elfmotat

I've thought about this some more, and I have an answer more along the lines of what the OP is asking for, granted that dV/dx=-ma is taken as a postulate (time-translation symmetry). Say for simplicity the forces acting on a particle are conservative, and can therefore be modeled by a scalar potential V. If we posit that there is a quantity E which is constant over time consisting of two terms, V and another we'll call T, then we know: [math]\frac{dE}{dt} = \frac{dT}{dt} + \frac{dV}{dx} \frac{dx}{dt} = \frac{dT}{dt} - mav = 0.[/math] So we have: [math]dT = m v dv[/math] Or: [math] T = \frac{1}{2} mv^2 + T_0[/math] where [math]T_0[/math] is a constant of integration which can be taken to be zero.

The most important constant for cosmological red-shift would be the gravitational constant G. The most straightforward way to consider variable constants is to promote them to scalar fields. This is exactly what, for example, Brans-Dicke gravity does. The constant 1/G is replaced by a scalar field [math]\phi (x^{\mu} )[/math]. Brans-Dicke gravity has pretty much been ruled out -- the tunable parameter [math]\omega[/math] must be >40,000 to be consistent with current observations. But with a value that large its predictions are basically indistinguishable from General Relativity, so it doesn't solve any problems dealing with red-shifts. One recovers GR as [math]\omega \to \infty[/math]. A very large but finite value for [math]\omega[/math] would be incredibly strange, and seems unnatural. So not only is a variable gravitational constant pretty much ruled out, but even if it weren't it wouldn't help explain the apparent expansion of the universe.

I think this is probably the best way to do it because it's general and doesn't depend on some arbitrary choice for a potential. Bonus: the same approach also works for finding KE in Special Relativity, where: F dx = (dp/dt) dx = v dp = mv d(γv) which you can integrate by parts to get (γ-1)mc2.

The disagreement here seems to stem from whether or not the complete electric field [math]\mathbf{E} (\mathbf{r} )[/math] is known, or just the field at some specific points. I don't think anyone would disagree that complete knowledge of [math]\mathbf{E} (\mathbf{r} )[/math] ensures complete knowledge of [math]\rho (\mathbf{r})[/math], by the fact that [math] \epsilon_0 \nabla \cdot \mathbf{E} (\mathbf{r} ) = \rho (\mathbf{r})[/math].

Yes. For example: [math] \langle 0| a^{\dagger} \, a \, a^{\dagger} |0 \rangle = A \langle 0 | 1 \rangle = 0[/math], where A is some normalization constant. Also, the operation [math]a |0 \rangle = 0[/math] is sometimes referred to as "killing/annihilating the vacuum/ground state." In lectures or notes you might see someone say "such and such operator will annihilate the vacuum, leaving such and such terms left over..."

There is a big difference between "this scenario may make for useful approximations" and "I can imagine this hypothetical object, therefore all conclusions drawn about the hypothetical world in which it exists must also be true of our world." The former is perfectly fine. The latter makes zero sense. So we're in agreement that there's no circularity necessary? Good. And you add nothing to our understanding of time by stipulating that time is change in time. I don't know what you mean by "only one time." This seems like it could be true or false, depending on exactly what you mean. So we're arguing about unfalsifiable nonsense? I don't know how to argue with blanket assertions. It's generally a good idea to learn physics before you try to make arguments based on physics. For any unit system, you need a basis set of quantities which spans the entire set. Sometimes, those basis quantities are chosen to be [time], [length], [mass], and [charge]. However, there's no particular reason to choose them. You could equally well use [acceleration], [density], [current], and [energy], for example. In that choice energy has fundamental dimensionality. The choice is completely arbitrary. So I guess we've established that you're incapable of reading. I want to get a better understanding of time. Your definition has not done that for me. I also want to know why you're clinging to misleading, overtly circular, and useless metaphysical definitions. I can't wrap my brain around what you could possibly gain from thinking about time in this way. Well then, I suppose we're done, aren't we?

Sorry for the delay, I've been busy with exams. You can't be serious. So you're claiming that because physicists sometimes analyze idealized systems to develop useful approximations or intuition, using a clearly unrealistic dictionary as the basis for a logical argument about reality is valid? That doesn't even begin to make sense. Even if I granted you that there is no operational definition of time, that does not preclude a definition in terms of other terms which are operationally defined. So no circularity necessary. So are you saying that changes can occur without any time elapsing? That doesn't answer the question of how changes can occur without time. Different Lagrangians are used for different problems, as I'm quite sure I've stated multiple times already. You can define whatever type of Lagrangian you want. It depends on the type of kinetic or potential energy you're considering. I really thought I made this easy to follow last time around, but the "kinetic" and "potential" are just names given to terms in Lagrangians which happen to be useful. The names themselves can apply to a whole variety of things, including field kinetic terms, gravitational potentials, self-interaction potentials, etc., etc. It is generally understood what is meant by the context of the problem. Plus, I gave you a wonderful definition of energy which you previously ignored: the conserved Noether current generated by time-translation symmetry. That's not the "dimension of energy" (whatever that means), that's 1 Joule expressed in terms of kilograms, meters, and seconds. What does that have to do with anything? What do you even mean by "you're wrong"? That doesn't even make sense. I accused you of using fallacious arguments (specifically rhetorical tautologies, which are not the same as logical tautologies). You somehow twisted this into an argument over the definition of "tautology," completely missing the point. READ WHAT I'M SAYING. I wasn't aware there were rules. Whose rules are these? This is too good. It's an abstraction because you say so. Wonderful. That's definitely not what we're arguing about or anything. So you've given us an admittedly circular and useless definition, yet you still cling to it? Bizarre. No wonder we're not getting anywhere.

Basically it just comes from the fact that [math]a |0 \rangle = 0[/math]. So if you have some operator [math]M[/math], then [math]Ma |0 \rangle = M \, (0) = 0.[/math]. Exactly.

So, you accept that signals from inside the light-cone can be detected, just not from far-away objects? That's weird. I'm not sure how to argue with such an unusual position. How about massive particles from cosmic rays, neutrinos, etc.?

That's just false. How about sound waves? Humans use those pretty often.

I don't believe this is true either. And I'm telling you that this makes for a poor comparison with reality, because dictionaries aren't complete. Did you ignore that part last time? Wrong. You can't use a hypothetical complete dictionary to draw conclusions about reality. Also this is a false dichotomy. Why only those choices? I simply don't agree that exact definitions need to be text-based. And we cannot see changes except through time. So congratulations, we're back to square one. I don't need to. As I said, you start by defining a Lagrangian - as in you include whatever terms you want. After you've defined it, you work out what the physical consequences would be and compare the predictions with experiment. As it happens, some useful Lagrangians include terms which people have decided to call the "kinetic" and "potential" terms. They got those names because they happen to be useful for modeling the real world, so it's nice to have names to call things. You can certainly construct Lagrangians without them. These are all well-defined math words that you should be able to look up yourself. "In rhetoric, a tautology (from Greek το αυτο, "the same" and λόγος, "word/idea") is a logical argument constructed in such a way, generally by repeating the same concept or assertion using different phrasing or terminology, that the proposition as stated is logically irrefutable, while obscuring the lack of evidence or valid reasoning supporting the stated conclusion. (A rhetorical tautology should not be confused with a tautology in propositional logic.)[a]" http://en.wikipedia.org/wiki/Tautology_%28rhetoric%29 Please do me a favor and actually read my posts before you respond to them. It's frustrating having to say the same things over and over. I accused you of using rhetorical tautologies. Somehow you got it in your head that we were actually discussing logical tautologies (which makes no sense given the context of the conversation). Except for the fact that I TOLD YOU EVERYTHING ABOUT IT! What I want to know is this: if time is an abstraction of change, then why can't we use information about change to figure out information about time? If time is the abstraction of change, surely knowledge of change would imply knowledge of time. If you say this is false then you must at least admit that "time is the abstraction of change" is a very misleading and probably useless definition. Which has been my point from the beginning.

"Preciously" makes him sound like Gollum.

Except dictionaries aren't really complete, so this makes for a poor comparison with reality. If you can explain how you're getting from "most words are in the dictionary" to "all definitions are circular," then do it. If not then I don't accept this as a valid argument. I don't see how I'd drive in circles. A particle is equipped with a Lagrangian, L(x(t),v(t)). The particle will always travel along paths x(t) such that ∫Ldt is stationary. In classical mechanics the Lagrangian is the particle's kinetic energy plus potential terms. (The Lagrangian is defined, then its consequences are worked out. Building physical models then comes down to merely finding Lagrangians which agree with observation.) You're confusing the formal logic definition of a tautology with rhetorical tautologies, the latter of which I have been accusing you of using. The problem is that you've introduced additional objects into what was supposed to be a closed system. I'm giving you a scenario where I've defined all changes in space. You're claiming time is an abstraction of change. I'm giving you everything you need to know as far as changes are concerned. Why can't you tell me anything about the time?

I asked you to explain how you can logically jump from "most words are in the dictionary" to "all definitions are circular." You didn't. I agree with you. More unfounded claims. Okay... I don't think you know what a tautology is. By your standard any definition is tautological. That's clearly a bad standard. It doesn't matter. I gave you a contained system (if the complexity of "man walking" is confusing you, substitute "particle moving"), and all of the information about all of the changes in that system. If time is an abstraction of change, like you say, you should be able to work out the man's velocity without me having to tell you. That makes no sense, so your definition of time is clearly flawed. This is incomprehensible to me. Please explain more clearly. Are you serious? http://en.wikipedia.org/wiki/Euclid%27s_Elements

That isn't what you originally said. You said "every definition is circular." Regardless, I still don't buy it. You haven't justified this claim. I completely agree with everything you say here, except for the notion that force and mass are circular. I gave you a mass-independent definition of force. Why isn't that good enough? You don't get to artificially restrict the bounds of my answer just because good ol' Newton didn't think of it himself back in the day. We can go deeper and talk about mass: how it comes from the masses of individual particles, that those particles are actually quantum field excitations, and mass is the coefficient on the quadratic term in the field Lagrangian. Then we could talk about mass renormalization, and even the Higgs mechanism. Or we could go the other route: we could talk about how all forces come down to four fundamental different types of interaction (really just two at macroscopic scales), their descriptions in terms of field theory, etc. All to convince you that mass and force are not circular. You can't just say, "Newton didn't think of it, therefore it's not Newtonian, therefore I win." Well, I mean you can say it, but it's pretty silly. I don't see how that's circular. It seems the definition of "survivor" you're using is "organism that lived long enough to pass on its genes." So you just wrote the definition of "survive" tautologically. The definition itself isn't circular. 1 elfleg = 0.89 m = 2.92 ft. = 35 in. Yes, the length of my leg is 1 elfleg by the definition of an elfleg. How is that tautological? Let's say a man walks 10 m at constant velocity. How long did it take? Why do you think it is that you can't tell me? Now break that 10 m into two halves. Since he traveled at constant velocity, the time for him to cross each half is also halved. Now break it into quarters, then eighths, etc. Eventually you'll get down to extremely tiny changes in position, yet the time for those changes to occur is still completely undefined. Why do you think this is? If time were "an abstraction of change" then why can't you tell me anything about the time intervals in the above example system, given that you know literally everything there is to know about all the changes that occur within the system? Are you so clever that you can invent information I haven't given you? If not, then I don't see how you can claim "time is an abstraction of change," given that it's impossible reconstruct information about time by using only information about changes.

Yes, good, you can read. You claimed every definition is somehow circular. I just gave you a definition. Tell me where it's circular. That doesn't change the fact that there is a definition of force which makes no reference to mass. The definition [math]F_i = \partial_i L[/math] still works in Newtonian mechanics. Energy is the conserved Noether current generated by time-translation symmetry. Nobody cares what Darwin did or did not know. The subject of Darwinian evolution is not restricted to the life and beliefs of Charles Darwin. If I have introduced a circular definition, please explain where. It does me no good if you don't tell me how my logic is flawed. I was demonstrating that circular (i.e. making reference to itself) definitions can still contain useful information. I then contrasted the useful example against the nonsense sophistry you've been spouting. I already gave you a definition: the length of my leg is one elfleg. Please tell me where that tautological. That's self-contradictory. You can't say that they're the same, except one is different. Then they're not the same. Since we've been doing this for ages now and you still haven't given me a useful definition of the word "change," what's to stop me from claiming "change is an abstraction of time"? That's just as meaningful as what you wrote: as in, it's not.

I don't have a PhD. I just took the time to learn physics before trying to come up with my own theories. People should be encouraged to learn, not to develop vague convoluted "theories." If you're frustrated by the responses you're receiving, you should take it as an encouragement to learn more. But most importantly, ask questions before making statements.

I define the length of my leg as a new unit called the elfleg. Tell me where that's circular and I'll buy you a doughnut. Sorry to be the one to break it to you, but physics has advanced since Newton. Lagrangian mechanics for example, an alternative formulation of Newtonian mechanics, makes defining force extremely simple: the spatial derivative of the Lagrangian. No reference to mass whatsoever. Darwinian evolution does not say that "the fittest survive." All it says is those that did survive could pass on their genes, whereas those that didn't survive couldn't. I don't see how you can go from "all words are in the dictionary" to "all definitions are circular." How are you making that jump? Regardless, the problem is not necessarily recursion. There are perfectly sensible recursive definitions. For example [math]\phi = \sqrt{ \phi +1}[/math] is a definition of the Golden Ratio. It is a useful definition because information can be extracted from it. We can figure out the numerical value of [math]\phi[/math] because despite its definition being recursive, it is still well-defined. What you've essentially done with your "time is change" nonsense is say, "hey guys, I figured out that [math]x[/math] is actually [math]y[/math]." So then I ask, "well then, what is [math]y[/math]?" And you respond with "[math]y[/math] is [math]x[/math]." That tells me nothing. All it says is that if [math]x=y[/math] then [math]y=x[/math]: a tautology. It gives me no useful information. You've accomplished a change in variable, presumably for aesthetic purposes. That's why I earlier called it "a pedantic shift in vocabulary."

What? You're asking vague questions and pretending the answers should be obvious. You tell us the answers. Ignoring the fact that you did say more about it literally one sentence prior, how does that answer my question? You're defining time in terms of change. I want to know how you're defining change, so as to prevent your definition of time from being circular. That is, how can you define change without explicit reference to time? Saying "time is not physical" is not an answer. Even if I granted you that time isn't physical, the question still remains.

I'll employ Ophiolite's checklist: Your post fails on several levels. You are using terminology without apparently understanding what it means. ​For example the words "state," "interference," (and about a dozen or so others), are technical words with technical definitions. You're using them in a nonsensical manner. In some cases your usage is exactly contrary to its meaning. ​Asymptotic freedom, for example, has absolutely nothing to do with "parallel plates." It has to do with strong coupling at short distance scales. You have introduced terms that are not used in this branch of science, yet have failed to define them. ​For example: "virtually physical contact," "geometric reality," etc. You have made assertions without providing any support. ​You haven't explained why we're identifying particles with spacetime, how this is mathematically modeled, or how you can get testable predictions from any of this. You have made assertions that are directly contradicted by the evidence. ​For example you say "gravity too, comes from strong interacting particles." That can't possibly be correct. We know for sure there are particles which interact gravitationally but not strongly. There is no logical connectivity between the points of your argument.

Indeed, he's yet to respond to this point. All he said was "time is not physical" the last time I brought this up.

Agreed. That pretty closely mirrors my thoughts.

Fair enough. I wish I had a less cliche way to put it. I can't think of any examples of where calling something out for what it is would be bad in a scientific setting. Some social settings may call for lack of honesty in order to preserve people's feelings. But in science we're interested in honesty, not feelings. The usual social courtesies do not and should not apply. It's usually illuminating to see things put bluntly instead of tippy-toeing around the issue -- if not for the people directly involved then for any third parties who stumble upon the conversation. I don't disagree with anything you say here. I just don't see the problem with simultaneously calling crackpottery crackpottery.

If you're looking for an ultra-specific experiment then do it yourself. If Nichols and Hull could do it over a century ago, I don't see why you should have any problems now. I'd be willing to bet my entire savings account that you won't find anything surprising. The scientific process is not in question here. The problem is that you're expecting us to do all of your work for you. All of the links posted here can be easily found with a quick google search. The physics and math involved are not particularly complicated. The half-dozen experiments you've been linked to are not particularly hard to understand. You consistently refuse to meet us half way. If you want to see a particular experiment, search for it yourself. If it hasn't been done, do it yourself. We're not your servants. Put in a little effort.