timo

Ok, quick answer then: You´re trying to heat cold coffee to sell it as an energy drink.

My statement was frame-independent in the sense that it applies in any frame of reference. The constant acceleration an object has in its own frame of reference comes from the force F=0 it experiences in its own frame of reference. Note that F, a and v are three-vectors; they are not invariant under transformations, meaning they can be zero in one frame but non-zero in another.

You wouldn´t. Any non-zero constant acceleration applied for a sufficient amount of time would do, for example. However, as Klaynos mentioned, the energy required to reach a velocity arbitrary close to c is a limiting parameter here. Technically, this will show in that you simply cannot have an acceleration profile that will result in v>c. Example: If you accelerate a mass m with a constant force F, the acceleration is given by [math] a = \sqrt{1-v^2 / c^2} \, F / m [/math] and goes towards zero as v approaches c (also note that if v<<c, then a = F/m as you know it from Newtonian Mechanics).

Ok, so just to add: In this case you can see the 1st equation as the definition of what the electic potential is supposed to be: The potential energy a test charge would have normalized to the test charge's electric charge. The 2nd equation tells you how to actually calculate this potential from a given charge distribution (potentials from different charges just add up, so you can calculate the potential for arbitrary charge distributions, as Swansont mentioned).

I´ve no idea, mainly because I am unsure what "EPE" is. I do know the term "test charge" as a negligibly small charge that´s put into an electric (or even electromagnetic) field to measure it by observing the reaction of the test charge due to the influence of the electric field; for example by determining the force F=qE acting on it. So in your case I´d assume the potential is reconstructed from the information obtained by some test charge (as opposed to the other case, where the point charge q is the source of the field). Just a guess, though (please state what "EPE" is, I´m probably not the only one who doesn´t see that).

In GR, mass is not the sole source of gravity. Its role is (partly) replaced by energy, which is conserved in particle annihilation.

According to the message that comes up when you hit the "report post" button, the button is not intended to report posts that were posted in the wrong forum. I don´t know how much posts get reported these days but when I still had access to the reported posts forum it wasn´t too much. In fact I have sometimes used the button for that purpose and not yet gotten any negative feedback because of that. Imho, a lot of threads that should be in Speculations stay in the physics sections quite long, even though people reposonding there explicitely state that it was the wrong forum. What about allowing the report post function to be used to report threads that ended up in the wrong section, too? Advantages: - Threads go where they belong more quickly (matter of taste if that´s an advantage or doesn´t really matter). - Posts consisting of only the "wrong forum"-message become redundant (I personally see this as a bigger advantage than the previous point - those posts can look rather unfriendly). Disadvantages: - Dunno if it causes an increased amount of moderation, especially when people get too pedantic about the issue.

Have you looked up the term "gravitational field"? Since I seem to be a bit lonely with my view that the term "gravity" does not mean "gravitational force", let me briefly present what I consider gravity: Gravity is the concept that explains the observed attraction between massive bodies (the gravitational interaction). Clasically, theories of interactions consist of two parts: - The field equation that defines the field (the gravitational field, here) as a function of its sources (mass, here) - and describes its dynamics, but that´s not important, here. - The part that defines the influence of the field on other particles. This part comes as an additional term to the equation of motion of those particles. In Newtonian Gravity, this additional leads to the equation of motion of a particle to alter from [math] a=0 [/math] to [math] a = \frac{m}{m} g [/math], where g is the gravitational field (I´ve explicitely written m/m as a hint on the problem with massless particles, which cannot be described with Newtonian physics, anyways). So now back to your original post: Whether the term gravity really is defined as the gravitational force or not seems pure semantics to me. What you seem to be bothered about is why the gravity of earth (whatever that is) is not constant but depends on the object it acts on (if it is the gravitational force). My point is quite simple: There is an object (a concept) associated to gravitational interaction, the gravitational field, that has exactly the property you are missing in the gravitational force: It only depends on the source, not on the object it acts on.

The organization that organizes the FIFA world cup: http://en.wikipedia.org/wiki/Fifa

What are you talking about? Some sort of sports? Which one? Cricket?

I dunno the values but cm/h intuitively seems incorrect. I´d expect something in the order of cm/s or m/s.

You´re pretty much right except with your premise that gravity was the gravitational force acting on an object. You´d like to look up the term "gravitational field". Sadly, the english wikipedia entry on the subject sucks (the german and the spanish version seem ok, in case you speak either language). EDIT: http://en.wikipedia.org/wiki/Law_of_universal_gravitation under the heading "gravitational field" might be a start.

Isn´t "infinite" pretty much by all standards?

There is a large number of methods for solving differential equations. Usually, the best choice is the easiest solution that already gives acceptable results in an acceptable time. Also, the method employed might depend on the type of additional conditions you are given (boundary conditions or initial conditions). An example for a very simple integration of a diff. eq. (an equation of motion) is http://www.wisci.org/wiki/Geodesic_equation . It is not a guide for numerical integration but it is a complete example of starting from a diff. eq. and obtaining a numeric solution. Not sure if that helps you, but perhaps you can extract some information from it. It would probably help if you´d post what kind of process we are talking about and what the diff. eqs. are.

Google and Wikipedia are your friend when you want "some useful information on <insert topic here>". Forums are typically better-suited for specific questions or for getting other people´s opinions (general information about something is not an opinion). A better kind of question would have been "how do you think I should organize my talk? Which topics should I cover? ...". That´s something where a personalized response might be better than a one-size-fits-all article on Wikipedia or the webpages you find on google. Not that I have a problem with your thread, but I don´t think you´ll get something out of it: Best case you´ll get a few people whose knowledge about the topic can be reduced to two or three sentences throwing in these sentences. In that case you´re probably better off with google. Well, hopefully the SFN members prove me wrong, now.

Isn´t magic and that stuff outside of physics by definition? I think the magic spell "create light" loses it´s magic when the spell is a whistling and the required magic ingedient is a noise-triggered power switch that toggles a lightbulb.

Pseudo-random numbers produced by the standard PC are generated by algorithms, that´s why they are pseudo-random even though the "pseudo" is often omitted. We´ve had several threads about this on SFN in the past so doing a search for the keywords "random numbers" should give some useful results.

This is a commonly accepted statement but imho an incorrect one. It slightly depends on where you draw the line between GR and SR. Most people tend to draw the line such that they call all the stuff you learn in school or basic university lectures SR and everything beyond that GR - in this case you might argue that you cannot fully apply SR for a particle that accelerates. Others draw the distinction line at the point where you allow arbitrary coordinate transformation - it´s a question of taste whether you´ll need arbitrary coordinate transformations here so there´s no definite answer. I tend to make the choice whether it´s SR or GR dependent on whether I need any form of non-trivial spacetime geometry (i.e. gravity) like those described by the Einstein equations - you certainly don´t need gravitational interaction for this example of time dilatation.

The meaning of the term "time" in time dilatation is not the same as in time being a spacetime dimension. It´s one word for two different things, one being the name for the 4th coordinate needed to uniquely label different points in spacetime (so it´s something like the x-,y- and z-coordinate) and the other one being related to length of trajectories in spacetime (something like the circumference of a circle). Your idea in general seems correct but it is missing a few crucial points (in addition to the incorrect math). Some random comments: - You assume that both objects reach the same point t=90 s. This is only partly correct since just because they both reach points which have the same time coordinate doesn´t mean they reach the same point. In fact, assuming they both started at the point with the same space and time coordinates it is easy to realize they don´t reach the same point since one object did move in the space direction while the other didn´t. You need to make a turn in space direction midways to get back to the same point. - The 90 s is called "coordinate time" and is related to the meaning of time as a dimension. It is to some extend arbitrary. The 45 s (or the 90 s for the other guy) is called "eigentime" or "proper time" and related to the length of curves. It is not arbitrary. It is what physicists call "invariant". - Time dilatation means that two observers start and end a path through spacetime at the same points (equal time coordinates and equal space coordinates and of course some equal coordinate time for the distance) but measure different eigentimes because they took a different path. - Correct velocities (for massive particles) in your notation have to obey [math] c^2 v_t^2 - v_x^2 = c^2[/math]. You should use physically correct velocities obeying this "normalization condition". It´s not too much additional work and it gives your post some predictive power and makes it easier for others to understand what you are saying. - In this reply I assumed you wanted to know to what extent your understanding is compatible with the mainstream view (i.e. Relativity). In this case, this subforum was the correct one to post in. In you wanted to propose "a new theory" to the world, then the speculations forum had probably been more appropriate since we have the agreement (it´s a silent agreement since no one bothered posting a rule concerning this, yet) that the physics forums should only be mainstream physics.

In math mode it would probably read [math]F_g = \frac{m_1 m_2}{r^2} [/math] Note: - You can see the code by hitting "quote" on my post or by moving the mouse over the equation. - The equation is wrong (unless G=1). - Read http://www.scienceforums.net/forum/showthread.php?t=4236 for more information on TeX support.

F = G m M / r² => r² = C * m with C = GM/F. So distance squared is proportional to mass m when C is constant. Not sure what sense that makes but the statement technically can be considered correct. EDIT: ^^ Forget that, I think I missed your point. You are looking to derive Newton's gravitational law from proportionality relations, are you? Given enough relations, that should be possible with a little combinatory work, leaving a single proportionality constant that Newton called G.

What was your direct proof ?

It shouldn´t be too hard to find some data and make a rough calculation on the efficiency, gib.

Yes. See reference #3 above.

If everything goes right, then nothing goes wrong.