Yeah I think SR is easier to jump into for the layman than QM. A lot of the weirdness of QM can be discussed without the math, but you need background on waves, like diffraction, interference, and superposition. It’s probably a bit much for one student’s paper.
Yes, but with finite dimensional spaces you can’t even get the uncertainty principle (the best you get is incompatible observables).
I’d say the basic maths of QM certainly isn’t beyond the ken of mere mortals like myself, but it still makes the basics of SR look like a cakewalk.
I also disagree with anyone who says you can have any understanding of QM without investigating the maths. Just a look at the postulates of QM in any conventional axiomization of QM will tell you that.
It strikes me that a nice paper would be to go this route, and maybe look at a one of two of the common “disproofs” of SR that still get bandied about, and discuss where the flaw in the “proof” is. Again, there is nothing intrinsically hard here. But it would make for a very satisfying paper.
Do you mean specifically the position/momentum-uncertainty? Because for e.g. spin observables, you certainly get an uncertainty relation in finite dimensional Hilbert spaces. And of course, if you’re being nitpicky, you could just as well point out that even in infinite dimensional Hilbert spaces you don’t actually get the position/momentum uncertainty, since the eigenstates of position and momentum aren’t square-integrable functions and hence are non-normalizable; so you have to generalize to what’s sometimes called a ‘rigged’ Hilbert space or Gelfand triple. Of course, this only strengthens your point, as in those concepts there’s probably more math than you’d ever need for the whole of SR…
The uncertainty principle (in its full glory) is for observables described by unbounded operators which in turn implies an infinite dimensional Hilbert space.
I suppose strictly speaking you could sidestep the issue of operators with sets of eigenvalues that are empty by taking care to make more explicit that it’s the spectrum of the operator and not its set of eigenvalues that define what you can measure for an observable. Still that’s not to say that you don’t encounter serious problems from the choice of space and algebras that seem to be forced on you.
Which again proves the point about how much complicated QM is compared to SR!
Well, bounded operators can’t fulfill canonical commutation relations, but still, as long as their commutator doesn’t vanish, there’s still a bound on their simultaneous measurability given by the Robertson-Schrödinger relation. In what sense is that not an uncertainty principle ‘in its full glory’?
My son has narrowed his focus to SR. I am a bit relieved. I think it will still be quite challenging.
This will be a good review for me.
I think it’s a basic postulate that analogies suck. Typically, they have to shortchange some element. Now the idea is to convey a particular element of the concept, but typically people start trying to either extend the analogy beyond what applies, or overanalyze the basis of the analogy.
An example: take the analogy of the expanding universe. One analogy is to use the blueberry muffin - the dough starts small with the blueberries near together, and as it bakes, the muffin spreads and enlarges, and the blueberries move apart. That’s great, it shows how the universe gets larger, and the stars (and galaxies) move apart without getting larger themselves.
Except a blueberry muffin still has a center.
Manipulation of complex matrices is a pain in the ass. Linear alge-what?
I took the time to watch the videos. His presentation style is more like a professor giving a lecture with a whiteboard, with lots of gestures and the use of expressions and such to help convey his meaning. It isn’t a presentation style suitable for a text description.
My impression: he’s got some goofy bits, like using a slang expression to start his point. His example of an astronaut with a baseball is wrong. It isn’t really that obvious or intuitive when he extends distance and time to infinity to drive his paradox that spawns the idea of spacetime.
But if you understand time as a dimension analogous to spatial dimensions, he the proceeds to use trigonometry and algebra to derive the special relativity equations, and gives a somewhat helpful visual approach to understanding how moving through time as a dimension affects the visual in the spatial dimensions.
There is a lot of plugging in values he has worked out that we just have to accept without seeing the derivation. And there’s an unfortunate bit where he calls something an equation that is only one term and no equals sign.
Back to basic (special) relativity- I’m coming up with all kinds of crazy questions:
**yanked from Wikipedia: Postulates of special relativity - Wikipedia
Postulates of special relativity[edit]1. First postulate (principle of relativity)
The laws by which the states of physical systems undergo change are not affected, whether these changes of state be referred to the one or the other of two systems of coordinates in uniform translatory motion. OR: The laws of physics are the same in all inertial frames of reference.
2. Second postulate (invariance of c)
As measured in any inertial frame of reference, light is always propagated in empty space with a definite velocity c that is independent of the state of motion of the emitting body. OR: The speed of light in free space has the same value c in all inertial frames of reference.
The two-postulate basis for special relativity is the one historically used by Einstein, and it remains the starting point today. As Einstein himself later acknowledged, the derivation tacitly makes use of some additional assumptions, including spatial homogeneity, isotropy, and memorylessness.[1] Also Hermann Minkowski implicitly used both postulates when he introduced the Minkowski space formulation, even though he showed that c can be seen as a space-time constant, and the identification with the speed of light is derived from optics.[2]**
In the basic books I have been reading, they make a big deal of “no preferred inertial reference frames”. Basically, they say that I should have no way to tell if I’m moving versus the “other guy” moving. An experiment with magnet and current loop and electrical field was specifically mentioned in one book.
But today, we can look at the cosmic microwave background. As I have heard it, it is (nearly) the same in all directions, but only after correction for motion. That is, it is “bluer” if you look in the direction of travel. Is this correct? If so, does this establish a preferred reference frame?
I seem to remember some references to “the fixed stars” in discussions of general relativity- is this related?
As shown in the above image, a burst of light is sent from the (S)ource the the (D)estination, and in doing so the light passes through the tube, while the tube is moving at 260,000 km/s. Thus the light, relative to the tube, is only moving at 40,000 km/s.
But to those on board the tube, they will measure the speed of the light as it passes through the tube, as 300,000 km/s, meaning, the speed of light itself.
In other words, the speed of the light passing through the tube, relative to the tube itself, is NOT 300,000 km/s, but those on board the tube, it seems as though it actually is 300,000 km/s even though it is moving through the tube at a relative speed of 40,000 km/s.
Thus the speed of light is “measured” or “observed” to be the same in all frames of reference, rather than it be truly be the speed of light in all frames of reference.
For further coverage of this, see special relativity - Is it a postulate or a well proven fact that speed of light remains constant w.r.t any observer? - Physics Stack Exchange
Incorrect.
Correct.
Incorrect again.
How are you defining what something “really” is, except by experiment? If every conceivable experiment tells you the same thing, on what basis can you say that that’s wrong?
As another way of saying this:
You state that everyone in your story agrees that the light is moving at 300,000 km/s. The stationary folks see the light moving at 300,000 km/s, and so do the people on the tube. That is all correct.
You then subtract the speed of the light and the speed of the tube. While that is something you can plug into a calculator, it doesn’t have anything to do with anything physical. You can take the two velocities (v=260,000 km/s and c=300,000 km/s) and compute the speed that the people on the tube will see the light as having. But that computation isn’t just “subtract the velocities”:
speed of light pulse for tube people = (c - v)
but rather the full relativistic version:
speed of light pulse for tube people = (c - v) / (1-cv/c[sup]2[/sup])
In the full computation, the bare subtraction is scaled by an additional factor of (1-cv/c[sup]2[/sup]). With a little bit of algebra, you can see that this second answer works out to be exactly c. So, if your stationary observers do their physics correctly, they will correctly predict that the tube people will observe the speed of light to be 300,000 km/s.
And throughout the story, everyone still sees the light moving at 300,000 km/s. The stationary observers could choose to arbitrarily subtract 300,000 km/s and 260,000 km/s and get 40,000 km/s, but what are they computing? That’s one of an infinite number of computations you could do with those quantities: c-v or c-2v or c-v[sup]2[/sup]/c or … . These are all things you could compute, but they don’t relate to anything physical.
Now that’s funny.
Does that mean you concur, or no? Do you disagree with some part of the quoted statement or the rest of the previous post?
Not sure where you got the “story” from ?
As stated, for further coverage of this, see http://physics.stackexchange.com/que.../143645#143645
You will find the tube there along with the equations.
“Story” is just a shorthand for the thought experiment. The characters in the story are the stationary observers and the observers on the tube. You could replace “story” with “scenario” or “thought experiment” if you’d like.
I followed the link. My post was aiming to point out a possible (subtle) misconception you might have had in reading that linked page.
The subtlety can be expressed in the following statements:
(1) The stationary observers see the light moving 40,000 km/s faster than the tube. [CORRECT]
(2) The light is moving at 40,000 km/s relative to the tube. [INCORRECT]
These two statements are not equivalent. The first statement is given in your link. The second statement is given in your post, and perhaps leads to your conclusion that:
The observed speed is the only speed. There is no deeper “true” speed. It is true that the stationary observers can subtract v from c and obtain a value of 40,000 km/s, but why would one interpret that computation as giving you some “true” speed of light? If there were a second tube inside the first moving at 220,000 km/s, you wouldn’t say that there are two “true” speeds of light, one at 40,000 km/s and one at 80,000 km/s depending on which tube you pick. That’s because this subtraction doesn’t mean anything physical regarding the speed of light.
There is a certain calculation that does yield a physically telling result, and it gives the speed of the light relative to the tube (either tube in the two-tube example). And that calculation will yield c in both cases:
For some reason I can’t load physicsstackexchange on chrome. I get an error message that it timed out.
You’re using the link in post 52 right? Not the corrupted links in posts 57 and 58?