Quotes from BBC Radio4 program 'In Our Time' with Melvyn Bragg: https://www.bbc.co.uk/programmes/b006qykl/episodes/a-z/a
In 2002 'The Physics of Reality' explores the incompatibility of quantum mechanics with gravity theory.
Is that supposed to be a reference to support the supposed incompatibility of quantum mechanics with relativity? You were talking about relativity with a specific context of electrodynamic phenomena like photons. That is special relativity, not general relativity (which has to do with gravity.) My responses to you all specifically were about special relativity and quantum mechanics.
34 minutes in, on 29th of May 2008 'Probability', describes the probabilistic nature of quantum mechanics.
18th of December 2008 'The Physics of Time', discusses the need to resolve the nature of time itself.
30 minutes in, on May 3rd 2009 'The Measurement Problem in Physics', Roger Penrose speaks about Bohm's theory, describing it as '...not revolutionary enough', 'the cat must either be alive or dead.'
40 minutes in, on September 23rd 2010 'Imaginary Numbers', Prof Marcus de Sautoy and friends beautifully describe the necessity of complex numbers.
None of these statements are in any way relevant to our conversation that I can see. Especially that last one.
40 minutes in, on Feb 12th 2015 'The Photon', Prof Susan Cartwright ascribes Niels Bohr with the casual quote '...anybody who thought that they understood quantum mechanics had demonstrated that they did not understand quantum mechanics'. I do appreciate that this is hearsay and I will keep a eye out for a direct quote. So you are correct that it was not Feynman anyhoo.
The first page of the textbook I learned quantum mechanics has the quote from Bohr and a similar one from Feynman. The fact that quantum mechanics is confusing and unintuitive is beyond dispute. Your claim that there is no consistent relativistic quantum mechanics is simply wrong. Quantum gravity is a different unknown, and we do have theories for it, the problem is the lack of practical tests to distinguish them.
Definition of terms (which may require further clarification).
The term 'complex time' is not mine but I use it because it is less obfuscating of its purpose than the term " imaginary time" coined by Stephen J Hawking in 'A Brief History of Time' Bantam 1989, P141.
"Imaginary time" refers treating time as a pure imaginary number. "Complex time" implies both real and imaginary parts. You are contradicting yourself here about whether it is your term or not. I don't have that book, but Hawking certainly meant only imaginary time, so what you are saying is different.
None of what you said comes close to being a definition.
The term 'covariant system' refers to the universe and everything in it being directly mathematically inter-related. I am making the assumption that physical reality must be essentially the same thing from all perspectives both inertial and accelerated.
A formal statement of the assumption you give is simply the "principle of relativity." (with caveat that it is experimentally obvious that inertial and accelerating frames can be distinguished due to "fictitious" forces.)
Roger Penrose develops the time slice argument whereby the sequence of events alters with perspective, which is what led me to consider the possibility that time is an inherently complex dimension. Penrose makes the assumption that nature is something which exists in the same form irrespective of perspective, despite any difference in timing of the sequence (if not the order) of its development as observed from differing perspectives. As is required by the conservation of energy and charge as well as conservation of the momentum which relates them.
I don't see the relevance of any of this to your "complex time" concept. These statements basically mean that the universe is what it is regardless of what frame you choose to write the numbers down in. Just like the contents of writing on a piece of paper don't change no matter how you rotate it, just how easy it is for you to read based on how you are looking at it.
Standard definitions of the term 'covariant' may have been narrowed by the process of mathematical development but their meaning continues to refer to things which are the same from all perspectives, as used by Einstein in his 1921 lectures, see: Einstein A. ‘The Meaning of Relativity’ Princeton lectures 1921, translated by Prof. E.P. Adams, Princeton University Press 1922). I quote from page 11,
"We can thus get the meaning of the concept of a vector without referring to a geometrical representation. This behaviour of the equations of a straight line can be expressed by saying that the equation of a straight line is co-variant with respect to linear orthogonal transformations."
That use of the word covariant is rigorously correct, unlike yours which has no relation to the definition of that word. The use of that word has not narrowed over time. You will note how it is directly talking about vector transformations, which is the context in which that word has meaning in physics.
'Orthogonality' is a real word. What I am attempting to express is the idea that the three perpendicular spatial dimensions do not have or retain that relationship when time is dilated, which it always is to some extent. Further, that the divergence from orthogonality is not absolute but varies with your perspective because that divergence is not covariant, its basis being artificial.
The basis vectors in an arbitrary frame in special relativity are non-orthonormal (Orthonormal is like orthogonality, but also refers to being of unit length.) You expressing that as if it is a novel consequence of your ideas only makes it seem like you haven't studied basic relativity in any depth.
By 'the linear component of complex time' I am referring to the real component not its complex conjugate.
"complex conjugate" is where you take a complex number and change the sign of the imaginary part. It is not in opposition to the "real component." Please look up a basic introdiction to complex numbers, and learn the terms "real part" "imaginary part" "complex conjugate" "magnitude" "phase." Your sentence here does not tell me anything other than that you don't know what the words you are using mean.
The term 'scalar' might be better, either way I am attempting again to avoid the use of the terms 'real' and ' imaginary' because they call the validity of the argument into question before it is even made. There is nothing any less than 'real' about the complex conjugate of a complex number, ask any engineer, we use them all the time because there is no substitute for their expression of that aspect of reality which diverges from a scalar measure of the dimensions you are using.
No, scalar, means "not a vector" which is a different concept. Use the words real and imaginary, like everyone else. Pretty much everyone wishes those terms were different but if you want to communicate with other people, you are stuck with them. You use the word "we" as if "engineers" is a group that you are part of but I am not. I have a degree in engineering, and work daily as an engineer. If you actually are a qualified engineer, then why do I keep having to explain to you concepts from entry level courses?
Also, for reference, it does depend on the context, often, such as in electromagnetic waves, only the real part is meaningful, and the imaginary part is actually just there as a mathematical shortcut that saves you a bunch of trig identities, but has no effect as long as you only do linear operations, but it is completely context dependent.
To use the terms 'space-like' and 'time-like' would be to make the arguments impenetrable to anyone not already deeply invested in the math as developed in the first chapter of ‘The Classical Theory of Fields’ Landau L. & Lifshitz E. USSR Academy of Science 1967, English Translation by Moreton Hamermesh, Pergamon Press, Sydney 1971, or similar.
No, they are basic concepts, that can be taught easily without diving into any of the mathematical details of relativity with simple space-time diagrams. Refusing to use common terms because they are "too complicated" is insulting.
I use the term 'complex time' and the equation exposing the gradual collapse of distance with increasing relative velocity, to describe how it is possible that our observation of the the sequence of the traverse of a single quantum can change with our perspective. It is just a different take on relativity which may help to simplify our understanding, hopefully bringing it within the grasp of our imagination and thus becoming useful in the design of devices such as the emdrive.
But as I have said it is mathematically useless, and has no physical consequences whatsoever.
meberbs,
you insist that there is no paradox within quantum mechanics. This is hard for me to understand when the behaviours of exchange particles are inherently non-local and cannot be described in the same way that we describe the macroscopic world. Hidden variables violate causality. Many worlds, string theory and other complicated 'work arounds' are attempts to resolve that paradox. What we need is a theory which explains both the macroscopic and the particle worlds, which explains both the experimental results supporting relativity and those supporting quantum mechanics, within a single credible explanation.
Nothing you listed is a paradox. A paradox is something contradictory, such as killing your own grandfather before your parents were born. What you listed is horribly confusing and unintuitive, but completely mathematically consistent. Quantum mechanics already links up just fine with the macroscopic world. Just like any credible new physics theory, it is consistent with previous theory in the appropriate limit. In this case the limit is the limit of large numbers. QED is perfectly consistent with special relativity, and as I said in my previous post, the various interpretations of quantum mechanics produce equivalent results, so which actually happens is purely philosophical.
Complex time is satisfying to me because it places us firmly in the present moment, it allows us to specify the energy difference between our presence and another’s.
Except as far as I can tell, it doesn't do that. You have not given a single example of how you could use complex time to describe the simplest of physical systems such as a ball rolling down a hill.
We have a specific location whose energy is directly proportional to our velocity multiplied by our mass in charges, relative to other locations.
How can a location have energy? An object has energy a location is just a point in space (or space-time). You can have a "potential" at a location (see gravitational potential, electric potential, etc.) You still sound like you are throwing words together in grammatical sentences without regard for their meaning. Although after this post, I am getting the impression that you should know better than to do that.
Attempts to define the concept of complex time have been around at least since 1988 and I have quoted my own incomplete attempts directly.
As stated before "complex time" with both real and imaginary parts is not something that anyone else has talked about ever to my knowledge. Your attempts have essentially no definition, and lots of unsupported assertion.
Your refusal to recognise such reflects rejection of the ideas, not the lack of an attempt to define them.
You have refused to recognize just about everything I have said. Your statements can be boiled down into 2 categories, ones that are statements of fact that contribute nothing, and are already well known (despite you presenting them as novel ideas), and ones that are complete gibberish, as you continue talking about "complex time" and asserting that is solves all sorts of problems, yet you might as well be saying "agsfhusv solves ajsfijdbsf" The problems you state don't exist, and you have not provided a definition for complex time that can describe even a basic situation.
All I can do is recommend them as hitherto unexplored solution to both quantum paradox and emdrive thrust.
Neither of which have been shown to exist, even if you actually were providing something useful.