What's So Special About Special Relativity?

[Solitary]

SPECIAL RELATIVITY

Central to the discussion of special relativity is the idea of an inertial frame (or reference). This is basically a coordinate system, which might be attached to an observed object or to the observer, which undergoes no acceleration. Consequently, the relative velocity between two inertial frames is necessarily constant, providing what we refer to as uniform motion Einstein based on two postulates:

1. No physical measurement can distinguish one inertial frame from another.
2. The speed of light (in vacuum) is the same in all inertial frames, regardless of any motion of the source.
Postulate (1) is also known as the Principle of Relativity and is a generalization of the idea of Galileo: that uniform motion is undetectable by mechanical experiments. This Galilean Principle of Relativity accounts for the fact that there are no obvious effects of the earth's motion through space, as it orbits the sun (at a tangential speed of about 17 000 km/hr !). For example, objects released from the top of a tower fall vertically downwards (towards the centre of the earth), as they would if the earth were stationary and not at some angle which depends on the earth's tangential speed.

Einstein thought that Galileo's principle should apply to the whole of physics, including electromagnetic phenomena.

Postulate (2) derives from the idea of Maxwell that light behaves as a travelling wave, containing oscillating electric and magnetic fields which can advance  in a vacuum at a speed, denoted by the symbol c , which depends only on two basic constants of electrostatic and magnetic theory. The fields require no medium for their existence, unlike the case of sound waves (for example) whose velocity within a gas (or liquid or solid)  affected by any motion of this medium. Previously, physicists had assumed that light waves behave somewhat like sound, propagating though an invisible medium which they termed the (aluminiferous).

 Attempts to measure the speed of the earth relative to the ether failed; in particular, the Michelson-Morley experiment (performed repeatedly between 1881 and 1930) showed that light travels with the same speed in two perpendicular directions, which is impossible if the earth is moving (due to its orbit around the sun) through an ether.

From Einstein's two postulates, several properties follow as a matter of pure logic. One of these is an effect called length contraction: the "measured" length (in the direction of motion) of an object which is moving at uniform speed v relative to an observer is less than if the object were stationary. The length measured when there is  relative motion is called the proper lengthand  all other lengths are called improper.

The length-contraction effect can be expressed mathematically improper length = (1/gamma) (proper length) <where 1/gamma = (1 - v^2 / c^2)^(1/2) and is less than unity; here  means to the power of, so ^(1/2) means taking the square root. Since the value of c (= 3.00 x 10^8 m/s) is so large, length contraction is entirely negligible (e.g. 1 part in 2 x 10^12 for v = 1000 km/hr) for objects such a cars, trains and airplanes.

There is no change in dimensions of the object which are perpendicular to the relative velocity v ; therefore it might be expected that a fast-moving cube would appear squashed (in the direction of motion) in a high-speed photograph. However light from different parts of the cube takes different times to reach the camera, so the photograph is  a record of the object at a single instant of time. This illustrates the difference between a true measurement and a simple observation.

 In fact, the cube would appear as if it had been rotated (through a fixed angle), due to the combined effects of length contraction and the finite (limited) speed of light.

Magnetic force can be thought to arise from electrostatic interaction, plus the length-contraction effect. For example, a metal contains potentially-mobile negative electrons and an equal number of immobile positive charges.  In the absence of any electrical current, two parallel wires exert no force on each other because the attractive forces (electrons in one wire attracting positive charge in the other, and vice versa) are exactly balanced by repulsions (electrons in one wire repelling those in the other, likewise for the positive charges).

With an equal current travelling in the same direction in each wire, the repulsive forces are unchanged (there is no relative motion between the electrons or positive charges) but the attractions are increased, since the positive charge "sees" the distance between the moving electrons as contracted (equivalent to an increase in negative charge per unit length of the wire) or vice versa. This increase is seen as a net attractive force between the two wires, usually attributed to the magnetic effect of the currents.
 We can say that Special Relativity unites the concepts of magnetic and electrostatic force into a single electromagnetic force.

Time dilation

Another effect predicted by special relativity is time dilation : a clock moving at uniform speed relative to an observer would be "measured" to run slow, arising from the properties of space-time and not from the finite speed of light. By analogy with the above, we can define an interval of  proper time as a difference in the readings of a clock which is stationary with respect to the observer; where there is relative motion, we measure an improper time interval. Analysis of a simple situation  shows that  align="CENTER">improper time interval = (gamma) (proper time interval)
 
     
Since gamma &gt; 1, the interval between ticks of a "moving" (relative to the observer) clock is greater than for a "stationary" clock, so "a moving clock runs slow". This effect has been verified by carrying highly-accurate atomic clocks aboard aircraft and comparing their "readings" with those of an identical clock which remained stationary. Although the difference in elapsed time is miniscule, the extremely high accuracy of the atomic clock has allowed the time dilation effect predicted by Special Relativity to be verified.

A more extreme (but hypothetical) example is the case of two twins: one remains on earth, the other journeys at a high speed (approaching the speed of light) to a distant star and back. Upon returning, the moving twin will have aged less than the twin who stayed on earth. Although this is not a simple situation, since accelerations are necessarily involved in the return journey, detailed analysis shows that Special Relativity gives the right answer for the difference in age.

             Relativistic mass

 Einstein published a paper which shows that Newton's second law (F = ma) applies to any object, travelling at any speed v, provided its usual mass (called the rest mass, if measured when the object is stationary) is replaced by a relativistic mass given by: relativistic mass = (gamma) (rest mass) Since gamma &gt; 1, there is a relativistic increase in mass. Therefore, if a constant force F is applied to a stationary object, it initially accelerates at a constant rate a = F/m0 (where m0 is its rest mass) but as the speed v approaches c , gamma becomes significantly larger than unity, the relativistic mass m significantly exceeds m0 and the rate of acceleration (a = F/m) decreases. In fact, the acceleration tends towards zero as v approaches c :

No material object can travel at or above the speed of light (in vacuum). At high speeds, the work done by the force F goes into increasing the relativistic mass, rather than the speed. In other words, energy provided by the force is converted into mass. Einstein introduced the concept of the total energy E of an object E = m c^2 = (gamma) m0 c^2 = K + m0 c^2 as being the sum of its kinetic energy K and its <B>rest energy</B> E0 = m0 c^2 . From this equation, it is easy to show that the correct general formula for kinetic energy is:K = (gamma - 1) m0 c^2<rather than the classical expression: K = (1/2) m0 c^2 .

 However, Einstein's general formula is consistentwith the classical expression, since for v&lt;&lt;c we can use the binomial theorem (1+x)^n = 1 + n x + (1/2)n(n-1) x^2 + ... = 1 + n x (approximately) if x&lt;&lt;1 with  x = -v^2/c^2  and  n = -1/2 , so that gamma = (1+x)^n , givin >K = (1 + nx - 1) m0 c^2 = (nx) m0 c^2 = (-1/2) (-v^2/c^2) m0 c^2 = (1/2) mo v^2 For v&lt;&lt;c, Special Relativity gives the same result as Classical Physics, an example of the Correspondence Principle which states that a new scientific theory must give the same predictions as an older theory under conditions in which the older theory has already been found to be correct. One situation in which speeds comparable to c are routinely achieved is in the acceleration of charged particles, for example electrons in a TV tube, oscilloscope or electron microscope, or other particles in a nuclear accelerator.
 

Solitary

[Colanth]

That still doesn't answer the question of why it's called special relativity and not, say, ordinary relativity.

[JonathanG]

Isn't it because it only applies to a special case?

[Colanth]

Yes - and Solitary posted a wall of text without pointing out the special case - which, alone, would have answered his question.

[josephpalazzo]

Yes - and Solitary posted a wall of text without pointing out the special case - which, alone, would have answered his question.

The real theory is General Relativity. If you would take a course, SR would occupy the first chapter, and GR, the next 19 chapters, sort of.  Think of Newton's F = ma. When a = 0, you have constant speed, a special case of F=ma. SR is a special case of GR as it deals only with inertial frames of reference. But in the real world, you have forces, you have matter interacting with other pieces of matter, you have acceleration, IOW, non-inertial frames of reference, which are the real thing to study - in space you are in free fall, the natural state of matter. So the free falling lab is where you do all of your calculations, draw your graphs, etc. It's like studying mechanics, which is divided into kinematics and dynamics. If you only study kinematics, your grasp of  mechanics will be very superficial. Similarly, if you only study SR, your grasp is very, very limited. The real thing is GR, where space-time is intricately linked to gravity. But to do that, you need to study quite a bit of mathematics, such has manifolds, tensors, and operations between tensors, parallel transport, geodesics, and the metric tensor, which defines the geometry of spacetime. If one had to resume GR in one sentence, it would be: matter curves spacetime, and curved spacetime determines the path of an object.

[Solitary]

That still doesn't answer the question of why it's called special relativity and not, say, ordinary relativity.

This: "Central to the discussion of special relativity is the idea of an inertial frame (or reference). This is basically a coordinate system, which might be attached to an observed object or to the observer, which undergoes no acceleration." Solitary

[Solitary]

Yes - and Solitary posted a wall of text without pointing out the special case - which, alone, would have answered his question.

The real theory is General Relativity. If you would take a course, SR would occupy the first chapter, and GR, the next 19 chapters, sort of.  Think of Newton's F = ma. When a = 0, you have constant speed, a special case of F=ma. SR is a special case of GR as it deals only with inertial frames of reference. But in the real world, you have forces, you have matter interacting with other pieces of matter, you have acceleration, IOW, non-inertial frames of reference, which are the real thing to study - in space you are in free fall, the natural state of matter. So the free falling lab is where you do all of your calculations, draw your graphs, etc. It's like studying mechanics, which is divided into kinematics and dynamics. If you only study kinematics, your grasp of  mechanics will be very superficial. Similarly, if you only study SR, your grasp is very, very limited. The real thing is GR, where space-time is intricately linked to gravity. But to do that, you need to study quite a bit of mathematics, such has manifolds, tensors, and operations between tensors, parallel transport, geodesics, and the metric tensor, which defines the geometry of spacetime. If one had to resume GR in one sentence, it would be: matter curves spacetime, and curved spacetime determines the path of an object.

So the special theory isn't the real theory when it came first? This doesn't explain why it's special when it is central to the theory: "Central to the discussion of special relativity is the idea of an inertial frame (or reference). This is basically a coordinate system, which might be attached to an observed object or to the observer, which undergoes no acceleration." And you don't need a wall of text about the general theory to know that. Solitary

[JonathanG]

"Special" has a very specific application here, as in a subset of a broader theory (in this case, general relativity).

The fact that it came first doesn't matter.  Physicists and mathematicians often seek to "generalize" their results, which makes them more powerful.

[Solitary]

"Special" has a very specific application here, as in a subset of a broader theory (in this case, general relativity).

The fact that it came first doesn't matter.  Physicists and mathematicians often seek to "generalize" their results, which makes them more powerful.

I never said that made it special, I said this does: no acceleration. Coming first is with reference to it not being the "real" theory. So of course it doesn't matter that it came first unless you think it isn't the real theory. You are correct that the general theory is a broader theory, but that in no way subtracts from the special being used when there is no acceleration or that it makes it not a real theory because it is used for a specific application any more than the general theory makes it real when it is also used for a specific application---accelerated motion.

The quote is for the Special Theory of relativity and explains it very well, why the need to bring up the general theory at all. If you know the General theory explain it in a different post so people that aren't familiar with it don't get confused by bringing it up here as if the Special theory doesn't matter because it isn't the "real" theory. And make sure you use abstract symbols, that most people don't understand, so you can show off your expertise with higher mathematics instead of sharing your knowledge with the dummies here.  :roll: Solitary

[Colanth]

The quote is for the Special Theory of relativity and explains it very well, why the need to bring up the general theory at all.

Because "Special Relativity" is really "a special case of General Relativity", so if you don't understand GR you can't understand one single application of GR (otherwise called SR).  It's like understanding 3 and 5 but not understanding addition, but claiming that you understand how to add 3 and 5.  Adding 3 and 5 is just a special case of general addition, and if you don't understand general addition you can't understand adding 3 and 5.  You can understand that they're 8, but that's not understanding adding them.

[Solitary]

The quote is for the Special Theory of relativity and explains it very well, why the need to bring up the general theory at all.

Because "Special Relativity" is really "a special case of General Relativity", so if you don't understand GR you can't understand one single application of GR (otherwise called SR).  It's like understanding 3 and 5 but not understanding addition, but claiming that you understand how to add 3 and 5.  Adding 3 and 5 is just a special case of general addition, and if you don't understand general addition you can't understand adding 3 and 5.  You can understand that they're 8, but that's not understanding adding them.

And I can say you can't understand General Relativity unless you understand Special relativity because general relativity is an addition to Special Relativity that came first, and that is why it is taught first. If one can't understand how things that aren't accelerating are relative to an observer, how can they understand that when they are accelerating they gain mass and time gets shorter as measured by an observer not accelerating, and that the length as measure by an observer standing still gets shorter when it's a lot harder to understand? If you can't understand X-Y=X and X+y=X , how can you understand V=V1+V2 divided by 1+V1+v2 divided by c2? Solitary

[josephpalazzo]

And I can say you can't understand General Relativity unless you understand Special relativity because general relativity is an addition to Special Relativity that came first, and that is why it is taught first.

Sure, if one wants to study dynamics, you first learn kinematics. If you want to study calculus, you first study algebra. But it's not the point of which comes first. Now imagine studying physics with just high school algebra. How much will you understand the laws of physics without calculus?

If one can't understand how things that aren't accelerating are relative to an observer, how can they understand that when they are accelerating they gain mass and time gets shorter as measured by an observer not accelerating, and that the length as measure by an observer standing still gets shorter when it's a lot harder to understand?

All of the effects of SR have been known for more than 100 years. SR, like Euclidean geometry, is a closed subject -- that is, we know everything that we can possibly know from it, and therefore, there is no active research being conducted in SR. Only crackpots and ignoramuses still question SR. The rest of scientists have moved on. The current research is in GR, coupled with thermodynamics and QFT.

Now in your case, you don't have the math, you refuse to upgrade your knowledge, you spend your time searching for websites to copy and paste, and then you want to discuss SR like a philosopher ruminating from his ivory tower. That's not how physics, or any other science, is done.

Now if I said to you that in GR, velocity as a concept is ill-defined, would you understand that? I think not. To come to that conclusion, you would need to study manifolds and parallel-transport. Or if I would say that in a Black Hole, the thermal radiation can destroy information, would you understand that? I think not. You would need to understand not only QFT per se as in how QFT gives you the Standard Model, but also how QFT is applied to GR, which is an altogether different field of research. And I can tell right off that this would be beyond your comprehension. It's not that I'm saying you're an idiot, it's just that I know you don't have the background to tackle these concepts. But you are an idiot IF you think you know this stuff better than I do.

[Solitary]

First of all, Time as measured by clocks in a gravitational field does not follow the rules of special relativity. Relative velocity in GR turns out to be a tricky concept as it is in SR, when one of the objects is accelerating.

You want to know the relative velocity of an object "now". In order to determine "now", you have to use some defintion of simultaneity. But one of the lessons SR tells us is that simultaneity is relative. If the velocity is changing with time due to acceleration, the concept of relative velocity also becomes ill-defined.

In a Black Hole, the thermal radiation can destroy information. But any thermal system can be assigned an entropy via the Gibbs law dE = S dT. Thus, we can calculate the black hole entropy by the noticeable effect that we can calculate the black hole temperature by the noticeable effect that the quantum radiation is thermal.

This is, I think, what people like you, are getting at when they say that black hole entropy is responsible for the information loss.

I could say it in another way, that black hole information loss is responsible for black hole entropy. The simple fact of the matter is that they are the same thing in slightly different terms. Solitary

[josephpalazzo]

I could say it in another way, that black hole information loss is responsible for black hole entropy. The simple fact of the matter is that they are the same thing in slightly different terms. Solitary

Wow! If it were that simple, we wouldn't have developped the Holographic Principle, the AdS/CFT Correspondence Principle and the present Firewall-Fuzzball controversy. The best physicists in the world haven't figured out that much, but you with backward knowledge of physics knows it all.  


//Keep philosophying from your ivory tower, you're making great strides.// sarcasm off

[Solitary]

I could say it in another way, that black hole information loss is responsible for black hole entropy. The simple fact of the matter is that they are the same thing in slightly different terms. Solitary

Wow! If it were that simple, we wouldn't have developped the Holographic Principle, the AdS/CFT Correspondence Principle and the present Firewall-Fuzzball controversy. The best physicists in the world haven't figured out that much, but you with backward knowledge of physics knows it all.  


//Keep philosophying from your ivory tower, you're making great strides.// sarcasm off

I never said I figured it out. Like you said they are principles and the Fire-Fuzzbal is controversial.
One aspect that both Einstein (Special Relativity) and Quantum Mechanics agreed upon is that time exists as a continuum where the past, present and future events exist simultaneously.

 Quantum information exist in two forms as holographic information within a 2D dimension (wave function) and as a 3D object within the space-time.Similar to the teleportation process of quantum information that occurs within Black Holes, a type of retro-causation process could also be occurring on a larger scale where by events from the past and the future are effecting each other.

For now, it seems appropriate to me, to assume both information conservation and no firewalls, seeking some way of reconciling the two. This might involve truly radical revisions in the foundations of quantum mechanics, or bizarre nonlocal dynamics outside the black hole. If we are forced to accept that firewalls really exist, then we will need a deeper understanding of their dynamical origin than the indirect argument AMPS provided.

Of course all this is in the quantum world and mathematics, not what we experience in our everyday lives. Solitary