Does My Wrist Watch Physically Beat Slower?

[ghwellsjr]

Hello,

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." Does that mean literally?

My own speculation:

Although time does slow down when I travel at a speed close to the speed of light, my wrist watch will not beat any faster or slower because it is just a mechanical device that beats every earthly second.

I am not sure though.

Kingfire, there are at least two different competing interpretations of special relativity on this forum.

1) First, there is what is known as the Lorentz Ether Theory (LET). If you are basing the answer to your question on this interpretation, the answer to your question would be, yes. Yes, your watch physically beats slower. That's because, according to LET, there are time shifts in the transmittal of electrical forces between and within physical objects, resulting in actual changes in speeds of physical interactions, including clock mechanisms (affecting tick rates, etc.).

The answer under any interpretation or understanding of any form or version of LET, past or present, is not yes. Even though Lorentz believed in a literal ether defining an absolute rest state, only in which light propagates at c, he, and all other LET adherents never claimed that the Earth was ever stationary in it.

Therefore, since the Earth must be traveling at some unknown speed and in some unknown direction through the ether, clocks on the Earth are already beating slower than the presumed absolute time defined by the ether. So if you take off from the Earth in the same direction that the Earth is traveling through the ether, then your wristwatch will beat out seconds more slowly than earthly seconds. However, if you take off in the opposite direction, you could actually be stationary in the ether, in which case your wristwatch will beat out seconds faster than earthly seconds.

So the correct answer according to LET is: "unknown".

I already gave the correct answer under SR in my first post.

 

[PeterDonis]

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.

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*.

Only if on that diagram red 3D spaces are added the coordinates make sense.

On your interpretation, perhaps. But there are other interpretations.

We better stop arguing about this. It doesn't help either way.

I'll stop if you will.

 

[Tomahoc]

interesting discussions.. so SR and LET are identical in mathematical formulation.

Peterdonis. Going to this example. Supposed you had a missile launched from Earth traveling at 0.99c aimed at a target in Tau Ceti, and in it's frame only 2 seconds would elapse traveling 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.

 

[PeterDonis]

Peterdonis. Going to this example. Supposed you had a missile launched from Earth traveling at 0.99c aimed at a target in Tau Ceti, and in it's frame only 2 seconds would elapse traveling 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.

Supposed after 30 seconds, you have order from the President to abort it.

Meaning, 30 seconds after launch in the Earth frame.

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.)

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.

 

[tiny-tim]

Welcome to PF!

Hello Kingfire! Welcome to PF!

(are you still there? )

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

 

[Tomahoc]

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?

 

[PeterDonis]

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.

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.

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.

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.

 

[PeterDonis]

Tomahoc, one other thought regarding the Tau Ceti scenario; I suggest that you consider carefully this statement I made a few posts ago:

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.

 

[Tomahoc]

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)

 

[PeterDonis]

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.

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.

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.

 

[Tomahoc]

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 I am 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.

 

[PeterDonis]

what I'm asking or the scenerio I am interested is not exactly it

For future reference, it helps to ask the question you're really interested in up front.

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.

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).

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).

 

[bobc2]

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 occurring 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 textbooks 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.

 

[Tomahoc]

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.

 

[PeterDonis]

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".

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 textbooks 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.)

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.)

 

[PeterDonis]

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).

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.

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.

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).

 

[Tomahoc]

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?

 

[Dale]

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?

 

[PeterDonis]

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?

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.

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.

 

[Tomahoc]

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?
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.
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.

Have you forgotten something. To avoid the missile sending the signal back to Earth's past. It has to receive it at 30 seconds too. So the aether frame in our scenerio acts like delay buffer. Because if it receives it less than that. It can send the signal to Earth before Earth sends it. In our examples. Remember We are dealing only with scenerio where tachyons velocity is fixed to the aether frame so don't go back to the old assumptions that the tachyons velocity is frame dependent (which is what make you worked example or inequality valid).

 

[PeterDonis]

To avoid the missile sending the signal back to Earth's past. It has to receive it at 30 seconds too.

Not if the tachyon velocity is independent of the emitter's motion. See my post #51.

don't go back to the old assumptions that the tachyons velocity is frame dependent (which is what make you worked example or inequality valid).

No, it isn't. My worked example assumes that the velocity of the tachyon emitted by the Earth is fixed at w in the Earth frame, which will be true only if the tachyon velocity is independent of the state of motion of the emitter (since the missile is moving in the Earth frame). Since we don't know if the Earth frame is the aether frame, we don't know if the speed w is the same as the (fixed) tachyon speed in the aether frame, but that doesn't matter; all we need to know is that w is fixed. (My example doesn't even analyze the trajectory of a return tachyon emitted by the missile; for that case, see below.)

It is true that there is a case my worked example doesn't cover: the case in which the tachyon emitted by the Earth goes backwards in time in the Earth frame (or the tachyon emitted by the missile--but they can't both go backwards in time in the Earth frame, for the reasons I gave in post #51). But that's easy to fix; as I said before, just work the problem in the aether frame instead (since the tachyon can't go backwards in time in that frame--the fastest it can travel is instantaneously), and add a nonzero velocity e for the Earth. Then, as I said before, there are two cases to cover, the case where e and v (the missile velocity) both have the same sign (i.e., Earth and missile are moving in the same direction) and the case where e and v have opposite signs (i.e., Earth and missile are moving in opposite directions). It is straightforward to extend my worked example to cover this case, which also allows you to extend the analysis to the return tachyon emitted by the missile as well.

 

[Tomahoc]

Not if the tachyon velocity is independent of the emitter's motion. See my post #51.



No, it isn't. My worked example assumes that the velocity of the tachyon emitted by the Earth is fixed at w in the Earth frame, which will be true only if the tachyon velocity is independent of the state of motion of the emitter (since the missile is moving in the Earth frame). Since we don't know if the Earth frame is the aether frame, we don't know if the speed w is the same as the (fixed) tachyon speed in the aether frame, but that doesn't matter; all we need to know is that w is fixed. (My example doesn't even analyze the trajectory of a return tachyon emitted by the missile; for that case, see below.)

It is true that there is a case my worked example doesn't cover: the case in which the tachyon emitted by the Earth goes backwards in time in the Earth frame (or the tachyon emitted by the missile--but they can't both go backwards in time in the Earth frame, for the reasons I gave in post #51). But that's easy to fix; as I said before, just work the problem in the aether frame instead (since the tachyon can't go backwards in time in that frame--the fastest it can travel is instantaneously), and add a nonzero velocity e for the Earth. Then, as I said before, there are two cases to cover, the case where e and v (the missile velocity) both have the same sign (i.e., Earth and missile are moving in the same direction) and the case where e and v have opposite signs (i.e., Earth and missile are moving in opposite directions). It is straightforward to extend my worked example to cover this case, which also allows you to extend the analysis to the return tachyon emitted by the missile as well.

I've been analyzing your statements the past couple of hours. But if both the Earth and missile travels opposite from each other at say 0.9999c (or whatever), and you are watching in a station at middle of them. And you are in the ether frame. Then when Earth sends instantaneous signal after 30 seconds to missile, and missile sends another at the same 30 seconds. Then they can both receive it instantaneously at 30 seconds. In this case, their time is somehow synchronized, contrary to what you said it can't be synchronized bec they are timelike and not spacelike, may I know your comment?

 

[PeterDonis]

may I know your comment?

If you keep on changing the parameters, of course you're going to change the answer. Now it appears that "30 seconds" means "30 seconds in the ether frame", which is different than 30 seconds by Earth's clock or 30 seconds by the missile's clock. So you're talking about signals being sent between different events than the ones we were talking about before. These two events *are* spacelike separated (because they both occur at the same time, 30 seconds, in the ether frame).

 

[Tomahoc]

If you keep on changing the parameters, of course you're going to change the answer. Now it appears that "30 seconds" means "30 seconds in the ether frame", which is different than 30 seconds by Earth's clock or 30 seconds by the missile's clock. So you're talking about signals being sent between different events than the ones we were talking about before. These two events *are* spacelike separated (because they both occur at the same time, 30 seconds, in the ether frame).

Ey if its 30 seconds at ether frame, it is also 30 seconds at both Earth and missile. If not, what time then??

 

[Vandam]

You have a serious obsession with solipsism. I am not a solipsist, if you believe that I have EVER made statements indicating that then please point them out and I will retract or explain them.

If you are not a solipsist, meaning you believe in an outside real world, then relativity of simultaneity leads automatically to Block universe.

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.

What physical meaning? We talk physics on this forum.

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*.

No. observational evidence leads to block universe. See below.

Do you agree that the common mathematical feature, the Lorentz transform, is what each uses to make all of its experimental predictions?

What are 'experimental predictions'? What is 'experimental evidence'?

Observation.

The LT matches what you observe. Indeed.

But what do you observe?

In order to observe an event (f.ex. a clock showing specific time indication), that event has to exist before you observe it and lightbeams travel from that event to your retinae. (If you refute this it is pointless to talk about 'observation'. What is left is only the image of an event you 'see' in your brain as a mental awareness with no cause or origin creating that image. Solipsism.)

Hence the experimental or observational evidence gives us information of that's going on in our 3D world. A 3D world that exists before you 'observe' any events of it, because we have to wait until the lightbeams reach our retinae.
The fact we do not know yet (now) what happens out there in our 3D world 'now' doesn't mean there are no specific events out there in 3D world.

What do the LT transformations tell us?

Green coordinates tell us that in the 3D world of Mr Green with wristwatch 0.5, event A is at .5 distance. The experimental/observational evidence for Green tells us that event A is simultaneous with his wristwatch .5 (event E), which means those two events are/were both part of one 3D world. (3D world = simultaneous events. Non-simultaneous events can never be part of one 3D world.)

The experimental/observational evidence for Red tells us that event A is simultaneous with event R, which means that they are/were both part of one physically real 3D world, a different one than Green's 3D world. That only makes sense in SR, not LET.

LT and the experimental/observational evidence shows that LET is wrong, but SR correct.

Of course you can say that the observational evidence is correct in LET if you consider red's observational evidence an illusion, a mathematical fiction. But is this physics? Lorentz knew the LT were problematic in his ether context. (I will not repeat his quote.)
Einstein's contribution was to solve that problem by changing the illusion into reality so to speak.
It means the relativity of simultaneity is not only a mathematical exercise on your calculator on the kitchen table, but a description of what is really happening with and in the real physical 3D worlds in 4D spacetime. Experimental and observational experiment (f.ex Einsteins train experiment) show us Block Universe.

 

[Vandam]

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".

Can you show us how that (bold) works?
So the moving guy is from his illusion bubble observing slower ether time? Gets too philosophical for me.

You say 'thinks'.
I'm interested what is out there in 3D space. Physics. Not what he thinks. Nor illusions.

(Or are you going to tell me that 3D world is an illusion? Be carefull. If you do, you are a solipsist)

 

[Dale]

If you are not a solipsist, meaning you believe in an outside real world, then relativity of simultaneity leads automatically to Block universe.

No, it doesn't. LET is a counter example. Another counter example would be a universe where any arbitrary spacelike 3D surface is "real" and the postulates of relativity hold locally, such an example could be made compatible with GR and therefore a much better candidate for "reality" than the block universe. There could well be other counter examples.

What are 'experimental predictions'? What is 'experimental evidence'?

An experimental prediction is the value expected on some specific measuring device in a given setup. Experimental evidence is the actual value obtained on the measuring device in a given setup.

E.g. a particle accelerator produces a stream of atoms moving at v relative to the laboratory. When measured at rest those atoms emit radiation with a characteristic frequency f0. What frequency, f, will be measured from the moving atoms with a receiver at rest wrt the lab mounted perpendicular to the stream?

Both the block universe and LET will use the LT to determine the experimental prediction which is the expected value of f. Since they both use the LT to calculate it they must unavoidably both obtain the same value for f.

Therefore the actual measured value of f can either confirm both LET and the block universe or it can contradict both. It cannot possibly confirm one and contradict the other since they both predict the same value of f.

Can you provide a counter-example? Any experiment where LET uses the LT to predict some measured value and where the block universe uses the same LT to predict some different value? It seems like a patently false claim to me.

I think that all you can do is to make a strawman LET which doesn't use the LT to make its predictions or continue to make irrelevant philosophical or historical objections about LET.

 

[Dale]

Can you show us how that (bold) works?

Easy. The laboratory has a set of local rods and local clocks which are synchronized using light signals in the laboratory frame. According to LET these are related by the LT to the true time and space coordinates in the ether frame. I will denote local coordinates as the primed coordinates and the aether coordinates by unprimed variables.

A clock at rest at the origin of the ether frame has a constant position x=0. So by the LT in the lab frame it reads time:
t' = γ (t-vx/c²) = γt

Since γ>1 the aether clock appears to run slow according to the local clocks.

 

[bobc2]

Easy. The laboratory has a set of local rods and local clocks which are synchronized using light signals in the laboratory frame. According to LET these are related by the LT to the true time and space coordinates in the ether frame. I will denote local coordinates as the primed coordinates and the aether coordinates by unprimed variables.

A clock at rest at the origin of the ether frame has a constant position x=0. So by the LT in the lab frame it reads time:
t' = γ (t-vx/c²) = γt

Since γ>1 the aether clock appears to run slow according to the local clocks.

So, what is the justification for using the Lorentz transform in this context (it is easy to show the justification in the context of Einstein-MInkowski)?

 

[Dale]

So, what is the justification for using the Lorentz transform in this context (it is easy to show the justification in the context of Einstein-MInkowski)?

Please don't avoid my question of post 53: Do you agree that the common mathematical feature, the Lorentz transform, is what each uses to make all of its experimental predictions?

The justification is that it is a postulate of the theory that local frames are related to the ether frame by the LT. And, of course, that postulate is supported by the data.

 

[bobc2]

Please don't avoid my question of post 53: Do you agree that the common mathematical feature, the Lorentz transform, is what each uses to make all of its experimental predictions?

I have never denied the commonality of the Lorentz transformations in both interpretations of special relativity. I've noted that more than once. So, I think I will present a new interpretation of special relativity using the Lorentz transformations as a postulate (I can think of a number of arbitrary possibilities)--now, that proves that Einstein-Minkowski is not necessarily the correct interpretation.

The justification is that it is a postulate of the theory that local frames are related to the ether frame by the LT. And, of course, that postulate is supported by the data.

DaleSpam, the Lorentz theory is not based on that postulate, it was originally based on an ad hoc derivation of the Lorentz transformation for times to account for the negative speed of light experimental results. They were derived for special cases (the length contraction may have later been added on as a postulate--I don't remember for sure). Einstein-Minkowski is a foundational theory that is applied for the most general case. It is not surprizing that Lorentz's electron theory should be compatible with Einstein's general theory for electrodynamics. Actually, Lorentz's original formulations had error's that were corrected by Poincare' and others. And Poincare' actually carried Lorentz's theory into the more general arena (which I think was a departure from the original intent of the theory) and understood the Lorentz transformations to form a group (I believe it was Poincare' who coined the term Lorentz transformation).

 

[PeterDonis]

Ey if its 30 seconds at ether frame, it is also 30 seconds at both Earth and missile. If not, what time then??

The Earth and the missile are both moving in the ether frame, so t = 30 seconds in the ether frame is *not* t' = 30 seconds in the Earth frame or the missile frame. You keep on switching numbers around so I'm not sure which numbers you are thinking of for this example, but if we take 0.9999c as the speed of the Earth and the missile in the ether frame, then gamma is about 71, so t = 30 seconds in the ether frame corresponds to t' = 30/71 seconds, or about t' = 0.42 seconds in the Earth frame or the missile frame. So a tachyon that travels instantaneously in the ether frame, and is launched at t = 30 seconds in the ether frame, will hit the Earth (or the missile) when the Earth's clock (or the missile's clock) reads about 0.42 seconds.

 

[PeterDonis]

Looking back over my previous posts, I found a couple of errors that need to be corrected:

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).

I was wrong here. If the Earth and the missile both set their clocks to zero when the missile is launched, then the two events "Earth clock reads 30 seconds" and "missile clock reads 30 seconds" (each event located on the appropriate worldline, Earth's or missile's) will *always* be spacelike separated. So I was wrong to say that a light pulse launched from Earth when Earth's clock reads 30 seconds could ever reach the missile before the missile's clock reads 30 seconds.

However, I was still correct in the original example (when I assumed the missile's speed was 0.99c) when I said a light pulse launched from Earth when Earth's clock reads 30 seconds would reach the missile before the missile hits Tau Ceti (at a distance of 12 light years in the Earth frame). That's because if the missile's speed is 0.99c, the missile will take a lot longer than 30 seconds, by its own clock, to reach Tau Ceti. That is, I was wrong to assume that the missile's time of flight, by the missile's own clock, would be only 2 seconds if the missile's speed was 0.99c.

So I also got this wrong:

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)

The time dilation factor for v = 0.99c is only about 7, so the time between launch and the President issuing the recall order, in the missile's frame, is 30/7 seconds, or about 4.3 seconds. That doesn't change the rest of my conclusions; the light pulse will still catch the missile well before it reaches Tau Ceti (since, as I said, that result is an invariant and I derived it in the Earth frame without using any values in the missile frame). The missile's time of flight, by its own clock, will be the time of flight by Earth's clock, 12/.99 years, divided by gamma = 7, or about 1.7 years; and 4.3 seconds is still *much* shorter than that, so in the missile's frame, Earth is still much closer than Tau Ceti when the light pulse is launched.

 

[PeterDonis]

the Lorentz theory is not based on that postulate, it was originally based on an ad hoc derivation of the Lorentz transformation for times to account for the negative speed of light experimental results.

Originally, yes. But once again, don't confuse the physics with the history of the physics. You say later on in this same post that the theory was later modified; when we talk about "LET" in terms of the physics (as opposed to the history of the physics) we are talking about whatever the "best current version" of the theory is. That would seem to be this:

And Poincare' actually carried Lorentz's theory into the more general arena (which I think was a departure from the original intent of the theory) and understood the Lorentz transformations to form a group (I believe it was Poincare' who coined the term Lorentz transformation).

In other words, the "best current version" of LET covers the "more general arena" and is therefore mathematically equivalent to what you are calling "Einstein-Minkowski" SR. Since both are mathematically equivalent, it's pointless to talk about which "postulates" each one uses. You can derive "Einstein-Minkowski" SR *without* taking the LT as a postulate, if you pick your other postulates appropriately. The point is that each theory contains a mathematically self-consistent system, and it's the *same* system, mathematically, in both theories.

 

[Dale]

I have never denied the commonality of the Lorentz transformations in both interpretations of special relativity. I've noted that more than once.

OK, then the conversation should really be concluded. Since they both use the LT for all of their experimental predictions then all of their experimental predictions must be identical. Since all of their experimental predictions must be identical there can be no experiment which could distinguish between the two.

Do you disagree in any way with that chain of reasoning? If so, please explain.

So, I think I will present a new interpretation of special relativity using the Lorentz transformations as a postulate (I can think of a number of arbitrary possibilities)--now, that proves that Einstein-Minkowski is not necessarily the correct interpretation.

Exactly. Now you are getting the idea. There can always be more than one way to interpret the same equation, so there will always be multiple interpretations which cannot be distinguished empirically and therefore no interpretation can claim to necessarily be the correct one.

DaleSpam, the Lorentz theory is not based on that postulate, it was originally based on an ad hoc derivation of the Lorentz transformation for times to account for the negative speed of light experimental results. They were derived for special cases (the length contraction may have later been added on as a postulate--I don't remember for sure). Einstein-Minkowski is a foundational theory that is applied for the most general case. It is not surprizing that Lorentz's electron theory should be compatible with Einstein's general theory for electrodynamics. Actually, Lorentz's original formulations had error's that were corrected by Poincare' and others. And Poincare' actually carried Lorentz's theory into the more general arena (which I think was a departure from the original intent of the theory) and understood the Lorentz transformations to form a group (I believe it was Poincare' who coined the term Lorentz transformation).

All of those are excellent philosophical/historical reasons for prefering the block universe interpretation of the LT over the LET interpretation of the LT.