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Fredrik
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:rofl: I didn't notice that signature until now. It made me laugh, so maybe you should have been nominated for the humor award.
Yeah, it's probably not the intended use of the signatures, but this is a very low-budget campaign so I have to use cheap options!PeterDonis said:DaleSpam, no fair electioneering in your sig!
Excellent! You can just put me as a write-inFredrik said::rofl: I didn't notice that signature until now. It made me laugh, so maybe you should have been nominated for the humor award.
DaleSpam said:Yeah, it's probably not the intended use of the signatures, but this is a very low-budget campaign so I have to use cheap options!
The PF Sitting (it's easier to sit than stand when typing on a computer) Yearly Committee on Fair and Open Awards (PSYCo FOA1) has met and has deemed that such electioneering violates neither the rules nor the spirit of the awards process.1This committee is so new that we don't even have an official name, let alone a cool acronym, for it. Probably never will.PeterDonis said:DaleSpam, no fair electioneering in your sig!
PeterDonis said:Well, you used the word "frame" yourself in the OP. What did you mean by it?
#1 is the most general term: I would define it as any way of assigning coordinates to events that meets certain very basic conditions (for example, that events which are "close together" should have coordinates which are close in value). Normally we try to have the assignment of coordinates to events be "sensible", meaning there will be some reasonable relationship between the coordinates and something with physical meaning; but in principle we don't have to do this, it just makes calculations easier.
#2 and #4 are basically the same thing: they refer to special cases of #1 in which the metric in the given coordinates assumes the standard Minkowski form: [itex]d\tau^{2} = dt^{2} - dx^{2} - dy^{2} - dz^{2}[/itex]. In flat spacetime (i.e., when gravity is negligible), such a frame can be global (i.e., it can cover the entire spacetime); but in curved spacetime (i.e., when gravity is present), such a frame can only be local; it can only cover a small region of spacetime around a given event (how small depends on how accurate we want our answers to be and how strong gravity is).
#5 is a particular instance of #2 and #4 such that an object we are interested in is at rest at the spatial origin in the given frame. In flat spacetime, again, this can be true globally; but in curved spacetime it will only be true locally.
#3 has at least two meanings that I'm aware of:
#3a: A "preferred frame" can be a particular instance of #1 (i.e., it can be any kind of frame, not necessarily an inertial/Lorentz frame) that matches up in some way with a key property of the spacetime we are interested in. For example, in the FRW spacetimes that are used in cosmology, the "comoving" frame, the frame in which the universe looks homogeneous and isotropic, is a preferred frame, because it matches up with the symmetries (homogeneity and isotropy) of the spacetime. The reason such a frame is "preferred" is that calculations are easier in a frame that matches up with the symmetries of the spacetime.
#3b: A "preferred frame" can also be a particular frame that is picked out by someone's physical theory as being "special", regardless of whether there is any actual physical observable that matches up with it. For example, the "aether frame" in LET is a preferred frame in this sense.
"The important point to grasp here is that the spacetime structure, the four-dimensional structure, of the spaceship is just as rigid and unchanging as it is in classical physics. This is the essential difference between the discarded Lorentz contraction theory and the Einstein contraction theory. For Lorentz, the contraction was a real contraction of a three-dimensional object. For Einstein, the "real" object is a four-dimensional object that does not change at all. It is simply seen, so to speak, from different angles. It's three-dimensional projection in space and its one-dimensional projection in time may change, but the four-dimensional ship of spacetime remains rigid.
Here is another instance of how the theory of relativity introduces new absolutes. The four-dimensional shape of a rigid body is an absolute unchanging shape. We can slice spacetime so the shape of a spaceship depends on the motion of the frame or reference from which we make the slice, but (as J.J.C. Smart writes in the introduction to his anthology, Problems of Space and Time), "the fact that we can take slices at different angles through a sausage does not force us to give up an absolute theory of sausages".
stglyde said:Agree with him?
stglyde said:So the "frame" in "general frame", "Inertial frame", etc. are all 3D while the above is referring to a 4D "frame"?
DaleSpam said:Sure you can. As long as you specify the reference frame you certainly can make such comparisons and statements. They are not invalid statements, just frame-variant.
I have not seen that book nor that author previously. It appears to be a pop-sci book, not a serious reference book.stglyde said:I think some confusion of mine can be traced to Martin Gardner book "Relativity Simply Explained" when he mentioned:
Yes, except for the idea of the universe having an edge. However, I would strongly recommend that you learn some serious relativity before worrying about quantum mechanics. The entanglement question is a non-issue, but I think that you need quite a bit more background in both SR and QM, and SR is a far easier theory to begin with.stglyde said:DaleSpam, you are saying that a "now" can indeed exist simultaneously for all spots in the universe" contrary to what Martin said (?). So quantum entangelment is indeed simulaneous here and at the edge of the universe at "now" (meaning you can imagine someone doing something now at the edge of the universe and that is simulaneous to here on earth)?
DaleSpam said:I have not seen that book nor that author previously. It appears to be a pop-sci book, not a serious reference book.
Yes, except for the idea of the universe having an edge. However, I would strongly recommend that you learn some serious relativity before worrying about quantum mechanics. The entanglement question is a non-issue, but I think that you need quite a bit more background in both SR and QM, and SR is a far easier theory to begin with.
stglyde said:"Now, according to the special theory there is no "preferred" frame of reference: no reason to prefer the point of view of one observer than than another. The calculations made by the fast-moving astronaut are just as legitimate, just as "true," as the calculations made by the slow-moving astronaut. There is no universal, absolute time that can be appealed to for settling the difference between them. The instant "now" has meaning only for the spot you occupy. You cannot assume that a "now" exists simultaneously for all spots in the universe".
DaleSpam said:Neglecting gravitational effects, you can define an inertial frame of reference which extends infinitely in all three directions in space and infinitely into the future and past. In that frame there is one "slice" labeled by t="now". That slice extends infinitely in all three directions in space but only for one instant in time.
You can also define a different inertial frame which is moving at a constant velocity wrt the first. This frame is equally valid, but will slice things differently. The "now" slice of that frame will also extend infinitely in all three directions in space.
So as long as you define your frame you can talk about the simultaneity of distant events.
stglyde said:Guys. In LET. As you fly in near light speed. Instead of you being 6 foot tall, you would become merely 1mm in height as length contracts. Won't this mess up or ruin any physics of the atoms (for example, the electrons being nearer the nucleus, etc)? Hope someone can explain this. Thanks.
stglyde said:Let's say the Earth got destroyed by china oversized nuclear arsenals 50 years after the traveller left. So from the frame of view of the traveller. He could say Earth got destroyed before he left (because his reaching NGC is simultaneous).
stglyde said:How do you define an inertial frame that is common to the traveller traveling at lightspeed (or near the speed of light because I know nothing massive can move at the same of light) to the observer left on earth?
PeterDonis said:Yes, his description does a good job of capturing the essence of the 4-D spacetime viewpoint. However:
Not quite; a "frame" is a particular way of *describing* the 4-D spacetime by slicing it up (in Gardner's terminology) into 3-D slices (which are then called "surfaces of simultaneity" or "slices of constant time" or something like that) such that (a) each 3-D slice is labeled by a unique value of a fourth coordinate, "time" ("fourth" because it takes three coordinates to specify a point in each 3-D slice), and (b) each event in the spacetime appears in one and only one 3-D slice. Particular objects are then 4-D subregions of the whole 4-D spacetime, and different ways of slicing will "cut" the subregions at different angles, so the shapes of the slices of the objects will be different.
I'll briefly rephrase my previous descriptions of the types of frames in this terminology:
#1: A general "reference frame" imposes no constraints on how the slicing is done, as long as it meets the above requirements (a) and (b).
#2/#4: An "inertial frame" or "Lorentz frame" imposes the following additional constraints on the slices: (c) each 3-D slice is spatially flat, i.e., it's a Euclidean 3-space; (d) the spatial coordinates in the slices are assigned such that the spatial coordinates of any object that is moving inertially (i.e,. it feels no force--it is weightless) are linear functions of the time coordinate. (The coefficients in these linear functions are the "velocity components" in each spatial direction.)
As I noted before, in a flat spacetime, an inertial frame can cover the entire spacetime and meet the above requirements. In a curved spacetime, it can't; it can only cover a small local piece of the spacetime around a given event.
#5: A "rest frame" is an inertial frame that we choose such that (e) a particular object that we're interested in has spatial coordinates (0, 0, 0) in every 3-D slice (i.e., it is "at rest" at the origin at all times).
[Edit: I should also add that the 3-D slices have to be spacelike slices, which is implicit in Gardner's description.]
PeterDonis said:First of all, you admit that the traveller can't actually move at the speed of light, he can only get very close to it. Let's assume he moves at a speed such that, by his clock, it only takes him 1 second to get from Earth to NGC 4203.
Second, the traveller *cannot* say that the Earth got destroyed before he left, because the Earth was still there when he left; he was *at* Earth at that event, so anything that occurs on Earth after he leaves will be seen by him to have a later time than the event of his leaving. He will, however, see it take much less time for China to destroy the Earth; instead of 50 years, it will take a small fraction of a second.
You don't, because they are in relative motion. The traveller's inertial frame is not the same as the Earth's inertial frame (or the inertial frame of anyone at rest on the Earth). They "slice" the 4-D spacetime up into 3-D slices at different angles. It would really help you to take a step back and think about what that means.
stglyde said:Supposed initially NGC 4203 and Earth is at rest at a distance of 10.4 million light years (ignoring the motion of galaxies). Then you started your travel there from earth. And NGC 4203 got destroyed 100 years later in the rest frame of earth. But it took you 1 second to reach NGC 4203 from Earth . So in your frame and time. NGC 4203 was destroyed before you left Earth. In the frame of someone on earth. NGC 4203 was destroyed after you left Earth.
stglyde said:But supposed the distance and speed is unknown. And there is no way to apply the Lorentz transformation.
stglyde said:But if LET preferred frame can be distinguished. Then it can be known (but I know LET preferred frame is unknowable.. at least for now).
The nucleus, the electrons, and all of their associated fields and interactions will also be length contracted. The result is that nothing will be noticeable within the moving frame. Light will still focus on the retina, enzymes will still catalyze their reactions, etc.stglyde said:Guys. In LET. As you fly in near light speed. Instead of you being 6 foot tall, you would become merely 1mm in height as length contracts. Won't this mess up or ruin any physics of the atoms (for example, the electrons being nearer the nucleus, etc)? Hope someone can explain this. Thanks.
PeterDonis said:stglyde said:Guys. In LET. As you fly in near light speed. Instead of you being 6 foot tall, you would become merely 1mm in height as length contracts. Won't this mess up or ruin any physics of the atoms (for example, the electrons being nearer the nucleus, etc)? Hope someone can explain this. Thanks.
Only if the distance and speed relative to the LET preferred frame were also known. But if they're known relative to the LET preferred frame, and we know which inertial frame the LET preferred frame is, then the distance and speed are known relative to *any* inertial frame. So if we suppose the distance and speed are unknown, that has to include being unknown relative to the LET preferred frame.
DaleSpam said:It has nothing to do with location, only relative velocity. Two inertial observers which are millions of lightyears apart but at rest wrt each other share the same rest frame. Two inertial observers passing near each other at .9c relative velocity do not share the same rest frame. The first two will always agree on simultaneity, despite the fact that they are far apart. The second two will generally disagree on simultaneity, despite the fact that they are close together.
Why would you say that LET doesn't have a "graphical interface"? You can use all of the same graphical techniques from SR. A spacetime diagram is nothing more than a position time diagram, which is used by every student to study Newtonian physics.stglyde said:About LET. Someone here says the Lorentz Transform is all that matters. SR is a way to graphically plot it. LET to physicalize it. For tachyons that travel faster than light. SR says in from other coordinates (or frames) you can see other frames going back in time (by deshifting the plane of simultaneity). How about in LET, can anyone draw any illustration of what it means for some frames able to view other frames as going backward in time when LET doesn't have the graphical interace as SR. So how do you graphically illustrate LET? I just can't imagine it since it doesn't have any minkowski spacaetime diagram. I guess this is the initial problem and concern in the original message of this thread.
Consider a duel with tachyon pistols. Two duelists, A and B, are to stand back to back, then start out at 0.866 lightspeed for 8 seconds, turn, and fire. Tachyon pistol rounds move so fast, they are instantaneous for all practical purposes.
So, the duelists both set out --- at 0.866 lightspeed each relative to the other, so that the time dilation factor is 2 between them. Duelist A counts off 8 lightseconds, turns, and fires. Now, according to A (since in relativity all inertial frames are equally valid) B's the one who's moving, so B's clock is ticking at half-speed. Thus, the tachyon round hits B in the back as B's clock ticks 4 seconds.
Now B (according to relativity) has every right to consider A as moving, and thus, A is the one with the slowed clock. So, as B is hit in the back at tick 4, in outrage at A's firing before 8 seconds are up, B manages to turn and fire before being overcome by his fatal wound. And since in B's frame of reference it's A's clock that ticks slow, B's round hits A, striking A dead instantly, at A's second tick; a full six seconds before A fired the original round. A classic grandfather paradox.
DaleSpam said:If you understand the scenario in SR then you almost have it in LET also. To make the final step from SR to LET simply boost your scenario by an unknown v to get to the aether frame. You get a causality violation regardless of v.
The key is the velocity addition. In LET measured velocities still follow the usual relativistic velocity addition rule. In the tachyon pistol scenario this allows things to go backwards in time in the aether frame.
Here is a brief introduction:stglyde said:I don't know what you are talking about with the velocity addition.
DaleSpam said:If a tachyon pistol fires projectiles at any v>c then there is some frame where it would go backwards in time relative to the aether frame. I can work out the math for you if you like.
stglyde said:But this doesn't make sense in LET. Something is not right. When A is actually physically contracting and time dilated... A sees B with half his time. Then B seeing A half B time. There seems to be some kind of loop error.
PeterDonis said:There actually is one other assumption required in this scenario: that the spacelike curve the tachyon fired from the pistol follows is frame-dependent; the usual assumption appears to be that the tachyon velocity v is fixed relative to the emitter (the pistol in this case). For example, if you look at a typical scenario that uses tachyons to create closed loops, where A sends a message to B and then receives B's reply *before* he sent the original message, in order for the reasoning to go through, it has to be the case that tachyons emitted by B travel along spacelike curves that are not parallel to the curves followed by tachyons emitted by A--put another way, B's tachyons travel at some fixed v > c relative to B, while A's tachyons travel at the same v > c relative to A; but B's tachyons do *not* travel at v relative to A. (If they did, they would not be going backwards in time relative to A, so A could never receive B's reply before he sent his message.)
An LET theorist could, in principle, claim that travel backwards in time relative to the aether frame was impossible because tachyons always have to travel at some fixed velocity v > c *relative to the aether frame*. This would not prevent tachyons from appearing to travel backwards in time relative to some other frames, but it would prevent "closed loop" scenarios; you could never send a message using tachyons and receive the reply before you sent the message.
stglyde said:And continued "This would not prevent tachyons from appearing to travel backwards in time relative to some other frames". What other frames for example in the case of the Tachyon pistol duel scenerio?
stglyde said:Are you saying another observer "C" watching the duel would see A being hit 6 seconds before A fired the shot yet it doesn't actually happen in A or B frame?
PeterDonis said:Well, you used the word "frame" yourself in the OP. What did you mean by it?
#1 is the most general term: I would define it as any way of assigning coordinates to events that meets certain very basic conditions (for example, that events which are "close together" should have coordinates which are close in value). Normally we try to have the assignment of coordinates to events be "sensible", meaning there will be some reasonable relationship between the coordinates and something with physical meaning; but in principle we don't have to do this, it just makes calculations easier.
#2 and #4 are basically the same thing: they refer to special cases of #1 in which the metric in the given coordinates assumes the standard Minkowski form: [itex]d\tau^{2} = dt^{2} - dx^{2} - dy^{2} - dz^{2}[/itex]. In flat spacetime (i.e., when gravity is negligible), such a frame can be global (i.e., it can cover the entire spacetime); but in curved spacetime (i.e., when gravity is present), such a frame can only be local; it can only cover a small region of spacetime around a given event (how small depends on how accurate we want our answers to be and how strong gravity is).
#5 is a particular instance of #2 and #4 such that an object we are interested in is at rest at the spatial origin in the given frame. In flat spacetime, again, this can be true globally; but in curved spacetime it will only be true locally.
#3 has at least two meanings that I'm aware of:
#3a: A "preferred frame" can be a particular instance of #1 (i.e., it can be any kind of frame, not necessarily an inertial/Lorentz frame) that matches up in some way with a key property of the spacetime we are interested in. For example, in the FRW spacetimes that are used in cosmology, the "comoving" frame, the frame in which the universe looks homogeneous and isotropic, is a preferred frame, because it matches up with the symmetries (homogeneity and isotropy) of the spacetime. The reason such a frame is "preferred" is that calculations are easier in a frame that matches up with the symmetries of the spacetime.
#3b: A "preferred frame" can also be a particular frame that is picked out by someone's physical theory as being "special", regardless of whether there is any actual physical observable that matches up with it. For example, the "aether frame" in LET is a preferred frame in this sense.
Sure, but that is not a separate assumption from LET. If, as LET asserts, the laws governing physical experiments are invariant under the Lorentz transform then this follows.PeterDonis said:There actually is one other assumption required in this scenario: that the spacelike curve the tachyon fired from the pistol follows is frame-dependent; the usual assumption appears to be that the tachyon velocity v is fixed relative to the emitter (the pistol in this case).
Certainly, but then the tachyons would be measurably inconsistent with the Lorentz transform, disproving LET, or at least requiring modifications to say that the Lorentz transform had limited applicability.PeterDonis said:An LET theorist could, in principle, claim that travel backwards in time relative to the aether frame was impossible because tachyons always have to travel at some fixed velocity v > c *relative to the aether frame*.
No reason. The "e.g." in my parenthetical comment means "for example". Any v>c would work equally well.stglyde said:"Any scenario which violates causality in SR violates causality in LET. The only way around it is to have the aether measurably violate the principle of relativity (eg tachyonic signals go at 2c, but only in the aether frame)"
Ok. Let's say the tachyons travel faster than c relative to the aether frame (why must it be 2c and 1.5c Dalespam?).
You need to be careful here. It is one thing to discuss legitimate scientific theories of the past, but it is another to speculate on new personal theories.stglyde said:But then what if for sake of discussion, the LET aether also had unlimited speed limit with the speed of light only the speed for normal particles? ... In this scenerio with unlimited velocity in the nLET