Quite. Expectation value has an exact technical meaning, very closely related to the expected value in statistics. It is not really open to people to "believe" it means something else....unless of course they want to out themselves as idiots.Please Register or Log in to view the hidden image!
Well, "very closely related" is close enough for jazz..Please Register or Log in to view the hidden image!
No that is a logical mistake. Belief in (Darwinian) evolution does not an idiot make. Assumption of guilt without evidence does an idiot make...Please Register or Log in to view the hidden image!
You don't need to "believe" in Darwinian evolution. You are just using the word "belief" in the daily way of using it. I say I believe the Sun will come up tomorrow but it really requires no "belief".
IMO, it is pretty well established that in the early universe, quantum was weighted to the self-assembly of the helium and hydrogen atoms. Origins https://home.cern/science/physics/early-universe# This seems to suggest a natural preference for certain rare events (the formation of elements) to occur as a result of the value potentials contained in the early and later sub-atomic chaotic conditions directly following the BB or in Supernovae. The table of elements is a statistical table. Hence, the theory of Large number of rare events should apply to this and indeed has been used in mineralogy with great success. (see Robert Hazen).
Right, does using the equation E = Mc^2 require "belief" in SR? You bet it does! Belief has several definitions. If you intentionally cherry pick the wrong definition no one should be able to use the word belief except in context of "religious belief" or "daily casual use". But there is a third real definition; Belief https://www.merriam-webster.com/dictionary/belief Something wrong with that kind of belief? It is the verified scientific context on which I base my beliefs. That is why I always quote the science behind my expressed beliefs. You may not agree with the science, but you cannot argue the veracity of my belief in science (I believe that falls under "ad hominem"). p.s. all human endeavors, including science, are based on beliefs by humans. No one can claim exclusive Truth, right?
I see W4U has waved his wand of weasel-wording at "belief" now. In this thread, the usage of 'belief' is akin to 'faith' - something believed in the absence of compelling evidence/proof. Example: I may believe in God or the afterlife, despite me acknowledging sufficient evidence to support it. Contrarily, SR can be shown to be a working model. It does not require faith in the absence of evidence. The evidence is there in black and white. So, no. One need not believe in SR, since one can simply verify it or falsify it at their convenience.
You mean something like the uncertainty principle? In this thread or any thread, my usage of belief in context of mainstream scientific knowledge is in accordance with definition #3 in the Merriam-Webster dictionary. Read the quoted (linked) definition. Do you not believe in scientific knowledge? If you believe different, then it is you who is in error, not I. How presumptuous can you get. I don't accuse you of being illiterate, do I?
That is a lie. I am a hard atheist and I have NEVER claimed such a thing. You are positing a false example. Is that on purpose? But you do believe SR is reliable science, no? Or are you prepared to declare that YOU know SR is true? Have you verified and falsified the theory or are you "accepting" SR as true from peer reviewed papers, like religious people accept Christ because it is "written" ? Belief https://www.merriam-webster.com/dictionary/belief Yes, one can believe in SR and in a host of other mainstream science, on the basis that it has been verified and falsified and that proof can be produced by linking to reliable sources, as I always do. I believe in science when it has been peer reviewed. Are you a peer? Don't be ridiculous.
True enough. My point was a bit different, though, namely that with a mathematical term like expectation value, you can't make up your own definition of it and decide to "believe" that, instead of the meaning it actually has.
If you would actually read what I post or take a cursory look at the links I provide ( I'm on ignore?) you may change your thinking. The attitude you display is prejudicial and mostly from ignorance of what I actually post. My scientific sources are impeccable. My use of quoted texts and my conclusions why they are pertinent are open for debate, not for ridicule. But that is true for everyone who posts here, no? Statistically which is the most abundant element in the universe? Was its appearance a 50/50 quantum uncertainty or was it's probabilistic emergence weighted in accordance with certain extant relational values? Hydrogen https://www.livescience.com/32983-what-are-ingredients-life.html
Physics & Math Schrödinger’s Cat Lives On (Or Not) at the Age of 80 Discover how Schrödinger’s cat went from obscurity to pop-culture celebrity. BY PAUL HALPERNTUESDAY, NOVEMBER 10, 2015 THE NATURE OF REALITY https://www.pbs.org/wgbh/nova/article/schrodingers-cat-lives-on-or-not-at-the-age-of-80/
Wish he had picked a Goldfish It would be dead by now Please Register or Log in to view the hidden image!
OK, let's do this properly.... the Uncertainty Principle. Consider a so-called quantum state. This is an element in vector space of functions (usually called an Hilbert space) which, according to Schrödinger himself, has a representation as a wave function i.e takes values from the interval \([-1,1]\). This state vector is often denoted by the symbol \(\psi\), but of course any symbol will do just as well. Max Born suggested that the square of the wave function, which obviously takes values from the interval \([0,1]\) should be interpreted as a probability distribution. So, since the Schrödinger operator, a Hamiltonian, yields the total energy of the state, knowing the frequency of this wave gives you the energy (or momentum) of the vector. But applying the position operator to the same function gives no information about the position. Conversely, knowing the position implies single probability peak at \(x\), say, but then all information about the wave function and it's energy (momentum) has been lost. As was rightly said earlier, you cannot in principle know both. Or to be posh - the momentum and position operators, whose sum is simply Schrödinger's Hamiltonian, do not commute.
One could quibble about energy vs momentum, as different operators are used for each but the instructive point is that this is not a measurement issue: it is intrinsic in the QM model. Interestingly - for a chemist - there is another uncertainty relation, between energy and lifetime of the state. States with long lifetimes have well-defined energy but those with a short lifetime have a less well defined energy. This leads to something called "uncertainty broadening" in spectroscopy, by which excited states with short lifetimes give rise to broader spectral lines than those with long lifetimes.Please Register or Log in to view the hidden image!
Thanks, that'll keep me busy for awhile...Please Register or Log in to view the hidden image! Question: is "uncertainty broadening" the same thing as "natural broadening"? Broadening due to local effects Natural broadening[edit] https://en.wikipedia.org/wiki/Spectral_line#Natural_broadening
Thank you for that - it is a new one on me. But then, my chemistry courses concluded when dinosaurs roamed the earth.
If I may be permitted to address that misconception. Actually the brain cannot function at all without belief, according to Anil Seth. That's why we have beliefs and why those beliefs can be false. According to Seth, the brain can only make a best guess of what it believes (expects) the incoming information represents. If the brain does not believe what it is processing, it cannot recognize it. How Does Your Brain Construct Your Conscious Reality? (SOUNDBITE OF TED TALK) (SOUNDBITE OF MUSIC) To witness the actual demonstration of how "belief shapes our cognition", watch this really interesting video. Seth gives you a peek into how consciousness shapes our reality. https://www.ted.com/talks/anil_seth_your_brain_hallucinates_your_conscious_reality
Write4U - if you were genuinely interested in science (as you claim) then you would learn some, rather that quoting some drivel from the internet. I remind you this is a Physics and Math subforum. Non-scientific drivel belongs elsewhere
