Incoming links: Frame of reference
A subset of Spacetime diagram.
The key insights that it gives are:
- future and past are well defined: every reference frame sees your future in your future cone, and your past in your past coneOtherwise causality could be violated, and then things would go really bad, you could tell your past self to tell your past self to tell your past self to do something.You can only affect the outcome of events in your future cone, and you can only be affected by events in your past cone. You can't travel fast enough to affect.Two spacetime events with such fixed causality are called timelike-separated events.
- every other event (to right and left, known as spacelike-separated events) can be measured to happen before or after your current spacetime event by different observers.But that does not violate causality, because you just can't reach those spacetime points anyways to affect them.
Animation showing how space-separated events can be observed to happen in different orders by observers in different frames of reference
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Quantum Mechanics 12b - Dirac Equation II by ViaScience (2015)
Source. - youtu.be/tR6UebCvFqE?t=23 particle at rest
- youtu.be/tR6UebCvFqE?t=322 unidirectional movement without a potential
- youtu.be/tR6UebCvFqE?t=507 shows that observers in different frames of reference also see different spin. We are reminded of how magnetism is just a side effect of special-relativity.
- youtu.be/tR6UebCvFqE?t=549 Dirac equation solution for the hydrogen atom, final result only + mentions fine structure prediction.
Explains how it is possible that everyone observes the same speed of light, even if they are moving towards or opposite to the light!!!
This was first best observed by the Michelson-Morley experiment, which uses the movement of the Earth at different times of the year to try and detect differences in the speed of light.
This leads leads to the following conclusions:
- to length contraction and time dilation
- the speed of light is the maximum speed anything can reach
All of this goes of course completely against our daily Physics intuition.
The "special" in the name refers to the fact that it is a superset of general relativity, which also explains gravity in a single framework.
Since time and space get all messed up together, you have to be very careful to understand what it means to say "I observed this to happen over there at that time", otherwise you will go crazy. A good way to think about is this:
- use Einstein synchronization to setup a bunch of clocks for every position in your frame of reference
- on every point of space, you put a little detector which records events and the time of the event
- each detector can only detect events locally, i.e. events that happen very close to the detector
- then, after the event, the detectors can send a signal to you, who is sitting at the origin, telling you what they detected
Spin is one of the defining properties of elementary particles, i.e. number that describes how an elementary particle behaves, much like electric charge and mass.
Possible values are half integer numbers: 0, 1/2, 1, 3/2, and so on.
The approach shown in this section: Section "Spin comes naturally when adding relativity to quantum mechanics" shows what the spin number actually means in general. As shown there, the spin number it is a direct consequence of having the laws of nature be Lorentz invariant. Different spin numbers are just different ways in which this can be achieved as per different Representation of the Lorentz group.
Video 1. "Quantum Mechanics 9a - Photon Spin and Schrodinger's Cat I by ViaScience (2013)" explains nicely how:
- incorporated into the Dirac equation as a natural consequence of special relativity corrections, but not naturally present in the Schrödinger equation, see also: the Dirac equation predicts spin
- photon spin can be either linear or circular
- the linear one can be made from a superposition of circular ones
- straight antennas produce linearly polarized photos, and Helical antennas circularly polarized ones
- a jump between 2s and 2p in an atom changes angular momentum. Therefore, the photon must carry angular momentum as well as energy.
- cannot be classically explained, because even for a very large estimate of the electron size, its surface would have to spin faster than light to achieve that magnetic momentum with the known electron charge
- as shown at Video "Quantum Mechanics 12b - Dirac Equation II by ViaScience (2015)", observers in different frames of reference see different spin states
Quantum Mechanics 9a - Photon Spin and Schrodinger's Cat I by ViaScience (2013)
Source. Quantum Spin - Visualizing the physics and mathematics by Physics Videos by Eugene Khutoryansky (2016)
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