Does My Wrist Watch Physically Beat Slower?

by Kingfire
Tags: relativity, speed of light, time, wrist watch
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 Quote by Vandam My diagram shows perfectly what LET means. In my diagram the ETHER frame is very well indicated. In that ether frame the primed coordinates do not make sense, unless they are mathematical fictous ad hoc numbers, just like Lorentz admited himself.
On the LET interpretation, the primed coordinates correspond to coordinate assignments that the moving observer would make. LET says that those assignments are not the "true" coordinates, but it still gives them a perfectly well-defined meaning.

 Quote by Vandam But apparently you can not give me the context in which the numbers make sense.
I already have, repeatedly. I just did it again, above. But you either can't understand or refuse to accept that LET is an *interpretation*, just as the "block universe" is an *interpretation*.

 Quote by Vandam Only if on that diagram red 3D spaces are added the coordinates make sense.
On your interpretation, perhaps. But there are other interpretations.

I'll stop if you will.
 P: 36 interesting discussions.. so SR and LET are identical in mathematical formulation. Peterdonis. Going to this example. Supposed you had a missile launched from earth travelling at 0.99c aimed at a target in Tau Ceti, and in it's frame only 2 seconds would elapse travelling to it. Supposed after 30 seconds, you have order from the President to abort it. You know you can't reach the missile using any radiowave because it can't go beyond light speed. Supposed tachyons could travel in the aether frame only and instantaneously (and normal light and matter can't). When you sent out the tachyon abort signal at 30 seconds... it should reach the missile at its 30 seconds time too right? But then by this time, the target in Tau Ceti is already destroyed at 2 seconds in the missile frame. Is this example right? Or can you reach the missile at 1.8 seconds even after you sent out the tachyons at your 30 seconds using tachyons that uses the aether frame? I don't believe in tachyons. But just want to understand the concept and limitations.
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 Quote by Tomahoc Peterdonis. Going to this example. Supposed you had a missile launched from earth travelling at 0.99c aimed at a target in Tau Ceti, and in it's frame only 2 seconds would elapse travelling to it.
2 seconds in the missile's frame. It would still take 12/.99 years (Tau Ceti is approximately 12 light years away, we'll assume it's exactly 12 light years here) in the Earth frame.

 Quote by Tomahoc Supposed after 30 seconds, you have order from the President to abort it.
Meaning, 30 seconds after launch in the Earth frame.

 Quote by Tomahoc You know you can't reach the missile using any radiowave because it can't go beyond light speed.
No, you don't know that. The missile will take 12/.99 years, or 12.12 years, in the Earth frame to reach Tau Ceti. A radio pulse traveling at the speed of light will take 12 years flat. But 0.12 years is a lot more than 30 seconds, so a radio pulse sent out 30 seconds after the missile leaves, in the Earth frame, will catch up with the missile before it reaches Tau Ceti. I just derived that result in the Earth frame, but since it's a result about an invariant--the crossing of two worldlines--it must hold in any frame, including the missile's frame.

(This means, of course, that in the missile's frame, the time between launch and the President issuing the order is *much* less than 30 seconds; in fact it's 30 seconds divided by the time dilation factor, which is something like 10^8, so it's on the order of a hundred nanoseconds. In that time, the missile has gotten closer to Tau Ceti--or, rather, Tau Ceti has gotten closer to the missile--by only a very small fraction of the total distance; so in the missile's frame, the radio pulse simply has a shorter distance to travel than Tau Ceti does, so it reaches the missile first.)

 Quote by Tomahoc Supposed tachyons could travel in the aether frame only and instantaneously (and normal light and matter can't). When you sent out the tachyon abort signal at 30 seconds... it should reach the missile at its 30 seconds time too right?
No. As I said in the other thread where you asked about tachyons, we don't have a theory of tachyons, so we don't know what the rule would be that determines which spacelike worldline a tachyon travels on. But if we assume that the Earth's rest frame is the "aether frame", then a tachyon pulse sent out at Earth time t = 30 seconds after launch would arrive at the missile at Earth time t = 30 seconds after launch; which, as I noted above, would be missile time t' = 100 nanoseconds or so after launch, so it would be way before the missile reached Tau Ceti.

Of course, this depends on the Earth's rest frame being the "aether frame". However, we can make a much more general statement, because we've already proven (I just did it above) that a light pulse emitted at Earth time t = 30 seconds after launch will reach the missile before it hits Tau Ceti. But *any* tachyon pulse, regardless of how it travels, must reach the missile before a light pulse emitted from Earth at the same time, because any tachyon must, by definition, travel faster than light. So if a light pulse can reach the missile in time, then so can any tachyon pulse, regardless of the exact laws governing tachyons.
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Hello Kingfire! Welcome to PF!

(are you still there? )
 Quote by Kingfire Some physics books tend to say that "your wrist watch will be beating slower when you travel at the or close to the speed of light."
not if you're still wearing it

time dilation is only relevant between two clocks (or a clock and an observer) if they have different velocities
P: 36
 Quote by PeterDonis 2 seconds in the missile's frame. It would still take 12/.99 years (Tau Ceti is approximately 12 light years away, we'll assume it's exactly 12 light years here) in the Earth frame. Meaning, 30 seconds after launch in the Earth frame. No, you don't know that. The missile will take 12/.99 years, or 12.12 years, in the Earth frame to reach Tau Ceti. A radio pulse traveling at the speed of light will take 12 years flat. But 0.12 years is a lot more than 30 seconds, so a radio pulse sent out 30 seconds after the missile leaves, in the Earth frame, will catch up with the missile before it reaches Tau Ceti. I just derived that result in the Earth frame, but since it's a result about an invariant--the crossing of two worldlines--it must hold in any frame, including the missile's frame. (This means, of course, that in the missile's frame, the time between launch and the President issuing the order is *much* less than 30 seconds; in fact it's 30 seconds divided by the time dilation factor, which is something like 10^8, so it's on the order of a hundred nanoseconds. In that time, the missile has gotten closer to Tau Ceti--or, rather, Tau Ceti has gotten closer to the missile--by only a very small fraction of the total distance; so in the missile's frame, the radio pulse simply has a shorter distance to travel than Tau Ceti does, so it reaches the missile first.) No. As I said in the other thread where you asked about tachyons, we don't have a theory of tachyons, so we don't know what the rule would be that determines which spacelike worldline a tachyon travels on. But if we assume that the Earth's rest frame is the "aether frame", then a tachyon pulse sent out at Earth time t = 30 seconds after launch would arrive at the missile at Earth time t = 30 seconds after launch; which, as I noted above, would be missile time t' = 100 nanoseconds or so after launch, so it would be way before the missile reached Tau Ceti. Of course, this depends on the Earth's rest frame being the "aether frame". However, we can make a much more general statement, because we've already proven (I just did it above) that a light pulse emitted at Earth time t = 30 seconds after launch will reach the missile before it hits Tau Ceti. But *any* tachyon pulse, regardless of how it travels, must reach the missile before a light pulse emitted from Earth at the same time, because any tachyon must, by definition, travel faster than light. So if a light pulse can reach the missile in time, then so can any tachyon pulse, regardless of the exact laws governing tachyons.
I should have added more 9 in the 0.99c. This is a a case when rounding off doesn't work.

Supposed the aether frame is not the earth's rest frame.. but somewhere out there.... is it not always the case that when the aether frame is used, 30 seconds on earth is synchronized to 30 seconds on the missile? You mean it varies depending on the location of the aether frame even when tachyon speed is instantaneous?? How do you find the location of the aether frame if you both want the earth's and missile to be both sychronized at 30 second worldline?
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 Quote by Tomahoc I should have added more 9 in the 0.99c. This is a a case when rounding off doesn't work.
Well, what exact numbers do you want to use? I'm using the numbers you wrote down; if you want to use different ones, feel free to give them.

 Quote by Tomahoc Supposed the aether frame is not the earth's rest frame.. but somewhere out there.... is it not always the case that when the aether frame is used, 30 seconds on earth is synchronized to 30 seconds on the missile?
No; which frame is the ether frame has nothing to do with that question. The answer to it is always "no", because the Earth and the missile are in relative motion.

 Quote by Tomahoc You mean it varies depending on the location of the aether frame even when tachyon speed is instantaneous??
What varies? I don't understand what you're asking. If you mean, does the fact that tachyons travel faster than light vary, no, it doesn't; the *definition* of a tachyon is that it travels faster than light, and if it travels faster than light in any frame, it travels faster than light in every frame.

 Quote by Tomahoc How do you find the location of the aether frame if you both want the earth's and missile to be both sychronized at 30 second worldline?
You can't; the Earth and the missile are in relative motion, so their clocks can't be synchronized. See above.
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Tomahoc, one other thought regarding the Tau Ceti scenario; I suggest that you consider carefully this statement I made a few posts ago:

 Quote by PeterDonis I just derived that result in the Earth frame, but since it's a result about an invariant--the crossing of two worldlines--it must hold in any frame, including the missile's frame.
Do you see what this means? It means that the question you are asking--can the radio pulse catch up to the missile before it reaches Tau Ceti--can be answered without having to use any frame except the Earth frame. You have a distance D from Earth to Tau Ceti; a speed v for the missile; and a time t after launch that the radio pulse goes out. Those three facts, all by themselves, are enough to answer the question: if we take D and v as given, you can calculate exactly the latest time t at which the radio pulse can go out and still reach the missile before it hits Tau Ceti. I suggest that you work that answer out first, before you even start thinking about tachyons in this scenario.
P: 36
 Quote by PeterDonis Well, what exact numbers do you want to use? I'm using the numbers you wrote down; if you want to use different ones, feel free to give them. No; which frame is the ether frame has nothing to do with that question. The answer to it is always "no", because the Earth and the missile are in relative motion. What varies? I don't understand what you're asking. If you mean, does the fact that tachyons travel faster than light vary, no, it doesn't; the *definition* of a tachyon is that it travels faster than light, and if it travels faster than light in any frame, it travels faster than light in every frame. You can't; the Earth and the missile are in relative motion, so their clocks can't be synchronized. See above.
In my query. There is the assumption that the tachyon velocity is not frame dependent, meaning not fixed relative to earth but fixed relative to the aether which can be anywhere. In this example, if we send aborting signal after 30 seconds. It should arrive at the missile 30 seconds?

Also ignore the distance is tau ceti. Imagine it is so far off that light speed is not enough to reach it because it is far. I thought tau ceti is hundreds of light years away and I'm assuming 0.99999999999c (or put any 9 where it is far enough)
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 Quote by Tomahoc There is the assumption that the tachyon velocity is not frame dependent, meaning not fixed relative to earth but fixed relative to the aether which can be anywhere.
In other words, you don't know what the tachyon's velocity is in any frame, because you don't know which frame is the aether frame.

 Quote by Tomahoc In this example, if we send aborting signal after 30 seconds. It should arrive at the missile 30 seconds?
Since you don't know the tachyon's velocity in any frame, you can't predict when it will reach the missile. However, you can still draw some conclusions just by working the problem in the Earth frame. See below.

 Quote by Tomahoc Also ignore the distance is tau ceti. Imagine it is so far off that light speed is not enough to reach it because it is far. I thought tau ceti is hundreds of light years away and I'm assuming 0.99999999999c (or put any 9 where it is far enough)
In other words, you want a scenario where the President's order goes out too late for a light pulse to reach the missile before it hits Tau Ceti, correct? I'll assume that's your intent in what follows.

In my last post, I said we can figure out everything in the Earth frame; I was hoping you would pick up on that, but I'll go ahead and do it now. All quantities are relative to the Earth frame in what follows. We have a distance D to Tau Ceti, a speed v < 1 for the missile (I'm using units in which c = 1), and a time t after the missile launch when the President's order goes out. We want t to be large enough that the radio pulse emitted then from Earth can't reach the missile before it hits Tau Ceti.

We assume that the missile is launched at time $t_0 = 0$. The time the missile reaches Tau Ceti is:

$$t_m = \frac{D}{v}$$

The time the radio pulse reaches Tau Ceti is (the pulse is sent at time t and travels at speed 1):

$$t_r = t + D$$

We want $t_r > t_m$, which gives

$$t + D > \frac{D}{v}$$

or, rearranging terms,

$$t > D \frac{1 - v}{v}$$

Now suppose we have a tachyon pulse that travels at speed w > 1 in the Earth frame (we don't know w's exact value, but we can still work with it as an unknown variable). We can run the same type of analysis as above to find the time $t_y$ that a tachyon pulse emitted at t will reach Tau Ceti:

$$t_y = t + \frac{D}{w}$$

If we want the tachyon pulse to catch the missile before it reaches Tau Ceti, we must have $t_y < t_m$, which gives

$$t + \frac{D}{w} < \frac{D}{v}$$

or, rearranging terms,

$$t < D \frac{w - v}{w v}$$

So if the time t lies between the two limits given above, i.e., if we have:

$$D \frac{1 - v}{v} < t < D \frac{w - v}{w v}$$

then the tachyon pulse will be able to catch the missile before it hits Tau Ceti, but a radio pulse will not.

I'll stop here to let you digest the above; it should give you an idea of how to calculate when each pulse will reach the missile, as well as when it will reach Tau Ceti.
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 Quote by PeterDonis In other words, you don't know what the tachyon's velocity is in any frame, because you don't know which frame is the aether frame. Since you don't know the tachyon's velocity in any frame, you can't predict when it will reach the missile. However, you can still draw some conclusions just by working the problem in the Earth frame. See below. In other words, you want a scenario where the President's order goes out too late for a light pulse to reach the missile before it hits Tau Ceti, correct? I'll assume that's your intent in what follows. In my last post, I said we can figure out everything in the Earth frame; I was hoping you would pick up on that, but I'll go ahead and do it now. All quantities are relative to the Earth frame in what follows. We have a distance D to Tau Ceti, a speed v < 1 for the missile (I'm using units in which c = 1), and a time t after the missile launch when the President's order goes out. We want t to be large enough that the radio pulse emitted then from Earth can't reach the missile before it hits Tau Ceti. We assume that the missile is launched at time $t_0 = 0$. The time the missile reaches Tau Ceti is: $$t_m = \frac{D}{v}$$ The time the radio pulse reaches Tau Ceti is (the pulse is sent at time t and travels at speed 1): $$t_r = t + D$$ We want $t_r > t_m$, which gives $$t + D > \frac{D}{v}$$ or, rearranging terms, $$t > D \frac{1 - v}{v}$$ Now suppose we have a tachyon pulse that travels at speed w > 1 in the Earth frame (we don't know w's exact value, but we can still work with it as an unknown variable). We can run the same type of analysis as above to find the time $t_y$ that a tachyon pulse emitted at t will reach Tau Ceti: $$t_y = t + \frac{D}{w}$$ If we want the tachyon pulse to catch the missile before it reaches Tau Ceti, we must have $t_y < t_m$, which gives $$t + \frac{D}{w} < \frac{D}{v}$$ or, rearranging terms, $$t < D \frac{w - v}{w v}$$ So if the time t lies between the two limits given above, i.e., if we have: $$D \frac{1 - v}{v} < t < D \frac{w - v}{w v}$$ then the tachyon pulse will be able to catch the missile before it hits Tau Ceti, but a radio pulse will not. I'll stop here to let you digest the above; it should give you an idea of how to calculate when each pulse will reach the missile, as well as when it will reach Tau Ceti.
Many thanks for the details. I digested it, but what I'm asking or the scenerio im interested is not exactly it (although ill put it in my notebook for detailed study). The scenario I'm interested is the following.

If instantaneous tachyons can reach the missile. And the missile sending back another signal. It can reach the earth before earth send it. This is what happen if the tachyons are frame dependent. But if the tachyons velocity which can be any speed up to instantaneous is always
Fixed relative to the aether frame. Then no backward time loop possible. In this case, the tachyons signal sent out 30 secs from earth reaches the missile also at 30 seconds? Because if its earlier, it can produce a situation where earth can receive it before it sends out the signal.
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 Quote by Tomahoc what I'm asking or the scenerio im interested is not exactly it
For future reference, it helps to ask the question you're really interested in up front.

 Quote by Tomahoc If instantaneous tachyons can reach the missile. And the missile sending back another signal. It can reach the earth before earth send it. This is what happen if the tachyons are frame dependent.
By "frame dependent" you mean, I assume, "the tachyon always has the same speed relative to the emitter". In that case, yes, you're correct, you can have a round-trip tachyon signal arrive before it was sent.

 Quote by Tomahoc But if the tachyons velocity which can be any speed up to instantaneous is always Fixed relative to the aether frame. Then no backward time loop possible.
Yes, that's correct; if the tachyon's speed is always fixed relative to the *same* frame (which we can call the "aether frame") regardless of the emitter's state of motion, then a round-trip tachyon signal can never arrive before it was sent; the quickest it can arrive is at the same instant it was sent (if the return signal is emitted at the same instant the outgoing signal arrives).

 Quote by Tomahoc In this case, the tachyons signal sent out 30 secs from earth reaches the missile also at 30 seconds?
If you mean 30 seconds according to the Earth frame, then yes, *if* the Earth frame is the aether frame. If not, no, the signal will arrive at the missile at some other time, which could be earlier or later than 30 seconds, depending on how the Earth is moving relative to the aether frame.

However, even if the signal arrives at the missile earlier than t = 30 seconds in the Earth frame, the return signal still won't arrive before it was sent, *if* tachyons always travel at the same speed relative to the aether frame. Remember that the return signal is traveling in the opposite direction to the outbound signal; that means the effect of the Earth's velocity relative to the aether frame is exactly the opposite on the return signal from what it was on the outbound signal. For example, suppose the outbound signal travels "backwards in time" by 1 second, so it arrives at the missile at t = 29 seconds. Then the return signal will travel "forwards in time" by the same amount, because it's traveling in the opposite direction; so it will arrive back at t = 30 seconds (assuming it is emitted at the same instant the outbound signal is received).
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 Quote by tiny-tim Hello Kingfire! Welcome to PF! (are you still there? ) not if you're still wearing it … time dilation is only relevant between two clocks (or a clock and an observer) if they have different velocities
Good comment, tiny-tim. That is exactly the situation with Einstein-Minkowski special relativity.

However, in the context of the Lorentz Ether Theory (LET) the situation is physically different. Lorentz specifically based his derivations on the consideration of a fixed ether and the results of transmittal times between objects and within objects--all processes occuring in one time evolving 3-D world. So, all observers are living in the same 3-D world. Thus, the watch the moving guy is wearing (he's moving relative to the ether) is physically ticking more slowly than it would if the guy were at rest relative to the ether.

However, due to Lorentzian processes affecting this guy (length contractions and time time dilations) as well as affecting the guy's wrist watch, he does not notice the fact that his clock is ticking slower, etc.

Again, it should be emphasized that the basis of Lorentz's (and Poincare's, et. al.) derivations make LET significantly different than the Einstein-Minkowski theory of special relativity, notwithstanding the common mathematical feature, i.e., Lorentz transformations.

It should be noted that hardly any physicists doing special relativity do it in the context of the fixed ether concept. Virtually all physicists doing relativity operate with derivations based on the Einstein-Minkowski concept. I recently reviewed several of my old text books and reference books on special relativity and found all of them following the Einstein-Minkowski formalism (Bergman, Rindler, Weyl, Naber, Baruk "Classical Field Theory", etc.). Even all of the popularizations follow Einstein-Minkowski, with only an occasional brief mention of LET.

That's why I kind of feel like LET is more of a red herring to be put on the table any time someone begins to infer that the 4-dimensional spacetime somehow relates to physical reality.

p.s. I notice that those on this forum who present LET as though it were on a par with Einstein-Minkowski never use the Lorentz ether concept with the implied force transmittal delays, etc., as a basis for explaining the phenomena associated with relativistic speeds. They either couch explanations in the context of Einstein-Minkowski spacetime or else just do Lorentz transformation numerical calculations, avoiding any reference to underlying foundational concepts of special relativity. Not even a comparison of alternative physical concepts are considered relevant.
P: 36
 Quote by PeterDonis For future reference, it helps to ask the question you're really interested in up front. By "frame dependent" you mean, I assume, "the tachyon always has the same speed relative to the emitter". In that case, yes, you're correct, you can have a round-trip tachyon signal arrive before it was sent. Yes, that's correct; if the tachyon's speed is always fixed relative to the *same* frame (which we can call the "aether frame") regardless of the emitter's state of motion, then a round-trip tachyon signal can never arrive before it was sent; the quickest it can arrive is at the same instant it was sent (if the return signal is emitted at the same instant the outgoing signal arrives). If you mean 30 seconds according to the Earth frame, then yes.
No I mean 30 seconds in the missile frame. Because if it reaches the missile at say 1 sec or 25 seconds (let's say it travels continuous and no target), it can produce a scenario where earth can receive it before sending out. Now does it mean 30 seconds on earth and 30 seconds on the missile are simultaneous to the aether frame? If yes. How do you make the aether frame simultaneous to it when they are in relative motion. This is what I was trying to understand.
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 Quote by bobc2 However, due to Lorentzian processes affecting this guy (length contractions and time time dilations) as well as affecting the guy's wrist watch, he does not notice the fact that his clock is ticking slower, etc.
It's more than that; the moving guy also thinks that the clock of the guy at rest relative to the ether is ticking slower than his. "Time dilation" in this sense is still symmetric. It's just that LET gives a privileged status to the guy at rest relative to the ether; his perception is the "true" one, and the perception of the moving guy, who thinks the guy at rest's clock is ticking slower, is an "illusion".

 Quote by bobc2 It should be noted that hardly any physicists doing special relativity do it in the context of the fixed ether concept. Virtually all physicists doing relativity operate with derivations based on the Einstein-Minkowski concept. I recently reviewed several of my old text books and reference books on special relativity and found all of them following the Einstein-Minkowski formalism (Bergman, Rindler, Weyl, Naber, Baruk "Classical Field Theory", etc.).
The formalism is the same for LET as it is for what you are calling "Einstein-Minkowski". The only difference is the interpretation. It would be more correct to say that virtually all physicists doing relativity operate on the Einstein-Minkowski *interpretation*; they view spacetime as a 4-D object, not as a 3-D object that "changes with time". (I'm not sure "virtually all" is correct here either; the ADM formalism in GR does not take this view, and a considerable number of relativists have worked on that.)

 Quote by bobc2 That's why I kind of feel like LET is more of a red herring to be put on the table any time someone begins to infer that the 4-dimensional spacetime somehow relates to physical reality.
I would agree that LET is not a popular interpretation. I would also agree that is a less parsimonious interpretation, since it postulates that one inertial frame has a special status, but gives no way of telling which one it is, so the special status doesn't have any experimental consequences.

However, the "block universe" interpretation, at least the strong version that has been argued here (and is also argued by certain physicists in popular books) is subject to similar criticisms, because the strong "block universe" interpretation is more than the simple claim that "4-dimensional spacetime somehow relates to physical reality". It is the claim that 4-dimensional spacetime *is* physical reality, period. That's a very strong claim, which also goes beyond the experimental evidence we have, not to mention that all of our current candidates for a theory of quantum gravity say it's false--they all view 4-dimensional spacetime as an emergent, approximate phenomenon, not as fundamental. (There are also issues involving determinism, which I've talked about before.)
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 Quote by Tomahoc No I mean 30 seconds in the missile frame.
That's not possible with any of the numbers you've given; a curve going from t = 30 seconds on the Earth's worldline to t' = 30 seconds on the missile's worldline would be timelike, not spacelike. In fact it will be timelike for a missile traveling at any speed fairly close to that of light (off the top of my head I think all that's required is a gamma factor of 2, which requires a missile speed of 0.866c).

 Quote by Tomahoc Because if it reaches the missile at say 1 sec or 25 seconds (let's say it travels continuous and no target), it can produce a scenario where earth can receive it before sending out.
Not if the tachyon always travels at the same speed in the ether frame. It's easy to show this: just work the problem in the ether frame. There are two possible cases in that frame: Earth and missile both moving in the same direction, and Earth and missile moving in opposite directions. It's straightforward to show for each case that if the tachyon travels at a fixed speed w relative to the ether frame, the Earth can't receive it before it sends it. And since both events occur on the Earth's worldline, their time ordering is invariant; if the signal is received after it's sent in the ether frame, it's received after it's sent in any frame. Work it out.

 Quote by Tomahoc Now does it mean 30 seconds on earth and 30 seconds on the missile are simultaneous to the aether frame?
They can't possibly be if the missile is traveling at any significant fraction of the speed of light, because the two events will be timelike separated, not spacelike separated. Only spacelike separated events can be simultaneous in any frame.

 Quote by Tomahoc How do you make the aether frame simultaneous to it when they are in relative motion. This is what I was trying to understand.
I think you're going at it the wrong way around. Try what I suggested above: work the problem in the ether frame, treating the tachyon speed w as an unknown, but fixed in that frame. Work it out and you will find that the tachyon signal can't be received on Earth before it is sent for *any* tachyon speed w greater than 1, including speed w = infinity (i.e., the tachyon travels instantaneously in the ether frame).
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 Quote by PeterDonis That's not possible with any of the numbers you've given; a curve going from t = 30 seconds on the Earth's worldline to t' = 30 seconds on the missile's worldline would be timelike, not spacelike. In fact it will be timelike for a missile traveling at any speed fairly close to that of light (off the top of my head I think all that's required is a gamma factor of 2, which requires a missile speed of 0.866c). Not if the tachyon always travels at the same speed in the ether frame. It's easy to show this: just work the problem in the ether frame. There are two possible cases in that frame: Earth and missile both moving in the same direction, and Earth and missile moving in opposite directions. It's straightforward to show for each case that if the tachyon travels at a fixed speed w relative to the ether frame, the Earth can't receive it before it sends it. And since both events occur on the Earth's worldline, their time ordering is invariant; if the signal is received after it's sent in the ether frame, it's received after it's sent in any frame. Work it out. They can't possibly be if the missile is traveling at any significant fraction of the speed of light, because the two events will be timelike separated, not spacelike separated. Only spacelike separated events can be simultaneous in any frame. I think you're going at it the wrong way around. Try what I suggested above: work the problem in the ether frame, treating the tachyon speed w as an unknown, but fixed in that frame. Work it out and you will find that the tachyon signal can't be received on Earth before it is sent for *any* tachyon speed w greater than 1, including speed w = infinity (i.e., the tachyon travels instantaneously in the ether frame).
So back to my original question. A tachyon aborting signal sent at 30 secs that travels always at the same speed in the ether frame can't reach the missile in time (which takes only 2 secs to reach tau ceti). Do you agree? Bottom line is. Tachyons with velocity fixed in the aether frame is an inefficient or not effective method to abort any signal (assuming normal light speed not enough to abort it (I know I gave wrong figures which makes it reacheable but ignore this as this Is not my main inquiry or concern).

Anyway. How many seconds in the missile frame can it receive the earth signal which is sent at 30 seconds assuming tachyons velocity (instantaneous in our case) is fixed relative to aether frame. How do you solve for it?
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 Quote by bobc2 Again, it should be emphasized that the basis of Lorentz's (and Poincare's, et. al.) derivations make LET significantly different than the Einstein-Minkowski theory of special relativity, notwithstanding the common mathematical feature, i.e., Lorentz transformations.
Do you agree that the common mathematical feature, the Lorentz transform, is what each uses to make all of its experimental predictions?
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 Quote by Tomahoc So back to my original question. A tachyon aborting signal sent at 30 secs that travels always at the same speed in the ether frame can't reach the missile in time (which takes only 2 secs to reach tau ceti). Do you agree?
The missile only takes 2 seconds *in the missile frame*. It takes longer in the Earth frame--how much longer depends on the speed of the missile and the distance in the Earth frame to Tau Ceti. I've made this point repeatedly.

As for your question, I've given you enough information already to work out for yourself under what conditions a tachyon pulse can or cannot reach the missile in time; you can work the entire problem in one frame (I worked it in the Earth frame). Have you read through the worked example I gave?

 Quote by Tomahoc Bottom line is. Tachyons with velocity fixed in the aether frame is an inefficient or not effective method to abort any signal, assuming normal light speed not enough to abort it.
No, this is not true. I've already stated that repeatedly as well. By definition, tachyons travel faster than light in any frame; that means that you can't assume that if a light pulse can't get there in time, a tachyon pulse can't get there in time either. You have to work the numbers and see.

 Quote by Tomahoc How many seconds in the missile frame can it receive the earth signal which is sent at 30 seconds assuming tachyons velocity (instantaneous in our case) is fixed relative to aether frame. How do you solve for it?
Again, have you read through the worked example I gave? It included an inequality that relates the time the earth signal is emitted (30 seconds in your case, but I left it as a variable so you could try different values if you want), the distance to Tau Ceti, the speed of the missile, and the speed of the tachyon, all in the Earth frame. If this inequality is satisfied, the tachyon can catch the missile before it hits Tau Ceti. That gives you a good starting point to answer other questions.

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