怎么推断出我“不知道对每个粒子的世界线并不相交，不相交的世界线又个鸡毛相互作用。” ？
来个因果和invariant under SR transformation的问题
版主： verdelite， TheMatrix
#21 Re: 来个因果和invariant under SR transformation的问题
上次由 forecasting 在 2024年 10月 19日 20:42 修改。
#22 Re: 来个因果和invariant under SR transformation的问题
你这智商，根本不适合搞科学研究，我给你举个例子
你妈年龄比你大，是你妈
你家门口大街上卖烤红薯的大妈年龄也比你大，
问，烤红薯大妈是不是也是你妈？
你妈的，这种简单的问题也想不明白，楼上一楼子的傻毴
另外，什么叫sr transformation？ special relativity？
你妈，根本没有sr transformation，只有lorentz transformation
你妈年龄比你大，是你妈
你家门口大街上卖烤红薯的大妈年龄也比你大，
问，烤红薯大妈是不是也是你妈？
你妈的，这种简单的问题也想不明白，楼上一楼子的傻毴
另外，什么叫sr transformation？ special relativity？
你妈，根本没有sr transformation，只有lorentz transformation
forecasting 写了： 2023年 11月 23日 08:34 众所周知，事件A是事件B的原因，则A发生的时间早于或者等于B，这一时间序记作A>=B, 并且在任意洛伦兹变换之下不变。反过来，如果两事件A>=B，并且这一时间序在任意洛伦兹变换之下不变，那么能否确定事件A是事件B的原因？
除我而外，谢绝人身攻击，请举出物理实验或者做理论推断以支持你的看法或者否定别人的看法，可以聊天放松气氛，不许胡说理论，缺基本知识和辩品的请绕行。
#23 Re: 来个因果和invariant under SR transformation的问题
来来，给我们看一下你的科研结果，比如论文或者专著，看有啥科研结果。在社区大学做科研，你的确不容易。弃婴千枝 写了： 2024年 10月 19日 20:41 你这智商，根本不适合搞科学研究，我给你举个例子
你妈年龄比你大，是你妈
你家门口大街上卖烤红薯的大妈年龄也比你大，
问，烤红薯大妈是不是也是你妈？
你妈的，这种简单的问题也想不明白，楼上一楼子的傻毴
另外，什么叫sr transformation？ special relativity？
你妈，根本没有sr transformation，只有lorentz transformation
看到你大一大二才学什么曾家的量子力学还读不懂，我差点笑死。我是15岁学李代数被绊倒了，从此不愿意再看李代数，比你差远了。
上次由 forecasting 在 2024年 10月 19日 21:09 修改。
#24 Re: 来个因果和invariant under SR transformation的问题
应该改成“你家门口大街上卖烤红薯的大妈是弃婴妈妈的双胞胎姊妹，年龄也比弃婴大，弃婴千枝 写了： 2024年 10月 19日 20:41 你这智商，根本不适合搞科学研究，我给你举个例子
你妈年龄比你大，是你妈
你家门口大街上卖烤红薯的大妈年龄也比你大，
问，烤红薯大妈是不是也是你妈？
你妈的，这种简单的问题也想不明白，楼上一楼子的傻毴
另外，什么叫sr transformation？ special relativity？
你妈，根本没有sr transformation，只有lorentz transformation
问，烤红薯大妈是不是也是你妈？
你妈的，这种简单的问题也说不清楚想不明白，弃婴就是一傻毴”
#25 Re: 来个因果和invariant under SR transformation的问题
看你这恼羞成怒的样子，我可以认为你已经明白了你顶楼问题的愚昧与荒唐，就像forecasting 写了： 2024年 10月 19日 20:47 来来，给我们看一下你的科研结果，比如论文或者专著，看有啥科研结果。
看到你大一大二才学什么曾家的量子力学还读不懂，我差点笑死。我是15岁学李代数被绊倒了，从此不愿意再看李代数，比你差远了。
你爹比你大，但是比你大的不一定是你爹
ok？
#27 Re: 来个因果和invariant under SR transformation的问题
你需要首先定义问题里的”A是B的原因“。一般在相对论里，这里定义成A发射一束光线到B。依照这个定义，你的结论是成立的。forecasting 写了： 2023年 11月 23日 08:34 众所周知，事件A是事件B的原因，则A发生的时间早于或者等于B，这一时间序记作A>=B, 并且在任意洛伦兹变换之下不变。反过来，如果两事件A>=B，并且这一时间序在任意洛伦兹变换之下不变，那么能否确定事件A是事件B的原因？
除我而外，谢绝人身攻击，请举出物理实验或者做理论推断以支持你的看法或者否定别人的看法，可以聊天放松气氛，不许胡说理论，缺基本知识和辩品的请绕行。
#28 Re: 来个因果和invariant under SR transformation的问题
没法清楚定义因果，才想到先看看物理怎么说。可引来了满版脏话，真开眼了。老实讲，说一些玩笑式样的牵涉当事人的轻脏话也就算了，看到的却是农村泼妇撒泼大骂的口吐莲花，真让人受不了。有些人哪，出身市井，又在寂寞的农村社区大学搞科研，过得窝火 啊。
好多年前一个小朋友问我啥是因果，就是日常所说因果如何定义。说不清楚，所以后来想，或许物理能给出严格定义，而且能推广。用你这定义，好像也解决不了问题，得先假设有光信号联系两事件，而且，用光信号联系的两事件可能有因果关系，不是必然有因果关系。
上次由 forecasting 在 2024年 10月 19日 22:28 修改。
#29 Re: 来个因果和invariant under SR transformation的问题
最简短的回答是，不能。forecasting 写了： 2023年 11月 23日 08:34 众所周知，事件A是事件B的原因，则A发生的时间早于或者等于B，这一时间序记作A>=B, 并且在任意洛伦兹变换之下不变。反过来，如果两事件A>=B，并且这一时间序在任意洛伦兹变换之下不变，那么能否确定事件A是事件B的原因？
首先确定一下，这个楼只谈 SR，不谈广相，也不谈量子力学。
其次，相对论是物理，
cause and effect 不是物理，
所以，相对论不谈 cause and effect。
从这个意义来讲，对楼主问题的回答是，不能。
在相对论的框架内可以谈论因果，情爱，或生老病死，都可以。但那不是物理。
唯一可以确定的是，如果在一个惯性系看来， B在Ａ的未来光锥内，
那么，在另一个惯性系看来，Ｂ也在Ａ的未来光锥内。
另，信号的传递并不总是光速，
postman 的速度肯定不如光速。
2023年12月，张雪峰在一个直播片段中表示“文科都是服务业，什么是服务业？总结称一个字就是‘舔’，就是‘爷, 我给你笑一个’”。这一言论引发网民争议。
#30 Re: 来个因果和invariant under SR transformation的问题
看下面这句话，本来也就是用SR讨论因果：OPQ 写了： 2024年 10月 19日 22:25 最简短的回答是，不能。
首先确定一下，这个楼只谈 SR，不谈广相，也不谈量子力学。
其次，相对论是物理，
cause and effect 不是物理，
所以，相对论不谈 cause and effect。
从这个意义来讲，对楼主问题的回答是，不能。
在相对论的框架内可以谈论因果，情爱，或生老病死，都可以。但那不是物理。
唯一可以确定的是，如果在一个惯性系看来， B在Ａ的未来光锥内，
那么，在另一个惯性系看来，Ｂ也在Ａ的未来光锥内。
另，信号的传递并不总是光速，
postman 的速度肯定不如光速。
顺便说一句，不是说你，我发现有些满嘴脏话的物理人，中英文都有阅读障碍，或者思维有问题，但不妨碍它觉得自己能搞科研啊。
#31 Re: 来个因果和invariant under SR transformation的问题
你学什么的？
相对论和量子场的口头禅就是Causality
特别是quantum gravity
到你嘴里竟然不提了
LOL
相对论和量子场的口头禅就是Causality
特别是quantum gravity
到你嘴里竟然不提了
LOL
OPQ 写了： 2024年 10月 19日 22:25 最简短的回答是，不能。
首先确定一下，这个楼只谈 SR，不谈广相，也不谈量子力学。
其次，相对论是物理，
cause and effect 不是物理，
所以，相对论不谈 cause and effect。
从这个意义来讲，对楼主问题的回答是，不能。
在相对论的框架内可以谈论因果，情爱，或生老病死，都可以。但那不是物理。
唯一可以确定的是，如果在一个惯性系看来， B在Ａ的未来光锥内，
那么，在另一个惯性系看来，Ｂ也在Ａ的未来光锥内。
另，信号的传递并不总是光速，
postman 的速度肯定不如光速。
#33 Re: 来个因果和invariant under SR transformation的问题
本就是转过chatGPT的那段话回复那“后因前果”的帖子，没想到又火起来了。
可还是没解决问题，单靠物理，没法找到等价于因果的定义，再考虑其他吧。差不多想明白了。
单靠物理解决不了，真不甘心。
征询答案：完全依照物理给出因果的定义。
可还是没解决问题，单靠物理，没法找到等价于因果的定义，再考虑其他吧。差不多想明白了。
单靠物理解决不了，真不甘心。
征询答案：完全依照物理给出因果的定义。
上次由 forecasting 在 2024年 10月 20日 08:59 修改。
#35 Re: 来个因果和invariant under SR transformation的问题
纯粹是垃圾，竟然有人会煞有介事地去读forecasting 写了： 2024年 10月 20日 07:57 http://library.lol/main/24E8E105B6B5D82 ... D083F5865E
Enrico Fermi的量子力学，中译本，后面是英文本
LOL
#37 Re: 来个因果和invariant under SR transformation的问题
chatGPT对你这回贴的评论：
弃婴千枝对Enrico Fermi的《量子力学》中译本的评论，显然带有非常负面的主观情绪。我们可以从以下几个角度来评估这段评论的合理性和是否合适。
1. Enrico Fermi的学术地位
Enrico Fermi 是 20 世纪最重要的物理学家之一，他在多个领域（包括量子力学、统计力学、核物理等）做出了杰出的贡献。Fermi 的量子力学著作具有很高的学术价值，尤其是对于物理学历史和研究的发展有重要影响。因此，称Fermi的《量子力学》为“垃圾”显然是一种极端且不公正的评价。这种说法既缺乏对Fermi贡献的尊重，也可能误导不了解这本书价值的读者。
2. 中译本的评价
如果弃婴千枝的评论是针对某个具体版本的中译本质量，那么对翻译质量的批评应该具体指出翻译中的问题，而不是直接全盘否定。翻译的确可能存在问题，尤其是科学著作在翻译过程中，某些概念和术语的传达可能不够准确，影响读者理解。但即便如此，翻译质量的缺陷和原著的学术价值是两码事。称整本书“垃圾”并不能帮助真正解决翻译质量问题。
3. 评论的语气与合适性
弃婴千枝的评论语气显然是粗鲁和不尊重的，尤其是在讨论学术话题时，过于情绪化的表达不仅显得不专业，也缺乏建设性。即便中译本有不足，理性的、基于事实的批评能够引发更好的讨论，而这种粗暴的评论则更容易引起争论和误解。
4. 是否应该去读这本书？
尽管可能有质量不高的译本，Fermi的《量子力学》仍然是物理学中有影响力的经典著作，特别是对于了解物理学历史和基础理论的人来说，阅读它是有益的。如果有能力的读者能够直接阅读英文版，这可能是更好的选择，但这并不意味着任何版本的中译本都应被简单地贬低为“垃圾”。
总结：
弃婴千枝对《量子力学》的评论是不恰当的，既没有提供具体的证据来支持他的观点，也缺乏对Fermi本人及其作品的应有尊重。即便是翻译质量存在问题，这样的极端语言不仅不合适，也不利于建设性的学术讨论。批评应当基于事实，而非情绪化的贬低。
#39 Re: 来个因果和invariant under SR transformation的问题
在物理学中，因果关系（causality）是一个核心的概念，贯穿于从经典物理到现代物理的各个领域。因果研究关注的是事件之间的时间顺序、关联性和相互影响。以下是物理学中因果关系研究的一些关键领域：
1. 经典力学中的因果性
在经典力学（如牛顿力学）中，因果性是直观且确定的：一个原因（如力的作用）会导致一个明确的结果（如物体的加速度）。因果性在经典物理中是时间对称的，过去的状态完全决定未来的演化。力学方程（如牛顿第二定律）本质上反映了因果关系。
2. 狭义相对论与因果性
爱因斯坦的狭义相对论为因果性增加了新的限制。在狭义相对论中，因果性受到光速的限制，即信息或相互作用不能以超光速传播。这意味着在时空中，事件的因果结构受限于光锥的结构：一个事件只能影响其光锥内的其他事件，而光锥外的事件则与它无因果联系。这一原则确保了因果性不被破坏。
3. 量子力学中的因果性
量子力学的概率性带来了因果性的新挑战。在经典力学中，因果关系是确定的，而在量子力学中，测量结果具有概率性。例如，量子态的测量结果并不是完全由初始状态确定的，而是通过概率分布给出。然而，量子力学仍然遵循某种形式的因果性，尤其是贝尔不等式和纠缠现象中的“非定域性”并没有违反因果性——虽然纠缠粒子可以瞬时相关联，但信息的传递仍然不能超越光速。
4. 量子场论中的因果性
在量子场论中，因果性受到更加严格的要求。费曼图描述了粒子之间的相互作用，而这些相互作用必须保持因果性，即事件只能在光锥内相关。量子场论的结构设计中，场算符必须满足因果性要求，尤其是在时空分离的区域，场算符的交换关系确保了不能违反狭义相对论的因果性约束。
5. 广义相对论与因果性
在广义相对论中，时空本身可以弯曲和扭曲，这带来了因果结构的新复杂性。例如，黑洞事件视界内部的因果结构是特殊的，外界的事件无法影响事件视界内的任何事物。此外，广义相对论允许时空结构的极端情况，比如虫洞和闭合类时曲线（closed timelike curves, CTCs），在这些结构中，理论上存在时间旅行的可能性，这可能导致“因果性悖论”。
6. 热力学与因果性
热力学第二定律（熵增加原理）描述了物理系统向更无序状态发展的趋势，体现了时间箭头的一个方向性。这意味着虽然基本物理方程是时间可逆的，但热力学过程中的因果性似乎是单向的：热量只能自发地从高温物体流向低温物体。统计物理中的熵为这种不可逆性提供了统计解释。
7. 量子信息与因果性
在量子信息论中，因果性问题与量子计算和量子通信密切相关。例如，量子纠缠和量子非定域性揭示了量子系统的奇特性质，但这些现象始终遵循因果性的基本约束，即信息不能以超光速传播。此外，量子信息论中还研究了量子态之间的因果关联，如通过量子信道的传输。
8. 因果结构与量子引力
在量子引力的研究中，因果结构的概念进一步复杂化，因为在极端情况下（如普朗克尺度下），时空可能不再具有经典的光锥结构。目前尚不清楚如何在引入量子效应时保持因果性的完整性。这是量子引力理论（如圈量子引力或弦理论）正在探索的一个关键问题。
9. 因果集（Causal Set Theory）
因果集理论是一种发展中的量子引力候选理论，它尝试通过用离散的因果关系来构造时空。该理论假设时空的基本结构不是连续的，而是由一系列离散事件组成，这些事件通过因果关系联系在一起。这种理论尝试在时空的微观结构中保留因果性，解决了在微小尺度下的时空问题。
10. 量子因果模型
近些年，量子因果模型（Quantum Causal Models）作为一种新的研究框架，旨在理解和量化量子系统中的因果性。这种方法将经典因果推理技术扩展到量子系统中，试图通过贝叶斯网络等工具在量子层面分析因果关系。
总结：
物理学中的因果研究横跨了从经典物理到现代量子物理和引力理论的多个层面。在经典理论中，因果关系简单且确定；而在量子理论中，因果性变得更加复杂，但基本原则仍然存在。在现代物理的前沿，因果性问题在时空的微观结构和量子引力等问题中仍然充满挑战。
1. 经典力学中的因果性
在经典力学（如牛顿力学）中，因果性是直观且确定的：一个原因（如力的作用）会导致一个明确的结果（如物体的加速度）。因果性在经典物理中是时间对称的，过去的状态完全决定未来的演化。力学方程（如牛顿第二定律）本质上反映了因果关系。
2. 狭义相对论与因果性
爱因斯坦的狭义相对论为因果性增加了新的限制。在狭义相对论中，因果性受到光速的限制，即信息或相互作用不能以超光速传播。这意味着在时空中，事件的因果结构受限于光锥的结构：一个事件只能影响其光锥内的其他事件，而光锥外的事件则与它无因果联系。这一原则确保了因果性不被破坏。
3. 量子力学中的因果性
量子力学的概率性带来了因果性的新挑战。在经典力学中，因果关系是确定的，而在量子力学中，测量结果具有概率性。例如，量子态的测量结果并不是完全由初始状态确定的，而是通过概率分布给出。然而，量子力学仍然遵循某种形式的因果性，尤其是贝尔不等式和纠缠现象中的“非定域性”并没有违反因果性——虽然纠缠粒子可以瞬时相关联，但信息的传递仍然不能超越光速。
4. 量子场论中的因果性
在量子场论中，因果性受到更加严格的要求。费曼图描述了粒子之间的相互作用，而这些相互作用必须保持因果性，即事件只能在光锥内相关。量子场论的结构设计中，场算符必须满足因果性要求，尤其是在时空分离的区域，场算符的交换关系确保了不能违反狭义相对论的因果性约束。
5. 广义相对论与因果性
在广义相对论中，时空本身可以弯曲和扭曲，这带来了因果结构的新复杂性。例如，黑洞事件视界内部的因果结构是特殊的，外界的事件无法影响事件视界内的任何事物。此外，广义相对论允许时空结构的极端情况，比如虫洞和闭合类时曲线（closed timelike curves, CTCs），在这些结构中，理论上存在时间旅行的可能性，这可能导致“因果性悖论”。
6. 热力学与因果性
热力学第二定律（熵增加原理）描述了物理系统向更无序状态发展的趋势，体现了时间箭头的一个方向性。这意味着虽然基本物理方程是时间可逆的，但热力学过程中的因果性似乎是单向的：热量只能自发地从高温物体流向低温物体。统计物理中的熵为这种不可逆性提供了统计解释。
7. 量子信息与因果性
在量子信息论中，因果性问题与量子计算和量子通信密切相关。例如，量子纠缠和量子非定域性揭示了量子系统的奇特性质，但这些现象始终遵循因果性的基本约束，即信息不能以超光速传播。此外，量子信息论中还研究了量子态之间的因果关联，如通过量子信道的传输。
8. 因果结构与量子引力
在量子引力的研究中，因果结构的概念进一步复杂化，因为在极端情况下（如普朗克尺度下），时空可能不再具有经典的光锥结构。目前尚不清楚如何在引入量子效应时保持因果性的完整性。这是量子引力理论（如圈量子引力或弦理论）正在探索的一个关键问题。
9. 因果集（Causal Set Theory）
因果集理论是一种发展中的量子引力候选理论，它尝试通过用离散的因果关系来构造时空。该理论假设时空的基本结构不是连续的，而是由一系列离散事件组成，这些事件通过因果关系联系在一起。这种理论尝试在时空的微观结构中保留因果性，解决了在微小尺度下的时空问题。
10. 量子因果模型
近些年，量子因果模型（Quantum Causal Models）作为一种新的研究框架，旨在理解和量化量子系统中的因果性。这种方法将经典因果推理技术扩展到量子系统中，试图通过贝叶斯网络等工具在量子层面分析因果关系。
总结：
物理学中的因果研究横跨了从经典物理到现代量子物理和引力理论的多个层面。在经典理论中，因果关系简单且确定；而在量子理论中，因果性变得更加复杂，但基本原则仍然存在。在现代物理的前沿，因果性问题在时空的微观结构和量子引力等问题中仍然充满挑战。
#40 Re: 来个因果和invariant under SR transformation的问题
Causality and its relationship with physical effects are fundamental to our understanding of the universe. In physics, causality refers to the principle that a cause must precede its effect in time, and that events can influence each other only through causal interactions. This principle shapes many branches of physics, from classical mechanics to quantum field theory, and extends to modern areas like quantum gravity and quantum information theory. Below is an overview of causality research in various areas of physics:
1. Causality in Classical Physics
In Newtonian mechanics, causality is straightforward and deterministic: a force (cause) acting on an object produces acceleration (effect) as per Newton's second law. The equations of motion are time-reversible, meaning that knowing the system’s state at one moment in time allows one to predict both future and past states with certainty.
Determinism is central in classical physics, where systems evolve in a predictable way based on initial conditions. Causality is aligned with this determinism, and cause-and-effect relations follow logically from the system's governing laws.
2. Causality in Special Relativity
In Einstein’s theory of special relativity, causality is more subtle due to the role of the speed of light as a fundamental limit. Events are causally connected if one event lies within the light cone of the other. This establishes a clear division between events that can influence one another (inside each other’s light cone) and those that cannot (outside the light cone).
The principle of causality in special relativity forbids any influence from propagating faster than light, ensuring that effects cannot precede their causes in any inertial reference frame. This restriction is fundamental to preserving the consistency of spacetime.
3. Quantum Mechanics and Causality
In quantum mechanics, causality is probabilistic rather than deterministic. Measurement collapses a quantum state into a definite outcome, but this outcome is inherently probabilistic, governed by the wavefunction's probabilities. While individual events are unpredictable, the evolution of the wavefunction itself is deterministic under the Schrödinger equation.
Quantum entanglement challenges classical notions of causality. In an entangled system, measurements performed on one particle instantly affect the state of another, even if the particles are separated by large distances. However, this phenomenon, known as "nonlocality," does not allow faster-than-light communication, preserving causality. This paradoxical relationship between quantum entanglement and causality is a subject of ongoing research in foundations of quantum theory.
4. Causality in Quantum Field Theory (QFT)
In quantum field theory, causality is embedded in the structure of spacetime and the propagation of fields. The fundamental requirement in QFT is that operators associated with measurements in spacelike-separated regions must commute. This ensures that events outside each other's light cone cannot causally influence one another, preserving relativistic causality.
QFT also introduces the concept of locality, meaning that interactions occur only between fields at the same point in spacetime. This is crucial for maintaining causal consistency with special relativity.
5. Causality in General Relativity
In general relativity, the nature of spacetime itself is dynamic, influenced by the distribution of mass and energy. This leads to a more complex understanding of causality since the spacetime geometry, including the structure of light cones, can change in response to matter and energy.
Exotic solutions to Einstein’s equations, such as closed timelike curves (CTCs), suggest the possibility of time travel, where an event could be both a cause and its own effect. However, these solutions are speculative and may not be physically realizable due to quantum effects. Understanding causality in such contexts remains an open question in theoretical physics.
6. Causal Sets and Quantum Gravity
In approaches to quantum gravity, such as causal set theory, spacetime is hypothesized to be fundamentally discrete rather than continuous. In this view, spacetime is composed of a set of discrete events connected by causal relationships. The causal structure of spacetime is more fundamental than its geometry, which emerges from the causal relations between events.
Loop quantum gravity and other quantum gravity theories also investigate how causality might behave at the Planck scale, where classical spacetime concepts break down. One of the biggest challenges in quantum gravity is to reconcile the causal structure of general relativity with the probabilistic nature of quantum mechanics.
7. Thermodynamics and Causal Arrows
The second law of thermodynamics introduces an arrow of time, stating that in a closed system, entropy tends to increase over time. This suggests a preferred direction of cause and effect, with systems evolving from states of lower entropy (cause) to states of higher entropy (effect).
While the microscopic laws of physics are time-symmetric (they work the same forwards and backwards in time), the second law provides an effective time-asymmetric behavior in macroscopic systems. This asymmetry is crucial for understanding causal processes in statistical mechanics and thermodynamics.
8. Causal Inference in Quantum Information Theory
Quantum causal models aim to extend classical causal reasoning to quantum systems, addressing how quantum processes might exhibit causal relationships. These models attempt to understand the flow of information and how quantum correlations can be explained causally.
Quantum information research also explores whether quantum mechanics offers new types of causal structures, particularly in systems involving entanglement and superposition. These investigations have led to new insights into the nature of quantum communication, quantum cryptography, and computation.
9. Causality and the Measurement Problem
The quantum measurement problem poses a challenge to standard interpretations of causality. In the Copenhagen interpretation, the act of measurement causes the collapse of the wavefunction, but this process is not described by the Schrödinger equation, raising questions about how cause and effect work during measurement.
Alternative interpretations, such as many-worlds or decoherence, attempt to resolve these causal ambiguities by removing the need for wavefunction collapse, though they introduce other conceptual challenges. Understanding how measurement interacts with causality is an ongoing topic in the philosophy of quantum mechanics.
10. Future Directions: Causality in Fundamental Physics
In modern theoretical physics, understanding causality at the deepest level remains a key challenge. Integrating quantum mechanics with general relativity, for example, could require a new framework where spacetime and causality emerge from more fundamental principles.
Holography and the AdS/CFT correspondence suggest that causality in a quantum gravitational system can be encoded in a lower-dimensional quantum field theory. This hints at deeper connections between information, spacetime, and causality that are not yet fully understood.
Conclusion
Causality is a central organizing principle in all of physics, from the deterministic laws of classical mechanics to the probabilistic nature of quantum mechanics, and from the structure of spacetime in relativity to emerging quantum theories of gravity. While classical physics offers a clear and intuitive picture of cause and effect, modern physics presents more complex and often counterintuitive notions of causality, particularly in quantum systems and at the boundaries of known theories. The study of causality continues to be a critical area of research, especially as physicists strive to unify quantum mechanics and general relativity into a single theory of quantum gravity.
1. Causality in Classical Physics
In Newtonian mechanics, causality is straightforward and deterministic: a force (cause) acting on an object produces acceleration (effect) as per Newton's second law. The equations of motion are time-reversible, meaning that knowing the system’s state at one moment in time allows one to predict both future and past states with certainty.
Determinism is central in classical physics, where systems evolve in a predictable way based on initial conditions. Causality is aligned with this determinism, and cause-and-effect relations follow logically from the system's governing laws.
2. Causality in Special Relativity
In Einstein’s theory of special relativity, causality is more subtle due to the role of the speed of light as a fundamental limit. Events are causally connected if one event lies within the light cone of the other. This establishes a clear division between events that can influence one another (inside each other’s light cone) and those that cannot (outside the light cone).
The principle of causality in special relativity forbids any influence from propagating faster than light, ensuring that effects cannot precede their causes in any inertial reference frame. This restriction is fundamental to preserving the consistency of spacetime.
3. Quantum Mechanics and Causality
In quantum mechanics, causality is probabilistic rather than deterministic. Measurement collapses a quantum state into a definite outcome, but this outcome is inherently probabilistic, governed by the wavefunction's probabilities. While individual events are unpredictable, the evolution of the wavefunction itself is deterministic under the Schrödinger equation.
Quantum entanglement challenges classical notions of causality. In an entangled system, measurements performed on one particle instantly affect the state of another, even if the particles are separated by large distances. However, this phenomenon, known as "nonlocality," does not allow faster-than-light communication, preserving causality. This paradoxical relationship between quantum entanglement and causality is a subject of ongoing research in foundations of quantum theory.
4. Causality in Quantum Field Theory (QFT)
In quantum field theory, causality is embedded in the structure of spacetime and the propagation of fields. The fundamental requirement in QFT is that operators associated with measurements in spacelike-separated regions must commute. This ensures that events outside each other's light cone cannot causally influence one another, preserving relativistic causality.
QFT also introduces the concept of locality, meaning that interactions occur only between fields at the same point in spacetime. This is crucial for maintaining causal consistency with special relativity.
5. Causality in General Relativity
In general relativity, the nature of spacetime itself is dynamic, influenced by the distribution of mass and energy. This leads to a more complex understanding of causality since the spacetime geometry, including the structure of light cones, can change in response to matter and energy.
Exotic solutions to Einstein’s equations, such as closed timelike curves (CTCs), suggest the possibility of time travel, where an event could be both a cause and its own effect. However, these solutions are speculative and may not be physically realizable due to quantum effects. Understanding causality in such contexts remains an open question in theoretical physics.
6. Causal Sets and Quantum Gravity
In approaches to quantum gravity, such as causal set theory, spacetime is hypothesized to be fundamentally discrete rather than continuous. In this view, spacetime is composed of a set of discrete events connected by causal relationships. The causal structure of spacetime is more fundamental than its geometry, which emerges from the causal relations between events.
Loop quantum gravity and other quantum gravity theories also investigate how causality might behave at the Planck scale, where classical spacetime concepts break down. One of the biggest challenges in quantum gravity is to reconcile the causal structure of general relativity with the probabilistic nature of quantum mechanics.
7. Thermodynamics and Causal Arrows
The second law of thermodynamics introduces an arrow of time, stating that in a closed system, entropy tends to increase over time. This suggests a preferred direction of cause and effect, with systems evolving from states of lower entropy (cause) to states of higher entropy (effect).
While the microscopic laws of physics are time-symmetric (they work the same forwards and backwards in time), the second law provides an effective time-asymmetric behavior in macroscopic systems. This asymmetry is crucial for understanding causal processes in statistical mechanics and thermodynamics.
8. Causal Inference in Quantum Information Theory
Quantum causal models aim to extend classical causal reasoning to quantum systems, addressing how quantum processes might exhibit causal relationships. These models attempt to understand the flow of information and how quantum correlations can be explained causally.
Quantum information research also explores whether quantum mechanics offers new types of causal structures, particularly in systems involving entanglement and superposition. These investigations have led to new insights into the nature of quantum communication, quantum cryptography, and computation.
9. Causality and the Measurement Problem
The quantum measurement problem poses a challenge to standard interpretations of causality. In the Copenhagen interpretation, the act of measurement causes the collapse of the wavefunction, but this process is not described by the Schrödinger equation, raising questions about how cause and effect work during measurement.
Alternative interpretations, such as many-worlds or decoherence, attempt to resolve these causal ambiguities by removing the need for wavefunction collapse, though they introduce other conceptual challenges. Understanding how measurement interacts with causality is an ongoing topic in the philosophy of quantum mechanics.
10. Future Directions: Causality in Fundamental Physics
In modern theoretical physics, understanding causality at the deepest level remains a key challenge. Integrating quantum mechanics with general relativity, for example, could require a new framework where spacetime and causality emerge from more fundamental principles.
Holography and the AdS/CFT correspondence suggest that causality in a quantum gravitational system can be encoded in a lower-dimensional quantum field theory. This hints at deeper connections between information, spacetime, and causality that are not yet fully understood.
Conclusion
Causality is a central organizing principle in all of physics, from the deterministic laws of classical mechanics to the probabilistic nature of quantum mechanics, and from the structure of spacetime in relativity to emerging quantum theories of gravity. While classical physics offers a clear and intuitive picture of cause and effect, modern physics presents more complex and often counterintuitive notions of causality, particularly in quantum systems and at the boundaries of known theories. The study of causality continues to be a critical area of research, especially as physicists strive to unify quantum mechanics and general relativity into a single theory of quantum gravity.
#41 Re: 来个因果和invariant under SR transformation的问题
经过测试，阉割版的chatGPT也比 北美理论物理学家强！forecasting 写了： 2024年 10月 23日 09:05 Causality and its relationship with physical effects are fundamental to our understanding of the universe. In physics, causality refers to the principle that a cause must precede its effect in time, and that events can influence each other only through causal interactions. This principle shapes many branches of physics, from classical mechanics to quantum field theory, and extends to modern areas like quantum gravity and quantum information theory. Below is an overview of causality research in various areas of physics:
1. Causality in Classical Physics
In Newtonian mechanics, causality is straightforward and deterministic: a force (cause) acting on an object produces acceleration (effect) as per Newton's second law. The equations of motion are time-reversible, meaning that knowing the system’s state at one moment in time allows one to predict both future and past states with certainty.
Determinism is central in classical physics, where systems evolve in a predictable way based on initial conditions. Causality is aligned with this determinism, and cause-and-effect relations follow logically from the system's governing laws.
2. Causality in Special Relativity
In Einstein’s theory of special relativity, causality is more subtle due to the role of the speed of light as a fundamental limit. Events are causally connected if one event lies within the light cone of the other. This establishes a clear division between events that can influence one another (inside each other’s light cone) and those that cannot (outside the light cone).
The principle of causality in special relativity forbids any influence from propagating faster than light, ensuring that effects cannot precede their causes in any inertial reference frame. This restriction is fundamental to preserving the consistency of spacetime.
3. Quantum Mechanics and Causality
In quantum mechanics, causality is probabilistic rather than deterministic. Measurement collapses a quantum state into a definite outcome, but this outcome is inherently probabilistic, governed by the wavefunction's probabilities. While individual events are unpredictable, the evolution of the wavefunction itself is deterministic under the Schrödinger equation.
Quantum entanglement challenges classical notions of causality. In an entangled system, measurements performed on one particle instantly affect the state of another, even if the particles are separated by large distances. However, this phenomenon, known as "nonlocality," does not allow faster-than-light communication, preserving causality. This paradoxical relationship between quantum entanglement and causality is a subject of ongoing research in foundations of quantum theory.
4. Causality in Quantum Field Theory (QFT)
In quantum field theory, causality is embedded in the structure of spacetime and the propagation of fields. The fundamental requirement in QFT is that operators associated with measurements in spacelike-separated regions must commute. This ensures that events outside each other's light cone cannot causally influence one another, preserving relativistic causality.
QFT also introduces the concept of locality, meaning that interactions occur only between fields at the same point in spacetime. This is crucial for maintaining causal consistency with special relativity.
5. Causality in General Relativity
In general relativity, the nature of spacetime itself is dynamic, influenced by the distribution of mass and energy. This leads to a more complex understanding of causality since the spacetime geometry, including the structure of light cones, can change in response to matter and energy.
Exotic solutions to Einstein’s equations, such as closed timelike curves (CTCs), suggest the possibility of time travel, where an event could be both a cause and its own effect. However, these solutions are speculative and may not be physically realizable due to quantum effects. Understanding causality in such contexts remains an open question in theoretical physics.
6. Causal Sets and Quantum Gravity
In approaches to quantum gravity, such as causal set theory, spacetime is hypothesized to be fundamentally discrete rather than continuous. In this view, spacetime is composed of a set of discrete events connected by causal relationships. The causal structure of spacetime is more fundamental than its geometry, which emerges from the causal relations between events.
Loop quantum gravity and other quantum gravity theories also investigate how causality might behave at the Planck scale, where classical spacetime concepts break down. One of the biggest challenges in quantum gravity is to reconcile the causal structure of general relativity with the probabilistic nature of quantum mechanics.
7. Thermodynamics and Causal Arrows
The second law of thermodynamics introduces an arrow of time, stating that in a closed system, entropy tends to increase over time. This suggests a preferred direction of cause and effect, with systems evolving from states of lower entropy (cause) to states of higher entropy (effect).
While the microscopic laws of physics are time-symmetric (they work the same forwards and backwards in time), the second law provides an effective time-asymmetric behavior in macroscopic systems. This asymmetry is crucial for understanding causal processes in statistical mechanics and thermodynamics.
8. Causal Inference in Quantum Information Theory
Quantum causal models aim to extend classical causal reasoning to quantum systems, addressing how quantum processes might exhibit causal relationships. These models attempt to understand the flow of information and how quantum correlations can be explained causally.
Quantum information research also explores whether quantum mechanics offers new types of causal structures, particularly in systems involving entanglement and superposition. These investigations have led to new insights into the nature of quantum communication, quantum cryptography, and computation.
9. Causality and the Measurement Problem
The quantum measurement problem poses a challenge to standard interpretations of causality. In the Copenhagen interpretation, the act of measurement causes the collapse of the wavefunction, but this process is not described by the Schrödinger equation, raising questions about how cause and effect work during measurement.
Alternative interpretations, such as many-worlds or decoherence, attempt to resolve these causal ambiguities by removing the need for wavefunction collapse, though they introduce other conceptual challenges. Understanding how measurement interacts with causality is an ongoing topic in the philosophy of quantum mechanics.
10. Future Directions: Causality in Fundamental Physics
In modern theoretical physics, understanding causality at the deepest level remains a key challenge. Integrating quantum mechanics with general relativity, for example, could require a new framework where spacetime and causality emerge from more fundamental principles.
Holography and the AdS/CFT correspondence suggest that causality in a quantum gravitational system can be encoded in a lower-dimensional quantum field theory. This hints at deeper connections between information, spacetime, and causality that are not yet fully understood.
Conclusion
Causality is a central organizing principle in all of physics, from the deterministic laws of classical mechanics to the probabilistic nature of quantum mechanics, and from the structure of spacetime in relativity to emerging quantum theories of gravity. While classical physics offers a clear and intuitive picture of cause and effect, modern physics presents more complex and often counterintuitive notions of causality, particularly in quantum systems and at the boundaries of known theories. The study of causality continues to be a critical area of research, especially as physicists strive to unify quantum mechanics and general relativity into a single theory of quantum gravity.
