Tachyons travel backward in time?

RandallB

I think I understand what you are driving at, but you are stating part of your case poorly.

Example; assume you can detect and use the information from a tachyon passing by at twice the speed of light in our reference frame and know that it came from a Gamma Burst Event some 10 light years away.

That would signal us that 5 years ago a GBE occurred and we won’t see the light form it for 5 more years. Such an early warning signal, not only does not send information into the past, it does not mean “it would appear that event happened before it even started”.
It would only signal us 5 years in advance of receiving a message with normal light tell us about a GBE that happened 10 years ago. Even with light we know the information is 10 years old, receiving the information 5 years early does not make it appear the event happened before it started.

Also from standard Doppler effects already useful within SR we would know tackyons traveling at such a speed in our reference frame view would not be seen to travel at that same speed any other reference frame. Every frame would see a different speed, meaning no one speed as every frame should see a variety of different speeds for them, so measuring their speed would also be required to get usful info.

So I don’t see where SR would require tachyons cause even the appearance of “backwards time”. However, understanding that does not improve the chance that such a thing traveling faster than light or gravity might exist anywhere but in our imaginations.

JesseM

It's because of the relativity of simultaneity in different frames; if the tachyon signal moves FTL in our frame, but the event of it being emitted still happens before the event of it being received, there must be some other frame where the event of it being received happened before it was emitted. For example, suppose in my frame the tachyon is moving at 10c in the +x direction, so if it's emitted at position x=0 light-seconds at time coordinate t=0 seconds, then at time coordinate t=10 seconds it will have reached the position x=100 light-seconds in my frame. Now consider the frame of an observer who is moving at 0.6c relative to me in the +x direction of my coordinate system, using his own coordinate system x' and t', with his x'-axis parallel to my x-axis, and the zero position on each of our coordinate systems coinciding at a coordinate time of t = t' = 0. In this case, our coordinates will be related by the Lorentz transformation:

[tex]x' = \gamma * (x - vt)[/tex]
[tex]t' = \gamma * (t - vx/c^2)[/tex]
[tex]\gamma = \frac{1}{\sqrt{1 - v^2/c^2}}[/tex]

And here with v=0.6c, [tex]\gamma[/tex] is 1.25. If we plug in the coordinates x=0, t=0 in my frame (the event of the tachyon emission), the Lorentz transformation tells us that in the other observer's frame this event happened at x'=0, t'=0. But if we plug in coordinates x=100, t=10 (the event of the tachyon being received), in this observer's coordinate system this happens at the coordinates:

x' = 1.25 * (100 - 0.6*10) = 1.25 * 94 = 117.5
t' = 1.25 * (10 - 0.6*100) = 1.25 * -50 = -62.5

So you can see that in this coordinate system, the tachyon was received a full 62.5 seconds before it was emitted. It's just part of the way the Lorentz transform works that if you pick two events with a spacelike separation (like two events on the worldline of a tachyon), you'll always be able to find a pair of frames which disagree about which of the two events happened earlier than the other, as well as some frame where the events happened simultaneously.

If you agree that it's possible for a tachyon to be received before it's emitted in some frame, then if tachyons obey the postulate of relativity that says they should follow the same laws in every inertial frame, then it must be possible for ever frame to see a tachyon received before it's emitted. This means that if you are moving away from me, and I send you a tachyon signal such that it moves FTL but forward in time (you receive the signal at a later time than I emitted it) in my frame but it's moving backwards in time (you receive it at an earlier time than I emitted it) in your frame, and then you send a reply which moves FTL but forward in time but backwards in time in my frame, then it can work out that I'll receive your reply before I sent the original signal, a violation of causality. Again, check out the page with the minkowski diagrams illustrating such a situation that I linked to near the beginning of this thread.

RandallB

Nonsense
That is a gross misunderstanding of SR simultaneity!
First you establish a preferred frame with t=10 at x= 6, 10, 100 all happening simultaneously.
When you calc t’= -62.5 at x=100(x’= 117.5) for one of those events; no problem with that.
But then you assume that event is simultaneous with the x’=0 starting point at t’= -62.5 (near x= -47) only because the t’ times are the same!
Not only does “relativity of simultaneity” not say those events are simultaneous, SR specifically states you cannot consider them as simultaneous events.

Orthodox SR does not even acknowledge the t= 0 times at x = 6, 10 and 100 as being simultaneous! And also says a preferred frame should not be assumed.
I understand Astrophysics does use a preferred reference frame based on CMBR. I have no real problem with that. But what will never work is using two different frames as preferred at the same time as you are doing here. Once you define one preferred frame all other frames must be considered inaccurate for establishing causality, you cannot have two preferred frames.

Your thought experiment will need to reroute the tachyon back into local proximity with the starting point in one or both frames, and attempt to show it returning before it started. And that is not going to happen in any thought experiment that follows the SR rules rationally.

Another poor reference for describing SR events, there are lots of them;
“ …superluminal transmission. Alice transmits from event P and the signal is instantaneously received by Bob at event Q. Alice and Bob are at rest relative to each other. ”
FTL and instantaneous are not the same thing, NO where in SR does it expect FTL to mean instantaneous. It is a bad starting assumption that renders the entire example pointless and false.

JesseM

What are you talking about? I never said anything about x=6 or x=10, the only coordinates I mentioned in the first frame were (x=0, t=0) and (x=100, t=10), which aren't simultaneous in this frame. And this frame is not "preferred", it's just the one where the tachyon signal is moving at 10c.
Er, yes, any events which have the same time-coordinate in a given frame are simultaneous in that frame (in this case the primed frame). Do you disagree?
Do you understand that the phrase "relativity of simultaneity" means that different frames disagree about whether a given pair of events are simultaneous or not? If so, then you need to specify what frame you're talking about when you say "you cannot consider them as simultaneous events", since simultaneous events in one frame are non-simultaneous in others. Two events which happen at the same primed t' coordinate in the primed frame are simultaneous in that frame, but those same events will have different nonprimed t coordinates in the unprimed frame, so they'll be non-simultaneous in that one.
They are simultaneous in the unprimed frame where they have the same t-coordinate. They are not simultaneous in any absolute sense, since other frames will define these events as non-simultaneous. If you don't understand that different frames disagree on whether events are simultaneous or not, and that there is no absolute truth about whether events are "really" simultaneous or non-simultaneous, then you have missed the whole point of the concept "relativity of simultaneity".
I haven't assumed a preferred frame. On the other hand, if you think there is a single real truth about whether events are simultaneous, then you are assuming a preferred frame (i.e. the frame where events with the same time coordinate are 'really' simultaneous).
Not a physically preferred frame (in the sense of the laws of physics obeying different equations in this frame), no. Just a frame that's simplest to work in because the distribution of matter and the curvature of spacetime. Anyway, here we are talking about frames in the sense of coordinate systems in the curved spacetime of GR, not inertial coordinate systems in the flat spacetime of SR.
The whole point of SR is that no inertial frame can be preferred! Are you saying that, when working on an SR problem, you think there is a single preferred frame whose definition of simultaneity is the "correct" one? If so, you have really, really missed the point, what you're suggesting is more like an aether theory than SR.
One of the SR rules is that the laws of physics work the same way in every inertial frame--that's the first postulate! So no frame can be physically preferred in any way. If there's one frame in which it's possible for a tachyon signal to arrive at an earlier time-coordinate than it was sent, then this must be possible in every inertial frame, according to relativity.
In any single frame they're not the same thing, but the point is that for any two events that have a spacelike separation (i.e. only an FTL signal could have both events on its worldline), you can always find some inertial frame in which they happened at the same time-coordinate. So, if I start with a frame where the signal moved at 1.00000001c, I can find another frame where the signal was instantaneous (the time-coordinate of it being sent is the same as the time-coordinate of it being received in this frame).

RandallB

Of course I disagree; any of those events are seen as happening at the same time in your reference frame. The point made by SR is that those events cannot be simultaneous regardless of how it seems to you. They could only be simultaneous if and only if your frame is the one and only “preferred frame”. And as I said SR does not allow for that.

You set the experiment to for 10 units of time, with your other frame moving 6 units of distance, light moving 10 units of distance and your tachyon moving 100 units in those ten units of time, Is that a trivial part of your own thought experiment you did not see?

You’re the one declaring for a preferred frame for x’ otherwise exactly how do you establish simultaneity of anything anywhere with event x’=117.5 t’=-62.5. In your example SR can only define the causality relationship of that event with one and only one other event t=10 x=100. SR cannot and does not define those two events as simultaneous with any other events includes those with t=10 or t’=-62.5 wherever they may be.

Again no, you need to re-read Einstein, there is no such thing as “simultaneous” within a frame – that was his point that events with any space like separation seen as happening at the same time within a single frame still cannot be considered as “simultaneous” by anyone. You’ve been around long enough to know that.

The rest is just not worth commenting on except to say that if there is anything that is FTL such as a Graviton, Higgs Particle or Tachyon it should be obvious they would have to follow rules of physics beyond what know now. And nothing so far shows that such rules exist. But if they do they do not need to cause “backwards time”.

DaleSpam

Hi Randall,

If two events happen at the same time they are simultaneous. That is the definition of simultaneity. The relativity of simultaneity just means that two events which happen at the same time in one inertial frame will not happen at the same time in another. The relativity of simultaneity is not the absence of simultaneity, it just means that you have to specify the reference frame in which they are simultaneous.

JesseM

I don't understand--are you saying that events which happen at the same time in my frame are not "simultaneous" in my frame? Or are you suggesting that the term "simultaneous" itself is supposed to refer to some frame-independent "real truth" about whether events happened at the same time or not, so that happening at the same time in my frame doesn't mean they are "really" simultaneous? Either one would be wrong, in relativity each frame has its own definition of simultaneity (which is just the same thing as happening at the same time-coordinate in that frame), and no frame's definition is more "true" in any absolute sense than any other's. Look at Einstein's own comment here about a thought-experiment with two frames, the frame of a train moving relative to the train tracks and the frame of an embankment at rest relative to the train tracks:
Likewise, take a look at section 3 on the relativity of simultaneity from this page from a professor at the University of Pittsburgh:
And in A.P. French's book Special Relativity, a standard undergraduate textbook, on p. 74 he writes:
In Edwin Taylor and John Wheeler's Spacetime Physics they discuss the same train thought-experiment that Einstein was talking about in the section I quoted above (and which is also illustrated with a little animation here), on pp. 62-63:
Sure, in the first frame an observer at rest in the second frame would move 6 light-seconds in the same time that a photon would move 10 light-seconds and the tachyon would move 100 light-seconds. But I was only talking about the tachyon's motion as seen in both frames, not the motion of a photon or an observer at rest in either frame.
I don't understand what you mean by "establish simultaneity"--if you're talking about some concept of absolute simultaneity, then as I explained, relativity rejects such a concept. Simultaneity differs for different inertial frame, and no inertial frame is more valid than any other in SR. In the first frame, the event of the tachyon being received (by a station 100 light years from the Earth in this frame, say) happens 10 seconds after the event it is sent from Earth; in the second frame, the event of the tachyon being received at that same station happens 62.5 seconds before the event of the signal being sent from Earth. And in that second frame, every other event with time-coordinate t'=-62.5 is "simultaneous" with the event of the tachyon signal being received at x'=117.5, t'=-62.5.
First you refer to "event x’=117.5 t’=-62.5" and then you say "SR can only define the causality relationship of that event with one and only one other event t=10 x=100"--when you say "other event", are you imagining that these are two separate events? The event of the tachyon signal being received at the station is a single event, it just has different coordinates in two different frames; in the first frame it has coordinate (x=100, t=10), and in the second frame it has coordinates (x'=117.5, t'=-62.5).
Two events which have the same time-coordinate in that frame are simultaneous in that frame, that's all that simultaneous means. Look at the example of the two lightning strikes at either end of the train, events which definitely have a spacelike separation; in Einstein's thought-experiment, the observer on the embankment defines these events to be simultaneous, while the observer on the train defines them to be non-simultaneous.
As far as I know, no physicists have suggested that the graviton or the higgs particle would need to move FTL; gravitational effects are only thought to travel at the speed of light, for example.
But relativity is more like a symmetry condition about any possible laws of physics, not a set of physical laws in itself. The first postulate says that all laws of physics should obey the same equations in all inertial frames; every time we discover new laws of physics, we can check whether the equations of this new law obey the first postulate. For example, the laws of quantum field theory were found long after 1905, but they do have the property of "Lorentz-symmetry" meaning the equations are unchanged under the Lorentz transform, so they're compatible with relativity. The point about tachyons is that if the laws governing them are Lorentz-symmetric ones which are compatible with relativity, then if it's possible to use tachyons to send information faster than light, it must also be possible to use tachyons to send information backwards in time. Of course it is also possible that tachyons would obey laws that are not Lorentz-symmetric in which case relativity would be proven wrong, and it is also possible (probably most likely) that the fundamental laws of physics will turn out not to allow FTL information transfer in the first place.

RandallB

No this is not what simultaneity means!
Any one frame can ignore all other frames and show separated simultaneous events and get usable answers as long as it never uses a value defined in some other frame. Simultaneity says that the simultaneous space like separated results you find using such a “preferred frame” cannot be understood as actually being simultaneous.

Sure even Einstein uses the word simultaneous within individual frames for SR speed problems such as trains and embankments. That is how he illustrated getting to the conclusion that simultaneous events in one frame were not simultaneous in the other frame. Likewise simultaneous events in the other frame were shown to not be simultaneous in the first.
From that Einstein established the principle of simultaneously, in order to maintain a consistent set of physics laws usable in all frames of reference. The simple rule of simultaneity is that simultaneous events within a single reference frame cannot be considered as actually being simultaneous - That's It!
If not that rule, then you must establish a single “preferred frame” and use a different set of SR physics laws in all others or at least recognize simultaneous observations in those other frames as wrong.

Now you and Jesse seem to think that simultaneity can be used to identify the correct time for tachyon in absolute values well enough to when it reached a distant point to know realtive to local time.

Balderdash.
If either of you could do that, then I have simple challenge one of you should be able to solve – no tachyon needed. If you can do it for tachyons, this should be easy.

Use Jesse’s problem where the other frame moves at 0.6c with observers at x= 0 & 10 and x’ = 0 & 5.
Do the math to be sure we all agree on the fallowing three sets of truly simultaneous events based on SR simultaneity rules:

A: x = 0 correctly observes a flash of light (following the tachyon) start off at t=0
simultaneously x’ = 0 sees the same flash start at t’=0

B: x =5 meets x’ =0 at t=8 1/3
simultaneously x’= 0 meets x = 5 at t’ = 6 2/3

C: x = 10 sees the flash of light arrive at t = 10
simultaneously x’ = 5 sees the same flash arrive at t’ = 5

When did the simultaneous C events occur before or after simultaneous B events ?

Observer x = 5 claims before as do all other x observers while x’=0 claims after as do all other x’ observers!

If either of you can solve this using SR and simultaneity, without a preferred reference frame. I will issue an apology and a retraction.
But I expect an unambiguous definitive answer for one or the other before or after!
If not you have no business claiming to do any better with a hypothetical tachyon at even greater distance.

DaleSpam

You seem to have some mistaken notions about the concepts "simultaneous" and "prefered". The fact that two given spacelike separated events happen to be simultaneous in a given frame in no way makes it a "prefered" frame. It may be "prefered" in the sense that some computations are easier to carry out in that frame, but not in the usual sense that the laws of physics are in any way different in that frame.

First, C=(10,10) is the same event as C'=(5',5'). They are not separate events, they are the same event written in the coordinates of different reference frames. Similarly with A=(0,0) and A'=(0',0') and B=(8.33,5) and B'=(6.67',0'). Remember, events are the spacetime equivalent of points. A point does not become two points simply because you can write it in two different coordinate systems.

Now, events C and B have spacelike separation. In the unprimed frame B occurs before C (B-C=(-1.67,-5)), while in the primed frame B' occurs after C' (B'-C'=(1.67',-5')). In the (double primed) reference frame moving at 1/3 c relative to the unprimed frame the two events are simultaneous (B''=(7.07'',2.36''), C''=(7.07'',7.07''), B''-C''=(0'',-4.71'')).

For ANY arbitrary pair of events with spacelike separation you can always find a reference frame where they are simultaneous, another where one occurs before the other, and a third where the order of occurence is reversed.

JesseM

What does "actually simultaneous" even mean? No one is claiming that there is any absolute simultaneity involved, each frame uses its own distinct definition of simultaneity, and all frames are equally valid as far as physics goes. "Preferred frame" is used to denote the notion of a frame where the laws of physics take a different, preferred form than in other frames (like in the old aether theories where light would only move at c in all directions in the rest frame of the aether, in other frames its speed would be different in different directions), but I'm in no way using such a preferred frame. The whole argument about tachyons is based on the idea that the laws of physics governing tachyons should work the same way in every frame, so if you can show that tachyons move instantaneously or backwards in time in terms of one frame's definition of simultaneity, it must be possible for tachyons to move instantaneously or backwards in time in terms of every frame's definition of simultaneity. If you deny this, and say tachyons can behave this way in some frames but not others, then it is you who are postulating a preferred frame!
What does "actually being simultaneous" mean? If you're suggesting that there is some absolute truth about whether events are simultaneous, which is different from the definition of simultaneity used by a particular frame, that's the opposite of what Einstein was trying to show. If you're just saying that there is no absolute definition of simultaneity, that we can only talk about "simultaneity" relative to a particular frame but that all frames are equally valid, then I agree entirely, that's what I've been saying all along. And if you combine that with the first postulate which says the laws of physics must work the same way in every frame, then if it's possible to send tachyon signals which move instantaneously or backwards in time according to one frame's definition of simultaneity, then it must be possible to send tachyon signals which move instantaneously or backwards in time according to any other frame's definition of simultaneity too.
What are you talking about? I never said anything about absolute values. I just said when the tachyon departs and when it arrives using a particular frame's coordinate system.

What do you mean by "local time" anyway? Do you mean something different than "the time in a particular frame"? After all, frames of reference in SR are not "local" to a particular region, they are coordinate systems that describe events throughout the entirety of spacetime.
Yes, that's right, x' = gamma*(x - vt) = 1.25*(5 - 0.6*8 1/3) = 1.25*(5 - 5) = 0
Yes, it's correct that x'=0, t'=6 2/3 in the primed frame has spatial coordinate x=5 in the unprimed frame, since:
x = gamma*(x' + vt') = 1.25*(0 + 0.6*6 2/3) = 1.25*4 = 5. And it's also true that
t = gamma*(t' + vx'/c^2) = 1.25*(6 2/3 + 0.6*0) = 8 1/3.

So, all you're really saying here is that the event with coordinates (x=5, t=8 1/3) in the unprimed frame has coordinates (x'=0, t'=6 2/3) in the primed frame. These aren't two simultaneous events, it's just a single event that is assigned different coordinates in the two coordinate systems.
Again, this is just the same event assigned different coordinates in the two coordinate systems, not two simultaneous events...but yes, your numbers are correct again.
Sure. What's the problem here? Since B and C are spacelike separated (neither event lies within the other event's light cone), different frames can disagree on which event happened first and which happened second. That's just a standard feature of relativity. However, without tachyons no physical signal can travel between B and C, so there's no frame that sees information going FTL or backwards in time.
I don't understand what you mean by "solve this". It's an accepted fact that because different frames disagree about simultaneity, they can also disagree about which of two spacelike separated events happened earlier and which happened later. Do you disagree that this is an accepted fact? If you do disagree, I can quote various sources on SR which point this out. And if you agree that this is widely accepted, then again, what's the problem?
Again, if you think I'm claiming there's some sort of absolute truth about simultaneity, you've got my argument completely backwards. Simultaneity is relative to one's choice of reference frame. For any single tachyon signal, different frames disagree about whether it's going forward in time or backward in time, and there is no absolute truth about this. The point is that if you have a frame A where a tachyon signal is going FTL but forwards in time and another frame B where it's going backwards in time, then by the principle that anything which is physically possible in one frame must be physically possible in all frames (the first postulate of relativity), it must be possible to send a second tachyon signal in reply to the first which is going FTL but forwards in time in frame B, and backwards in time in frame A. With the combination of the two signals, you can arrange things so that the event of an observer receiving the reply actually happens in the past light cone of the event of the same observer sending the original tachyon signal, so in this case all frames agree that the reply was received before the first signal was sent (these two events have a timelike separation rather than a spacelike one, meaning there can be no disagreement about their order).

RandallB

DaleSpam & JesseM you guys got some es’planen’ to doo
Do I really need to spell this out as if you were a fifth grader?
The C event is a set of observations made by a single observer located at x=10 including 1.getting nose to nose with another observer located at x’=5 with a clock on display 2. Receiving enough photons from two clocks in the local vicinity to make note of t=10 and t’=5 on those two clocks. 2. observing enough photons from a flash of light to indentify it as the flash starting at simultaneous events A & A’.
The C’ event is another set of observations made by a completely different observer in another reference frame. Collecting a differ group of sampling photons, confirming the same information about getting nose to nose, times on a couple clocks, and a flash of light that has just appeared.

Likewise I take B & B’ to be a pair of events as are A & A’, each pair being "actually simultaneous” paired events with no spacelike separation between the two. [I have no problem with using a four variable description of these pairs as (x,t,x’,t’) but the two variable (x,t) or (x’t’) for each separate event is no less a complete description for where both events occurred.]

JesseM asks “What does "actually simultaneous" even mean?”
That means for the above three pairs of events is that not only does each pair appear simultaneous in the x & x’ frames; but as they are not space like separated they will be “actually simultaneous” as measured by any and every other possible reference frame you might come up with. (Try if you like).

It also means, Einstein simultaneity tells me that apparent same time events with spacelike separation such as t=0 for x= 0, 5, & 10 within a frame, CANNOT be considered to be "actually simultaneous" even if I live on that frame no matter how weird in might seem to me.

Obviously you and JesseM disagree with me which being us to your second sentence:
[b]“The fact that two given spacelike separated events happen to be simultaneous …”[\b]
Clearly you and JesseM feel that it is possible find a case where spacelike separated events in a common reference frame are “actually simultaneous”.
Such as when JesseM concludes that the x' = 117.5 t' = -62.5 is “actually simultaneous” with x’=0 t’= -62.5 and therefore the tachyon would have ended at x’ = 117.5 before it started at x’=0

Neither of you need to convince me of the tachyon example,
just one of you show us you have the math to demonstrate any two space like separated in a reference frame such as t = 10 for x = 5 and 10 “actually simultaneous”. Meaning that any and all other reference frames will either agree they are simultaneous OR if any alternate frame disagrees you have math convincing to observers in such other frames the their observations are wrong and your evaluation of the two events as simultaneous is correct.

If you can do that in the nonFTL case I will accept your applying whatever math you are using in the FTL case.
But if your appoch cannot be confirmed in the nonFTL case I’ll never accept in the FTL example.

JesseM

OK, I see why you referred to two events here. I was confused because it isn't really necessary to have an observer right next to an event and at rest in a given frame in order to assign coordinates to that event in the frame. For example, if I see an event 10 light years away in my rest frame, I can just use the fact that light moves at c in my coordinate system, and conclude that the event happened at a time-coordinate 10 years earlier than the time on my watch when I saw it.

But we can do it your way--in this case we can imagine an observer at rest in the C frame at position x=10 in that frame, and we can imagine another observer at rest in the C' frame at position x'=5 in that frame, and the two will meet at exactly the moment that the light reaches them. So we really have three events here--the event of the first observer's clock ticking t=10, the event of the second observer's clock ticking t'=5, and the event of the light being detected at that point in space. But note that it's not as if specific events require specific coordinate systems to describe them--as long as these events have zero spatial and temporal separation between them, we would say that the event of the of the first observer's clock reading t=10 has coordinates t'=5 in the C' frame, and likewise the event of the second observer's clock reading t'=5 has coordinates t=10 in the C frame. Would you agree?
When you say "three pairs of events" are you referring to the paragraph below? (I put '3' in italics because you actually wrote '2' there, but I think you meant to write '3')
If we assume the spatial and temporal separation between these events is infinitesimally small (assuming pointlike observers, and assuming the observations are all made at precisely the time the spatial separation between them reaches zero) then these events are simultaneous in every frame. After all, in the C frame all six events have precisely the same coordinates (x=10, t=10), and in the C' frame all six events have precisely the same coordinates (x'=5, t'=5). And if you plug some new velocity into the Lorentz transform, you'll still find that these six events all have the same coordinates in your new frame. "Same coordinates" means "same time coordinate", so no matter what frame you pick, all six events happen simultaneously in that frame. But this is only because the spatial and temporal separation between the events is zero--if there is any nonzero spatial separation [tex]\Delta x[/tex] or a nonzero temporal separation [tex]\Delta t[/tex] between two events in any given frame, then all frames cannot agree they are simultaneous. In the case where the spatial separation or the temporal separation between events is nonzero, then if the spacetime separation between two events is timelike ([tex]c^2 \Delta t^2 - \Delta x^2 > 0[/tex]) or lightlike ([tex]c^2 \Delta t^2 - \Delta x^2 = 0[/tex]) in a given frame, then all frames will agree the events happened at different times, and all frames will agree on which happened first, while if the spacetime separation between the events is spacelike ([tex]c^2 \Delta t^2 - \Delta x^2 < 0[/tex]) then one frame will say the events were simultaneous, while other frames will say they happened at different times but disagree about which happened first and which happened second. Is there any of this you disagree with?
I have never argued that events can be "actually simultaneous" as you define it (all frames agreeing they are simultaneous), except in the special case where both events happened at the exact same point in space and time (zero spatial separation and zero temporal separation). Do you think I have ever argued that events at different points in spacetime like (x=0,t=0) and (x=5,t=0) and (x=10,t=0) can be "actually simultaneous"? If so, what quote of mine lead you to believe I was saying that? I have been saying the exact opposite, that simultaneity is relative to your choice of reference frame (again, assuming we're talking about events with a separation between them), that events which are simultaneous in one frame will be non-simultaneous in others, and there is no "real truth" about the matter. For example, in post #58 I said:
...and then provided numerous quotes from authoritative sources to back it up. I thought you might have been arguing that there is a "real truth" about simultaneity, which is why I did that...are you saying you agree that there is no frame-independent truth?
Here you seem to be quoting DaleSpam in post #60 where he writes:
So clearly he is talking only about simultaneity relative to a particular frame, not absolute simultaneity. Again, can you provide a quote from either of us that claims separated events can be "actually simultaneous" in a frame-independent sense, as opposed to just being simultaneous relative to a particular frame?
No, I believe nothing of the sort. I really have no idea what lead you to believe I was arguing that.
Uh, I never said anything like that either. These events are only simultaneous in the C' frame which uses these coordinates, so the tachyon was received before it was sent in that frame, while in other frames it was sent before it was received. The only case in which you have information going backwards in time in all frames is when you send two tachyon signals, in the manner I described at the end of that post:
Let me give a numerical example of this to make it more clear. Suppose we have an observer Alice at rest at position x=0 in the C frame, and another observer Bob at rest at x'=0 light-seconds in the C' frame, and moving at 0.6c in the +x direction relative to the C frame. Say Alice and Bob start out at the same position at x=0 in the C frame and x'=0 in the C' frame. So at a time of t=156 2/3 seconds in the C frame, Bob will be at position of x = 156 2/3*0.6 = 94 l.s. in the C frame. Now suppose that at t=156 2/3 seconds, Alice sends a tachyon signal which moves at 10c in the C frame, so that 10 seconds later at t=166 2/3 seconds, the tachyon signal has reached position x=100 l.s. In those 10 seconds, Bob has moved an addition 6 l.s. in the C frame, so he will arrive at x=100 l.s. at the same moment.

So, the event of Bob receiving the tachyon signal happens at x=100 l.s., t=166 2/3 s in the C frame. What about Bob's own rest frame C'? In this frame the event has coordinates:

x' = 1.25*(100 - 166 2/3*0.6) = 0
t' = 1.25*(166 2/3 - 100*0.6) = 1.25*(106 2/3) = 133 1/3

Also, in Bob's frame C' Alice has been moving in the -x' direction at 0.6c since their positions coincided at t'=0, so at t'=133 1/3 her position in this frame is x' = -0.6*133 1/3 = -80 l.s.

Now, suppose at this same moment of t' = 133 1/3 when Bob receives the tachyon signal from Alice, Bob immediately sends a tachyon reply which moves at 10c towards Alice in his frame (this is where the first postulate of relativity comes in--if it's possible to send a signal at 10c in the coordinates of one frame, it must be possible to send a signal which moves at 10c in another frame). After about 8.5106383 seconds in the C' frame, at time t' = 133 1/3 + 8.5106383 = 141.84397, the tachyon signal catches up to Alice, since it is now at position x' = -10*8.5106383 = -85.106383, and meanwhile she has moved -0.6*8.5106383 = -5.106383 so her new position is also x' = -80 - 5.106383 = -85.106383. So, the coordinates in the C' frame of Alice receiving the reply are x' = -85.106383, t'=141.84397.

Now go back to Alice's frame and see when she receives the reply. Again, this can be done with the Lorentz transform:

t = 1.25*(141.84397 + 0.6*-85.106383) = 1.25*(90.78014) = 113.4752 seconds.

And of course, since Alice is always at the origin in her coordinate system, the position of this event is:

x = 1.25*(-85.106383 + 0.6*141.84397) = 0

Anyway, the thing to note is that the event of Alice receiving Bob's reply actually happened earlier in Alice's frame than the event of her sending the original tachyon signal at t=156 2/3 seconds! She actually received Bob's reply before she sent her first message, so if Bob had just replied by sending her message back to her, she'd know what message she was going to send before she sent it. And the event of Alice receiving Bob's reply has a timelike separation from the event of her sending the message, so all inertial frames agree on the order of these two events.
I have never, ever argued that events with a spacelike separation can be "actually simultaneous" in the way you describe, and neither has DaleSpam as far as I can tell. Both of us have consistently said that simultaneity is relative to a particular frame of reference--each frame has its own judgment about whether two events are simultaneous.
Seems to me you have just failed to understand the actual argument, and that the argument you imagine that I and DaleSpam are making has no resemblance to what we were really saying.

RandallB

Don’t have time to review your entire post but here is the important part you need to address But yes you did, see your post #53; I don’t agree because you keep declaring that apparent simultaneous time observations at spacelike separations in x’ can be considered as real simultaneous events per simultaneity – thus you say the t’ of -62.5 at x’ = 117.5 is simultaneous with with the t’ = -62.5 for x’=0 and therefore Before the start.
If you did not make this assumption (a preferred frame assumption by the way) explain exactly how you decided the x’ = 117.5 arrival happened before the x’=0 start?

Obviously those results give the appearance of “backwards” time to x’ observers. BUT IT DOES NOT give that appearance to them if they apply the rules / understanding of SR simultaneity!
You guys seem to think “simultaneity” says something like “you may consider same time events within a common frame to be simultaneous”! Or as you put it “that simultaneity is relative to your choice of reference frame”!
That could not be more wrong, SR says nothing of the sort nor is it a part of “the way the Lorentz transform works”. Simultaneity applies uniformly the same in any frame of reference as any physics rule should. It says that those observers in order to truly understand the reality of their own reference frame must recognize that spacelike separated common time events cannot automatically be considered simultaneous! Additional, SR cannot and is not the tool to establish any two spacelike separated as being simultaneous.

Dang, that makes it hard to use, how can astrophysicists get any work done!
They make an assumption!
A non SR, lets ignore Simultaneity for a special case inside a few thousands of light-years around ( more if we can get by with it). You cannot call such a departure from SR “relativity” and they don’t – it’s called Astrophysics as they presume to establish a preferred reference for at least a local region of space (but often much larger) based on the CMBR. (Particale Physics doesn’t need or use such a device AFAIK)
.........And by the way SO DID YOU!
When you started the problem in post # 53 you made it clear that the tachyon was ten times faster than light, and it was clear you intended that to mean after t=10 light and the tachyon would simultaneously reach x=10 and x= 100. Unless you make it clear that those two events may not be simultaneous, and how you proceed with that fact included you simply cannot assert that you did not start without a preferred frame assumption.
Frankly IMO you cannot even state the problem without making that assumption.
And once you do it is exclusive, no other frame can be considered preferred and all time ordering issues must be converted the one preferred frame. That means you cannot draw conclusions from the t’ observations as you did.

So unless you can state clearly how you avoided using preferred frames and still defined which space like separated events happened when relative to a single observer like at x’=5 or x=10 your example is pointless.

But by sticking with your original preferred frame I can state the following.
Tachyon and Light starting at t=t’=x=x’=0 arrived simultaneously at t=10 at locations x=100 and x=10 respectively in the preferred frame.
Additionally the t’=5 at x’=5 is simultaneous with t’ = -62.5 at x’ = 117.5

However if you were using some level of science beyond what Astrophysics uses, now is the time to spell it out

DaleSpam

Yes, I suppose we do have some explaining to do as you are woefully ill-informed about some basic terminology and concepts in SR. However, I will leave the long explanatory posts to JesseM since I do not have the energy or patience to educate you properly.

Please spend the time and effort to learn the basic concepts (spacetime, event, Lorentz transform, simultaneous, Minkowski diagram, spacetime interval, timelike, and spacelike) for yourself, and then come back and see if these comments make more sense.

JesseM

I really don't understand how you think these quotes mean I'm saying events are "actually simultaneous" (which you define as meaning not just simultaneous in one specific frame, but rather 'they will be “actually simultaneous” as measured by any and every other possible reference frame you might come up with') when the parts in bold show quite clearly I am talking about simultaneity relative to a specific frame only. Seriously, can you explain your reasoning? Is there something I'm missing about your definition of "actually simultaneous", or do you think it's somehow incorrect to talk about simultaneity in a specific frame (as I showed with my quotes in post #58, real physicists, including Einstein, talk this way all the time, it's just standard terminology to say that events which have the same time-coordinate in one frame are 'simultaneous' in that specific frame).
What does "real simultaneous events per simultaneity" mean? I always talk about relative simultaneity, not absolute or "real" simultaneity, which is eliminated altogether in relativity. This is how all physicists use the term "simultaneity", did you not read those quotes in post 58?
Sure, those two events are simultaneous in the primed frame. They are non-simultaneous in the unprimed frame. There is no single fact about whether or not they are "really" simultaneous, relativity rejects all notions of "real" frame-independent simultaneity.
It happened before the start in the primed frame, and after the start in the unprimed frame. Neither one represents any sort of frame-independent "actual" truth, they are both statements that are specific to a particular frame, and relativity says all frames are equally valid.
If there is only a single tachyon signal, I agree that it does not move "backwards in time" in any objective frame-independent sense, so there is no causality violation here. But that is why I keep saying over and over (and you keep ignoring it) that the key is to have two tachyon signals, an original and a reply, with the first signal moving FTL but forwards in time in frame #1 (and backwards in time in frame #2), and the second signal moving FTL but forwards in time in frame #2 (and backwards in time in frame #1). The end result is that the event of the first observer receiving the reply happens before the event of his sending the original signal, and there is a timelike separation between the event of his receiving the reply and the event of his sending the original signal, so all frames do agree on the order of these two events, and this is a genuine causality violation. If you think this reasoning is wrong, please address the numerical example with Alice and Bob that I gave near the end of post #63.
"As any physics rule should"? Do you think velocity applies uniformly the same way in any frame of reference too, so that if I am at rest in one frame I must be at rest in all frames? That isn't true even in Newtonian physics! Anyway, if you honestly disagree that it's standard practice to give each frame its own different definition of simultaneity, look over the quotes from real physicists that I gave in post #58. When Einstein writes "Events which are simultaneous with reference to the embankment are not simultaneous with respect to the train, and vice versa (relativity of simultaneity)", do you think he is agreeing with you or with me? When A.P. French writes "An immediate consequence of Einstein's prescription for synchronizing clocks at different locations is that simultaneity is relative, not absolute ... Our judgment of simultaneity is a function of the particular frame of reference we use", do you think he's agreeing with you or me? And when John Wheeler and Edwin Taylor write "Did the two lightning bolts strike the front and the back of the train simultaneously? Or did they strike at different times? Decide! Strange as it seems, there is no unique answer to this question. For the situation described above, the two events are simultaneous as measured in the Earth frame; they are not simultaneous as measured in the train frame. We say that the simultaneity of events is, in general, relative, different for different frames." -- do you think they are agreeing with you or me?
So when you say "cannot automatically", you are claiming that there is some truth about "actual simultaneity", so that there would be a specific frame where events that have the same time coordinate in that frame actually are simultaneous? This is the exact opposite of what relativity claims, and if you insist on this without being willing to consider the possibility you might be misinformed or to address the numerous quotes from professional physicists which say the opposite, then I really think this should be reported to the moderators, because you're violating the rules here about not arguing about relativity's validity or endorsing your own personal theories, this sort of thing can mislead people who come to these forums trying to learn about mainstream physics.
No, they pick a particular coordinate system to work in, without granting that coordinate systems' judgments about simultaneity any special truth, just like they use the velocities of galaxies in a particular coordinate system without claiming that our galaxy is "really" at rest or that distant galaxies are "really" moving at close to the speed of light.
Only in that frame. In other frames these events would be non-simultaneous. Simultaneity is relative to your choice of frame, just like velocity.
No preferred frame assumption, because I didn't say anything about these events being simultaneous in other frames, or about this frame's perspective being any more valid than any other frame's perspective. If I said some object's velocity was 0.8c in a particular frame, would you assume I was making the claim that it had an absolute velocity of 0.8c which all frames would have to agree on?
I don't need to make any assumptions about absolute simultaneity or preferred frames at all. You are really completely confused here.
I avoided using preferred frames because I said nothing whatsoever that would lead a person with understanding of SR to imagine I was postulating a preferred frame, or doing anything other than making frame-specific claims about simultaneity. But you apparently lack even a basic understanding of the way simultaneity works in SR.
The frame is not "preferred". It is just the frame I started out working with, where the tachyon has a speed of 10c and these two events; I can and did show that in a different, equally valid frame the tachyon's speed is different, and these events are non-simultaneous.
In the unprimed frame these events are simultaneous. In the primed frame they are non-simultaneous. Simultaneity is relative to your choice of frame in relativity, hence the phrase, "relativity of simultaneity".
Only in your ignorant fantasy version of astrophysics is there any objective, frame-independent truth about whether different events are simultaneous or not. I'm sure you've never taken an actual course or studied the mathematical details, because if you had, you'd know that simultaneity in astrophysics is every bit as coordinate-dependent as velocity in astrophysics, there is no frame-independent "objective truth" about either one.

peter0302

Sorry for not replying earlier. It seems obvious to me that if gravity is _solely_ an attractive force, but antiparticles are actually moving backwards in time, then the attraction would happen in reverse time, causing the appearance of a repulsion.

Conversely, if antimatter and normal matter gravitationally repel one another, and antiparticles move backwards in time, then antiparticles would appear to be gravitationally attracted to normal matter in normal time.

JesseM

Actually, gravity is time-symmetric, meaning the laws of gravity are unchanged under a time-reversal transformation--in physical terms, this means that if you look at a film of objects moving under the influence of gravity, there's no way (aside from changes in entropy) to determine if you're watching the film being played forwards or if it's being played backwards. The reason it seems asymmetric is because of entropy, like how a falling object will smack the ground and dissipate most of its kinetic energy as sound and heat--if a falling object had a perfectly elastic collision with the ground so that no kinetic energy was dissipated in this way, each time it hit the ground it would bounce back up to an equal height as before, so this would look the same forwards as backwards (and the reversed version of the collision where kinetic energy is dissipated is not ruled out by the laws of physics, it's just statistically unlikely that waves of sound and the random jostling of molecules due to heat would converge to give a sudden push to an object that had been previously been resting on the ground...if it did happen, though, it would look just like a reversed movie of an object falling to the ground and ending up resting there). Likewise, any situation where no collisions are involved, like orbits, will still be consistent with the laws of gravity when viewed in reverse.