17 minutes ago, swansont said:

What do you think is the “definition” of time? (in a physics sense) Is it something other that “that which is measured by a clock”?

and what would a definition of a "clock" be? Any oscillation can be used as reference to define some kind of time.

18 minutes ago, swansont said:

Please keep speculations in its own thread in the speculations section, rather than hijacking someone else’s thread with that discussion.

the neutrino oscillation is an active research topic that is not yet fully understood. as of now, assuming the neutrino having a mass is just as much speculation given our current experimental results. There are even some conflicting data which are partially at odds with invariant nature, though there may still be other explanations. there is a reason why Lorentz violation is considered, including experiments that could test for it.

16 minutes ago, Killtech said:

and what would a definition of a "clock" be? Any oscillation can be used as reference to define some kind of time.

Any regular oscillation, sure. And?

“the neutrino oscillation is an active research topic that is not yet fully understood. as of now, assuming the neutrino having a mass is just as much speculation given our current experimental results. There are even some conflicting data which are partially at odds with invariant nature, though there may still be other explanations. there is a reason why Lorentz violation is considered, including experiments that could test for it.”

The passage I was objecting to was about perceiving different flows of time. I should have edited the quote further, but then again, I was hoping you could discern mainstream physics from non-mainstream

5 minutes ago, swansont said:

The passage I was objecting to was about perceiving different flows of time. I should have edited the wuote furthr, but then again, I was hoping you could discern mainstream physics from non-mainstream

the OP mentioned the scenario of a a massless particle oscillating and mentioned the conflict this causes with time himself - and thereafter made some speculations about the speed of light vs "time" i did not fully follow.

9 hours ago, Killtech said:

what would a definition of a "clock" be?

Some time ago, I came up with the perfect definition of a clock. Note that the definition of time is that which is measured by a clock, so the definition of a clock cannot reference time. But one can define a clock without referring to time by providing instructions on how to build a clock. The instructions to build a clock is the definition of that clock.

10 minutes ago, KJW said:

Some time ago, I came up with the perfect definition of a clock. Note that the definition of time is that which is measured by a clock, so the definition of a clock cannot reference time. But one can define a clock without referring to time by providing instructions on how to build a clock. The instructions to build a clock is the definition of that clock.

Hehe, yeah, been there. At which point i figured these instructions can be more or less reduced to the definition of the SI second. Maybe you understand why i use that a bit synonymous with the definition of a clock - for the lack of an alternative as physics books tend to skip on defining on what counts as a clock.

And you have another issue. Those instructions will still be somewhat arbitrarily chosen, a convention that is. They cannot be deducted as a unique choice from the laws of nature. Thinking as mathematicians would, we can have a look at the entire set of possible instructions and start to distinguish and classify them by what effects they have. We would have to constrain this set by additional rules to ensure the resulting device yields reproducible results regardless how it got there (no kind of hysteresis effects). and if i give you some other set of instructions, say for a specific coordinate time, will that be a clock as well? This leads to finding the set of all possible interpretations of spacetime compatible with our reality.

11 hours ago, Killtech said:

the OP mentioned the scenario of a a massless particle oscillating and mentioned the conflict this causes with time himself - and thereafter made some speculations about the speed of light vs "time" i did not fully follow.

The OP asked a question, and responses should try to answer that question, and attempt to clear up any misconceptions, with mainstream science. It’s not an invitation to introduce non-mainstream discussion.

Even now, after the topic has been split, we expect mainstream science. Non-mainstream science can only take place in their own thread in the speculations section

1 hour ago, Killtech said:

At which point i figured these instructions can be more or less reduced to the definition of the SI second.

I have been involved in building ~10 atomic clocks, and at no time did the definition of the second enter into the process. The definition of the second has changed since the fist atomic clocks were built - a fact you continue to ignore - so they could not have depended on it.

2 hours ago, KJW said:

Note that the definition of time is that which is measured by a clock, so the definition of a clock cannot reference time.

I disagree. We do that all the time with definitions. How can you not, for a finite set of words that only reference each other? Even if it takes multiple steps, you end up in a circle.

23 minutes ago, swansont said:

I disagree. We do that all the time with definitions. How can you not, for a finite set of words that only reference each other? Even if it takes multiple steps, you end up in a circle.

so if you define time as “that which is measured by a clock” and a clock "that which measures time" you explained nothing. if you do that, you end up with definitions which are so devoid of any meaning that from them you cannot even deduct that time is measured in numbers and that it establishes a compare relation, like which time interval is longer.

Sorry, you have to put more work into that. look at how such definitions are done in math so you come up with something that can be worked with at all. For example look at how math defines a metric in order to be able to use the concept of distances. You need a bare minimum like that.

Basically you have to define either time or clocks at least by the properties / rules they are subject to. something that characterizes them. That's how mathematitians and geometers always approached this - and to their surprise they figured this rarely leads to a unique construct but rather classes of such.

39 minutes ago, swansont said:

I have been involved in building ~10 atomic clocks, and at no time did the definition of the second enter into the process. The definition of the second has changed since the fist atomic clocks were built - a fact you continue to ignore - so they could not have depended on it.

In germany, there is an "Eichbehörde". if you construct a clock that you cannot show that it obliges by the SI specifications of the second, you won't be allowed to call it as such nor use it for any business - i.e. a taxi would not be allowed to use such a clock since it could measure whatever the creator desired to rip off the customer.

1 minute ago, Killtech said:

so if you define time as “that which is measured by a clock” and a clock "that which measures time" you explained nothing. if you do that, you end up with definitions which are so devoid of any meaning that from them you cannot even deduct that time is measured in numbers and that it establishes a compare relation, like which time interval is longer.

Sorry, you have to put more work into that. look at how such definitions are done in math so you come up with something that can be worked with at all. For example look at how math defines a metric in order to be able to use the concept of distances. You need a bare minimum like that.

Basically you have to define either time or clocks at least by the properties / rules they are subject to. something that characterizes them. That's how mathematitians and geometers always approached this - and to their surprise they figured this rarely leads to a unique construct but rather classes of such.

Instructions to build a clock doesn’t define time. “take a mass and suspend it from a string” is not a definition of time, but you didn’t seem to have a problem with that “definition”

“defining” time is an issue of metaphysics - telling people what time “is”. Physics is interested in how it behaves - the measurement.

Define length without any self-reference.

1 minute ago, swansont said:

Instructions to build a clock doesn’t define time. “take a mass and suspend it from a string” is not a definition of time, but you didn’t seem to have a problem with that “definition”

i do very much have a problem with this, hence check my answer to @KJW about his suggestion.

2 minutes ago, swansont said:

“defining” time is an issue of metaphysics - telling people what time “is”. Physics is interested in how it behaves - the measurement.

it is a topic of geometry amongst others and mathematicians had quite some trouble to figure our a usable ways to do it.

3 minutes ago, swansont said:

Define length without any self-reference.

These are the definitions at the very core of Riemann geometry and more general, metric spaces in analysis. They explore the concept of length by the properties it has.

Here is how much you can dwell of this definition, starting with simple ideas to the generalization for more general geometries: https://en.wikipedia.org/wiki/Arc_length

It really boils down to those 4 core properties: https://en.wikipedia.org/wiki/Metric_space#Definition

Edited April 21Apr 21 by Killtech

8 hours ago, Killtech said:

and what would a definition of a "clock" be? Any oscillation can be used as reference to define some kind of time.

I'm glad you used the words 'can be' allowing for the possibility of other ways to define and measure time, although some negative resistance and other non linear oscillators may also present an issue.

Just now, Killtech said:

These are the definitions at the very core of Riemann geometry and more general, metric spaces in analysis. They explore the concept of length by the properties it has.

Here is how much you can dwell of this definition, starting with simple ideas to the generalization for more general geometries: https://en.wikipedia.org/wiki/Arc_length

It really boils down to those 4 core properties: https://en.wikipedia.org/wiki/Metric_space#Definition

The problem with this is that this is just where mathematics and physics diverge.

Physicists relax condition 2, the positive definiteness requirement,

This is the same misconception you showed in the parent thread.

Sets do not require a metric.

That is optional additional structure.

Edited April 21Apr 21 by studiot

1 hour ago, Killtech said:

i do very much have a problem with this, hence check my answer to @KJW about his suggestion.

it is a topic of geometry amongst others and mathematicians had quite some trouble to figure our a usable ways to do it.

I’m pretty sure the concept of a year with seasons dates back quite a way. The concept of a day probably much further. So, not quite that difficult to find a usable way.

1 hour ago, Killtech said:

These are the definitions at the very core of Riemann geometry and more general, metric spaces in analysis. They explore the concept of length by the properties it has.

Here is how much you can dwell of this definition, starting with simple ideas to the generalization for more general geometries: https://en.wikipedia.org/wiki/Arc_length

It really boils down to those 4 core properties: https://en.wikipedia.org/wiki/Metric_space#Definition

“Arc length is the distance between two points along a section of a curve.”

“Length is the distance” is self-referential. And if you do it with coordinates and positions, now you have to define those without being self-referential. You can’t define things in terms of other things without eventually looping back. I wouldn’t be surprised if there’s a math theorem that shows this. If I have 10 elements in my lexicon, I can define the first in terms of 9 other options, but the second leaves me 8 options, and so on. 10 elements but only 9 unique definitions.

3 minutes ago, swansont said:

I wouldn’t be surprised if there’s a math theorem that shows this.

Around the turn of this century, I devised such a theorem. Basically, any dictionary based only on words must contain words that are either undefined or circularly defined. One way around this is for a dictionary to also contain pictures. In the case of defining a clock in terms of instructions on how to build it, one also avoids the problem associated with a dictionary based only on words.

Just now, KJW said:

Around the turn of this century, I devised such a theorem. Basically, any dictionary based only on words must contain words that are either undefined or circularly defined. One way around this is for a dictionary to also contain pictures. In the case of defining a clock in terms of instructions on how to build it, one also avoids the problem associated with a dictionary based only on words.

You can certainly have fun with the definition and basic theory of a set.

16 minutes ago, swansont said:

I’m pretty sure the concept of a year with seasons dates back quite a way. So, not quite that difficult to find a usable way.

and the many conflicts around it. solar or moon year? a common or a leap year? there are many variants of this term, so we need different prefixes to distinguish between then when it isn't clear from the context. so when it comes to accounting the passing of years, it turned out highly contentious topic in politics and religion...

26 minutes ago, swansont said:

“Arc length is the distance between two points along a section of a curve.”

“Length is the distance” is self-referential. And if you do it with coordinates and positions, now you have to define those without being self-referential. You can’t define things in terms of other things without eventually looping back. I wouldn’t be surprised if there’s a math theorem that shows this. If I have 10 elements in my lexicon, I can define the first in terms of 9 other options, but the second leaves me 8 options, and so on. 10 elements but only 9 unique definitions.

would you really mistake a introductionary explanation for a random reader with a formal definitions that follow afterwards??

length is defined via a distance, which math calls a metric d as a mapping to the real numbers and it is defined by the follwing 4 properties:

1. \(d(x,x) = 0 \)
2. \(d(x,y) > 0\) if \(x \neq y\)
3. \(d(x,y) = d(y,x) \)
4. \(d(x,z) \le d(x,y) d(y, z)\)

So it references itself to declare the rules that specify its characteristic properties. But it gives us something to work, enough to establish basic geometric concepts. first and foremost, it at least establishes that length is a positive number. Note that this definition is deliberately open for various possible implementations, so it knows that the concept of length cannot be uniquely determined this way and there are multiple non-equivalent possibilities this allows. This is why you will sometime encounter a term like d-length and d'-length to distinguish between different measures of length. There is the concept of isometry to compare different concept of length and establish if they yield an equivalent measure.

Edited April 21Apr 21 by Killtech

1 hour ago, Killtech said:

length is defined via a distance, which math calls a metric d as a mapping to the real numbers and it is defined by the follwing 4 properties:

So length is defined as a 'distance', d , between numerical points mapped on a manifold according to the 4 above mentioned rules.

That's not self-referential at all ...

Edited April 21Apr 21 by MigL

2 hours ago, Killtech said:

and the many conflicts around it. solar or moon year? a common or a leap year? there are many variants of this term, so we need different prefixes to distinguish between then when it isn't clear from the context. so when it comes to accounting the passing of years, it turned out highly contentious topic in politics and religion...

So? This doesn’t actually address anything. You said “it is a topic of geometry amongst others and mathematicians had quite some trouble to figure our (sic) a usable ways to do it.” and astronomy offers several options that were used and therefore usable.

2 hours ago, Killtech said:

would you really mistake a introductionary explanation for a random reader with a formal definitions that follow afterwards??

length is defined via a distance,

And I asked for a definition that’s not circular. Length and distance are synonyms. You’re jumping into the math without actually answering the question I asked, or the objection that started this tangent.

4 hours ago, Killtech said:

In germany, there is an "Eichbehörde". if you construct a clock that you cannot show that it obliges by the SI specifications of the second, you won't be allowed to call it as such nor use it for any business - i.e. a taxi would not be allowed to use such a clock since it could measure whatever the creator desired to rip off the customer.

Yes, that makes sense from a commerce perspective. In the US weights and measures standards are the province of NIST, which is in the Dept. of Commerce. Commercial measurements have to trace back to the government standard, and worldwide standard, so people can do business with each other

It has nothing to do with issues with physics.

4 hours ago, Killtech said:

Basically you have to define either time or clocks at least by the properties / rules they are subject to. something that characterizes them

And yet we’ve gone very long stretches where this was not the case. There are different version of an hour (one is 1/12 of the period of daylight, so it varies over the course if a year, or with latitude) but yet the concept of time still existed. What time is is not the same as how we define any particular unit of it*

Standardizing was driven by commerce.

*same thing applies to length, and you must tacitly agree with this, because you offered up a mathematical definition rather than cite the SI definition of the meter, or any other standard.

52 minutes ago, swansont said:

And I asked for a definition that’s not circular. Length and distance are synonyms. You’re jumping into the math without actually answering the question I asked, or the objection that started this tangent.

Not true, maybe that is so in colloquial language but not in science, or at least not in math. The distance between two points is one value given a metric, but the length between them varies by the chosen path. The distance is always the minimal length between two points. At least according to the definitions i know.

Now back to your objection, how does your definition of time and clocks even prevent some nonsense like your example “take a mass and suspend it from a string” from being a clock? if your definition does not even demand clocks to provide their measurements as numeric values, then it becomes so weak anything would count. that is my objection to the way you would define those terms. a definition is meant to give rules to recognize if something meets these criteria or not, so you can test things against this definition same way as you test the assumed laws of nature.

1 hour ago, swansont said:

So? This doesn’t actually address anything. You said “it is a topic of geometry amongst others and mathematicians had quite some trouble to figure our (sic) a usable ways to do it.” and astronomy offers several options that were used and therefore usable.

usable, yes. disagreeing, also yes. if you have different and disagreeing definitions of time it requires to distinguish between them carefully and establish transformation behavior.

the neutrino oscillations, if we had more efficient ways to observe it would also provide usable means to measure time. If they were subject to CPT violations (hence not entirely Lorentz invariant), such a time standard would drastically differ from other clock based on an atomic standard.

7 minutes ago, Killtech said:

Not true, maybe that is so in colloquial language but not in science, or at least not in math. The distance between two points is one value given a metric, but the length between them varies by the chosen path. The distance is always the minimal length between two points. At least according to the definitions i know.

And we were using colloquial language, so…

7 minutes ago, Killtech said:

Now back to your objection, how does your definition of time and clocks even prevent some nonsense like your example “take a mass and suspend it from a string” from being a clock?

I doesn’t, because I described a pendulum, as instructions for building a clock. I did not tell you how to operate the clock, but that wasn’t what was asked for.

You can make fancier clocks, but the “physics package” is a mass suspended on something. Some of the rest of it is the readout, but a clock display is not a clock.

7 minutes ago, Killtech said:

if your definition does not even demand clocks to provide their measurements as numeric values, then it becomes so weak anything would count.

The clocks I worked on don’t provide such output, and several of them still comprise the best continuously-running cold-atom microwave clocks in the world.

7 minutes ago, Killtech said:

that is my objection to the way you would define those terms. a definition is meant to give rules to recognize if something meets these criteria or not, so you can test things against this definition same way as you test the assumed laws of nature.

I think clocks good enough to be incorporated into the BIPM timescale (and given maximum weighting in their algorithm) should count, and these are the ones that just output a 5 MHz signal.

7 minutes ago, Killtech said:

usable, yes. disagreeing, also yes. if you have different and disagreeing definitions of time it requires to distinguish between them carefully and establish transformation behavior.

But I’m not the one claiming that a clock output defines time, and if you are suggesting that then we have lots of definitions, because no two clocks will ever agree, as long as the measurement is precise enough.

And transformation behavior is just calibration, which is what timekeepers do as part of their job. The USNO Master Clock, for example, is a weighted average of close to a hundred clocks, all of which disagree to some small extent.

7 minutes ago, Killtech said:

the neutrino oscillations, if we had more efficient ways to observe it would also provide usable means to measure time. If they were subject to CPT violations (hence not entirely Lorentz invariant), such a time standard would drastically differ from other clock based on an atomic standard.

It would likely be much less precise for a variety of reasons but it would not “differ” as such. A neutrino that oscillated every ~3 km would oscillate at ~100 kHz. Then you have poor signal/noise because of detection problems. If you could overcome the latter it would be about the same precision as a quartz clock but much bigger.

Just now, Killtech said:

At least according to the definitions i know.

Yeah well you don't know it all and seem unwilling to accept anything outside your knowledge.

For instance your 'metric' or distance function is only one of many possible ones satisfying the strict mathematical definition, some are most definitely not minimal.

Just now, swansont said:

Some of the rest of it is the readout, but a clock display is not a clock.

Interesting observation.

Early mediaeval church clocks (for example the oldest still working such clock in the world at Winchester Cathedral) did not have a display at all !

All the monks of the day needed to know was when certain times of the ecclesiastical day happened and the clock chimed or rang bells to denote this.

I This was a bit like the end of class bell in my schooldays.

Edited April 21Apr 21 by studiot
spelling

2 minutes ago, studiot said:

Interesting observation.

It’s a pet peeve of mine, mainly from social media posts saying “look at this neat clock” and it’s a possibly neat display hooked up to a rather mundane physics package, which what does the measurement

Apologies it is Salisbury Cathedral's clock. Not being religeous I tend to get them mixed up, though I appreciate the engineerjng of their day.

Edited April 21Apr 21 by studiot

6 hours ago, Killtech said:

so if you define time as “that which is measured by a clock” and a clock "that which measures time" you explained nothing. if you do that, you end up with definitions which are so devoid of any meaning that from them you cannot even deduct that time is measured in numbers and that it establishes a compare relation, like which time interval is longer.

Distance is that which is measured with a ruler. Time is that which is measured with a clock. We don't analyse the nature of distance, do we? Time doesn't require an ontological analysis. i.e. What is time? That is philosophy; physics, seeks to only describe the behaviour of natural phenomena.

1 hour ago, swansont said:

It would likely be much less precise for a variety of reasons but it would not “differ” as such. A neutrino that oscillated every ~3 km would oscillate at ~100 kHz. Then you have poor signal/noise because of detection problems. If you could overcome the latter it would be about the same precision as a quartz clock but much bigger.

for a massless neutrino, this becomes interesting when we compare that frequency to a photon traveling parallel to it with the same frequency in a starting frame. if we measure the both frequencies from another frame moving with velocity v relative to the base frame in the direction of both particles, the photon frequency becomes red shifted, but the neutrinos either won't be or it will be by another value. Such would be the nature of CPT violation. Sure, in the base frame, both time measurements would agree, in the other frame they wouldn't. so what now?

52 minutes ago, StringJunky said:

Distance is that which is measured with a ruler. Time is that which is measured with a clock. We don't analyse the nature of distance, do we? Time doesn't require an ontological analysis. i.e. What is time? That is philosophy; physics, seeks to only describe the behaviour of natural phenomena.

Not an ontological discussion, but about our model of spacetime. Because for every given ruler which measures a curved geometry you can derive and construct another ruler which will measure the same space to be flat (at least locally. but it holds globally for most standard topologies). This is why you have to be specific about the choice of rulers you use.

to put it in other words: is spacetime curved or is it flat and it is just our rulers that change in length (and clocks) depending on region due to some local physical interactions / conditions? There is a class of physical interactions which makes it impossible to distinguish between these two possibilities and so it boils down to a different choice of clocks and rulers. For a theoretical purpose, the specification matters.

Edited April 21Apr 21 by Killtech

1 minute ago, Killtech said:

for a massless neutrino, this becomes interesting when we compare that frequency to a photon traveling parallel to it with the same frequency in a starting frame. if we measure the both frequencies from another frame moving with velocity v relative to the base frame in the direction of both particles, the photon frequency becomes red shifted, but the neutrinos either won't be or it will be by another value. Such would be the nature of CPT violation. Sure, in the base frame, both time measurements would agree, in the other frame they wouldn't. so what now?

cosmic neutrino background red-shift has indirect evidence to support it, but this is, once again, a distraction from the topic being discussed.

Come up with actual evidence and there’s something to discuss. But you’re basing this on a what-if scenario that has no evidence and on a premise we know to be false (massless neutrino), so it’s based on yet another conjecture that some new neutrino exists.

1 hour ago, swansont said:

Come up with actual evidence and there’s something to discuss. But you’re basing this on a what-if scenario that has no evidence and on a premise we know to be false (massless neutrino), so it’s based on yet another conjecture that some new neutrino exists.

there is no evidence that they have any mass either. the only reason why it is speculated it to have a mass is due to the discovery of their oscillation. but so far all experiments trying to determine it came empty handed. Also no experiment found any evidence of them moving any slower then photons, in fact in observations of cosmic events they do arrive before photons do but that is due to non exotic reasons. So we are coming to a point where the matter is getting more complex and alternative explanations are looked into for a reason.

Edited April 22Apr 22 by Killtech