measure a difference in the speed of two beams of light moving in different directions.

This statement has no bearing on special relativity, which never mentions different directions. It confuses the issue in my view.

I accept that MM made it easier to accept the constancy of c for all observers, but this gives the impression that it provides experimental support, which it does not.

 

[fuzzy127]

Thanks everyone for all your help. This should help me get started. If I have any more questions I will post again. Thank you!

 

[yogi]

MMx did not disprove the existence of an ether. The ether was superfluous, but not disproved. SR was economic in the number of postulates needed to expalain the null results (in truth the results were not null, but much less than what was expected for the Earth's orbital velocity). The beauty of SR was its simplicity and symmetry ..In contrast to LET, SR did not depend upon physical changes to take place; afortori there was no need for ad hoc hypothesis to explain observation contractions in terms of real length changes in relatively moving frames.

 

[yogi]

It is hard to believe that Einstein did not know of MMx - even his biographers have struggled to explain his vague reluctance to admit of this - my own guess, and it is of course, just a guess, is that Einstein felt SR was a principle theory, not something constructed to explain a particular experiment. The 1905 paper at some point (if my memeory is correct), even makes reference to the fact that the result is required in order to conform with the experiments.

 

[Daverz]

In the second paragraph of Einstein's famous first SR paper, after discussing examples of "asymmetries which do not appear to be inherent in [electrodynamic] phenomena" he says:

Examples of this sort, together with the unsuccessful attempts to discover any motion of the Earth relatively to the ``light medium,'' suggest that the phenomena of electrodynamics as well as of mechanics possesses no properties corresponding to the idea of absolute rest.

I interpret this as meaning that Einstein was generally aware of MMx and other experiments but had not consulted the original papers.