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Einstein proved (w/ relativity):
* There is no absolute distance
* There is no absolute time
* There is no absolute velocity including "at rest"
* There is no absolute mass
However there is absolute acceleration (which is key to General Relativity). But what is cool is how it also shows even the fundamental forces arent absolute. A magnetic field arrises from an electric field due to relativity and vice versa. Very little is absolute but some things are, so cool...
@freemo Doc Freemo wrote (Oct 18, 2024, 07:04 PM):
> [...] However there is absolute acceleration (which is key to Gen. #Relativity).
Yes, there is (we can define and measure) (the magnitude of) _acceleration_ _of a specific participant_, _at some particular event_, as the <a href="https://en.wikipedia.org/wiki/Circumcircle#Other_properties">radius of cuvature</a> of _the_ time-like worldline traced by that participant; by means of a Cayley-Menger determinant as expression of <a href="https://en.wikipedia.org/wiki/Heron%27s_formula#Alternate_expressions">Heron's fomula term</a>; cmp. https://mathstodon.xyz/@MisterRelativity/109622725097842951
However:
There also is (we can also define and measure) "radar acceleration", https://arxiv.org/abs/0708.0170 for instance, i.e. _of one specific participant_, _at some particular event_, _in reference to some other participant_.
> [...] A magnetic field arrises from an electric field [...] and vice versa [...] due to
... (cue drumroll) ...
motion!, i.e. having a choice of different reference systems; with members of distinct ref. systems generally not remaining pairwise in coincidence wrt. each other, nor (pairwise) at rest wrt. each other.
p.s.
> * There is no absolute distance
Please discuss this statement for the case of
- a regulation size <a href="https://en.wikipedia.org/wiki/American_football_field">American football field</a> (presumably strictly 120 yards long, with two goals standing at rest wrt. each other this exact distance apart on the two endlines)
- and a row of cars, driving along a sideline at constant speed \(\beta ~ c\) ...
> * There is no absolute time
Please discuss this statement for the case of muons (which -- pretty much always, so far -- were found to have <a href="https://pdglive.lbl.gov/Particle.action?node=S004">mean life duration \(\overline{\tau_{\mu }}\)</a> of about 2.2 micro seconds ...
> However:
> There also is (we can also define and measure) "radar acceleration", https://arxiv.org/abs/0708.0170 for instance, i.e. _of one specific participant_, _at some particular event_, _in reference to some other participant_.
When we say that something is not relative in the context of relativity we just mean there is some [privileged value. You can always measure something in a relative way even if it does have some absolute value with meaning.
> ... (cue drumroll) ...
>
> motion!, i.e. having a choice of different reference systems; with members of distinct ref. systems generally not remaining pairwise in coincidence wrt. each other, nor (pairwise) at rest wrt. each other.
The point is that if you have some object with a magnetic field that magnetic field can look like an electric field due to relativity effects. This is unrelated to the fact that a moving field will give off the other field. Also to be clear it isnt all motion, only acceleration causes this not velocity.
> Please discuss this statement for the case of
> - a regulation size <a href="https://en.wikipedia.org/wiki/American_football_field">American football field</a> (presumably strictly 120 yards long, with two goals standing at rest wrt. each other this exact distance apart on the two endlines)
Since we dont operate at near-light speeds, or in extreme gravitational gradients the effects of relativity are small enough that they can be ignored for us in every day life. But the point is if i were going fast enough the effect can become significant and a football field may be a wildly different length depending on the conditions it is expierncing (speed, gravity, etc).
> Please discuss this statement for the case of muons (which -- pretty much always, so far -- were found to have <a href="https://pdglive.lbl.gov/Particle.action?node=S004">mean life duration \(\overline{\tau_{\mu }}\)</a> of about 2.2 micro seconds ...
Muons, like anything with a half-life at the quantum level, including radioactive material, does not have a fixed half-life like you suggest. The half-life described is only when the observer is in the same frame of reference as the muon. If the observer or muon are moving relative to eachother the half life changes and is no longer a constant.
@freemo Doc Freemo wrote (Oct 24, 2024, 12:33 AM):
> When we say that something is not relative in the context of relativity we just mean there is some [privileged value.
Some (of "us") might be in the habit of calling such values "proper".
(In the sense of ownership of a value: "the value characterizing those participants themselves who can carry out the necessary measurement themselves"; or at least, in thought-experimental descriptions: being imagined as having this ability.)
But I don't (like to) use this word "proper" at all, because it begs the question whether "improper values" and (foremost) "improper ways of measuring" might be possible and admissable.
No! -- Any measurement, according to its thought-experimental description and understanding, is accomplished foremost by those (participants) who are (or: whose relations among each other is) described by the measured value.
Anything else is at best an attempt ("by others") at estimating a value (which characterizes "the owners", and which could be (at least thought as being) actually determined and re-checked by those "owners" themselves). For example: If "we" (nearly) correctly determine the geometry of a molecule (although that's "owned" by its constituent atoms); or if "we determine" the geometry/kinematics of a galaxy cluster (although that's foremost and definitively to be determined, and owned, by its constituents; at least in anthropomorphizing thought-experimental descriptions, i.e. "us putting ourselves in their shoes".)
Or at worst ... [contd.]
#relativity