Tipler 1976: Clarifying Symbol Meaning

In summary, the conversation discusses the usage of a symbol in Tipler's 1976 paper, "Causality Violation in Asymptotically Flat Spacetimes." The symbol resembles the symbol for Future Null Infinity but its usage does not align with the expected meaning. It is not defined in the paper, so it is assumed to be standard notation. The symbol is later found in a similar context in Hawking and Ellis. Possible interpretations include the closure of the future domain of dependence and the empty set. It is suggested to consult Hawking and Ellis for clarification.
  • #1
hawkdron496
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TL;DR Summary
A request for notational clarification in an old paper
I'm reading Tipler's 1976 paper, "Causality Violation in Asymptotically Flat Spacetimes" and he keeps using a symbol which seems to resemble the symbol for Future Null Infinity in a strange font, but it's usage doesn't make sense with what I would expect if that's what the symbol meant. He doesn't define it anywhere in the paper, so I assume it must be standard notation that I'm missing. The symbol in question is the one that in the first photo we're interested in the causal past of, and in the second photo, we're evaluating at the point q.
1664495301460.png
1664495325270.png
 
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  • #2
##J^-(X)## is the region visible from ##X##, so ##J^-(\mathfrak{I}^+)## would be the region visible from infinity, which matches up with the text you quote. What's the problem?
 
  • #3
Ibix said:
##J^-(X)## is the region visible from ##X##, so ##J^-(\mathfrak{I}^+)## would be the region visible from infinity, which matches up with the text you quote. What's the problem?
I'm not clear on what it means when he takes ##\mathfrak{I}^+(q)##. Is it just the set of null rays going off to infinity that pass through q?
 
  • #4
hawkdron496 said:
I'm not clear on what it means when he takes ##\mathfrak{I}^+(q)##. Is it just the set of null rays going off to infinity that pass through q?
Could be, or maybe the portion of future null infinity that's in the future of ##q##. Not sure. I'll look in Wald later if nobody else answers you first.

Do you have a link to Tipler's paper?
 
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  • #6
Paywalled, unfortunately, but thanks.
 
  • #7
Ok, can't find any use of ##\mathfrak{I}^+(q)## in Wald. It might just be a typo for ##I^+(q)##, which is the interior of the future lightcone of event ##q##? Difficult to comment without more context.
 
  • #8
If I recall, it says that it follows the notation of Hawking and Ellis.

For those without access to the article, it might be good (as @Ibix suggests) to give more context of the questionable notation…. That is, give the whole sentence or paragraph where it is used. Thus, one can match up the definitions, then the notations.
 
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  • #9
Will do: the relevant paragraph is here:
1664755901898.png


The questionable notation is in the Proof section of the proposition.
 
  • #10
I presume ##\tilde{D}^+## is the closure of ##D^+##? I'm also not sure what ##\phi## is supposed to be, unless it's meant to be the empty set symbol ##\emptyset##. If so, I think ##\mathfrak{I}^+(q)\cap\tilde{D}^(S)=\phi## makes sense in context if interpreted as ##{I}^+(q)\cap\tilde{D}^(S)=\emptyset## - i.e. if ##\mathfrak{I}^+## is a typo for ##I^+##.

If anyone disagrees with me they're probably right - I'm literally doing this with my phone in one hand and Wald in the other.
 
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  • #11
Ibix said:
I presume ##\tilde{D}^+## is the closure of ##D^+##? I'm also not sure what ##\phi## is supposed to be, unless it's meant to be the empty set symbol ##\emptyset##. If so, I think ##\mathfrak{I}^+(q)\cap\tilde{D}^(S)=\phi## makes sense in context if interpreted as ##{I}^+(q)\cap\tilde{D}^(S)=\emptyset## - i.e. if ##\mathfrak{I}^+## is a typo for ##I^+##.

If anyone disagrees with me they're probably right - I'm literally doing this with my phone in one hand and Wald in the other.
From what I've been able to find online, the symbol ##\tilde{D}(S)## is the same as the usual symbol for domain of dependence, but only for timelike curves rather than any causal curve, according to this stack overflow post:

https://physics.stackexchange.com/q...pment-or-future-domain-of-dependence-why-is-d

The symbol is from Hawking and Ellis, apparently.
 
  • #12
So, that strange notation occurs again, later in the paper:

1664813604416.png

which makes it feel less likely that it's a typo.
 
  • #13
I agree it seems less likely to be a typo if it recurs. I'd get hold of a copy of Hawking and Ellis, then, if I were you.
 
  • #14
Ibix said:
I agree it seems less likely to be a typo if it recurs. I'd get hold of a copy of Hawking and Ellis, then, if I were you.
Yep, I suppose I will. Thank you for the help.
 
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FAQ: Tipler 1976: Clarifying Symbol Meaning

What is the significance of "Tipler 1976" in the title?

"Tipler 1976" refers to a research paper published by physicist Frank J. Tipler in 1976. The paper discusses the concept of clarifying the meaning of symbols in physics, specifically in relation to the laws of thermodynamics.

What is the main focus of "Clarifying Symbol Meaning" in Tipler 1976?

The main focus of "Clarifying Symbol Meaning" in Tipler 1976 is to address the confusion and ambiguity surrounding the use of symbols in physics, particularly in the laws of thermodynamics. Tipler argues that a clear and consistent use of symbols is crucial for accurate and meaningful communication in the field of physics.

What are some examples of symbols discussed in Tipler 1976?

Some examples of symbols discussed in Tipler 1976 include the symbols for energy, work, heat, and entropy. Tipler explains how these symbols have been used interchangeably or inconsistently in different contexts, leading to confusion and misunderstandings in the field of physics.

How does Tipler propose to clarify the meaning of symbols in physics?

Tipler proposes a set of guidelines for using symbols in physics, including defining symbols clearly, using them consistently, and avoiding ambiguity. He also suggests the use of standardized symbols in order to promote clear and accurate communication in the field.

What impact did Tipler 1976 have on the field of physics?

Tipler 1976 sparked a discussion and debate among physicists about the use of symbols in physics. It highlighted the importance of clear and consistent communication in the field and led to a greater emphasis on defining and using symbols accurately. Tipler's guidelines are still referenced and followed in the field today.

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