Author Topic: What's So Special About Special Relativity?  (Read 3993 times)

Re: What's So Special About Special Relativity?
« Reply #15 on: August 31, 2013, 06:09:26 PM »
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:

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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 You are not allowed to view links. Register or Login, 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.

Offline entropy

Re: What's So Special About Special Relativity?
« Reply #16 on: August 31, 2013, 09:22:41 PM »
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 You are not allowed to view links. Register or Login, 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:

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Offline Solitary

Re: What's So Special About Special Relativity?
« Reply #17 on: August 31, 2013, 11:31:42 PM »
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



Quote
Black 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.
There is nothing more frightful than ignorance in action.

Offline entropy

Re: What's So Special About Special Relativity?
« Reply #18 on: September 01, 2013, 08:32:03 AM »
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.

Offline Solitary

Re: What's So Special About Special Relativity?
« Reply #19 on: September 01, 2013, 09:25:05 AM »
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.
There is nothing more frightful than ignorance in action.

Re: What's So Special About Special Relativity?
« Reply #20 on: September 01, 2013, 10:02:26 AM »
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 You are not allowed to view links. Register or Login, 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:

You are not allowed to view links. Register or Login

You get can get really bogged down with the notion of time. Just recently Lee Smolin published his You are not allowed to view links. Register or Login. 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.

Offline entropy

Re: What's So Special About Special Relativity?
« Reply #21 on: September 01, 2013, 12:21:01 PM »
Quote from: "Solitary"

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.

Offline entropy

Re: What's So Special About Special Relativity?
« Reply #22 on: September 01, 2013, 12:30:47 PM »
Quote from: "josephpalazzo"

You get can get really bogged down with the notion of time. Just recently Lee Smolin published his You are not allowed to view links. Register or Login. 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. :)

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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.

Offline Solitary

Re: What's So Special About Special Relativity?
« Reply #23 on: September 01, 2013, 01:10:05 PM »
Quote
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.

Quote
An 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
There is nothing more frightful than ignorance in action.

Re: What's So Special About Special Relativity?
« Reply #24 on: September 01, 2013, 03:55:35 PM »
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: You are not allowed to view links. Register or Login

Re: What's So Special About Special Relativity?
« Reply #25 on: September 01, 2013, 10:33:06 PM »
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.

Offline entropy

Re: What's So Special About Special Relativity?
« Reply #26 on: September 02, 2013, 12:20:17 PM »
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: You are not allowed to view links. Register or Login


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:

Quote
The 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.
« Last Edit: September 02, 2013, 12:37:29 PM by entropy »

Re: What's So Special About Special Relativity?
« Reply #27 on: September 02, 2013, 12:32:40 PM »
Dammit Joe, you used the word 'tensors'. GTFO!  :P
Which means that to me the offer of certainty, the offer of complete security, the offer of an impermeable faith that can\'t give way, is the offer of something not worth having.
[...]
Take the risk of thinking for yourself. Much more happiness, truth, beauty & wisdom, will come to you that way.
-Christopher Hitchens

Re: What's So Special About Special Relativity?
« Reply #28 on: September 02, 2013, 01:32:57 PM »
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

Offline Solitary

Re: What's So Special About Special Relativity?
« Reply #29 on: September 02, 2013, 01:35:24 PM »
Question:

It is known that the 100s of particles are all made from how many fundamental particles?

Solitary
There is nothing more frightful than ignorance in action.

 

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