Farsight

I'd like electrodynamics to be in with quantum mechanics and quantum electrodynamics rather than classical mechanics.

Spyman: yes, I know the author doesn't favour the frozen star interpretation. I think he got that wrong. No, I didn't read chapter 6.4. I'll read it now... huh, proper time, fooey. OK, what's this: This allows us to easily generate geodesic paths in terms of r as a function of t. If we do this, we will notice that the paths invariably go to infinite t as r approaches 2m. Is our 2-dimensional surface actually singular at r = 2m, or are the coordinates simply ill-behaved (like longitude at the North pole)? Sounds promising. The only singularity in the intrinsic curvature of the surface occurs at r = 0. A singularity in curvature is a red herring. That's essentially the rate of change of time dilation, what's important is where it's total. In order to plot r as a function of the proper time t we would like to eliminate t from the two geodesic equations (3). Proper time again. People just don't seem to understand that time is a measure of motion. Infinite time dilation means no more motion. we can confirm that the radial coordinate passes smoothly through r = 2m as a function of the proper time t. There is no proper time. It's an illusion that uses a stopped clock. But what's this? We can also express the Schwarzschild coordinate time t explicitly in terms of alpha by multiplying the two relations Alpha is just some angle, and we must perform a complex integration around the singularity at r = 2m, offsetting the result by ±pi (assuming the path of integration doesn’t make any complete loops around the singularity). This is not surprising, because the t coordinates are discontinuous at r = 2m, so we cannot unambiguously “carry over” the labeling of the t coordinates in the region r > 2m to the region r < 2m. This is performing a hop and a skip to jump over the end of time. Those two little wings at r=2m stop the show: This is junk, we don't move in time: Alternatively we could imagine a single universe with two families of particles, whose proper times increase in opposite directions of the coordinate time t. (In fact, John Wheeler once speculated that anti-matter particles might be modeled as particles moving backward in time.) This is good stuff: The existence of two distinct inner regions is perhaps not surprising if we note that an in-falling object requires infinite coordinate time to cross the boundary at r = 2m, It then talks about changing the coordinate system, and mentions Kruskal-Szekeres coordinates. But it still doesn't get past the t=inf at r=2m. Interesting though.

Damn. I dropped in to http://www.sstd.rl.ac.uk/stereo-soho/announcements.html to look at all the stands then had a chat with the organisers about why I thought this was so crucially important. All by the board I suppose. But it's interesting that Lute Maleki (http://www.oewaves.com/index.php?p=content&mid=2&id=5) seems to be into photonics. For photonics read opticks: Are not gross bodies and light convertible into one another? No, when you "stop a photon" we don't call it a photon any more.

I think there might be a distinction to be found in measuring the fine structure constant [math]\alpha =\ \frac{e^2}{(4 \pi \varepsilon_0)\hbar c}\ [/math], at least when the time dilation is gravitational. See SpaceTime Mission: Clock Test of Relativity at Four Solar Radii but note that I view this as a relativity/electrodynamics matter rather than a string theory test. "SpaceTime is a mission concept developed to test the Equivalence Principle. The mission is based on a clock experiment that will search for a violation of the Equivalence Principle through the observation of a variation of the fine structure constant, α. A spatio-temporal variation of α is expected in some string theories aimed at unifying gravity with other forces in nature. SpaceTime uses a special tri- clock instrument on a spacecraft which approaches the sun to within four solar radii. The instrument consists of three trapped ion clocks based on mercury, cadmium, and ytterbium ions, in the same environment. This configuration allows for a differential measurement of the frequency of the clocks and the cancellation of perturbations common to the three. The observation of any frequency drift between each of the clocks, as the tri-clock instrument approaches the sun, signals the existence of a scalar partner to the tensor gravity. Some relevant details of the mission design are discussed in the paper."

Mr Skeptic: agreed. I agree with this more than you might appreciate. There isn't any volume! Spyman: re that answer, IMHO you never reach the centre. Have a read of http://www.mathpages.com/rr/s7-02/7-02.htm and look out for this: "...if the same trajectory is described in terms of Schwarzschild coordinate time, the infalling object traverses through infinite coordinate time in order to reach the event horizon..." It isn't as inevitable as next Monday, it's as inevitable as the end of time.

No problem with that Swanson, but icarus seems to be trying to justify "a negative mass", and I don't buy it.

Noted Swanson. I rather oversummarised there and left out the microwave cavity. All: see http://tf.nist.gov/cesium/fountain.htm which includes the image below. Merged post follows: Consecutive posts merged It's just a different way of looking at it. Imagine you're watching some scene, and can press a time dilation button. Then everything in the scene goes slower. Your button might equally be labelled a slow motion button. But the observer inside the scene doesn't notice slower motion. He uses his NIST fountain clock and counts 9,192,631,770 microwave oscillations to define his second, then he defines his metre as the distance travelled by light in free space in 1⁄299,792,458th of a second, and hey presto, he always measures the local speed of light to be 299,792,458 m/s.

Apologies, I couldn't follow that, icarus. If you raise an object you give it gravitational potential energy. You add energy to it. This energy has a mass-equivalence, so you increase the mass. Gravitational potential energy has positive mass. There's some issue here regarding standpoint. See Gravitational binding energy and note where it says: "The gravitational binding energy of an object consisting of loose material, held together by gravity alone, is the amount of energy required to pull all of the material apart, to infinity. It is also the amount of energy that is liberated (usually in the form of heat) during the accretion of such an object from material falling from infinity." The important thing to note, is that this object hasn't gotthis energy. That's why it's a negative as per the next sentence: "The gravitational binding energy of a system is equal to the negative of the total gravitational potential energy, considering the system as a set of small particles." There isn't actually any negative energy, and there isn't actually any negative mass, just less positive energy and so less positive mass in the bound system.

I think my argument stands, Snail. See http://casa.colorado.edu/~ajsh/schwp.html and note that "Eddington-Finkelstein coordinates differ from Schwarzschild coordinates only in the relabelling of the time. The problem is that time is a cumulative measure of motion, and from where we're all standing, there just isn't any. The local "observer" cannot adopt a new coordinate system to escape that coordinate c=0, not in all eternity. He will never observe anything, ever.

I should read it all I suppose. Apologies for not doing so. But did you mean energy density of the gravitational field? Surely a gravitational field is only there because the energy density is not uniform. And your response perhaps hints at what the underlying issue is, and it's a big one, to do with cause and effect: what stuff? You're doing geometry, so you might have a head start on why this is so important. Think back to that Einstein quote: "the energy of the gravitational field shall act gravitatively in the same way as any other kind of energy". Forget about the planet and look just at the surrounding space. There's no "stuff" there. Just curved spacetime, which one can think of as a geometrical distortion. And there's no "stuff" in a gravitational wave either. Take a look at LIGO re length change in the interferometer arms, and imagine a gravity wave passing through a cubic lattice that represents flat space. Take a snapshot, and the presence of the gravity wave is betrayed by those lattice lines that are now curved instead of straight. The curvature is the presence of energy-momentum. Yes, no problem re potential energy. This whole issue revolves around the fact that mass per se isn't the cause of a gravitational field, energy is. Or more properly, a non-uniform energy density. And that's what a gravitational field is. I read this 1920 Einstein quote: "According to this theory the metrical qualities of the continuum of space-time differ in the environment of different points of space-time, and are partly conditioned by the matter existing outside of the territory under consideration. This space-time variability of the reciprocal relations of the standards of space and time, or, perhaps, the recognition of the fact that “empty space” in its physical relation is neither homogeneous nor isotropic, compelling us to describe its state by ten functions (the gravitation potentials gμν)..." ...and I can't reconcile it with the FLRW metric which says The FLRW metric starts with the assumption of homogeneity and isotropy of space. It also says where Σ ranges over a 3-dimensional space of uniform curvature. If there's curvature, the space can't be homogeneous. Me too. What I was saying to ajb about a gravitational wave maybe applies to a photon too. Any chance either of you guys could ask around for an answer to this one?

I'm not a novice, but thanks anyway. On page 111 he says this is an equation relating derivatives of the metric to the energy density so maybe there'll be something in there that will help. Merged post follows: Consecutive posts mergedAmr: thanks for chipping in too. This seems to be a trickier problem than I thought.

I don't think there's an answer to this one, because there is no spacetime inside the event horizon. That might sound a bit of a surprise, but think about what a volume is: a distance multiplied by a distance multiplied by a distance. If the coordinate speed of light at the black hole event horizon is zero as measured by observers in the universe at large, there's nothing with which you can calibrate distance. If you switch to the "proper time" of the infalling observer who measures c locally to be 299,792,458 m/s, it takes him forever by our clocks to make a measurement. So you're still a bit stuck. See http://www.mathpages.com/rr/s7-02/7-02.htm where Kevin Brown discusses the "geometric interpretation" (as exemplified by Misner/Thorne/Wheeler's "Gravitation") and the "field interpretation" (as in Weinberg's "Gravitation and Cosmology"). He favoured the former, but the latter gives a black hole picture which is more of a "hole" than the MTW picture, and seems to be gaining more acceptance.

Thanks ajb, but I confess I'm still not clear on this. For reference: [math]G_{\mu \nu} + \Lambda g_{\mu \nu}= {8\pi G\over c^4} T_{\mu \nu}[/math] Can I can try and ask the question another way? Imagine you measure gravitational time dilation at locations in the space around a planet, and at locations within the planet. All these locations lie on a circular horizontal plane. When you then plot the time dilation, you find you're effectively plotting a "Newtonian" gravitational potential: http://en.wikipedia.org/wiki/Gravitational_potential If you now turn this upside down, surely what you have is a plot of spatial energy density, what Einstein called "the energy of the gravitational field". His following words "shall act gravitatively in the same way as any other kind of energy" are a reminder that a non-uniform energy distribution causes gravity, and that matter only causes gravity because of the "energy content". But this spatial energy isn't contained within in the matter. If we could somehow lose the matter whilst somehow retaining this non-uniform spatial energy distribution, the latter would cause a gravitational field in its own right. The guys I was talking to said this spatial energy isn't included in the EFEs, and I note on the last page of document 30, Einstein talks about a first approximation, but the document is truncated at that point, and I'm a bit stuck. Any further assistance you can offer would be appreciated.

I was kicking something around with a few guys a couple of weeks back, and something came up. I wonder if anybody here could confirm or or counter what I was told? In The Foundation of the General Theory of Relativity on page 185 of Doc 30, 3.6 Mbytes, Einstein says "the energy of the gravitational field shall act gravitatively in the same way as any other kind of energy". The people I was talking to said that this energy is not included in the Einstein Field Equations. They seemed to know what they were talking about, but I thought surely not? I'd appreciate any information you can offer.

Cough. I see E=hf has been mentioned. Oddly enough, people don't really think much about action. Take a look at various pictures of the electromagnetic spectrum and then take a look at Planck's constant. Pay careful attention to the Value section where it says this: The dimensions may also be written as momentum multiplied by distance. It's related to displacement current.

Replace your tube of marbles with a steel rod 13000 miles long, and whack one end of it with a hammer. The speed of sound in steel is about 13000 mph, so it's an hour before the other end moves.

Swanson, let me rephrase: hold an object 100m above the ground. It has no discernible kinetic energy, but it does have gravitational potential energy. Now drop it. Ignoring air resistance, at the instant just before it touches the ground, it now has kinetic energy, and it also has less potential energy. However the total energy of that object is unchanged. See http://www.physicsclassroom.com/class/energy/U5l2a.cfm "When the only type of force doing net work upon an object is an internal force (for example, gravitational and spring forces), the total mechanical energy (KE + PE) of that object remains constant. In such cases, the object's energy changes form." Icarus: if I can reiterate: Like Einstein said, "the energy of the gravitational field shall act gravitatively in the same way as any other kind of energy". The energy is positive. It only looks negative if you invert the energy density to plot gravitational potential like the depiction at http://en.wikipedia.org/wiki/Gravitational_potential We know from conservation of energy and from relativity that the kinetic energy of a falling body comes from the potential energy of that body. Throw a body up into the air and the kinetic energy is converted to potential energy. Throw it hard enough to give it escape velocity and the potential energy is gone forever - because it's in the body, not in the gravitational field. Now play it backwards: as a body falls to earth, its potential energy is converted into kinetic energy, which is dissipated and radiated away on impact. The potential energy is no longer present, and the mass of the body has been reduced in line with Does the Inertia of a Body depend upon its energy content?. Hence that potential energy is [math]+ m_{gp}c^2 [/math].

Severian: when you calculate the "in-principle" position of those particles, you can only do it by moving particles around. So you have to account for your calculation in your calculation, which leads to a recursive state which breaches the principle. Another way to object to your assertion is to assert that those current theories of the universe are incomplete. For example, those rolling-dice quantum fields, in the guise of a man, can calculate.

Icarus: the positive one is true. See The Foundation of the General Theory of Relativity and look at page 185 where Einstein says "the energy of the gravitational field shall act gravitatively in the same way as any other kind of energy". This energy has a mass-equivalence. Consider a region of space where the stress-energy "density" is uniform. Now add an immense concentration of energy tied up as matter, in the form of a planet. The surrounding space is "conditioned" by this, and its energy density is increased with proximity, and is no longer uniform. The result is a gravitational field. There is no negative energy at any location therein. Gravitational energy is often considered to be a negative because "Newtonian" principles are applied, wherein a falling body is considered to have more energy than a stationary body at altitude. What's actually happening is that some of the energy within the stationary body is converted into the kinetic energy of the falling body. This energy within the stationary body is called gravitational potential energy. It's the difference between the internal energy of a body "at rest" and at some given temperature up in space, as compared to the internal energy of the same body at rest and at the same temperature in a region of lower "gravitational potential". Gravitational time dilation is key to this, whereupon internal subatomic motion occurs at a reduced rate, and conservation of energy applies. The easiest way to grasp it is to say to yourself that the energy difference between a fast-spinning disk and a slow-spinning disk pays for the kinetic energy of the latter.

See http://tf.nist.gov/cesium/fountain.htm to read about the NIST caesium fountain clock and http://en.wikipedia.org/wiki/Second for the definition of the second: "Since 1967, the second has been defined to be the duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium 133 atom. This definition refers to a caesium atom at rest at a temperature of 0 K (absolute zero), and with appropriate corrections for gravitational time dilation." In essence lasers are employed to cause hyperfine transitions, which are electron spin flips within caesium atoms. This emits light of a given "frequency", which is measured by a detector. I put the word frequency in italics above because frequency is measured in Hertz, which is defined as cycles per second. What the detectors essentially do, is count incoming microwave peaks. When they get to 9,192,631,770, that's a second. Hence the frequency is 9,192,631,770 Hz by definition. Note the mention of gravitational time dilation in the wiki article. If you were to take this clock and place it in a region of low gravitational potential, it would be like pressing a slow-motion button. All electromagnetic and other processes would then occur at a reduced rate, including the motion of the light towards the detector. However regardless of this, when the detectors get to 9,192,631,770, that's a second. It's important to realise here that in this situation, the light is moving slower and this is why the second is bigger. We then use this second... to measure the speed of light! That's why we always measure the local speed of light in vacuo to be 299,792,458 m/s. NB: provided you avoid the radial length contraction of general relativity, the metre is not affected. It's defined as the distance travelled by light in free space in 1⁄299,792,458th of a second, so the slower light and the bigger second cancel each other out.

Sounds as if you guys are finally cottoning on to Time Explained. A clock clocks up motion, not time. PS: You can't quantize gravity.

No it doesn't get from point A to B in zero time, it's isn't at one point, and it's limited to c.

None of the balls "have" any kinetic energy. They only have kinetic energy in relation to something else with a different relative motion. The kinetic energy is "in the motion", not in the balls. You can simplify matters by talking about a universe consisting of only two balls, one yellow, and the other red & blue with a mass of 2kg, and you can work out 5000 and 10000 joules for each. But this is only the kinetic energy of one ball with respect to the other. To obtain the kinetic energy of "the universe" you have to treat the universe as an absolute frame and ascertain the velocity of the balls with respect to it. This is not defined, so the answer is indeterminate.

It's been a while since I visited this forum. I noticed a rule change regarding speculations, reinforced by this header post from Dave: I also note a number of threads which feature speculations, including this one. Can I say this: the multiverse is pseudoscience. There's no scientific evidence for this speculation, and even though it has a veneer of "mainstream" respectability, it is untestable moonshine. It is not science. Whilst many do not currently share this view, I am confident that one day they will.