Length Contraction
Is it Really a “Real” Thing?
Maxwell’s Electromagnetic Wave Equation is traditionally read as a three-dimensional wave equation containing a fixed speed of light. An alternative way to read the mathematics is that
Maxwell’s 3D Wave Equation contains a Fixed 3D Speed.
NeoClassical Relativity (NCR) is based on this interpretation of Maxwell’s mathematics.
My reformulation of Special Relativity is based on the premise that The Speed of Light is a three-dimensional combination of the Speed of Oscillation and Speed of Linear Travel. Mathematically, this postulate can be written as the “3D Speed Equation”
Equation (1) ________________ c² = u² + v²
{Where, (u) is the speed of oscillation in two spatial dimensions, and (v) is the speed of travel in the third.}
The Physics of Time
In the last post, we saw how in NeoClassical Relativity (NCR) the concepts of Spacetime-Interval and Time-Dilation are merely two sides of the same coin — as can quickly be shown below.
If we rearrange equation (1) and multiply across both sides by time-squared (t²) to get
Equation (33) ___________ (ut)² = (ct)² — (vt)²
This is a version of the “Spacetime Interval” equation, which is traditionally written as
Equation (34) ___________ (ct-₀)² = (ct)² — (vt)²
By combining equations (33) and (34) we get
Equation (35) ______________ ut = c(t-₀)
And rearranging equation (35) gives us
Equation (36) ____________ t = (c/u)(t-₀)
This is Einstein’s Time Dilation Equation (note: c/u = γ).
Time Dilation and the Spacetime Interval are the essence of Einstein’s Special Relativity. But it is the interchangeable nature of time-dilation and the spacetime-interval that is the Fundamental Essence of NeoClassical Relativity. This interchangeable nature reinforces the argument that Special Relativity is really about one thing, and one thing only: “The Physics of Time…”
So if that is indeed the case, what is “Length Contraction” all about then?
The Simple Answer
Well, the simple answer is that “Length Contraction” is merely a theoretical necessity for the consistency of a fixed one-dimensional speed of light.
However, it is worth fleshing this out, and giving some context as to how this idea came about in the first place…
Up and Down vs. Back and Forth
The idea of length contraction had been entertained by many prominent physicists long before Einstein reproduced it in his Theory of Relativity. Einstein’s apparent “confirmation” of length contraction, however, was merely an indirect consequence of the methodology that he used to derive the concept of Time-Dilation.
The concept of Time-Dilation was the result of a thought experiment that Einstein constructed involving a light-clock on a train. In the experiment, Einstein described comparing the up and down motion of light from the point of view (POV) of two different observers; and in order to preserve a fixed linear speed of light, he deduced that time must be different for the different observers, and the calculation of that difference is how he arrived at time-dilation.
Given this result, his next move was sort of obvious. Having just compared the up and down motion of light from the POV of two different observers, Einstein now proceeded to compare the back and forth motion of light from the POV of the same two observers. And in doing so he found the mythical length-contraction.
However, while the concept of Time-Dilation is legitimate, the concept of Length-Contraction is not!
Einstein’s thinking about an up and down cycle was legitimate (because in doing so he had correctly described a cycle that occurred perpendicular to motion) and so it generated a legitimate result. But his idea about a back and forth oscillation was flawed (because light does not oscillate and travel in the same dimension) and so it generated a flawed result.
Confirmed or Not?
In NCR, Length-Contraction, like 4-Dimensional Spacetime, is a mathematical fantasy (necessitated by a one-dimensional fixed speed of light); and just like we saw with 4D spacetime, length-contraction is completely unnecessary to explain The Physics of Time…
Interestingly, however, that doesn’t stop physicists from claiming it is a reality. For although most textbooks couch the explanation of length-contraction in purely mathematical terms; many authors and prominent physicist have claimed that length-contraction has been confirmed by experiment. But has it? Has it Really?
When physicists say that experiment has confirmed theory, what they really mean is that they have a mathematical theory that goes by a certain name (in this case “length-contraction”) and that theory makes certain predictions, and some experiment has been carried out that confirmed these predictions. So the so-called “confirmation” of length contraction simply means that some physicists have seen some experimental results that they are convinced is a confirmation of length-contraction. But I simply refuse to believe this nonsense. To me, a physicist telling us that he has witnessed such a thing is about as reliable as a child telling us that she has seen Santa Clause — you often simply see what you want to see…
Not a Thing!
Time Dilation and the Spacetime Interval are the essence of Einstein’s Special Relativity. It is worth noting that in Minkowski’s reworking of Einstein’s work, length contraction doesn’t really feature.
In NCR, length contraction is just NOT a real thing at all!…
Essentially, Einstein stumbled upon “time dilation” by unintentionally, but correctly, treating light as a moving cycle — a moving oscillation. But he subsequently muddies the waters when he felt the need to apply the same idea in a different direction, and in so doing found the mathematical construct called “length-contraction”.
The fact that the idea of length contraction was favoured by many prominent physicists of the time, probably goes a long way towards explaining how such a strange idea was so readily, and widely, accepted.
Many readers, I’m sure, will get annoyed at my summary dismissal of length-contraction and argue that length-contraction is supported by the Lorentz Transformation Equations. And my response to them would be: “Yes. Yes, it is! And that’s because the Lorentz Transformation Equations are also incorrect…”
I will address the validity of the Lorentz Transformation Equations in the next post but one; but first I need to address the issue of “Absolute Motion”…
© Kieran D. Kelly
This is Post #8 in the series on NeoClassical Relativity Theory
