# Principle of Relativity > **Principle of Relativity**: The [The Laws of Physics](The%20Laws%20of%20Physics.md) are the same in all [Inertial Reference Frames](Inertial%20Reference%20Frame.md), meaning that no physical experiment can distinguish one inertial frame from another. We can elaborate on this a bit by saying: the *equations* that make up the laws of physics-our best attempt at describing reality-are the same in any non accelerating [Reference Frame](Reference%20Frames.md). We can run any experiment we'd like, in any [Inertial Reference Frame](Inertial%20Reference%20Frame.md), and they will *all yield the same results*. Our main definition, while quite succinct, suffers from two main drawbacks: the [Shortcomings of Language](Shortcomings%20of%20Language.md) and [certain words are doing a lot of work](Word%20doing%20a%20lot%20of%20work.md). The term "[The Laws of Physics](The%20Laws%20of%20Physics.md)" is used differently in different contexts. This is a shortcoming of language. Sometimes it references the *equations* describing our natural world. Other times it refers to the actual underlying processes themselves that generate our natural world. In our definition of the Principle of Relativity, the Laws of Physics simply reference the *equations* describing the natural world. Likewise, "[Inertial Reference Frame](Inertial%20Reference%20Frame.md)" is doing a lot of work in that definition. It implies a constant velocity and some position. When we say that "the laws of physics are the same in all inertial references frames, *meaning that no physical experiment can distinguish one inertial frame from another*", what is being implicitly said is "the *position and velocity* associated with any inertial reference frame cannot be detected by *any experiment*". The Principle of Relativity addresses several fundamental questions about reality: * Does a particular way of looking at the world, or a certain property or object in the world, depend on your perspective? If so, how? If not, why? * More scientifically, which aspects of the universe are *relative* (dependent on an observers perspective) and which ones are not? --- ## Equivalent Statements Our original definition can be restated in in two equivalent ways: 1. There is no preferred position or velocity in the universe 2. Steady motion is undetectable ### No Preferred Position or Velocity There is no state picked out as somehow special, against which other states could be measured - at least as far as the laws of physics are concerned. Put another way: there is no "absolute" [Reference Frame](Reference%20Frames.md). This is merely another way of saying[^3]: * All [Inertial Reference Frames](Inertial%20Reference%20Frame.md) are equivalent, or * The fundamental laws of physics are the same, whatever your state of (non accelerating[^4]) motion The [The Laws of Physics](The%20Laws%20of%20Physics.md) don't pick out any **position** in the universe as special - they are invariant with respect to position. If you perform an experiment in London you'd expect the same results to hold if you were to perform it in Sydney. The laws of physics don't pick out any **velocity**[^1] as special either. This is less intuitive. When we talk about velocity, strictly speaking it is always measured with respect to something else. Given two objects, the distance between them is well defined, and their *mutual velocity* is the derivative of that distance with respect to time. However, there is no such thing as "the velocity", full stop. This is often obscured to us in daily life. If I am driving at 40 mph, it feels like surely that is "the correct" velocity I am moving at. In this case it is relative to the earth. But I could also measure my velocity relative to Jupiter - perhaps it is 50,000 mph. The laws of physics say that there is no way of claiming either of these velocities are "the correct" velocity. Our intuitions *want* there to be a "correct" velocity - they want there to be some preferred [Reference Frame](Reference%20Frames.md) that we can measure speed with respect to that is correct. But that simply isn't so. ### Steady Motion is Undetectable The Principle of Relativity states that in quiet, undisturbed conditions, within an isolated bubble with no access to the outside world[^2], there is absolutely nothing you can do to establish either the amount or direction of your motion: steady motion is undetectable. Put another way: > Steady motion has no perspective independent meaning in our universe. To start, how is this statement derived from our original definition? We can reason as follows: * If the laws of physics are the same in all inertial frames, this literally means no position or velocity is special * Then, any experiment conducted in any inertial frame will yield the same results * This implies that it is *impossible* to distinguish between different inertial frames * Hence, steady motion is *undetectable*! There is no experiment we could run that would be able to detect it To help update our intuitions, let me make the claim that *there is no such thing as being stationary* in an absolute sense. At it's core, the problem is that the statement "I am stationary" is meaningless. This is no different than any other relative term. For instance, consider describing someone as "tall". Tall relative to what? Relative a redwood tree they are tiny. Relative to a mouse they are enormous. Generally when someone says they are tall they *implicitly* mean "I'm tall relative to the average human". When someone says "I'm stationary", they implicitly mean "I'm stationary relative to the objects in my immediate surroundings". However, without *context*, simply saying "I'm moving quickly" or "I'm not moving at all", *has no meaning* in a universe like ours in which all speed is relative and steady motion can't be detected. It is impossible for an object to be stationary, and it is impossible for an object to not be stationary. You are always stationary with respect to yourself and some objects around you, but you are always moving relative to most things in the universe and even most things on this planet. And you are moving at many different speeds and directions relative to those things. Simply put, our motion is always ambiguous; we cannot ever say what it is without stating it relative to something else. Say I pass you on the highway at 80mph. From my perspective you may be stationary and I moving. From your perspective I am stationary and you are moving.T here is no absolute right answer to the above question of who is moving. All that we can say is that we are each moving *relative* to the other. We could perhaps use the word "omnimotional" to describe the situation. Pick any speed and direction you like, and *that* is your motion relative to some particle somewhere in the universe. ### How are the two ways of describing relativity linked? Remember we said that there are two equivalent ways of describing the Principle of Relativity: 1. There is no preferred position or velocity in the universe (all inertial [Reference Frames](Reference%20Frames.md) are equivalent) 2. Steady motion is undetectable How are these two descriptions logically related? At first glance it may be hard to see how one implies the other. This is largely due to the [Shortcomings of Language](Shortcomings%20of%20Language.md) and [certain words doing a lot of work](Word%20doing%20a%20lot%20of%20work.md). We can link them as follows: * If there is no preferred position/velocity, then any frame is as valid as any other for describing the [The Laws of Physics](The%20Laws%20of%20Physics.md). * This implies that experiments cannot depend on the velocity of the frame of reference. In other words, the velocity is not detectable in the. This implies steady motion (Constant velocity) is not detectable. * If steady motion were detectable, then this implies the laws of physics are condition on motion? Maybe? "Since the laws of physics and the *outcomes of experiments are the same in all inertial frames*, there is no experimental way to distinguish between being at rest and moving at a constant velocity." The italicized section is doing a lot of work. It is say that *all experiments outcomes would be the same in any inertial frame*. This means that *any experiment done to determine your velocity would return the same result*, and this means that *there is no way to detect your velocity*! I think chatgpt is interchanging "inertial frames" and "preferred position and velocity" * If steady motion were detectable, then the laws of physics may be conditional on the motion. But they are not. They are invariant. Hence, no preferred velocity or position. When we say that “the laws of physics do not depend on the velocity of the reference frame,” we are essentially stating that “the equations representing our deepest understanding of nature and reality do not depend on the velocity of the reference frame.” This is not necessarily saying that "the underlying nature of reality does not depend on velocity of..." --- ## Bad Intuitions **Bad Intuition #1 - Relying on memory of past acceleration** Imagine that you are in a rocket ship and accelerating towards a planet. As you near the planet, you stop acceleration and move at a constant velocity. As you pass the planet by, you think to yourself "well clearly it is I who am moving and the planet is stationary, this must violate the principle of relativity!". The reason it does not is that it is relying on your memory. Your memory and records of having accelerated are indeed part of your history, but they do not affect the equivalence of inertial [Reference Frames](Reference%20Frames.md) after the acceleration has ceased. --- links: [Einstein](Einstein.md) [Physics](notes/Physics.md) [Waves in an Impossible Sea](Waves%20in%20an%20Impossible%20Sea.md) created: 2020-11-25 modified: 2020-11-25 References: * Einstein, pgs (107) [^1]: Keep in mind that you always have an approximately infinite number of velocities occurring at any given time. You have a velocity between *you* and every other subatomic particle in the universe. What physicists long sought after was some sort of stationary object (e.g. the aether) that your velocity with respect to was some how the "correct" velocity. [^2]: Our intuition does not play nice with the principle of relativity, since we are never noticeably in an isolated bubble. [^3]: Why are the above two bullets equivalent statements? The second bullet could be restated as "the fundamental laws of physics are the same, whatever your inertial reference frame". This literally means that all inertial reference frames are equivalent. The first bullet could be restated as "all inertial reference frame are equivalent *with respect to the laws of physics*" (this is another example of the [Shortcomings of Language](Shortcomings%20of%20Language.md) - it is implicit that the inertial reference frames are equivalent with respect to the laws of physics.) [^4]: Now note that we never denied the existence of a preferred **acceleration**. That is because there is a preferred acceleration: zero. There is a special class of paths, known as **inertial trajectories**, which are those that aren't undergoing any acceleration at all. Unlike position or velocity, if you were sealed in a spaceship you could tell whether you were being accelerated. If you were, the spaceship would push on you in that direction.