Will people be able to travel back into the past consistently without encountering the well-known paradoxes of time travel? Apparently science fiction writers can now be inspired by Lloyd's new theory and write about time travel through quantum teleportation and post-selection.
Dr. Gali Weinstein
General relativity theoretically allows the existence of closed time loops (CTC). These are trajectories in space-time - a trajectory of a particle moving towards and returning to the point from which it left - and therefore it is a closed loop. Some physicists believe that such loops exist in exotic regions where space-time is as warped and different as in the depths of black holes. The possibility of the existence of such loops first came up in 1949 with the proposal of Kurt Gedel, who discovered a solution to Einstein's field equations from general relativity made possible by CTC. Such loops allow the traveler who follows them to come into contact with his former self. It is a trip to the past that changes the past and causes the famous grandfather paradox: we can perform some action in the past - intentionally or unintentionally - thereby changing history or making our future not exist.
But these time-like loops are not the only possible mechanism for returning to the past. Quantum mechanics may allow time travel into the past even in the absence of CTC relativity in the geometry of space-time.
Quantum mechanics provides possibilities for time travel even in the absence of CTC in the geometry of space-time. One of the well-known versions of time travel was described in Feynman's Nobel lecture and is called John Wheeler's telephone. Feynman says that he received a phone call at the Princeton School of Advanced Studies from Professor Wheeler, in which he said: "Feynman, I know why all electrons have the same charge and the same mass." Feynman asked why. Wheeler replied: "Because they are all the same electron!" Then he explained on the phone, "Let's say that the world lines, which we usually think of as moving forward in time and space - instead of just moving up in time, they are in a huge loop, and then, when we cross the loop in a plane that corresponds to fixed time, we see many, many world lines And those represent electrons, except for one thing. If in one section it is the world line of an ordinary electron, in the section where it repeats itself and it has returned from the future to the past, we have the wrong sign for the self-time - for the self-velocities - and this is equivalent to changing the sign of the charge, so this part of the orbit will act like a positron." And so Wheeler's phone means that an electron is a positron moving backwards in time.
David Deutsch of the University of Oxford proposed CTC in quantum theory to solve some paradoxes of time travel. Deutsch thought about quantum computing and therefore about the grandfather paradox in the context of quantum computers. Let's say a quantum particle has states 0 or 1. It moves on a CTC and then it interacts with some particle so that the 0 becomes a 1 and the 1 becomes a 0. Such a particle represents a grandfather paradox. According to Deutsch a person can remember that he killed his grandfather without ever having committed this terrible crime. It prevents the change of the past and the erasure of its existence. How?
Deutsch makes this suggestion in line with Hugh Ebert's interpretation of the multiple worlds. If we ignore the quantum formalism and speak in ordinary language then according to Ebert's interpretation we are talking about the existence of different universes that exist at the same time. Frank Tipler (of Tulane University in New Orleans) claims that the parallel worlds interpretation restores determinism to quantum mechanics. For example Heisenberg's uncertainty relations according to which it is not possible to measure with infinite precision the position of the particle and its momentum at the same time. According to Ebert's interpretation, the other worlds are in interaction with our world and therefore if we try to measure the position of the particle, the interaction of the particle with its counterpart in the other universes will cause its momentum to be very large. Therefore, if you add the interpretation of the parallel worlds, Albert Einstein's famous saying becomes valid: "God does not play with dice"
According to Deutsch we focus on the evolution of the particle around CTC according to Ebert's interpretation when we are given a collection of values or worlds. Let's say a traveler goes back in time and meets himself. According to Deutsch, he is found and not found at the same time. Because there is a cluster of worlds: in half of the worlds he meets himself and can change the past and in the other worlds he does not meet himself. In the worlds where he doesn't meet himself he again goes back in time and then in half of the worlds he meets himself and God forbid comes back... what do you think? This is compared to the collapse where the time traveler has only one option, just like classic time travel.
Deutsch claims that in the state of collapse quantum mechanics remains mysterious and paradoxical. whereas in Ebert's interpretation it is not so. In the universes where the encounter takes place, the viewer appears from nowhere (another location) and the final state in each such universe is that there are two versions of the viewer, with two ages: when the older viewer began his life in a universe where the encounter did not occur. In universes where the encounter did not occur, the viewer enters the area and disappears into nowhere (another universe). In the final state in each of these universes the observer is not found, when he travels to the universe where the encounter took place. All of Ebert's worlds are related to some large sheet whose geometry does not make up space-time in the usual sense of the word.
Seth Lloyd of MIT offers a different solution. He suggests that CTCs from general relativity are just one possible mechanism for traveling backwards in time. Lloyd defines the CTC as a communication channel from the future to the past. Hence, he can use the well-known quantum communication channel called teleportation: the perfect transition of a quantum state between two entities (usually called Alice and Bob), using a common entanglement mode: quantum entanglement - two identical particles in different locations are connected in such a way that when we change the state of one particle, the other particle immediately changes in the same way, no matter how far it is from the first particle. This interweaving is combined with quantum measurement and classical communication on Bob's part and is what allows quantum states to be sent between the sender and the receiver.
Various researchers have shown that quantum teleportation can lead to time travel (quantum entanglement and teleportation). Just as quantum mechanics allows teleportation in space, it also does not rule out teleportation in time. The quantum entanglement works both in space and time (space-time). Researchers have suggested a time warp. If we change the state of the particle today, this can change the state of the same particle tomorrow, even if the particle does not exist between today and tomorrow. The strangest thing about teleportation is that it happens instantly, meaning as soon as the particle disappeared yesterday it will appear tomorrow. Makes sense?!? Therefore entangled quantum particles are able to move into the future without actually being present during the time between now and the future. Let's say we want to teleport a time traveler from one place to another. We create a twisted pair A and B and place them one in A and the other in B. In fact a time traveler cannot travel during this period and only quantum information that completely describes the traveler passes between the stations. The information moves from A towards B, so the measurements at A started the journey. But since the teleportation happens instantaneously it can be said in the same way that the measurement at point B caused the journey. So who provoked whom in this move?
This question led Lloyd to investigate a version of CTC based on a combination of quantum teleportation and postselection. Received as a result of time travel called post-selected time travel. This combination leads to a quantum channel to the past that also provides a consistent solution to the grandfather paradox.
The post selection or the late selection works in the following way: we are given a large number of bits from which we want to assemble significant information. The question arises which combination of bits will give information that is meaningful? The most efficient way to solve the problem is to try every combination of bits until we find the combination that works. But this is a very tedious move. The late choice solves the problem as follows: different combinations are tried randomly and then a choice is made whose condition is that the answer must be a correct answer. In this way, the wrong answers are automatically ignored. In quantum computing: means allowing the quantum computer to choose certain outcomes and not others.
We need to look for and select events where certain combinations of bits lead to certain information because we identify combinations that occurred after the information in question was assembled in post-selection. That is, post-selection means that a trait is selected after the main part of the experiment has actually already ended. A well-known example: a photon can behave like a particle or a wave (particle-wave duality). The way it behaves depends on the measuring device. The two aspects, particle or wave, being incompatible, are never observed at the same time. This is the complementarity in quantum mechanics, the Copenhagen principle. To bridge the predictions of quantum mechanics and common sense, it was proposed that the quantum particles know in advance through hidden variables which experiment will be performed on them. According to this they can decide which behavior to reveal to us. This idea was disproved by Wheeler in the "late choice" experiment.
Wheeler performed a version of the double slit experiment using a Mach-Zehnder interferometer and classical control of the beam splitters (late choice of whether to close or open the interferometer). The viewer chooses whether to check the wave or particle nature of the photon after it has already passed through the slits by controlling the beam splitter. Therefore the particle cannot know in advance through hidden variables the type of experiment that will be performed. Wheeler's experiment was performed and the quantum predictions were confirmed. Recently, a quantum delayed selection experiment was proposed using a quantum beam splitter in the state of superposition of nonexistent and the interferometer in the superposition of open-closed at the same time, so it can measure the particle and wave behavior of the photon at the same time. The photon is therefore forced to be in a state of superposition of a particle and a wave at the same time. Then the photon can be detected before choosing whether the interferometer is open or closed. This means that it is possible to choose whether the photon behaves like a particle or a wave after it is detected. Therefore, the quantum control makes it possible to explore a field that cannot be explored classically.
Lloyd says this can be explained by the famous Schrödinger's cat thought experiment: long after Schrödinger's cat is supposedly killed or not, the viewer can choose to determine whether it is dead or alive or to determine whether it is dead and alive.
Will people be able to travel back into the past consistently without encountering the well-known paradoxes of time travel? Apparently science fiction writers can now be inspired by Lloyd's new theory and write about time travel through quantum teleportation and post-selection. How does Lloyd's mechanism work?
Let's say there is a passenger moving on CTC - he moves back and forth in time. The interlacing is between the forward and backward moving parts of the loop. Instead of entwining two photons as during normal quantum teleportation, Lloyd and Ephraim Steinberg entwined two properties of one photon: the photon's polarization (which represents the photon's present) and its trajectory (which represents its past). Then they inserted a wave plate that could change or not the polarization of the photon. Since the photon's polarization and trajectory are intertwined, the wave plate affects the trajectory, i.e. the past. This move leads to the wave plate working whenever the teleportation fails (meaning the grandfather could be killed whenever time travel to the past was not possible) and the wave plate not working whenever the teleportation succeeds (meaning the grandfather could not be killed whenever it was possible to travel back to the past ).
Under these conditions time travel can only occur in a consistent and non-paradoxical way on post-selection time-like loops. These provide a quantum time machine that avoids the grandfather paradox. Entwined states on such loops enable time travel even when CTC time-like loops in space-time (i.e. general relativity) do not exist at all.
Let's say that Alice creates one entangled state at some time and sends Bob what she created. At a later time Bob creates a time machine from a compact wormhole and this allows him to send the entangled particle for some short time back in time. A CTC is created. Bob deterministically chooses to send a chain of bits to Alice in the past. Bob reads a proof of some theorem in the book and sends the proof directly to Alice. Alice as a result publishes the proof in the past book and that is exactly what Bob reads. Where does the proof come from?…
Alice can use the information that Bob sends back to her in time to write a sentence in the book. In Alice's future, Bob uses the same book where Alice wrote the sentence to decide what information to send her back in time so Alice learned the sentence from Bob and Bob learned it from Alice.
Lloyd claims that when you look at the paradox in depth you see that CTC and post selection intervene and prevent the paradox from happening. Bob chooses the data and he writes the proof so he is the author of the proof. Similarly if Alice is aware of Bob's choices, she can write the sentence when she chooses the initial state and then she is the author of the sentence in the past book. This is how you can distinguish the author in the future from the author in the past.
Lloyd says his mechanism for time travel is a good fit for Wheeler's phone because it can be applied to the creation and launch of quantum entangled particle-antiparticle pairs. Quantum particles such as photons and electrons are not bound by time pressure. The quantum state that describes them evolves both forward and backward in time. In fact, it can be thought that there is apparently no causality in quantum mechanics and that what happens in the future can affect the past. As we recall, Wheeler showed in the late selection experiment that an unobserved photon passes through two slits simultaneously and can still be affected by a late measurement that occurs after the apparent experiment has ended.
Time travel to the past in the absence of general relativity closed time-like loops in the formalism that Lloyd proposes can be thought of as a kind of quantum tunneling backwards in time, which can also occur in the absence of a classical route from the future to the past.
Virtually every theory of quantum time travel yields strange results, which are both illogical and pathological. Hence the researchers argue among themselves about the different models.
Charles Bennett raised an objection to Lloyd's model. Although the grandfather paradox will not occur, too many possible but improbable events will occur: for example, let's say there is a manufacturer of rifle bullets. He would be more inclined to produce defective rifle bullets if that bullet was going to be used by a time traveler to kill his grandfather, or his rifle would not be able to shoot at grandfather, or some quantum fluctuation would cause the rifle to misfire and shoot in a different direction rather than at grandfather at the last moment; And it is unlikely that a manufacturer of rifle bullets would have a greater tendency to make defective rifle bullets. This is a distorted probability that is very close to the paradox that we want to avoid. Daniel Gutesman asks: What is the difference between the paradox we want to prevent and this distorted probability? When you change the physics in this way, strange things happen and this is inevitable since we are dealing with CTC and time travel.
links
http://physics.aps.org/story/v27/st5
http://www.technologyreview.com/view/419893/quantum-time-machine-solves-grandfather-paradox/
http://www.popsci.com/science/article/2010-07/quantum-time-machine-lets-you-travel-past-without-fear-grandfather-paradox
http://www.newscientist.com/article/dn22453-entangle-schrodingers-cat-to-up-its-quantum-weirdness.html?cmpid=RSS%7CNSNS%7C2012-GLOBAL%7Conline-news
http://www.youtube.com/watch?v=CpADep0d2Tc
97 תגובות
Raphael,
In the comments at the beginning of the discussion I wrote explicitly (for example in the response from May 17 that starts with "again, I...") that the compactification of 6 out of 10 dimensions is just one of the ways to explain how it is possible that we only notice 4 dimensions if the universe is 10 dimensional according to string theory . There are other explanations that include large dimensions, but they are: a. more complicated.
B. are more constrained by observations (neither option has been experimentally disproved and of course none has been verified by strong evidence, but large dimensions are currently more constrained).
third. less popular among the scientific community.
For these reasons, I concentrated my explanations on compact dimensions although throughout the discussion I did not say that this was the only option.
My comments have been waiting for over 12 hours in quarantine.
I will try to write again without stepping on the blocking robot mines.
Look for a video called Lawrence Krauss and Brian Greene talk String Theory
At minute 40, a possibility is raised that the additional dimensions are not compact but enormous in size.
I got stuck again. we will wait
Well, I sent a reply containing a link and got stuck in the basements. Here it is again without the link, hopefully this time it will go through:
I recommend listening to this conversation between Brian Greene and Lawrence Krauss at minute 40:00
Brian Green talks about the possibility that the extra dimensions are not compact but the opposite.
Search on YouTube: Lawrence Krauss and Brian Greene talk String Theory
I recommend listening to this conversation between Brian Greene and Lawrence Krauss at minute 40:00
Brian Green talks about the possibility that the extra dimensions are not compact but the opposite.
https://www.youtube.com/watch?v=3kn5XKKZEFU
forgiveness? God forbid, babble to your heart's content, what do I care? If you have questions about the physics or mathematics of the dimensions of space, I'd be happy to try to help, but like I said, it requires at least a common language, which I don't think we have at the moment.
WD
I did mean the case where we live in a three-dimensional world but we can only distinguish two dimensions. The third dimension exists in a big way but we don't notice it not because it is compact but because we don't have the measuring tool that can notice it. I have not yet seen the link you sent. I hope not to disappoint you and distort it according to my distorted religious view as much as I can.
post Scriptum. Sorry Malbanzo hope you don't mind me continuing to ramble a bit with WD
Raphael
'Suppose we live in a world with only 2 dimensions...'
Since space is two-dimensional, three-dimensional objects simply do not exist in it. It seems to me that you are confused by saying let's say we are only able to distinguish two dimensions.
If the space is more than two-dimensional but we can only distinguish two dimensions, three-dimensional objects can still be distinguished, but they may "behave" in a way that may seem a little strange to us.
I will probably regret linking you to this because you will find some way to twist it into some kind of crooked religious concept but there is a movie that deals with it
https://www.youtube.com/watch?v=Mfglluny8Z0
Raphael,
If you live in a two-dimensional world then according to the definition of dimension and the definition of space, everything that is in space (a vector or a set of vectors, for example a subspace) is at most two-dimensional (otherwise your space is not two-dimensional by definition). So you won't be able to distinguish XNUMXD objects because they don't exist. What you said is nonsense again. I'm sorry, I was really happy to talk to you and I'm glad that there are people who are interested, but if you write that in a two-dimensional world three-dimensional objects cannot be distinguished, it's a sign that you really don't understand what a vector space is or what a dimension is.
The term "compact dimension" would work for you if you studied mathematics. You can't expect to know things you've never learned, it's not something to be offended or ashamed of. I'm not trying to scold you or insult you, but I repeat that there is a huge gap between your questions and the level of knowledge required to understand the answers I gave you, and the level of knowledge you demonstrate on the subject. I would be happy to try to help but I don't think I can explain any more clearly than I did and if you insist that there is a difference dimension between dimension 7 and dimension 2, or there is a problem with the definition of a compact dimension, then we don't have a common language and I can't help you. The questions you ask are mathematical questions in the fields of geometry and topology and to answer them you need at least a basic understanding of the concepts in these fields. In particular, an understanding of what is a vector space, what is a basis, what is a dimension, etc.
Although I don't have the knowledge and language of a scientist, I think I know what I'm talking about.
I will give the following example:
Suppose we live in a world with only 2 dimensions.
We can distinguish entities (or whatever you call them) with one dimension as well as entities with zero dimensions
But we cannot distinguish 3-dimensional entities.
In this case is it said that we do not notice the third dimension because it is small/compact etc.?
of course not.
That's why this term "compact" dimension doesn't work for me.
Raphael
It's not that a line has one dimension, just one dimension is enough to describe a straight line
It's not that a square has two dimensions, just two dimensions are enough to describe a square
It's not that the cube has 3 dimensions, just three dimensions are enough to describe a cube
A straight line can still exist in a space with more than one dimension, a square can still exist in a space with more than two dimensions, and a cube can still exist in a space with more than three dimensions
You seem to be very confused about the concepts of spatial dimension and how they work.
I will ask you a question that I hope will help you understand the problem. When you look at the three-dimensional space you see around you, how do you divide the axes of the dimensions? How do you know which direction is the direction of which dimension?
Albanzo
Thanks! The question you asked at the end is intriguing, and I want to think about it. By reduction I meant the concept of projection, for example - projecting a spherical surface onto a plane, as in creating a geographic map. Indeed, the correct word in this context is really "throw"...
Miracles,
First, what is meant by 3D Euclidean space? I assume you mean R^3. Second, what is meant by "reduce"? If the intention is to find a subspace of R^3 that is a torus, then obviously it is. Go to the mafia, look at a donut... here is a subspace of R^XNUMX which is a torus. 🙂
The idea of compactification is that you look at a particular case of string theory where 6 of the 10 dimensions behave in a certain way. It is not an R^10 space that something is done to make it four dimensional, but to begin with we are looking at a space in which 6 out of the 10 dimensions are hard to distinguish. If that's what you meant, then your analogy is not good because you started with R^3, which is a space where all dimensions are clear. A better analogy would be to look at another three-dimensional space - for example T^2 XS^1 where T^2 is a torus and S^1 is a circle, and ask if it is possible to create a situation where we don't notice a circle and think we live on a torus.
Raphael,
I'm sorry, but we're going in circles. There is no such thing as the "first dimension", the "third dimension" or the "thousandth dimension". It just doesn't exist. Dimensions of a space are, for that matter, members of the base group, and it is in particular not an ordered group. You can go back to the example of the frog - there are two dimensions, in one the frog notices and in the other he doesn't. Is the one she notices the first or the second? A mathematically meaningless question. It seems to me that if you want to ask more questions you must at least understand what a space is and what a dimension is.
Not exact.
A line has one dimension
A square has two dimensions
The cube has 3 dimensions
Raphael,
The dimensions do not have a serial number.
Think of a round sheet of paper with a diameter of 30 cm and a thickness of 0.1 mm. The page is three-dimensional: it has length, width, and thickness. But it is meaningless to ask whether the width is the first dimension or perhaps the length or perhaps the thickness. The only thing that can be said is that there are 2 dimensions measuring 30 cm, and another one measuring 0.1 mm. Moreover, the "length" and "width" can be chosen however you like, the main thing is that they be vertical (perhaps this is not mandatory either..)
The same goes for string theory. There are the usual 3 dimensions that cannot be distinguished between them. There is one more dimension of time. And there are another 7 (?) dimensions that we do not know from everyday life today (I am not knowledgeable enough to know if there is a difference between them).
albentezo,
To be sure I understand.
In the space of 10 dimensions of string theory, what are the three dimensions we notice?
Do we notice dimensions 1,2,3, 4, 10 and dimensions XNUMX-XNUMX we do not notice,
Or we notice dimensions 8,9,10 and dimensions 1-7 we don't notice (this is what I understood until now)
Or maybe we notice dimensions 5,6,7 or 2,4,6 or something else?
Albanzo
Thanks! Yes, I meant that there is no "edge" to a certain dimension.
You mentioned Taurus. Is it possible to reduce from a XNUMXD Euclidean space to a torus, or a sphere or a cylinder? Or only for the Euclidean plane?
Miracles,
Definitely yes. In fact, the compactification is usually performed with periodic language conditions (for example, if one dimension is added, then it is taken as a circle and in the case of the frog this will turn the space in front of the area of a cylinder). I don't know if the word "circular" is correct here because if you do a compactification to more than one dimension you don't have to do it symmetrically (for example, it can be done on a torus), but if you mean "periodic" then the answer is definitely yes.
Raphael,
Clarification regarding point number 1: This is true in our case, not in general. It is possible to mathematically write a space with d dimensions and a space with d+1 dimensions (or even more), in which there would be no possible way to nest the "small" space inside the "large" one (to nest is the mathematical term that means to insert one space inside the other). In our case, we are not looking at the general case, but at a more specific case - where we know for sure that the small (four-dimensional) space goes inside the large (ten-dimensional) space - simply because otherwise we would not see the four-dimensional space when we look around . In answer to your question, in this specific case then the small space can be nested an infinite number of times inside the large one and this is due to the continuity of the additional dimension (which guarantees that there are an infinite number of points on it, each of which is a metric of the small space. Even if it were discrete but infinite in size this would still be true).
Raphael,
1. True, if the added dimension is continuous then in particular the d-dimensional space can be inhabited an infinite number of times within the d+1-dimensional space. I don't understand what you are trying to say here. I referred to your comments about the dimensions being "before" each other or "after" each other, that a dimension fits inside a point, etc. If you have more questions related to placing a small space within a larger space, ask and I will try to answer.
2. Did someone say somewhere that what the frog notices changes the facts? According to string theory, we live in a ten-dimensional world but only perceive four, just as the frog lives in two-dimensional space but only perceives one. As I wrote to you in previous responses - string theory can only be mathematically consistent if our universe has ten dimensions. If this is true, the question arises, why do we *seem* to live in a four-dimensional world? Why do we only notice four out of ten? So like I said, the most common, simplest and most accepted solution is that six of the ten dimensions are compact and small and therefore we don't notice them even though they exist. The facts are that there are ten dimensions (this is according to string theory, which of course has not yet been adequately tested experimentally. I'm not trying to say that we know for sure that our universe has ten dimensions, just explaining the structure of string theory).
Whether the frog notices or not does not change the facts.
Albantezo, is it true:
In an N+1 dimensional space there are infinitely many N dimensional spaces.
A lot of thread, and there is no thread...
By the way, there are rumors that God is pulling the strings, up there….
Albanzo
Can the extra dimension also be round? That is, the strip you described, could be a cylinder with a circumference of 1 cm?
Raphael,
You made a pretty serious salad here, and without insulting, it seems to me that most of your confusion stems from the fact that you invent concepts and ideas for yourself that have no grip on reality. For example, it is quite clear that you use it incorrectly and do not differentiate between dimension and space, things that in mathematics are completely separate. Again, my goal is not to offend, but only to explain to you why I cannot answer the things you asked - because from a scientific point of view, they are nonsense. I will try to explain the principle again in a simple way through an example.
Imagine a two-dimensional space, which includes one axis (hereafter x) which is infinite (say from minus infinity to infinity) and another axis (hereafter y) perpendicular to x which is compact and 0 cm long (say from 1 to 0.99999). The whole space looks like a narrow and endless strip, a sort of endless strip. Now imagine a frog walking on the leash. The width of the frog is XNUMX cm, so it cannot really move on the y axis. As far as she knows, the space she lives in is a one-dimensional space in which you can only move forward and backward along the x-axis (in both directions you can move as much as you want because the x-axis is infinite). She does not notice the extra dimension at all because she cannot move in it due to its size. Now note that the dimension hidden from the frog's eyes (y-axis) does not "infinitely enter a point" and neither do shoes. He is neither "before" any other dimension nor "after", he is not at the beginning, middle or end. is non-negative (which I still haven't figured out what that means, assuming you don't mean pseudo-Riemannian sheets). This is another dimension that is compact and because of its size (relative to the frog), the frog is unable to notice it, at least until you build a sufficiently advanced particle accelerator.
Sorry, I can't explain it in more detail than I have already explained several times.
Second, why does it matter and how does it lead you to the fact that there must be a space or dimension or something that enters infinitely many times at a point.
What part two?
And what about the second part?
You yourself wrote that in an N+1 dimensional space there are an infinite number of N dimensional spaces.
All six additional dimensions in string theory are smaller than the smallest dimension we notice (dimension zero, i.e. a point).
So what will be the size of the smaller dimension?
'Therefore if the extra dimensions are smaller than our dimensions then they must be infinitely smaller.'
Why must they be infinitely smaller than them?
Second, why does it matter and how does it lead you to the fact that there must be a space or dimension or something that enters infinitely many times at a point.
Right. In an N+1 dimensional space there are infinitely many N dimensional spaces.
And so if the extra dimensions are smaller than our dimensions then they must be infinitely smaller than them.
The smallest entity (perhaps there is a more appropriate word) that we know is a point with 0 dimensions, so I assume that the next dimension in the line should enter infinitely many times at this point, and so on up to dimension #10.
Raphael
It seems to me that either you do not fully understand what a dimension is or your explanation does not properly explain your intention.
If you look at a two-dimensional surface (and imagine that it is infinite in every direction). Neither dimension is greater than the other.
Even in your example the dimensions themselves are not greater than each other. But simply, as you said, in an N+1 dimensional space there are an infinite number of N dimensional spaces.
Wow, after a week in the interrogation cellars we were finally released
albentezo,
I re-read your answer again because for a moment it sounded to me like explaining that a person is deaf because he can't hear. After further reading I understand that the principle is a consequence of more fundamental principles of quantum mechanics? What fooled me was the work that it was an actual string. You can say, that is, if we had the technology, we would actually measure a string and not a record of a field or something like that.
On another topic, yahoo referred to an article about an article that sounds very important
https://journals.aps.org/prd/abstract/10.1103/PhysRevD.95.103504
https://www.universetoday.com/135570/new-explanation-dark-energy-tiny-fluctuations-time-space/?ref=yfp
Know?
albentezo,
Rather, I assumed that quantum theory requires the principle, I was simply tempted to think (for a moment) that if there is an actual string in the basis, somehow the uncertainty principle does not exist in the basis and is actually the result of an approximation that we make.
Regarding the inflation debate, it will be interesting to see how it develops
I will try to explain what I mean. Looking at the three dimensions we notice shows that each dimension is infinitely greater than the dimension below it. An infinite number of points enter a line, an infinite number of lines enter a two-dimensional space, an infinite number of two-dimensional spaces enter a three-dimensional space.
If we say that the extra dimensions are larger than our dimensions then I will assume that in a 4-dimensional space infinitely many XNUMX-dimensional spaces like ours will fit, but if we say that the extra dimensions are smaller than ours then I will expect that the next extra dimension will fit infinitely many times within a point and so on.
A one-dimensional space (or two-dimensional or three-dimensional) of one micron is still included in the spaces we know and not beyond them and no matter how small it is.
Again I don't understand. What is a "negative dimension"? I assume you don't mean a dimension with a negative signature (ie, Lorentzian rather than Euclidean). If that's what you mean, then the compact dimensions are Euclidean in principle, but I have a feeling that's not what you're asking.
If our universe has 10 dimensions as predicted by string theory, we need to explain why we only notice four (three spatial and one temporal). The simplest (and most popular) explanation is that six of the ten are compact and very small, so we don't notice them at all. Think for that matter that there was another dimension in our universe but it could only be moved a hundredth of a micron to the right or left. Since it is so small relative to us, we would not notice at all that we can move in this dimension, and as a result we would not notice it at all (just as a dot that is stuck to a sheet of paper and cannot move up or down, but only right-left and forward-backward actually in a two-dimensional world). Of course, this explanation is heuristic and is only a simplified version of the more precise mathematical explanation. There are other ways to explain why we don't notice six of the dozen dimensions of string theory, and these ways can include large dimensions, but they are less simple and less popular.
A point is a zero-dimensional object, but that's not what it's about. It is about how many dimensions the space has in which the point moves. It's hard for me to answer because I really don't understand what you are asking, what is a negative dimension and what is the connection to the points.
Spring,
The debate that is now emerging about inflation requires an article in science that is more in-depth than what is in Vint. possible?
Regarding the dimensions, I meant whether the additional dimensions are larger than our dimensions or smaller than them. But you already answered at the end that they are smaller. Can we say that the extra dimensions are negative because the point we know has zero dimensions....
albentezo,
Thanks, waiting 🙂
Shmulik,
I wrote you a response but for some reason it is on hold. If she is not released soon I will write you another comment.
Shmulik,
I didn't quite understand. Why can't a quantum theorist come up with an explanation for the uncertainty principle? In my opinion, these teachings explain the principle very well. In quantum theories the quantities we measure are not really fundamental properties of reality: particles (or strings) are not characterized by position or momentum but by earlier quantities of which position and momentum are derivatives. As a result, position and momentum are not independent as in classical theories and measuring one affects the other. It's a verbal heuristic explanation but I don't really understand what's unsatisfactory about it (of course it can be made mathematical-rigorous but it seems to me that here and now is not necessarily the place and the time).
I am not an expert on inflation and I have not had the chance to delve into the works of Avi Leib and his colleagues. Yes, I will say that all the times I had the chance to rub shoulders with the subject, I always got the strong impression that this is a well-founded Torah (both theoretically, an aspect I had a little more time to deal with, and observationally, which I had much less time for) and I never came across any significant evidence against it. But the bottom line is that my response won't be worth anything until I actually read the Harvard guys' arguments.
Raphael,
The strings can split and connect but they obey the laws of quantum mechanics and not classical mechanics. Therefore, if the split happens for a short enough time before reconnecting then the length does not have to be preserved. That is, a meter-long string can split into two meter-long strings each, provided that it connects back to the meter-long string quickly enough (or the two new strings are shortened to a length of half a meter each, etc.).
I really don't understand the question about the dimensions. The universe we see around us is three-dimensional. Now take a page - it is two-dimensional. Where are the two dimensions of the page in relation to the three dimensions of space? At the beginning, at the end, in the middle? I don't understand what that means at all. Space has three dimensions, but on the surface of the page one of the three is constant (approximately the page is completely flat). In string theory there are ten dimensions, but six of them are very small (compact) and we don't notice them. Like a creature that clings to the sheet of paper and therefore thinks it lives in a two-dimensional world, even though we notice three.
albentezo,
I have the kind of annoying question that tries to make the world Newtonian again:
You wrote that the string is the most real there is. Wire with length and tension. Why or how does Heisenberg's uncertainty principle emerge from a vibrating string?
I remember you wrote that string theory is quantum theory. This basically means that there is no hope that this Torah will come up with a deep explanation of the principle. Is it so?
And something else you have. Where are you on the inflation debate?
http://www.ynet.co.il/articles/0,7340,L-4962124,00.html
If so, is it correct to say that on the one hand it is possible to split each string into more strings whose length is constantly getting smaller and on the other hand to unite more and more strings into one string whose length is constantly increasing? Or is there an end to the length or length of a string?
Another question - where are the three dimensions of space we know in relation to the ten dimensions of space of string theory? At the beginning, at the end, in the middle?
Yes you can. In fact, in the framework of string theory, the explanation for all processes in nature is by the splitting and unification of strings (strings that are cut in half or strings that are tied together and become one).
"Really a thread". So can it be cut in half?
It is not that the theory does not determine what precedes what. It's that neither of them precedes the other. Maybe you have some familiarity with electric fields and charges - on the one hand an electric charge reacts to the field around it and feels a force as a result of the field, and on the other hand it contributes to it because it itself produces a field. If the charge is small then the field it creates is negligible and it is possible to work in an approximation where the charge feels the force from the external field but does not change it. It's the same thing - the string is both affected by the geometry of the space in which it moves and changes it. At low energies the change it creates is small and can be neglected.
The string is the most real there is. He is really a thread. As I said in a previous comment, he did not put a code to anything, nor an analogy to anything, nor some mysterious or supernatural thing. It is simply a wire with a certain length, and a certain tension. And that he is the "engine" and "cannot be a particle", etc., is just an attempt to impose your ideology on string theory. The string is not a motor. He just made a string. a piece of string. Under the right conditions, this wire looks like an electron to us. Under other conditions, it looks like a photon (which is the electromagnetic force). Under other conditions, it looks like a quark, etc., etc. The different modes of vibration of the string are the different particles we know from nature.
I understand that the theory does not determine what came before what.
Is this string a real thing or is it just an alias for a formula that describes it?
That is, if he is the "engine" of all particles and forces, then he himself cannot be a particle or a force.
The answer is "both". When someone writes string theory, he is actually describing a string that moves in a certain space, and it is necessary to specify in which space it moves (that is, what is the shape, because as we know - what defines a certain space is its geometry, which is mainly the trapezium). On the other hand, the very string affects this space because the string also includes the gravitons - the particles that carry the force of gravity that actually determine what the shape of the space is. That is, when I determined that my string moves in a space of a certain shape, I actually determined a space with a certain configuration of strings. In the approximation of low energies, we will usually treat the space as constant (that is, we will neglect the interaction of the string's movement in the space, the so-called backreaction), but it can certainly be said that what determines the geometry of the space is the collection of strings (and membranes) that are inside it.
The subject is really fascinating. If possible I will ask a few more questions. Does this string depend on space-time (in this case a 10-dimensional space) or does space-time depend on it? That is to say that its vibrations create the space-time.
no God….
...but hey, there is a "string of a certain length with a certain tension".. (this is already more convincing. and even less funny).
If string theory is correct, then all the particles we know are different modes of vibration of the same string. It does mean that all the matter and all the forces in the world derive from one source, but there is no freedom here for a physical interpretation: the source is a string. That is, any mystical/religious/philosophical argument that stems from string theory and the fact that everything in the universe comes from one source has to deal with the fact that this source is a string of a certain length with a certain tension. If it works out for someone with his faith, let him be perfumed. But to me it seems a bit funny to say that God is a shoelace (or alternatively that God created a shoelace and the whole universe is contained within it).
I have no idea how you get to this from string theory, but let's skip the small and unimportant details on the way to what you really want to get to: a physical expression that you can stick the subtraction from infinity theorem to. Well, I'm sorry to tell you, but it's doomed to fail, because this phrase has no meaning. It is about the pasting of several words together that are supposed to create the feeling that there is something deep and meaningful there, but actually when you check the matter for two seconds you find that it is a hash of words empty of content and devoid of any meaning.
I don't understand that much but according to what I read it could be that if the string theory turns out to be correct then the answer is yes.
why do you think so?
Wd
It seems to me that your "no" was too hasty.
No (regarding the last question) (so you can ditch your standard infinity subtraction mysticism attachment)
https://he.wikipedia.org/wiki/%D7%AA%D7%95%D7%A8%D7%AA_%D7%94%D7%A9%D7%93%D7%95%D7%AA_%D7%94%D7%A7%D7%95%D7%95%D7%A0%D7%98%D7%99%D7%AA
Thanks.
That is, that one electron field occupies the entire space and the entire time, past, present, future?
And another question, is the definition of a field correct for an electron type particle only or also for all other types of particles? Or maybe we can even say that there is only one field in the entire universe and the different types of particles that we see are a derivative of that single field?
In modern physics, particles are not fundamental objects but are the way we perceive a certain low energy field. In other words, according to our latest knowledge there are no particles at all in the classical sense, but there are fields and in some places the field behaves as if it were a particle or a collection of particles. In the entire universe there is only one electron field and all the electron "particles" we observe are all derived from that field. In this sense, all electrons in the world are indeed the same electron.
Wheeler replied: "Because they are all the same electron!"
Does anyone know if this theoretical possibility that all the particles in the world (or at least all the electrons in the world) are actually the same particle still exists and has not been scientifically disproved?
A nice but imaginary theory. Can be used as a fine script for a James Cameron movie
Are you also opposed to quantities that are represented (in quantum mechanics) by non-commuting operators because we cannot measure them with perfect precision?
I didn't understand the sentence "sometimes the entropy of a closed system will decrease by a point fluctuation" - in which closed systems in the NMS does the entropy decrease beyond the negligible fluctuations around the maximum value?
If because of the platitudes inherent in the statistical mechanical explanation you refuse to accept the second law as a law of nature - ignore this explanation. The law is true even without it.
The point that since and sometimes entropy of a closed system will decrease in point fluctuation - it is not a "law of nature" (unlike the conservation of momentum or energy for example). Therefore, the programming of something beyond that should not be dismissed as possible (although it is not at all clear that this condition is met for time travel).
extension:
And I still don't understand the objection to distinguishing the entropic arrow of time due to the plaktatios. Are you also opposed to the concept of wavelength because you cannot measure or produce light with perfect accuracy?
excellent. It is clear then that deviations in entropy become negligible when you reach multi-particle systems - this is what I aimed to show.
I think you need to separate the second law of thermodynamics from the statistical explanation given to it. The second law is a law of nature and is axiomatic. It was true even before Boltzmann's explanation. In the big picture - the entropy of the universe increases with the progress of time.
Technion
The example I gave is the so-called Motz Einstein - an example I don't see in the course you presented.
I will demonstrate to you through something that appears in the course summaries:
On page 15 you discuss a spin system.
Consider N spins in a 0 magnetic field (when none of the directions is preferred).
Assume that m spins are directed up and Nm spins are directed down. The entropy is also proportional to the log of N choose m.
Suppose that initially m<
Suppose now that we have reached the state m=N/2 - in this state the entropy is maximum.
The system will not rest, it will continue to change and if we approach it after some time, m will be different from N/2 - and since entropy is the log of N choose m, then in the dry definition the entropy has decreased.
By the way, if you open N choose m around m=N/2, you will find that it is a Gaussian that gets the maximum value at m=N/2 and the typical standard deviation is sqrt(N) - this means that the typical deviation from the condition m=N/2 It is from a square of (sqrt(N- that is, with 10^6 spins, expect that half of them will be up and half will be down, up to 1000 spins here and there.
This means that entropy in the aspect of log multiplicity of states will oscillate up and down in SD of unit (multiple Boltzmann constant) after reaching equilibrium.
This is an insignificant fluctuation at the macroscopic level, but it indicates something fundamental - the second law of thermodynamics is not a fundamental law but a statistical result - therefore to rule out movement in time based on entropy as it is here, is ridiculous - entropy is a well understood mechanism and it does not refer to the question of movement in time at all And certainly not fooling her.
More advanced theories include the concept of entropy and then maybe (and just maybe) there is something to talk about, and still only theories that are not completely clear and do not have the certainty that statistical mechanics has
deer,
I am not clear about the treatment you have described here and I am not familiar with the terminology you used or what your definitions are for energy, particles, deviations, possible states, properties, etc. I don't know how you came to the conclusion that there would be "characteristic deviations" at the rate of 10^3 or what you mean by that, since already from a relatively small number of particles the probability of being in the most probable macroscopic state becomes delta-like and the other macroscopic states are completely improbable.
Could you direct me to the place in this document where the treatment you presented here is supported? http://technion.ac.il/~ronen/lectures/pdf/termostat.pdf
A reference to the literature can also be appropriate.
(By the way, 10^6 particles is nothing. In 1 cm14 of the room you are sitting in, there are about XNUMX orders of magnitude more particles.)
If you look at page 624-626 of the book Fundamentals of Statistical And Thermal Physics by F. Reif, you can see a semi-proof of entropy increasing with time.
It is still not clear - how did you decide that the second law is violated countless times every day without us measuring it.
If I remember correctly, Poincaré proved that cosmic entropy must decrease at some point. This is mainly what depressed and unsettled Boltzmann
However, a question arises here: Can the entropy of a system of the magnitude of Avogadro's number or higher decrease in a period of time of the lifetime of the universe? The answer is apparently negative. According to s. polytechnic.
And another question: if we take into account the time reversal of the laws of mechanics, why doesn't entropy increase even when the arrow of time is reversed? Why does it rise only towards the future? Doesn't this indicate that the universe at the moment of the big bang had low entropy? The answer is apparently positive.
But at the time of the great debate between Poincaré and Boltzmann they still did not know about the bang, and this was not in Boltzmann's favor.
Technion,
I didn't understand at all what I was saying.
Before there was statistical mechanics they knew to say that there is a quantity called entropy, it is not clear why but it always increases. Boltzmann and Co. came and showed that if you look at all the energy as a sufficiently large accumulation of particles, you can understand why this size "always" increases - the system has N possible states and with the highest probability it will be found with certain properties up to a certain deviation and therefore, since the system can change In the end she does find herself in a good approximation of her situation in the most reasonable situation.
This understanding means something significant - entropy does not always increase!!!
Thus a system of 6^10 packets of energy and divided it into two identical boxes - the most likely state is 6^0.5X10 packets of energy in each box - this is the state with the highest entropy and is called S. Wait long enough and you will reach this state. The system will not rest after that and since characteristic deviations will be at the rate of 3^10 energy doses, the entropy will decrease after reaching its maximum rate S!
This is a small and insignificant lesson for everyday life and everything you said is true, but its meaning is that you cannot include the rule of the negative derivative of entropy in the box of fundamental laws of the universe and you cannot rule out the physical feasibility of, say, time travel, based on this law that is violated countless times without You measure it
deer,
A large enough collection of particles is actually any natural system we know (that is, except for an experiment with three electrons in UHV in the laboratory). In the case of sufficiently large systems, the deviations from equilibrium are not only insignificant, but negligible. Statistical mechanics gives a nice explanation for the second law, but before that it was a postulate. Again, almost every book I know refers to it as a fundamental/physical law.
As for time travel, I'm afraid you're wrong. We know that the direction of the time arrow is the direction of entropy growth - the derivative of entropy with respect to time is non-negative.
Technion,
It is quite clear that in a conventional scenario, for a large enough collection of particles it is unlikely that the second law of thermodynamics will be significantly violated - but the fact that it is a statistical law and not a fundamental principle of physics is significant.
Note that my comment came in response to claims that time travel violates the second law of thermodynamics and is therefore impossible. This is not true because if matter and energy can be transferred from the past to the future - it is very possible that the number of states changes so that the entropy decreases - the second law of thermodynamics in the simple formulation of log multiplication of states is a simple and understandable matter and therefore it is also understood when it is violated.
And yet - it is very possible that time travel is impossible for a hundred other reasons.
deer,
Read the definition for "law of nature" - exactly the second law of thermodynamics. This is how it is also called and attributed in the scientific literature.
The probability that the second law will be violated becomes zero for any practical need already from a relatively small number of particles. In practice you will never observe a violation (exclude negligible fluctuations in equilibrium).
zviman,
Conventional statistical mechanics describes the second law of thermodynamics as a static law that results from the behavior of large clusters of particles - which means that there is no obstacle to violating it given the correct mechanism.
It is possible that in more advanced (and uncertain) theories entropy has a greater role, but until then, it is not correct to treat it as such a fundamental law of nature.
A moment of Hebrew:
Entropy - a measure of the degree of disorder in the system.
Anthropy - comes from the Greek word anthropos, man. The anthropic principle is derived from it - relations between man and the world.
Logic puzzle for those interested:
Is it possible to explain the Wheeler experiment without resorting to the worst of all - going back in time and reversing entropy?
Warning: this is alternative physics, but consistent with our knowledge of quantum mechanics.
I wanted to add something about Wheeler's phone. This is a thought experiment and a picturesque name.
According to quantum theory, or rather quantum computing, it is not possible to transfer quantum information over the phone?
Does anyone know why quantum information cannot be transmitted over the phone?
Because according to quantum mechanics if we say Alice has a certain quantum state then if she sends it on the phone to Bob he will be able to make copies of the state and this is forbidden according to quantum theory.
What is allowed is this: if Alice and Bob share some kind of bit in an entangled state (the famous APR experiment), then Alice can send Bob a qubit and this sending is called teleportation.
And such a communication channel is allowed in quantum theory and it is very important to understand.
Emanuel
If humanity has destroyed the world then no one will come from the future to save it....
What does it have to do with the right to choose? What makes you think that there is even such a thing (freedom of choice....)
And regarding parallel universes - the fact that it is unlikely does not make it impossible.
Zvi, the topic of entropy, inability to reverse the direction of the arrow of time and quantum mechanics is a very big topic. It has to do with quantum statistical mechanics. This is not my field and I know quite a bit about it.
The field is also related to classical and quantum information theory (Schnon's definition of information anthropology) and therefore ultimately also to quantum computing. Examples involve quantum particles and they can talk on the Wheeler electron-positron phone... 😉 🙂
Emanuel, David Deutsch (born in our country, in Haifa...) is one of the menaces in Hugh Ebert's multiple worlds theory. Read his book: The Fabric of Reality
He also supports Richard Dawkins and to the best of my recollection he mixes up Ebert and Dawkins…. 🙂
In any case, he has proof of the existence of the multiple worlds. Even in Israel Lev Weidman believes in the interpretation of the multiple worlds. Widman works in Yakir Aharonov's group at Tel Aviv University and they deal with the problems of quantum measurement.
The interpretations of quantum theory and quantum thought experiments are on the border between physics and the philosophy of physics, and that's why I called the article quantum philosophy. Because these are things that are debated. It's not like a quantum experiment that has an agreed upon result. Regarding the interpretations: multiple worlds, discussion of the thought experiments, different explanations for time travel - this is subject to various debates and it is not always possible to verify everything in an experiment, such as the interpretation of the multiple worlds...
Yaron,
If you create a quantum entanglement then in fact a time traveler cannot be launched during this time and only quantum information that completely describes the traveler can be launched.
Regarding the wormhole. The article deals with quantum time travel, i.e. time-like loops even in the absence of such general relativistic loops in the geometry of space-time. That is, you don't need a black hole or warped space-time to travel to the past (assuming of course that you can travel to the past...), but there are other mechanisms that will allow you to do this and they are quantum mechanisms: quantum teleportation in time.
Wormholes are solutions of the field equations of Einstein's theory of relativity and therefore it is a time travel into a relativistic past.
In fact, the thoughts of the researchers that I brought here about time-like loops and a journey into the past in quantum time are intended to develop two lines of thought:
1) There are theoretical problems in quantum computing: quantum computing is being thought about even though quantum computers are still far from being realized: interference in communication channels, quantum cryptography, etc. 2) The researchers strive to formulate a theory of quantum gravity - that is, a theory that will somehow include general relativity and the laws of quantum mechanics.
Sorry, I got Avogadro's number wrong.
Elemental particle teleportation and quantum entanglement are possible. But a person who is composed of 6.24E13 and more elementary particles. How will each and every particle be intertwined while preserving their position and relative function in the body?
The article does not discuss time travel through a wormhole, which is a kind of tunnel where the laws of physics are broken,
and is a shortcut between distant galaxies. That is, a journey not only in space but in time in the same way.
Regarding the possibility of traveling at a speed higher than the speed of light, here is for example the speed of an electron in a metal in centimeters per second, and these are the group speed of the electron wave 0.7C. That is, the group speed of the electron wave (not electromagnetic) is tens of meters higher than the speed of the electron. I would like to hear more about different time travel options like I presented.
The material is interesting but the messy and dry writing makes it unreadable and monotonous.
Too bad.
Before going back to the past, you should (or can) add a spray to the comments of each individual post...
If time travel is possible it means that the direction of entropy can be reversed.
Therefore, in the meantime, time travel is against the laws of physics as we know them.
Anyway, the article reminded me of a genius foreign film
Time crimes - timecrimes
Enjoy
You can travel to the future and that is proven. Satellites, the space station and even airplanes do this every day in a minimal way, but if it is possible to reach a speed close to the speed of light, it will be possible to travel to the near and medium future in a relatively short time.
If time travel is possible, why don't they reach us from the future and prevent humanity from destroying the world?
Time travel is not possible within the physical laws of our world for the simple reason
If it is possible to travel in time to the future or the past, then basically everything is determined and everything is known and we do not have the right to choose
Regarding parallel universes that supposedly solves this paradox
If there are parallel universes then their number should be infinite and the splitting should be every micro micro micro second
In short, this is theoretical mathematics and nothing more