Significance of Special Relativity

[Oscar Wilde]

Allow me to preface this by saying that I am only a student of physics, and that I have much respect for the work of those who came before me.

I have familiarized myself with SR through my own research on the internet (perhaps a grave error), and I am quick to acknowledge that I do not understand the key fundamentals behind SR. However, I have also made an effort to understand what General Relativity says, and though I do not understand its derivation, I still have some feeble idea of what it "says", that mass and energy are two different manifestations of the same "thing" (and if this is wrong then please, correct me).

Getting to the actual question, it is my understanding that SR is saying that, forgive me if I make an error in my brief explanation, two observers can see an event in two different perspectives, but both are "correct" when they explain what they saw. Anyway, this seemed logical and I can kind of understand what is being said. However, I cannot see the significance of SR, though I have a base idea that it must be incredibly significant. I now implore you to enlighten me to how SR is significant, and how it functions (answering one will invariably lead to the other).

Thanks,

Oscar

 

[Mentz114]

Special relativity is necessary to resolve the 'Gallilean' paradox in electrodynamics. The simple pre-SR relativity allowed velocities to be added simply and assumed all clocks are synchronised. This results in predictions that different observers ( from moving frames) will see different outcomes to experiments.

The problem is resolved by SR. Einstein postulated that the velocity of light remains constant in all frames and SR emerges from this.

This is a very brief answer, because SR tells us a lot more, perhaps the most important being that physical laws must be expressed in 'covariant' form in order to be valid in all inertial frames.

 

[Fredrik]

The most important thing in my opinion is that combined with quantum mechanics, special relativity leads almost immediately to the concept of non-interacting elementary particles, which suggests that the next step is to figure out a way to describe interactions between these particles. The theory that does that the best is called the standard model (of elementary particle physics). It's a quantum field theory formulated entirely in the framework of special relativity.

So SR is definitely much more than an intermediate step on the way to GR.

 

[Dale]

I think that the most significant thing about relativity is the elegant way that it unifies apparently separate concepts like space and time or energy, momentum, and mass, or the electric and magnetic fields.

 

[CompuChip]

Getting to the actual question, it is my understanding that SR is saying that, forgive me if I make an error in my brief explanation, two observers can see an event in two different perspectives, but both are "correct" when they explain what they saw.

Yes, that is one of the key concepts, and it sounds very logical.

The key point however, which makes special relativity remarkable, is that the speed of light is the same for all observers moving relative to one another. For example, suppose that you are standing on some spaceship and another spaceship is whizzing by at 90,000 km/h. It shoots off a rocket at 10,000 km/h relative to itself. Intuitively you would expect that you see the rocket moving at 100,000 km/h. However, suppose that the moving vessle doesn't shoot off a rocket, but a beam of light. Now you would expect that the light is moving at the speed of light, c relative to the firing ship and c + 90,000 km/h relative to you. According to SR, this is not true: both observers see the light move at speed c.
This has profound consequences, for example: when you try to read off the clock in the moving spaceship it will appear to run slower (because the light reflecting off it to hit your eye doesn't move at c - 90,000 km/h toward you but at c) and it will appear to be shorter (because light reflecting off the front end of the ship has to travel twice the length of the ship more than light reflecting off the back, but will travel at the same speed - so together with the light from the back at some time you will receive light reflected from the front at an earlier time). Hence, relative motion has a simultaneous effect on space and time, and the effects on either are so strongly correlated that since SR we like to speak of "spacetime" in which space and time are treated (more or less) on equal footing.

Why is this important? Well, imagine now that we're not talking about spaceships but elementary particles. You are standing at rest in a laboratory (at CERN, for example) and you are watching a particle fly by at 90% of the speed of light, which may emit some other particle ahead of it - or in any other direction. The effects of SR become important here, for example: unstable particles live longer (basically, the "internal clock" of the decaying particle appears to tick slower for you)!
Special relativity is therefore a very important part of everyday life in particle accelerators, for example. But also in cosmology, it is sometimes important.

We now have the concept of Lorentz invariance, which means about as much as: despite (or thanks to) light moving at the same speed to all observers, physics looks the same to all observers. Suppose I have some theory (electromagnetism, for example) and do some experiment with magnets and electric fields, and measure something. You are in a car moving at 120 km/h on the highway, and want to repeat my experiment. It seems no more than logical that you actually will find the same result as I did. Now mathematically, I can calculate what result you should find considering that you are moving. If electromagnetism is Lorentz-invariant, this should be the same as my result. Note that this is not as trivial as it might sound. The classical example is a bar magnet being pulled through a conducting ring, see for example this Wikipedia page.

Nowadays, we have so many highly accurate experimental verifications of special relativity, that Lorentz invariance is more or less a basic requirement of any new candidate-theory we write down (i.e. if it isn't compatible with SR, then it's no good).

 

[Oscar Wilde]

Thank you very much for your answers!

I appreciate the time you took to answer this question, and I certainly have a new "perspective" :) on SR. I am surprised to learn of its importance in new theories, cosmology, and even in particle accelerators.

Thanks once again

 

[rchenkl]

Yes, that is one of the key concepts, and it sounds very logical.

The key point however, which makes special relativity remarkable, is that the speed of light is the same for all observers moving relative to one another. For example, suppose that you are standing on some spaceship and another spaceship is whizzing by at 90,000 km/h. It shoots off a rocket at 10,000 km/h relative to itself. Intuitively you would expect that you see the rocket moving at 100,000 km/h. However, suppose that the moving vessle doesn't shoot off a rocket, but a beam of light. Now you would expect that the light is moving at the speed of light, c relative to the firing ship and c + 90,000 km/h relative to you. According to SR, this is not true: both observers see the light move at speed c.
This has profound consequences, for example: when you try to read off the clock in the moving spaceship it will appear to run slower (because the light reflecting off it to hit your eye doesn't move at c - 90,000 km/h toward you but at c) and it will appear to be shorter (because light reflecting off the front end of the ship has to travel twice the length of the ship more than light reflecting off the back, but will travel at the same speed - so together with the light from the back at some time you will receive light reflected from the front at an earlier time). Hence, relative motion has a simultaneous effect on space and time, and the effects on either are so strongly correlated that since SR we like to speak of "spacetime" in which space and time are treated (more or less) on equal footing.

Why is this important? Well, imagine now that we're not talking about spaceships but elementary particles. You are standing at rest in a laboratory (at CERN, for example) and you are watching a particle fly by at 90% of the speed of light, which may emit some other particle ahead of it - or in any other direction. The effects of SR become important here, for example: unstable particles live longer (basically, the "internal clock" of the decaying particle appears to tick slower for you)!
Special relativity is therefore a very important part of everyday life in particle accelerators, for example. But also in cosmology, it is sometimes important.

We now have the concept of Lorentz invariance, which means about as much as: despite (or thanks to) light moving at the same speed to all observers, physics looks the same to all observers. Suppose I have some theory (electromagnetism, for example) and do some experiment with magnets and electric fields, and measure something. You are in a car moving at 120 km/h on the highway, and want to repeat my experiment. It seems no more than logical that you actually will find the same result as I did. Now mathematically, I can calculate what result you should find considering that you are moving. If electromagnetism is Lorentz-invariant, this should be the same as my result. Note that this is not as trivial as it might sound. The classical example is a bar magnet being pulled through a conducting ring, see for example this Wikipedia page.

Nowadays, we have so many highly accurate experimental verifications of special relativity, that Lorentz invariance is more or less a basic requirement of any new candidate-theory we write down (i.e. if it isn't compatible with SR, then it's no good).

Thanks CompuChip. I didn't understand it quite well before either.