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What is Special Relativity?

Thu, 3rd Dec 2015

Before general relativity changed the world came Einstein's first theory

Caroline Steel

Special relativity is a beautiful scientific theory; beautiful in the fact that it revolutionised the face of science by overthrowing Newtonian mechanics, and also beautiful in its simplicity. Einstein published his theory of special relativity in 1905; the theory describes how travelling at different speeds affects the length of objects and how fast or slow time passes. It is the simplest form of general relativity, as it only considers objects travelling at a constant speed - hence the title Ďspecialí. Accelerating objects are left for general relativity to explain. Einstein published his complete theory of general relativity in 1915, ten years after special relativity; this year marks the 100th anniversary of his publication.

Although special relativity is little heard of, it plays an integral part in all our lives. Alterations in length and time due to special relativity have to be accounted for in everyday objects, such as global positioning systems (GPSs). Because of the genius persona that society has assigned Einstein, it is often falsely assumed that special relativity is too hard to understand, when in fact the whole of special relativity is actually derived from two very simple principles.

The Principles of Special Relativity

The First Principle of Special Relativity

You are sitting on board a train, willing the train to pull away. Finally you hear the beeping doors, indicating your train is about to depart. You look out of your window at the train on the adjacent track and watch as you glide past it. Only, once youíve pulled past the other train you donít see the world rushing past, but the completely stationary station. It was the other train that pulled off in the opposite direction.

Steam train

Everyone can relate to this story, it has happened to all of us. This is because, once you have stopped accelerating, there is no way to tell if your train is moving or not. Once you are moving, everything inside the train behaves as though you are stationary; your cup stays still on your table and you can walk up and down your carriage freely, as if itís not hurtling forward at 60 mph. This is because the laws of physics are the same regardless of whether you are stationary or moving at a constant speed.

But, when you look out of the window and see the world zooming past, does that not tell you, you are moving? No, it does not! All that tells us is that we are moving relative to the Earth, but we canít really know how fast we are moving, or even if we are moving at all, as the Earth itself isnít stationary. The Earth is orbiting the sun, the sun is orbiting the center of our galaxy, and our galaxy is also constantly rotating, not to mention that the universe is constantly expanding.

There is no way to know if something is moving or not; this is the first principle of special relativity.

The Second Principle of Special Relativity

You and your friend Erwin each buy a high-speed rocket to fly in, and decide to show off to your friend Rosalind. You have a race; Rosalind stands on earth looking up at you and measures your speeds. She measures your speed to be 20,000mph and Erwinís to be 15,000mph.

1 special relativity

However, Erwin is also measuring your speed and in his opinion you are travelling at only 5,000mph. That is because 5,000mph is the difference between your two speeds. Therefore, you have no absolute speed, how fast you are travelling depends on how fast the observer is travelling in comparison to you.

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To test this observation further, you launch a ball out of the front of your rocket at 1,000mph. To you the ball is travelling at 1,000mph, Rosalind measures it to be travelling at 21,000mph and Erwin measures it to be travelling at 6,000mph. This again demonstrates how speed is relative, the ball has no absolute speed of its own and its speed depends on how fast the observer is travelling in comparison to it.

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Both you and Erwin discover a new button which turns on super powerful thrust engines in your rockets. When you press your button you travel at half of the speed of light (c/2), and when Erwin presses his button he travels at one quarter of the speed of light (c/4). You decide to test to see if your previous observations also apply to light; you flash your torch, releasing a beam of light. You measure the speed of the beam to be the speed of light (c). Based on your previous observations, you would expect Rosalind to measure the speed of the beam to be 1.5c, because she observes a beam ejected at speed c, from a rocket travelling at c/2. However, this is not what happens, Rosalind also measures the beam to be travelling at c. In fact, Erwin also measures your beam to be traveling at c. You, Rosalind and Erwin all record the beam to be travelling at exactly the same speed.

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The speed of light is the same for all observers; this is the second principle of special relativity.

How can the speed of light be the same for all observers?

If you think that this is extremely strange, you are not alone. The fact that light travels at the same speed for all observers directly contradicts the previous example using the ball. However, it can be explained. We all know that:

Speed = distance/time

In order for all observers to agree on the speed of light, distance and time change depending on the observerís speed. The faster you are travelling the slower time moves and the more objects shrink! So your watch is moving slower than Erwinís watch and Erwinís watch is moving slower than Rosalindís watch; a ruler on board your rocket is shorter than a ruler on board Erwinís rocket and Erwinís ruler is shorter than Rosalindís. These alterations mean that everyone measures the speed of light to be the same.

For speeds that arenít near the speed of light, time and distance change by a minuscule amount. Every time you get the train, time does slow down and objects do shrink, but by such a small amount that you could never detect it. However, there are instances this difference is significant.

Special Relativity in Action

If we were able to travel closer to the speed of light, special relativity would have large consequence. For example, you decide to go off in your rocket and travel round space at half the speed of light (c/2), for four years. However, when you get back you find that in fact 30 years have past for Rosalind! This is because you were traveling faster than the earth so time was passing slower for you than for Rosalind Ė resulting in you only aging four years compared to her 30.

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Although examples like the one above do not yet occur in everyday life, the effects of special relativity do frequently have to be accounted for, especially in electronics such as GPSs. Most people have probably used a GPS. They are so commonplace that it is easy to forget how clever they really are; you can stand anywhere in the world with a device as small as your phone, and be told your position on the globe to within less than half a meter!

GPS receivers work by receiving a signal from at least four out of 24 of the positioning satellites we currently have in orbit around the earth. Each emits a signal, which is picked up by the receiver. The receiver then calculates its position by measuring the time taken for each signal to arrive from the satellites, which it knows the positions of. To ensure that the receiver and the satellite agree on the time the signal is sent, special relativistic effects have to be accounted for. Due to the fact that an observer on the ground sees the satellites moving relative to them, special relativity predicts that their clocks should move more slowly. If this difference in time were not accounted for, errors in position would occur at a rate of ten kilometers per day!

2015 marks the 100th anniversary of one of the most ground breaking scientific papers ever produced; a paper that gave the world space travel, satellites, GPS and a greater understanding of our universe. Letís hope we donít have to wait another 100 years for the next one.

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Relativity states that "the speed of light remains constant"..and special relativity for me simply states that "slow u go,fast u die!"..."fast u go the, slow u die!" chintan, Thu, 3rd Dec 2015

https://www.quora.com/What-is-the-difference-between-general-and-special-relativity ijaz, Fri, 4th Dec 2015

As stated via Special Relativity(SR), there is no way in which you can detect whether or not you are at absolute rest in space, you therefore have no detectable absolute reference, and in turn, it also becomes impossible to measure absolute motion. Thus we are left with relativity instead. Physicist say that it is logical for these absolutes to be ignored, since these absolutes can not be detected. This then gives the false impression that the absolutes do not even exist. In turn, for over 100 years, the simpletons of this world have been told to not be interested in the absolute cause. How on Earth can SR be absolutely understood, if these absolutes are to be excluded. Obviously there is an absolute cause behind SR. SR does not just occur as the result of some kind of magic, meaning there is an absolute foundation of which SR resides within, the foundation which makes SR occur. With the absolutes revealed, SR becomes so easy to understand that even the simpletons themselves can understand it. All of the bizarre phenomena of SR vanishes in a flash. Sean, Fri, 4th Dec 2015

... overthrowing Newtonian mechanics ... I disagree. As long as the velocity is sufficient low Newton is my man. I would say 99,99 % of all calculations in mechanics are done by the way Newton showed us. Bernd, Sat, 5th Dec 2015

This is a typical explanation of Relativity theory.

It's never done anything for me, and it's not actually how Relativity theory was developed.

Einstein didn't go "I'm guessing that the speed of light is constant-> Relativity!" no, he got the basic idea from Lorentz and worked it backwards. It turns out much easier to go backwards than forwards, like Lorentz did, but you still lose something, you lose the 'why'.

So, it's not well known, but you can actually *derive* Special Relativity from Newtonian Mechanics and Maxwell's equations. But you have to do it really, really, really carefully. And that's what Lorentz did.

If you do this, you find there's three things that happen to a system of charged particles (i.e. atoms and molecules) when they accelerate:

1) they get shorter ("Lorentz contraction")
2) they move more slowly ("Time dilation")
3) there's a fixed difference in time between the front and back ("Lack of simultaneity")

From these three systematic distortions that happen to material things, you can show that, due to what happens to your rulers and clocks, that a system of rulers and clocks will always measure the speed of light to be constant, and you can prove the principles of relative motion.
wolfekeeper, Wed, 9th Dec 2015

"What's the difference between general and special relativity?"

The essential difference is that spacetime have not to be warped by masses or energy, to apply special relativity. If it is, general relativity have to be used.
So, for example, in absence of massive objects or others which can warp spacetime, we can use SR even to treat accelerating spaceships, as in the "twin paradox".

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lightarrow
lightarrow, Wed, 9th Dec 2015

Lightarrow,

We can't use SR to teat accelerating spaceships.

SR works with non-accelerating reference frames. Constant velocities. As such it is a good way to demonstrate and explain relativistic effects.

Real life situations are a bit more complicated than that and that's where General Relativity is used. arthur.manousakis, Thu, 10th Dec 2015

One thing General relativity and Special relativity have in common, are both can alter space-time and lead to the exact same changes in space-time. These two are equivalent, relative to space-time, at some level. They are two paths leading to the same place.

General relativity changes space-time via mass and distance but not by time. It does not matter if gravity cause the mass to collapse quickly or slowly, the final space-time well is only dependent on the final mass-geometry. With special relativity changes in space-time occur via mass, distance and time, with the starting mass not critical to the result. The  seems to imply an equivalence of mass and distance (GR) and time and distance (SR). This reduces to mass equivalent to time.

The equivalence of mass and time.

Consider two space-time references that exist side-by-side. The one on the left has time moving faster and the one on the right has time moving slower. In this hypothetical example, I am in the left reference (faster) and I place my hand in the right reference (slower) to dribble a basketball. Because time is moving slower in the right reference, where my hand and ball is, if I try to dribble the ball at the correct speed for my reference, I notice the ball moves slower.

What I will need to do is push harder, with greater force, to make the ball move at the correct speed for my reference. After the ball hits the ground and rebounds, as I go to push down on the ball, I notice the ball, although moving at the correct speed, now appears to have more inertia. The difference in time, between these two reference, has the impact of altering the inertia of mass. While the higher force at the same speed seems to add to more mass, since velocity is normalized. puppypower, Thu, 10th Dec 2015


We can't use SR to teat accelerating spaceships. Guess why I have specified that? Because your is a common mistake.And were I wrote that you have to work in the accelerated reference frame? You have a spaceship accelerating with respect to an inertial reference frame and you make your computations in that inertial frame.But you can't invoke the equivalence principle in the sense that spacetime does not become warped only because you are in an accelerating (instead that inertial) frame: the spacetime stays the same (if that is what you intended to say).

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lightarrow
lightarrow, Fri, 11th Dec 2015

One main difference between SR and GR is special relativity SR defines one space-time reference, while GR usually defines a range of space-time references; space-time well.

With SR we can go anywhere in the rocket ship and be in the same space-time reference, since the entire rocket is in motion with the same velocity=V. With GR the surface of the planet is in a different space-time reference than the core of the earth. The core of the earth is like the twin that ages slower, since it is deeper in the space-time well.

With GR, if I was on the surface and I could stretch my arm to the center of the earth and dribble a basketball , I would notice changes in inertia relative to the surface. This is due to the equivalence of time and mass. This equivalence allows  the space ship, via SR, to simulate any reference of the earth by altering speed. The time bridge used to alter inertia is relativistic mass.


puppypower, Fri, 11th Dec 2015

I have always wondered about space time and why the speed of light should be a posit and not an effect of something more fundamental. I respectfully suggest the answer may be within the atom. If the fundamental particles with mass that make up the atom were to spin with a tangential velocity of C. The effects of SR are the same. A sphere spinning about its axis has an interesting property. If you move the axis in any direction the mean velocity of the spinning object does not change provided the spin velocity is greater than velocity of the axis movement. As the axis moves the forward motion is deducted from the backward velocity as the edge spins away and adds to the forward motion as the opposite edge spins towards the motion. The effect is the mean velocity remains constant. If you do the vector diagram you will find that the resultant combined velocity is √c≤-v≤. as the distance S is equal in each case t1=s/c and t2=s/√c≤-v≤. so λ=t2/t1=c/√v≤-c≤=1/√v≤-c≤.This of course is SR. In addition if these particles have a total mass m. Then the kinetic energy of the particles spinning is Ĺmc≤. If this is the total energy trying to get out then the same energy must be available to stabilise the atom. So we get energy in the atom to be E=mc≤. All the results of SG are identical in each case, but we now have fundamental time relating to the fundamental particle and space being just space. This obviously causes problems with GR. If you follow the argument further then C must be the speed of energy transfer, gravitational lensing becomes automatic and there are other explanations for orbital distortion in mercury. dhjdhj, Fri, 11th Dec 2015

Did anyone spot my deliberate mistake? the calculation is right but Time dilation is given by λ=1/1-v≤/c≤. Sorry not used to the formula producing system on the web site dhjdhj, Fri, 11th Dec 2015

Simple I can understand SR with my schoolboy maths but GR defeats me with tensors and whatnot syhprum, Fri, 11th Dec 2015

In my last post I pointed out the observation that with SR the entire object in motion with velocity V has the same space-time reference. While in GR, an object, like a planet or star will exist in range of space-time references; space-time well.

Based on this difference we can simulate GR with SR if we accelerate the space-ship. This allows the space ship to move along the space-time well via incremental increases in velocity. Since velocity is d/t and acceleration is d/t/t, we added time to help us get closer to the impact of GR mass.

GR brings up an interesting consideration. Since GR can define a space-time well, that will set up a range of references, then the core of the earth or star exists in a different space-time reference than the surface. The core is like the twin in the twin paradox that is aging slower. The surface twin ages faster. In this example, GR sort of simulates two SR references; stationary and moving twin. How does the time difference between core and surface, impact the interaction of the core with the surface? GR is creating a potential in time that is not only perpetuated by the well but is expanding over time. Distance is contracted but does not compound like time. In the twin paradox, one twin is younger but he is not permanently thinner in space.

One way to answer this is to start with two identical factories that make widgets, side by side, but in two different space-time references. Both factories are making 1 defect per hour, and both using X energy per hour.  The one moving slower in time, will appear to use less energy and generate less entropy on a normalized time scale. The 2nd law has less impact on the slower core reference in a normalized scale. Entropy will still increase but at a slower rare; normalized.

The result will be a dual potential appearing between surface and core connected to energy/entropy, due to the time difference. This is reflected, in part, in the pressure of the core generating heat; more energy, as well as limiting the degrees of freedom in the matter of the core for less entropy. One might also expect a flux of energy/entropy from core to surface, which in turn, would reflect the time potential difference. However, the well is also causing the references of the core and surface to linger, expanding the time gap.

One interesting observation is the core of the earth rotates faster than the surface. One way to explain this is connected to the release of energy and entropy in the core, due to the lingering time potential with the surface. The expanding universe shows a net flow in the direction of expanding reference.

Another way to look at this is the core is expressing the past, when the earth rotated faster. puppypower, Sun, 13th Dec 2015

This is a great article, very clear and well explained, certainly has improved my understanding of relativity and I love the diagrams! lorentzviolator, Wed, 6th Jan 2016

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