Exploring the Possibility of Time as a String

[ZapperZ]

You can measure space through motion. As an example, take a sphere and measure its Gaussian curvature in a point by applying the standard differential geometry procedure (i.e. by moving along a loop around the point). You can implement this operation instantly or (not being in rush) consuming an infinite amount of time. Therefore this measurement is time-independent but as a result you have measured the distance between two opposite points of your sphere (its diameter).

So in other words, if we dump Special Relativity completely, we can implement this instantaneously, and you won't need any time?

Zz.

 

[vld]

So in other words, if we dump Special Relativity completely, we can implement this instantaneously, and you won't need any time?

Please, don't slant. Take the infinite amount of time if you want.

 

[vld]

You were the one who brought up tunneling of alpha particle.

Please don't use a frame-up! Here are your own words:

Come again? Alpha decay can be described as a tunneling process that is independent of any oscillatory motion of the nucleus consituents. In other words, even when they do not move, they will still tunnel through.

Incidentally, from these words I deduce that you don't consider tunneling as one of
the forms of motion.

 

[ZapperZ]

Please, don't slant. Take the infinite amount of time if you want.

But that is what I don't understand. The motion takes TIME, and you are essentially measuring the displacement. I could put a measuring tape along the path and achieve the same thing, no? If not, how are you to know how far you have moved? So how did I know what the length is? Did I just assumed some "simultaneous" event on the front and back of the measuring tape that allowed me to know of such a thing? Did Einstein went out of his mind by insisting on the use of light as a measuring device for both space AND time?

I would like to see you publish this in, let's say, AJP and see if you can argue that such a measuring process requires NO involvement of any time at all in your measuring device.

Zz.

 

[ZapperZ]

Please don't use a frame-up! Here are your own words:

I take that back. I meant that you were the one who brought up alpha particle as being THE representation of radioactive decay. One such process attributes this to tunneling.

Incidentally, from these words I deduce that you don't consider tunneling as one of
the forms of motion.

That is not correct. I gave my explanation based on the alpha particle. I did not give my explanation for tunneling phenomenon in general. Besides, you haven't defined how "forms of motion" is related to tunneling process in general. My argument earlier is that the time rate of decay of a free neutron has nothing to do with any spatial displacement. Yet, its decay rate is well-defined.

Zz.

 

[josh1]

You can measure space through motion. As an example, take a sphere and measure its Gaussian curvature in a point by applying the standard differential geometry procedure (i.e. by moving along a loop around the point). You can implement this operation instantly or (not being in rush) consuming an infinite amount of time. Therefore this measurement is time-independent but as a result you have measured the distance between two opposite points of your sphere (its diameter).

vld, in the context of this thread, what does special relativity have to say about doing things instantly? What does it say about the absolute meaning of distances in space compared to distances in spacetime? Does special relativity really allow the sort of time-independence that you`re talking about? Are these things related?

 

[vld]

vld, in the context of this thread, what does special relativity have to say about doing things instantly? What does it say about the absolute meaning of distances in space compared to distances in spacetime? Does special relativity really allow the sort of time-independence that you`re talking about? Are these things related?

Of course, nothing can happen instantly, and in a real physical system one will need a finite time to measure a distance. But this artificial theoretical construction shows that you can use ANY amount of time to measure a distance, which is what actually means that such a measurement is time-independent. But an important point is also that it is GR (not SR) that might help us to get insight into the deeper properties of time and motion. In fact, the very postulate that "nothing can happen instantly" might be a good starting point in the exploration of these properties. As for the absolute meaning of distances, I don't think this makes much sense because to measure a distance one has to compare it with some other distance (that is, involving at least two entities and their relationship).

 

[ZapperZ]

Of course, nothing can happen instantly, and in a real physical system one will need a finite time to measure a distance. But this artificial theoretical construction shows that you can use ANY amount of time to measure a distance, which is what actually means that such a measurement is time-independent. But an important point is also that it is GR (not SR) that might help us to get insight into the deeper properties of time and motion. In fact, the very postulate that "nothing can happen instantly" might be a good starting point in the exploration of these properties. As for the absolute meaning of distances, I don't think this makes much sense because to measure a distance one has to compare it with some other distance (that is, involving at least two entities and their relationship).

But you have not even addressed by what it means to measure a "space" or a "length". Your "theoretical construction" doesn't tell me how I could measure it. Compare that to how SR/GR indicates how length and time are measured.

Zz.

 

[vld]

(b) second, GR does contain time in its formulation : you still need coordinates (t,x)

(ict,x)

But neither has the absolute time I was speaking about before in special relativity. Furthermore, since the 30 ties it is well known that one can reformulate GR as a theory of scattering gravitons in a Minkowski background (so the geometrical interpretation isn't necessary at all).

The existence of various equivalent formulations of GR, including graviton scattering, torsion, polarisable medium, etc., means that the underlying physical reality might be richer than any of that theories. When we deal with something unknown, none of the working models has to be dismissed beforehand. The hidden variables model has the right to be explored as well.

When a theory has excess bagage, we can take two attitudes :
(a) either these hidden variables exist and we have to reformulate the theory with respect to them (GR as a particle theory in a fixed background)
(b) they don't exist and we have to find a formulation which eliminates them.

Now if you say that coordinates are in the category (b), then GR, as it stands now, determines only an evolution in terms of the clock time associated to one observer.

I thought this was the main idea of GR: the entire evolution is determined locally

But clock time is itself an observable, which we agreed to be associated to a periodic motion in space which again requires an auxilliary notion of time and space. Hence, we are again at our starting point : find a deterministic theory for which GR is an effective approximation !

That is what I was talking about: out notion of time might be incomplete being conditioned by periodic motions of matter around us but eventually converted in a concept of absolute uniform time. Realising that time is neither absolute nor uniform (not speaking about its anisotropy) makes this concept richer.

What the rest of your comments are concerned : the speed of light is not a fundamental but emergent quantity (you are kind of forced to do this if you want to save realism and accept QM).

I thought that the speed of light is not a limit in QM since some quantum processes are assumed to happen instantaneously (e.g. the reduction of a quantum state).

 

[josh1]

As for the absolute meaning of distances, I don't think this makes much sense because to measure a distance one has to compare it with some other distance.

Yes, one must introduce standard rulers. But according to relativity, one must also introduce standard clocks because there can still be disagreement in when measurements are made. What we need are quantities whose measured properties do not depend on the choice of standard rulers and clocks consistent with the principles of relativity. One helpful notion is that of proper length. We define the proper length of an object as being that measured by an observer at rest with respect to that object. Different observers who are not at rest with respect to that object will measure a different length because their clocks will not record time at the same rate that the proper clock does. This impossibility of separating time and space is the core idea of relativity.

 

[Careful]

(ict,x)

Whatever you want

The existence of various equivalent formulations of GR, including graviton scattering, torsion, polarisable medium, etc., means that the underlying physical reality might be richer than any of that theories. When we deal with something unknown, none of the working models has to be dismissed beforehand. The hidden variables model has the right to be explored as well.

Euhh, I insisted throughout this thread on determinstic hidden variable reformulations ! I thought that was clear.

I thought this was the main idea of GR: the entire evolution is determined locally

Hem, I was talking about GR not having a good deterministic reformulation yet (and one will have to do its utmost best to make it local !)

That is what I was talking about: out notion of time might be incomplete being conditioned by periodic motions of matter around us but eventually converted in a concept of absolute uniform time. Realising that time is neither absolute nor uniform (not speaking about its anisotropy) makes this concept richer.

True, clocktime is conditioned by periodic motions, but as I said before, clocktime is a derived concept (with an underlying Newtonian time).

I thought that the speed of light is not a limit in QM since some quantum processes are assumed to happen instantaneously (e.g. the reduction of a quantum state).

Ah, just forget about this reduction of the wave function and all that crap. There is clearly something else going on, but whatever it is, it must involve things traveling faster than light in vacuum (just as in QFT correlations outside the lightcone do exist), but we have to properly define signals so that they do not travel faster than light in vacuum (the no FTL signalling theorem in QFT). Clearly, this implies that SR must be only true at the coarse grained level (the level of signals).

 

[josh1]

...reduction of the wave function...must involve things traveling faster than light in vacuum...we have to properly define signals so that they do not travel faster than light in vacuum...

To make sure we`re on the same page here, what did you mean by these remarks?

 

[Careful]

To make sure we`re on the same page here, what did you mean by these remarks?

You have to read it as follows :

Ah, just forget about this reduction of the wave function and all that crap.
There is clearly something else going on,

(That is the *single* mechanism reproducing the quantum correlations must be very different from wave + measurement)

but whatever it (this mechanism) is, it must involve things traveling faster than light in vacuum (just as in QFT correlations outside the lightcone do exist), but we have to properly define signals so that they do not travel faster than light in vacuum (the no FTL signalling theorem in QFT).
Clearly, this implies that SR must be only true at the coarse grained level (the level of signals).