danshawen:
James R said:
It can be helpful to think of length contraction as analogous to a rotation.
Yes it is, in the context of the specific question I am addressing here.
The most important word there, however, was "
analogous". I am making an analogy. No analogy is perfect. An analogy is not a precise description of a thing; it is a description that compares the similarities between two things, while glossing over differences.
A "rotation" of unbound energy is another mode of propagation of energy, in fact, the ONLY other mode of propagation, other than in a straight line at c.
I don't understand what you're talking about when you say "propagation of energy". Energy isn't an object. It's a property.
There is a deep relationship between the two modes of propagation of energy, but it isn't even close to the kind of physical rotation Minkowski proposed. Rotation relative to what? With what point as the origin or center of rotation? Which direction is the rotation, in 3D, 4D or otherwise? Gotcha again. And again.
Mathematically, one can talk about a Lorentz transformation as a kind of "rotation". But you must realise that this, too, is an analogy. The word "rotation" is being used in a very general sense to describe a particular coordinate transformation. You should not imagine that this kind of "rotation" is somehow meant to correspond to your usual notion of a rotation in 3 dimensional space. For a start, Lorentz transformations tranform both space and time coordinates.
Minkowski rotation is not physically either real or meaningful in connection with the relationships between length contractions and time dilations, in four dimensions or otherwise.
I don't know what you mean by this. A Lorentz transformation (or "Minkowski rotation" if you prefer) allows us to calculate what happens to events and intervals when the frame of reference changes. I don't know what you mean when you claim this is "meaningless". After all, we can check the results against experiments.
It has the flaw of treating time as though it were physically spatial in terms of a rotation AND as a physical length that is somehow rotating in both 3 and in 4 dimensions, without adequately explaining either.
Every book I've read that discusses Lorentz tranformation has seemed clear enough to me. You'll have to be more specific about where you think the mathematical flaw comes in. It would be good if you could point to experimental results that disagree with the theory, if you know of any.
He seems unable to decide whether bound energy is the same physical thing as energy propagating a c.
I don't understand what you're talking about. Can you explain in more detail?
Every physical dimension in this universe in every direction is light travel time, not some mangled Pythagorean complex expression of physical lengths commingled with time.
This sentence makes no sense. Common experience shows that some physical dimensions are spatial dimensions, not time dimensions.
Our current standards of length are based on the simple fact of the identity of space with light travel time.
No. Associating a length with a time interval requires the use of a velocity.
If they were not, one would expect there to be a "standard" for rotation to go along with standards of length. If "at rest" has no rotation, then neither does any other reference frame. Contraction is real. Rotation isn't. This simple fact is the reason that the empty spaces between atoms are physically no more substantial (although distinctly different) than Doppler shifts, and Minkowski never suggested that Doppler shifts were rotations. Why not? Most mathematicians get their minds tangled into knots tighter than physical ones when trying to get a handle on this. It's the reason that Bell's Theorem doesn't apply both to QM and SR simultaneously. I'm not sure it really applies to either, and I don't care.
You've lost me.
No it isn't. If you are referring to applications to critical mass cross sections, for example, this geometry doesn't actually work. It doesn't work for any application. Not that anyone involved in such activities would even be able to tell you how badly it fails. It's classified, and they are bound by non-disclosure and other agreements designed to make certain that no one else is let in on the secret. I'm not. I'm telling you, Minkowski rotations applied to Lorentz covariance and the Interval used to derive them is so much mathematical trash.
Luckily, I don't have to rely on your authority. I can use my understanding to work out whether Lorentz transformation make sense, "work" or "fail". They seem to work very well, as far as I can tell. It looks like your classified sources haven't done their homework.
No energy transfer event that is not entangled or the same event in this universe is "simultaneous" in the way Minkowski conceived it.
You're over-complicating things. The definition of simultaneity is straight forward. You don't have to worry about quantum entanglement to understand the notion of simultaneity.
Time is very much grainier than the propagation of unbound energy at c in a straight line. It is the quantum field which can transfer energy between rotational (bound) and linear (unbound) propagation modes that is the key to understanding this.
You seem to be going off on a tangent here. Perhaps you should start a new thread...
The moment a mathematician tries to "plant" the origin of an absolute space into inertialess relativistic space, or even non-static Euclidean dimension of higher order Hilbert spaces, the results of any subsequent calculation based on solid geometry will be as flawed as they are needlessly tortured by an insistence of calculating dynamics based on a static model of geometry.
Which mathematicians in particular are you thinking of who have tried this "planting" you've referred to?
You realise that the theory of relativity is not a theory of "absolute space", I assume. It's a theory that involves ... relativity.
This is the principle reason why relativity doesn't "play nice" or "get along" with geometry, the topology of a sigma field, in quantum mechanics, quantum field theory, or anything else.
In what sense does it not "play nice"? Can you give me a particular example?
The only reason General Relativity works like solid geometry at all is that until VERY RECENTLY it has mostly dealt exclusively with interaction of bound energy that is matter. As such, it is a SLOW process being described, not FASTER ones involving interaction with unbound energy traveling at c.
Do you have any references that I can look at as to where GR fails in respect of fast processes? Are there incompatible experimental results that you are aware of?
Wheeler's derivation of the LT for Special Relativity using a photon trapped between mirrors (like our laser cavity) is wrong. The photons are trapped simply because for as long as they are reflected from the electrons on the surfaces of the cavity mirrors, it shares the inertia of the spacecraft. The endwise laser cavity in our thought experiment above is basically the same situation, but at no point did I suggest that the unbound photons in the laser beam were anchored in any particular region of space the way Wheeler did. I didn't need to. The situation is no different, yet it allows an alternate method of deriving both length contraction and time dilation WITHOUT REFERENCE to an origin of a coordinate system. The respective Doppler shifts can be relied upon to yield a similar result without geometry that depends on absolute space or position in an inertialess vacuum. If you understand relativity, you also understand that geometry is of limited utility in a universe defined in all cases by energy transfer events. There is no absolute space other than the geometric centers of the bound energy that is matter. Those centers are not "really" physically fixed with respect to the space they occupy, nor with respect any other particle of matter or boson. There is no absolute time other than the instant of "now" of quantum entanglement, which is intimately related to the properties of the quantum field in which energy that is bound or unbound is merely an excitation.
It sounds like you agree that time dilation and length contraction occur, but you believe that standard derivations of the formulae are flawed in some way. Perhaps you could start a new thread that presents your preferred derivation method. I would be interested to take a look.
Sure you were! 
