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  #1  
Old 11-07-2014, 04:17 PM
Jackknifed Juggernaut Jackknifed Juggernaut is offline
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Yet Another Question on Relativity

I plan on taking my kids to watch Interstellar this weekend, and wanted to give them a rudimentary summary of Relativity beforehand. Then I realized that I'm really not equipped to do that very well, so it would be great if someone could lead to me to a kid-friendly description of it on the web.

A related question I have is this:

Relativity tells us that an astronaut launched into space at a speed close to the speed of light will age far slower than her fellow humans on earth. Since the speed of light is constant regardless of which direction or speed one is traveling, time actually moves slower for the astronaut causing her to age slower.

But from the perspective of the astronaut, isn't it true that the earth is actually moving away from her at close-to-light speed? Isn't another way to look at this that she is basically standing still and that it is the earth that is actually moving? If so, why wouldn't the people on earth be aging slower than her?

I hate to post-and-run, but I have a train to catch so I hope the question is clear.
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Old 11-07-2014, 04:39 PM
Quercus Quercus is offline
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Originally Posted by Jackknifed Juggernaut View Post
I plan on taking my kids to watch Interstellar this weekend, and wanted to give them a rudimentary summary of Relativity beforehand. Then I realized that I'm really not equipped to do that very well, so it would be great if someone could lead to me to a kid-friendly description of it on the web.

A related question I have is this:

Relativity tells us that an astronaut launched into space at a speed close to the speed of light will age far slower than her fellow humans on earth. Since the speed of light is constant regardless of which direction or speed one is traveling, time actually moves slower for the astronaut causing her to age slower.

But from the perspective of the astronaut, isn't it true that the earth is actually moving away from her at close-to-light speed? Isn't another way to look at this that she is basically standing still and that it is the earth that is actually moving? If so, why wouldn't the people on earth be aging slower than her?

I hate to post-and-run, but I have a train to catch so I hope the question is clear.
You're right that because velocity is relative, once the astronaut is cruising along, nobody can really say whether they're moving and the Earth is still, or vice versa.
BUT acceleration is NOT relative. When the astronaut is firing engines and speeing up, everyone, in any frame of reference, can agree that she is accelerating and the Earth is not.
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Old 11-07-2014, 04:41 PM
Great Antibob Great Antibob is offline
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Just as a note, this is basically a restatement of the Twin Paradox, on which minds much greater than mine have already weighed in.
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Old 11-07-2014, 08:29 PM
JWT Kottekoe JWT Kottekoe is offline
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It's important to note that, while this is indeed the Twin Paradox, the name is a misnomer. It might more aptly be named the Twin Puzzle. There is no paradox, it is completely understood within the theory of special relativity. Special Relativity is conceptually difficult, since it shatters our common sense about space and time, but it can be understood quite well with high school mathematics.

The same cannot be said for General Relativity, which involves deep mathematics. I understand that the movie involves travel through wormholes. That still hypothetical concept can only be understood with a firm grounding in General Relativity.
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Old 11-08-2014, 07:22 AM
NUFOIB NUFOIB is offline
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Understanding Special Relativity is conceptually easy breezy. It is incredibly intuitive and straight forward.

However, if you are being taught about Special Relativity, yet at the same time the cause of special relativity is not being revealed to you, then good luck when it comes to trying to completely understand it.

Due to the circumstances of Special Relativity, no absolutes can be detected, such as absolute length or absolute rest, etc. In turn, since the absolutes are undetectable, any interest in them was thrown out the window long long ago. Thus we are left with just Special Relativity. Thus no absolute cause of the special relativity is being handed to those interested in special relativity.

Thus absolute understanding is lost.

However, if you choose to agree that complete understanding is greater in size than incomplete understanding, and thus, unlike today's physicists, you choose to explore completeness, then you are off to a good start.

Now,... the first logical step is to start off with absolutes.

If you analyze the idea of absolute motion, that goes on within an absolute 4 dimensional environment known as Space-Time, before you know it you independently bump into Special Relativity, and you also independently derive all of its equations. This you do, even if you have absolutely no education within the field of physics at all.

Too see this analysis in action, watch the 9 mini videos at http://goo.gl/fz4R0I ( total time = 1 hour 39 min. )
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Old 11-08-2014, 09:25 AM
Asympotically fat Asympotically fat is online now
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Originally Posted by Jackknifed Juggernaut View Post
I plan on taking my kids to watch Interstellar this weekend, and wanted to give them a rudimentary summary of Relativity beforehand. Then I realized that I'm really not equipped to do that very well, so it would be great if someone could lead to me to a kid-friendly description of it on the web.

A related question I have is this:

Relativity tells us that an astronaut launched into space at a speed close to the speed of light will age far slower than her fellow humans on earth. Since the speed of light is constant regardless of which direction or speed one is traveling, time actually moves slower for the astronaut causing her to age slower.

But from the perspective of the astronaut, isn't it true that the earth is actually moving away from her at close-to-light speed? Isn't another way to look at this that she is basically standing still and that it is the earth that is actually moving? If so, why wouldn't the people on earth be aging slower than her?

I hate to post-and-run, but I have a train to catch so I hope the question is clear.
This is relativity: someone on the Earth reckons the astronaut's clock is running slower than there own, whereas the astronaut reckons the person on the Earth's clock is running slower than his own.

This may seem contradictory, but it is not as what would actually be contradictory is a lack of symmetry between the astronaut and the observer on Earth. A key point to realize is that the failure of simultaneity at distance means that when the astronaut's clock says time X and he reckons at the same time the Earth clock says time Y, the Earth bound observer will generally not reckon the astronaut's clock to read time X when his clock reads time Y.

NB: This is not the twin paradox, the twin paradox involves the astronaut turning around at some point and returning to Earth, allowing the two clocks to be compare side-by-side, rather than from distance.
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Old 11-08-2014, 11:41 AM
eschereal eschereal is offline
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Man, I am getting a headache thinking about this.

The effects of Special Relativity are the same as the effects of General Relativity: if you could accelerate away from the earth at the correct rate, the time dilation you experience could n theory exactly match the time dilation caused by the spacetime distortion of the earth's gravity. I do not think that rate of acceleration would be one G, but I could be wrong.

Of course, keeping in sync with the earth would be darn near impossible. The earth is not a fixed object, it would always have a vector of motion that you would have to account for (not sure how that would work if you were moving in a polar direction). Beyond that, the final frontier is far from flat, you would always be crossing some kind of gravitational gradient that would complicate your attempts to keep your clocks in sync – perhaps by knowing your rate of acceleration and being able to observe the earth clock, you might, with absurdlyy fine instruments, be able to measure the gravitational shape of the space you are traversing.
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Old 11-08-2014, 12:22 PM
Chronos Chronos is offline
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Quoth NUFOIB:

Due to the circumstances of Special Relativity, no absolutes can be detected, such as absolute length or absolute rest, etc.
This is absolutely incorrect. There are plenty of absolutes in special relativity, and most actual work in special relativity is done dealing nearly entirely in those absolutes. They're just not the same absolutes that we're used to from Newtonian physics.
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Old 11-08-2014, 12:49 PM
Andy L Andy L is online now
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Originally Posted by Jackknifed Juggernaut View Post
Relativity tells us that an astronaut launched into space at a speed close to the speed of light will age far slower than her fellow humans on earth. Since the speed of light is constant regardless of which direction or speed one is traveling, time actually moves slower for the astronaut causing her to age slower.

But from the perspective of the astronaut, isn't it true that the earth is actually moving away from her at close-to-light speed? Isn't another way to look at this that she is basically standing still and that it is the earth that is actually moving? If so, why wouldn't the people on earth be aging slower than her?
Yes, from the point of view of the astronaut the Earth folks are aging slowly, while from the point of view of the Earthers, the astronauts are aging slowly. In that case, there is complete symmetry and neither the astronaut nor the folks on Earth would be justified in saying that their clock is "right" and the other's clock is "wrong."

If the astronaut turns around and comes back home, the symmetry of the situation is broken and the astronaut ends up being significantly younger than the stay-at-homes - but if someone on Earth leaves Earth after the original astronaut and travels fast enough to catch up with the astronaut, it's the second astronaut who is younger.
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Old 11-10-2014, 10:16 PM
NUFOIB NUFOIB is offline
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This is absolutely incorrect. There are plenty of absolutes in special relativity, and most actual work in special relativity is done dealing nearly entirely in those absolutes. They're just not the same absolutes that we're used to from Newtonian physics.
Well I can't be that wrong.

My parents, for what reason's I'm not sure of, had pulled me out of school long before I had a chance to receive any education in the field of physics.

However, as I said, if you analyze the idea of absolute motion, that goes on within an absolute 4 dimensional environment known as Space-Time, before you know it you independently bump into Special Relativity, and you also independently derive all of its equations.

This was exactly what I did. I recored the 9 videos since people seemed not to believe that I did such. My methods are 100% unique, thus the work is of no other but my own.
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Old 11-10-2014, 11:17 PM
Chronos Chronos is offline
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So, you're saying that you're certain there are no absolutes, because if there were, you would have found them, because working all on your own, you've managed to find everything there is to find in SR. Is that an accurate summary of what you're saying?
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Old 11-12-2014, 09:32 AM
NUFOIB NUFOIB is offline
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So, you're saying that you're certain there are no absolutes, because if there were, you would have found them, because working all on your own, you've managed to find everything there is to find in SR. Is that an accurate summary of what you're saying?
That's basically the opposite of what I have said.
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Old 11-12-2014, 09:39 AM
NUFOIB NUFOIB is offline
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If you start with a straight forward analysis of absolute motion which takes place within an absolute 4 dimensional environment known as Space-Time, before you know it you independently encounter Special Relativity, and you also independently derive all of its equations. In turn, you have exposed the absolute foundation of which Special Relativity resides within. You therefore fully understand Special relativity itself.

Last edited by NUFOIB; 11-12-2014 at 09:40 AM.
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Old 11-12-2014, 09:46 AM
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[...] before you know it [...]
I think you should be more explicit here in step 2.
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Old 11-12-2014, 12:25 PM
NUFOIB NUFOIB is offline
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I think you should be more explicit here in step 2.
WELL WE CAN CHIT CHAT IN FRAGMENTS AND GET NOWHERE, or look at the art, so to speak, before having a discussion about it.

The overall step by step move, leading from pure absolute on over to Special Relativity, takes 1 hour and 38 minutes to cover via video.

To attempt to expose the entirety here, such that one can then initiate a discussion about it, would take a heck of a lot of time and effort.

Watch the 9 mini videos at http://goo.gl/fz4R0I ( total time = 1 hour 39 min. )

Unfortunately, most folk don't bother to look at the videos. This would be about the same as discussing the entire contents of the Bible, yet the contents of Bible can not be revealed except in very very small fragments. Or perhaps having a discussion about a painting but no one will bother to look at its entirety but demand instead to view only tiny fragments of the painting one after another, such that its entirety can never and will never be seen.
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Old 11-12-2014, 09:59 PM
Chronos Chronos is offline
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...And if someone had claimed to have independently reconstructed the contents of the Bible by keeping a detailed dream journal.
  #17  
Old 11-12-2014, 10:58 PM
eschereal eschereal is offline
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... Watch the 9 mini videos at http://goo.gl/fz4R0I ( total time = 1 hour 39 min. )

Unfortunately, most folk don't bother to look at the videos....
Yeah, see, there is a reason for that. Videos are a very sucky format for obtaining complex information. I mean, if you want to see them dig up a fire ant hill that was filled with molten aluminum, or watch what happens when you try to blow soap bubbles at -20°F, yeah, videos can be useful. But if you cannot present your work in a text-like format that can be easily navigated non-sequentially, we have to wonder what the deal is. Why just video?
  #18  
Old 11-12-2014, 11:38 PM
Blue Blistering Barnacle Blue Blistering Barnacle is offline
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My son has chosen to discuss relativity AND quantum physics for his seventh grade research paper. I hope we can find nice summaries in minute physics and Kahn U.

Any library book suggestions for this age would be appreciated. We already have "relativity for dummies"
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Old 11-12-2014, 11:40 PM
Blue Blistering Barnacle Blue Blistering Barnacle is offline
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BTW, "Relativity for Dummies" would not be too bad for OP.
  #20  
Old 11-12-2014, 11:41 PM
Blue Blistering Barnacle Blue Blistering Barnacle is offline
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Also BTW, how was the movie? The ads intrigue me.
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Old 11-12-2014, 11:48 PM
Chronos Chronos is offline
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Barnacle, my first suggestion would be that he separate the two topics and just pick one of them. There's not really any particular connection between relativity and quantum mechanics, beyond the fact that a lot of people don't understand either. Specifically, I would recommend that he go with the relativity: Special relativity can be understood, nearly in its entirety, by a bright 7th-grader who's had algebra. Quantum mechanics can't be understood by anyone.

Oh, and this is the best introduction to special relativity I've ever seen. It's long, but if he takes it slowly, piece by piece, he's probably competent to process most of it.

General relativity is more complicated, and he won't have the math to do it justice, but nobody expects that of a 7th-grader.

Last edited by Chronos; 11-12-2014 at 11:52 PM.
  #22  
Old 11-13-2014, 08:45 AM
NUFOIB NUFOIB is offline
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Yeah, see, there is a reason for that. Videos are a very sucky format for obtaining complex information. I mean, if you want to see them dig up a fire ant hill that was filled with molten aluminum, or watch what happens when you try to blow soap bubbles at -20°F, yeah, videos can be useful. But if you cannot present your work in a text-like format that can be easily navigated non-sequentially, we have to wonder what the deal is. Why just video?
You make a fine example.

Talking about examples, here is a sneak preview of that discussed within the videos.

http://www.outersecrets.com/real/image/picnequa.png
  #23  
Old 11-13-2014, 10:20 AM
Blue Blistering Barnacle Blue Blistering Barnacle is offline
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Barnacle, my first suggestion would be that he separate the two topics and just pick one of them. There's not really any particular connection between relativity and quantum mechanics, beyond the fact that a lot of people don't understand either. Specifically, I would recommend that he go with the relativity: Special relativity can be understood, nearly in its entirety, by a bright 7th-grader who's had algebra. Quantum mechanics can't be understood by anyone.

Oh, and this is the best introduction to special relativity I've ever seen. It's long, but if he takes it slowly, piece by piece, he's probably competent to process most of it.

General relativity is more complicated, and he won't have the math to do it justice, but nobody expects that of a 7th-grader.

Thanks. I'll share this with him (and his teacher).
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Old 11-13-2014, 12:38 PM
Asympotically fat Asympotically fat is online now
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Thanks. I'll share this with him (and his teacher).
Chronos's advice is good and for the reasons he stated, I would recommend Six Easy Pieces by Richard Feynman as a good starting point
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Old 11-13-2014, 12:46 PM
Jackknifed Juggernaut Jackknifed Juggernaut is offline
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Also BTW, how was the movie? The ads intrigue me.
Unfortunately we weren't able to watch it last weekend as the IMAX versions were sold out. I'll try again this weekend.
  #26  
Old 11-13-2014, 12:46 PM
NUFOIB NUFOIB is offline
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Thanks. I'll share this with him (and his teacher).
FOR YOURSELF, or even folks who have retired from school many many years ago, there is the way in which a full understanding of Special Relativity can fit in your mind in an almost purely visual manner. To discover Special Relativity on your own in this manner, all you need to be able to do is think.

If you can simply analyze the concept of "motion" in your head, even with your eyes closed, then you can independently discover Special Relativity all by yourself. If, however, thinking is no your thing, and thus you have to be taught instead, then there are plenty of websites that will "Teach" you about Special Relativity.

Too see the thought method in action, watch the 9 mini videos at http://goo.gl/fz4R0I ( total time = 1 hour 39 min. )
  #27  
Old 11-13-2014, 01:01 PM
Whack-a-Mole Whack-a-Mole is offline
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Specifically, I would recommend that he go with the relativity: Special relativity can be understood, nearly in its entirety, by a bright 7th-grader who's had algebra. Quantum mechanics can't be understood by anyone.
I'm not so sure. I mean, I agree quantum mechanics is difficult and certainly the mathematics is well past a 7th grader (past most undergrads too I'd think). But do you really need the math to have a basic grasp of any of it? Especially for 7th graders?

I think the concepts can be grasped just fine. Enough to let the implications blow their minds. Richard Feynman said that the double-slit experiment “has in it the heart of quantum mechanics". I think a good explanation of the double slit experiment to 7th graders is very doable and sets the stage for why QM is mind blowing.
  #28  
Old 11-13-2014, 01:47 PM
Blue Blistering Barnacle Blue Blistering Barnacle is offline
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I'm not so sure. I mean, I agree quantum mechanics is difficult and certainly the mathematics is well past a 7th grader (past most undergrads too I'd think). But do you really need the math to have a basic grasp of any of it? Especially for 7th graders?

I think the concepts can be grasped just fine. Enough to let the implications blow their minds. Richard Feynman said that the double-slit experiment “has in it the heart of quantum mechanics". I think a good explanation of the double slit experiment to 7th graders is very doable and sets the stage for why QM is mind blowing.
Yeah, he may insist on keeping to his plan of doing both. I probably shouldn't worry too much- it's really an English paper, not a science paper. I imagine that he could paint with a broad brush, bring out the weird highlights of each, and finish with a description of their mutual incompatabilities and a mention of efforts to unify them with quantum gravity. It might look more like newspaper science writing.

That is still pretty complicated. I still that he will get more out of focusing on just one of these (such as special relativity) and getting a deeper understanding. But all I can do is guide...
  #29  
Old 11-13-2014, 01:51 PM
Blue Blistering Barnacle Blue Blistering Barnacle is offline
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... I imagine that he could paint with a broad brush, bring out the weird highlights of each, and finish with a description of their mutual incompatabilities ...
On the subject of incompatabilities, I thought that relativity was accounted for in QED (and QCD?). Am I wrong about this? Or is it the wrong kind of relativity (special, not general)?
  #30  
Old 11-13-2014, 02:02 PM
Blue Blistering Barnacle Blue Blistering Barnacle is offline
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[...Oh, and this is the best introduction to special relativity I've ever seen. It's long, but if he takes it slowly, piece by piece, he's probably competent to process most of it.

...
Looks dense for my son. I'll read it and enjoy it. I don't think he will get through it.
  #31  
Old 11-13-2014, 02:13 PM
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On the subject of incompatabilities, I thought that relativity was accounted for in QED (and QCD?). Am I wrong about this? Or is it the wrong kind of relativity (special, not general)?
Right.

Special relativity plus quantum mechanics is fine and their combination indeed serves as the basis for QED and more. General relativity, which introduces dynamics into spacetime itself, has not been successfully handled by any quantum theory.

How long is this report meant to be? A few options, depending on length:

- Pick one of QM, SR, or GR (in that preference order) to give a "gee-whiz" report about the weird stuff that happens. There would be no understanding conveyed, just a magic show to excite the masses.

- Pick SR and discuss both the weird stuff and its underpinnings. The two postulates of special relativity are very easy to understand, and all the weird stuff that falls out from these can be demonstrated quantitatively without much work. (Contrast: the postulates of quantum mechanics.)

- Pick one or two or three of the topics and treat them together in a report about new physics of the 20th century. This would be a history paper more than a science paper discussing the historical contexts surrounding the development of these ideas. If the treatment were cursory, one could hint about what new physics might be on the horizon for the 21st century. If the treatment were in depth, than just a single topic could fill the whole report easily.
  #32  
Old 11-13-2014, 09:16 PM
Chronos Chronos is offline
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Quoth Whack-a-Mole:

I'm not so sure. I mean, I agree quantum mechanics is difficult and certainly the mathematics is well past a 7th grader (past most undergrads too I'd think). But do you really need the math to have a basic grasp of any of it? Especially for 7th graders?
Yes. There are four different things you can hope to do with quantum mechanics. First, you can do the math. This is beyond the scope of a 7th-grader, or even of most adults, but it can be done. Second, you can seek out analogies for quantum behavior. This can be done, in some cases, but most of the analogies suck, and either fail to convey anything interesting, or require your audience to already understand the thing you're trying to explain. Third, you can develop an intuitive understanding of it. Or rather, you can hope to do that, but nobody, even including the physicists who are comfortable with the calculations, ever really has much luck with it. Absent any of these first three, about all you're left with is what amounts to just reciting trivia facts. Anyone can do this, if they find some source for the facts, but this is mind-numbingly boring.
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Old 11-13-2014, 09:27 PM
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From my naive point of view, I don't see what makes the basic math of quantum mechanics (that of vector spaces with a positive-definite complex inner product?) intrinsically more difficult than the basic math of special relativity (that of vector spaces with a (3, 1)-signature real inner product?). But then again, I don't understand any physics...
  #34  
Old 11-14-2014, 12:53 AM
Half Man Half Wit Half Man Half Wit is online now
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From my naive point of view, I don't see what makes the basic math of quantum mechanics (that of vector spaces with a positive-definite complex inner product?) intrinsically more difficult than the basic math of special relativity (that of vector spaces with a (3, 1)-signature real inner product?). But then again, I don't understand any physics...
Well, I'm not sure there's much to the idea that quantum mechanics is intrinsically more difficult---you can certainly treat even classical mechanics with mathematics of great complexity, i.e. the full formalism of Poisson manifolds, symplectic structures, etc.; it's just that usually, you can do useful things in classical mechanics (or special relativity) using simpler math than you need to do anything useful in quantum mechanics. Part of that is certainly that we don't yet know how to do the same things in a simpler way---QM is still a relatively new subject, and while there has already been some great simplifications regarding things that were done early on, much of it is still somewhat rough-and-ready pioneer work. But in general, you need to delve more deeply into the subjects to make progress---in SR, you can basically get away with thinking of the Lorentz group as being a set of matrices acting on vectors by multiplication, while if you're doing, say, particle physics, you need to look somewhat more seriously at the attendant group- and representation theory.

Also, since the fundamental equation of QM is a partial differential equation which can get quite complicated even for simple problems, you need to know a bit about the attendant theory; and depending on what you're interested in, and how you approach these subjects, you'll need at least some passing familiarity with things like operator algebras, functional integration (for solving Feynman integrals), of course linear algebra, and so on. There's even people working out a category theoretic formulation of QM. So I don't think it's really the case that you can say 'you need to know this math for SR, and that math for QM', with this math being in some sense less complex than that math, and either being some fixed field of study, but rather, that you have your own mathematical toolbox that you apply to your field of study in whatever way you can---with the observation being that typically, nontrivial things can be done using simpler tools in SR than in QM, and equally or even more complex tools being needed for general relativity, quantum field theory or string-/M-theory etc.
  #35  
Old 11-14-2014, 10:47 AM
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To start with, you're not going to get very far in QM without calculus, while you can do most of SR without it. Remember, the question is in the context of a seventh-grader.
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Old 11-14-2014, 10:52 AM
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Fair enough. I am thinking of how, for example, in discussions of quantum computing, all that seem to be used are finite-dimensional spaces (no calculus! Just the manipulation of complex matrices). But perhaps looking only at that cannot be considered going very far into the actual physics.

Last edited by Indistinguishable; 11-14-2014 at 10:54 AM.
  #37  
Old 11-14-2014, 11:02 AM
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Originally Posted by Chronos View Post
Yes. There are four different things you can hope to do with quantum mechanics. First, you can do the math. This is beyond the scope of a 7th-grader, or even of most adults, but it can be done. Second, you can seek out analogies for quantum behavior. This can be done, in some cases, but most of the analogies suck, and either fail to convey anything interesting, or require your audience to already understand the thing you're trying to explain. Third, you can develop an intuitive understanding of it. Or rather, you can hope to do that, but nobody, even including the physicists who are comfortable with the calculations, ever really has much luck with it. Absent any of these first three, about all you're left with is what amounts to just reciting trivia facts. Anyone can do this, if they find some source for the facts, but this is mind-numbingly boring.
I disagree it is boring or that examples without math are uninteresting or not of much use.

There are many successful books and TV shows from the likes of Carl Sagan and Stephen Hawking and Brian Greene and Brian Cox (to name a few) that suggest explaining these complex subjects to the public in an understandable way and without advanced (or even any) math are very popular. More, these scientists felt it is important to explain the complex things to the public in a way the public can understand (doesn't hurt they make money on it too).

These are 7th graders so the math is out. What you can do is excite them about the fascinating world that is around us and how it really works. I think that is a worthwhile endeavor and can be interesting for them. While some refinement and a true, deep understanding is lost without the math there is still plenty there to intrigue people.

Last edited by Whack-a-Mole; 11-14-2014 at 11:03 AM.
  #38  
Old 11-14-2014, 11:08 AM
Indistinguishable Indistinguishable is offline
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Originally Posted by Indistinguishable View Post
Fair enough. I am thinking of how, for example, in discussions of quantum computing, all that seem to be used are finite-dimensional spaces (no calculus! Just the manipulation of complex matrices). But perhaps looking only at that cannot be considered going very far into the actual physics.
For example, the perspective given by Scott Aaronson here could be introduced and discussed in substantial depth without any calculus. But, sure, one wouldn't be able to solve the Schroedinger equation for specific Hamiltonians or such things.

Last edited by Indistinguishable; 11-14-2014 at 11:09 AM. Reason: Keep in mind, always, that I am a stranger to what I am talking about
  #39  
Old 11-14-2014, 11:43 AM
Pasta Pasta is offline
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Originally Posted by Indistinguishable View Post
But perhaps looking only at that cannot be considered going very far into the actual physics.
I look at the issue (i.e., the 7th grader context) from the other direction: what is the simplest thing you can do that demonstrates a non-intuitive physical consequence of SR or QM using only the tools and the "classical" ("intuitive"?) knowledge the student already has. For QM and a 7th grade student, you get the empty set here. For SR and a 7th grade student, you can take the postulates of SR and demonstrate quickly (and with nothing more complex than the Pythagorean theorem) the consequences of time dilation and length contraction. In principle you could go much further still, but it would get tedious quickly without more advanced tools.
  #40  
Old 11-14-2014, 07:11 PM
Punoqllads Punoqllads is offline
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Note that it's GR that's significant in Interstellar, not SR. One plot point (this is not a spoiler) involves the passage of time near the event horizon of a black hole. Put simply, under GR, being close to a massive object has effects similar to accelerating in empty space under SR.
  #41  
Old 11-14-2014, 07:18 PM
Yumblie Yumblie is offline
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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.
  #42  
Old 11-14-2014, 09:23 PM
Asympotically fat Asympotically fat is online now
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Quote:
Originally Posted by Indistinguishable View Post
Fair enough. I am thinking of how, for example, in discussions of quantum computing, all that seem to be used are finite-dimensional spaces (no calculus! Just the manipulation of complex matrices). But perhaps looking only at that cannot be considered going very far into the actual physics.
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.
  #43  
Old 11-15-2014, 01:54 AM
Francis Vaughan Francis Vaughan is offline
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Quote:
Originally Posted by Pasta View Post
For SR and a 7th grade student, you can take the postulates of SR and demonstrate quickly (and with nothing more complex than the Pythagorean theorem) the consequences of time dilation and length contraction. In principle you could go much further still, but it would get tedious quickly without more advanced tools.
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.
  #44  
Old 11-15-2014, 11:35 AM
Half Man Half Wit Half Man Half Wit is online now
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Originally Posted by Asympotically fat View Post
Yes, but with finite dimensional spaces you can't even get the uncertainty principle (the best you get is incompatible observables).
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...
  #45  
Old 11-15-2014, 03:31 PM
Asympotically fat Asympotically fat is online now
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Originally Posted by Half Man Half Wit View Post
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!
  #46  
Old 11-16-2014, 05:16 AM
Half Man Half Wit Half Man Half Wit is online now
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Originally Posted by Asympotically fat View Post
The uncertainty principle (in its full glory) is for observables described by unbounded operators which in turn implies an infinite dimensional Hilbert space.
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'?
  #47  
Old 11-16-2014, 08:43 AM
Blue Blistering Barnacle Blue Blistering Barnacle is offline
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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.
  #48  
Old 11-18-2014, 01:51 AM
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Quote:
Originally Posted by Chronos View Post
Second, you can seek out analogies for quantum behavior. This can be done, in some cases, but most of the analogies suck, and either fail to convey anything interesting, or require your audience to already understand the thing you're trying to explain.
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.

Quote:
Originally Posted by Indistinguishable View Post
Fair enough. I am thinking of how, for example, in discussions of quantum computing, all that seem to be used are finite-dimensional spaces (no calculus! Just the manipulation of complex matrices).
Manipulation of complex matrices is a pain in the ass. Linear alge-what?
  #49  
Old 11-18-2014, 05:11 AM
Irishman Irishman is offline
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Quote:
Originally Posted by eschereal View Post
Yeah, see, there is a reason for that. Videos are a very sucky format for obtaining complex information. I mean, if you want to see them dig up a fire ant hill that was filled with molten aluminum, or watch what happens when you try to blow soap bubbles at -20°F, yeah, videos can be useful. But if you cannot present your work in a text-like format that can be easily navigated non-sequentially, we have to wonder what the deal is. Why just video?
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.
  #50  
Old 11-18-2014, 01:35 PM
Blue Blistering Barnacle Blue Blistering Barnacle is offline
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Back to basic (special) relativity- I'm coming up with all kinds of crazy questions:

yanked from Wikipedia: http://en.wikipedia.org/wiki/Postula...ial_relativity

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?

Last edited by Blue Blistering Barnacle; 11-18-2014 at 01:37 PM. Reason: bolded quote, added separating lines
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