# Relativity and Probability Waves

• PaulMurphy
In summary, Feynman's SOH is a mathematical procedure that predicts the probabilities of different outcomes of a physical system.
PaulMurphy
I don't know enough physics to know where my reasoning or assumptions are incorrect in this post. Please point me in the right direction so I can fill the holes in my knowledge that led to this conjecture:

In Einstein’s Theory of Relativity, there is no absolute motion, no absolute rest and every differentially moving frame of reference is equally valid. Observers in differentially moving frames of reference will measure an object’s speed, radioactive decay rate (time) and mass to have different values. These measurements from differentially moving frames of reference are all equally valid.

In the case of gravity, I suggest that an observer in one frame of reference will map the gravitational fields present in the Universe differently than an observer in a differentially moving frame of reference. In essence, each relatively moving frame of reference has a separate gravitational topology of the Universe. They would each create a different map of gravitational fields from their own equally valid perspectives.

I suggest that every particle that could potentially be observed has a range of properties that would be observed to have different values when measured from differentially moving frames of reference.

If particles could theoretically be measured to have different values for properties when viewed from relatively moving frames of reference, then maybe the values of these properties are described by a separate history in a way similar to Feynman’s Sum Over Histories and the probability wave for each property has the locally highest probability for the most likely value in each local frame of reference.

Thanks!
Paul Murphy

No, the two do not "differ" in the same way.

Relativity simply means that the same object looks different from different perspectives. For example what you see as a vertical line I might see as a diagonal line because our orientations are different. We will measure different components (x extent and y extent) but we can map one perspective to the other via a relativity transformation (coordinate rotation in this case).

Einstein's relativity is a bit harder to grasp because we normally think of time as a universal absolute and not as one component in the space-time separation of two events.

In the above cases (when applied to classical systems) there is a single objective history for an object, it is just broken down into components differently due to different observers.

In the Feynman's SOH one is rather summing over all the available classical histories to determine the transition amplitude (and thence transition probability) between two observations. What's happening while this summing is going on is necessarily not observed. In one sense this summing might be considered just a calculation method i.e. purely a mathematical procedure. Remember it doesn't predict deterministically a single system's behavior, it rather predicts probabilities which are confirmed over many trials of the same experiment.

Most importantly, as far as seeing the misalignment of the two cases you're trying to identify, there is no relativity transformation from one path to another path within these many histories. Each may be distinctly different from the other. If you want to better understand Feynman's SOH look up http://en.wikipedia.org/wiki/Huygens-Fresnel_principle" which states (roughly) that a wave propagates as if everywhere along its wave-front a point source is emitting a spherical wave with the same amplitude. Thus to see how the wave looks at a given point you can sum over the contributions from each point on a surface it crosses. Applying this recursively you have a classical "sum over histories" of a wave.

Feynman's SOH is a manifestation of the wave part of the wave-particle duality for quantum particles. Now there is in this duality a deeper "relativity principle" in the relative representation of the system, sort of a "relativity of reality" which lies deep in the heart of QM. But this "relativity" lies at a distinctly different level of abstraction from the conventional space-time relativity and they are not the same.

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## 1. What is the theory of relativity?

The theory of relativity is a scientific theory developed by Albert Einstein in the early 20th century. It states that the laws of physics are the same for all non-accelerating observers and that the speed of light in a vacuum is constant regardless of the observer's frame of reference.

## 2. How does relativity relate to probability waves?

According to the theory of relativity, the laws of physics remain the same for all observers, regardless of their frame of reference. This includes the laws governing probability waves, which describe the likelihood of a particle's position or momentum. Therefore, relativity has a direct impact on the understanding and interpretation of probability waves.

## 3. What are probability waves?

Probability waves, also known as wavefunctions, are mathematical representations of the probability of finding a particle at a certain location or with a certain momentum. They are a fundamental concept in quantum mechanics and are used to describe the behavior of particles at a subatomic level.

## 4. How does relativity impact our understanding of probability waves?

Relativity helps us understand that probability waves are not absolute and can change depending on the observer's frame of reference. This is because the speed of light, which is a crucial factor in probability wave equations, is constant for all observers regardless of their relative motion.

## 5. Are there any practical applications of relativity and probability waves?

Yes, there are many practical applications of both relativity and probability waves. For example, the theory of relativity has been used to develop GPS technology, and probability waves are crucial in the development of quantum computers and technologies such as MRI machines. These theories also have implications for our understanding of the universe and the behavior of matter at a microscopic level.

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