Galileo and Lorentz transformation

[Dale]

meopemuk, do you agree with the following statement?

Let S and S' be two coordinate systems that are related to each other through some invertible transformation relation T(A)=A' where A' and A are the coordinates of some arbitrary event in S' and S respectively. Then, if the bomb explodes at event A in S then it explodes at event A' in S'.

 

[meopemuk]

meopemuk, do you agree with the following statement?

Let S and S' be two coordinate systems that are related to each other through some invertible transformation relation T(A)=A' where A' and A are the coordinates of some arbitrary event in S' and S respectively. Then, if the bomb explodes at event A in S then it explodes at event A' in S'.

It is obvious that simple re-labeling coordinates of events cannot make the events change or disappear. So, different "coordinate systems" always agree on the physical nature of events.

However, my point is that inertial transformations of observers are not always reducible to simple re-labeling of coordinates. It is true that space translations and rotations amount to simple coordinate changes. Observers related by space translations and/or rotations see the same explosion at different coordinate points. However, time translations and boosts are different. Two observers related by a time translation may disagree about the explosion. The same with boosts: two observers moving with respect to each other may disagree about the explosion. So, boosts cannot be represented exactly as pseudo-rotations of the Minkowski space-time coordinates. Boost transformations have also non-trivial dynamical components.

Eugene.

 

[Dale]

It is obvious that simple re-labeling coordinates of events cannot make the events change or disappear. So, different "coordinate systems" always agree on the physical nature of events.

Good. This is what I mistakenly thought you were saying, and I am glad to know that your position is not as extreme as I was understanding.

Two observers related by a time translation may disagree about the explosion.

Before reacting to this, let me clarify:

If S and S' are related by the transformations
t' = t + 5
x' = x
y' = y
z' = z

And if the explosion occurs at A = (t, x, y, z) = (1,2,3,4)

Are you suggesting that it is possible that the explosion does not occur at A' = (t', x', y', z') = (6,2,3,4)?

If this is not your claim then are you merely pointing out the obvious fact that at t' = 1 the explosion has not yet occurred? Or are you emphasizing the fact that that for some instantaneous observation made at O' = (6,0,0,0) the light from the explosion at A' has not yet reached O' and so the instantaneous observer does not visually see the explosion?

If none of these are your intent, please explain in detail what you mean.

 

[A.T.]

The principle of relativity does not tell us anything certain about what observers A(t) can say about the bomb 'b' and what observers B(t) can say about the bomb 'a'. The principle of relativity does not allow you to connect measurements performed by different observers on the same system.

Says who? The principle of relativity is based on empirical experience. Is there any empirical data to justify the above restriction of this principle?

Observers related by space translations and/or rotations see the same explosion at different coordinate points. However, time translations and boosts are different.

First you want to have them all on equal footing, and now you say they are different?

Two observers related by a time translation may disagree about the explosion.

Only if you mean your "instantaneous observers" who observe a single time coordinate only. Consequently for a space translation you would have to consider observers who observe a single space coordinate. They would disagree on many things as well. I find both concepts rather useless so far.

 

[yuiop]

...

However, my point is that inertial transformations of observers are not always reducible to simple re-labeling of coordinates. It is true that space translations and rotations amount to simple coordinate changes. Observers related by space translations and/or rotations see the same explosion at different coordinate points. However, time translations and boosts are different. Two observers related by a time translation may disagree about the explosion. The same with boosts: two observers moving with respect to each other may disagree about the explosion. So, boosts cannot be represented exactly as pseudo-rotations of the Minkowski space-time coordinates. Boost transformations have also non-trivial dynamical components.

Eugene.

You seem to be implying that because observer(s) translated in time will disagree about about whether an event occurred or not, that it follows that two observers that are separated by a boost will also disagree.

First of all there are some obvious distinctions. Two observers that are at rest with the same physical location and separated only by a time translation are in fact one and the same observer. Tom Yesterday and Tom Today can not see each other, while Tom Stationary and Tom Moving can. Only one way communication exists between Tom Today and Tom Yesterday. Tom Yesterday can leave messages for Tom Today but Tom Today can not leave messages for Tom Yesterday. Tom Stationary and Tom Moving on the other hand can communicate both ways with each other. So the temporally separated pair of observers (T.Yesterday and T.Today) are not in any way comparable to the dynamically separated pair of observers (T.Stationary and T.Moving).

This makes your statement "It is important to note that it is impossible to have a relativistic theory in which dynamical effects are associated only with time translations ..." dubious, because time translations ARE unique. As far as I know, no experiment has shown that we can travel backwards in time and yet we are free to move forwards or backwards in the spatial dimensions. The time coordinate in the invariant interval, always has a different sign from the three other spatial coordinates because the time coordinate is not exactly the same as other three coordinates.

 

[meopemuk]

Good. This is what I mistakenly thought you were saying, and I am glad to know that your position is not as extreme as I was understanding.

Before reacting to this, let me clarify:

If S and S' are related by the transformations
t' = t + 5
x' = x
y' = y
z' = z

And if the explosion occurs at A = (t, x, y, z) = (1,2,3,4)

Are you suggesting that it is possible that the explosion does not occur at A' = (t', x', y', z') = (6,2,3,4)?

If this is not your claim then are you merely pointing out the obvious fact that at t' = 1 the explosion has not yet occurred? Or are you emphasizing the fact that that for some instantaneous observation made at O' = (6,0,0,0) the light from the explosion at A' has not yet reached O' and so the instantaneous observer does not visually see the explosion?

If none of these are your intent, please explain in detail what you mean.

In your example there are two inertial observers S and S' that are related by a time translation. Observer S' makes his observations 5 hours later than observer S. So, if observer S saw the explosion, then observer S' sees only the aftermath of the explosion (5 hours later). So, these two observers (based on their measurements) make rather different conclusions about the state of the explosive device. It is not appropriate to say that the views of the two observers can be related by a simple re-labeling of coordinates of events.

Note also that observer S cannot "see into the future", i.e., 5 hours ahead. He can confidently say only about what he actually sees - the explosion. Similarly, observer S' cannot "see into the past". From his perspective, the bomb is seen as a bunch of scattered pieces. So, the opinions of S and S' about the state of the bomb are quite different. It is not possible to use the principle of relativity to reconcile these two opinions. The two opinions can be related to each other if we know the dynamical law (the Hamiltonian) which controls the time evolution of the system - the bomb.

Now, if in the above example you replace "time translation" with "boost" you will obtain a similar situation: two observers S and S' (moving with respect to each other) disagree about the state of the bomb. The two conflicting descriptions can be reconciled if we know the dynamical effect of boosts on the state of the bomb. This can be done if we know the interacting "boost generator".

Eugene.

 

[yuiop]

That was, in fact, Lorentz's explanation of the null result of the Michaelson-Morley experiment when he derived the Lorentz transforms. That theory, however, would require that only physical objects contract with motion, not the space between them while Einstein's theory requires that space itself contract and that all motion, not just electromagnetic, slow down. A version of the Michaelson-Morely experiment, called, I think, the "Kennedy experiment" showed that Einstein's theory was right and Lorentz's was wrong.

I do not think you are giving the full story here when you say Lorentz's (theory) was wrong and a lot depends on what you mean by Lorentz's theory. His early idea that relativistic effects could be explained purely in terms of physical length contraction only, due to motion relative to the ether was wrong, but his later ideas of physical length dilation AND physical time dilation due to motion relative to the ether are entirely consistent with the predictions of Special Relativity and the differences between LET and SR are only philosophical. I think the experiment you refer to is more commonly referred to as the Kennedy-Thorndike experiment.

 

[Dale]

In your example there are two inertial observers S and S' that are related by a time translation. Observer S' makes his observations 5 hours later than observer S. So, if observer S saw the explosion, then observer S' sees only the aftermath of the explosion (5 hours later). So, these two observers (based on their measurements) make rather different conclusions about the state of the explosive device. It is not appropriate to say that the views of the two observers can be related by a simple re-labeling of coordinates of events.

So, if I understand correctly you are only saying that the state of the bomb at t=1 (exploding) is not the same as the state of the bomb at t'=1 (intact). Is this a correct characterization of your claim? Is this all you intend to say? Because if so it seems a rather trivial point.

What about the state of the bomb at t'=6? Are you unwilling to assert that the state of the bomb at t'=6 is the same as the state of the bomb at t=1 (exploding)?

 

[meopemuk]

First you want to have them all on equal footing, and now you say they are different?

This is a great question! Yes, in Wigner-Dirac relativistic theory (either classical or quantum, does not matter) all 10 types of inertial transformations between observers are treated on equal footing. All of them are members of the Poincare group. There is no preference.

In order to use the Poincare group of inertial transformations in (quantum) physics we need to define a unitary representation of the group in the Hilbert space of the observed system. (If you are more comfortable with classical physics, you can make replacements "Hilbert space => phase space" and "unitary representation => representation by canonical transformations". All arguments will remain valid.) Only then we can apply various inertial transformations to state vectors of the system and/or operators of observables. Only then we can say how the physical system is seen by different observers. There is an infinite number of ways how one can build a unitary representation of the Poincare group in the Hilbert space. So, we need to choose a unique way which agrees with observed physics.

It is easy to build a non-interacting representation of the Poincare group in the Hilbert space of any N-particle system. However, this representation is not interesting for obvious reasons. So, let us build another representation, which takes interactions into account. From experience we know that results of time translations depend on interactions between particles. Therefore, the Hermitian representative of the generator of time translation (the Hamiltonian) must have an interacting form: H = H_0 + V. What about 9 other generators? We can confidently say that space translations and rotations do not have any interacting effects. These transformations remain the same as in the non-interacting case. Their Hermitian generators are non-interacting P = P_0, J = J_0.

Dirac was first to notice that in the situation described above it is not possible to assume that the Hermitian representative K of the generator of boosts remains non-interacting. Poincare group properties demand that, unlike P and J, the operator K must contains interaction terms K = K_0 + W. Therefore, boost transformations (similar to time translations) must induce non-trivial dynamical changes in the state of the system.

In this theory all inertial transformations are treated on equal footing. However, their effect on physical states can be rather different.

Only if you mean your "instantaneous observers" who observe a single time coordinate only. Consequently for a space translation you would have to consider observers who observe a single space coordinate. They would disagree on many things as well. I find both concepts rather useless so far.

Yes, I use "instantaneous observers", and it is not difficult to imagine how such observers can be realized in practice. I don't buy the space-time symmetry, so I am not going to conclude that "space-local" observers must exist as well. I don't even understand how such "space-local" observers can exist. They can't see beyond the infinitesimally small space region around them? To me it's just nonsense.

Eugene.

 

[meopemuk]

So, if I understand correctly you are only saying that the state of the bomb at t=1 (exploding) is not the same as the state of the bomb at t'=1 (intact). Is this a correct characterization of your claim? Is this all you intend to say? Because if so it seems a rather trivial point.

Yes, the point I make about the state of the bomb is rather trivial and standard. It does not deserve much discussion.

What about the state of the bomb at t'=6? Are you unwilling to assert that the state of the bomb at t'=6 is the same as the state of the bomb at t=1 (exploding)?

I disagree with your use of time labels t'=1, t'=6, etc. They create an impression that observer S' (or observer S) can see into the past or into the future. I insist on using the notion of "instantaneous" observers. These observers can see only what is before them in just one time instant. So, they assign only one time label to all their measurements. They read this label from the clock that they use.

The use of instantaneous observers is important for

1. treating all inertial transformations (including time translation) on equal footing.
2. Using the full power of the Poincare group
3. Desribing the results of time evolution and boost transformations as action of the Poincare group representation in the Hilbert space (or phase space) of the physical system.

The point is that when you use "long-living observers", then time translations are (sort of) losing their non-trivial dynamical status. From the point of view of "long-living" time-shifted observers S and S' there is no much difference in the bomb behavior. Both of them see the same explosion, simply they see it at different times. So, it appears that time translation is not more complicated than changing the value of the parameter t.

With my choice of "instantaneous observers" it becomes obvious that time translations have a non-trivial dynamical effect. It is also easier to make the point about the similar dynamical effect of boosts.

Eugene.

 

[A.T.]

Only if you mean your "instantaneous observers" who observe a single time coordinate only. Consequently for a space translation you would have to consider observers who observe a single space coordinate. They would disagree on many things as well. I find both concepts rather useless so far.

Yes, I use "instantaneous observers", and it is not difficult to imagine how such observers can be realized in practice. I don't buy the space-time symmetry, so I am not going to conclude that "space-local" observers must exist as well. I don't even understand how such "space-local" observers can exist. They can't see beyond the infinitesimally small space region around them?

No, they just see a 2D slice of 3D space. Like sitting in a box with a thin looking slit and pretending the third space dimension doesn't exist.

To me it's just nonsense.

Of course it is nonsense. Just like your "instantaneous observes" who open their eyes only once for a moment, and pretend that time doesn't exist.

 

[meopemuk]

You seem to be implying that because observer(s) translated in time will disagree about about whether an event occurred or not, that it follows that two observers that are separated by a boost will also disagree.

I am not saying that there is a cause-effect relationship between the two statements. Rather both of these statements result from the fact that any interacting representation of the Poincare group must have its time translation and boost generators dependent on interactions.

This makes your statement "It is important to note that it is impossible to have a relativistic theory in which dynamical effects are associated only with time translations ..." dubious, because time translations ARE unique. As far as I know, no experiment has shown that we can travel backwards in time and yet we are free to move forwards or backwards in the spatial dimensions. The time coordinate in the invariant interval, always has a different sign from the three other spatial coordinates because the time coordinate is not exactly the same as other three coordinates.

This is true that time has some unique properties - we cannot move back in time. However, when I speak about inertial transformations between different reference frames I am not suggesting to actually rotate, shift, or boost them physically. The same for time translations. In order to access the point of view of a past observer, there is no need to move backwards in time. For example, we can learn about Kepler's observations by reading his books.

Eugene.

 

[yuiop]

The same for time translations. In order to access the point of view of a past observer, there is no need to move backwards in time. For example, we can learn about Kepler's observations by reading his books.

Eugene.

Which echoes my statement about one way communication between time translated observers. Kepler can communicate information to us, but we can not communicate our knowledge to Kepler. It is as if there is a permanent event horizon between time separated observers in some ways analogous to the one way communication between spatially separated observers either side of the event horizon of a black hole.

... Formulas of special relativity are perfectly OK for systems not involving interactions, e.g, in the time clock where a free photon is bouncing between two mirrors. However, if interactions are present (as in the case of unstable particles), then Lorentz transformations and other SR formulas (such as the time dilation law) must be modified to take this interaction into account...

Is the light clock "interaction free"? A photon has momentum and in principle its reflection off a mirror could be detected by a sensitive enough device, so reflection counts as an interaction. In order for a light clock to have any meaning as a measurement device you would have to detect the arrival of the photon and that is surely an interaction. In any interaction free model, all measurements of any dynamic process would be impossible and the whole model becomes meaningless or useless.

 

[meopemuk]

Of course it is nonsense. Just like your "instantaneous observes" who open their eyes only once for a moment, and pretend that time doesn't exist.

My "instantaneous observers" see instantaneous states of the physical system. So, the time evolution is described as a change of perception in the chain of observers connected by time translations. This time evolution is treated on equal footing with other inertial transformations (space translations, rotations, boosts). It is generated by the Hamilton operator, just as other transformations are generated by the operators of momentum, angular momentum, and boost, respectively. The ten generators satisfy Poincare commutation relations. This is a powerful approach that allows one to move quite far in the description of dynamics of relativistic systems.

Your "permanent observers" see entire system's "history" rather than individual states. In this case the whole notion of the time evolution becomes redundant, because you cannot evolve "history". The most you can do is to re-assign t-labels. But this is not true time evolution. In your approach the similarity between different types of inertial transformations becomes hidden. I am not sure how you can use the idea of the Poincare group and the entire powerful apparatus that comes with it.

Eugene.

 

[meopemuk]

Is the light clock "interaction free"?

Of course, strictly speaking, the light clock is not interaction-free. Photons reflect from mirrors, and this reflection is caused by some kind of interaction. However, the duration of these interactions is very short, and most of the time the photons propagate freely. So, the nature of the photon-mirror interaction has a negligible effect on the rate of the light clock in any frame of reference. For its role as a time-keeping device, the nature of interactions in the light clock can be ignored.

Eugene.

 

[Dale]

I insist on using the notion of "instantaneous" observers. These observers can see only what is before them in just one time instant. So, they assign only one time label to all their measurements. They read this label from the clock that they use.

I don't understand what you intend to convey with this concept of the "instantaneous observer". Can your "instantaneous observers" observe multiple spatial locations? If so, then which spatially separated events are observed? How does the light cone relate to this?

Frankly, I am with A.T. on this, it seems utterly useless. You appear to be going out of your way to solve a problem that you admit is experimentally undetected. And in any case it is most definitely not standard SR.

 

[yuiop]

I don't understand what you intend to convey with this concept of the "instantaneous observer". Can your "instantaneous observers" observe multiple spatial locations? If so, then which spatially separated events are observed? How does the light cone relate to this?

I would say the "instantaneous observer" can observe multiple spatial separated events and they will all be located on the past light cone. In the instant the observer makes his observation he sees information represented by the simultaneous arrival of multiple light signals at that instant and the further away the event is the further back in time it is. I understand that much, but I must admit I do not yet see the larger picture of where Eugene is going with his ideas.

..You appear to be going out of your way to solve a problem that you admit is experimentally undetected...

If Eugene is using standard equations of accepted theories then surely that is accptable topic of discussion and surely the job of any theory is to make predictions. By definition a prediction is deduction of what will happen before it has been measured rather than explaining why it was detected after the fact.

 

[Dale]

If Eugene is using standard equations of accepted theories

That is exactly what he is not doing. Using standard equations of SR there is no hesitation in answering my above question unambiguously with the assertion that the state of the bomb at t'=6 is the same as the state of the bomb at t=1.

 

[meopemuk]

I would say the "instantaneous observer" can observe multiple spatial separated events and they will all be located on the past light cone. In the instant the observer makes his observation he sees information represented by the simultaneous arrival of multiple light signals at that instant and the further away the event is the further back in time it is. I understand that much, but I must admit I do not yet see the larger picture of where Eugene is going with his ideas.

kev, you get the idea right. The instantaneous observer can see all space around him. I don't want to go too far into the "light cone" stuff. I am afraid, this will make our discussion even more confusing than it is right now. Let us just limit this discussion to a small-size laboratory, for which the finite speed of light propagation can be ignored. So, the information collected by the observer relates to a single time instant (in his own frame).

If Eugene is using standard equations of accepted theories...

I haven't invented the Poincare group and its use in relativistic physics. You can read about it in (for example) S. Weinberg, "The quantum theory of fields", vol. 1. Unfortunately, Weinberg does not spend any time discussing the detailed nature of observers and transformations between them. But if you analyze carefully what is done there, you'll conclude that all this is about "instantaneous observers".

Eugene.

 

[meopemuk]

That is exactly what he is not doing. Using standard equations of SR there is no hesitation in answering my above question unambiguously with the assertion that the state of the bomb at t'=6 is the same as the state of the bomb at t=1.

I am not arguing with that. But this (simple re-labeling of the time parameter) is not what I call "time evolution" or "application of the time translation transformation". We are talking about "time evolution" when we know the state at t=1 and ask what will be the state at t=6? In order to answer this question, we need to know the full Hamiltonian of the system and solve quite a non-trivial physical problem.

The situation is similar with boosts. Suppose I know the state of the system seen by the observer at rest (v=0). I am asking what will observer v=6 see in the same system? My point is that usual Lorentz transformations is not the exact answer to this question. Just as in the case of time translations above, in order to have a full answer one needs to know the (interaction-dependent) boost operator for the system and solve a non-trivial set of equations.

Eugene.

 

[Dale]

I am not arguing with that. But this (simple re-labeling of the time parameter) is not what I call "time evolution" or "application of the time translation transformation". We are talking about "time evolution" when we know the state at t=1 and ask what will be the state at t=6?

I never asked for the state of the bomb at t=6, I only asked for the state of the bomb at t'=6. I was not even asking about time evolution since I know that you insist on your idea of instantaneous observers.

You have made the rather strange statement that the same bomb could explode in one reference frame and not in another and I am still trying to understand what you mean by that. So far when I probe for details I find that you don't mean anything significant at all but are just saying trivial things (e.g. the bomb exploding at t=1 does not mean that it exploded at t'=1) or making odd re-definitions of standard terms (e.g. requiring "observers" to be instantaneous). Can you now answer the question I posed several posts ago with a clear and unambiguous statement:

If S and S' are two reference frames related by the transformations
t' = t + 5
x' = x
y' = y
z' = z

And if they are observing the same system with a bomb. If the bomb explodes at A = (t, x, y, z) = (1,2,3,4), then are you suggesting that it is in any way remotely possible that the explosion does not occur at A' = (t', x', y', z') = (6,2,3,4) when these two different observers are observing the same bomb?

Feel free to make the bomb a quantum device if desired, but please answer the question this time.

 

[meopemuk]

You have made the rather strange statement that the bomb could explode in one reference frame and not in another and I am still trying to understand what you mean by that. So far when I probe for details I find that you don't mean anything significant at all but are just saying trivial things or making odd re-definitions of standard terms. Can you now answer the question I posed several posts ago with a clear and unambiguous statement:

If S and S' are two reference frames related by the transformations
t' = t + 5
x' = x
y' = y
z' = z

They are observing the same system with a bomb. If the bomb explodes at A = (t, x, y, z) = (1,2,3,4), then are you suggesting that it is in any way remotely possible that the explosion does not occur at A' = (t', x', y', z') = (6,2,3,4) when these two different observers are observing the same bomb?

Of course, "permanent" observers A and A' as defined by you will see the same explosion. Observer A will see the explosion at time t=1 (by his clock). Observer A' will see it at time t'=6 (by his clock). A and A' are basically identical "permanent" observers. The only difference between them is that their clocks show permanent lag.

Eugene.

 

[Dale]

OK, that is a good response, and we agree. Although I understand that you don't like the idea of "permanent" observers so I understand that your above response is a qualified response.

However, since I am not asking about time evolution and only asking for information about the state of the bomb at one instant of time for each observer you should be able to answer the question wrt your "instantaneous" observer idea also. If the bomb is exploding for your "instantaneous" observer in the unprimed frame at t=1 then is there any way that it is not exploding for your "instantaneous" observer in the primed frame at t'=6?

Note, I am not asking about the evolution of observations from one instantaneous observer to the next in either frame and I am not interested in the unprimed instantaneous observer at t=6 nor in the primed instantaneous observer at t'=1.

 

[meopemuk]

If the bomb is exploding for your "instantaneous" observer in the unprimed frame at t=1 then is there any way that it is not exploding for your "instantaneous" observer in the primed frame at t'=6?

If I understand correctly your definitions, then your "primed" and "unprimed" observers are two twins standing in the same place at the same time point. One twin's clock shows 1 p.m. Another twin's clock shows 6 p.m. They are looking at the same explosion, and they both see the same thing. The only point they disagree about is the "time label" of the explosion. They can settle their dispute by synchronizing their clocks.

Eugene.

 

[Dale]

OK, it seems like we agree and that you are not really saying anything non-standard; you are saying it in a non-standard way.

 

[meopemuk]

OK, it seems like we agree and that you are not really saying anything non-standard; you are saying it in a non-standard way.

The non-standard point that I am making is this: If the "unprimed" twin stands still and the "primed" twin moves with a high speed, then they may disagree about the explosion.

This statement disagrees with special relativity. However it follows rigorously from the principle of relativity + Poincare group + postulates of quantum mechanics.

Eugene.

 

[Dale]

The non-standard point that I am making is this: If the "unprimed" twin stands still and the "primed" twin moves with a high speed, then they may disagree about the explosion.

In your previous posts you justified this statement by an argument that time translated reference frames have disagreements and therefore boosted reference frames must also. Since we have concluded that time translated frames do not disagree then I fail to see how boosted frames would.

 

[meopemuk]

In your previous posts you justified this statement by an argument that time translated reference frames have disagreements and therefore boosted reference frames must also. Since we have concluded that time translated frames do not disagree then I fail to see how boosted frames would.

We've concluded that your "primed" and "unprimed" frames agree about the explosion. However, these two frames cannot be regarded as connected by a time translation. The only difference between them are the readings of their clocks, which are purely conventional numbers anyway.

If you want to consider two (instantaneous) frames connected by a real time translation, then one of them will be the "unprimed" twin when his clock shows 1 p.m., the other one is the same "unprimed" twin when his clock shows 6 p.m. The former observer does see the explosion. The latter observer does not see the explosion. In my definition (which is somewhat non-standard, I agree) these are two different observers, and results of their measurements are obviously different.

Eugene.

 

[Dale]

If you want to consider two (instantaneous) frames connected by a real time translation, then one of them will be the "unprimed" twin when his clock shows 1 p.m., the other one is the same "unprimed" twin when his clock shows 6 p.m. The former observer does see the explosion. The latter observer does not see the explosion. In my definition (which is somewhat non-standard, I agree) these are two different observers, and results of their measurements are obviously different.

Yes, we agreed on the trivial statement that if the explosion occurs at t=1 then the explosion does not occur at t=6. Again, you are not saying anything non-stanard, you are just saying typical stuff in a provocative way, e.g. insisting that we consider the unprimed observer at t=1 to be a different observer than the unprimed observer at t=6.

Frankly, it seems that you started out with the goal to say something surprising like "different observers may disagree about the bomb's explosion" and then proceeded to redefine the word "observer" for the sole purpose of making the statement true.

 

[meopemuk]

you are just saying typical stuff in a provocative way, e.g. insisting that we consider the unprimed observer at t=1 to be a different observer than the unprimed observer at t=6.

I don't know why you think this is provocative? These two (instantaneous) observers are clearly different. Their measurements lead to different results regarding the bomb's explosion and many other things.

By the same logic, the (instantaneous) unprimed observer moving with speed v=0 is different from the unprimed observer moving with non-zero speed. So, we may expect that their measurement results would be different. In particular, they may disagree about the bomb's explosion. Why not?

Eugene.

 

[Dale]

I don't know why you think this is provocative?

So now you want to switch from a semantic argument over the word "observer" to a semantic argument over the word "provocative"?

 

[meopemuk]