Galileo and Lorentz transformation

[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]