I've now worked my way through the problems at the end of Chapter 1 of James Binney and David Skinner's 'The Physics of Quantum Mechanics'. And I found them to be manageable. Much more so than some of the problems in later chapters, by the looks of it. The ones in Chapter 1 are no doubt intended as gentle warm-up exercises.
Useful warm-up exercises. If nothing else, they forced me to remind myself of some complex number calculation rules.
The last problem, about an infinite series of potential wells, was the most interesting one. The first task is to find the probability of an electron being in the nth well. A quantum state vector for the electron's location is specified, with probability amplitudes provided as a function of n. So it's pretty straightforward to calculate the probability of the electron being in the nth well as a function of n.
The next task is to determine the probability of finding the electron in well 0 or anywhere to the right of it. I duly calculated the sum of all those probabilities from well 0 to infinity after looking up the appropriate summation formula on Wikipedia.
Only to realise that I could have spared myself the trouble: I could have found the answer more easily by employing a symmetry argument, since the probabilities are arranged symmetrically around 0 and must add up to 1.
But I don't regret my detour. It's given me a bit more practice in infinite series calculations. And that's of course what these problems are all about: practice, practice, practice.
Indeed, I find it very difficult to just read a physics textbook and understand it all without getting some practice in manipulating the mysterious mathematical symbols those texts tend to be peppered with. While I fear that at least some practice is necessary to achieve understanding in physics, I don't think it's sufficient.
Is the potential well probability amplitude distribution given in the problem discussed above realistic? If so, where do those probabilities come from? How and why do electrons move from one well to another? Is it meaningful to say that an electron is in a particular well before we've measured its location? Is it ever meaningful to say that an electron is in a particular well? I'm sure it's possible to be rather good at problem solving without understanding very well what the problem is about.
To adapt a quote I read somewhere many years ago: Physicists often expect to be regarded as profound thinkers even though you can find the most simple-minded people among them, unable to do anything that requires them to think unless it can be achieved by combining symbols in a way which is more a matter of practice than of deep thought.
George, I just came across your blog and have scanned some of it. I have a similar interest in SR, but I do not have your physics background. I assess it from a purely "philosophical" perspective. You pose these questions re constant speed of light:
ReplyDelete1. "How did physicists come to accept it?"
It seems to me that they came to accept it on the basis of the empirical measurement of the two-way speed of light. But what that does not, and cannot, tell us it whether the speed of light IS constant (Einstein) or merely "measured as constant" (Lorentz).
2. "Is it based on convention, theory or observation?"
Clock synchronization in SR is based on convention, I believe. I see from scanning some of your previous posts that you have put a great deal of effort into contemplating this question. It is also based on "theory" (axiomatic presuppostions) as far as the one-way speed of light goes. SR and LR (Lorentizian relativity) differ here also.
3. "Are there any alternative conventions or theories that are compatible with observation and experiment?"
Absolutely. I saw you cite Sexl and Mansur, so you know this.
I'm sure I have not said anything in this comment that you have not already contemplated and formed your own conclusions about.
For a variety of reasons (which I assume you're aware of) the whole concept of "relative simultaneity" seems absurd, as a physical matter, to me. It's fine as a mathematical "shortcut," which Lorentz said it was (but utterly fictitious as a matter of "reality").
But I get the sense that you're not so convinced of this "absurdity." Do you care to discuss the topic further with me?
Georg: I have read your posts on SR more carefully now. I am commenting here, rather than in response to specific posts you have made years ago, because I'm not sure you'll notice them otherwise.
ReplyDeleteYou correctly point out that a "clock adjustment" is not necessarily tantamount to "clock synchronization.
I have seen many theoretical physicists say that, in theory, there is no way to empirically test the one-way speed of light. Any such attempt would be circular, because one must start with certain assumptions before be able to undertake such a "test."
Therefore, in any theory of relative motion, the one-way speed of light is merely POSTULATED, not observed or proven. At least that is my understanding.
I have a lot more I would like to share with you in order to get your input. But again, my thoughts on this topic (such as the twin paradox) are mainly non-technical and fundamental, so I'm not sure how interested you would be in them.
Let me know when you check you blog again, OK?
As you correctly noted in a prior post, SR does not really dispense with the notion of "absolute rest" (an aether), it simply posits an infinite number of them. In SR every single inertial frame of reference MUST (not may) be regarded as absolutely motionless. Everything in the universe that is moving with respect to it, is "really" moving. It alone is "not moving" (motionless).
ReplyDeleteHow artificial can you get? It's all sleight of hand and bogus, the way I see it. It's built on inherent conflict and inconsistency, where every observer in a different frame of reference disputes the claims of every other, and insists that he, and he alone, is right.
This is due to the alleged "reciprocity" of time dilation, etc., which is "required" because simultaneity is purportedly "relative."
If A and B are moving with respect to each other (and both acknowledge this) then each must claim that the other is moving and that he is not.
You mentioned the concept of (lack of) memory. Einstein's example of the relativity of simultaneity requires the train passenger to "forget" that he bought a ticket, boarded a train, felt and saw himself accelerating, and then settled into uniform motion. Having forgot all that (and ignoring fundamental laws of mechanics) he claims to be motionless. Doesn't that seem to be absurd to you?
Since when is "objective, physical reality" premised on the subjective mistakes of a fool on a train who claims the train tracks (and everything else he can see which is attached to the earth's surface--trees, fence posts, houses, etc.) are all moving while he remains motionless?
They cannot both be "right," as a matter of elementary logic. They could both be wrong, of course, to the extent that they each claim to be "motionless."
I just keep adding comments, Georg, because I would like to express my thoughts (which I've held a long time) to someone who might understand them (in other words, someone who will give them serious consideration rather than just insist that "physicists who accept SR as describing reality can't be wrong").
ReplyDeleteIt seems to me that the (mathematical) consistency of SR is strictly dependent on the strict enforcement of arbitrary protocols which could not accurately reflect "reality."
Take an astronaut who, after years of preparation for a trip to the moon, sits in a space capsule atop a massive amount of rocket fuel and then blasts off. At that point he knows HE is moving (not the earth away from him and the moon toward him). Acceleration is absolute, even in SR.
So why in the world would he assume that he has suddenly come to a "dead stop" the second he quits accelerates, and that, at that instant, the earth has begun moving away from him? No astronaut would do that.
He would know that vis-à-vis the earth, the relative motion between them is a result of his motion, not the earth's. He would therefore, knowing SR (or, more accurately, know the Lorentz transformations), know that HIS clock has slowed down, not the earth clock. This alone simply and convincingly resolves the so-called "twin paradox."
He is the one who accelerated; he is the one moving; and therefore he is the one who is aging more slowly. What's the problem?
There is none, until the dictates of SR create a problem. SR forces him to falsely assume he is not moving. If he rejects this, then he rejects SR in favor of a theory of relativity motion which posits absolute simultaneity. If he wants to maintain any credible, coherent theory which explains the situation he MUST reject SR. It is simply not the case the earth clock is running slower, so why would he "assume" otherwise?
Bertrand Russell once said (perhaps paraphrasing) "Special Relativity IS the Lorentz transformations." But those transformations were developed (by Lorentz, with help from Poincare) to explain events in the context of a theory of relative motion which presupposed absolute simultaneity. Many physicists today seem to ignore this fact. They act at though, if the predictions generated by the LT are verified, then "special relativity" has been confirmed. They don't seem to distinguish between the LT, per se, and SR.
ReplyDeleteEvery single experiment which is said to "confirm" SR also "confirms" Lorentzian relativity. The GPS uses LR, not SR. It posits a "true," preferred absolute frame (the non-rotating ECI) and proceeds accordingly. From what I understand, it would be impossible to create a working GPS relying on SR.
In similar fashion, cosmologists use what nobel-prize winner George Smoot has called the "cosmic rest frame" (the CMB) to calculate the motion of the very earth the observations are made from.
Furthermore, LR is equally applicable to all frames, not just inertial frames. Why in the world does physics hang onto what seems to be a clearly inferior and wholly inadequate (from a physical, rather than purely mathematical standpoint)? I really can't understand it.
Hi there - thank you for your interest in my blog.
DeleteIt looks like you are asking questions very similar to the ones I've been grappling with over the last few years. In a nutshell, why is it that SR comes up with such strange-seeming results - in particular regarding simultaneity and one-way speeds - when there doesn't seem to be anything in the observed phenomena that's all that strange.
I broadly share your concerns though not necessarily all of your conclusions. For example, it is not necessarily true that an astronaut moving away from Earth "is the one who is ageing more slowly". According to my analysis, that would depend on Earth's acceleration history and would only be true in such absolute terms if all of Earth's past accelerations had cancelled out, which seems somewhat unlikely.
The root cause of the conceptual confusion which I think reigns in SR lies in its concept of simultaneity. SR authors routinely confuse 'clock adjustment', which can be arbitrary, with 'clock synchronization', which must meet additional criteria if that concept is to retain any of the standard meaning it has in our language, in particular a symmetry requirement if signalling methods are used.
Hopefully my blog posts on these issues explain my thinking in greater detail and with greater clarity, but I'd be happy to discuss any specific questions you may have by email: Georg.Lentze@talktalk.net. Many thanks, Georg.
I said: "They act at though, if the predictions generated by the LT are verified, then "special relativity" has been confirmed. They don't seem to distinguish between the LT, per se, and SR."
DeleteA look at the wiki article entry for Hafele–Keating experiment demonstrates this confusion. https://en.wikipedia.org/wiki/Hafele%E2%80%93Keating_experiment
There it is claimed that "Because the Hafele–Keating experiment has been reproduced by increasingly accurate methods, there has been a consensus among physicists since at least the 1970s that the relativistic predictions of gravitational and kinematic effects on time have been conclusively verified." It is clear from the context of the article that they are equating "relativistic predictions of...kinematic effects on time" with the predictions of SR.
But the actual results were that, considering only the velocity effects (and ignoring the GR gravitational effects) on clocks, that: "a clock aboard the plane moving eastward, in the direction of the Earth's rotation, had a greater velocity (resulting in a relative time loss) than one that remained on the ground, while a clock aboard the plane moving westward, against the Earth's rotation, had a lower velocity than one on the ground."
To restate this.
1. The clock travelling westward showed the least time elapsed (and was therefore going to slowest, given the LT--which says faster moving clocks run slower).
2. The "stationary" clock on earth, was in the "middle" with respect to the measured amount of time elapsed, and
3. The clock travelling westward showed the least amount of time elapsed, i.e., it moved the "fastest."
This is NOT what SR would predict. This is what an AST theory, positing the ECI as the preferred frame, predicts.
The wiki article even acknowledges this, indirectly It prefaces it's summary of results by saying: "Considering the Hafele–Keating experiment in a frame of reference at rest with respect to the center of the earth..."
To make the correct predictions, you MUST use the non-rotating ECI frame as the preferred frame.
So, again, verifying the accuracy of the LT predictions about time dilation do NOT necessarily confirm SR. The LT are just as essential to the predictions of a theory of relative motion which posits absolute simultaneity. Confirming the accuracy of the LT confirms those theories at least as much as (in this case more than) it confirms SR.
Georg said: "According to my analysis, that would depend on Earth's acceleration history and would only be true in such absolute terms if all of Earth's past accelerations had cancelled out, which seems somewhat unlikely."
ReplyDeleteYes, I see your point with respect to an "absolute" framework. In practice, it seems that there is a need for a hierarchical structure when selecting the "preferred frame" for purposes of establishing absolute (in name only) simultaneity. The ECI needs to be used for terrestrial (on or near earth) observations and calculations, the barycenter of the solar system for planetary motions, etc., with the center of mass for the scale being selected serving as the as posited "motionless" point. So, as with general relativity, there is no "global" (universal) metric which applies everywhere. The dominant gravitational mass in a given "locality" provides the base line.
Georg said: "The root cause of the conceptual confusion which I think reigns in SR lies in its concept of simultaneity. SR authors routinely confuse 'clock adjustment', which can be arbitrary, with 'clock synchronization', which must meet additional criteria if that concept is to retain any of the standard meaning it has in our language, in particular a symmetry requirement if signalling methods are used."
If one adopts an AST (absolute simultaneity theory), then the speed of light will be anisotropic in all but one (preferred) frame. But it seems to me that such a theory itself requires a starting point that is "arbitrary" in the sense that it cannot be proven and is merely a fundamental assumption.
For me, a major criterion for such a selection would have to be whether it makes any physical sense. If it doesn't, it's out, I don't care how much it may seem to "simplify" calculations. For me, SR is out.
If I understand you correctly, you're basically saying that Einstien's "synchronization" method presupposes speed of light isotropy. That's plausible, on it's face, but it does not lead to a logically coherent theory from a physical standpoint.
Your point seems to be that the clock's are not "truly synchronized" if the premise is not true. If so, I agree, but there doesn't seem to be any way to empirically test such an assumption (or it's negation).
But it is ridiculous (as I see it) to claim that "simultaneity" is a matter of subjective perception. A person near a thunderclap would see the lightning and hear the sound virtually simultaneously, while a more distant observer will see the lightning flash first and only later hear the sound. But we would never say that the sound (i.e. the cause of the sound) occurred at different times for different observers. That would, as you note, make the whole notion of simultaneity meaningless from any objective viewpoint.
What you reduce to a confusion about "simultaneity" I would probably say is a confusion about standards. Just different ways of looking at the same thing, I figure. If you have an infinite number of "standards" then, in effect, you have no standard whatsoever.
If you say two thing happen "simultaneously" if and only if a given person perceives them as simultaneous, then you have perhaps a theory of human psychology, but not a theory about the physical world.
P.S.: I just responded here, rather than in an email, as you suggest, because I don't get along well with email. I'm not sure why you suggested an email response. Are you wanting to conserve space on this blogsite?
Coming back to the astronaut, as between him and his earth twin, he is the one who "sped up," hence the need for rocket fuel, etc. While he may have "slowed down" with respect to some other frame of reference, he is the one "moving" (i.e. moving faster) as between the two of them.
ReplyDeleteSR, in effect, resolves the paradox by saying that the earth twin frame must be preferred. It is the one which gives the "correct" answer, when applying the LT. Perfectly understandable, to me anyway. What's not coherent is the claim that the two frames are "equally valid" and, essentially, the claim that each clock must run slower than the other. One of the two must be moving "faster" than the other, whatever frame of reference is used. You can't say that neither is right, nor that both are right, when each claims that HE is not moving. At least one of them must be wrong when asserting such claims.
I guess what I've been trying to say here is something like this: While you tend to pinpoint the problem with confusion about the "concept" of simultaneity, and improper semantical usage of that term (which I agree with), to me that's a somewhat esoteric and indirect way of expressing the problem.
ReplyDeleteI tend to look at it in more everyday, fundamental terms, to wit: Without getting into the analysis of linguistic patterns terms involving abstract concepts, the whole notion of relative simultaneity is simply prima facie absurd, once you think about it.
Take Einstein's own "explanation" of it. HE can explain why the train passenger sees things differently, because HE has postulated that the train is moving. He knows this. If the train passenger was allowed to know it also, he too would agree that the two lightning flashes were simultaneous using his "proper" and "normal" frame of reference (the earth's surface). He wouldn't claim the two strikes happened at different times using that knowledge and that perspective.
But he is not allowed to know this, and is compelled to say that he is NOT moving. Hence he claims that the strikes were NOT simultaneous and, furthermore, that anyone who claims they were is mistaken (presumably because they don't know THEY are the ones moving, while the train remains motionless).
Poincare had made this same observation years earlier, to wit: that the Lorentz transformations could serve to establish a strictly subjective sense of relativity, if each and every observer was unaware of, or otherwise chose not to acknowledge, his own motion.
But, like Lorentz, he never for one minute took such a state of affairs to be "true." The "relativity" thereby established was just an artifact of ignorance, not something "real."
For SR to get the results it desires, every observer is prohibited from acknowledging that his clock might be the one moving (faster). But the requirement is absurd, from any common sense standpoint. When I'm driving 60 mph down the freeway, I know that, as between the two, my auto is moving, not the road.
This may be a bad analogy, but....
DeleteIf I'm sitting on my porch looking at the green grass of my lawn, and stop each passerby and ask him what color the grass is, he way say "green." Perhaps none of them can explain, on the basis of scientific theory, *why* it is green (photosynthesis, chlorophyll, whatever), but they are nonetheless certain that it is green. They don't need a scientific explanation to see and know that.
That's kinda the distinction I'm trying to make between saying that SR's problems are explained by noting a misuse/misunderstanding of the concept of "simultaneity" and simply saying that SR is obviously wrong, even without a formal, technical analysis of just where the "scientific theory" went wrong. You don't need to even know that to know it is wrong.
To carry the analogy to it's conclusion, if someone came up with a "scientific hypothesis" that all grass would appear to be blue to the human eye, then I know that theory is wrong, without even asking about the assumptions it is based on, see what I'm getting at?
DeleteEven in SR, acceleration is "absolute." This merely means that it is not frame-dependent, and that an accelerating object is seen as such by all observers. It does not mean that some standard for absolute rest has been established--that's a different kind of "absolute."
ReplyDeleteSo, what happens then in SR? In those cases (and only those cases) different observers (including the accelerating observer) AGREE on which object is "really moving." In contrast, as between two observers in uniform motion, but travelling at different speeds, SR requires that every observer say that "the other guy" is the one moving (never them).
So, in SR, acceleration is calculated by reverting to lorentizian relativity. In those cases, there is no disagreement about who is moving. Since it is the moving clock that runs slow (per the LR), it is therefore agreed, in SR, that the accelerating clock runs slower, and this is not a mutually reciprocal phenomenon.
So, as I have asked before, why should an accelerated object suddenly treat itself as "motionless" as soon as it stops accelerating and settles into uniform motion? Has the law of inertia suddenly been suspended?
If an astronaut is uniformly accelerated at the rate of 1 g, he will be near the speed of light in about a year. For that entire year, both he and his earth compatriots agree that he is moving away from them, not vice versa. But then, suddenly, the astronaut is supposed to conclude that he is motionless while the earth moves away from him at near the speed of light, the second he stops accelerating?
I don't think so! This is the absurdity of the arbitrarily imposed requirement of "memorylessness."
Thanks for your additional comments. I sympathise with your view. When I was told at school that the (one-way) speed of light is the same for every observer, I couldn't believe it. And I didn't feel the explanations given in our textbooks and by our teachers were satisfactory. It's not just that the claim seemed wrong, it looked as if it just couldn't be right as a matter of principle. My lecturers on my physics undergraduate course were unable or unwilling to shed any more light on the matter. That's why I've been trying to get to bottom of just why physicists make this claim and what exactly, if anything, is wrong with it.
ReplyDeleteHowever, I don't think it's quite as easy as you suggest to say whether and in what sense an observer is 'really moving'.
In the case of movement on Earth, say on a train, it may seem straightforward. But appearances can be deceptive.
What if two spaceships somewhere out in space crossed paths? Which of them is 'really moving'? They may each have complex acceleration histories behind them. Neither of them may be in a frame of reference in which light propagates in symmetrical conditions.
In theory, a train passenger could happen to be in a frame of reference in which light does propagate in symmetrical conditions in all directions, while an observer on the platform is not. According to my analysis, that depends on their complete respective acceleration histories.
It's true that these histories may be impossible to reconstruct, so we may have to make some pragmatic choices regarding our time coordinates, if we want to use any.
I agree that, for many purposes, our choice could be to use Earth as a 'preferred' frame (just because we live on it), relative to which we determine which events are 'simultaneous' and which aren't. But if, say for some cosmological calculations, we opt for the solar system or our galaxy or the microwave background as the 'preferred' frame, you end up with the same disagreements on which events are 'simultaneous'.
I'm happy to accept that physicists find it easiest to define time coordinates in all frames in the same way (using light signalling). It's just that, in that case, they shouldn't be using the language of simultaneity (and one-way speeds, without any qualifications) to describe their results - Georg
Well, Georg, remember that SR is a theory of "relative motion," as is lorentzian relativity. Lorentz, like Newton, freely admitted that it would be impossible to detect any object that was "truly" motionless. At best we can detect relative motion. That's why I tend to put phrases like "really moving" in scare quotes.
DeleteSo, I agree with your analysis that a complete knowledge of acceleration history would be required to know what's "absolutely moving." But that's not really my point here.
I'm not trying to say that there is some way of knowing what is ABSOLUTELY moving and what isn't. My point is simply that SR is absurd. The claim that there is, and can be, no known preferred frame, standing alone, may be just fine. But what does that claim entail for theoretical purposes?
Does it mean that if I'm walking at a steady clip down to the liquor store, then I must presume that the liquor store is coming to me, while I remain motionless? I don't think so.
Just because we can't be sure about what is "absolutely" moving doesn't mean any old half-baked theory of relative motion is acceptable.
Again, these are theories of RELATIVE, not absolute, motion. As between (let's say only) two objects, is it impossible to know which of the two is moving with respect to the other? I can't know if my car is moving down the road, or if the road, and everything else on the earth's surface is moving past me while I remain motionless?
If so, then we can never know anything about motion. SR only says we can know nothing. You can throw laws of physics (such as F = MA) out the window. If we hit a ball over the fence, we can't know if the fence and the crowd watching are all moving toward the ball (while also going up and down) while the ball just remains motionless?
It's "possible" that we are all "brains in a vat." Does that theoretical possibility therefore compel us to take the possibility seriously?
You say: "I'm happy to accept that physicists find it easiest to define time coordinates in all frames in the same way (using light signalling)."
I am not happy to accept that, except perhaps as a strictly mathematical fiction. When proponents of SR start trying to claim that SR is "true," (i.e., representative of objective reality), as they are so often inclined to do, then I have seriously problems with their claims. SR does NOT comport with physics and "reality" as we otherwise believe it to be.
Ernst Mach, the proto-positivist, said the geocentric and heliocentric views of planetary motion were "equally valid." But what did he really mean by that? He followed with the observation that "but the universe is only given once." In other words, BOTH views could not be true. If either one of them was true, then the other couldn't be.
That's the problem with SR. As between any two given objects, it cannot be that if each claims he is not moving, then each claim is equally valid. Both cannot be motionless while there is relative motion between them.
Perhaps I'm not making much sense to you. Basically, I guess my point is that, even assuming we can never know anything about anything with ABSOLUTE CERTAINTY, that does not then mean that the most absurd postulations are plausible.
I said: "That's the problem with SR. As between any two given objects, it cannot be that if each claims he is not moving, then each claim is equally valid. Both cannot be motionless while there is relative motion between them."
DeleteI repeat this statement for emphasis. Even if we can't, in a given instance, say for sure which of two relatively moving objects is "really moving," it must be true that in any and every conceivable frame of reference, one of them is moving "faster than the other." That would be true even if different frames would give you different answers. Either way, they cannot both be motionless, as SR requires us to say. If both say that only the other is moving, then at least one of them is simply WRONG, no matter how "equally valid" you might want to say each claim is "in theory" when you are ignorant of the facts.
If I have flipped a coin and have it hidden under my hand, then "in theory," it could be either heads or tails. The odds are 50-50. But those are only the odds of me guessing right. As a matter of fact the "odds" are 100% to 0%. It is what it is, either heads showing, or tails showing, whether I happen to know it or not.
Georg, you say: "But if, say for some cosmological calculations, we opt for the solar system or our galaxy or the microwave background as the 'preferred' frame, you end up with the same disagreements on which events are 'simultaneous'."
DeleteYes, this is quite true. And it would be true of any theory of relative motion. In a general sense, it would be true of any scientific theory pertaining to any subject whatsoever. We must always postulate something, and we can never know anything with absolute certainty.
But such problems are by no means unique to SR, so, for me, that's not what isolates and identifies SR's most obvious flaws. If that were the only problem I saw in SR, then I would not have any serious objections to it.
I keep trying to say basically the same thing in different ways, because I've run into this problem before when discussing SR with other people interested in the theory. For that reason, I'm not sure that what I'm saying seems of any real significance to you. I'm am NOT objecting to the lack of absolute certainty in SR, or any other theory. All theories share that "defect."
But the issue of certainty to be a common concern with some others I have spoken with. Somehow the focus shifts to what can be known for certain, and the subtle inference seems to be that if something can't be known for certain, then any conjecture is possible, and therefore just as valid as any other. I believe that line of (implicit) reasoning is fallacious.
To say it again (for perhaps the fifth time), the fact that SR presupposes certain things in defining simultaneity is, in itself, of no particular concern to me. Any theory must do that. My concern is with the implications of the presupposition chosen. If those implications lead to incoherent or obviously false conclusions, then I will say the theory is defective for THAT reason, not for the reason that it presupposed something that can't be proven.
Am I making any sense to you?
God only knows how many relativists have told me that Galileo "proved" that you can't discern which of two relatively moving objects is actually moving. He never made any such claim. In fact, he claimed the opposite.
ReplyDeleteThis is the guy who, after having been forced, under threat of torture, to recant his claim that the earth moved around the sun, muttered, under his breath, on his way out of the inquisition chamber: "And yet it moves!"
He said that in a windowless cabin, under a ship's deck, one could not detect his own motion (or lack thereof), that's true. But he went on to say that once the sailor went up on deck, saw the sails fully billowed, etc., then he would know he was moving past the fixed objects on the shoreline, and would have no reason to believe that they were moving past him, while he remained motionless.
His "parable" of the ship was really just arguing for the acceptance of the notion of inertia, and refuting the ancient claims that if the earth was moving, then a ball thrown straight up in the air could not land at a spot on the earth that was directly below it's starting point.
Put another way, he was arguing that we can "know" that we are in motion, even though we cannot "feel" our motion or empirically prove we are moving. We "know" such things by legitimate deduction from other known facts.
Georg said: "I'm happy to accept that physicists find it easiest to define time coordinates in all frames in the same way (using light signalling)."
ReplyDeleteEinstein tried for years to resolve the puzzles created by the Michaelson-Morley experiment. He finally hit on the notion that simultaneity is relative. But this notion falls apart on analysis. If a star 10,000 light years away goes super-nova today, we won't know it for 10,000 years. But then, when we do, we won't say it happened "now" (the moment we first saw it). We say it happened 10,000 years ago (when it did). That is absolute simultaneity, not relative simultaneity.
What evidence is there that simultaneity is relative? None whatsoever that I'm aware of. Einstein gave only one thought experiment in support of it. But that example contradicts the very premise it attempts to "prove," i.e., that the speed of light is constant in all inertial frames.
The guy on the embankment is midway between the two lightning flashes. So is the guy on the train. They are each either at rest or in uniform motion (in inertial frames). So, if the speed of light is constant in all inertial frames, both the passenger and the "stationary" onlooker would see the two beams SIMULTANEOUSLY. The light is travelling the same distance in each frame. If it takes a different amount of time for light to travel the same distance (on the train), i.e., if the beams don't reach the passenger simultaneously, then the speed of the two is not the same. Neither end of the train moves with respect to the passenger, no matter how fast the train is going.
It has been proven that light takes longer to go from San Franciso to New York that it does to go from New York to San Francisco, but the distance between them never changes. Per SR, light is supposed to travel at a uniform speed irrespective of the motion of the source or receiver.
How can Einstien "prove" that the speed of light is constant (and therefore that simultaneity is relative), in all frames when the very example he uses to demonstrate it contradicts the premise he is seeking to prove?
If, as Al did, you try to explain the difference by saying the passenger is moving away from one beam and toward the other, then you contradict the principle that all frames are equally valid and that that there is no way to detect uniform motion. If we explain his perception by saying we know he is moving, we now have a way of detecting who is moving and the earth's frame would have to be the preferred one, since it is the one where light travels isotropically.
See what I'm sayin, Georg?
Since you have made no comment for a week or two, Georg, I assume you're not interested in discussing the substance of SR.
ReplyDeleteWhile your analysis and comments are insightful and worthwhile, I don't think they're anything new. They seem to boil down to the observation that we can't discern "absolute" motion, and therefore can't discern absolute simultaneity. But since Newton, if not Galileo, that has been generally accepted by physicists as far as I know.
But of course Newton nonetheless went on to codify mechanics with astute and consistent analysis. If a reasonable study of physics requires knowledge of absolute motion, then we might as well throw it all out.
Or, I suppose, one could take the position that there is no need for physics to be "reasonable." That seems to be the tacit assumption underlying SR.
Hi again - I haven't commented recently because the discussion seemed to be moving in circles. For a summary of my analysis of the concept of 'simultaneity' in SR - which I regard as problematic - I refer you to this post: http://understanding-relativity.blogspot.co.uk/2012/08/convention-in-relativity-my-findings.html. All the best, Georg
ReplyDeleteWell, Georg, I don't think we're "going in circles" so much as we're just talking about two completely different things.
ReplyDeleteI have, several times, acknowledged, and told you that I agree with, your analysis of simultaneity. But that's not the problem with SR, per se.
If you're dissatisfied because there is no ETERNAL, IMMUTABLE, INDISPUTABLE Platonic TRUTH in physics, OK. You're right, there isn't, regardless of your preferred theory of relative motion. We can never know, with absolute certainty, what two things are "simultaneous."
Simultaneity is, and must be, a matter of convention. I'm not even arguing that.
I'm just saying that if you're going to posit two things as "simultaneous" for the purposes of formulating physical laws, then your postulation should at least be physically meaningful. Relative simultaneity is not physically meaningful, in my opinion. Other theories of relative motion are physically meaningful, but most modern physicists have abandoned sensible concepts of simultaneity.
I think you are ignoring my discussion of that point, which is different than simply saying something like: "If there are no absolutely certain premises, then any old premise, sensible or not, will do just fine."
Quoting from wiki:
ReplyDelete"Some features of the conventionality of synchronization were anticipated by Henri Poincaré. In 1898 (in a philosophical paper) he argued that the postulate of light speed constancy in all directions is useful to formulate physical laws in a simple way. He also showed that the definition of simultaneity of events at different places is only a convention.... A substantive discussion of Einstein synchronisation's conventionalism is due to Reichenbach. Most attempts to negate the conventionality of this synchronisation are considered refuted..."
https://en.wikipedia.org/wiki/Einstein_synchronisation
"A mathematical form of the relativity of simultaneity ("local time") was introduced by Hendrik Lorentz in 1892, and physically interpreted (to first order in v/c) as the result of a synchronization using light signals by Henri Poincaré in 1900. However, both Lorentz and Poincaré based their conceptions on the aether as a preferred but undetectable frame of reference, and continued to distinguish between "true time" (in the aether) and "apparent" times for moving observers.
Poincare derived local time by assuming that the speed of light is invariant within the aether. Due to the "principle of relative motion", moving observers within the aether also assume that they are at rest and that the speed of light is constant in all directions (only to first order in v/c). Therefore, if they synchronize their clocks by using light signals, they will only consider the transit time for the signals, but not their motion in respect to the aether. So the moving clocks are not synchronous and do not indicate the "true" time."
https://en.wikipedia.org/wiki/Relativity_of_simultaneity
Lorentz invented the concept of local time (with relative simultaneity) 13 years before Einstein wrote his first paper on SR. It was not a "new" notion. But both he and Poincare denied that local time was "true" time, as Einstein mandated. Lorentz said it was merely a mathematical fiction, created as a shortcut. Their theory of relative motion assumed, but by no means requires, the physical existence of an actual "aether." Both of them acknowledged that a motionless aether could not be detected, although many seem to be unaware that they held this view.
So they did not reject SR because simultaneity was conventional or because they believed that absolute motion was detectable. They just didn't see the concept of relative simultaneity as physically coherent (although they knew it was mathematically coherent--they invented it for mathematical (only) uses.
I have been talking about the reasons they (and many others then and now) refuse to give physical credence to SR. They too were aware of your assessment of simultaneity, but that wasn't the reason they rejected SR. They didn't agree with SR as a physical interpretation of relative motion. So, as I said, I think you and I are talking about completely different issues.
Georg: The introduction to your blog says: "This blog is motivated by my desire to understand the special theory of relativity, in particular the principle of the constancy of the speed of light for every observer."
ReplyDeleteDo you think you understand SR now? If you conclude that the constancy of light speed is merely an unproven postulate does enable you to "understand" it? What is your understanding of SR at this point?
Interesting question, thanks.
ReplyDeleteYes, I think I understand it now.
My understanding can be summarised as follows:
1) The constancy of the two-way speed of light is an empirical fact.
2) The constancy of the two-way speed of light follows from two more basic empirical facts: a) the no-overtaking rule for electromagnetic waves (two such waves emitted at the same time from the same place and in the same direction will always travel in tandem, regardless of the relative speeds of the bodies emitting the light) b) in a frame of reference in which light propagates in symmetrical conditions in all directions and clocks are synchronized using Einstein's signalling method, a body travelling at the speed v is length-contracted by the relativistic factor.
3) The one-way speed of light is not constant if we use the word 'speed' in the normal sense of the word, namely speed as measured by correctly synchronized clocks.
4) The one-way speed of light in SR is just what could be called a coordinate speed: it is constant because SR makes it so by choosing time coordinates in such a manner that that speed is constant. However, clocks adjusted in line with this choice of time coordinates are not synchronized. Much of the strangeness of SR is a result of the use of clocks (of time coordinates) which ae not synchronized (such that events with equal time coordinates are not necessarily simultaneous).
That's it in a nutshell. I realise that this brief summary may give rise to further questions - but I hope to have answered those questions in my more detailed blog posts!
"...I hope to have answered those questions in my more detailed blog posts!"
ReplyDeletePerhaps you have done so and I missed it. So let me ask you this:
You say:
"The one-way speed of light is not constant if we use the word 'speed' in the normal sense of the word, namely speed as measured by correctly synchronized clocks...clocks adjusted in line with this choice of time coordinates are not synchronized. Much of the strangeness of SR is a result of the use of clocks (of time coordinates) which are not synchronized (such that events with equal time coordinates are not necessarily simultaneous)."
Questions:
1. How, in your opinion, would clocks be correctly synchronized?
2. Or are you just saying there is no correct way and that no way chosen would be "necessarily" correct?
Answers to your questions can be found here: http://understanding-relativity.blogspot.com/2012/05/newtons-idea-of-simultaneity.html and in a number of other blog posts.
ReplyDeleteBriefly:
1. Clocks at A and B (assumed to be at rest relative to each other and unaccelerated) can be correctly synchronized by setting them to the same time when identical signals emitted in opposite directions from the mid-point between A and B arrive at A and B, provided the signals are emitted and propagate in symmetrical conditions. The signals could be light signals but equally they could be objects accelerated by means of identical acceleration mechanisms.
2. No, the procedure described above is correct, it will synchronize clocks. The difficulty lies in establishing whether or not the conditions of emission and propagation are symmetrical in opposite directions. If we don't know this, then we can't be sure whether or not the procedure synchronizes clocks. In SR as well as in Newton's theory, the conditions of emission/propagation are not always symmetrical: if they are symmetrical in a first frame, then they can't also be symmetrical in a second frame moving relative to the first - see for example the blog post mentioned above for details.