How do you even define "traveling in time"? Movement is a change of position over time, so how does that work when you're talking about the position in the time dimension?
Simple: in relativity, you travel through paths in space-time, not merely in space; speed is the rate of change in space-time relative to your proper time and, in fact, everyone is already travelling in time to the future.
Time travel to the past, well, that is another thing, but the basic idea is the same: the difference being that your speed through time is oriented towards the past for at least a portion of the journey. Alternatively, you can say that you have time traveled to the past if, at any point, you are inside the past light-cone of a point you started at. Finally, another way is to talk about closed timelike curves: your trajectory intersects with itself at some point with an earlier proper time. The first technically fails in non-orientable manifolds; the middle one can say you are time traveling even if you are not doing anything special if you are in a weird enough space-time (your example with the photon, for example); but the latter will always be unambiguous.
If someone asks you "Do ghost particles exist? Yes or No?", what's your answer and why?
I don't read that question as a question about ghost particles, since the answer would not yield a better understanding of ghost particles, nor would it predict any new testable properties.
It's not a philosophical question and it does yield a better understanding of ghost particles. Let's take a look at possible good answers:
a. Physicist A thinks they exist, finds a theory where their apparent inconsistent properties make sense and explains how the old theory worked in terms of the new one.
b. Physicist B thinks they don't exist, and rewrites the theory so that it agrees with experiment without using ghosts.
Even if they still haven't made predictions, their new theories could be conceptually simpler and highlight something that the old one didn't. And since the old theory was incorrect, you could hope to fix it by making small corrections to the new one. New interpretations of physical theories should not be underestimated. Feynman, for example, interpreted quantum mechanics as the "sum over possibilities" formulation, quickly found quantum electrodynamics, and won the Nobel for it.
Tub wrote:
Of course the scientific question is: "Does this set of formulas, which includes unobservable particles, accurately describe the experimental results we obtained?"
No, it isn't. I'll elaborate on this a bit more because it's a major source of confusion for physics students and it should help someone reading this thread.
Physics is not just a collection of formulas, it's irresponsible to go and solve a physics question by writing down all the equations you have and trying to get an answer out of them, because deep down these formulas assume something. When you write pV=nRT you assume the gas is ideal, when you write F=ma you assume the system is not losing or gaining mass during motion, when you write m1*v1i+m2*v2i = m1*v1f + m2*v2f you assume there are no external forces.
If you just write down all formulas you remember you can assume blatantly contradictory things and get it all wrong (and guess how often I've seen this happen). Even if you do get something right this way, you get it in the same sense that astrology can get something right.
And for the case of QFT, the formulas are not mathematically rigorous, most of the integrals diverge to infinity. To make sense out of them you need to see how fast the integrals diverge, then "correct" the constants of the theory by letting them vary when the length scale of spacetime becomes larger so that they "absorb" the divergences and you get finite results. But then comes GR and says that equations are the same for all length scales, and that we can't cheat by modifying the constants. Because of this, we have two theories that work very well but disagree with each other at a fundamental concept. Because of this, their predictions should be similar only if we're lucky (spoiler: we're not).
Is it sensible to assume the discrepancies are insignificant for some experiments and just brute force formulas? Certainly it is, but that can't go on forever. Eventually we'll have to take this paradox seriously and resolve it, and it all comes down to a question Einstein asked way back. "Is spacetime a well-defined physical entity?" It looks like philosophical gibberish, but it's more fundamental to science than the formulas. If spacetime is well defined, then QFT is right, it makes sense to talk about a large spacetime and a small one and it's OK to vary the constants, let's reformulate GR. If it is not, then GR is right, we can only talk about spacetime because there's matter in it, and QFT should be changed instead.
Eventually we'll have to take this paradox seriously and resolve it, and it all comes down to a question Einstein asked way back. "Is spacetime a well-defined physical entity?" It looks like philosophical gibberish, but it's more fundamental to science than the formulas. If spacetime is well defined, then QFT is right, it makes sense to talk about a large spacetime and a small one and it's OK to vary the constants, let's reformulate GR. If it is not, then GR is right, we can only talk about spacetime because there's matter in it, and QFT should be changed instead.
Just a quibble here: if GR were a fully Machian theory, this would be correct; but it is not -- you have well defined spacetimes in GR in the complete absence of matter in all (or essentially all) points (see special relativity and Schwarzschild solutions). Push comes to the shove, GR is not a very Machian theory at all (because of vacuum solutions). And in fact, depending on what you mean by "well defined", GR gives an arguably more well-defined spacetime that the options -- because it is even more deterministic that Newton's laws.
Rather, the problem with GR and QFT is that the space-time given by GR is not defined in the context of QFT because the stress-energy-momentum tensor is only defined in probabilistic terms; so you don't have a well defined GR-spacetime in the context of QFT.
My knowledge of GR is essentially zero outside the derivation of Einstein equations and the Schwarzchild and Friedmann solutions, so maybe I went too much in that territory, but come on, is Schwarzchild really a vacuum solution? The tensor is 0, yeah, but it's obvious that the singularity accounts for matter. Without mathy stuff like boundary conditions, singularities and other finitude checks, there are many different solutions (in that sense the millenium prize problem on Navier-Stokes was solved a long time ago). Take what I say with a huge grain of salt, but I really think that, given the appropriate math constraints, GR is Machian (it was derived with Machian thought in mind), although I use the term Machian in a very fuzzy way, so I don't know if it's correct.
Even if I made a mistake in the previous statement, I still stand by my point. Renormalization makes no sense if you want to put gravity in QFT. There are some people who try to quantize GR directly and although there's a lot of hype that all integrals are finite and there's no renormalization, what they don't tell you is that there's no QFT in their theory either :P
Mainstream approaches to quantum gravity require renormalization to stabilize the constants when they go to infinity, so that there's no scale dependence at large scales, where GR holds. Not totally satisfactory because it's still a perturbative treatment, but a good idea nonetheless.
Oh, and thanks for the great discussion :D
Oh, no argument re: normalization; I was quibbling with the quoted bit.
Now, you may complain (not without merit) that the Schwarzschild solution is not a vacuum solution; technically, it it the same solution you would get in a space-time minus one point. So it can be a full vacuum solution depending on your spacetime.
Leaving technicalities aside, Mach's principle, in a nutshell, relates the inertia to the distribution of masses; you can't have inertia without having a distribution of masses, and this distribution determines inertia for each constituent. Since GR couples inertia and geometry, you can state this as 'no inertia = no geometry'.
Thus, the notion that a single point mass can determine inertia (it determines a full spacerime!) is distinctly non-Machian — there are no other masses relative to which you can use to determine inertia for the singularity, but it is there anyway (as the parameter M).
Moreover, the very fact that you can get a vacuum solution (special relativiy) makes GR a non-Machian theory.
But lets persevere: lets examine the multiple possible solutions you can get. Any solution is fully determined by appropriate boundary conditions*; but the fact that you can have two solutions that differ by gravitational waves is a blow against Mach's principle: here you have distortions in inertia propagating around. You can even have an otherwise vacuum solution with gravitational waves, where you have distortioins in inertia propagating in a geometry that is determined by no matter at all.
So yeah, while GR was derived with Machian thinking, it ended up being distinctly non-Machian. Einstein realized this the moment he saw Schwarzschild's solution.
* Indeed it is only by selecting vey special boundary conditions one can really attain any "Machianess" in GR.
The point is that Mach's principle is not a statement about mathematical formulation, it's a principle that should apply to solutions that represent physically relevant states. To illustrate better what I'm saying. You get the Schwarzchild solution. Do test particles in GR really move in its geodesics? Actually no, because the probe can have some mass and it'll distort the metric a bit. So, the Schwarzchild solution is a very good approximation, but still an idealized solution, which by definition can't be tested. And you can't use an idealized system to refute a physical principle.
What if we consider the flat space of SR? Well, if you want to describe the simplest motion of a particle with a mass, it'll deform the metric again. So you have to "couple" the particle with the SR metric and they'll interact. So, in GR the SR metric is idealized, it's a good approximation, but doesn't correspond to any physical phenomenon.
And about gravitational waves, the solutions effectively describe mass coming from infinity in one direction and going to infinity in the other, which is also unphysical. In the real world, a system would start oscillating and slowly fill the space with waves. At no point in motion the waves would occupy the entire spacetime.
My argument is: take a very reasonable mass configuration for a state of the universe, specify the initial conditions (and boundary if needed) and let the system evolve through GR. At every point during this motion Mach's principle applies.
From a purely mathematical view, the GR equations admit non-Machian solutions (it also admits solutions with time machines, btw). However, it's impossible for any sane physical system to get to them, so saying that GR is not Machian based on these solutions is inaccurate, also because they're found by imposing high degrees of symmetry and represent a measure zero of the set of possible solutions.
Einstein did change his mind about Mach's principle, he also was against quantum mechanics after helping to create it. In both matters, I think his earlier work is better.
So I went doing some refresher on this, and I remembered this book: specifically, pages 75 and 76. If you can't view it, let me know and I will summarize it; I had to login to be able to see the pages in question.
Bottom line is: Mach's principle is very vague; depending on how you state it, GR is Machia or non-Machian, or both in varying degrees. He goes through 8 versions of the principle in the linked parts, but there are many more variants.
I must admit that most of your posts go well above my head, but I got curious about the Mach's principle.
Do I understand correctly that it's a physical-philosophical question of how do we know that an object is "motionless"? That if we define it as "motionless" by comparing it to the average distribution of mass in the entire universe, this opens up many difficult questions?
The principle also seems to deal with whether an object is in inertial or non-inertial motion. For example, how do we know that an isolated object is "rotating" if we don't have anything to compare it to? But this part sounds strange to me because rotation can be measured by measuring the centrifugal force that's applying to different parts of the object. (And in GR it even causes frame dragging, which I also assume is measurable.)
On the other hand, an object orbiting another object (such as a planet) is also "rotating" but experiences no centrifugal forces... (but isn't it actually in inertial motion according to GR?)
Do I understand correctly that it's a physical-philosophical question of how do we know that an object is "motionless"? That if we define it as "motionless" by comparing it to the average distribution of mass in the entire universe, this opens up many difficult questions?
It is a bit mote than that: Mach's principle is basicaly the notion that you can't even talk about motiin unless it is in relation to something, hence inertia onky exists in relation to other stuff.
Warp wrote:
For example, how do we know that an isolated object is "rotating" if we don't have anything to compare it to? But this part sounds strange to me because rotation can be measured by measuring the centrifugal force that's applying to different parts of the object.
In a fully Machian theory, the centrifugal forces would only exist because of the distribution of mass in the rest of the universe; if there were nothing else in the universe but the "spinning" object, a Machian theory would say that it feels no centrifugal force. In GR, you can actually have a rotating universe (Gödel's solution), so it fails the Mach test in this front; but:
Warp wrote:
(And in GR it even causes frame dragging, which I also assume is measurable.)
The Lense-Thirring effect is actually expected in a Machian theory: a sufficiently heavy rotating "bucket" would affect the inertia of the other things in the universe.
Warp wrote:
On the other hand, an object orbiting another object (such as a planet) is also "rotating" but experiences no centrifugal forces... (but isn't it actually in inertial motion according to GR?)
It is inertial motion if the orbit is solely due to gravity, yeah.
The centrifugal force is one of the many so called inertial forces: that is, forces that only appear in non-inertial frames (they have been historically misnamed as "fictitious forces" or "pseudo forces"). In one of the formulations of Mach's principle, inertia only exists in relation to other things; if there is nothing you are rotating relative to, you are not rotating at all; there is no rotational inertia, just as there would be no translational inertia. So the rest of the universe must be non-empty so that your inertia exists, and hence so that you can feel an inertial force such as the centrifugal force. Put in another way, all frames are inertial if the universe is empty, so you can't change to a reference frame where you have an inertial force.
Of course, Mach's principle is a philosophical one -- Mach was a philosopher, not a physicist -- so it makes no attempt at explaining how the contents of the universe would go about generating inertia. GR does give a possible mechanism -- the contents of the universe define the geometry of the universe, and geometry defines inertia -- but in such a way that gives GR a non-Machian character, depending on how you formulate the principle.
I don't understand why the centrifugal force felt by a rotating object would depend on the rest of the universe...
The original argument was a bit like this. Suppose you start rotating now. Your body would feel the centrifugal force. According to Newton, your rotation can be considered absolute, the centrifugal force appears because your previous frame was more inertial than the one you are now.
Mach would give a different explanation, he believed that all motion is relative, so he has to answer the question of why the centrifugal forces happen when your rotating frame is no more different than the non-rotating one. To solve this he assumes that all matter in the universe is "linked" somehow, so that in your frame, the movement of the rest of the universe relative to you interacts with your body and causes the centrifugal force.
In Newtonian gravity, the gravitational attraction of a solid sphere is the same if it's rotating or at rest. That means the sphere can move without changing the force it exerts in the rest of the universe, and thus, is decoupled from it. In GR the rotation of a massive body will cause changes to its gravitational field by way of frame dragging, so GR is more Machian than classical gravity in this phenomenon.
Joined: 10/27/2004
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Question about electrical circuitry. Hopefully something simple for you folks.
This guide for Taco's boiler zoning valves has something that is screwing with my brain. Specifically, the section "Wiring Note" on page 3. What are the principles in action that allow two separate power sources to not interact, as though they are two separate circuits, when they are connected at a common point?
A hundred years from now, they will gaze upon my work and marvel at my skills but never know my name. And that will be good enough for me.
The amount of electric current entering a node (or any set of nodes) of a circuit must equal the amount of current leaving it. Connecting two circuits with a single wire doesn't cause current to flow between them because, if it did, one of them would have current flowing out, and the other current entering in. That would make one of them accumulate positive electric charge, and the other negative. They could only interact with two connections, because then the current entering one through the first wire can be cancelled by the current leaving through the second one.
In practice, most electronic circuits already are connected at a point, the ground state of the electrical network. In general, it's not safe to connect points of them because the extra connection at ground almost always causes a short circuit.
The amount of electric current entering a node (or any set of nodes) of a circuit must equal the amount of current leaving it. Connecting two circuits with a single wire doesn't cause current to flow between them because, if it did, one of them would have current flowing out, and the other current entering in. That would make one of them accumulate positive electric charge, and the other negative.
Isn't that, actually, a pretty accurate description of a capacitor?
The amount of electric current entering a node (or any set of nodes) of a circuit must equal the amount of current leaving it. Connecting two circuits with a single wire doesn't cause current to flow between them because, if it did, one of them would have current flowing out, and the other current entering in. That would make one of them accumulate positive electric charge, and the other negative.
Isn't that, actually, a pretty accurate description of a capacitor?
Why not? A capacitor is basically two plates connected by a single connection and a potential difference between the two plates. Electric current moves from one plate to the other, and thus positive charges accumulate in one plate and negative charges in the other.
The plates of the capacitor are not connected by any material that can conduct electric current. If that was the case, either the tension of the two plates would be the same, or the flow of current would dissipate energy due to resistance, which in an ideal capacitor doesn't exist.
The plates are separated by a dielectric that gets polarized by the tension difference. Current only "passes" through the capacitor because it converts the energy of the current into an electric field inside the dielectric and converts it back to electric current at the other plate.
Anyway, whatever happens inside the capacitor, it's still electrically neutral, and doesn't accumulate charge, it just polarizes the charge it already has. Like I said before, the amount of current entering has to be the same as the current leaving it.
I think I understand what Warp's getting at:
If you have Circuit A, and Circuit B, which have a single conducting link between them, can you not consider the entirety of Circuit A, Circuit B, and the non-conducting medium between them, to be a single large capacitor?
It will almost certainly have a capacitance so low as to be negligible, but it's not zero.
So you end up with a "circuit" from A over the conducting wire, to B, then back through the "capacitor" to A again.
I think this wiki section describes what I'm trying to talk about.
Yeah, there is parasitic capacitance, resistance, and inductance between the circuits. The capacitance in the wires or in the medium is just one of many effects that can make the signal in one circuit interfere with another. They happen even without wired connections, and for power circuits (operating at 50 or 60Hz), noise is much more significant than that interference, so it doesn't make much sense to consider them without also including noise.
Even when you consider these effects, it's still true that the total current entering a node is the same as the total current leaving it. The circuits interact now because the parasitic elements introduce more than one connection between them. I didn't take parasitic elements into account because it's a bit unimportant considering Ferret Warlord's question, which is treated well in the approximations adopted in high school physics.
Joined: 10/27/2004
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Looks like I'll have to practice my Kirchoff then. It's just that it almost seems like you'd end up getting currents flowing in opposite directions. I'll look further into it.
Either way, thanks for the response.
A hundred years from now, they will gaze upon my work and marvel at my skills but never know my name. And that will be good enough for me.
I don't know how interesting others here will find this, but I did a little derivation today in my free time involving a mesh of resistors.
Suppose you have a rectangular lattice of resistors in a grid configuration, approaching the continuum limit. The lattice has width X and height Y. The boundaries of the lattice are held at given (not necessarily constant) potentials. Your task is to find the voltage at an arbitrary point, V(x,y). You may take the individual cells of the grid to be square (dx = dy), although it is not especially difficult to work with rectangular cells.
I assumed that the vertically-oriented resistors have a resistance of Ry(x,y) while the horizontally-oriented resistors have a resistance of Rx(x,y).
What partial differential equation does the voltage satisfy? Under what conditions does it reduce to the Laplace equation? Which of Kirchhoff's two laws is applicable?
My derivation is about a page in length, so this is not a tremendously difficult problem. Still I'm curious as to how others here would solve it and I would also like to know if it can be reduced to or derived from the continuous version of Ohm's law.
I was reading the list of Nobel laureates in physics, and I noticed that the vast majority of those prizes are for particle/quantum physics and electromagnetism, and only a very small minority of them are for other subjects such as astrophysics. (Even Einstein got his Nobel prize for particle physics rather than his most famous work.)
I wonder why that is.
I was reading the list of Nobel laureates in physics, and I noticed that the vast majority of those prizes are for particle/quantum physics and electromagnetism, and only a very small minority of them are for other subjects such as astrophysics. (Even Einstein got his Nobel prize for particle physics rather than his most famous work.)
I wonder why that is.
Particle physics is the most fundamental area of physics; electronics has the most practical application. This is why these areas tend to get given the nod.
Einstein got given a prize for explaining the photoelectric effect because general relativity was still not universally accepted at the time, and had little experimental data to back it up. The wording of the award is "services to theoretical physics", which may well have meant the committee thought GE was worth acknowledgement but did not want to condone a theory with no experimental evidence.
I wonder why Einstein didn't get a Nobel for his work on relativity even later, when it was pretty much experimentally established that yes, it's a very good description of reality.
