there are a number of alternative relativistically invariant wave equations, at least one of which is first order in time — SophistiCat
But also first order in space, I think? So the four solutions (advanced spin up, advanced spin down, retarded spin up, retarded spin down) reduce to two (advanced and retarded). — Kenosha Kid
Sure, but scattering also obeys the Pauli exclusion principle, so there must be two holes: one for the scattering electron to go to, and one for the scattered electron to go to (see the Feynman diagram in the OP). And those scattered electrons can scatter again, each requiring two holes, and so on and so forth. So it's a proliferation of backwards hole emission and transmission events. — Kenosha Kid
No, because the probability distribution of the incident electron will still multiply the probability distribution of acceptor sites. — Kenosha Kid
some relativistic formulations of the wavefunction equation have two solutions: w and its complex conjugate w* — SophistiCat
All, I believe. — Kenosha Kid
The advanced wave must be similarly causal but in reverse. For an advanced wave to be emitted from a particular point on the screen (describing an electron hole in reverse), that point must be capable of doing so. Otherwise the retarded wavefunction depiction of the electron leaving the cathode is unjustified in the first place. — Kenosha Kid
In the case of both microstate exploration and decoherence, the precise state changes constantly. An electron on the screen which might forbid an incident electron at time t might not be present at time t'. A particular configuration of scatterers that would destroy the wavefunction at time t might permit it at time t'.
The signature pattern of the double slit experiment is not one event but many thousands. What we see then is not just the value of the probability density of the electron, but also the statistical behaviour of the macroscopic screen. Over a statistical number of events, the pattern must be independent of changes in the precise microstate of the screen. — Kenosha Kid
I think it's more economical than parallel universes. — Kenosha Kid
Because the electron's birth and death are the true boundary conditions of its wavefunction! And here we turn to relativity. The relativistic wavefunction is of the form [E−V]2=[p−A]2+m2. This puts time and space on equal footing (both energy and momentum are squared), requiring knowledge of the particle at two times, not just one. — Kenosha Kid
There is no guarantee here that this will eventually reduce the number of intersections with the screen to 1. But we are a long way from the original Copenhagen picture of an electron that might be found anywhere. I expect that, if we could solve the many-body Dirac equation for the universe (well, it would have to be some cosmologically-consistent generalisation of it), it probably would resolve to 1 intersection. — Kenosha Kid
Genes cannot be selfish or unselfish, any more than atoms can be jealous,
elephants abstract or biscuits teleological.
U.S. intelligence agencies warned the White House last year that President Trump’s personal lawyer Rudolph W. Giuliani was the target of an influence operation by Russian intelligence, according to four former officials familiar with the matter.
The warnings were based on multiple sources, including intercepted communications, that showed Giuliani was interacting with people tied to Russian intelligence during a December 2019 trip to Ukraine, where he was gathering information that he thought would expose corrupt acts by former vice president Joe Biden and his son Hunter.
The information that Giuliani sought in Ukraine is similar to what is contained in emails and other correspondence published this week by the New York Post, which the paper said came from the laptop of Hunter Biden and were provided by Giuliani and Stephen K. Bannon, Trump’s former top political adviser at the White House. — WaPo
From the overlap integral of the retarded wavefunction with the advanced wavefunction:
In transactional QM, this is the very meaning of the Born rule. — Kenosha Kid

When a particle moves from event (r,t) to (r',t'), it still does so by every possible path (Feynman's sum over histories). If you sum up every possible r' at t' and normalise, you recover the wavefunction at t'. — Kenosha Kid
Ah, I see. This is deeper than I'd realised. Simply multiply whatever complex number by whatever physical unit: we never see that. I see I have 10 fingers and that I'm 5.917 feet tall, but I have never weighed (12 + 2i) stone. — Kenosha Kid
I'm getting confused now between ontologically real and real as in has no imaginary component. — Kenosha Kid
The OP holds that the complex wavefunction is an ontic description -- or fair approximation to such -- of how particles propagate through space and time as we represent them. How we describe the relationship between time and space is intrinsically complex, just from straight relativistic vector calculus, which happens to be the language quantum field theory is written in. There are other languages for describing relativity that can do away with the imaginary number and it may well be that in future we can generalise QFT in a similar way; such an endeavour would be part of a general relativistic quantum mechanics. So I don't hold the complex wavefunction to be an ontic description of the particle itself, rather it encodes the ontology of the wavefunction in our spacetime representations accurately, e.g. encodes information vital for doing the physics. — Kenosha Kid
But these aren't physical either. It is simply that complex exponentials are much easier to manipulate than individual sines and cosines. — Kenosha Kid
But no complex quantity can be physical in itself, i.e. we can't observe it in nature. — Kenosha Kid
That's actually not an uncontroversial statement. The wavefunction is frequently referred to epistemologically as the total of our knowledge about a system. The OP basically states that it encoded more ignorance than knowledge. — Kenosha Kid
he wavefunction can be written as a real function multiplied by a complex phase defined everywhere (this is trivial: a complex number has magnitude and phase). The phase is important for interference effects, but makes no difference when it comes to observables. The former is why I believe in an ontic wavefunction, and the latter is why the wavefunction might be considered epistemic. — Kenosha Kid
I hope to provide an argument that utilizes the prime principle of confirmation to show that objective beauty provides evidence in favor of the hypothesis of theism over that of atheism. — Daniel Ramli
This does not put time and space on equal footing. The solution requires knowledge of u at one time and two places. These are generally derived from physical considerations, e.g. where the electron wavefunction must vanish: two positions where the wavefunction is zero at one time: generally the start. — Kenosha Kid
[The relativistic wavefunction] puts time and space on equal footing (both energy and momentum are squared), requiring knowledge of the particle at two times, not just one. This is why in relativistic quantum theories, we do not proceed by specifying an initial state, time-evolving it forward, and asking the probability of spontaneously collapsing to a particular final state. Rather, we have to specify the initial and final states first, then ask what the probability is. — Kenosha Kid
The true boundary conditions — Kenosha Kid
This idea of the absolute square is important. It is how we get from the non-physical wavefunction to a real thing, even as abstract as probability. Why is the wavefunction non-physical? Because it has real and imaginary components: u = Re{u} + i*Im{u}, and nothing observed in nature has this feature. The absolute square of the wavefunction is real, and is obtained by multiplying the wavefunction by its complex conjugate u* = Re{u} - i*Im{u} (note the minus sign). Remembering that i*i = -1, you can see for yourself this is real. We'll come back to this. — Kenosha Kid
The latest Times investigation into the president’s tax data and other records found that more than 200 companies, special-interest groups and foreign governments had patronized Mr. Trump’s properties, funneling in millions of dollars, while reaping benefits from him and his administration.
“As president, Mr. Trump built a system of direct presidential influence-peddling unrivaled in modern American politics,” writes an investigative team that has been covering the president’s finances and taxes for almost four years. — New York Times

I've not heard of this, do you have any names or reading to suggest? — Isaac
In retrospect, I think you are right that determinism is neither here nor there in the issue of moral responsibility and free will. — Olivier5
Indeed, and 'complicated' is certainly right, but is it that you think such a notion of free-choice need be abandoned for that reason? Or are you more in favour of rolling up one's sleeves and getting stuck in nonetheless? — Isaac
I'm sometimes required to help plead for judicial leniency on the grounds of a person's upbringing or environment. The basis for such action is that somewhere in this muddle we (those involved at the time) can agree that such influences were outside of the person's preferred choices. — Isaac
What intrigues me is the expression "what we've been talking about all this time is not what we thought it was". I'm afraid I can't quite make sense of this. A word has to mean what we (community of language users) think it means doesn't it? Could you perhaps rephrase? — Isaac
What really matters morally is the difference between having one's actions driven by desires an thoughts one considers one's own, and having one's hand forced by the unwanted desires of others, or desires and thoughts one does not consider one's own (psycho-pathology). All of this can be dealt with without having to send a single electron through any slits! We just don't need to know, in most cases, anything about ultimate cause, we only need go a few steps back and see if such causes are still within or outside of what we consider ourselves. — Isaac
Yeah, I can't really stand "...therefore X doesn't exist" conclusions (where X is some common feature of our language). I think, 'well what on earth have we all been talking about all this time then?'. — Isaac
‘Free will’ is the conventional name of a topic that is best discussed without reference to the will. It is a topic in metaphysics and ethics as much as in the philosophy of mind. Its central questions are ‘What is it to act (or choose) freely?’, and ‘What is it to be morally responsible for one’s actions (or choices)?’ These two questions are closely connected, for it seems clear that freedom of action is a necessary condition of moral responsibility, even if it is not sufficient. — Strawson, RET
Where is the university? All you've shown me are buildings and grounds and students and faculty and books and equipment. Where in all of that is the university you promised to show me? — Pfhorrest
I experience, personally, a capacity to choose options at random. — Olivier5

Santorum saying the quiet part loud. — StreetlightX
Stunned Pundits Criticize Trump For Refusing To Denounce His Base
CLEVELAND—After failing to condemn the group’s violent behavior and rhetoric during the first presidential debate, President Donald Trump came under fire from stunned political pundits Wednesday for refusing to denounce his base. “I’ve been reporting on these debates for decades, and frankly, I don’t know what the president was thinking when he declined to clearly and openly disavow thousands of violent, radicalized people who his reelection dearly depends on,” said ABC’s George Stephanopoulos, who, along with flabbergasted pundits from CNN, MSNBC, and CBS, noted that the president had several opportunities to distance himself from the people upon which his entire image, campaign, and presidency relied, and yet ignored them all. “How can Trump, as the sitting president, get away with this type of behavior that he’s totally normalized at every turn? It really shouldn’t be that hard for him to look at the camera, say their names, and then denounce his stalwart supporters whose votes are crucial for an election victory.” At press time, political pundits blasted Democratic candidate Joe Biden for refusing to explicitly denounce the extreme pro-Green New Deal rhetoric on the left. — The Onion, Wednesday 12:35PM
Rather, we'd work out what it is we still mean by 'responsible' despite determinism. — Isaac
Well, the neural network and the full connectome of the nematode Caenorhabditis elegans have been fully mapped. Simulating this neural network produces an identical response to different experiments when compared to a biological worm. If we are able to do this for our own brains we can expect similar results. But C. legans has only 302 neurons, orders of magnitude less than humans and the network complexity doesnot even come close. However, it is possible and hopefully we will be able to achieve this. — debd
We’ve now looked at almost 30 or 40 years of Donald Trump’s tax returns and his financial records, analyzed his inheritance. This wellspring that came from “The Apprentice” — that’s an amount of income unlike anything he experienced in any other aspect of his life.
It sounds like a big thing you’re learning is that when it comes to the kinds of deals in which somebody else borrows the Trump name and uses it, Donald Trump is swimming in money, but when it comes to a business that he buys and tries to operate, like a big golf course, those become big financial black holes.
The less decision-making authority Donald Trump has on a business, the more money that business is going to make. And the more he’s involved in designing a business, setting it up and creating a business plan, the more likely it is to have trouble. — NYT
