Einstein2087
Chrono Cadet
Why are you speaking in codes? What "complex conjugate"? All the numbers are real here.
For someone who likes to rely on exact math in his arguments, you sure know how to be vague...
heh
- Thread starter ruthless
- Start date
Why are you speaking in codes? What "complex conjugate"? All the numbers are real here.
For someone who likes to rely on exact math in his arguments, you sure know how to be vague...
recall15
Dimensional Traveler
The same discussion but on French Language...
Quoted:
<font color="blue">
Est-ce qu'un référentiel est nécessairement quelque chose de matériel ?
Bon si on recommençait, dis-moi où est-ce que'il y a une aberration mathématique...
Soit R un référentiel au repos (celui du laboratoire). R' le référentiel en mouvement, les transformations de Lorentz donnents :
x'=(x-vt)/sqrt(1-v²/c²)
t'=(t-vx/c²)/sqrt(1-v²/c²)
On a pris pour convention : O et O' coïncide à l'instant t=t'=0. Je m'intéresse de près au mouvement de point O' se déplaçant à la vitesse de la lumière, on a évidemment : x=ct, si on remplace dans l'expression on an :
x'=(ct-ct)/sqrt(1-c²/c²)=0/0 indétermination
t'=(t-cct/c²)/sqrt(1-v²/c²)=0/0 indétermination.
Bon là on sait bien que O' est en x'=0 non ? (j'aimerais que tu surmonte ton blocage, la physique n'est pas limitée qu'aux maths).
Pour moi il est possible de faire un prolongement par continuité.
-snip-
J'ai pas le temps de faire les calculs, je vulgarise juste un peu...
Pour l'article d'Alcubierre, on étudie la possibilité qu'un vaisseau puisse voyager, entre deux points A et B séparé d'une distance D, avec une durée inférieure à D/c dans le temps des observateurs au repos. (Pour le temps du vaisseau c'est connu, c'est la dilatation des durées).
On peut se dire que ce n'est pas possible puisque la théorie de la relativité restreinte n'autorise tout simplement pas des vitesses supérieures à c. Mais le monde physique est bien gouverné par la théorie de la relativité générale, où grâce au principe d'équivalence, la théorie de la relativité restreinte est valable localement. Il est important de comprendre cette notion de localité. L'aritcle d'Alcubierre dit donc que le vaisseau spatial est quasi-immobile dans son propre référentiel, mais une contraction de l'espace-temps à l'avant du vaisseau, et une dilation à l'arrière provoque une vitesse qui peut excéder la vitesse de la lumière, mais localement la relativité restreinte n'est pas violée.
Pour comprendre exactement de quoi il en retourne, il est important de se baser sur les modèles inflationnistes du big bang standard. Je rappelle simplement de quoi il en retourne : quand on observe des régions opposées de nous, distante d'environ 13 milliards d'année lumière, nous remarquons que ces régions sont à la même température, d'ailleurs le plus frappant est : quelque soit la direction vers laquelle on se tourne, le rayonnement fossile est exactement à la même température, à des fluctuations de quelques pourcents près. Or ceci est incompréhensible puisque ces régions n'ont jamais été en contact (distantes de plus de 13 milliards d'années lumière, donc ils n'ont jamais pû échanger un seul photon), et donc a fortiori homogénéiser leur tempéraure. On peut se dire que c'est une énorme coïncidence, mais ce n'est pas satisfaisant comme explication.
Pour expliquer ces observations, les astrophysiciens ont inventé un mécanisme qui a l'air fou, mais qui est conforme à la théorie de la relativité générale : les modèles inflationnistes. Pour commencer, lors du big bang, l'univers était très petit et homogène (ce qui veut dire que toutes les régions peuvent homogénéiser leur température), gouverné par une seule force unique. En se dilatant, l'univers se refroidit et les forces commencent à se séparer par le mécanisme de rupture spontanée de symétrie. Lorsque la gravitation s'est séparée des autres forces, il s'est produit un phénomène appelé inflation, où la taille de l'univers a augmenté très très vite, l'expansion a dépassé la vitesse de la lumière, même si les autres corps présents à ce moment avait uen vitesse locale très faible. Il faut comprendre que c'est l'espace qui s'est dilatée très vite, et non les corps qui ont bougé vite. Donc à ce moment, les régions se sont perdues de vu, et lorsque cette expansion faramineuse s'est terminée, la lumière peut alors reconnectée ces régions.
L'article d'Alcubierre se base donc sur une dilatation de l'espace temps comme dans les modèles inflationnistes totu en gardant des vitesses locales très faibles. Dans la suite de l'article, Alcubierre étudie une certaine métrique de l'espace-temps qui permet ce type de voyage. Les caractéristiqeus de la métrique sont :
* espace-temps loin du vaisseau complètement plat
* au voisinage, il y a une bulle
* le vaisseau est en chute libre, grosso modo il ne subit pas de dilatation du temps, 5 secondes passées dans le vaisseau = 5 secondes pour A ou B au repos.
[/COLOR]
more at:
aller plus vite que la lumiere? /ttiforum/images/graemlins/devil.gif /ttiforum/images/graemlins/devil.gif /ttiforum/images/graemlins/devil.gif
Einstein2087
Chrono Cadet
Sorry for the misunderstanding.
I've used the star to denote simple multiplication, as in 2*3=6. It seemed like the clearest way to write the equation, given the limits of our text-only forum.
And I assure you, that when I write equations on paper, I do not use '*' for multiplication (nor to I write the full word 'gamma' to denote the greek letter) /ttiforum/images/graemlins/smile.gif
RainmanTime
Super Moderator
Happy to help... /ttiforum/images/graemlins/smile.gif
RMT
Einstein2087
Chrono Cadet
No fair! You cheated!
Posting a ready-made GIF image from an online article is not the same as posting your own formula.
Posting a ready-made GIF image from an online article is not the same as posting your own formula.
RainmanTime
Super Moderator
What is "cheating", exactly?
At least it had the actual gamma symbol. I suppose I could have created the equations myself in Powerpoint and saved them as a gif to my photobucket account. I just took the lazy way out. So I'd cop to being lazy, but not a cheat.
RMT
Einstein2087,
I think it's 2, it's gotta be. When you say "break down" I don't think it will be made untrue, it will be made much more accurate. So eventually, someday, we'll know what we need to do to accelerate "matter with mass" up to C, and everything we currently know will still hold true.
RainmanTime once described "mass" as a tensor instead of a scalar. I don't care if that turned out to be true or not, or if Ray was the 1st to describe mass this way or not, it's DAMN fun to think about an abstract concept like that. I never would have thought of anything like that myself, and I feel I owe Ray an eternal debt of gratitude for taking the time to explain it to me.
Making something a tensor instead of a scalar is the type of thinking that could make all the old rules still hold true and give us an understanding on how to get around all those boring nuisances when v=c.
I think it's 2, it's gotta be. When you say "break down" I don't think it will be made untrue, it will be made much more accurate. So eventually, someday, we'll know what we need to do to accelerate "matter with mass" up to C, and everything we currently know will still hold true.
RainmanTime once described "mass" as a tensor instead of a scalar. I don't care if that turned out to be true or not, or if Ray was the 1st to describe mass this way or not, it's DAMN fun to think about an abstract concept like that. I never would have thought of anything like that myself, and I feel I owe Ray an eternal debt of gratitude for taking the time to explain it to me.
Making something a tensor instead of a scalar is the type of thinking that could make all the old rules still hold true and give us an understanding on how to get around all those boring nuisances when v=c.
Darby
Epochal Historian
s19n,
You might be mixing up some math terms above. Tensors include scalars. And I believe that Ray pointed that out. Scalars are tensors of rank 0...vectors are rank 1 and other tensors with higher dimensions are of rank n > 1 the exact rank dependent on the number of dimensions involved.
But defining mass as a true tensor, something above tensor rank 0, is just a matter of definition. One can always nake up a definition that involves a true tensor and name it "mass". It's not something fundamental. But we already have a mass term that is a vector or tensor depending on whether you're looking at it classically or non-classically (QM). It's called momentum. P = mv (classical definition)
BTW: 2 is correct even though its somewhat trivial (in definition, not in its effect on reality). All scientific theories are approximations of reality technically true only to the stated limits of their domains. Newtonian relativity and mechanics breaks down at high velocities approaching C; SR breaks down in strong gravitational fields; GR breaks down at C and very near black holes; QM breaks down quantifying gravity, etc.
But there is really one thing that we shouldn't state without very good cause when we're talking about situations at the limit of the domains. And that is "it's obvious". It's not. The math might say that this or that is obvious but we are pushing the edge of the envelope when we approach the limit.
Here's the problem. I give you the following math statement
QP - PQ > 0
That's a true statement but I don't think that anyone is going to say that it's obvious that multiplying two numbers together twice but inverting the position of the numbers the second time and then substracting the result of each computation would be anything other than 0.
2 X 3 = 6
3 X 2 = 6
6-6 = 0
But in quantum mechanics what I first stated is true. In fact, the equation was just about the first equation discovered by Heisenberg in 1925. The exact equation was:
QP - PQ = ih/2Pi
Transposing Q (position) with P ( momentum) does not commute when you multiply the terms. The result of the multiplications do not give the same answer because the rule, as Dirac realized, involves matrix multiplication and not straight arithmetic multiplication.
So we need to be careful of the term "obvious" in physics. It's not obvious until we have experimental verification.
The equation, BTW, is the precise definition of the Uncertainty Principle of QM. It says that you first precisely measured the position (Q) of a particle and them simultaneously attempted to measure the precise momentum (P) of the same particle. You next precisely measured the precise momentum of the particle and attempted to simultaneously measure the position of the same particle. The result is the limit, the absolutely most accurate limit, of your ability to simultaneously measure both...ih/2Pi. The limit on accuracy has nothing to do with the method, instruments used or how accurate the instruments are. If the result was zero the matrix terms commute and you could measure both position and momentum simultaneously to an arbitrary degree of precision.
You might be mixing up some math terms above. Tensors include scalars. And I believe that Ray pointed that out. Scalars are tensors of rank 0...vectors are rank 1 and other tensors with higher dimensions are of rank n > 1 the exact rank dependent on the number of dimensions involved.
But defining mass as a true tensor, something above tensor rank 0, is just a matter of definition. One can always nake up a definition that involves a true tensor and name it "mass". It's not something fundamental. But we already have a mass term that is a vector or tensor depending on whether you're looking at it classically or non-classically (QM). It's called momentum. P = mv (classical definition)
BTW: 2 is correct even though its somewhat trivial (in definition, not in its effect on reality). All scientific theories are approximations of reality technically true only to the stated limits of their domains. Newtonian relativity and mechanics breaks down at high velocities approaching C; SR breaks down in strong gravitational fields; GR breaks down at C and very near black holes; QM breaks down quantifying gravity, etc.
But there is really one thing that we shouldn't state without very good cause when we're talking about situations at the limit of the domains. And that is "it's obvious". It's not. The math might say that this or that is obvious but we are pushing the edge of the envelope when we approach the limit.
Here's the problem. I give you the following math statement
QP - PQ > 0
That's a true statement but I don't think that anyone is going to say that it's obvious that multiplying two numbers together twice but inverting the position of the numbers the second time and then substracting the result of each computation would be anything other than 0.
2 X 3 = 6
3 X 2 = 6
6-6 = 0
But in quantum mechanics what I first stated is true. In fact, the equation was just about the first equation discovered by Heisenberg in 1925. The exact equation was:
QP - PQ = ih/2Pi
Transposing Q (position) with P ( momentum) does not commute when you multiply the terms. The result of the multiplications do not give the same answer because the rule, as Dirac realized, involves matrix multiplication and not straight arithmetic multiplication.
So we need to be careful of the term "obvious" in physics. It's not obvious until we have experimental verification.
The equation, BTW, is the precise definition of the Uncertainty Principle of QM. It says that you first precisely measured the position (Q) of a particle and them simultaneously attempted to measure the precise momentum (P) of the same particle. You next precisely measured the precise momentum of the particle and attempted to simultaneously measure the position of the same particle. The result is the limit, the absolutely most accurate limit, of your ability to simultaneously measure both...ih/2Pi. The limit on accuracy has nothing to do with the method, instruments used or how accurate the instruments are. If the result was zero the matrix terms commute and you could measure both position and momentum simultaneously to an arbitrary degree of precision.
Darby,
Yep, Ray pointed that out. So I should clarify that in the past, Ray described "mass" as a tensor of rank 3 instead of the convential rank 0. (... A 3x3x3 matrix). While I can't read tensor math, I had fun thinking for the first time ever about redefining something fundamental. I would have never done that on my own. The only experience that comes close, was when I saw the Matrix movie for the first time. *SPOILER ALERT* I never once thought we could all be in a computer simulation, and when I saw that scene where he escapes from his little pod and the camera zooms out to reveal the humans are all linked together in virtual reality I was like "whoooaaaaaa, thats an amazing idea!". And the first time Ray described a fundamental as a matrix instead of a lone scalar it was just like that. "whoooaaaaa! duuude!"
I thought I'd finally be able to accept concepts like "massless particles" without suspending disbelief. Yes, I even hoped it be the beginning of a "single domain" era as other fundamentals were redefined with more ranks. Can't blame me for dreaming can you?
Please have patience with Darby, I'm about to ask a question that might sound very silly.
Why would we multiply "Position" against "Momentum"? Position of all things? Position relative to what?? Momentum is something that belongs to the paticle, it's mass times it's velocity. Except I've been told (by you and others) that position is meaningless without some point of reference. There is no absolute set of coordinates, so what gives with Q ?
Yep, Ray pointed that out. So I should clarify that in the past, Ray described "mass" as a tensor of rank 3 instead of the convential rank 0. (... A 3x3x3 matrix). While I can't read tensor math, I had fun thinking for the first time ever about redefining something fundamental. I would have never done that on my own. The only experience that comes close, was when I saw the Matrix movie for the first time. *SPOILER ALERT* I never once thought we could all be in a computer simulation, and when I saw that scene where he escapes from his little pod and the camera zooms out to reveal the humans are all linked together in virtual reality I was like "whoooaaaaaa, thats an amazing idea!". And the first time Ray described a fundamental as a matrix instead of a lone scalar it was just like that. "whoooaaaaa! duuude!"
I thought I'd finally be able to accept concepts like "massless particles" without suspending disbelief. Yes, I even hoped it be the beginning of a "single domain" era as other fundamentals were redefined with more ranks. Can't blame me for dreaming can you?
Please have patience with Darby, I'm about to ask a question that might sound very silly.
Why would we multiply "Position" against "Momentum"? Position of all things? Position relative to what?? Momentum is something that belongs to the paticle, it's mass times it's velocity. Except I've been told (by you and others) that position is meaningless without some point of reference. There is no absolute set of coordinates, so what gives with Q ?
Einstein2087
Chrono Cadet
The position relative to your chosen point of reference. And you're free to choose that point of reference anywhere you want, as long as you are consistent about it.
And don't forget that the answers you'll get will be, of-course, only valid in the same reference frame in which you expressed Q.
Not true.
Velocity is just as relative as position. Saying that a car has "a velocity of 50 mph relative to the ground" is no different than saying that the car is "2 miles north of the Empire State Building". There is no such thing as "an absolute speed of 50 mph", any more then there is a thing as "an absolute position of 2 miles".
And of-course, what is true for velocity, is also true for momentum. Since p=mv, and v depends on your point of view, it follows that p also changes when you change reference frames.
As for the relation that Darby gave for P and Q:
QP - PQ = ih/2Pi
The cool thing about it, is that it is true in ALL reference frames. No matter what your point of view is, and no matter what physical system your studying, you'll ALWAYS get QP - PQ = ih/2Pi. It is true that different point of views will give you different matrices for P and Q, but these differences "miraculously" cancel one another when you do the calculation.
Einstein2087
Chrono Cadet
Actually, the real meaning of the uncertainty principle goes far deeper than this.
The equation QP-PQ=ih/2Pi means that particles cannot simultaneouly HAVE an exact position and an exact momentum. It isn't just a matter of measurement. It is a fundamental property of the quantum world: states with a definite momentum and states with a definite position are mutually exclusive. You can't have both at the same time, regardess of whether an actual measurement is made.
Darby
Epochal Historian
E2087,
Thank you for pointing that out. I can only image Heisenberg, Jordan, Born and Dirac's reactions when they suddenly realized the actual meaning of what Heisenberg had discovered in that simple equation. It's been over 80 years since the equation was found and not a single experiment has ever resulted in giving anyone reason to modify it.
Again, thanks.
Thank you for pointing that out. I can only image Heisenberg, Jordan, Born and Dirac's reactions when they suddenly realized the actual meaning of what Heisenberg had discovered in that simple equation. It's been over 80 years since the equation was found and not a single experiment has ever resulted in giving anyone reason to modify it.
Again, thanks.
RainmanTime
Super Moderator
Hi folks,
I'd have to go back and look to be sure, but I thought that this was how I was describing "matter" (where my definition of "matter" is not the same as "mass" in that I believe "matter" is an integral measure of Mass over Time, in much the same way that "motion" is an integral measure of Space over Time). In any event, that was just my theory.
The basis for my belief that Mass should be treated as a vector (tensor of rank 1), just as we treat space, comes from the fact that we already understand that inertia (when it comes to rotational dynamics) is a tensor (rank 2). The Newtonian equations for rotational motion already show and tell us that mass/inertia is not a scalar quantity, because when we write the rotational equivalent for Newton's second law we see:
Tau = I*Alpha (Note: Bold indicates vector/tensor quantities)
This equation is the rotational analog to:
F = m*a
But there is a distinction between "m" and "I" that we often overlook: The Inertia quantity in the first equation is, actually, a tensor of rank 2. In other words, we DO NOT and CAN NOT treat the mass of an object as a point-mass when it comes to rotation. The distribution of mass about the principles axes is important to the rotational dynamics of an object. Whereas, in the translational form of the Second Law, we DO treat mass as a point-quantity scalar.
This difference has always troubled me, and we all even KNOW that it is incorrect to treat mass as a point-quantity. This is what got me theorizing that our simplification of the concept of mass into a point-mass is in error, and that the thing that might unify our approach to translational and rotational Newtonian dynamics would be to treat mass as a vector. If we did this, and then accepted that Mass and Matter are different as I have suggested, then it would propagate to Matter being a higher order tensor over and above Mass (because it includes Time).
Anyway... just wanted to clear that up. Again, this is all just my musings...Not saying it is "right".
RMT
I'd have to go back and look to be sure, but I thought that this was how I was describing "matter" (where my definition of "matter" is not the same as "mass" in that I believe "matter" is an integral measure of Mass over Time, in much the same way that "motion" is an integral measure of Space over Time). In any event, that was just my theory.
The basis for my belief that Mass should be treated as a vector (tensor of rank 1), just as we treat space, comes from the fact that we already understand that inertia (when it comes to rotational dynamics) is a tensor (rank 2). The Newtonian equations for rotational motion already show and tell us that mass/inertia is not a scalar quantity, because when we write the rotational equivalent for Newton's second law we see:
Tau = I*Alpha (Note: Bold indicates vector/tensor quantities)
This equation is the rotational analog to:
F = m*a
But there is a distinction between "m" and "I" that we often overlook: The Inertia quantity in the first equation is, actually, a tensor of rank 2. In other words, we DO NOT and CAN NOT treat the mass of an object as a point-mass when it comes to rotation. The distribution of mass about the principles axes is important to the rotational dynamics of an object. Whereas, in the translational form of the Second Law, we DO treat mass as a point-quantity scalar.
This difference has always troubled me, and we all even KNOW that it is incorrect to treat mass as a point-quantity. This is what got me theorizing that our simplification of the concept of mass into a point-mass is in error, and that the thing that might unify our approach to translational and rotational Newtonian dynamics would be to treat mass as a vector. If we did this, and then accepted that Mass and Matter are different as I have suggested, then it would propagate to Matter being a higher order tensor over and above Mass (because it includes Time).
Anyway... just wanted to clear that up. Again, this is all just my musings...Not saying it is "right".
RMT
The Double-Slit Experiment
you tube 1
you tube 2
another view of this experiment might help with your mass idea...
you tube 1
you tube 2
another view of this experiment might help with your mass idea...
recall15
Dimensional Traveler
and
Quoted:
Over the years, the experiment has been conducted in a number of different ways. In 1961, Claus Jonsson performed the experiment with electrons, and it conformed with Young's behavior, creating interference patterns on the observation screen. Jonsson's version of the experiment was voted "the most beautiful experiment" by Physics World readers in 2002.
In 1974, technology became able to perform the experiment by releasing a single electron at a time. Again, the interference patterns showed up. But when a detector is placed at the slit, the interference once again disappears. The experiment was again performed in 1989 by a Japanese team that was able to use much more refined equipment.
The experiment has been performed with photons, electrons, and atoms, and each time the same result becomes obvious - something about measuring the position of the particle at the slit removes the wave behavior. Many theories exist to explain why, but so far much of it is still conjecture.
more at:
link to <a href="http://physics.about.com/" target="_blank">http://physics.about.com/ </a>
Quoted:
Over the years, the experiment has been conducted in a number of different ways. In 1961, Claus Jonsson performed the experiment with electrons, and it conformed with Young's behavior, creating interference patterns on the observation screen. Jonsson's version of the experiment was voted "the most beautiful experiment" by Physics World readers in 2002.
In 1974, technology became able to perform the experiment by releasing a single electron at a time. Again, the interference patterns showed up. But when a detector is placed at the slit, the interference once again disappears. The experiment was again performed in 1989 by a Japanese team that was able to use much more refined equipment.
The experiment has been performed with photons, electrons, and atoms, and each time the same result becomes obvious - something about measuring the position of the particle at the slit removes the wave behavior. Many theories exist to explain why, but so far much of it is still conjecture.
more at:
link to <a href="http://physics.about.com/" target="_blank">http://physics.about.com/ </a>
Packerbacker
Quantum Scribe
My take on all of this:
The electron may be a nominal particle traveling through a medium.
In passing it creates a bow wave similar to that of a speedboat in water.
So the bow wave created prior to the slits will pass through the second slit, and the bow wave created after the electron passes through the slit generates a second bow wave which interferes with the first, and the effect is displayed on the 'screen.' behind the slits.
But if the electron is intercepted by a detector at the first slit it is taken out of the experiment can cannot generate the second wave.
Proposal: Cut another slit in the screen itself so the electron can pass through without impedance. The detector is placed behind the screen.
Let's employ a thought experiment and mount the double slits and screen on a pivoting arm which can swing upward and completely out of the way. With the slits and screen removed, there is a clear path from the source of the electron and the detector. The electron is thus detected as a particle.
If the slits and screen are now lowered, an interference effect ought to be created. Why not? But the electron should still be detected as a particle. Why not? Hence, both effects should be exhibited by the electron's trip.
If the electron "knows" that it is being detected as a particle and not a wave, how does it also know that the detector is turned on and operating?. If it doesn't know this, it might make a mistake (believing the detector to be operating) and not show any effect at all.
The electron may be a nominal particle traveling through a medium.
In passing it creates a bow wave similar to that of a speedboat in water.
So the bow wave created prior to the slits will pass through the second slit, and the bow wave created after the electron passes through the slit generates a second bow wave which interferes with the first, and the effect is displayed on the 'screen.' behind the slits.
But if the electron is intercepted by a detector at the first slit it is taken out of the experiment can cannot generate the second wave.
Proposal: Cut another slit in the screen itself so the electron can pass through without impedance. The detector is placed behind the screen.
Let's employ a thought experiment and mount the double slits and screen on a pivoting arm which can swing upward and completely out of the way. With the slits and screen removed, there is a clear path from the source of the electron and the detector. The electron is thus detected as a particle.
If the slits and screen are now lowered, an interference effect ought to be created. Why not? But the electron should still be detected as a particle. Why not? Hence, both effects should be exhibited by the electron's trip.
If the electron "knows" that it is being detected as a particle and not a wave, how does it also know that the detector is turned on and operating?. If it doesn't know this, it might make a mistake (believing the detector to be operating) and not show any effect at all.