31
votes
How could Tycho Brahe determine positions without accurate clocks?
In observational astronomy the position of objects in the sky
(like stars and planets) is given in the equatorial coordinate
system by two angles: declination and right ascension.
In this coordinate ...
- 26.8k
26
votes
Accepted
On mathematical level, what exactly is time in Newtonian mechanics?
Here is one way to address your question.
"Time is defined so that motion looks simple." - Misner, Thorne, and Wheeler in Gravitation, p.23.
Continue through to p. 26 where they say
"...
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19
votes
How could Tycho Brahe determine positions without accurate clocks?
As an aside- Tycho achieved his legendary accuracy by building ever-larger angle measurement devices called quadrants. The largest was about 6 feet in diameter and he aimed its sighting line at a star ...
- 73.8k
12
votes
How could Tycho Brahe determine positions without accurate clocks?
Tycho Brahe had access to an excellent clock: the sky itself!
As others have mentioned, astronomers have several coordinate systems for specifying the positions of bodies on the celestial sphere. ...
- 9,869
10
votes
Accepted
Using time dilation to find universal frame of reference
I'm afraid your idea won't work. Time dilation is symmetrical. Suppose your frame of reference and mine are moving inertially relativity to each other. A clock in your frame will seem dilated relative ...
- 18.8k
7
votes
Finite distance, Infinite time?
This is correct and not too surprising. Each time it bounces, the ball loses some energy. But with the hypotheses in OP, the ball always has some mechanic energy left, so it is possible that it never ...
- 3,946
5
votes
How could Tycho Brahe determine positions without accurate clocks?
Most already said in other answers, But in his Tycho Brahe: a picture of scientific life and work in the sixteenth century, John Louis Emil Dreyer writes about how time was determined by Tycho and ...
- 151
4
votes
Why is spacetime in special relativity hyperbolic?
No, spacetime is not 4 dimensional Euclidean in Galilean relativity; it's 3+1 dimensional, where the time dimension is completely separate from the spatial dimensions and does not mix with them at all....
- 6,128
4
votes
Is it possible to measure an irrational amount of a physical quantity?
is it actually possible to measure irrational time through such a definition of a second?
Sure, simply use a different frequency standard. There is no reason that you must use caesium as your only ...
- 65.8k
4
votes
Using time dilation to find universal frame of reference
Axis Omega asked: "can a frame of reference in which time runs the fastest (there is the least amount of dilation) be found in which to compare to the rest of the universe?"
That is the ...
- 7,757
3
votes
Finite distance, Infinite time?
My analysis is this. Roundtrip time for a ball in one iteration is:
$$ t_n = S_n/\overline {v_n} ~,$$
Where $\overline {v_n}$ is average speed of ball in current bounce. Then according to problem ...
- 7,410
3
votes
Finite distance, Infinite time?
Here is a diagram of the bounces of a ball:
It seems that the ball will require an infinite number of bounces to come to rest. Intuition says that it will take an infinite amount of time for this to ...
- 600
3
votes
Is it theoretically possible to create a 'time bubble', where inside the bubble time will stop or at least slow down radically?
Sure you can! You will need:
One (1) large spherical shell of ordinary matter
It can be shown that inside a spherical shell like this, the amount of time $\tau$ experienced by an observer at rest ...
- 38.3k
3
votes
Accepted
Is this $x$-$t$ graph possible? Is the distance decreasing over time in this graph?
The velocity should be displacement over time, while the speed is the distance over time. In contrast to displacement, which is a vector and could have a negative sign, the distance is the length ...
- 54
2
votes
How could Tycho Brahe determine positions without accurate clocks?
The answer by PM-2Ring makes an excellent and often overlooked point: before clocks, astronomers were not dependent on crude mechanical devices, they had star-based timekeeping.
It is worth noting ...
- 151
2
votes
What governs the rate at which time passes?
The question as formulated here does not quite make sense. Time, like any other value, can only be defined relative to something else- similarly to how it wouldn't make sense to ask why space is ...
- 86
2
votes
What governs the rate at which time passes?
Time passing at any rate other than 1 second per second is a logical impossibility (not just a physical impossibility).
A second is currently defined as "$9192631770$ cycles of Cs-133 transition&...
- 5,917
2
votes
Is it possible to measure an irrational amount of a physical quantity?
Yes it’s impossible to get a direct measurement whose result is irrational. But it’s not so much that you’re comparing to a reference quantity but rather because every measurement has finite precision ...
- 9,253
2
votes
Is there something that violates "time locality"?
This sounds like the fact that the state of a system is determined by its state in the past. If you keep track of all the relevant data, then in order for some event to affect some variable on the ...
- 171
2
votes
Why is spacetime in special relativity hyperbolic?
related: Is spacetime in special relativity hyperbolic?
ANS: The spacetime in special relativity is not hyperbolic (is not a [curved] hyperbolic geometry).
Similarly, the geometry of Euclidean space ...
- 8,677
2
votes
On mathematical level, what exactly is time in Newtonian mechanics?
In my opinion the idea of time is related to a fixed relation between some physical events. The numbers of full moons, or day/night cycles between the repetition of a sky configuration, which we call ...
- 12.3k
1
vote
Why is spacetime in special relativity hyperbolic?
It's an outcome of the absolute nature of the motion of light. But to begin at the beginning ...
Since antiquity, the notion of rest and motion were distinct ideas. One was the negation of the other. ...
- 12.1k
1
vote
At which fraction of light speed could I expand ten times, and 100 times, my clock's ticking?
You need to use the Lorentz transformation from your frame of reference to the reference frame moving relative to you. The calculation becomes simpler if you assume that the measurement between the ...
- 165
1
vote
Accepted
Is the speed of objects in time, in Galilean Relativity, a constant and invariant speed relative to all reference frames?
Yes. The "different speeds through time" of Relativity are a consequence of the fact that, in Relativity, time is an observer-dependent quantity. In Galilean spacetime, time is absolute to ...
- 7,876
1
vote
Is the speed of objects in time, in Galilean Relativity, a constant and invariant speed relative to all reference frames?
There isn't much to say... Yes, universality of time is a basic postulate of Newtonian mechanics, one of the first axioms that you see when you start learning the theory.
- 2,256
1
vote
Is it possible to measure an irrational amount of a physical quantity?
You can not measure anything irrational, if you for example measure the circumference of a circle, you will never have a multiple of pi.
The concept of measuring is allways comparing with a unit and ...
- 3,435
1
vote
Physical meaning of a time dependent $g_{00}$
Physically this makes no difference. Without this redefinition you just have an arbitrary lapse function $N(t)$ in the $g_{00}$ component, but it is not dynamical.
See my answer here Why the FLRW ...
- 3,055
1
vote
Accepted
Calculating the one-direction speed of light
The flaw is that you can't assume the clocks stay synchronized. Assuming they stay synchronized is equivalent to adopting Einstein synchronization, and thus adopting the convention that the one-way ...
- 16.7k
1
vote
Is it theoretically possible to create a 'time bubble', where inside the bubble time will stop or at least slow down radically?
Very common and close to this is Gravitational Time Dilation. If you are outside of a gravitational field and looking in, the things within the gravitational field are moving through time more slowly ...
- 2,832
1
vote
Why do we tend not to use the time equation for bound states in non-relativistic QM?
This is used all the time. What you are doing is deriving the time-evolution for an eigenstate of the Schrödinger operator (ie a solution of the time-independent Schrödinger equation).
Such solutions ...
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