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I'm afraid we have different understandings of what "explicit" means, at least for this case. "Explicit" as in "He gave me very explicit directions on how to get there." (Taken from Oxford's dictionary). Yes, I'm sure about that. https://www.ippp.dur.ac.uk/~krauss/Lectures/QuarksLeptons/QED/GaugeInvariance_2.html Read under the heading "Local Gauge Invariance". IOW: You can re-define the local phase at will as long as you accompany such change by the corresponding gradient in the gauge field. What is "the" phase now? No wonder phase velocity is not an observable. You can concoct situations in which phase and group velocity are essentially the same. I'd venture to say that for those cases you can "measure" the phase velocity. What you're doing (secretly) is, of course, measuring the group velocity, and using the theory to deduce a value of the phase velocity consistent with it and with the choice of quantum state (or "ray") that you have obtained in that particular gauge. No. You got this totally wrong. Quantum waves are not sinusoidal. For starters, they are not real functions. They typically go like complex exponentials. No. I can write A=XY/Z, the relation be totally right, and neither A, nor X, Y or Z be measurable. In fact, what you both are saying contradicts the principles of mainstream quantum mechanics --except for free particles. If the particle is interacting, the so-called Hamiltonian has a potential energy term, and the momentum (the inverse wavelength) does not commute with it, so the principles say no, you can't measure both at the same time. They're called "incompatible." You both are confusing a component (among infinitely many) of the quantum state with the whole quantum state. More on this: https://www.mathpages.com/home/kmath210/kmath210.htm And so on, and so on, and so on...

No it isn't.

Lol. Not a thing!

Good point. I assume either a natural steam reforming of methane: CH4 + H2O <-> 3H2 + CO (endothermic), in which case one might expect to find carbon monoxide associated, or else from natural cracking of hydrocarbons. But as hydrogen molecules are small, they may migrate away from the source of production, complicating efforts to determine how they were generated.

For current UK Prime Minister: Is a few years behind the times too. Could probably provide a better answer, if it were up to date on current events.

Ok, so there is at least some hints regarding pipetting errors in the qPCR (a delta of 1 is about a 2-fold change, which should not be happening in replicates). But obviously that does not seem to be an issue with the GAPDH. Obviously, we do not know if it is realistic whether your target is about 1000-fold different in abundance and that the differences are caused by differential extraction (I would consider it somewhat unlikely though). Main things I would suspect fall into the area of sample handling, and potential assay issues. So a few things to check include: - quality of mRNA samples - was it a 2-step? Can there be issues there? - are the protocols well-established for the specific primer combinations? What are the PCR efficiencies for them? - is there a possibility of contamination? What levels do you typically have for an extract of your control sample? - is there a possibility of degradation?

Please tell us more when you reply as more detail makes it easier to help. Differentiation is a process. A differential is the result of that process. (That is differential as a noun) But differential as an adjective refers to the difference between two values eg the differential pressure between inside and outside = (inside pressure - outside pressure) But there is considerably more required to understand things. Why is this posted in homework help ? Is this really homework or are you asking about mathematical theory, in which case you will attract more attention and answers if you placed it in the mathematics section.

Sound waves do not obey Lorenz transformations. This is the key result implied but not explicitly stated (you have to think about it to find it) in the first postulate in Einstein's theory of relativity.

Very interesting question. See one of my preferred: The multiplication of bananas by umbrellas.

I think this is the way it is with most any subject. Before we learn, we make guesses using only what we know. Those guesses live in the gaps in our knowledge, and get forced out as we learn more and more about a subject.

Reality is defined as physicality, matter and energy. “Nothingness” or “emptiness” is NOT reality because it has no bearing on it, we can’t measure an amount of physical “space” or “time”, because they’re not physical objects, physical “realities”. They’re the absence of such. Literal “space” has no effect on space. Not a surprise that ‘nothingness’ has not effect on nothingness. Let me clarify once again: gravity doesn’t literally slow down Light by the way of physically “pulling” on the photon particles or however you might describe it, but rather, distort Reality (I call reality, reality, scientists call it “space-time”, I do not) itself and diverts and “bends” reality, which Light travels through. The space itself is distorted/warped with gravity “pulling” reality itself towards the singularity. Light merely travels in the straightest line possible from its source (think a laser) unless diverted by a material object (reflection) or curved by distortion of Reality (gravity). Non-Euclidean Geometry proves this point. Light travels in a straight line but appears to be curved from an outside observer. This is why black holes have Light discs around their event horizons, Reality being nigh-infinitely distorted, and therefore time, for Light to be able to be perceived as being slow (in reality, their true speed is Infinite). Kind of like when you watch a wheel/rim of a car in motion, sometimes it may appear to be spinning slowly, and sometimes in reverse, but in reality, it is traveling extremely fast. Or a fan spinning around very fast, but sometimes it appears to be going slowly. Same concept. If black holes bend Reality, then it will bend/curve the path of Light towards the it’s gravitational singularity. This is why spacial objects get slingshot around gravitational singularities, be it planets, stars, or black holes. It is just much more obvious in black holes due to their size and strength of their gravitational pull. All celestial objects bend and curve Light, by means of gravity. It is why the speed of Light (when reflected backwards to the sender) can be measured. The One-way speed of Light cannot be measured accurately within Reality (space-time) due to the Universal effects of ALL gravitational singularities in existence. It needs to be done in a vacuum and with no Reality (space-time) warping done by gravity. Don’t worry, unlike you I haven’t lost my imagination and conformed myself to false beliefs and “supposed truths” as you probably do. You derive your “objective” truths from whatever the scientific consensus is. I derive mine transcendentally. Did you just admit to your imagination as being “quashed” due to attainment of more knowledge? I don’t know but I hope to never be like that. Me personally? My imagination is derived from logic and knowledge and is the reason I do and why I ponder these things. I’d argue your imagination is one of if not the most important faculty when it comes to scientific thinking and understanding. Do you really think that all great scientific pioneers simply conformed to the scientific consensus of their times? Be it Galileo against geocentricism, or Einstein’s development of his theory of relativity, these all stemmed from their observations of reality, and their imaginations to expound from their observations.