Is the Lorentz contraction a 'fudge factor'?

Scythian1950, nyphdinm, and Mike1942f all have good answers.

Yes, you could say that it's a consequence of the constancy of c, speed of light in vacuo.

So you might ask, "Well, what causes that?"

Of course, you can always ask an endless chain of 'why's that?' questions, every time there's another answer, so the endpoint has to be some simple principle or model that you can pin all the results on.

The late John Wheeler had a wonderful analogy, in the form of a parable, for this. It is the parable of the surveyors. (This will be from memory, so some details will be off, but the essence of the analogy will be wholly intact.)

A certain town had a team of daytime surveyors and another team of nighttime surveyors. Both teams chose a benchmark at the center of the town square for an origin of coordinates. The daytimers had a high-precision compass, which they used for determining north, and from that, all the other compass directions. They went to work, busily measuring and recording positions of all the important buildings, and property boundaries, and other features in the town.

At sunset, the daytime team would pack up and the nighttime team would set up, and make all the same measurements; only for their reference north, they used the North Star.

When both teams had submitted their findings, the town council was confused. Every feature in the town was assigned different east-west (±x) and north-south (±y) coordinates by the two teams. Unable to decide whose results to use for official purposes, they handed the whole mess over to the town mathematician, Al Unpierre.

Al compared the two sets of results, and with a little trial-and-error, found that despite the different coordinates, the sum of their squares remained invariant. With this discovery, he did a few more calculations, and quickly hit upon the answer -- the daytimers simply had their directions θ=6º counterclockwise from those of the nighttimers. He was then able to write a simple formula that could be used to convert day (x,y) to night (x',y'), and back. He presented his findings to a grateful town council, who rewarded him handsomely.

What Al found was the rotation transformation that converted between the two sets of coordinates:

[x'] = [cosθ -sinθ] [x]

[y'] : :[ sinθ cosθ] [y]

[x] = [cosθ sinθ ] [x']

[y] : :[-sinθ cosθ] [y']

The analogy here is with motion which is confined to one space coordinate (x), and together with the time coordinate (T), any 'event'=point in spacetime, can be 'located,' at (x,T).

Another frame of reference (x',T'), which shares its event-origin, (0,0), with the 1st, and is moving along x at constant speed v, is related to the 1st by a "boost" transformation. Before presenting that, we note that in order to 'mix' space and time coordinates, they must be put into the same units. This can be done by using the universal constant, c:

t=cT

which converts times into spatial units. This will convert speeds into unitless numbers,

v=dx/dT; β=v/c=dx/cdT=dx/dt

Then the boost transformation is found to follow the rule:

[x'] = [ 1/√(1-β²) β/√(1-β²) ] [x] = [ γ βγ] [x]

[t'] : : [ β/√(1-β²) 1/√(1-β²) ] [t] : :[βγ γ ] [y]

where γ = 1/√(1-β²)

Now when one boost is followed by another, the speed of the result ≠ sum of the two individual boost speeds, just as when composing rotations, the slopes don't add, but the angles, θ, do. And knowing that slope = tanθ, you can verify that there is a quantity, the "velocity parameter" α, that adds when boosts are combined, defined by

v/c=β=tanhα

And then, γ=coshα; βγ=sinhα; so that

[x'] = [coshα sinhα] [x]

[t'] : : [sinhα coshα] [y]

[x] = [coshα -sinhα] [x']

[t] : : [-sinhα coshα] [y']

and so it looks like spatial rotation, except with hyperbolic trig functions in place of the circular ones, and with both sinh's having the same, rather than opposite, signs.

So just as rotating an object in space, changes its x and y-coordinates, while preserving its lengths, 'boosting' in spacetime changes x and t-coordinates (apparent lengths and times), while preserving proper lengths and proper times between the same pair of events. The lesson is that apparent lengths of things in motion are not their "real" lengths, any more than a building, seen from an angle, suddenly has a different width than it had when you were standing directly in front of it, because that apparent width is foreshortened, and not its real width.

Same with time lapses between events seen from different moving frames. The only difference between the spatial rotation, and the spacetime boost, is that the "metric" quantity has a "+" sign for rotations, and a "-" sign for boosts:

(length)² = ∆x² + ∆y²

(proper length)² = ∆x² - ∆t² : } {whichever of

(proper time)² = ∆t² - ∆x² : : } {these is positive

We often use analogies to help understand matters that are difficult to conceive hence I tend to see Lorentz contraction and special relativity from the view of material science. With materials, there is a physical property of the material called Young's Modulus which relates stress to strain, it's how you can squish or stretch something, there is also something called Mohr's circle which relates stresses to perpendicular strains, squish a marshmelow and the sides come out. Well the three dimenions of space and the dimension of time are all dimensions of space-time just as height, width and depth are dimensions of an object, hence the speed of light is the moulus of space time, and both time dilation and Lorentz contraction are perpendicular strains to the stress of velocity. Perhaps not a perfect analogy but it shows that the contraction is just a facet of space and time being the same thing. It isn't a fudge factor.

Pretty arrogant way to ask a question about someting you really don't understand. Simply put, the Lorentz contraction is a natural consequance of the speed of light being a constant regardless of the motion of the frame of reference read "laboratory") it is measured in. If I am moving toward a star at a high speed, and you are stationary and we both measure the speed of light form that star, we both ge the same numercial value for the speed. Einstein showed this in 1905. You can construct a simple thought experiment to work out th econtraction.

Consider a clock made up of two mirrors facing each other separated by some distance and a beam of light that bounces between the mirrors. A unit of time measured by this clock is one round trip of light between the mirrors. Suppose we build two such clocks and you take one and I take the other in a spaceship. I move past you at a high speed and what you see my clock doing is sending a beam of light along a slanted path that starts at one mirror at say, time t = 0, and hits the other mirror at time t1 but after I have moved a distance v*t1 where v is my speed. So the path is no longer vertical and is longer than the path your clock's beam travels. So yo can form right triangles and work through the math and you get the Lornetz contraction (or time dilation) out of it.

It isn't just particle accelerators - the consequences of the contraction apply to the clocks in the GPS satellites orbiting the earth and the mathematical adjustment has to be applied for accuracy of position even at their low speed because the clocks are so precise.

It is a real consequence of how the universe works.

We model what causes it, we don't "know" anything except what Nature shows us.

It is not a fudge factor, it is a scale factor based on perspective in 4D spacetime. Just as you can see a multi-story building between your thumb and finger (if you are far enough away), and can use surveying techniques to get corrected sizes. So we can scale from what we measure at rest, to what the moving frame will measure.

it's how the universe works, and is well-understood.

dark matter, on the other hand, is very much a fudge factor to explain observations that don't otherwise make sense. we postulate matter with certain properties to fit the observations but haven't detected it (a tough job, since it shares several key properties with neutrinos), nor have we demonstrated that something else may be happening instead.

It's the other way around, the "normal, Newtonian" world that we think we're living in is a fudge factor. What causes it? It's an example of an "approximate symmetry". For another example, we live and travel as if we're on flat ground, but we really aren't. We live on a ROUND planet. It just seems flat to us.