Incoming links: Length contraction
This is a well known though experiment, which Richard Feynman used to emphasize
- infinite wire with balanced positive and negative charges, so no net charge, but a net magnetic field
- a single charge moves parallel to wire at the same speed as the electrons
In the above experiment:
- from the wire frame, the charge feels electromagnetic force, because it is moving and there is a magnetic field
- from the single charge frame, there is still magnetic field (positive charges are moving), but the body itself is not moving, so there is no force!
The solution to this problem is length contraction: the positive charges are length contracted and the moving electrons aren't, and therefore they are denser and therefore there is an effective charge from that frame.
This is also mentioned at David Tong www.damtp.cam.ac.uk/user/tong/em/el4.pdf (archive) "David Tong: Lectures on Electromagnetism - 5. Electromagnetism and Relativity" "5.2.1 Magnetism and Relativity".
How Special Relativity Fixed Electromagnetism by The Science Asylum (2019)
Source. 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
What you would see the moving rod look like on a photo of a length contraction experiment, as opposed as using two locally measured separate spacetime events to measure its length.
Light watch transverse to direction of motion. This case is interesting because it separates length contraction from time dilation completely.
Of course, as usual in special relativity, calling something "time dilation" leads us to mind boggling ideas of "symmetry breaking": if both frames have a light watch, how can both possibly observe the other to be time dilated?
And the answer to this, is the usual: in special relativity time and space are interwoven in a fucked up way, everything is just a spacetime event.
In this case, there are three spacetime events of interest: both clocks start at same position, your beam hits up at x=0, moving frame hits up at x>0.
Those two mentioned events are spacelike-separated events, and therefore even though they seem simultaneous to you, they are not going to be simultaneous to the moving observer!
If little clock one meter away from you tells you that at the time of some event (your light beam hit up) the moving light watch was only 50% up, this is just a number given by your one meter away watch!