| gruff5
|
| 225449. Wed Oct 31, 2007 9:06 am |
 |
|
Davini said: | Quote: |
Er, the Lorentz factor is constant… relative speed is always v. The above doesn’t include the inertial frame change that Stella experiences, you’ve stayed in the outbound frame. |
Yes, the Lorentz factor changes for Stella in my scenario because I've chosen to stay in the outward bound frame - I was vague about that and have edited the story to make that clear, ta!
Terra's speed relative to this frame stays at v and Stella's jumps up to some value larger than v. Maybe that makes it harder to calculate the numbers, but I don't think so for someone who know's what they're doing!
But just numbers don't give me an "ah hah!" deep sense of what's behind the asymmetry. In my story Stella sets off to catch up with Terra at some relativistic factor (anyone know what?) times v and by doing that her point on that Lorenz factor graph goes way up on that almost vertical bit and that's what causes her time to dilate more than Terra's. This way we can just think about time dilations and not get confused trying to think about distance contractions as well. |
|
|
|
 |
| Davini994
|
|
|
|
|
| gruff5
|
| 225691. Wed Oct 31, 2007 3:22 pm |
|
|
That's brill, Davini, it's not the hairy beast I had been fearing. So, for my scenario and for v = 0.8c that gives v' = 0.98c and I'll edit & stick that in now.
I've been on a mission of pickiness with that book - it's library, but hasn't stopped me scribbling on it (in pencil, dammit!). They also get their Lorentz factors mixed up all over the place. Says that it was M-M expt. that led Einstein to conclude speed of light is absolute (no, it was Maxwell eqns). I could go on....and its a popular book, see it all over the bookshops. |
|
|
|
|
| Southpaw
|
| 225709. Wed Oct 31, 2007 4:21 pm |
|
|
I love your adjectivising of 'library' there. That's like a nerd's version of 'cool' or 'sick' or 'phat'. "Man, that Star Trek episode was totally library, man."
It puts me in mind of the Calvin & Hobbes strip where Calvin likes to 'verb' words. "Remember when access was a thing? Now it's something you do. Verbing weirds language." |
|
|
|
|
| Davini994
|
| 225735. Wed Oct 31, 2007 5:46 pm |
|
|
| gruff5 wrote: | ...
Says that it was M-M expt. that led Einstein to conclude speed of light is absolute (no, it was Maxwell eqns).
... |
Not everyone believes Einstein when he says that. And when I say not everyone, I include me;)
So what you are saying is that in your new frame the Lorentz factor for the moving earth is constant at 1.5; for Ulysses it's 1 (stationary) for half the trip, then about 4.5 for the second half.
So then you are calculating the elapsed times of the round trip for the twins, as viewed from frame 3. You find a difference in the adjusted time that Ulysses and Homer experience, due to the different Loretz factors.
Which I can't see as being inherently wrong, and is a nice, elegant construction.
Not sure everyone would consider it complete though, as it doesn't prove no paradox , just that a third frame measures a difference in the elapsed times in Homer and Ulysses' frames. |
|
|
|
|
| gruff5
|
| 226103. Thu Nov 01, 2007 1:16 pm |
|
|
Davini said: | Quote: | | Not everyone believes Einstein when he says that. And when I say not everyone, I include me;) |
Yes, how could Einstein not have heard of such a ground-breaking result, well before 1905?! But Maxwell eqns were the central bit.
| Quote: | | So what you are saying is that in your new frame the Lorentz factor for the moving earth is constant at 1.5; for Ulysses it's 1 (stationary) for half the trip, then about 4.5 for the second half. |
'Yes' to those numbers. This framing comes out with the same result, but I feel it shows how it's the Lorentz factor producing the effect from velocity changes (that generally arise from accelerations).
| Quote: | | So then you are calculating the elapsed times of the round trip for the twins, as viewed from frame 3. You find a difference in the adjusted time that Ulysses and Homer experience, due to the different Loretz factors. |
Yes, precisely! BTW I'd call it frame 2, but we mean the same thing.
| Quote: | | Which I can't see as being inherently wrong, and is a nice, elegant construction. |
Thank you! :-) It helps me understand where the asymmetry comes from. Did you (or anyone else out there) find this helpful?!
| Quote: | | Not sure everyone would consider it complete though, as it doesn't prove no paradox , just that a third frame measures a difference in the elapsed times in Homer and Ulysses' frames. |
You're right there. I went to a friends when I 'came out' and she asked what I'd been doing. "Well," I said "this is going to sound totally nerdy, but...." and went on to tell her about relativistic effects on time, lengths and masses, E=mc2 etc etc She had never heard of any of this stuff (this is not uncommon) and was amazed and in awe. Then I told her about the twin paradox, thought about explaining it, swerved deftly away and asked after her cat instead.
The paradox is "Look, if I'm Ulysses (Stella) I can say I'm staying still in space and that Homer (Terra) is relatively moving, so he should be the one to age less." Now, we can do some SR maths, but will our SR novice be helped by that? You could say that Ulysses changes velocity and so "changes inertial frame" - well, true, but that is still opaque.
My way doesn't prove no paradox either because although Ulysses stays still initially, he then zips off at v'. So he's no long 'staying still'. It's a bugger!
Right, get ready to start pelting me with tomatoes and rotten eggs....
I just can't help feeling the paradox might go if we stopped thinking "all motion is relative" and went with ....... absolute space =8-O <ducks>.
We can't (yet) pin space down, but we could nominate one of the inertial frames as absolute space and then stick with that. Everything is then measured against its spatial coordinates. Its 'absolute clock' would be showing cosmic time http://en.wikipedia.org/wiki/Cosmic_time.
The SR maths is exactly the same, so you could say it's just a matter of semantics. But I think there's more to it than that. For me the hardest bit of SR to accept is that there is no absolute simoultaneity or order of events. In principle, if you could pin down absolute space; these would be unambiguous.
Then our SR novice needn't suggest that Ulysses can stay stock still and we might zap this damned parrotox? |
|
|
|
|
| Davini994
|
| 226105. Thu Nov 01, 2007 1:40 pm |
|
|
Yes, it's a nice way to think of it.
| Gruff5 wrote: | | My way doesn't prove no paradox either because although Ulysses stays still initially, he then zips off at v'. So he's no long 'staying still'. It's a bugger! |
But the wavefronts sorts it nicely in my opinion. It seems that I still can't convince you all though;)
| Gruff5 wrote: | | But I think there's more to it than that. For me the hardest bit of SR to accept is that there is no absolute simultaneity or order of events. In principle, if you could pin down absolute space; these would be unambiguous. |
You are really trying to get round this I can see. What you were talking about on other threads makes more sense now, I couldn't see where you were trying to get to:)
Problems I can see, top of my head:
You still don't have absolute order of events. All you've done is said "the order is more important in that frame".
And it wouldn't zap the paradox, would it? Because Homer and Ulysses both measure time in their frames, not the 'cosmic frame'.
So you aren't actually addressing what time they experience, i.e. how much they age, and how much they think the other will have aged, and reconciled the numbers.
You've worked out how long they will have aged in 'cosmic time'. But then at the risk of sounding more confrontational than I'd like, what does that matter?
Cosmic time is a sort of stepping stone in the mathematics in GR. It would be quite interesting to think about that though. I'd start from the position that it's not physically quantifiable. It will always be arbitrary in the real universe. |
|
|
|
|
| dr.bob
|
| 226245. Fri Nov 02, 2007 4:32 am |
|
|
| gruff5 wrote: | | For me the hardest bit of SR to accept is that there is no absolute simoultaneity or order of events. |
It may be hard for you to accept but, if the mathematics shows that this is the case, what choice do you have?
One of the most amazing things about Physics is that you can prove something is true mathematically and experimentally, even though it seems to fly in the face of common sense. After all, as Einstein said, common sense is just a set of meaningless prejudices acquired by the age of 18.
If you have problems accepting the results of SR theory, might I suggest you give Quantum Mechanics a very wide berth :) |
|
|
|
|
| Davini994
|
| 226261. Fri Nov 02, 2007 5:06 am |
|
|
| Dr B wrote: | | After all, as Einstein said, common sense is just a set of meaningless prejudices acquired by the age of 18. |
I like that Dr B. |
|
|
|
|
| Southpaw
|
| 226312. Fri Nov 02, 2007 5:53 am |
|
|
| Something I read in one of Michio Kaku's works regards quantum entanglement, which, as I understand it, means that for every particle/molecule/whatever in the universe, there is an exact double intextricably linked to it. This means that if something happens to one of the whatevers, ie its 'spin' changes, this automatically happens to the other, even if it's on the other side of the universe, simultaneously. However, Kaku states that this should be impossible, because this would mean that information could travel faster than c. As usually happens with these books and I, my brain failed a page or so after this and I haven't looked at it since. Can any of you Physi-gods do an idiot's guide on quantum entanglement, and the upshots thereof? |
|
|
|
|
| gruff5
|
| 226323. Fri Nov 02, 2007 6:05 am |
|
|
| dr.bob wrote: | "For me the hardest bit of SR to accept is that there is no absolute simoultaneity or order of events"
It may be hard for you to accept but, if the mathematics shows that this is the case, what choice do you have?. |
I think that's well dodgy. I don't think the maths does show that at all. This is what I've been saying, that the SR maths is the same either way and can't resolve this. Note that the maths for Newton's theories is also rigourous. Einstein used his intuition (not same as common sense) and post-Newtonian developments to inspire SR in the first place. Maths can come before or after this.
What's developments have there been since Einstein brought us SR? The obvious ones are cosmology and quantum mechanics. Einstein only knew about the stars of the Milky Way, so there was no obvious absolute frame, now we have one with the hubble flow. Just found a book by G.J.Whitrow that says, because of cosmic time: "The anomalies and discrepancies of time-ordering that arise in connection with SR are due not to the nature of the events themselves, but to the introduction of observers moving through the universe relative to the fundamental observers in their neighbourhood." |
|
|
|
|
| gruff5
|
| 226392. Fri Nov 02, 2007 7:18 am |
|
|
| Davini994 wrote: | Yes, it's a nice way to think of it.
But the wavefronts sorts it nicely in my opinion. It seems that I still can't convince you all though;) |
I'm afraid I haven't understood how exactly we get to the numbers 1/3 and 3. I'm not much good at arithmetic, so I found that the numbers in the wavefronts scene didn't help. Though I did manage to work out the Lorentz factor for 0.8c in my head, I almost fell off my chair in shock! I'm just wondering if Tipler was trying to illustrate relativistic-doppler shift, rather than the Twin Paradox itself?
| Quote: | | Cosmic time is a sort of stepping stone in the mathematics in GR. It would be quite interesting to think about that though. I'd start from the position that it's not physically quantifiable. It will always be arbitrary in the real universe. |
Is it? In what way (didn't think Einstein knew about it). No, it's not arbitrary and is quantifiable. We already quantify in saying that the universe is 13.7 billion yrs old. The precision of our quantification is only limited by the precision of our cosmological observations.
If we accept cosmic time, then we accept absolute space exists (nothing in SR maths against that). A fundamental clock showing cosmic time is motionless in absolute space whose coordinates correspond with those of cosmic time.
| Quote: | | You've worked out how long they will have aged in 'cosmic time'. But then at the risk of sounding more confrontational than I'd like, what does that matter? |
For the *maths* of SR? Not a jot. For the paradox? It could be the answer. The Alf/Stella/Terra triplets scenario show that although bodies in the real world feel accelerations when they change velocity, for this thought expt you can put accelerations out of the picture and concentrate on purely instantaneous velocity changes.
So, back to an intuitive (aka common sense?) look at the paradox. We say that the paradox comes from Stella changing her velocity. But a velocity change relative to *what*, exactly? If we say relative to Terra, then we're into a circular argument going nowhere. In the real world (away from this thought expt), we can feel a velocity change from inertia effects. But what's this funny 'inertia' stuff? Nothing in SR explains it. Need to move on from SR at this point.
There are all manner of reasons why the existence of an absolute space or aether (I'm going to use that loaded word) would matter. Here follows some ideas:-
Now, they say it's an amazing coincidence that inertial mass and gravitational mass are identical. Coincidences should tweak our common sense. It would seem likely to me that bodies feel inertia due to an interaction with an aether, so resolving how Stella can feel a changed velocity in the middle of nowhere. Then we wouldn't need new concepts (middlemen) like a Higgs field. It would simply be space/aether that she is interacting with.
Mach's principle would be explained by an interaction of matter bodies with the aether.
'Vacuum energy' and 'dark energy' currently sound like oxymorons because we tend to think of a vacuum as 'nothing'. Think about it as the energy of the aether instead.
What exactly are the strings of string theory? They're descibed as loops of pure energy. What on earth is pure energy? Vibrating knots in the fabric of space (aether) is more intuitive. Then matter and energy really are the same thing and aren't two sides of a coin - both are vibrating knots/loops in the aether.
Sorry about all that, but you did ask!! |
|
|
|
|
| Davini994
|
| 226519. Fri Nov 02, 2007 12:06 pm |
|
|
gonna have to break that up, there's so many bits. Lets start with the only easy one:
| Gruff5 wrote: | | I'm just wondering if Tipler was trying to illustrate relativistic-doppler shift, rather than the Twin Paradox itself? |
No, the relativistic doppler shift is used to demostrate the twin paradox. As I say, it's a standard weapon to heave on problems, it's not controversial in itself. Its simply a classical doppler shift, due to motion relative to the observer, with the time component also adjusted due to time dilation. |
|
|
|
|
| Davini994
|
| 226569. Fri Nov 02, 2007 2:15 pm |
|
|
I wish I could write as eloquently about this stuff as you do Gruff. Lets have a go at some of the details though: ;)
| Gruff5 wrote: | | Now, they say it's an amazing coincidence that inertial mass and gravitational mass are identical. Coincidences should tweak our common sense. |
Indeed; GR is, to a degree, based on these being the same thing.
That they are the same is equivalent to saying that objects fall at the same rate in a gravitational field (assuming no other forces). In terms of GR, they aren't falling, they are following a straight path. So the weight becomes irrelevant, and it's not surprising at all.
| Wiki wrote: | | Einstein's equivalence principle states that it is impossible to distinguish between a uniform acceleration and a uniform gravitational field. Thus, the theory postulates that inertial and gravitational masses are fundamentally the same thing. |
http://en.wikipedia.org/wiki/Gravitational_mass |
|
|
|
|
| Davini994
|
| 226573. Fri Nov 02, 2007 2:36 pm |
|
|
When you talk about aether, I still think you are talking about 2 things:
1) A priviledged reference frame
2) Something underlying the structure of spacetime, e.g. quantum foam.
And then there are thoughts about one influencing the other; these are sepate issues and need to be treated as such.
GR, for example, is more than happy with vacuum energy, but this doesn't necessitate a prividged reference frame.
I know I've said this before, and I don't think I'm convincing you too well. But have a think about it please, and I expect you'll probably come back and tell me what I mean;)
Which (from my point of view), covers off the comments about vacuum/dark energy, and string theory. I think.
Leaving... just inertia, and the resolution of this using aether 1). Which you've got me a bit flummoxed about, a very interesting thought. What you are proposing is some underlying field, which will enable us to define inertia. Then we wouldn't need the Higgs field. But these 2 things are sounding very similar.
I shall respond further once I have collected my thoughts, but look what I found!
| Wiki wrote: | | Towards the end of his life it seems as if Einstein had become convinced that space-time is a new form of aether, in some way serving as a reference frame for the property of inertia. |
http://en.wikipedia.org/wiki/Inertia#Relativity
So I think there is a lot of milage in this one. |
|
|
|
|
