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There are some great technical answers here so let me give you the more simplistic answers. First off you're asking how a moving charge creates a magnetic field and implying that it is because of a Lorentz transformation. This is not a correct association.

 

Currently in physics, there are some stopping points at which we simply say "It does", such as mass bending space-time and charges leading to magnetic fields. It just does and we don't have a deeper explanation for it. You can feel that we should keep looking for something deeper or you can say we've hit bottom, but that is meta-physics. In physics it is easy to get confused about the subtle difference between a description and an explanation.

 

We do, however, have mathematical models for these events that accurately describe a multitude of changing attributes. These models allow us to view the event from very different perspectives.

 

A Lorentz transformation is specifically a perspective shift.

 

When I model a ball and the forces governing its motion in three dimensions, there are a variety of points, vectors, etc that are part of that description. You simply see a ball on a screen. If however, you want to see the back of that ball, you may simply click and drag it somehow, but what is happening inside the computer is complex mathematical calculations of all the various points and lines. This is a transformation. (usually a "matrix transformation")

 

In a game in which you can throw a ball, there are things such as the weight of the object at any particular point, the effect of gravity on it, the angle at which it strikes a surface and its momentum. There is a vast host of considerations and inter-dependent calculations.

 

If I want to change what you see happen on the screen, (where the ball goes) I could move the ball or I could move you and if there was nothing but white space, you wouldn't prefer one explanation over the other.

 

With a Lorentz transform we also add another entire dimension that skews your perspective of a moving object and their perspective of you.

 

The Lorentz Transform and the speed dependent calculation typically called gamma, are a representation of that skewing. It's an angle between perspectives.

 

It is a way to determine what will be different about two different perspectives.

 

Finally, there is the one very confusing part caused by the loose use of the word "transformation". We can use it to transform from our skewed perspective of them, to their perspective of themselves and vice versa, but it does not transform from our perspective of ourselves to their perspective of themselves as may be implied linguistically.

 

This is why there is some confusion surrounding the supposed "Twins Paradox" because there is an implied expectation of a second step in a "transformation".

 

A "transformation" is a keyword meaning very specific things in mathematics. For instance, if I simply moved the ball on the screen instead of rotating it, that might be a simple translation instead of a transformation.

Creation time: Apr 11, 2013 08:27 PM PDT

 

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The Lorentz transform was developed specifically by studying the relationship of a moving interferometer with respect to a stationary medium. Lorentz did this a s first step in the development of Lorentz Ether Theory (LET).

 

Lorentz believed the ether automatically created an optical illusion at all speeds. He also believed that light speed was constant with respect to the medium but simply appeared to be constant with respect to a moving observer. IE it behaved like any other wave in a medium but something made it appear not to. He believed this happened through a physical shortening of the moving observer. (interferometer)

 

To create this perspective illusion is a simple application of angles. When you have one beam of light in a Michelson interferometer moving crossways and the other moving into/with the wind it's a simple relationship like a graph.

 

The crossways beam is like the hypotenuse of a right triangle and the beam of light travelling into the wind is the bottom leg while the actual crossways bar of the interferometer plays the role of the third leg.

 

When you think about it, if a spherical signal is emitted in a medium as an interferometer goes by (one perspective of the experiment) there is only one angle from the center of the emission at which that signal will hit the moving crossways mirror so that it can reflect back.

 

The point of his initial formulation was that a spherical emanation of light travel back and forth between moving mirrors but arrive simultaneously at the moving "origin" and it's important to note that this is all purely classical mechanics.

 

So there is only one length the co-moving arm of the interferometer can be shortened to because there is only one angle at which the original signal will strike the crossbeam mirror.

 

So as you can see by the image above, it's a little known fact that the change factor can actually be calculated through trigonometry functions. (change factor for .5C=1.1547)

 

And trig functions are inseparably related to Pythagorean theorem.

Creation time: Dec 04, 2013 06:19 AM PST

 

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"If you can't explain it to a six year old you don't understand it yourself" -Albert Einstein

 

I always try to adhere to this principle in my explanations and I think you'll find, as many others have, that I succeed where others fail.

 

To understand the Lorentz Transform you need to understand just the Lorentz factor and Lorentz's reasoning for coming up with this number we now call the "change factor" or "gamma."

 

To understand Lorentz's motivation you need to understand that he was developing a mathematical theory based upon mechanical wave system and the medium which governs it.

 

He was creating a mathematical model of an illusion. He believed that light was affected by the motion of the substance its waves propagated in or conversely the motion of our instruments through that medium.

 

The illusion he mathematically modeled is a situation in which even though light had to travel through more medium in one direction than in the other, everything is "squashed" together just the right amount that our measuring sticks etc would perfectly hide the effect.

 

Since then, Einstein insisted that there was no medium and the illusion was therefore reality. This transition of the math is what makes it so difficult to understand.

 

For a full development from scratch, please see: 1) Derivation of Lorentz from Classical by Shiva Meucci on Posts

Creation time: Nov 24, 2014 07:46 PM PST

 

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I must apologize for everyone attempting to explain the reason for maths with maths. It would give Alfred Tarski a giggle.

The experimental basis of the Lorentz transform is the Michelson-Morley experiment.

Let’s first break it down that the simplest component that represents the transform is the factor of change. It’s what ties it all together. So, since everyone should know that math is a means, not and ends and that it’s a tool for describing something else, let’s refine what you’re asking down to a more fine point.

What was Lorentz describing with the change factor and why?

The answer is that he was attempting to describe how the heck a Michelson interferometer could show a null reading if light is a wave travelling through a medium and that medium is moving with respect to the interferometer.

A who did what-what?

At the end of the 19th century, everyone knew light was a wave, and we know that waves move at a specific speed in their medium. (the stuff squishing up and stretching out to make a wave) And they figured the medium for light was still and all the planets just zoomed through the stuff. Well, instead of thinking as us as the ones moving, it’s easier to just think of ourselves as stationary and the aether as a wind, kinda like sticking your hand out the window in a car. You call it a wind but know the air outside is stationary and you’re just zooming through it. It’s just easier to see it as wind.

So, the waves of light would be carried along with the medium they are in just like the waves on the top of your coffee in the car as you zoom past a cop directing traffic. The problem is that if the police officer was looking at exactly how fast a particular wave of coffee was approaching him from his perspective on the ground, and he could shoot a radar gun at one of those waves in your coffee mug, the speed he would get is the velocity of the car (v) added to the normal velocity of the wave in its medium or (the normal speed inside the cup AKA “c”)

So that means this coffee obsessed police officer would measure coffee waves coming toward him at v+c and coffee waves going away at v-c.

Now what Michelson’s experiment was trying to do was basically the same as the cop’s radar gun, but Michelson was looking for light waves travelling faster and slower than normal. Michelson thought there was an “aether wind.”

That is to say, he thought everything is immersed in a river of “coffee” (AKA Aether) flowing past us and the waves on the surface (Light) getting carried along with the current could be measured.

To understand Lorentz’s motivations you must understand Michelson’s

Even though the experiment was designed to detect sped up and slowed down waves, and everyone knows we’re moving through the universe, it detected no difference between speed of the waves in one direction or the other. The experiment, however, wasn’t a little radar gun pointed at waves; instead he set up a wave “race” to detect the difference between waves that could run across the current and ones that had to run against it.

If some waves had to travel across the current and others against it, then if you make waves race back and forth, some will be at a disadvantage.

This is what his device did, it compared the speed of waves going one direction against waves going the other.

Imagine if you made two swimmers race each other in a river but you’re devious. The river is 10 meters across, so you just stick some stakes in the ground 10 meters apart along the river. Now, if you were a jerk, you could make one swimmer go back and forth across the river and the other one swim up to one stake and back down to the other and just pretend it’s a fair race.

Michelson figured he could make waves race like this and he knew that even when they are moving the same speed in the medium (swimming the same) one has an advantage over the other.

Though this race should obviously be unfair, Michelson’s experiment detected no difference between the swimmers’ arrival times. When you calculate it out, the swimmer going up and down in the river should definitely have to swim farther than the one going back and forth. Therefore the “null” result in arrival times made no sense.

 

This is the CRUCIAL part VERY few understand!! To understand what the Lorentz transform is, you must know what it describes!

Lorentz accepted that there was still a river as an undeniable fact. He accepted that the river was flowing was an immutable truth. He accepted the axiom that all the swimmers (the waves) move the same speed in the water and will be carried along with it.

Like a scientist watching an illusionist, he decided there had to be a trick and his friend George Fitzgerald suggested just what the smoke-and-mirrors illusion might be!

Shortening… The aether wind makes physical objects scrunch up ONLY in the direction of the wind (the longer path the swimmer would normally have to traverse) such that when you try to measure things out you get tricked because everything in the world, including you, gets all scrunched up in one direction and not in the other. He figured maybe the forces between particles are increased along the direction of the wind flowing across them.

Since light itself gets carried along with the current, we can’t even see our measuring stick lengthen and shorten as we point it different directions. It’s a crazy optical illusion right alongside the physical weirdness.

And with these things accepted as TRUE, he decided to create exacting math to describe the special illusion that would make it possible for swimmers going up and down the river and swimmers going across it to arrive back at the start at exactly the same time even though they travel the same speed in the water. IE the actual distance they have to swim becomes the same because the markers along the river-side we measure out, aren’t really as far apart as we think they are.

The reason to create a formula for the change factor is just to allow for every different possible wind speed up to the wave speed. (If the river is going as fast as, or faster than the swimmer, the one going upstream will never make it to to first stake to be able to swim back)

 

So the basis of the Lorentz transform is describing the effects a moving medium has on light and our perception of it. (and less importantly, objects)

Unfortunately, what happens when you abstract mathematics and disconnect them from physical phenomena you can get very confused about what you are describing with math. (it happens when trying to debug a computer program too)

Even worse though, you might end up one of the poor sods who doesn’t understand that math is a representative modeling tool that literally means nothing without linking it to reality. (there are actually a lot of these dysfunctional minds)

When we study the experiment a bit further, we will find that the whole experiment, even though we’ve created equality in path lengths, the total length the swimmers have to go is further than in a stationary environment.

If one thinks of time as just a measure of changes in the world and all particle interactions are electromagnetic, then if you’re moving through the medium and it takes longer for particles to interact in any way, then all things that occur in a frame moving through aether take longer to occur. Everything from clocks ticking to your brain thinking. (IE time dilation comes naturally from attempting to solve the illusion)

If you’d like to understand the experiment a little more please see my blog posts below. They progress from the simplest to the hardest concepts in relativity and do so from the Lorentz perspective.

(Numerous diagrams and a tiny bit of hyper-simple maths included)

Relativity Demystified

Creation time: Mar 15, 2017 07:49 PM PDT

 

 

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Yes and no. You must watch your presumptions very carefully.

Is there a difference between appearing and being? When you watch David Blaine shove a knife through his heart and you’re only allowed to inspect visually from a distance. Is appearing and being the same?

When you use Occam’s razor to eliminate all those things you do not directly test then the theory only supports the “fact” that the illusionist pierced his heart with a knife and no other description of unobserved phenomena is technically allowed in science.

“Why are you talking about this?”

Because, it’s not as simple as you’ve made it sound in a single statement. That’s oversimplification and it can lead to some serious problems like I’ve described above

Lorentz and specifically Larmor described constancy as an illusion caused by moving through a medium light was propagating in. The math, like any math in a theory, describes particular phenomena. The math is just a description of events and the events Lorentz and Larmor described was an optical illusion.

Anyone attempting to say it’s simply an extension of Galilean relativity is grossly misleading you.

Constancy is a behavior never seen or conceived of in any other situation or phenomena in the universe. Never before and never since. Understanding this fact is CRUCIAL to understanding exactly what is proposed by Einstein and Minkowski’s version of relativity.

Galilean relativity is about the phenomena being the same and also includes sound waves because the medium is carried along inside and therefore with the boat that Galileo used as a description.

If we allowed air o flow through the boat, or for that matter, through a plane, then galilean relativity would no longer apply to sound in the same way. It applies generally but it doesn’t defy mechanics.

Until relativity any scientist anywhere who wasn’t insane knew that a wave is not a thing on it’s own, it’s a description of a motion of a medium. Just like a jog that a jogger takes cannot exist if you remove the person jogging, a wave cannot exists without the thing waving.

That’s why one must specify that the medium for sound to travel in must be carried along with the boat or the plane for galilean relativity to apply.

Special relativity, however, proposes multiple new effects to the universe!

First is the ability of an action to exist without anything acting.

This removal of the medium allows light to “play the role of an infinitely great speed” as Einstein put it in OEMB and then this leads to the idea of constancy, to be physically real, instead of a faulty perception, for all observers.

For this to be mathematically possible one must add another dimension to account for the conflict between observers and then one must also propose that time is not the same from one place to another but that to xist in a different place is to also actually exist in a different time as well. This is in ADDITION TO clock rates not running the same and is not the same effect.

“Sounds like you saying relativity is wrong. Are you dumb, crazy or both?”

No, I’m saying that the precursor theory used the exact same math to describe the same phenomena in a subtly different way that doesn’t require us to propose lost of new effects for reality.

Length contraction, time dilation and the illusions of light constancy and relative simultaneity existed in the precursor theories BEFORE Einstein decided that the illusory parts were real. (and truthfully when you read his writings he didn’t know he was proposing that until he was pressured into using Minkowski conventions)

“Wait, you’re talking about aether and that’s eliminated by Occam’s razor!”

Oh really? So you’re saying that on one hand we have a medium that is difficult to probe so we can just eliminate it. …but then eliminating it requires for us to presume numerous completely and radically different non-physical effects for reality as well as adding infinite additional 3D realities. (that’s what reifying a 4th dimension does) and THAT’s using Occam’s razor?

“This is bull crap. Science is about what you can measure and you’re asking me to believe in something that can’t be measured! That’s pseudoscience!”

No, I’m not. You’ve simply been told it cannot be detected when in the intervening 100 years, every detection of it has been called something else or otherwise explained away.

…and mst importantly I’m simply saying that just because you haven’t figured out what David Blaine did to shove a knife in his chest doesn’t mean you should default to the irrational idea that he actually DID shove it in his chest, simply because you’re not allowed back stage. That’s irrationality dressed up as science. THAT is pseudoscience, not Occam’s razor.

At this point the amount of information I must relay becomes so enormous all I can do is hint at it.

The point is to focus on the fact that what seems like an open and shut simple case is not what it looks like at all.

There is an interpretation of the information that is more rational and also preserves the bulk of modern science almost untouched except for eliminating magical and non-physical beliefs.

One of the things that I can quickly call out is that the Sagnac effect behaves exactly as expected by classical and falsifies constancy.

Another is that, while the Michelson experiment should be null according to Lorentz aether as well, it should not be null if Fresnel’s proven idea of partial aether drag is correct. (coefficent of diffraction started as coeficient of aether drag and then was proven by Fizeau)

And when you examine Michelson’s original results you find that there is systematic signal in exactly the periodicity expected. (two oscillations of reading per 360 degree turn) It’s not only non random but exactly what one would expect of a partial dragging effect caused by the open air of the experiment.

This was replicated tens of thousands of times by Miller and there’s a huge history I won’t get into involving all the issues with interferometer setup and the use of monochromatic versus white light, but like I said… oceans of information so I’m just hinting.

To recap: It’s just not that simple.

The Lorentz transform is derived by describing the propagation of waves in a medium one is traversing when objects used in observation are altered by that state of traversal. The change of objects (shortening) creates an optical illusion which makes light seem constant in TWO-WAY light experiments. (It also alters electromagnetic interaction times thus altering the actual time for phenomena like brain waves to occur.)

…and no one-way speed of light experiment has ever been performed to differentiate Einstein’s version from Lorentz’s. We just picked one we liked better without experimental confirmation. (they’re called tests of light speed anisotropy for another hint)

Relativity Demystified

Creation time: Jan 14, 2018 01:26 AM PST

 

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The Lorentz transform is method for examining different perspectives of time, size, and position in space.

It is basically a mathematical form of the relationship between (at least) two perspectives that are skewed from one another. It is how we can switch between one view of a situation and another when relativistic effects like time dilation and length contraction are occurring which can make one observer's experience skewed from another.

It is more intuitive to understand it from the creator’s original reasoning than its current use!

It was created by Hendrik Lorentz on the suggestion of another scientist George FitzGerald to solve a weird problem that had developed in the scientific community. It was basically a settled fact that light was a wave, because numerous experiments on light showed behaviors only waves have.

At this point in history, a wave was understood as something that -cannot- exist on its own any more than a “jog” can exist without someone to do the jogging. A wave is just a motion of particles as they move around against unequal elastic forces after a disturbance from equilibrium.

(there’s another kind of wave called transverse but the principle is the same)

So if there is a vacuum in space, (no air particles) then something else must be waving! Something undetected is there! This was named “Luminiferous aether” (spelled “ether” in old literature) in honor of older concepts of space. The immediate question that occurred to people was “Where is it stationary?” or moving? Is it stationary with respect to the earth, our sun, the center of the galaxy, or what? Furthermore, is it turbulent and mixing around in currents or is it more like a jelly or a solid?

Albert Michelson, the first american Nobel prize winner, decided it was likely stationary with respect to the center of our galaxy instead of centered on us or our sun and then he also assumed it was more like a solid or a grid instead of a fluid. So he ignored the possibility that we might be caught in a current.

He then came up with an ingenious experiment to measure the speed of the earth with respect to this aether by measuring the effect of the wind that would be created by the earth passing through it. We already knew that the earth was moving around the sun at around 30 km/sec so he figured out that light would have to go further upstream than it would across so he made light race itself with a device called an interferometer.

Above is the simple idea and below is the more complex explanation found on the Michelson–Morley experiment Wikipedia page.

To his complete flabbergasted surprise, it seemed to be unaffected by the earth’s motion. Light didn’t seem to be affected by the aether wind he predicted.

Now, forgive the community of the time for ignoring the idea of currents, because during that day they had no examples of things like superfluids which have weird behaviors. They just assumed that, since light waves behaved like mechanical waves in a solid, the aether must be like a solid. Heaven forbid it’s like a superfluid, because then the result could be meaningless since moving with a current is like being stationary, or local wind could be crazy fast compared to the rest of the currents. (or something in between)

The Lorentz transform was designed to explain this odd result in aether.

That’s right, it’s a mathematical description of aether’s affect on light and matter. If you know the topical story about relativity this should be a little mind-boggling. You normally hear that relativity eliminated the aether and the Lorentz transform is the central calculation of relativity that deals with the length contraction and time dilation effects. Something should seem terribly wrong with this narrative. Follow a bit further and it should clear up a little.

This is where FitzGerald suggests how to solve the problem of the null Michelson experiment while retaining all the aether science up to that point. (we couldn’t go back to an earth centered universe) He suggested that perhaps the aether strengthens the bonds between particles in the direction of the wind and this perspective skewing is undetectable for us. Our rulers shorten up and the extra distance light would have to travel because of that weird upstream/downstream effect would be nullified by the shortening it causes.

So upon suggestion from FitzGerald, Lorentz presumes we are indeed moving through the aether but just can’t detect it because of an optical illusion. (just like an illusionist’s trick, light’s speed appears constant)

It turns out that with further examination from the scientific perspective of the time, if light has to travel further then all particle interactions would be plagued by this extra distance for the signal to travel. It was known back then that even solids are just collections of particles that influence each other from a distance and the signal for one to move the next would have to travel farther in the wind. Even applying force to a steel bar travels in a wave up the bar from particle to particle. Every interaction would be slowed down by light having to travel farther than normal. (chasing a target going upstream) Even our minds’ functions are governed by these interactions.

At first, it seems like the shortening up should cancel the time portion out, but it turns out that the only way to make the math work to fit the experiment is to leave some of the effect in, but in an even more mind boggling way.

This is the weird situation Lorentz mathematically modeled. Time dilation and length contraction led to experiments showing no effect on light no matter how fast you go. Even though the light is definitely affected!

At this point it’s crucial to understand that all the weird effects of relativity could be emulated with sound waves…

…if we had a weird material that shrank up just the right amount in response to wind. That material would have to shrink up the amount of the “Lorentz factor” or “Gamma” which is the basis of the Lorentz Transform. It’s a relationship between shrinkage and wind speed.

Now, imagine we have a flatbed truck with sound reflective surfaces placed at 90 degrees to each other and a speaker that can act as a microphone to both send and receive a chirp. If our device was made from this special material, no matter what direction we pointed it, the chirps would come back at the exact same time, whereas if it was all made from normal materials there would be a big difference.

Furthermore, if we constructed clocks out of this special material that used reflections of sound as the metronome, they would keep perfect time when stationary but would run slow when in motion. This is because, as you can see above, the whole experiment takes a bit longer overall when in motion but the clocks under the same weird shortening would still measure 20 milliseconds instead of the real 23.094 that is correct.

And this is how it all comes together into the full Lorentz transformation:

If I’m on the ground and I want to figure out what weirdness is going on in my little experiment after the truck takes off, but I don’t want to wait to go read all the readings after it stops, I can just look at the mathematical formulas I have to see what what the clocks read there compared to here and what distance they think they have traveled with their funny rulers will be mixed up a bit too. I can get all that information by using the Lorentz transform to transform my local readings to theirs on the truck.

Now if you are curious how on earth a mathematical description of a medium’s affect on light could be used to describe a world without that medium, then let me suggest you read these three blog posts:

Relativity Demystified

..and if you’re feeling really brave then you’ll enjoy this history paper that provides a context for all of modern physics based upon 19th century aether theory from the worlds foremost authority on modern aether theory:

[1804.01846] History of the NeoClassical Interpretation of Quantum and Relativistic Physics

UPDATE:

Further explication of the experimental grounding and the complications of interpretation can be found here:

Shiva Meucci's answer to Have any modern experiments refuted, or at least brought doubt upon, the results of the Michelson-Morley experiment?

Creation time: May 22, 2018 10:36 PM PDT

 

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What can be used as a system of axioms, hypotheses, definitions, conditions, observations so that we can deduce the Lorentz transformation? Are there any that give as no information on the nature of light and its speed other than merely defining c?

Aether theory is sufficient to arrive at the Lorentz transformations, as indeed it was aether theory which that math was derived to represent. (it existed before relativity, quite obviously)

It is crucial to understand that the Lorentz transforms were created as an attempt to model an optical illusion assumed to be occurring in the Michelson Morleuy experiment. This understanding of the impetus behind the math, strips away all confusion. The math is a model of light, constricted by the motion of its medium, occurring in a world where objects shrink in response the motion of that medium. It’s literally just a generalized version of some trig to deal with a “swimmer in a river” sort of problem.

Furthermore, it is possible, by stipulating the existence of some substance that shrinks in the presence of a wind, in appropriate proportion to that wind, to exhibit the “constancy” effect in sound. If one constructs “sound clocks” out of said shrinking material, then time dilation, length contraction, “the constancy of sound” and all the apparently strange concepts of relativity surrounding the behavior of light can also be assumed of sound. (quite absurdly)

As such it would not be necessary to consider the location or speed of the medium in such a theory for describing experiments constructed with that material. One could deprecate the very existence of air…

However, Einstein himself tried very hard to back out of the constancy postulate about light and repeatedly commented on the necessity of an aether after general relativity.

“Space without Aether is unthinkable…” - Albert Einstein, 1920, University of Leiden

This explanation below is a few years old but has various visualizations etc that will help:

Shiva Meucci's post in Relativity Demystified

Creation time: Sep 25, 2019 07:27 AM PDT

 

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The cosmic speed limit was actually created by Lorentz first before Einstein integrated it into his theory. It is a consequence of the math behind the "Lorentz factor".

 

The Lorentz factor was created by Lorentz because he was attempting to describe what he believed to be an illusion in nature. On the suggestion of George Fitzgerald, Lorentz interpreted the null of the Michelson-Morley (MM) to mean that, while there still truly was an "ether wind" (now called "aether") caused by moving through the luminiferous aether, that wind was undetectable because nature was configured such that it shortens up and alters time just the right amount to hide it from the experiment.

 

The math of the Lorentz factor and subsequent "transformation" is simply a mathematical model (a description) of this effect. It is a model of how aether affects objects so that they hide light's travel with respect to its medium. EG: A moving observer is experiencing light moving different speeds in each direction but can't detect it because of shortening and time effects. It appears to be constant when it, in fact, isn't.

 

So the "Why" behind the cosmic speed limit is that, in a MM experiment, if you reached the speed of light, that light could never reach the forward mirror to bounce back from it and therefore the time of the experiment (which requires the light to go into a wind and bounce back from the "escaping" mirror to complete) would take an infinite amount of time to complete.

 

All calculations become infinite because the experiment that the transformation was created to describe becomes infinite.

 

That is the reason why it was conceived and exists now regardless what other reasons people give you. They can't argue with these truths they can only add more information.

 

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Not sure what you are looking for in the way of an equation.

How about just showing you the classical geometric context Lorentz was working with, and the simple trig behind the Lorentz factor?

Above represents the comparison of path lengths light (or any simple wave in a medium) would have to traverse in a Michelson-Morley type experiment traveling at half the speed of the wave. The Lorentz factor is a simple geometric relationship. It’s just a comparison of growth rates.

However, I’m giving the answer before the details…

Let’s reduce it down to a very classical wave experiment. (mechanical wave in medium)

The above drawing represents the 50% time point of the duration of the experiment. IE The light has just struck the mirror positioned orthogonal to the motion, but it has not stricken the forward mirror yet.

Note: There is only one angle possible for the crosswind beam or path of the wave to traverse for it to reflect to the origin in motion. (Think this one out and you’ll agree)

This means that Lorentz, who was attempting to model a null in the michelson interferometer experiment, had to make a choice of lengthening the crosswind arm of the interferometer or shortening the co-wind arm to represent a null reading. A null reading is simply the simultaneous arrival of the signals back at the origin.

Both possibilities and their respective arm lengths, reflection points and total path lengths are shown in the image below. The smaller triangle is the shortened, instead of lengthened, choice that Lorentz went with to create the Lorentz factor.

(Warning: this image looks simpler than it actually is and requires a little extra thought to understand all the events. Visual angles/distances are not accurate.)

It is interesting to note that with a co-wind arm of 8.66 length, the reflection point for cross-wind occurs at 11.54 which is 50% of the total traversal distance. The reflection point for the co-wind (into a headwind) path occurs at 17.32 which is 75% of the total traversal distance and time.

This difference in reflection events with a simultaneous arrival time and equal traversal times/distances is the trick of the light and the entertaining illusion Lorentz intended to create.

None of these straight forward mechanics apply in a case of light speed constancy. All these mechanics which Lorentz created to describe a wave’s motion in a medium are missing in special relativity even though the math created to describe them is ported over directly.

Recapitulating, the math is kept, while what the math represents and is describing is discarded. No mechanics whatsoever are in place to describe the effect. Instead Minkowski influenced Einstein to warp reality itself around this math created by Lorentz. (Thus requiring additional dimensions and behaviors without mechanical rationality)

"The influence of the crucial Michelson-Morley experiment on my own efforts has been rather indirect. I learned of it through H.A. Lorentz's decisive investigations of the electrodynamics of moving bodies (1895) with which I was acquainted before developing the special theory of relativity. Lorentz's basic assumption of an aether at rest seemed to me not convincing in itself and also for the reason that it was leading to an interpretation of the Michelson-Morley experiment which seemed to me artifical" - Albert Einstein 1952, in a letter to Robert Shankland

Lorentz’s mechanics represent a situation in which the actual speed of light in one direction is different from another, but totals align perfectly every time.

The only way to separate special relativity from the semi-classical nature of Lorentz’s aether theory is this light speed anisotropy that is hidden in a two-way experiment.

The experiment to separate this classical set of mechanics from the mechanic-less version of relativity Minkowski influenced Einstein into has never been successfully carried out.

Said again: No experimental evidence supports preferring the aether-less version of relativity over the semi-classical version created by Lorentz.

Later in life, Einstein realized this truth but it was difficult to overthrow the perceptions created by his mentor, Minkowski.

"According to the general theory of relativity, space without aether is unthinkable; for in such space there not only would be no propagation of light, but also no possibility of existence for standards of space and time (measuring-rods and clocks), nor therefore any space-time intervals in the physical sense." -Albert Einstein 1920

Creation time: Oct 01, 2017 01:58 PM PDT

 

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No modern authors cover this subject in anything but a self-referential or extremely incomplete way. To properly derive the Lorentz factor, one must refer to classical mechanics and especially the aether (or Luminiferous Ether) because this was how it was derived.

 

IE: One must create the Lorentz factor from the concept of a physical mechanics of a wave in a medium.

 

This means that the the Lorentz factor would work for sound under particular circumstances and one could argue for "sound speed constancy" under those circumstances.

 

For those who learn better through audio/video, the following is a video of deriving the change factor from first principles. It starts out with the absolute very basics so it is quite long but worth the extra time:

http://youtu.be/Pxn9KGH5P1s

 

 

 

For those who learn via text, following is and excerpt from a website with an explanation but it assumes you have some understanding of basic wave mechanics etc:

 

Consider the following situation:

An alien species which lives in the vacuum of space determines to study sound in an atmosphere. They are incapable of surviving in an atmosphere so they use certain experimental devices to study mechanical waves in a medium (EG sound). In one of their first experiments they placed two sound reflecting surfaces at right angles from an emitter approximately ten feet from the emitter. These surfaces are held away from the emitter by the only building material they have access to which is also somewhat spring-like. They placed this assembly on a flatbed truck with the emitter at the tail end. It is arranged so that one sound reflective surface is closer to the front of the truck by ten feet and one surface is placed perpendicularly to the truck's axis, displaced from the emitter by ten feet. The experiment is placed at an elevation at which sound travels 1 foot per millisecond to simplify calculations.

The emitter is also a receiver that can only determine whether or not the sound reflected from each of the reflecting surfaces arrives at the same time or at different times and by how much the arrival times are displaced. Given what they know about wave mechanics so far, they determine that if the truck is put in motion, the waves will arrive at different times. Using this expected displacement, they believed they would be able to determine how fast the truck might be moving at any given time. They also believed that if there was a headwind they would be able to determine that as well since the motion of the truck was already known and they were pretty sure there was an awful headwind the truck was going into.

Unfortunately, after putting the truck in motion there was zero difference in the arrival times of the echos from the reflectors. No matter what speed the truck moved they both arrived back at exactly the same time and this was highly confounding to all their notions about the way waves in an atmosphere behaved.

(These images will be explained in greater detail later)

Thankfully, one of their respected scientists, Egeorg Gitzflerad, suggested it was the nature of their materials that was the cause. He believed that perhaps the wind was always just the right strength to caused the forward mirror to be scrunched toward the emitter just the right amount to make up for the expected difference.

Another scientist, Kehndri Orlzent, was fascinated by this development in their understanding of sound waves. He decided that it would be important to mathematically represent this concept of Gitzflerad's for the scientific community.

After some consideration of the experiment and some calculations, he figured out that the crosswind path would always be a certain angle away from perpendicular for a certain speed. This was true regardless of the distance away the crosswind mirror is placed. It could easily be represented like a graph. If the speed of the vehicle was half the speed of sound then whatever angle would allow the crosswind to be double the length of the experiment's motion would always be the angle of the spherical sound wave captured by the crosswind mirror.

 

- A Simple Geometry Problem -

Said another way, for every speed there is a right triangle that is created. If the experiment is put in motion from left to right, the path of first crosswind reflection makes a right triangle. This triangle can be envisioned with the hypotenuse on the left side with the other two legs on the x and y axes. The length of the hypotenuse will always be a length in proportion to the experiment's motion which is equal to the relationship between the speed of sound and the motion of the vehicle. This invariably creates a particular angle.

What is so interesting is that, with this angle defined, the problem can now be discussed and explored in terms of Pythagorean theorem and/or trigonometry. This means that there will be only one point at which a single wave will return to the source after traversing the crosswind.

Orlzent knew that we now have a known target quantity that the upstream or co-wind path length must be shortened by and it will always be related to the relationship between the speed of the experiment and the speed of sound. Just as sin, cosine and tangent are formulas that represent relationships between the sides of a triangle, there are derivatives of these that can also represent relationships between sides. This was Orlzent's first discovery of what would later be called gamma.

The way he discovered this was through the realization that a simultaneous arrival time could be reached by either shortening the upwind arm of the experiment or lengthening the crosswind arm. In considering our truck experiment at .5c (the speed of sound), this means that we can cause the path lengths to match by either lengthening the crosswind path or shortening the co-wind path.

Method 1: Simply find the ratio of the growth rates between the path traveled upwind and the path traveled cross-wind. In specific numbers, this means that the up/downstream sound path would take 26.666 seconds to traverse if the distance between the emitter and mirror remained 10. But because there is only one angle light will traverse, there is one particular distance the cross-wind path will be: 23.094. (how to find this will be explained further in method 2) Both of these path lengths grew larger than stationary, but at different rates. The relationship between their growth rates is 23.094/26.666=.866 So if we always want them to match, the cross-wind must be reduced by the difference of growth rates. The co-wind must be shortened by the amount it would otherwise gain beyond the cross-wind. This solution is useful for a single speed but does not provide a deep enough understanding yet to create a transformation for all speeds.

Method 2: Once again we consider that the up/downstream sound path would take 26.66 seconds to traverse if the distance between the emitter and mirror if the path remained 10. Using trigonometry and the principles established above we can easily find the length required for the crosswind leg of the experiment to achieve simultaneous arrival.(how much it would have to be extended) Using the simple calculation of cos^-1(.5) gives us the angle of 60 degrees. We know that during the total up/down that the sound travels, the experiment travels half that distance because it travels .5c. This means that when sound travels 26.66, the experimental equipment (the truck) only travels a grand total of 13.33. We also know that we can represent the motion of the experiment and the motion of the crosswind path as two right triangles. So basic geometry tells us that if we want the reflection point we must cut the experiment's motion in half to represent one right triangle. (see Equal Triangles above)

We now have a hypotenuse that is at a 60 degree angle and the x axis leg is 6.66 and the crosswind path is 13.33. It is simple to find that the sine of 60 is .866 and we multiply that by the hypotenuse to find the “opposite” (y axis) leg would have to be 11.54 long. This means that the crosswind leg would have to be 11.54 long for the arrival time to be simultaneous if the upstream/co-wind leg remained 10 long.

Method 3: Note: Method 2 must usually be discovered before method 3 can be easily understood. This is because it is more difficult to predict the length required of the upstream leg without having a specific target because there is an upstream and downstream component that cause some unexpected cancellation. Using the same principles discussed, we know that, though the length of the crosswind arm is set at ten feet, the angle at which sound will be reflected at .5c is still (cos^-1(.5)) 60 degrees. To find half the total crosswind path length for a 10 long crosswind arm, we can solve for the other dimensions in a number of ways:

A) Tangent(60) = “opposite” over “adjacent” gives us 1.732 which means that the length of the y axis leg is 1.732 times as long as the x axis leg. (10/1.732=5.77) Which we can use with the shortcut that the hypotenuse is 2x as long at .5c giving 11.54 and a total path length of 23.09

B) We know that the sine of 60 (opposite/hypotenuse) is .866 therefore hypotenuse/opposite = .866^-1 = 1.154 so if the crosswind leg remains 10 long, the hypotenuse = 11.54 and the total path length traveled by the crosswind is 23.09

 

Given this truth of a 23.09 crosswind, and because the experiment is traveling half the speed of sound, it will travel half as far for a total of 11.54 feet along it's path of travel (x axis) when the crosswind reflection is received.(refer to "equal triangles" diagram above) From this point there are numerous trial-and-error methods of arriving at the length the co-wind arm must be shortened to but let us instead focus on a deeper understanding of the problem from a variety of viewpoints instead of just the solution. This is part of the process of obtaining the understanding required for creating a transformation.

- Understanding the Implications -

If you know SR, you already know we must shorten the co-wind by gamma (.866) but your foreknowledge is cheating. It is very interesting and entertaining to find that when we invert the percentage of the path's growth along the crosswind path (from 20 to 23.09 = 1.154) we find that the amount the co-wind must be shortened to arrive at the same location. It is very similar to Pythagorean theorem. But how do we first make that leap of understanding without a process of trial and error? It is the equivalence of the triangles created by either lengthening one side or shortening the other that first gives the clue that shortening is precisely the inverse operation of lengthening.

"Gamma" is actually a simple relationship of growth patterns. Though average is not the proper term, it is “like” the average of the up and downstream (speed-up and slow-down) components after they are combined. For instance, gamma*gamma will give the total distance light must travel along the x axis if the length of the x axis arm is not altered. In our experiment at .5c if the sound had to travel all the way upstream and back down the 10 foot length the total path length would have been 26.66 instead of 20 and we can easily see that 1.154*1.154=1.333 which is the total growth of an unaltered co-wind path.

The angle of the crosswind is a representation of how much of the full (unshortened) growth pattern the crosswind it subject to. Notice that when we attempted to grow the crosswind to match the co-wind, we found that crosswind had to be lengthened to 11.54 to equal 1.33. (IE from 20 to 26.66) These two numbers are different at every speed but gamma*gamma will always arrive at the distance a wave would have to travel along the x axis if the experiment was not shortened.

Notice that the co-wind leg bears 100% of the effect of the wind (both sped up and slowed down) during it's traversal. The crosswind path is only partially affected by the wind because of its angle. However, as the experiment goes ever faster and the crosswind path remains the same length, the angle flattens out and the crosswind bears more of the wind's effect.

Why we have a gamma^2 final number is because the relationship explored is like one leg of a right triangle compared to the other leg doubled. IE the relationship in this case is like the relationship between the leg we've been calling opposite (y axis leg) and the one we call adjacent.(x axis travel) But we must duplicate the right triangle to consider the whole path length and then consider the relationship between the single “opposite” and the duplicated “adjacent”. It is a consequence of triangular relationships like Pythagorean theorem. More specifically, the reason gamma^2 gives us the unshortened path is because gamma is a squared relationship because the sides of a right triangle are a squared relationship. However, the reason gamma^2 is a result of Pythagorean theorem can be discussed more fully another time.

It is also interesting to note that as the speed of the experiment grows, the angle at which the crosswind travels flattens out in the same direction as the x axis travel. This causes the relationship between the legs of the triangle to change because “opposite” stays the same while “adjacent” grows. This gives us the strange non-linear changes we see in gamma at different speeds.

Finally gamma becomes infinite when the experiment reaches c because neither path can ever complete the trip. Neither path can ever reach the first mirror. (C is the universal speed limit in relativity because of what is equivalent to a divide by zero error)

 

- Summary -

The relationship between the movement of the experiment and angle of the crosswind path is a direct consequence of the relationship between the speed of the experiment and the speed of sound. IE:If sound travels 2x as fast as the experiment, the crosswind leg will be 2x as long. It is like a graph.

Therefore the angle created is a representation of two differing growth rates. The sine of the angle is another representation of that relationship. By using the sine of the angle, we can represent how much one side of a triangle must grow or the inverse to determine how much another side must shrink while maintaining the same triangle.

Gamma is a geometric representation of a relationship of growth rates. It is the result of solving the Michelson-morely experiment in a medium. The numbers and relationships represented by it do not exist if the wave travels as a constant with respect to a moving observer.

This is why gamma(inverse) can always easily be found on a scientific calculator by simply finding: SIN(COS^1(decimal of light speed))

(Go ahead, lean back. Take a nice deep breath and whisper “wow”)

- Conclusions -

The Lorentz transformation is designed as a mathematical illusion for light traveling in a medium. An observer who is ignorant of the wind will not be able to detect the wind and will mistakenly measure C as a constant at all speeds if they use the experimental setup described earlier with its ability to be "scrunched" by the wind.

This set of calculations therefore does not rely upon frame-independant “constancy” of the wave's speed but in fact depends upon the opposite to create the illusion of frame-independant “constancy”. This is a critical difference between Lorentz and Einstein.

Clocks which rely upon the transmission of the wave in the above experiment will be slowed by gamma because this is the amount of additional space the wave must traverse in one round trip, thus both length contraction and time dilation are incorporated in a purely mechanical wave model. (not frame-independantly constant) IE: If atomic clocks and biological processes are governed by EM interactions, time will be perceived at a different rate for a moving observer in this purely mechanical model.

Creation time: Dec 25, 2013 03:00 PM PST

 

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Yes, it was the very first interpretation

 

...and it was by Lorentz who was the originator of the central calculation for relativity, the change factor. While George Fitzgerald originated the general idea of "length contraction" it was Lorentz that took it from a fuzzy concept and made it into a rational and precise mathematical model which inherently gave us the additional concepts of time dilation, the illusion of light speed constancy and the illusion of the relativity of simultaneity.

 

That's right, I said "illusion"...

 

I've been working hard in recent years to raise awareness of history but it's been a slow process. The original idea and the math which describes it has a mixture of utterly illusory effects and real effects. Length contraction and time dilation are the real effects while constancy and broken simultaneity are illusions in Lorentz's theory.

 

The mathematical model was entirely developed to describe the effects of a differential speed between an observer and the medium in which light (the waves) was presumed to propagate, the "aether."

 

It's a mathematical model designed to describe the effects of a medium which we later removed

 

Ever wonder how the theory seems so wondrous and magical and possibly nonsensical? It's because we removed the reasoning for the math and believed math alone could sustain itself.

 

I'd go on and on about Tarski's undefinability theorem and how the simple minded can be led to believe math alone can prove itself but I digress. Suffice it to say that some people fail to understand the inherent superiority of a conversation about meta language because they childishly fail to recognize the difference between a symbol and what it symbolizes.

 

Wait, what?! Are you trying to say Einstein was wrong to remove aether?

 

Oh, I'm sorry were we talking about people, appeals to authority, and the sustained stupidity of large groups of people (AKA religion) or about rational concepts?

 

Here's the thing. Even in modern groups some people will refer to the CMB as a preferred frame which utterly contradicts relativity, or they'll arbitrarily select a preferred frame to solve the twins paradox and fail to continue examining if their explanation opens new holes (which it does) or we'll blithely refer to searching for Lorentz violation which also invalidates SR. They'll even try to explain effects in purely classical terms (*cough Sagnac effect cough*) utterly ignoring the way it violates relativity or insanely denying that it does but it all comes back to poor logic and a complete inability to process multiple views simultaneously.

 

Like a child or computer AI asked what happens when an immovable object encounters an irresistible force, they'll go back and forth insisting one or the other is true until they stack overflow and randomly stop at their last answer believing they have solved something.

 

"According to the general theory of relativity, space without aether is unthinkable; for in such space there not only would be no propagation of light, but also no possibility of existence for standards of space and time (measuring-rods and clocks), nor therefore any space-time intervals in the physical sense." -Albert Einstein 1920

 

But there's like, mountains of evidence against aether! Are you mad?

 

No, you've misunderstood me because you're ignorant (through no fault of your own) of the history of relativity and how it works. You don't understand that there is no appreciable difference mathematically between Lorentz Ether Theory (LET) and Special Relativity (SR) and that the only answer for choosing one over the the other is a philosophical argument about the application of occam's razor.

 

The mathematical model and all the described effects remain, yet we find that LET has zero apparent paradoxes or contradictions, has all the same described effects, and presumes no new strange principles of the universe which are non-mechanical in nature. It's complex but utterly rational and intuitive once you get the trick to it. This is utterly different from SR!

 

(...and actually there's even enormous problems of interpretation in the data about aether but that's another over-long story for another time)

 

Wait, so it's literally interpretation? Where? At what point?

 

The argument has been that the aether is an unnecessary additional component which adds nothing to the theory and must therefore be removed via Occam's razor. However, this is a little like saying that evolution is unnecessary because it's simpler to just presume god did it.

 

More specifically, because it is a mathematical model of an illusion it's more like being in the audience of a stage magician and never being allowed back stage. All people agree that every possible viewpoint from within the crowd shows that a man took a spear through the chest and removed it unharmed and no evidence to the contrary can ever be produced given the constraints of all known rules. Therefore it follows that what is observed readily and repeatedly is the only truly scientific discussion.

 

Any discussion of additional underlying mechanisms beyond observation, which are currently untestable, is a violation of the rules of science and therefore we must accept what is observed and tested as the only relevant theory.

 

Furthermore the argument goes that it is "metaphysics" to discuss possible mechanisms. (For things such as constancy) It is insisted that some new view of reality in which this new unique (magical) effect is possible must be accepted as a purely basic behavior of reality.

 

uhhh, what? I don't follow...

 

Aether provides a rational mechanism for all the weird effects of SR and what is more, matches the rest of reality without having to postulate utterly stand-alone new behaviors of the universe such as a wave without a medium. (A wave is an action that happens to a thing and we removed the "thing")

 

Most people either do not understand constancy (and the subsequent breaking of simultaneity) or eventually settle upon an explanation that makes sense in their head and sounds quite similar, but doesn't match the theory.

 

Here's a link below in which you can compare the older LET to the newer SR and understand precisely how and why the subtle philosophical differences are actually quite huge and can lead to different applications of the theory and therefore even to numerical differences in some special cases

 

(You'll also understand the weirdest effects intuitively because I give the underpinning of the illusion)

 

Take note that all explanations in the link fit modern interpretation of SR and only my commentary deviates from accepted norms and consensus:

 

Relativity Demystified

 

Well great, but is there anyone credible buying this or doing any work with it? How does it even help?

 

Yes, there is a small cabal at Cambridge solving numerous problems in physics using fluid dynamics. (though they try not to comment on any idea of aether and avoid the word) It's a little known fact that Maxwell's equations which are still crucial today are simply a special case of fluid dynamics.

 

Unsurprisingly, this methodology would inevitably lead to the unification of micro and macro physics in a rational and deterministic fashion.

 

All that fun magic nonsense gets thrown away and you have to weep for the loss of all your illusions of solipsism and free will, so I apologize in advance for your loss.

 

From the page of Ross Anderson:

 

Maxwell's fluid model of magnetism shows that a wavepacket travelling along a phase vortex in an Eulerian fluid obeys Maxwell's equations, is emitted and absorbed discretely, and can have linear or circular polarisation. What's more, the measured correlation between the polarisation of two cogenerated wavepackets is exactly the same as predicted by quantum mechanics, and observed in the Bell test.

 

(this paper is an extension of earlier work that provided mechanism for gravity while this particular paper destroys all magic in QM)

Creation time: Apr 24, 2015 12:18 AM PDT

 

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My series of quora blog posts addresses precisely this question in laymen's terms: Relativity Demystified

 

To summarize, the difference can only be expressed in meta-analytical terms because technically the two theories have been historically considered mathematically indistinguishable.

 

Specifically, in Special Relativity (SR) the aether has been eliminated and the inferences about what the mathematics say about reality is radically different from Lorentz Ether Theory (LET).

 

Note: In modern times we use the newer spelling with an 'a' to distinguish luminiferous aether from the gas "ether".

 

 

So, what's the same and what is the difference?

 

Both SR and LET have a mathematical model of effects described as:

 

a) Light Speed Constancy

b) Time Dilation

c) Length Contraction

d) Relative Simultaneity

e) Fourth Dimension of Time

 

In LET, some of these effects are real and others are a perspective illusion.

 

In SR all effects are real. The reality of these effects additionally infers the requirement of space-time unification.

 

 

So the older theory describes some effects as illusions and the newer theory accepts them as reality?

 

Specifically, LET describes length-contraction and time-dilation as mechanical electromagnetic effects and interactions between particles, light the fluid-like medium that light travels in ("ether") that result in the very real alteration of an observer's experience of time and actual physical length and this, in-turn, leads to the perspective illusions of "light speed constancy" and the subsequent illusion of disjointed simultaneity (relative simultaneity).

 

In addition, in LET a fourth dimension is simply a mathematical tool alone which used to keep up with the discrepancy of clock ticking rates. It is not inferred to exist at all.

 

SR, on the other hand, along with discarding any notion of "illusions" found in LET, has a very real and physically existent fourth dimension one traverses in a relationship to space.

 

 

Surprisingly, all of this is true within the exact same mathematical model.

 

This results in very strange consequences. Because we have additional information inferred in LET, we also can make some differentiations that SR is incapable of making and effects not present in SR at all.

 

For instance, there is zero example of the twins paradox found in LET because we presume a universal frame. This sounds just like the solution to the twins paradox in SR as well with the following caveat:

 

When there is time dilation and length contraction in one subject, there is time-contraction and length-dilation in the other relatively speaking.

 

What this means is that in Lorentz's theory it was possible to have three subjects in which a central observer of the three could look at one as having the conventional time-dilation and length-contraction found in SR but then look at the other and see the inverse effect of time-contraction and length-dilation!

 

Hence, LET, while having the same maths, had zero apparent paradoxes found in SR.

 

IE: There were inferences in how one might apply maths to the larger set of effects and circumstance that vary even though the basic concise and specifically defined maths of the model itself (how to deal with particular observations) is the same as SR.

 

 

Uhh, then why'd we pick SR over LET?

 

Because, technically, the rules of science can be interpreted as saying to do so.

 

In LET, it is presumed that the aether affects matter in a way that hides the aether itself from all known, if not strictly all, experiments. Therefore the theory presumes a mechanism which is not detected. This "addition" of mechanism, can be seen as needing to be eliminated via Occam's razor and therefore SR was selected as the preferred theory because of the elimination of the aether.

 

 

 

However, it bears mentioning that this same methodology applies to the following situation as well:

 

Two scientists are tasked with observing and scientifically describing the events surrounding the performance of a stage illusionist. They are not allowed behind stage nor will they ever be allowed to observe anything but the performances.

 

Both created detailed sketches, and mathematical models of the apparent devices and forces applied when the magician forces a spear through his chest and removes it. One proposes a set of mechanisms which presume the effect repeatedly observed is an illusion. The other only describes what is seen.

 

The scientist who includes a description of mechanism for illusion is technically, by the rules of science, in error. His theory must be eliminated via Occam's razor and the other scientists work must be preferred.

 

The question becomes if you believe that light-speed-constancy, relative-simultaneity, the twins paradox, space-time unity and other additions beyond Lorentz's description are irrational enough and different enough from the rest of reality to be presumed an illusion.

 

Or do you, instead, accept these wholly new and utterly novel effects in reality (light speed constancy, waves without medium etc) as newly discovered truths stumbled upon by re-interpretation of a mathematical model of rational effects (LET)?

 

Do you believe you've found the first real magician or do you presume that the "oohs and aahhhs" of the crowd are the typical reactions of the ignorant masses?

Creation time: Jun 29, 2015 02:02 AM PDT

 

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While Mark Barton and I have had long drawn out fights, his description is now predominantly accurate, though colored by modern orthodoxy and irrespective of history.

Lorentz’s theory of aether is basically relativity.

…but with aether and came first. His work with Poincare would have taken precedence over Einstein even in electromagnetism if it were not for some anomalies in the publication of Poincare’s corrections to his previous publications. The theory used to be called Lorentz-Einstein relativity for a very good reason.

I will not say that there is no value provided by a composer who creates a new symphony simply because he uses the same instruments. Einstein was a composer and his symphony was made up of instruments created by Lorentz, but it had characteristic differences that made it something new, and therefore not really plagiarism as many have claimed.

For years it has been pointed out that these two theories are mathematically indistinguishable. Additionally, the one experiment which could separate the two, a “one-way speed of light test” has never been satisfactorily performed.

A model or “theory” is a generalized description of mechanics.

Lorentz derived the factor of change (the very heart of relativity) from how a wave propagating in a medium would be perceived by a subject moving through that medium if that subject was perceiving an optical illusion.

IE: His theory (description) casts the idea of “constancy” as an illusion.

The “Constancy” of light is likely the most commonly misunderstood concept in all of science because the term is misleading. When the word is used in the context of Einstein’s relativity, it is an effect which defies all rational or mechanical thinking which is confined to a 3D world and appears to be a description of magic, or nonsense to a classical, intuitive, or mechanical mindset.

It is NOT simply the idea of a wave propagating at a constant speed and even the words “propagates the same speed for all observers” is extraordinarily misleading because one might be tempted to use the same phrase to describe a sound wave or any other wave.

“Constancy” in the parlance of relativity, is a property and behavior no other thing in the universe has ever been described as having. Only light.

Lorentz, at the suggestion of George Fitzgerald, decided to mathematically model how the Michelson-Morley could actually be null, even though the earth is definitely moving through that medium and light must propagate. Therefore it is a mathematical description of light actually having different speeds based on direction but this fact is covered up perfectly by the way motion through aether affects measuring devices.

Lorentz was modeling an optical illusion.

Consequently, the apparently constant speed of light was an illusion, and the apparent relativity of simultaneity was an illusion, but the shortening of objects was very real and so was a shortened objects perception of time.

What will surprise and befuddle most people in the field of relativity who do not have a grounding in its history is the fact that the illusion of “constancy” and the necessity of a 4th dimension could be inferred from a simple experiment with sound if we could create a material that shortens in response to wind (moving air) in the way that Lorentz supposed all material shortens in the presence of an aether wind.

For a longer and more in-depth description of his derivation, please see: Relativity Demystified

Lorentz’s illusion becomes Einstein’s reality.

Einstein was absolutely clear that he got his ideas from Lorentz and then gave it his own twist. Anyone who indicates otherwise is misleading you for the sake of hero worship.

"The influence of the crucial Michelson-Morley experiment on my own efforts has been rather indirect. I learned of it through H.A. Lorentz's decisive investigations of the electrodynamics of moving bodies (1895) with which I was acquainted before developing the special theory of relativity. Lorentz's basic assumption of an aether at rest seemed to me not convincing in itself and also for the reason that it was leading to an interpretation of the Michelson-Morley experiment which seemed to me artifical" - Albert Einstein 1952, in a letter to Robert Shankland

So, even though the math Lorentz developed was to describe the effects of an observer in motion with respect to a wave confined to move within its medium, Einstein ported this math directly over to his theory while discarding the mechanics which it described.

Instead of seeing an illusion, he decided that perhaps light behaved like nothing else in science or human experience. Furthermore, this completely novel and apparently magical (to a mechanical mindset) new behavior seen nowhere else in the universe requires an additional dimension added in to reality to have any semblance of mechanical consistency. (thus spawning a century of dissent and heated debate and argument from many nobel prize winners including Michelson himself)

Einstein applied Occam's razor in the following way:

If one is observing an illusionist and wishes to scientifically describe the events on stage while also knowing one will never have access to the illusionists secrets, then one must only describe what has been witnessed.

Therefore if one witnesses a spear go through the chest of the illusionist, the appropriate scientific description is the one observed. Velocities of the spear, positioning and vectors can all be accurately described. Only observational data can be used in strictly scientific terms.

Lorentz, however, describes a complex set of additional mechanics which show that no spear has actually pierced the illusionist. This description, because it has no direct evidence or observation, is a conclusion which is an artifact of the observer’s logic and therefore not strictly scientific per se.

Ergo, the aether would be removed by Occam’s razor.

However, Einstein, upon further examination later in life recognized the necessity of aether.

Upon development of general relativity, various inconsistencies begin to arise in idea of relative simultaneity and other well known paradoxes. Einstein later embraced a Mach’s idea of a gravitationally defined preferred frame in the universe which light must obey and called this concept aether. (Sometimes now associated with the Cosmic Microwave Background)

His famous lecture in 1920 at the university of Leiden, however, was ignored by others who refused to accept this necessary update to special relativity. This refusal persists today in most of those who teach relativity.

According to the general theory of relativity space without ether is unthinkable; for in such space there not only would be no propagation of light, but also no possibility of existence for standards of space and time (measuring-rods and clocks), nor therefore any space-time intervals in the physical sense. - Albert Einstein 1920

Now many theories including most mainstream quantum mechanical formulations rely upon preferred frame mechanics.

There has been a resurgence of aether theory called by anything but that name. From super-fluid quantum vacuum to quantum spin foam, everything new in modern science points to the thought that Einstein was right… He was right about the fact that he was wrong …and nobody listened.

One most damning aspect of humanity is their lack of acceptance of the flaws in their heroes.

“You imagine that I look back on my life’s work with calm satisfaction. But from nearby it looks quite different. There is not a single concept of which I am convinced that it will stand firm, and I feel uncertain whether I am in general on the right track.” — Albert Einstein, on his 70th birthday, in a letter to Maurice Solovine, 28 March 1949 (in B. Hoffman Albert Einstein: Creator and Rebel 1972, p.328)

Creation time: Jul 23, 2017 11:04 PM PDT

 

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Lorentz’s Kinematics when combined with Poincare’s electromagnetism comprise a mathematically equivalent theory. (With one major caveat)

This has often loosely been called Lorentz Ether Theory (LET) but now that more of the history around that time is clarifying through the release of letters etc, calling it LET is a little misleading.

The caveat is that “Mathematical equivalence” is not full equivalence. The constancy of light is a metaphysical concept that is only found in special relativity. It’s just a perspective illusion in Lorentz-Poincare relativistic theory but it’s considered a real truth of the universe in SR.

This leads to the fact that light’s speed is anisotropic in Lorentz-Poincare aether but isotropic in Einstein’s SR.

These facts are interpretation based, not math based.

Furthermore Einstein’s acceptance of Minkowski’s work and the conjoining of space and time are also metaphysical interpretations that are unique to the theory we now call Special Relativity. Minkowski simply represented new metaphysical interpretations (constancy, spacetime and relative simultaneity) in a mathematical way.

Lorentz, however, had a “Theory of Electrons" which was not equivalent.

Lorentz’s work, on its own was not equivalent even mathematically speaking.

Hopefully the alternative understandings here in various answers will be clearer with these distinctions.

Creation time: Dec 14, 2018 09:01 AM PST

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Explaining contraction with a single diagram is a really tall order. I think at least a couple diagrams and few words might be the bare minimum and that’s only for those who are already pretty familiar with the topic. Let me know how well you grasp these images I’ve made earlier for this purpose. These attempt to make you understand the reasoning at the deepest level by speaking about it within the context they were developed by Lorentz. As the inventor of contraction, understanding Lorentz’s reasoning is the best way to understand the mechanics.

So here’s my shot at the most concise explanation assuming you’re already pretty familiar with the subject:

If you think of sound reflecting off two equidistant paddles set at right angles on a flat-bed truck, once you put it in motion and you want the signals to still arrive back at the emitter simultaneously, (null on the Michelson) there’s two ways to do it. Lengthen the crosswind path or shorten the distance into the headwind.

FitzGerald proposed shortening, and Lorentz worked out the math:

BONUS! Lorentz and FitzGerald’s choice:

There’s still two ways to work it out mathematically, but while they could imagine of the idea of aether flowing across particles strengthening the bond in the direction of flow, there was no mechanical reasoning for aether to widen the distance between particles orthogonal to aether flow and cause lengthening of the cross-wind leg. IE: They could have opted for “Lorentz-FitGerald widening” instead of contraction to model the null Michelson experiment. (which was the whole purpose from the beginning)

Here’s a diagram of the various relationships of path lengths for light to follow in a moving michelson experiment. This diagram simultaneously shows alternatively shortening the “into the wind” path length/leg AND lengthening the cross wind leg of the experiment. Warning: this one takes some serious thought about the motion and location of mirrors at various times. For a hint, the left-most corner of the triangles represent the emission location at the start of the experiment and the green arrow represents the emitter/receiver location at the end of the experiment. Reflection location and actual paths traversed in each direction are labeled.

This shows that a classical idea of time dilation exists. It’s gamma^2. And if we widened objects instead of contracting them, then time dilation would be gamma squared instead of just gamma as it is now. (because the whole experiment time is extended by that much in each case)

Creation time: Sep 13, 2017 06:16 PM PDT

 

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The best way to avoid the math and specialist-speak is to over-simplify a little.

You’ll find the following useful from the “Lorentz Covariance” wiki:

They say that “Lorentz Symmetry” is "the feature of nature that says experimental results are independent of the orientation or the boost velocity of the laboratory through space."

Covariance and invariance are related in a sticky way, when we think of C being a constant we think of it as not varying from one frame to another, right? C is just C regardless what frame you are in. But for that to be true there has to be a way to shift our viewpoint one frame to another so that each of them sorta loses what the other gains since the times and measures are all weird in comparison to one another. They vary at the same time as you switch from one to the other in a way that is complimentary. So while there may be specifics that are important to someone doing the math, there’s not much difference for the rest of us.

So, generally, “Lorentz Invariance” is basically a reference to the idea that the laws of physics prove to the be same regardless of if you’re in motion or not.

Put another way, if you removed all the stars and planets, you’d have no way of knowing if the Earth was still or moving through the universe, not just because the idea of motion would no longer have meaning, but because theoretically, there’s no experiment that could detect if you’re moving or not. (except with relation to other bodies)

This is the generally accepted definition and understanding of the circumstances of the universe in modern consensus theoretical physics.

The significance, however, is a lot more subtle.

Most physicists today would say that the lack of detection of violations of Lorentz symmetry proves that the principles of special relativity still hold good as our best model. This would be what they find significant about it.

However, the meaning and interpretation can get very very muddy without those stuck deeply in the mud ever recognizing it.

The first point at which it becomes important is that the precursor to relativity, often called Lorentz Ether Theory (LET), is where the kinematics (motion and effects thereof) we are discussing come from. The reason all these “Lorentz” things are part of relativity is because Einstein used Lorentz’s kinematics model completely unchanged and then went on to add his own component which was the electromagnetism of these kinematics. This was in competition with Poincare (also using Lorentz kinematics) who was almost credited with relativity over Einstein but for a small publishing irregularity.

The difference is in interpretation!

If we look at the Lorentz-Poincare version of relativity, it’s still an aether theory. (while being mathematically equivalent to special relativity) This means it infers there is a preferred frame that exists, but what is more, it also infers that it’s nearly impossible to detect this frame because nature carries out a complex “optical illusion.”

Whenever someone is dealing with the confusing parts of relativity, they aren’t talking about the electromagnetism, they are talking about the kinematics. They are talking about Lorentz’s work NOT Einstein’s extension of it. (since it’s unchanged) This is because it’s a mathematical model of an optical illusion and nobody ever teaches you that or explains its reasoning. (an illusionists trick is only confusing when you don’t know the hidden mechanics underneath)

You can read more on that later in a link below, but suffice it to say that in Lorentz’s interpretation, the speed of light is only the same in all directions for one particular frame. By an ingenious set of interactions and mechanics that make perfect sense, the rest of the frames do this little weird averaging trick of two different speeds for light mixed up with time and altered measurement to give you the illusion of light being the same speed. (on average) …so long as you never test light’s speed in one direction alone!

This is called light speed “anisotropy” and the way to detect it is via a one-way speed of light test. Something never accomplished.

You didn’t misunderstand me just now. I just said that the one-way speed of light has never been successfully tested and there’s no experimental basis for preferring Einstein’s spacetime over Lorentz-Poincare aether. (One-way speed of light - Wikipedia)

All actual tests involve something that ruins the one-way testing in some fundamental way that makes it into a two-way average or a “synchronization error.”

So the question remains, would this illusion theory of Lorentz-Poincare also predict Lorentz invariance?

That is the big question and the answer is both yes and no based upon what interpretation you pick. If you pick the Lorentz interpretation of an actual aether and the 4th dimension as a handy notation device, then there’s light speed anisotropy inside a hidden perspective, but if you choose to believe in minkowsky spacetime where the 4th dimension gains some real physicality, then the detected difference in the one-way speed of light can be chalked up to a difference in simultaneity.

Said another way, your belief in the new claims of relativity make it possible to disregard any hard evidence of its falsehood that is apparent from the perspective of the neoclassical mechanics it was based upon.

Belief in the newer interpretation allows you to disregard the evidence against it.

Yet the math is the same.

What about Occam’s razor then?

“Everyone knows that aether was removed because of Occam’s razor!” First, that’s a matter of interpretation and preference not some sort of hard scientific ruling like experiment and evidence.

More importantly, however, is that it’s a completely irrational inversion of blatantly obvious truth.

1. Preferred frame mechanics, which require an aether, give us a reason for waves to exist. A wave is an action and granting it some sort of new separate existence is a brand new outrageous and irrational claim we must swallow for accepting relativity.

2. The removal of aether requires the acceptance of a 4th dimension as part of physical reality and time becomes something traversable like space instead of simply a measure of change as it was classically understood.

3. The 4th dimension used by Lorentz was simply mathematical convenience, but removing aether requires it become physically real to mathematically accomodate that interpretation and adds infinite possible additional 3D realities to exist in each moment. (for the same math)

4. This new waving of nothing also travels at a functionally infinite speed unlike anything else in existence.

5. Time doesn’t just run differently here and there, it also is a different time here and there.

So, does Occam’s razor remove the theory that says there’s a mechanical medium that’s difficult to detect because of an optical illusion, or does it remove the theory that adds infinite additional 3D realities for each moment and reifies the concept of an action existing without an actor …that moves infinitely fast?

“For velocities greater than that of light our deliberations become meaningless; we shall, however, find in what follows, that the velocity of light in our theory plays the part, physically, of an infinitely great velocity.” - Albert Einstein 1905, OEMB

On July 4th 1912, Einstein attempted to explain that one must consider the limits of the two major principles, equivalence and of the constancy of light. Further explaining that the constancy of light can only be maintained in spatio-temporal regions of constant gravitational potential. He continues:

"This is, in my opinion, not the limit of validity of the principle of relativity, but is that of the constancy of the velocity of light, and thus of our current theory of relativity." - Albert Einstein 1912, "Relativität und Gravitation. Erwiderung auf eine Bemerkung von M. Abraham", Annalen der Physik 38, 1912, pp. 1059-1064 (CPAE, Vol. 4, Doc 8), pp. 1061-1062.

…and after deeply considering special relativity every day for 15 years:

According to the general theory of relativity space without ether is unthinkable; for in such space there not only would be no propagation of light, but also no possibility of existence for standards of space and time (measuring-rods and clocks), nor therefore any space-time intervals in the physical sense. - Albert Einstein 1920, University of Leiden

Ergo, Einstein long accepted the need for preferred frame mechanics but understanding was lost to fashion, jockeying for fame, and poor historical investigation. (We played telephone for the past century)

Would you like to know more?

While I do need to update a few things, this blog explains the differences and how the illusion Lorentz modeled works and does so clearly with lots of pictures and examples: Relativity Demystified

This paper below relays the story of how all our current physics models are descendants of aether theory and how a fluid dynamical approach to modern physics is a revolution occurring currently in the background of modern theoretical development.

[1804.01846] History of the NeoClassical Interpretation of Quantum and Relativistic Physics

(Did I mention that all magical effects in physics fall to mechanical explanation and you no longer have to swallow that huge lump of irrational faith fed to you?)

Creation time: May 27, 2018 03:05 AM PDT

 

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Physically, it’s an adjustment amount that’s a bell curve scaling with speed.

It’s how to project what will happen to something that is moving fast based on the Michelson-Morley experiment.

Larmor was the first to propose it in its first form and Lorentz made it more generally applicable. What they were doing however, was attempting to create a physical mechanical explanation of a very counter-intuitive result in an experiment.

They started by presuming that they were describing the effects of an optical illusion.

That critical fact is almost never taught but completely solves every crazy weirdness of the theory.

Think of it this way. You know that sound gets carried along inside the air in an airplane because we don’t get any doppler effect talking to passengers ahead or behind us. Waves get carried along with thier mediums.

The speed of the waves in our morning coffee in the car aren’t locked with the ground, they travel with the coffee.

Light was known to be a wave around the 1880s when this was all coming to a head. So, they too would have intuitively understood that if you stick your head out of a car and listen to a bus pass by, you can hear the shift in frequency. It makes sense because you’re traveling through the medium that the waves travel in.

They are hitting you in the face faster from one direction and having to play catch-up from the other so it makes sense that they will hit you more or less “frequently.”

So, Michelson’s experiment assumed we (the earth) is moving through the medium light propagates in just like a car through air.

Now imagine you know all the above about waves and everything about the world makes sense then you stick a device out the window of your car that measures how long it takes a sound signal to travel upwind and down-wind. You would, of course, assume it would take longer for the sound wave to travel upstream in a headwind and faster downwind.

Michelson did for light and got what is reported as “null.” In the interest of accuracy I have to say it was not actually null, but for the sake of this explanation assume, like everyone else did, that it was perfectly zero. (we’ll save digression for comments)

That makes no sense! The only answer, therefore, is to figure out a way that nature is playing a trick on you and describe that mathemagically.

It’s just like looking at a magician on stage push a stake through his chest and live through it. You know nothing in reality works like that because you don’t believe in magic. You know there’s some sort of mechanic that’s hidden from you. It’s an illusion.

That is what the Lorentz transform originally was until Einstein told everyone the magical effect was real.

So, how does it work?

This is where we need some diagrams. You need to know how the experiment worked to be able to solve the problem like Lorentz did. First a note, however. He used a special property of the experiment itself as a way to accomplish the trick:

The experiment was the average of both upstream and downstream effects. It turns out that, counter to intuitive guesses, when you average the slowed upstream effect with the “sped up” downstream effect, they don’t actually cancel out. The faster you go the larger the leftover effect is. (That’s why the change factor is a bell curve. You gotta match this effect with your math to complete the illusion.)

It’s math to cancel out the effects of the wind.

Okay, so, how did he do that and how could anything be cancelled out?

He assumed that wind shortened up the objects traveling through the wind! Now we have to assume a few things. First, we have to assume that all matter reacts to the medium light was presumed to travel in prior to Einstein, and at the time it was called “ether” though we spell it “aether” now.

This meant that all of our measuring sticks are shortened in the direction of the wind but we cannot tell because the travel of light exactly matches this shortening and everything looks normal to us.

Since it was presumed at the time that everything was based on electromagnetism, then even things like two particles pushing against each other and even the period of time it takes for particles to move around is determined by the speed of light.

[Remember! What we’ve been talking about, however is that light according to a moving subject, has to play catch-up in one direction because of the wind, and races too fast in the other direction. But our experiment somehow doesn’t show it!]

It’s useful to keep thinking in terms of sound waves, so let’s imagine I have a special material that shrinks in response to wind and can make anything out of it. I make a flatbed truck and an experiment -exactly like the Michelson Morley- that measures a chirp that is emitted and echoed back.

In the experiment on the truck there’s just two surfaces 10 feet away to reflect sound from the original chirp.

So here’s the riddle Lorentz solved mathematically: How much would the material have to shrink to perfectly hide the truck’s motion?

The answer is dependent on the speed and has to be different for any given speed. The answer is an equation that takes your speed as an input and gives the amount of shrinkage needed as the output. The answer is the factor of change.

The Lorentz transform is just a version of the change factor that deals with more information but does the same trick to it.

“Okay cool, I can see length contraction but you never mention time dilation!”

Well that’s easy. If you look at the truck experiment above, the total round trip of the sound takes longer in a moving experiment. It does this by the change factor as well. The change factor is actually two numbers that are the inverse of each other, so in the example above it’s 1.1547 and .866 for .5C.

Remember that everything in classical terms is mediated by electromagnetic interactions in the aether. If it takes longer for two particles to transmit the “bumping into each other” because the effect has to travel through the medium both directions, then every interaction is slowed by motion through the aether by the change factor as well. [Notice 23.094 = 1.1547 * 20]

Therefore time dilation and length contraction and the appearance of light speed constancy could be demonstrated with sound if we just had that special material that shrivels up in response to air wind in the way they assumed matter shrinks up in response to the aether wind.

I won’t get into why it was rational to presume matter would shrink up because that’s a much longer subject that also has a history of scientific reasoning as well.

Instead, focus on the fact that this is an illusion with mechanics that work for a reason. Einstein removed the reason why it worked and kept the math describing the mechanics while discarding the mechanics themselves by presuming there is no aether. (He did it because he was focused on describing the electromagnetism and left the kinematics to lorentz.)

Instead, to fill this giant gaping explanatory hole in the mechanics, we presume there are infinite 3D realities in each single moment we can exist partially between and light can shortcut through it to effectively move at infinite speed. So next time someone says we removed aether via Occam’s razor to make things simpler you can just giggle at them. Now you know better. (Don’t try to argue! Facts and reasoning have no effect on cultural belief systems.)

If you’d like more laymen’s terms explanations look here: Relativity Demystified

If you’d like to see how aether has historically and continues to play a role in modern physics… if you’d like to understand why an aether revolution is brewing in major institutions right now. Check out this paper:

Published in Cosmos and History:

History of the NeoClassical Interpretation of Quantum and Relativistic Physics

Pre-print on Arxiv: [1804.01846] History of the NeoClassical Interpretation of Quantum and Relativistic Physics

Creation time: Sep 08, 2018 04:58 AM PDT