QuoteSPECIAL RELATIVITY
Central to the discussion of special relativity is the idea of an inertial frame (or reference). This is basically a coordinate system, which might be attached to an observed object or to the observer, which undergoes no acceleration. Consequently, the relative velocity between two inertial frames is necessarily constant, providing what we refer to as uniform motion Einstein based on two postulates:
1. No physical measurement can distinguish one inertial frame from another.
2. The speed of light (in vacuum) is the same in all inertial frames, regardless of any motion of the source.
Postulate (1) is also known as the Principle of Relativity and is a generalization of the idea of Galileo: that uniform motion is undetectable by mechanical experiments. This Galilean Principle of Relativity accounts for the fact that there are no obvious effects of the earth's motion through space, as it orbits the sun (at a tangential speed of about 17 000 km/hr !). For example, objects released from the top of a tower fall vertically downwards (towards the centre of the earth), as they would if the earth were stationary and not at some angle which depends on the earth's tangential speed.
Einstein thought that Galileo's principle should apply to the whole of physics, including electromagnetic phenomena.
Postulate (2) derives from the idea of Maxwell that light behaves as a travelling wave, containing oscillating electric and magnetic fields which can advance in a vacuum at a speed, denoted by the symbol c , which depends only on two basic constants of electrostatic and magnetic theory. The fields require no medium for their existence, unlike the case of sound waves (for example) whose velocity within a gas (or liquid or solid) affected by any motion of this medium. Previously, physicists had assumed that light waves behave somewhat like sound, propagating though an invisible medium which they termed the (aluminiferous).
Attempts to measure the speed of the earth relative to the ether failed; in particular, the Michelson-Morley experiment (performed repeatedly between 1881 and 1930) showed that light travels with the same speed in two perpendicular directions, which is impossible if the earth is moving (due to its orbit around the sun) through an ether.
From Einstein's two postulates, several properties follow as a matter of pure logic. One of these is an effect called length contraction: the "measured" length (in the direction of motion) of an object which is moving at uniform speed v relative to an observer is less than if the object were stationary. The length measured when there is relative motion is called the proper lengthand all other lengths are called improper.
The length-contraction effect can be expressed mathematically improper length = (1/gamma) (proper length) <where 1/gamma = (1 - v^2 / c^2)^(1/2) and is less than unity; here means to the power of, so ^(1/2) means taking the square root. Since the value of c (= 3.00 x 10^8 m/s) is so large, length contraction is entirely negligible (e.g. 1 part in 2 x 10^12 for v = 1000 km/hr) for objects such a cars, trains and airplanes.
There is no change in dimensions of the object which are perpendicular to the relative velocity v ; therefore it might be expected that a fast-moving cube would appear squashed (in the direction of motion) in a high-speed photograph. However light from different parts of the cube takes different times to reach the camera, so the photograph is a record of the object at a single instant of time. This illustrates the difference between a true measurement and a simple observation.
In fact, the cube would appear as if it had been rotated (through a fixed angle), due to the combined effects of length contraction and the finite (limited) speed of light.
Magnetic force can be thought to arise from electrostatic interaction, plus the length-contraction effect. For example, a metal contains potentially-mobile negative electrons and an equal number of immobile positive charges. In the absence of any electrical current, two parallel wires exert no force on each other because the attractive forces (electrons in one wire attracting positive charge in the other, and vice versa) are exactly balanced by repulsions (electrons in one wire repelling those in the other, likewise for the positive charges).
With an equal current travelling in the same direction in each wire, the repulsive forces are unchanged (there is no relative motion between the electrons or positive charges) but the attractions are increased, since the positive charge "sees" the distance between the moving electrons as contracted (equivalent to an increase in negative charge per unit length of the wire) or vice versa. This increase is seen as a net attractive force between the two wires, usually attributed to the magnetic effect of the currents.
We can say that Special Relativity unites the concepts of magnetic and electrostatic force into a single electromagnetic force.
Time dilation
Another effect predicted by special relativity is time dilation : a clock moving at uniform speed relative to an observer would be "measured" to run slow, arising from the properties of space-time and not from the finite speed of light. By analogy with the above, we can define an interval of proper time as a difference in the readings of a clock which is stationary with respect to the observer; where there is relative motion, we measure an improper time interval. Analysis of a simple situation shows that align="CENTER">improper time interval = (gamma) (proper time interval)
Since gamma > 1, the interval between ticks of a "moving" (relative to the observer) clock is greater than for a "stationary" clock, so "a moving clock runs slow". This effect has been verified by carrying highly-accurate atomic clocks aboard aircraft and comparing their "readings" with those of an identical clock which remained stationary. Although the difference in elapsed time is miniscule, the extremely high accuracy of the atomic clock has allowed the time dilation effect predicted by Special Relativity to be verified.
A more extreme (but hypothetical) example is the case of two twins: one remains on earth, the other journeys at a high speed (approaching the speed of light) to a distant star and back. Upon returning, the moving twin will have aged less than the twin who stayed on earth. Although this is not a simple situation, since accelerations are necessarily involved in the return journey, detailed analysis shows that Special Relativity gives the right answer for the difference in age.
Relativistic mass
Einstein published a paper which shows that Newton's second law (F = ma) applies to any object, travelling at any speed v, provided its usual mass (called the rest mass, if measured when the object is stationary) is replaced by a relativistic mass given by: relativistic mass = (gamma) (rest mass) Since gamma > 1, there is a relativistic increase in mass. Therefore, if a constant force F is applied to a stationary object, it initially accelerates at a constant rate a = F/m0 (where m0 is its rest mass) but as the speed v approaches c , gamma becomes significantly larger than unity, the relativistic mass m significantly exceeds m0 and the rate of acceleration (a = F/m) decreases. In fact, the acceleration tends towards zero as v approaches c :
No material object can travel at or above the speed of light (in vacuum). At high speeds, the work done by the force F goes into increasing the relativistic mass, rather than the speed. In other words, energy provided by the force is converted into mass. Einstein introduced the concept of the total energy E of an object E = m c^2 = (gamma) m0 c^2 = K + m0 c^2 as being the sum of its kinetic energy K and its <B>rest energy</B> E0 = m0 c^2 . From this equation, it is easy to show that the correct general formula for kinetic energy is:K = (gamma - 1) m0 c^2<rather than the classical expression: K = (1/2) m0 c^2 .
However, Einstein's general formula is consistentwith the classical expression, since for v<<c we can use the binomial theorem (1+x)^n = 1 + n x + (1/2)n(n-1) x^2 + ... = 1 + n x (approximately) if x<<1 with x = -v^2/c^2 and n = -1/2 , so that gamma = (1+x)^n , givin >K = (1 + nx - 1) m0 c^2 = (nx) m0 c^2 = (-1/2) (-v^2/c^2) m0 c^2 = (1/2) mo v^2 For v<<c, Special Relativity gives the same result as Classical Physics, an example of the Correspondence Principle which states that a new scientific theory must give the same predictions as an older theory under conditions in which the older theory has already been found to be correct. One situation in which speeds comparable to c are routinely achieved is in the acceleration of charged particles, for example electrons in a TV tube, oscilloscope or electron microscope, or other particles in a nuclear accelerator.
Solitary
That still doesn't answer the question of why it's called special relativity and not, say, ordinary relativity.
Isn't it because it only applies to a special case?
Yes - and Solitary posted a wall of text without pointing out the special case - which, alone, would have answered his question.
Quote from: "Colanth"Yes - and Solitary posted a wall of text without pointing out the special case - which, alone, would have answered his question.
The real theory is General Relativity. If you would take a course, SR would occupy the first chapter, and GR, the next 19 chapters, sort of. Think of Newton's F = ma. When a = 0, you have constant speed, a special case of F=ma. SR is a special case of GR as it deals only with inertial frames of reference. But in the real world, you have forces, you have matter interacting with other pieces of matter, you have acceleration, IOW, non-inertial frames of reference, which are the real thing to study - in space you are in free fall, the natural state of matter. So the free falling lab is where you do all of your calculations, draw your graphs, etc. It's like studying mechanics, which is divided into kinematics and dynamics. If you only study kinematics, your grasp of mechanics will be very superficial. Similarly, if you only study SR, your grasp is very, very limited. The real thing is GR, where space-time is intricately linked to gravity. But to do that, you need to study quite a bit of mathematics, such has manifolds, tensors, and operations between tensors, parallel transport, geodesics, and the metric tensor, which defines the geometry of spacetime. If one had to resume GR in one sentence, it would be: matter curves spacetime, and curved spacetime determines the path of an object.
Quote from: "Colanth"That still doesn't answer the question of why it's called special relativity and not, say, ordinary relativity.
This: "Central to the discussion of special relativity is the idea of an inertial frame (or reference). This is basically a coordinate system, which might be attached to an observed object or to the observer, which undergoes no acceleration." Solitary
Quote from: "josephpalazzo"Quote from: "Colanth"Yes - and Solitary posted a wall of text without pointing out the special case - which, alone, would have answered his question.
The real theory is General Relativity. If you would take a course, SR would occupy the first chapter, and GR, the next 19 chapters, sort of. Think of Newton's F = ma. When a = 0, you have constant speed, a special case of F=ma. SR is a special case of GR as it deals only with inertial frames of reference. But in the real world, you have forces, you have matter interacting with other pieces of matter, you have acceleration, IOW, non-inertial frames of reference, which are the real thing to study - in space you are in free fall, the natural state of matter. So the free falling lab is where you do all of your calculations, draw your graphs, etc. It's like studying mechanics, which is divided into kinematics and dynamics. If you only study kinematics, your grasp of mechanics will be very superficial. Similarly, if you only study SR, your grasp is very, very limited. The real thing is GR, where space-time is intricately linked to gravity. But to do that, you need to study quite a bit of mathematics, such has manifolds, tensors, and operations between tensors, parallel transport, geodesics, and the metric tensor, which defines the geometry of spacetime. If one had to resume GR in one sentence, it would be: matter curves spacetime, and curved spacetime determines the path of an object.
So the special theory isn't the real theory when it came first? This doesn't explain why it's special when it is central to the theory: "Central to the discussion of special relativity is the idea of an inertial frame (or reference). This is basically a coordinate system, which might be attached to an observed object or to the observer, which undergoes no acceleration." And you don't need a wall of text about the general theory to know that. Solitary
"Special" has a very specific application here, as in a subset of a broader theory (in this case, general relativity).
The fact that it came first doesn't matter. Physicists and mathematicians often seek to "generalize" their results, which makes them more powerful.
Quote from: "JonathanG""Special" has a very specific application here, as in a subset of a broader theory (in this case, general relativity).
The fact that it came first doesn't matter. Physicists and mathematicians often seek to "generalize" their results, which makes them more powerful.
I never said that made it special, I said this does: no acceleration. Coming first is with reference to it not being the "real" theory. So of course it doesn't matter that it came first unless you think it isn't the real theory. You are correct that the general theory is a broader theory, but that in no way subtracts from the special being used when there is no acceleration or that it makes it not a real theory because it is used for a specific application any more than the general theory makes it real when it is also used for a specific application---accelerated motion.
The quote is for the Special Theory of relativity and explains it very well, why the need to bring up the general theory at all. If you know the General theory explain it in a different post so people that aren't familiar with it don't get confused by bringing it up here as if the Special theory doesn't matter because it isn't the "real" theory. And make sure you use abstract symbols, that most people don't understand, so you can show off your expertise with higher mathematics instead of sharing your knowledge with the dummies here. :roll: Solitary
Quote from: "Solitary"The quote is for the Special Theory of relativity and explains it very well, why the need to bring up the general theory at all.
Because "Special Relativity" is really "a special case of General Relativity", so if you don't understand GR you can't understand one single application of GR (otherwise called SR). It's like understanding 3 and 5 but not understanding addition, but claiming that you understand how to add 3 and 5. Adding 3 and 5 is just a special case of general addition, and if you don't understand general addition you can't understand adding 3 and 5. You can understand that they're 8, but that's not understanding adding them.
Quote from: "Colanth"Quote from: "Solitary"The quote is for the Special Theory of relativity and explains it very well, why the need to bring up the general theory at all.
Because "Special Relativity" is really "a special case of General Relativity", so if you don't understand GR you can't understand one single application of GR (otherwise called SR). It's like understanding 3 and 5 but not understanding addition, but claiming that you understand how to add 3 and 5. Adding 3 and 5 is just a special case of general addition, and if you don't understand general addition you can't understand adding 3 and 5. You can understand that they're 8, but that's not understanding adding them.
And I can say you can't understand General Relativity unless you understand Special relativity because general relativity is an addition to Special Relativity that came first, and that is why it is taught first. If one can't understand how things that aren't accelerating are relative to an observer, how can they understand that when they are accelerating they gain mass and time gets shorter as measured by an observer not accelerating, and that the length as measure by an observer standing still gets shorter when it's a lot harder to understand? If you can't understand X-Y=X and X+y=X , how can you understand V=V1+V2 divided by 1+V1+v2 divided by c2? Solitary
Quote from: "Solitary"And I can say you can't understand General Relativity unless you understand Special relativity because general relativity is an addition to Special Relativity that came first, and that is why it is taught first.
Sure, if one wants to study dynamics, you first learn kinematics. If you want to study calculus, you first study algebra. But it's not the point of which comes first. Now imagine studying physics with just high school algebra. How much will you understand the laws of physics without calculus?
QuoteIf one can't understand how things that aren't accelerating are relative to an observer, how can they understand that when they are accelerating they gain mass and time gets shorter as measured by an observer not accelerating, and that the length as measure by an observer standing still gets shorter when it's a lot harder to understand?
All of the effects of SR have been known for more than 100 years. SR, like Euclidean geometry, is a closed subject -- that is, we know everything that we can possibly know from it, and therefore, there is no active research being conducted in SR. Only crackpots and ignoramuses still question SR. The rest of scientists have moved on. The current research is in GR, coupled with thermodynamics and QFT.
Now in your case, you don't have the math, you refuse to upgrade your knowledge, you spend your time searching for websites to copy and paste, and then you want to discuss SR like a philosopher ruminating from his ivory tower. That's not how physics, or any other science, is done.
Now if I said to you that in GR, velocity as a concept is ill-defined, would you understand that? I think not. To come to that conclusion, you would need to study manifolds and parallel-transport. Or if I would say that in a Black Hole, the thermal radiation can destroy information, would you understand that? I think not. You would need to understand not only QFT per se as in how QFT gives you the Standard Model, but also how QFT is applied to GR, which is an altogether different field of research. And I can tell right off that this would be beyond your comprehension. It's not that I'm saying you're an idiot, it's just that I know you don't have the background to tackle these concepts. But you are an idiot IF you think you know this stuff better than I do.
First of all, Time as measured by clocks in a gravitational field does not follow the rules of special relativity. Relative velocity in GR turns out to be a tricky concept as it is in SR, when one of the objects is accelerating.
You want to know the relative velocity of an object "now". In order to determine "now", you have to use some defintion of simultaneity. But one of the lessons SR tells us is that simultaneity is relative. If the velocity is changing with time due to acceleration, the concept of relative velocity also becomes ill-defined.
In a Black Hole, the thermal radiation can destroy information. But any thermal system can be assigned an entropy via the Gibbs law dE = S dT. Thus, we can calculate the black hole entropy by the noticeable effect that we can calculate the black hole temperature by the noticeable effect that the quantum radiation is thermal.
This is, I think, what people like you, are getting at when they say that black hole entropy is responsible for the information loss.
I could say it in another way, that black hole information loss is responsible for black hole entropy. The simple fact of the matter is that they are the same thing in slightly different terms. Solitary
Quote from: "Solitary"I could say it in another way, that black hole information loss is responsible for black hole entropy. The simple fact of the matter is that they are the same thing in slightly different terms. Solitary
Wow! If it were that simple, we wouldn't have developped the Holographic Principle, the AdS/CFT Correspondence Principle and the present Firewall-Fuzzball controversy. The best physicists in the world haven't figured out that much, but you with backward knowledge of physics knows it all.
//Keep philosophying from your ivory tower, you're making great strides.// sarcasm off
Quote from: "josephpalazzo"Quote from: "Solitary"I could say it in another way, that black hole information loss is responsible for black hole entropy. The simple fact of the matter is that they are the same thing in slightly different terms. Solitary
Wow! If it were that simple, we wouldn't have developped the Holographic Principle, the AdS/CFT Correspondence Principle and the present Firewall-Fuzzball controversy. The best physicists in the world haven't figured out that much, but you with backward knowledge of physics knows it all.
//Keep philosophying from your ivory tower, you're making great strides.// sarcasm off
I never said I figured it out. Like you said they are principles and the Fire-Fuzzbal is controversial.
One aspect that both Einstein (Special Relativity) and Quantum Mechanics agreed upon is that time exists as a continuum where the past, present and future events exist simultaneously.
Quantum information exist in two forms as holographic information within a 2D dimension (wave function) and as a 3D object within the space-time.Similar to the teleportation process of quantum information that occurs within Black Holes, a type of retro-causation process could also be occurring on a larger scale where by events from the past and the future are effecting each other.
For now, it seems appropriate to me, to assume both information conservation and no firewalls, seeking some way of reconciling the two. This might involve truly radical revisions in the foundations of quantum mechanics, or bizarre nonlocal dynamics outside the black hole. If we are forced to accept that firewalls really exist, then we will need a deeper understanding of their dynamical origin than the indirect argument AMPS provided.
Of course all this is in the quantum world and mathematics, not what we experience in our everyday lives. Solitary
Quote from: "Solitary"I never said I figured it out. Like you said they are principles and the Fire-Fuzzbal is controversial.
One aspect that both Einstein (Special Relativity) and Quantum Mechanics agreed upon is that time exists as a continuum where the past, present and future events exist simultaneously.
Quantum information exist in two forms as holographic information within a 2D dimension (wave function) and as a 3D object within the space-time.Similar to the teleportation process of quantum information that occurs within Black Holes, a type of retro-causation process could also be occurring on a larger scale where by events from the past and the future are effecting each other.
For now, it seems appropriate to me, to assume both information conservation and no firewalls, seeking some way of reconciling the two. This might involve truly radical revisions in the foundations of quantum mechanics, or bizarre nonlocal dynamics outside the black hole. If we are forced to accept that firewalls really exist, then we will need a deeper understanding of their dynamical origin than the indirect argument AMPS provided.
Of course all this is in the quantum world and mathematics, not what we experience in our everyday lives. Solitary
Not even close, but to shed some light on the Fuzzball-Firewall controversy for those interested:
(//http://i243.photobucket.com/albums/ff277/josephpalazzo/Firewallparadox.jpg) (//http://s243.photobucket.com/user/josephpalazzo/media/Firewallparadox.jpg.html)
To make it as simple as possible: In the diagram, the wiggly line going bottom to top is inside the Black hole, and could be a singularity, but that's not important. The two curved lines represent the horizon envelopping the BH: crossing that line is a point of no return. The curved line with the letters a and b is on a Rindler wedge ( I've used Rindler coordinates in my blog The Unruh Effect (//http://soi.blogspot.ca/2013/07/the-unruh-effect.html), equation 6). And R is Hawking radiation at an earlier time.
(1) An infalling observer would see a vacuum at a, and according to GR would feel nothing unusual in crossing the horizon( from the Equivalence Principle).
(2) The far away observer sees an entangles pair bb', where b is Hawking radiation at a later time. This comes from the Holographic Principle. (From String Theory, you can argue that this leads to tiny strings on the Horizon, making it a Fuzzball. But the controversy doesn't depend on this argument. I just added in case you wonder where does the Fuzzball come in.)
(3) The controversy brought by AMPS ( named after the authors, Ahmed Almheiri, Donald Marolf, Joseph Polchinski, James Sully) is that b' should be entangled with R. But another QM principle says that entangled pairs are monogamous ( to break an entangled pair requires a lot of energy). So either b is entangled with b', or it's entangled with R.
So we have a dilemna. AMPS are suggesting that the BH is really not empty space as suggested by (1) but a firewall. Susskind and Maldacena have proposed that R is connected to A by a wormhole. In fact, just about everybody - everybody that counts in physics, :) - have suggested different solutions, none resolves the controversy.
Quote from: "josephpalazzo"To make it as simple as possible: In the diagram, the wiggly line going bottom to top is inside the Black hole, and could be a singularity, but that's not important. The two curved lines represent the horizon envelopping the BH: crossing that line is a point of no return. The curved line with the letters a and b is on a Rindler wedge ( I've used Rindler coordinates in my blog The Unruh Effect (//http://soi.blogspot.ca/2013/07/the-unruh-effect.html), equation 6). And R is Hawking radiation at an earlier time.
First, I would like to congratulate you for your having mastered so much math and science. I would like to have had the capacity to achieve such mastery, but I don't have that capacity. Never-the-less, I do have a fair amount of curiosity about how things work. I have read through Brian Greene's books that are popularizations of current microphysics and macrophysics. I understand that such popularizations suffer from things like analogies that imply ontological status claims that are not supported by the math (or at least the math implies ambiguity about ontological status), so I always am cautious of taking such popularizations too literally. I try to take them as giving me a rough approximation of the state of ideas in physics as seen by current physicists.
One thing that I've tried to grasp in at least a rudimentary way, is what is meant by time in General Relativity and what is meant by time in quantum mechanics. I kind of get what time is taken to be in General Relativity - time is what is measured by a clock in an inertial frame. That is probably not completely right and may be a total misconception on my part. If that is basically what time is in GR, though, then I must admit that it doesn't actually help me understand what time actually is - especially with respect to what is probably suspectly analogously referred to as the "fabric" of space-time. With respect to quantum mechanics, I feel like I understand that even less (if that is possible). I have gotten the impression from some readings that I have done, that time is taken to be a kind of "absolute" - that is, that there is a fixed simultaneity throughout the universe. But that doesn't seem like it can be right because that seems to contradict the notion of time in GR.
I have done multiple Google searches with many different search parameters, but I haven't found any web site that answers my question about how the conceptions of time in GR and quantum mechanics compare.* And I'm curious that if they do have different conceptualizations of time, what implications follow from those differences - say with respect to trying to "unify" the two.
Anyway, when I read the passage of yours that I quoted above, it occurred to me that if there's one place where the nature of time in quantum mechanics and GR would have to be manifest the same way, it seems like it would be a singularity. If you are so inclined, I would appreciate any help you could give me in assuaging my curiosity about conceptions of time. A link to a site that would be likely to have the answers to my questions would be very helpful if you happen to know of any.
*I did run into this web page that I found pretty baffling but understood enough of it to be really intrigued:
//http://lareviewofbooks.org/review/quantum-absolutism-lee-smolins-time-reborn/
It simply amazes me how I can be wrong and not even close on a controversial subject, especially when a diagram shows the same as what I said---with no Fuzzball. :roll: Solitary
QuoteBlack hole complementarity is inevitable, if we assume the ?ve contents: unitarity, entropy-area formula, existence of information observer, semi-classical quantum ?eld theory for asymptotic observer, and general relativity for in-falling observer.
This reveals a situation that there is a ?rewall outside of the event horizon, while the apparent horizon is absent. Therefore, the ?rewall, if it exists, does not only modify general relativity for an in-falling observer, but also modifies semi-classical quantum ?eld theory for an asymptotic observer.
However, large the basic philosophy of black hole complementarity, AMPS introduce a ?rewall around the horizon. According to large rescaling, the ?rewall should be close to the apparent horizon. The ?rewall should be near the time-like apparent horizon and the ?rewall should not affect to future in?nity. A false vacuum lump can generate a spacetime structure with disconnected apparent horizons.
Quote from: "Solitary"One aspect that both Einstein (Special Relativity) and Quantum Mechanics agreed upon is that time exists as a continuum where the past, present and future events exist simultaneously.
I don't understand this. If quantum events are indeterminate, how can the future exist simultaneously with past and present events?
In an earlier post, you said this:
"You want to know the relative velocity of an object "now". In order to determine "now", you have to use some definition of simultaneity. But one of the lessons SR tells us is that simultaneity is relative."
I can see that the notion of past, present and future events existing simultaneously may not necessarily contradict the notion that simultaneity is relative, but I'm not sure how the notions dovetail together. Could you explain that?
I thought that your original post was a nice synopsis of Special Relativity. Thank you for posting it. I'm not sure why it was taken that your posting of it implied anything at all about the "value" of it with respect to General Relativity. I think maybe your subject line was taken as having more substance than you intended - I took it to be mostly word play to introduce the synopsis of Special Relativity that was to follow.
Quote from: "entropy"Quote from: "Solitary"One aspect that both Einstein (Special Relativity) and Quantum Mechanics agreed upon is that time exists as a continuum where the past, present and future events exist simultaneously.
I don't understand this. If quantum events are indeterminate, how can the future exist simultaneously with past and present events?
In an earlier post, you said this:
"You want to know the relative velocity of an object "now". In order to determine "now", you have to use some definition of simultaneity. But one of the lessons SR tells us is that simultaneity is relative."
I can see that the notion of past, present and future events existing simultaneously may not necessarily contradict the notion that simultaneity is relative, but I'm not sure how the notions dovetail together. Could you explain that?
I thought that your original post was a nice synopsis of Special Relativity. Thank you for posting it. I'm not sure why it was taken that your posting of it implied anything at all about the "value" of it with respect to General Relativity. I think maybe your subject line was taken as having more substance than you intended - I took it to be mostly word play to introduce the synopsis of Special Relativity that was to follow.
Thanks! That's very kind of you. You are correct about it being a synopsis, that's what I intended. You sure do ask hard questions to answer. #-o :-k I'm not sure I know either.
Just as Einstein's own Relativity Theory led Einstein to reject time, Feynman's Sum over Histories theory led him to describe time simply as a direction in space. Feynman's theory states that the probability of an event is determined by summing together all the possible histories of that event.
For example, for a particle moving from point A to B we imagine the particle traveling every possible path, curved paths, oscillating paths, squiggly paths, even backward in time and forward in time paths. Each path has an amplitude, and when summed the vast majority of all these amplitudes add up to zero, and all that remains is the comparably few histories that abide by the laws and forces of nature.
Sum over histories indicates the direction of our ordinary clock time is simply a path in space which is more probable than the more exotic directions time might have taken otherwise. So this leaves room for quantum events to occur. You have to remember this is in the world of quantum mechanics that is incomplete and not yet compatible with general relativity that may not be either. Also, as Feynman said, not even he understands quantum mechanics. However, it does work giving us so many things in modern technology and electronics. Solitary
Quote from: "entropy"Quote from: "josephpalazzo"To make it as simple as possible: In the diagram, the wiggly line going bottom to top is inside the Black hole, and could be a singularity, but that's not important. The two curved lines represent the horizon envelopping the BH: crossing that line is a point of no return. The curved line with the letters a and b is on a Rindler wedge ( I've used Rindler coordinates in my blog The Unruh Effect (//http://soi.blogspot.ca/2013/07/the-unruh-effect.html), equation 6). And R is Hawking radiation at an earlier time.
First, I would like to congratulate you for your having mastered so much math and science. I would like to have had the capacity to achieve such mastery, but I don't have that capacity. Never-the-less, I do have a fair amount of curiosity about how things work. I have read through Brian Greene's books that are popularizations of current microphysics and macrophysics. I understand that such popularizations suffer from things like analogies that imply ontological status claims that are not supported by the math (or at least the math implies ambiguity about ontological status), so I always am cautious of taking such popularizations too literally. I try to take them as giving me a rough approximation of the state of ideas in physics as seen by current physicists.
One thing that I've tried to grasp in at least a rudimentary way, is what is meant by time in General Relativity and what is meant by time in quantum mechanics. I kind of get what time is taken to be in General Relativity - time is what is measured by a clock in an inertial frame. That is probably not completely right and may be a total misconception on my part. If that is basically what time is in GR, though, then I must admit that it doesn't actually help me understand what time actually is - especially with respect to what is probably suspectly analogously referred to as the "fabric" of space-time. With respect to quantum mechanics, I feel like I understand that even less (if that is possible). I have gotten the impression from some readings that I have done, that time is taken to be a kind of "absolute" - that is, that there is a fixed simultaneity throughout the universe. But that doesn't seem like it can be right because that seems to contradict the notion of time in GR.
I have done multiple Google searches with many different search parameters, but I haven't found any web site that answers my question about how the conceptions of time in GR and quantum mechanics compare.* And I'm curious that if they do have different conceptualizations of time, what implications follow from those differences - say with respect to trying to "unify" the two.
Anyway, when I read the passage of yours that I quoted above, it occurred to me that if there's one place where the nature of time in quantum mechanics and GR would have to be manifest the same way, it seems like it would be a singularity. If you are so inclined, I would appreciate any help you could give me in assuaging my curiosity about conceptions of time. A link to a site that would be likely to have the answers to my questions would be very helpful if you happen to know of any.
*I did run into this web page that I found pretty baffling but understood enough of it to be really intrigued:
//http://lareviewofbooks.org/review/quantum-absolutism-lee-smolins-time-reborn/
You get can get really bogged down with the notion of time. Just recently Lee Smolin published his Time Reborn: From the Crisis in Physics to the Future of the Universe (//http://www.amazon.com/Time-Reborn-Crisis-Physics-Universe/dp/0547511728/ref=sr_1_1?ie=UTF8&qid=1378042883&sr=8-1&keywords=lee+smolin). I must confess that I didn't read it, but this is just to show that physicists are still grappling with the notion of time.
Now leaving all philosophical musings aside, in Relativity, time is simply what you would measure on a clock, which is made of matter, with something inside ticking with a regular beat. So when we look at time dilation, it means for a moving observer, his clock would slow down. Ditto for an observer moving into a greater gravitational field. You can debate ad infinitum whether this is real or apparent, but we do know that for communication satellites involved in GPS, their clocks have to take into account these two effects, otherwise they will get out of synchronization withing minutes.
Now in QFT, the notion of time only rears its ugly head when we look at commutation relationship. For instance, the position q and its conjugate momentum p, follows this simple rule:
[x,p] = i ?, where the square brackets means xp - px, the reason being is that these are operators in QM and don't commute.
These commutator relationship must be taken at equal time interval in order not to violate causality. This is taken care by defining 4-vectors x = (t,x,y,y,z) and p = (p[sub:2yo9xepr]t[/sub:2yo9xepr],p[sub:2yo9xepr]x[/sub:2yo9xepr],p[sub:2yo9xepr]y[/sub:2yo9xepr],p[sub:2yo9xepr]z[/sub:2yo9xepr]). By making everything 4-d tensors, QFT becomes Lorentz invariant, and SR is immediately incorporated into QFT. So a good deal of time in QFT is to make sure that such things as the Lagrangian and the Hamiltonian functions are Lorentz invariant. That way, time is effectively treated on equal footing with space, as Relativity demands.
Quote from: "Solitary"Just as Einstein's own Relativity Theory led Einstein to reject time, Feynman's Sum over Histories theory led him to describe time simply as a direction in space. Feynman's theory states that the probability of an event is determined by summing together all the possible histories of that event.
For example, for a particle moving from point A to B we imagine the particle traveling every possible path, curved paths, oscillating paths, squiggly paths, even backward in time and forward in time paths. Each path has an amplitude, and when summed the vast majority of all these amplitudes add up to zero, and all that remains is the comparably few histories that abide by the laws and forces of nature.
Okay, thanks for the response. It seems like what you are saying is that what is simultaneous in the "sum over histories" approach is all the potentialities. But I don't see where it makes physical temporal sense to say past and future potentialities exist simultaneously unless all of those potentialities exist in a physical way like Everett's Many Worlds interpretation - in which case the indeterminacy of QM appears to be an indeterminacy of knowledge of physical events, not an indeterminacy inherent in physical events themselves.
Quote from: "josephpalazzo"You get can get really bogged down with the notion of time. Just recently Lee Smolin published his Time Reborn: From the Crisis in Physics to the Future of the Universe (//http://www.amazon.com/Time-Reborn-Crisis-Physics-Universe/dp/0547511728/ref=sr_1_1?ie=UTF8&qid=1378042883&sr=8-1&keywords=lee+smolin). I must confess that I didn't read it, but this is just to show that physicists are still grappling with the notion of time.
That is the book that was reviewed in the link I provided in the post you were responding to. :)
//http://lareviewofbooks.org/review/quantum-absolutism-lee-smolins-time-reborn/
You may find that review to be informative.
Quote from: "josephpalazzo"Now leaving all philosophical musings aside, in Relativity, time is simply what you would measure on a clock, which is made of matter, with something inside ticking with a regular beat. So when we look at time dilation, it means for a moving observer, his clock would slow down. Ditto for an observer moving into a greater gravitational field. You can debate ad infinitum whether this is real or apparent, but we do know that for communication satellites involved in GPS, their clocks have to take into account these two effects, otherwise they will get out of synchronization withing minutes.
Now in QFT, the notion of time only rears its ugly head when we look at commutation relationship. For instance, the position q and its conjugate momentum p, follows this simple rule:
[x,p] = i ?, where the square brackets means xp - px, the reason being is that these are operators in QM and don't commute.
These commutator relationship must be taken at equal time interval in order not to violate causality. This is taken care by defining 4-vectors x = (t,x,y,y,z) and p = (p[sub:17rgqce0]t[/sub:17rgqce0],p[sub:17rgqce0]x[/sub:17rgqce0],p[sub:17rgqce0]y[/sub:17rgqce0],p[sub:17rgqce0]z[/sub:17rgqce0]). By making everything 4-d tensors, QFT becomes Lorentz invariant, and SR is immediately incorporated into QFT. So a good deal of time in QFT is to make sure that such things as the Lagrangian and the Hamiltonian functions are Lorentz invariant. That way, time is effectively treated on equal footing with space, as Relativity demands.
Thank you for that. It gives me solid concepts to track down and try to understand. Even though I don't grasp anywhere near all the nuances of your response, I do get the gist of it and it does answer the questions I had about the relationship of the notions of time in GR and QM and how time can be treated consistently in forming a union of the two theories.
QuoteNow leaving all philosophical musings aside, in Relativity, time is simply what you would measure on a clock, which is made of matter, with something inside ticking with a regular beat. So when we look at time dilation, it means for a moving observer, his clock would slow down. Ditto for an observer moving into a greater gravitational field. You can debate ad infinitum whether this is real or apparent, but we do know that for communication satellites involved in GPS, their clocks have to take into account these two effects, otherwise they will get out of synchronization withing minutes.
Wrong! And it's not up to debate and isn't a philosophical question. In the theory of relativity, time dilation is an actual difference of elapsed time between two events as measured by observers either moving relative to each other or differently situated from gravitational masses.
QuoteAn accurate clock at rest with respect to one observer may be measured to tick at a different rate when compared to a second observer's own equally accurate clocks. This effect arises neither from technical aspects of the clocks nor from the fact that signals need time to propagate, but from the nature of spacetime itself.
From the local frame of reference, relatively accelerated clocks move more slowly.
When two observers are in relative uniform motion and uninfluenced by any gravitational mass, the point of view of each will be that the other's (moving) clock is ticking at a slower rate than the local clock. The faster the relative velocity, the greater the magnitude of time dilation. This case is sometimes called special relativistic time dilation.
For instance, two rocket ships (A and B) speeding past one another in space would experience time dilation. If they somehow had a clear view into each other's ships, each crew would see the others' clocks and movement as going too slowly. That is, inside the frame of reference of Ship A, everything is moving normally, but everything over on Ship B appears to be moving more slowly (and vice versa).
From a local perspective, time registered by clocks that are at rest with respect to the local frame of reference (and far from any gravitational mass) always appears to pass at the same rate. In other words, if a new ship, Ship C, travels alongside Ship A, it is "at rest" relative to Ship A. From the point of view of Ship A, new Ship C's time would appear normal too.
A question arises: If Ship A and Ship B both think each other's time is moving slower, who will have aged more if they decided to meet up? With a more sophisticated understanding of relative velocity time dilation, this seeming twin paradox turns out not to be a paradox at all (the resolution of the paradox involves a jump in time, as a result of the accelerated (general relativity) observer turning around). Similarly, understanding the twin paradox would help explain why astronauts on the ISS age more slowly (e.g. 0.007 seconds behind for every 6 months) even though they are experiencing relative velocity time dilation.
Solitary
Quote from: "entropy"Thank you for that. It gives me solid concepts to track down and try to understand. Even though I don't grasp anywhere near all the nuances of your response, I do get the gist of it and it does answer the questions I had about the relationship of the notions of time in GR and QM and how time can be treated consistently in forming a union of the two theories.
Not too long ago there was a trend in physics to try writing all the laws of physics independent of time. Nowadays, I don't hear this call, and I don't know if this is good or bad. Is time fundamental or emergent as some are claiming? If you're interested in that, here's one place to get the gist of it: http://fqxi.org/data/forum-attachments/ ... omenon.pdf (http://fqxi.org/data/forum-attachments/Time_as_an_Emergent_Phenomenon.pdf)
Quote from: "Solitary"Quote from: "josephpalazzo"Now leaving all philosophical musings aside, in Relativity, time is simply what you would measure on a clock, which is made of matter, with something inside ticking with a regular beat. So when we look at time dilation, it means for a moving observer, his clock would slow down. Ditto for an observer moving into a greater gravitational field. You can debate ad infinitum whether this is real or apparent, but we do know that for communication satellites involved in GPS, their clocks have to take into account these two effects, otherwise they will get out of synchronization withing minutes.
Wrong! And it's not up to debate and isn't a philosophical question. In the theory of relativity, time dilation is an actual difference of elapsed time between two events as measured by observers either moving relative to each other or differently situated from gravitational masses.
Solitary
Anyone with reading skills would know that these two underlined statements mean the same thing. This is another occasion where you show that you are an intellectual fraud.
Quote from: "josephpalazzo"Not too long ago there was a trend in physics to try writing all the laws of physics independent of time. Nowadays, I don't hear this call, and I don't know if this is good or bad. Is time fundamental or emergent as some are claiming? If you're interested in that, here's one place to get the gist of it: http://fqxi.org/data/forum-attachments/ ... omenon.pdf (http://fqxi.org/data/forum-attachments/Time_as_an_Emergent_Phenomenon.pdf)
Thanks for the link to the PDF! It was - and will continue to be - a fascinating read. I say "will continue to be" because I've been reading it in skips and jumps over involved terminology that I'm not familiar with yet to get that gisty satisfaction and I'll be rereading it multiple times I'm sure. The creativity of postulating an expanding fourth dimension is especially laudable because it appears to be consistent with so many recognized deep and complex empirical patterns (quantum mechanics, relativity, entropy, etc.). The implications are really interesting. This implication really struck me:
QuoteThe Causal Arrow of Time: The causal and psychological arrows of time are related to the capability of our minds to record events, as well as imagine future events, based on the cause and effect logic learned via our empirical existence. However, neither the past nor the future exist out there. There is but one present, though observers may disagree on its nature, due to the inextricable, tautological relationship between measurement and light, light and time, and time and measurement.
This is contrasted with the notion of time
as the fourth dimension (that the paper discusses earlier) which implies that there is a "completed" block of all temporal events. Thinking about that notion always gives me a creepy feeling. I keep envisioning myself as a consciousness that is moving through a block of "pre-done" events. What I experience may be new to me, but the newness is just perception. It just psychologically feels like in such a universe there isn't
really anything new. It's all "pre"-determined. I'd be like a conscious robot only aware of moving through a predestined set of events. I suppose one could take joy in having consciousness because an aware robot following its program is more than an unaware robot following its program. That just doesn't feel particularly gratifying to me, though.
This paper implies that consciousness could be surfing an ephemeral "moment of now" wave of an expanding dimension. If quantum indeterminacy is real and not just a limitation of knowledge, then the wave our consciousness is riding is one where events unfold in regular, but not totally predictable ways. Mixing metaphors, there are wildcards in the deck with which the game of physical events is played. I'm not sure that being a surfer riding a wave that has some inherent unpredictability is "better" if I don't have the ability to will things to be a certain way other than they would otherwise be, but psychologically it still feels better to think of being a surfer riding a somewhat unpredictable wave - even if I'm
not really in control of anything - than a robot following a program that cannot be other than what it is.
Dammit Joe, you used the word 'tensors'. GTFO! :P
Quote from: "GurrenLagann"Dammit Joe, you used the word 'tensors'. GTFO! :P
Perhaps you won't believe me but tensors are not dangerous.
Proof: For any object that transforms from one coordinate system (x) to a different coordinate system (x'), a tensor is one that follows this rule ( tensor with one index=vector):
V[sup:19u6z6vy]a'[/sup:19u6z6vy] = {?x[sup:19u6z6vy]a'[/sup:19u6z6vy]/?x[sup:19u6z6vy]b[/sup:19u6z6vy]} V[sup:19u6z6vy]b[/sup:19u6z6vy].
See, it didn't kill anyone.
QED
:-D
Question:
It is known that the 100s of particles are all made from how many fundamental particles?
Solitary