Can someone explain length contraction?

In simple terms

Suppose that you are an observer that is traveling with a bar of 1 meter of length. In your particular case you will always agree that the bar has a length of 1 meter.

Others observer traveling at a different speed than you will say that the length of the bar is different than one meter.

There is not mistake in their analysis. I am assuming that they will do a well defined experiment and reach these conclusions.

Now the trick is that the observers that are at different speed are comparing the length of the bar with their own inertial reference frame (their own coordinate system). That means that each one of them are measuring the length of the bar relative to different things, The concept is hard, but if you want to be good in relativity you need to get use to it.

Is it important that they are measuring the length with respect to different things?. The answer is yes. You can show that none of the observers will agree with the measurement procedure of the other one. The reason is that they will see that the other is making a mistake. This idea is related to simultaneity. In this website there is a detailed explanation of what I mean.

http://en.wikipedia.org/wiki/Ladder_paradox

Then length contraction is a formula which tell you if you where in this particular reference frame and you measure the length of the bar to be L and another person in another reference frame measure the length of the bar, how will the two measurements be related. Obviously the idea is to use Lorentz transformation to go from one frame to the other and this is exactly the idea of length contraction.

I hope that it helps. My recommendation is to spent sometime thinking about it and playing with it until you get the idea. It is really tricky.

Einstein knew from the Maxwell Equations and experiments to determine the speed of light that it was the same for all observers regardless of the motion of the observer. How is that possible?

We start with the Train and pitcher thought experiment.

You are standing on the ground next to a train track. A train going 100 km/hr is going past. On a flat car is a baseball pitcher that you know can throw 195 km/hr fastballs throwing toward toward you. You have a radar gun so you can measure the speed of the baseballs.

What speed would you measure if the train was coming toward you? (100 + 195 = 295 km/hr )

What speed would you measure if the train was going away from you? (195 - 100 = 95km/hr)

Now we start Special Relativity:

Toward the end of the 1800s scientists measured the speed of light compared with the speed of the earth in orbit. They expected that knowing the speed of the earth going toward the source of light the velocities would add and that when going away from the source of light the velocities would subtract. BUT that is not what happened. It did not matter if they were moving toward the source or away from the source, they got the same value: roughly 3 * 10^8 m/s. VERY STRANGE! They were sure something was wrong. It was not possible, based on their assumption that Time and Space were absolute (unchanging) for that to be true.

Einstein's insight: He thought,"What if the speed of light IS absolute and Time and Space could change to make that true? What does that do to everything else? He worked it out for all the physical quantities. It works! What you get is consistent with what we observe in experiments.

This site will let you play with what happens at near light speed

http://hyperphysics.phy-astr.gsu.edu/hbase/relativ...

AETHER

Aether was proposed to provide a medium to propagate electromagnetic radiation. It works well for that. The problem is that for every thing else, it does not work. The physical properties required make no sense. Lorentz developed what we now call the Lorentz Transform to calculate the motion of the aether relative to another Frame of Reference to explain the observed fact that the speed of light is constant for all observers. That means the aether with the photons moves relative to the observer. Now comes the problem: For the aether to do what it does it must have a Modulus of Elasticity greater than steel. Think of standing in a river of very fast flowing water, it explains perfectly the motion of the small floating twigs (photons) moving past you, but why don't you feel the motion of the water (aether)?

This is why Special Relativity replaced Aether. Einstein re-derived the Lorentz Transform showing that it worked just as well if you assumed that space-time (Einstein's Great Insight) could expand and contract based on the relative motion of observers. Einstein resolved the above paradox, so SR replaced aether.

Einstein Special relativity is NOT simple

the basic idea is when two observers are at rest compared to each other and the object they measure that is the "rest value:

for very very complicates math reasons if one observer is moving compared to the other they each measure DIFFERENT values and they are both correct

it has to do with the strange property of the universe that everyone measures C the speed of light the same no matter how they are moving

this is post U level science

Length is measured within the course of journey...The direction of the speed vector. The equation describing the contraction is l =l0 sqrt(1 - (v/c)^2); where l0 is the rest mass size, l is the relativistic size, v is the velocity wrt the relaxation body, and c is mild pace in a vacuum. L(v) = sqrt(1 - (v/c)^2) is the Lorentz turn out to be, the equal one that indicates in both the time dilation and the mass inflation. What l =l0 sqrt(1 - (v/c)^2) tells us is that an observer external the moving framework, gazing the relocating object whiz by using (if he might) from a aspect factor exactly perpendicular to the course of journey, the external observer would see the length of the visiting object lower consistent with the given equation. And for the reason that this is relativity the place the whole thing is relative, the individual on board the moving object would see objects external on either part stretch. For this reason, in just right scifi, we see the whole lot outside move from the side to the entrance of the ship. That outside stretching outcome with the aspect stuff moving forward and aft of the relocating frame from the space farer's point of view. But the person on board could be unaware his ship was shrinking and observers outside would be unaware their world was stretching. That is for the reason that to the gap individual he isn't moving relative to his ship and to the outside observer just isn't moving relative to his frame (the relaxation frame) both. On the Science Channel lately, they protected the shrinking through supposing a man on a motorcycle could travel virtually mild pace. On the streets where the rider whizzed with the aid of, his twin brother sat on a bench ready for the rider to come back and give him a ride. Whenever the dual noticed his brother whiz by way of (and not pick him up), his brother and the bike regarded foreshortened within the course of travel. The foreshortening is real as far as the dual brother sittiing on that bench is concerned. I wrote a bit of Excel application to do one of the vital relativity calculations. Here is what we find when journeying at 99.9% the velocity of sunshine: gentle speed =299,792,458 m/sec speed of Mass = 99.Ninety% of sunshine velocity relaxation Mass =1,000 kg Relativistic Mass =2.2366E+04kg Relativistic Time = 2.2366E+01sec Relative length = 4.47p.Cm you can find the rushing object (the mass) may have gotten smaller to about four.Forty seven% of its leisure size in the course of the pace vector. For illustration, a one hundred m spaceship can be about 4.5 meters lengthy wrt the external veiwer. And if that mass have been going 100% mild speed, the relativistic length can be zero. From the facet, it would disappear all together. Understand, from the front and back (in the direction of travel), the external observer would see no alternate. The contraction works handiest fore and aft. Thus, as the outside observer moves faraway from immediately perpendicular to the path of journey, the ship will start to take on its natural look.