Alfred Centauri

I think that's the right question and I think the answer is "no" as there is no context for the concept "center" w.r.t. the universe. Crucial to the concept "center" is the concept "boundary". But, there can be no coherent concept of a boundary for the universe since the universe is all that there is - there is no meaningful notion of "outside" (on the "other" side of some alleged boundary to) the universe.

brian0918 (may I call you that?), the question is relevant to the TheEgoists rather confused statement "If some set is infinite, you are no closer or further from the end at any point" which is, evidently, part of this discussion is it not? Where is the end of an infinite set? Where is the center of the universe? Do you see any similarity in these questions?

Egoist, where is the center of the universe?

Although this is quite wide of the present topic, there is nonetheless some relevance. Has anyone else here looked at Penrose's Conformal Cyclic Cosmology model? To the extent that I understand it and loosely speaking, under certain conditions, the universe "loses track of how to keep time". Penrose proposes that, as the universe expands and particles decay, just such conditions occur and, in a specific sense, that state is indistinguishable from the state of the universe just after the "big bang". The relevance to this topic is tied up in the "loses track of how to keep time". Here's a quote: Physically, we may think that again in the very remote future, the universe “forgets” time in the sense that there is no way to build a clock with just conformally invariant material. This is related to the fact that massless particles, in relativity theory, do not experience any passage of time. We might even say that to a massless particle, “eternity is no big deal”. So the future boundary, to such an entity is just like anywhere else. With conformal invariance both in the remote future and at the Big-Bang origin, we can try to argue that the two situations are physically identical, so the remote future of one phase of the universe becomes the Big Bang of the next. Fascinating.

FWIW, there's a series of thought provoking posts concerning the existence, or lack thereof, of infinite sets here. I haven't read them carefully enough to comment but do plan to when (if) I find the time.

Well... the electromagnetic field (classically and quantumly) transports energy and momentum. Moreover, the quanta of light have no mass but do possess momentum and that momentum is subject to change by the gravitational "force". Finally, one doesn't even need the concept mass for momentum as momentum is the conserved "charge" associated with the spatial translation symmetry of nature. Let me add something here as a final thought to all this. Keep in mind that the entity "electron", while called a particle, cannot, even classically, be separated from it's associated electric field (Coulomb field) that extends over all space. While some might claim that the field is an abstraction, as I mentioned above, that field transports energy and momentum and so is physical as an inseparable part of the entity "electron". I mention this because when one speaks of (fundamental) entities acting (interacting) on (with) other entities, the notion of force doesn't seem so abstract when you consider that a "force" (interaction) field is an integral part of the entity - it's part of a fundamental entity's identity. What do fundamental entity's do? They interact. A fundamental particle that doesn't interact doesn't have an identity and thus doesn't exist. It is these interactions that are perceived macroscopically as forces (as well as radiation).

I'm confused, I thought you were going to support a claim that force is entirely redundant? Anyhow, I agree with the above. Momentum is conserved and, in analogy with conservation of electric charge and the continuity equation, force can be thought of as a "current" of momentum (think I = dQ/dt). Here's an old paper that suggests teaching Newton's 3rd this way. Dark energy?

No. You make the claim, you get the pleasure of supporting it. According to and in the context of QED, yes. However, in QED, virtual particles represent terms in an approximate solution (a perturbative expansion) to the field equations, i.e., a convenient (for calculation purposes) fiction. However, there is some contact with evanescent modes in classical EM and the virtual photons of QED. Nonetheless, QED is nothing more than an approximation to some deeper and undiscovered theory.

Really? I honestly cannot understand how one could draw that conclusion. Consider the following quote from my previous post: That statement should have demolished any notion that I equate force with rate of change of momentum. As to your worry that non-zero components of rate of change of momentum are non-physical when there is zero net rate of change, I ask you to look no further than your own pressure example. Despite the fact that the plate upon which atmospheric pressure is impressed appears to have zero change in momentum, it (as a whole) is in fact constantly changing momentum as the various molecules collide with the molecules of the plate. On average, however, the net change in momentum is zero. And for "action at a distance forces", e.g., electromagnetism, the transfer of momentum involved with the electromagnetic force is not a continuous process but rather a discreet process of emission and absorption of electromagnetic quanta. Opposing electromagnetic forces may result in zero net change in momentum on average but only because, on average, the momentum transfers that are physically occurring cancel en masse.

Grames, you've gone way afield with these examples. Let's return our focus to the essential disagreement. You claimed "[Newton's 2nd Law] fails to serve as a definition because it would exclude from the concept those forces that continue to exist in the absence of momentum changes because they are balanced by counter forces." I claimed that this is wrong, that Newton's 2nd Law applies to each force impressed on an object and that, just as it is valid to sum the forces impressed to arrive at a net force, it is valid to sum the (rate of) change in momentum associated with each force individually to arrive at the net (rate of) change in momentum; that Newton's 2nd holds for each force and counter force individually as well as for their sum. I do not see how the examples you have provided in your previous two replies relate to this disagreement. Newton's 2nd is a linear relationship between an impressed force (stimulus) and an object's rate of change of momentum (response). Due to this linearity, superposition holds. From Wikipedia: The flaw in the claim that Newton's 2nd excludes "forces that continue to exist in the absence of momentum changes" is , as I see it, the failure to recognize that "forces balanced by counter forces" implies "momentum changes balanced by counter momentum changes", i.e., FNET = F1 + F2 + ... = (dp/dt)1 + (dp/dt)2 + ... = (dp/dt)NET = 0

I confess I don't have the slightest idea what you mean by "substitution" here or even what your point is with this equation. (1) In my previous post, I simply added together two instances of Newton's 2nd: F1 = dp1/dt F2 = dp2/dt ------------------------------ F1 + F2 = dp1/dt + dp2/dt That's superposition. Consider the left hand side the "input" and the right side the "output". Because Newton's 2nd is linear, superposition is valid. If Newton's 2nd was a nonlinear equation instead like F = (dp/dt)2, superposition would not be valid as can be easily checked: (dp1/dt + dp2/dt)2 <> (dp1/dt)2 + (dp2/dt)2 (2) Your equation represents only the "left hand side" of Newton's 2nd so I don't see what you're trying to show here. You're just adding up forces; there's no dynamics content in your equation. (3) Without further context, it's not even clear if the sum in your equation is meaningful. Pressure and area are scalar quantities while force is a vector quantity. There should be distinct unit normal vectors, one for A1 and another for A2 else it should be specified that the normals and forces point in the same direction. Further, it isn't clear how A1 and A2 relate to each other. The equation only makes sense if A1 and A2 are (i) planes and (ii) part of a larger area plane area A = A1 + A2.

I agree with this but oddly, you apparently don't. See below. Wrong. There should be no net force. You missed the point if you think that I claim two different concepts of force. When dp/dt is zero, either there are no forces present (is that even possible?) or there are forces present that combine to cancel. Let forces F1 and F2 be impressed on an object. The net change in momentum is dp1/dt + dp2/dt = F1 + F2 from Newton's 2nd. This is just basic superposition. Nothing new here. If F2 = -F1 then dp2/dt = - dp1/dt so the net change in momentum is zero just as the net force is zero. Newton's 2nd holds for each force impressed on an object as well as their superposition. *the notation dp1/dt is to be understood to mean "the change in momentum associated with the force F1" and likewise for dp2/dt

On the contrary, an alleged referent for "force" (singular) that does not involve change in momentum is instead a referent for "forces" (plural). Now, one needs a structure for combining forces, e.g.., vector addition and thus combining changes in momentum. Bottom line, a referent for force (singular) necessarily displays observable change in momentum. In the case of statics, the (vector) summation of forces, via Newton's 2nd, implies the vector summation of change in momentum. That is, it is illogical to accept that forces can be balanced by counter forces and not accept that changes in momentum can be balanced by counter changes in momentum. Consider, as a metaphor, the case of a half full glass of water with a tight fitting lid. On might say there is no evaporation of the water. Yet, water is evaporating in this example. However, water is also condensing and at the same rate so there is no net evaporation.

Grames, my focus is precisely on your claim "Force is caused by your own muscles and external forces are felt by your own skin, that is the fundamental referent of the concept force." Perhaps I don't understand precisely what you mean by "fundamental referent". Would you elaborate? The point is, as your quoted text clearly points out, fully understanding the meaning of a concept is understanding which existents it refers to in reality, i.e., distinguishing the referents of force from all others. In the case of high school Newtonian mechanics, the referents of the concept "force" are those "influences" that change momentum... The alteration of motion is ever proportional to the motive force impress'd; and is made in the direction of the right line in which that force is impress'd. An astronaut aboard the ISS in orbit 'round the Earth is under the influence of gravitational "forces" and yet cannot (locally) distinguish this influence from a state of no influence, i.e., the astronaut perceives no external force as in your example of a fundamental referent. Nonetheless, the astronaut's momentum is changing while orbiting the Earth. It seems to me that your fundamental referents are more likely referents for the related concepts "weight" and "pressure".

Does one experience the "force" of gravity directly if one is in free fall? Does one experience the force on one's body from the atmospheric pressure directly? Moreover, can it be said that the meanings of the concepts that go by the name of force in the above and in your "weight of object in hand" example are the same?

This seems quite absurd. You claim that force from one's own muscles is the fundamental referent of the concept of force. Is the force of weight not a fundamental referent? Electric force? Magnetic force? You claim that masses are inferred from the force of weight. Would that be gravitational mass? Inertial mass? Both? Neither? If [electric] charge is inferred from electrical forces, would not magnetic charge be inferred from magnetic forces? Maybe a magnetic fluid instead? It seems to me that Tensorman is on the right track here. The mathematically precise definitions of force, mass, energy, etc. used in high school physics are indeed a far cry from the colloquial notions of force, mass, charge that are commonly used and that you seem to be referencing here.

Thank you. I was just about to jump in on that very point. It's important to remember that not only did the second ball's motion change but also the first, i.e., the second ball "acted" on the first too. This is essentially the content of Newton's 3rd law. The collision of the two billiard balls, the event, is the interaction (action and reaction) of the two (composite) entities.

The OP is, as I read it, quite perceptive and my responses go to that. OP asks "Can a force really be the cause of movement..isn't it just a way of describing movement (or acceleration)? I don't understand how to apply this concept." This is a deep question, what is force? Is it a cause or a description? I think the OP's question is related to the question asked here: http://www.physicsforums.com/showthread.php?t=117898 "I'm not surprised you don't understand what I'm asking, since I keep wondering if I'm just chasing my own tail here. OK: So, F=dp/dt is a "law"? If so, then it is stating a fact about the motion of bodies in the physical universe. It is placing a constraint upon the motion of an object, out of all the possible paths that it could take, the 'laws of physics' must tell us which one it actually does take. F=dp/dt does not do this, as it stands. You've got to replace F with something. Say, 'mg' for a simple projectile problem, or 'GmM/r^2' for an orbit problem. Here's what I'm getting at: if F=dp/dt is a law, what is the definition of a force?"

In Newtonian physics, the term mass can refer to either gravitational mass or inertial mass. Inertial mass is the m in F = ma, i.e., it is the constant of proportionality between force and acceleration. Inertial mass is the measure of inertia, the "resistance" to changes in momentum. Gravitational mass is the m in Newtons universal law of gravitation. Gravitational mass is, in a sense, a measure of the amount of matter that creates the gravitational field in analogy with how the amount of electric charge creates the electric field. There is nothing in Newtonian physics that requires the inertial mass and gravitational mass of an object to be numerically equal and yet, empirically, inertial mass and gravitational mass are equal. That's why objects of different inertial masses accelerate equally in a gravitational field - the inertial and gravitational masses exactly balance. Why this is so is unexplained in Newtonian physics. In General Relativity, there is no gravitational force, there is only one concept of mass, and that is as a measure of the invariant (or "rest") energy of an object. Different objects fall at the same rate because each is simply following the shortest (in a special sense - a geodesic) path through a curved spacetime.

To be even more careful, force is the change in momentum. In Newtonian mechanics, F = dp/dt = d(m*v)/dt = m*a and so force is proportional to acceleration. In relativistic mechanics however, (relativistic) momentum is not proportional to velocity (p = gamma*m*v) so force is proportional to acceleration only in the limit of vanishing velocity (gamma -> 1).

"Forces are existents." Mechanics can be formulated without the concept of force. Newtonian mechanics (F=ma etc.) can be derived from the more general Lagrangian mechanics (principle of stationary action, Noether's theorem etc.). Moreover, the concept of force as the cause of and proportional to acceleration does not hold in relativistic mechanics. In fact, in relativistic mechanics, the force and acceleration vectors are not, in general, in the same direction.

Peter Woit devotes a couple of pages to Hagelin in "Not Even Wrong". Some excerpts: "[As a graduate student], his interest in quantum field theory seemed to have a bizarre side to it, since he wanted to use it to explain how TM adepts were able to levitate..." "By 1995, Hagelin had written 73 scientific articles, most them published in very prestigious particle theory journals, many of them cited by more than a hundred later articles." "In recent years, Hagelin has stopped writing physics papers and has achieved notoriety..., most recently promoting the idea of fighting terrorism with a 'new Invincible Defense Technology based on the discovery of the unified field'." "Virtually every theoretical physicist in the world rejects all of this as utter nonsense and work of a crackpot, but Hagelin's case shows that crackpots can have PhDs from the Harvard Physics Department and a large number of frequently cited papers published in the pest peer-reviewed journals in theoretical physics."

Injustice? By what standard?

In any so-called infinite universe, are any two physical objects separated by an "infinite" distance?

I must disagree. According to GTR, gravitational waves, which carry energy-momentum, exist. While it's true that GTR is background free, this only means that there is no a priori geometry.