Question About Rindler Wedges

[Rade]

I have a question concerning this paper:

 

http://prl.aps.org/abstract/PRL/v106/i11/e110404

 

Would it make sense to consider that a quantum superposition of two Minkowski spacetime segments can occur within a "moment" at the junction of right and left Rindler Wedges ? That is, can we view the concept of "moment in time" as the transformation of left to right Rindler Wedges ? All comments appreciated.

[maddog]

I have a question concerning this paper:

 

http://prl.aps.org/a...106/i11/e110404

 

Would it make sense to consider that a quantum superposition of two Minkowski spacetime segments can occur within a "moment" at the junction of right and left Rindler Wedges ? That is, can we view the concept of "moment in time" as the transformation of left to right Rindler Wedges ? All comments appreciated.

I don't know that I can comment reliably until I have read the paper. This cost money to read it (whole beyond the abstract). It does seem interesting. Maybe if I do a google search on Rindler wedges.

 

maddog

[maddog]

Rade,

 

I found this link on Wiki Rindler Coordinates (Wedge).

 

Reading it I find very interesting. I have been think on a coordinate system that has a hyperbolic metric of distance that can be tuned to accommodate superluminal speeds.

 

I would like to get the article now (without paying for it). :rolleyes:

 

maddog

[Rade]

I would like to get the article now (without paying for it).

maddog

See this possible "draft" to the Phys Rev Lett published paper:

 

http://arxiv.org/pdf/1003.0720.pdf

 

and this by the same authors:

 

http://arxiv.org/pdf/1101.2565v1.pdf

 

==

 

Maddog, I was thinking of something like the "picture" below, with P=past Minkowski spacetime, F=future Minkowski spacetime, L=left Rindler Wedge, R=right Rindler Wedge. Then, where the four meet, at the "|" symbol, emerges the concept of a moment in time. Hence, also at "|" is where classical mechanics transforms into quantum mechanics and back again in such a way that includes both matter --> and antimatter <-- along spacetime intervals.

 

 

<------ P ----->L(up wedge)"|"R(down wedge)<----- F ----->

Edited August 16, 2012 by Rade

[maddog]

See this possible "draft" to the Phys Rev Lett published paper:

http://arxiv.org/pdf/1003.0720.pdf and this by the same authors: http://arxiv.org/pdf/1101.2565v1.pdf

Thank you for the links. I had not thought to look for a draft. :D

 

Maddog, I was thinking of something like the "picture" below, with P=past Minkowski spacetime, F=future Minkowski spacetime, L=left Rindler Wedge, R=right Rindler Wedge. Then, where the four meet, at the "|" symbol, emerges the concept of a moment in time. Hence, also at "|" is where classical mechanics transforms into quantum mechanics and back again in such a way that includes both matter --> and antimatter <-- along spacetime intervals.

 

<------ P ----->L(up wedge)"|"R(down wedge)<----- F ----->

Yes, I do see. The think that interests me is the Hyperbolic Geometry. Tuning the value of the Radius of Curvature of the local space (where the "I" is) can be equivalent to warping space to have a distant object appear close to you. Brian Green showed this effect on a Nova recently where he was going over the material in his recent book, "Fabric of the Universe". Go to the Nova on PBS look for his shows and view it through your browser. It is really engaging!

 

maddog

[Aethelwulf]

I have a question concerning this paper:

 

http://prl.aps.org/abstract/PRL/v106/i11/e110404

 

Would it make sense to consider that a quantum superposition of two Minkowski spacetime segments can occur within a "moment" at the junction of right and left Rindler Wedges ? That is, can we view the concept of "moment in time" as the transformation of left to right Rindler Wedges ? All comments appreciated.

 

 

I know where you are heading with this... We have had discussions before on the nature of time and if you can recall, we discussed equations I presented which could in a way describe moments in time.

 

I really don't know what to say... Only that, time itself is a factor of geometric properties, Minkowski spacetime is for flat space, the absence of geometry. Of course, when you wind the clock back in a universe, you find that time being a geometric property ceases to exist fundamentally - this meaning, that geometry disappears when the universe get's sufficiently hot and small enough. Our universe was born from timeless properties. Our equations today suit only the geometric aspect, or the flat aspect of spacetime which seems to work better since our universe is pretty much flat in every direction. This is called the flatness problem.

 

The paper you have cited, this one http://arxiv.org/pdf/1003.0720.pdf is interesting, but it relies on the premise that a past and future are real entities, which as far as my own studies have progressed, seems to be the wrong approach, but the paper could make use of past and future as a computational significance. For instance, there is a theory I hold in high regard by three physicists David Z. Albert, Yakir Aharonov, Susan D'Amato, presented a way to violate the uncertainty principle:

 

http://prl.aps.org/abstract/PRL/v54/i1/p5_1

 

BY stating that if something makes a measurement in the past and a measurement in the future one can with 100% certainty know the location and momentum of a particle in the present time frame. The thing to remember here however, is how one can make a measurement in the past and future when we are inexorably stuck in the present sphere of time (always). Their paper is of great significance in the statistical sense of particles and the nature of time - however, how realistic is the prediction if no one can measure past and future states when really all there is, is the present moment?

 

For this reason, I am usually forced to conclude that the past and future are just computational buzzwords with little physical significance.

[Aethelwulf]

Should something exist in time?

 

If time really does exist, you may as well think of ''moments'' in a quantized way - that being each moment of time are in fact segments quantized to fit the Planck Time. Each moment in time would be very small in this case. This is even assuming time has any kind of significance outside of the subjective feel of time passing. I will stress again, there is no evidence that time exists outside the subjective experience.

[Rade]

Should something exist in time?

Yes, all things that are not forever exist in time, as you said we discussed this before. In the philosophy I follow (that developed by Aristotle) time "exists" in the same way the number line ...1,2,3,4,5... "exist". The "present" and "past" and "future" are in time as the concept of the "now" the same way odd numbers or even numbers are in the number line. Thus, the "now" (which we also label past, present, future) exists in time, and each individual accidental "now" cannot exist separately apart from what it is in (which we call time). If time does not exist neither can the concepts of present, past, future because they are all intertwined. As stated by Einstein, none of the three takes priority over the other (e.g., physics cannot separate the present from the past from the future, the three occur simultaneously). This is why Einstein implied that the "present" is an illusion, it occurs simultaneously with the past and future, but, this does not mean that time also must be an illusion, the exact opposite is true for Einstein, time+space = spacetime exists as a thing.

 

If time really does exist, you may as well think of ''moments'' in a quantized way - that being each moment of time are in fact segments quantized to fit the Planck Time.

Well, as we discussed before, you do not define "moment" the same as I. Thus I do not find that there is a concept called "moment of time", there are only "intervals of time" and they can vary in duration, from very short and be quantized (e.g., Planck time) to very long and be classical (e.g., age of universe). In my philosophy there are only "moments in time", a completely different concept than "moments of time" that imo is better defined as "time segments with duration".

 

Each moment in time would be very small in this case.

So, see here how you switch to the concept of "moment in time", which in the last sentence you called "moment of time" ? I agree that each "moment in time" must have a very small duration. I suggest it is possible that the duration for a "moment in time" is shorter than Planck time and thus the importance of using the Rindler Wedge concept to understand the mathematics of "moments in time". This was the motivation for my OP question. It does appear the forum member Maddog also finds some value in relating "moments in time" (such as the past, present, future) to Rindler Wedges (but perhaps I error ? and Maddog will correct me).

 

I have a question that will help me better understand you. Would you say the the concept "Planck time" is a segment with a begin and end or a point that has no begin or end ? For me, it is defined as a segment but perhaps not for you ?

[maddog]

I suggest it is possible that the duration for a "moment in time" is shorter than Planck time and thus the importance of using the Rindler Wedge concept to understand the mathematics of "moments in time". This was the motivation for my OP question. It does appear the forum member Maddog also finds some value in relating "moments in time" (such as the past, present, future) to Rindler Wedges (but perhaps I error ? and Maddog will correct me).

Mathematically "shorter" maybe. The definition for Planck time is 10^-43 seconds (which is a 1 with 42 zeros between it and decimal point). A very small number, Much smaller than we can measure by about 25 orders of magnitude. So there is no current need to think even close to this interval of time.

 

I have a question that will help me better understand you. Would you say the the concept "Planck time" is a segment with a begin and end or a point that has no begin or end ? For me, it is defined as a segment but perhaps not for you ?

All intervals must begin and end to be defined as an interval. An instant of time would considered a point yet can not be precisely put at an exact value exactly when Heisenberg Uncertainty Principle is taken into account. We currently can measure events down to a resolution of about 10^-18 seconds. In Engineering the best time values are in picoseconds (10^-12 seconds). This is not anywhere near Planck time. So even points in time become in all practicality segments or intervals when something is brought into practice.

 

maddog