gravity waves vs electromagnetic waves

I think the experiments on the EPR and Bell inequality rule out most of the simplifications you would like to make. This paper being one of the more interesting and striking applications of entanglement.

And in a +++- universe x^2+y^2+z^2-(ct)^2 Hardline theoreticians set c=1 at this point ;-)

It is not for nothing that you generally check an FFT with a series of tests to ensure that it really does compute a Fourier transform and not one of the other zillion possible rotations that are self inverses.

Coding FFTs inspired at least one modern line of research into formulating physics using Clifford algebras (a generalisation beyond Penroses spinors and quaternions). It makes some things simpler and more intuitive once you have learnt the language (or so they tell me).

And to avoid location bias Penrose's spinors

I have spent far too much of my time shifting data between Fourier space and real space. Most of the other rotations aren't so interesting.

The other interesting family of matrix transforms that are are those that attempt to localise energy in both the temporal and frequency domain simultaneously. Wavelets and the like also have their uses.

are you certain that it's not a reflection?

Mmmh, yes that's a nice one. I haven't figured out how that works, but if I could come up with an analogue model using common RF signal processing methods, would that convince you of my point of view? It may take a while...

Jeroen --sticking my neck out-- Belleman

Well, it's a rotation, for sure. If you define a reflection as an transform that cancels when you do it twice, then I suppose it qualifies as a reflection too.

Jeroen Belleman

Interesting view. You have just re-invented something like Hilbert-space. But I would not call an FFT (or more general FT) rotation since the vector has not changed. It is just the vector represented in a different basis.

It is the same in quantum mechanics where we switch between position and impluse representation via a Fourier transform. And the fact that we need n cycles of a wave to measure the frequency with 1/n accuracy is Heisenbergs uncertainty relation, plus/minus some 2*pi and h-bar.

The number of possible transformation is really huge. 2^(2^aleph) where aleph is the number of cardinals, which of course is infinite. Just any set of orthogonal (better orthonormal) functions will do a basis, that is where integral(fi*fj)==0 for any combination of i and j.

But is explains only part of the story. It can not explain the interaction with matter.

Both views (wave and particle) viewed alone are wrong. Each works to explain certain aspects but not all. They help our simple brains to visualize it, but the "real picture" - whatever real means - is in the mathematics of quantum mechanics. That is the reason Feynman said "Shut up and calculate".

Our brains have not evolved to have a "view" for this. They evolved to understand things in spacial dimensions from about millimeters to kilometers and velocities from 0 to fast running.

The question if it _is_ might be just mood. It behaves like it is when do experiments. The rest is mythology or philosophy which Pauli called the systematic misuse of a specially crafted language.

Indeed so. I've been handwaving, saying that the interaction is quantized in lumps of hf, but I do not know where the value of h comes from. Some argument involving the elementary charge alone, or the charge over mass ratio of electrons, most likely. Planck's constant and the elementary charge pop up together in lots of places in physics.

I think that was Bohr. Never mind. The mathematics work. No problems with that.

Well, I keep looking for a way to tell. A classical argument that yields the value of h would do nicely. ;-)

Jeroen Belleman

You could contrive to leave a set of radar reflectors outside the black hole in the last stable circular orbit and then be able to notice when you stop getting reflections back from them. But your local experience on crossing the event horizon is that nothing special happens to you.

You can still see out to the rest of the universe (or more accurately see the light that falls into the black hole after you) albeit in a distorted form but you can no longer send signals out to it.

I blame quantum mechanics. But the truth is we don't know. I find Guth's early exponential inflation somewhat harder to swallow but it undoubtedly gives answers that are consistent with observations.

It is my limitation in explaining using natural language a field I haven't worked in for more than three decades.

My recollection is all paths lead to Rome some more quickly then others and with ever increasing gravitation gradients along its path as you get closer to the singularity leading to spaghettification.

The smallest theoretically possible black hole is thought to be determined by the uncertainly principle at around the Planck mass 22ug. (or at least it was when I was a student)

But if some of the string theories (which are incidentally even weirder) are right then it could be as low as the TeV range close to the upper working energy limits of the LHC. Observation of micro black holes signatures in LHC data would confirm that string theory might be onto something (I have my doubts). YMMV

See

The stability or otherwise of Planck mass black holes is an open question - they might fit the bill as a WIMP ie cold dark matter.

Of course, as that's a singularity: dividing by zero. Unless you employ an analytical continuation via complex time, IIRC something Hawking has played with (but I don't know the consequences of it).

You can always loop-integrate around a singularity to accumulate another i2pi or whatever, the amount giving the number of poles * turns, unless such is prohibited by dimensions or pathological conditions or something, of course.

Okay, so it's a different 'kettle' from the curvature-mass distribution 'fish'?

It's still confusing, because e.g. the Swartzchild metric is, I guess, used with, a basic black hole, which /is/ a mass-curvature distribution.

I don't think I've seen it articulated anywhere, but I appreciate that, you'd define the entirety of the universe as empty except for an overly-dense pimple, for analytical simplicity. With the intention and assumption that, as long as these things drop off in a reasonable fashion, we can apply the interesting part locally, without worrying about the tails out to infinity.

Thus, a black hole can be embedded in an otherwise flat, expanding universe (both of which are consistent with observations in different regions), and we know/infer a reasonable amount about both. Without having to solve the total system, which might end up intractible, or at least inconveniently complicated to make a given point.

But this leaves me wondering: has anyone actually tried modeling the universe, as we see it? It might not be very interesting, but it seems strange to me that the main theoretical bases are...oddly shaped measuring sticks.

Yeah, or if it's light, it spirals back in, or if it's perfectly radial, it red-shifts to nothingness. Or, perhaps, to CMB in a sense; or perhaps, eventually quantum tunnels out. Presumably, by the time it red-shifts to a temperature where the wavelength corresponds to, perhaps, the Swartzchild radius...

For that, I get: lambda_max = (4 pi)^2 r_s / x (x ~= 4.965) so it's proportional, no funny powers, and all of the unit constants cancel out, leaving geometric ratios (4 pi suggests a solid angle, squared for whatever reason; and the transcendental x constant comes from Wien's displacement law).

So, it's within an order of magnitude, and proportional. That's neat. Of course, it's a frequency longer than the present age of the universe (well, by exactly that much, obviously), so I don't know that that's really very interesting or useful. (Presumably, perhaps a nonzero amount of energy has left the universe as we know it, but measurable? No..)

Yeah, the known universe is something like 46e9 ly across, because, assuming it's expanded as far as anything else has since when we observed it, it would now be that far away from us (in an instantanous-distance sense). The light from that stuff was emitted about 13e9 y ago, and thus travelled 13e9 ly, but the matter has stretched apart since then.

So, heh... which one is right for a still-expanding universe? ;-)

For sure, it needs to embed the observations within it, at least as a low-energy or large-scale approximation or something like that. Just as Newtonian gravity is too compelling to discard wholly, and drops out of Relativity for v infty.

By the way, thanks for taking the time to answer our questions!

Tim

I think that would be testable then so we could tell if we were in a black hole.

Ok, so we can't reconcile the early universe with present science. It

That is what I've been trying to say. Something had to be different about gravity in those times. Or we are extrapolating so far beyond our data that our results are meaningless.

Quite a few of the results are tolerably meaningful. The distribution of the elements in the early universe - mostly hydrogen, some helium, and not much of anything heavier - fits the observations.

Do better, and you may get a Nobel prize.

Science isn't designed to get perfect results, but rather useful results. If it started claiming that any scientific explanation was perfect and incapable of refinement it would have become a religion, but that seems to be what you are asking for.

Lol. I'm not sure you have tried to understand anything I've said.

"Those times" are the realm of both gravity and quantum mechanics. We currently do not have any accepted theory for that. And if we have it, it would probably not be easy to verify it experimentally.

There's not a lot of point in understanding someone who is saying that he doesn't understand much, and would like it if nature were kind enough to be explicable with explanations he could understand.

Huh, So the metric is like choosing your coordinate system in 3-D. (OT.. story from grad school, I was taking a math physics course, For the final the prof had offered a reward for the best grade. (a copy of his book.. no big deal) I got to the bonus question which was solving for the shortest path between two points on a sphere. I knew the answer was a great circle, but in the rush of the exam I started the problem in Cartesian coordinates.. the equations turned "nightmarish"... I realized my mistake but was out of time... no prize but a good lesson :^)

Ditto Tim's thanks for your thoughtful answers.

George H.

Not sure what your point is. Science has always tried to extrapolate beyond the area where it is easy to do experiments. Analyzing the beginning of the universe will always be one of those areas and yet we continue to try to apply science.

That's an interesting viewpoint, but the transformation of a set of basis vectors is exactly the orthogonal basis in which the transform is expressed. Basically, 'transform of a basis vector' defines each column of the FT matrix.

The 'different basis' is just a set of orthogonal vectors, the question of rotation isn't answered yet.

So, it would be amusing to look at the simple cases. The two dimensional FFT is just a 2x2 matrix, and it preserves vector size and dot product (i.e. angle), so it can't be more than a rotation plus mirror-inversion.

Another thing about gravitational waves, just like electromagnetic waves, it should be possible to create an antenna to transmit and receive gravitational waves, by emitting and absorbing them.

ie. a gravitational wave transmitter can be two rotating masses, like the orbiting black holes, and a gravitational wave receiver could also be two orbiting black holes. However the receiver has to be have the two masses in the right orientation in order for the gravitation waves to be absorbed, and also it will be transmitting gravitation waves itself in the meantime..

Also when gravitational waves are "received" they are turned into mass not charge as with receiving electromagnetic waves.

If a gravitational wave receiver could be made with a diode equivalent, then a half wave receiver could be made that would increase in mass from gravitational waves, also ideally the gravitational wave receiver wouldn't have to be emitting mass in order to receive gravitational waves..

Possibly a configuration of multiple complex orbiting masses could absorb their own emitted gravitational waves while at the same time also absorbing gravitational waves that are emitted from the surroundings, ie a full wave rectifier gravity wave to mass converter :D

cheers, Jamie