KipIngram

Yes, I do think the costs would come down significantly once you no longer had to lift every single thing you needed out of Earth's gravity well.

Yes, I think a flashlight has a small amount of recoil, equal to the total momentum of all of the photons it emits.

It's interesting to me that supporters of both parties complain that the other party has committed gerrymandering. It's sort of a "catch all" for when one isn't getting one's way. The other mechanism that gets so abused is the electoral college; no one complains when their own candidate wins the electoral vote but not the popular vote - it's only invoked when it displeases.

Nonetheless, that is the process. In theory Trump is subject to impeachment and conviction at any time. But if the votes aren't there, the votes aren't there. The most important part of having an orderly society is that we respect our own processes. Wanting to bypass them when it suits you, but not when it doesn't, is a sure path to chaos.

Whether it's intentional or not, part of the religious mindset is to wear "armor" against counterarguments. Most people who are zealously religious (by that I mean that their words and behavior "broadcast" their faith) have had many people challenge their beliefs. They've become skilled at keeping that input from changing their mind. I think it's warranted in some cases, because not everyone who challenges their beliefs are motivated by simple quest for rationality and evidence processing - there are also people out there who simply want to tear religion down, as an end in itself.

I agree - that looks like an unachievable waveform to me.

Well, I think the magnet would pull on the whole ball to various degrees, create a force distribution throughout it. And then whether it rolls or gets dragged depends only on the friction coefficient between the ball and wheel. The magnetic attraction is not going to direction cause the ball to rotate, but contact with the wheel could, depending on the specific numbers an analysis revealed. But even if you grant rolling, the motion is still going to be transient and come to an end. It's entirely possible that the wheel might turn a bit when you first introduce the magnetic (i.e., when you "switch on" the magnetic field.) But the steady state solution to the entire problem is static. There will be no "unbalanced force" on the wheel, because the component of gravitational force on the ball tangential to the wheel will be precisely balanced by the component of the magnetic force on the ball tangential to the wheel. When this thing has no magnetic, we all know that the ball will be at the bottom of the wheel. It's still experiencing a gravitational force, but that force is normal to the wheel's inner surface. No tangential force - no motion. With the magnet in place the total force on the ball (gravitational and magnetic) will be... normal to the inner surface of the wheel. No tangential force - no motion.

I think the point of colonizing space (be it Mars, or Lagrange point stations, or whatever, provided the community is self-sustaining) is not about improving the lives of specific individual colonists in a cost effective way. The cost is staggering, and you could improve the lives of a far larger number of people by devoting the resources to improved lives on Earth. Those immediate outcomes aren't the point. The point is to spread the human species to other places. Let's say a plague or a nuclear war wipes out human life on Earth. If Earth is the only place we live, bye bye species. But if we live in other places insulated from those events by the distances of space then the human species would carry on. That's the point. Not to mention the human penchant to explore and to do things simply because they can be done. Pull up the opening theme for Star Trek: Enterprise on YouTube - it's a great tribute to the audacity of the human spirit.

Wait, let me get this straight. You're proposing that that the ball will roll up the incline of the raceway toward the magnet, and this rolling will drive the wheel counterclockwise continuously? No, that won't work. You don't even really have to do the math to show it won't work - this sort of thing never works. You're putting no energy in, and you noted the various ways energy can be lost. Conservation of energy prohibits all devices of this nature. If you execute a detailed analysis of the system correctly it will show that. If you do an analysis that does imply continuous rotation of the wheel then you made a mistake in the analysis somewhere. The other reason you know it won't work is that if it would work we'd have machinery all over the place that exploited the principle.

I was a little unsure whether to post this in the relativity or quantum section, so mods please move it if it fits better in quantum. Also, I'm not pushing the argument below out as "obviously true" - I'm just throwing out the idea for feedback and commentary. I've read about people trying to find magnetic monopoles. But given that the magnetic and electric fields are related to one another relativistically, there will always be a magnetic field (in some inertial frame) if there is an electric field in any inertial frame. Imagine that in my lab frame I set up a uniformly charged rod (long compared to the lab). In my lab frame the charge configuration is stationary, and I measure an electric field but no magnetic field. Now an observer flying through my lab will see charges in motion, and will measure a magnetic field. But that field exists purely because of the requirements of relativity. It seems that if monopoles existed then they would have to be detectable in the lab frame too. I'm not totally sure of that, but after all, they would be distinct particles. Is it possible for particles to exist in one frame but not in another frame? Anyway, that's the thought process - I'm wondering if the very relativistic origin of the magnetic field implies that it's created by the same particles that create the electric field, which would mean no further particles are required. Ooops - sorry for the duplicate post. Is it possible for me to delete posts I've created, or does that require moderator assistance?

Thanks Mordred; I'm reading. So, where did the approach I was taking fall down? I think I feel confident about taking a set of specified events in the S frame and moving them to the M frame - that's exactly what the Lorentz transform is supposed to do (connect those (x, ct) <--> (x', ct') pairs). That leaves me with the very presumption that the equation of motion x = At^2/2 + v(0)*t holds; is that itself something that's not strictly correct?

My original assumption was exactly that - that the two observers would each see constant acceleration but different values. I'm sort of tying my self in knots and going back and forth. My original plan was to identify the events that corresponded to the test object; if it starts with uniform acceleration A at t=0, then those would all have the (x, ct) form (At^2/2, ct). Those are good events that I can use the Lorentz transform on to find out what (x', ct') events you'd associate with them and thus have the x' vs. t' curve that you would measure. Bearing in mind that you see the test object with an initial velocity -v, then if you also see uniform acceleration we ought to be able to plug some of those values into x' = A't'^2/2 - vt' and arrive at a good value for A'. If you don't see uniform acceleration, then that wouldn't work. I wound up with non-working algebra when I tried that, but like I said earlier I may have just dropped the ball somewhere. I was trying to do it in a console editor session, so it wasn't the most friendly "visual" environment for such things. And my method presumed from the start that a single constant value for A' would result, so if that's not right it was bound to fall apart. But at any rate, I was finding it problematic. Then when I wrote the follow-on note I was focusing on velocities. I noted that I saw velocity advance by A each second, but that when I applied the velocity transformation rule I'd derived early (and confirmed online), I got non-uniform steps for the transformed velocity. That combined with the fact that our clocks do run at a fixed and unchanging ratio with respect to one another made me decide that you would not see a uniformly increasing velocity. But now I'm questioning that; I feel like maybe taking that simpler approach glosses over something. I'm not fully decided either way yet. I feel like the first approach I outlined above is the most solid and sure one, so I may make another pass at it without initially assuming your acceleration will turn out constant. It's a valid approach as long as we keep it general enough to handle either outcome. Ok, I think I showed myself that M's measurement will not yield uniform acceleration. Rather than slug through the algebra, I chose a specific numerical case. I set c=1, took v=beta=0.5, and took A to be 0.001c numerically. I solved for three different transformed event points and substituted those into what should be M's equation of motion solved for A'. I got different values in all three cases. The difference wasn't large, but I carefully carried all available digits of accuracy on my calculator , and I did it for three points (2, 4, and 6 seconds) and got a monotonically increasing value for A'. I don't know that I consider this final - I've done a good bit of numerical analysis in my time and while I'm pretty good at it I also know it can burn you if you aren't really, REALLY careful. My expressions were precise up until pretty near the end, so there wasn't long for round off error to accumulate. I'm hoping someone more knowledgeable will weigh in. In case anyone is interested, here is the analysis I just did. I use k for (1-v^2/c^2)^0.5 and b for v/c. 4. Acceleration. Let S observe a test object that is resting at (x,t) = (0, 0) and then initiates uniform acceleration A. S will associate these events with the object: E2 = (2A, 2c) E4 = (8A, 4c) E6 = (18A, 6c) All of these events can be translated into M's frame. E2' = (2Ak-2bkc, 2kc-2Abk) E4' = (8Ak-4bkc, 4kc-8Abk) E6' = (18Ak-6bkc, 6kc-18Abk) Assume A = 0.001c. Then E2' = (0.002ck-2ckb, 2ck-0.002ckb) E4' = (0.008ck-4ckb, 4ck-0.008ckb) E6' = (0.018ck-6ckb, 6ck-0.018ckb) This means that the (x', t') points at which M will observe the object are (0.002ck-2ckb, 2k-0.002kb) (0.008ck-4ckb, 4k-0.008kb) (0.018ck-6ckb, 6k-0.018kb) Let us further assume that c=1 and b=v=0.5. Then (0.002k-1k, 2k-0.001k) = (-0.998k, 1.999k) (0.008k-2k, 4k-0.004k) = (-1.992k, 3.996k) (0.018k-3k, 6k-0.009k) = (-2.982k, 5.991k) --------------------------- I think it's precise up to here, and the rest was carried a full calculator precision. Finally, for b=0.5 we have k = 2/(3^0.5) = 1.1547, so M's observation points are (-1.1524, 2.3082) (-2.3002, 4.6142) (-3.4433, 6.9178) Now note that M observes the object to have an initial velocity of -v, so if he is to observe uniform acceleration it would fit this equation of motion: x' = A't'^2/2 - vt' For any single data point (except t'=0) we can solve for A': A' = 2(x'+vt')/(t'^2) Recalling that v=0.5 and subtituting the values above for x' and t', we get A'(E2) = 6.501691e-4 A'(E4) = 6.508200e-4 A'(E6) = 6.514720e-4 When I was toying with the direct transformation of observed velocities I felt it implied that the acceleration seen by M would increase (at least for this case).

Hi. I decided last night to work through the derivation of the Lorentz transform. I've "learned about it" in the past, but I thought it would do me good to pay full and rigorous attention to the math each step of the way. So I started off, and before long had the the transform that relates the coordinates of an event (x, ct) for observer S and (x', ct') for observer M when S sees M moving at constant velocity v. So far so good. I had it written in matrix form, so I inverted it and confirmed that the transform and its inverse gave me the identity. Score one for the home team. Then I looked at the situation where S observes an object moving with constant velocity U, and worked out that M would also observe the object moving with a constant velocity U' and found the relationship between U' and U. Score again. Then I tinkered with S observing an object that was at rest at his x=0 for t<0, but at t=0 initiated uniform acceleration A. That ran me into trouble. I tried noting that at t=2 S would see the object at x=2A, giving me an event with coordinates (2A, 2c), and then transformed that into M's frame. I reasoned that for t<=0 M would have seen the object moving at velocity -v, an initial velocity, and then would see uniform acceleration with some value A'. Using the above mentioned transformed event, I had a location and a time that M would associate with the object, an tried to plug that into M's dynamic equation for uniform acceleration, x' = A't'^2/2 - vt' so I could solve for A' in terms of A and usual factors. It just went nowhere. I may have an error in my algebra that I haven't caught yet. But it also occurred to me that I wasn't sure whether inertial observers will agree as to whether an object is undergoing uniform acceleration. So that's my question. Do they, or do they not? I'd rather not chase an algebra error if the problem is conceptual. Somewhere upstairs I have a book that went through stuff like this, but I was hoping to work as much of this out as I could myself without going to a reference; I'll remember it better if I do. Thanks! Edit shortly later: I think I convinced myself that they do not. S sees velocities 0, A, 2A, 3A, etc. at one second intervals. Those intervals are not one second intervals for M, but they are fixed size intervals. My expression for velocity transformation was U' = (U-v) / (1 - uV/c^2). The numerator of that changes by fixed amounts each "tick," but the denominator is changing too, so the steps in U' are not the same. So it looks like M will observe non-uniform acceleration.

I have a book that does it that way, if I recall correctly. Principles of Electrodynamics by Melvin Schwartz. I always remember his opening sentence: "Electrodynamics is beautiful!"

I see a couple of ways to go on this. One common definition of "work" is "mechanical work"; the application of a force through a distance, or a torque through an angle. So with that definition energy is a much broader concept, since it can have many forms other than mechanical. Loosening the terminology a bit, I could also see using the word "work" for energy transfers that are "organized," in the sense that the result can be further manipulated and applied to various purposes. Energy can also have a disorganized form, like the random thermal motion of molecules in some material. That energy is still there, but unless you have a reservoir of lower temperature so that you can create a thermodynamic cycle you can't get it back into a useful form.

Sriman: you could think of H and B as roughly analogous to voltage and current in a resistive circuit. Don't read too much into the analogy, but just as V and I are proportional for a given resistor, H and B are proportional for a given material. But voltage obeys Kirchoff's Voltage Law - its integral around a closed path is zero -, whereas current obeys Kirchhoff's Current Law - the sum of currents entering or leaving any point in a circuit is zero. For H and B, you have similar behavior. The integral of B over any closed surface is zero (no magnetic monopoles, divergence of B is zero), whereas the integral of H around a closed path is equal to the ampere-turns encircled by the path (curl of H = J). In a medium of constant permeability both sets of relations would hold for both B and H, with appropriate proportionality factors. But that's the "physics difference" between them. H is something that satisfies a line integral / curl related law; B is something that satisfies a surface integral / divergence related law. Hope this helps!

Kjelleman: When you listen to the FM radio in your car, your radio is receiving signal energy initially produced in the station's transmitter. That energy got from the transmitter to the receiver via the field. So fields can possess and transfer energy; that makes them seem pretty real to me and not just a calculation technique. From what I've read they can possess and transfer momentum as well. My own working definition of a field in physics is the association of a value with all points throughout a region of space / spacetime. That value can be scalar, vector, tensor, whatever.

That Art Hobson paper linked above is fantastic.

First please let me echo the kudos for Mordred that I've seen many express. Dude, your explanations are fantastically lucid - thanks for being here. If I can even approach your level before I'm gone I'll be ecstatic. And yes - I'm also jealous of your smooth and easy use of LaTex. I didn't fret too much over the macroscopic top; I figured it was likely that the quantization had to apply to it too, literally, but I mostly took that as just an analogy to make it easier for the audience to picture what aspects of particles he was talking about. Mordred, I do have a question; something that I was hoping the video would address but it didn't. I get it that particles are excitation "packets" in the field; that makes total sense. But what keeps them that way? What aspect of the physics keeps those wave packets from spreading out? Is it something about the quantization that just doesn't allow it, or what exactly? That makes it sound like quantization of space and time are required, but I thought that was still debated? Oh - so after I sent that message above I went off to Google, and ran into this statement on another site: "Have a google on electron knot, and there's people out there saying the electron is stable because it is in essence a "knot" of field." So that means little or nothing to me beyond the vague concept at my current level of knowledge, but it sounds reasonable. Comments?

Cool. Nice lecture.

So far I'm finding versions of that video that have picture but no sound, and versions that have sound but no pictures. Tests on other YouTube videos seem to show that things are working fine. I'll keep looking... Ah - found one. Weird - don't know what was up with that.

Holy cow - he reminds me amazingly of a friend of mine that's now living and working in Malaysia. Striking resemblance. This has been a... vastly entertaining thread. I can't believe I got to age 54 without realizing that Einstein, was, in fact, a god. I'll have to hastily mend the error of my ways...

I just read a paper this past weekend that argued for a time-free expression of physics using stationary action principles. The author went to some length to discuss the history of time, beginning with the use of the sidereal day as the "standard," and went from there to Newton's use of the angle swept out in an orbit as a "stand-in" for time. Then he noted that since no body in the solar system is unperturbed by other bodies, that the swept angle of one body wasn't "ideal" in that sense. So the next step was a similar expression that included all bodies in the solar system. Finally he noted that in the strictest sense even that's not ideal, since gravity never "stops." So by the end of the paper he'd stated that the only truly correct standard of time would incorporate the dynamics of the full universe. Now, he was talking about our assignment of numerical values to instants in time, rather than the "raw notion" (if that means anything). And he limited the argument to classical physics. It was an interesting read; I'd post the link but I don't have it open in my browser anymore. I always felt that special relativity treats time as equivalent to the spatial coordinates (except for the i, of course), and the way that space and time can transform into one another in relativity always made me feel that they aren't just "treated together" but rather have a deep connection of some kind. I never felt that spacetime "rose out" of relativity - it seems more like part of the presumed background framework. On the other hand most of the introductory relativity texts go to some trouble to be very careful about the measurement of distance and duration by observers - that does sort of make them something perceived by observers (which could be anything of course - parts of the system "observe" one another in this way). I've pretty much decided that the notion of space doesn't really mean anything without objects in it - space seems to arise from relationships amongst those objects. Given how closely space and time "play together" I guess I feel that way about time too. Especially in general relativity, where the very shape of spacetime emerges from the "stuff" that's in it.

I don't necessarily expect physics to give an explanation to consciousness. However, if one wishes to claim that consciousness arises from existing physical laws, then under those circumstances I expect an explanation. A claim has been made (that my experience of self-awareness arises from the known laws of physics) - the burden of proof rests on the claimant. When Newton proposed that the planets move the way they do because of F = -GMm/r^2, we didn't simply accept that - we spent centuries showing that it was (almost) so. Ditto with general relativity, even more successfully (no little chink like Mercury's motion so far). Ditto again, even more because of how big a stretch it was initially, with quantum theory. I thought that was the whole point of science - make a claim, and then show conclusively that it is supported by evidence. Why should I let this claim skate in without subjecting it to the same standards? Especially when my own professional training (electronics / computers) tells me that the claim has a very, very low probability of being true?