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Hi all, Consider the Bargmann-Wigner equation, which is the relativistic wave equation for particles of arbitrary spin (i.e. valid for both bosons and fermions). This is a set of coupled differential equations for the components of the wave function, which is an object the type of which is in turn a representation of the Lorentz group. So for example, this would be a bispinor for the Dirac field, or a Rarita-Schwinger spinor for spin-3/2 particles, and so on. This equation can be generalised to curved spacetime backgrounds. I’ve struggled for a long time with the attempt to come up with some kind of geometric interpretation for this equation (or even just for the Dirac equation), in the same way as one can find geometric interpretations for the GR equations. Thus far unsuccessfully. Does anyone here know if such a geometric interpretation exists? Of course I know that it does not necessarily need to exist, but it would be really helpful if it did. With wave equations being in some sense representations of the Lorentz group, it ought to be possible to somehow bring this back to rotations in spacetime, though I struggle to find an intuitive, visualisable interpretation.

I learnt about this when I was a criminal fraud investigator in the Inland Revenue for reviewing potentially fraudulent invoices, accounts, till rolls etc. Apparently when someone tries to fake a list of numbers for nefarious purposes they are more likely to either choose a fairly even spread from 0 to 9 or over select 5 to 7 creating a bell curve when the numbers are plotted on a graph. It's not enough to convict, obviously, but is a useful investigative tool.

Obviously in most modern societies we are free to express pretty much anything we want (with notable exceptions, and with the caveat that some forms of speech will certainly result in consequences of various kinds). But - and let me play the devil’s advocate here - where does this fit into a larger picture? Is unrestricted freedom always necessarily a good thing, no questions asked? I hear so many people keep going on about their “right to free speech”, but very few ever talk about their corresponding responsibility to engage in ethical speech. People like freedoms, but they don’t like the responsibility that comes with it. If I say or do something that is deeply hurtful to a lot of other people, and is not conducive to peace, prosperity and well-being of society as a whole, in what sense is such a freedom to be considered ‘good’? Much has been said about people’s freedom to engage in whatever speech they want - but what about people’s freedom from forms of malicious or otherwise hurtful speech that is simply not compatible with a civilised and peaceful society that values the well-being of all its citizens? Before anyone responds, I’d like to point out that I grew up under a communist regime in the former Eastern Bloc, so I know first hand what it is like to live in a society that does not grant freedom of speech (well, theoretically you could say anything you wanted of course...but some things you were only ever going to say once, so effectively the freedom was severely curtailed). It isn’t just an academic concept to me, I’ve experienced it, and it is not a good thing. On the other hand though, I am also on the autism spectrum, and as such I am simultaneously more sensitive and vastly more conflict-avoidant that most neurotypical people. Some forms of speech with malicious intend, directed towards me, will affect me very deeply, and at the same time I am entirely incapable of confronting the speaker about it. So for everyone like myself, who is affected in different ways by harsh and malicious speech (essentially everyone who does not fully conform to the accepted norms of society) - where is our freedom from such forms of speech? Why is this never really debated? Given the choice, I would personally be very happy to trade some of my ‘freedom to’ for a bit more ‘freedom from’, if that is conducive to my overall wellbeing. Of course I am aware of the difficulties - who makes these decisions, based on what, etc etc...but still. I don’t have a very specific point to make, I just wanted to put this ‘freedom to’ vs ‘freedom from’ thing out there.

With all of the above being said, I think is also important to remember that the property of mass only exists at all because the universe is now in a state of comparatively low energy. If you go back to the early universe, prior to the point of electroweak symmetry breaking, the Higgs mechanism did not yet operate, so all elementary particles were massless. In that sense, mass is just the result of a broken symmetry.

You can publicly express support for any theory you want. But others can publicly express their displeasure, and ridicule you for it. Free speech is for all. Even on this forum, you are allowed to present alternate theories of human evolution. But you had better do it in good faith, and back it with evidence.

The reddening we see with the setting Sun is due to the blue end of the spectrum being scattered. Thus the light coming from the direction of the Sun has less Blue light and looks redder. The red-shft we see from distant galaxies cannot be due to a like effect. We measure red-shift by looking at the light's spectrum. In it are patterns of lines that are like "fingerprints" for elements. Each pattern isn't only unique, but it is produced in a certain point of the spectrum. If the red-shift was due to a scattering out of blue light, all you would see would be a dimming in the blue end of the spectrum. The spectral lines would still be there and in the same place. This is not what we see. Instead we see a shift of the whole spectrum towards the red. Spectral lines have moved further to the red end of the spectrum. The wavelength of the light itself has been changed, rather than just certain frequencies filtered out leaving redder light behind. (in fact, red-shifting will shift non-visible frequency ultraviolet into the visible light range.)

a) The variable is a map (in Python language: a dictionary or dict). Maps are pairs of unique keys and possibly non-unique values. Typical cases are lists of usernames (as keys) and the users' passwords (as values for the keys). In your case it is a map of string keys that each have an integer value. b) The curly brackets are a way to define dicts in Python. You should be able to literally type in a dict like "{'a':0, 'b':1, 'c':2}". Here, the case is just a bit more complicated because the term is { <elements are generated by a for-loop> }. c) The colon separates key and value in a dict, as in my example from case b). The loop generates key:value pairs a:i for all i in range. d) The statements are the a:i. The loop runs from 0 to len(a)-1. In this case from 0 to 5. e) As mentioned before, keys in a map are unique. So there can only be at most one value for the key 'a'. The usual behavior for maps and dicts is that setting d[key] = value will either create a key with the given value in d. Or, if the key already exists, it will keep the key and set the value to the new one given. In that context, it is at least the behavior I would expect from the loop: At i=0, it sets ind['a']=0. And then at i=4 it overrides the existing value with ind['a'] = 4.

Hey all, I have randomly discovered this thread on the net and here I am, making a new accound. So yeah, I can do the same thing as everyone else described. But I can do even more, I can sort of heal other people. Only tryed with head aches and somach crams so far, but it seems to be working every time. What I do exactely is start the 'feeling' in diaphragm, than move it to my right hand and then hover the palm over the affected area thinking intensely that I want to 'change the water' in the other person so that whatever causes the pain is neutralized. After 2-3 minutes I get an WOW from the subject that say the pain is completely gone. Here are my thoughts before stumbling on this thread: what I activate is some sort of electrical stimulus. This would explain the tingling or the hair rise when I move the 'feeling' through my body. And once is concentrated in my palm, somehow, it interacts with the other person. I wonder if everyone that can create this feeling can also heal others, could you guys give it a try and then come back to the forum and tell us if it worked? Thank you!