Units of spacetime in Minkowski metric

[phyti]

I think you have provided more clarification in this post than others, thanks.

Thanks for all your discussions, it requires me to think in detail about my responses.

I agreed that the light clock uses a distance and motion in its definition of time but now we're talking about clocks that don't use distance or motion so let's don't keep going around this circle.

If you're going to make this claim, you need to explain what you mean with regard to our current definition of the second. Please provide the details because I don't understand where distance or speed is involved.

Yes, they do and here is what they say about the current definition of the second:

I don't see any statement regarding distance, motion or the speed of light in this definition. Where do you see it?

1. "duration of 9,192,631,770 periods of the radiation"
Even this article is expressing the time (duration) in terms of wave lengths of light, which in this case is: λ = c/ν = 3*108/ 9*109 = 33mm. Obviously (wave length)*(frequency) = c, the distance light travels in 1 second, or 1 light second.

There are three parameters involved:
1) The speed of light.
2) The unit of distance.
3) The unit of time.

We can define any two independently and then define or measure the remaining one in terms of the other two. I'm just asking you why you feel that the only valid way is to define the unit of distance and the speed of light independently and then define the unit of time in terms of the other two, as opposed to either of the other two options. (And why you don't seem to understand that the current definitions define the speed of light and the unit of time independently and then define the unit of distance based on the other two.)

2. The um for distance x is the meter (m). The um for time t is the second. Light speed is cm per second. Then t = x/cm = nm/cm = n/c, i.e. a ratio of distances. Time is a ratio, a number, and numbers aren't physical but abstract relations. This is the same as the ratio vt/ct = v/c in a Minkowski diagram. Measurements have no independent existence beyond their intended purpose. Numbers are dimensionless thus "time" can only be a dimension in a mathematical sense.

You already accepted the current definition of a second, which is based on light speed, so it can't be independent of light speed.

Where did Einstein make that statement? Please provide an online reference and point to the specific location and/or provide a direct quote.

3. From 'The Meaning of Relativity', Albert Einstein, 1956: page 1.
"The experiences of an individual appear to us arranged in a series of events; in this series the single events which we remember appear to be ordered according to the criteria of "earlier" and "later", which cannot be analyzed further. There exists, therefore, for the individual, an I-time, or subjective time."

That time is dependent on observer speed follows from SR, authored by A. Einstein.

 

[Maxila]

I have to agree with Phyti that the SI definition of a second is ultimately the measure for the change of position of light. In spite of the temporal wording using "period" to describe wavelength. Each "period's" fundamental properties is a wave of length created by, and perpendicular to, the direction of a photon emitted from the cesium. It is the speed (the change of position energy) of a photon and length of those wave's that fundamentally cause's and define's the value of each "period" for the 9,192,631,770 waves that define the standard second.

Ultimately the time unit is relegated to being the description (unit measurement) for a change of position within a distance (the photons change of position within the distance of those waves); further as phyti said the time unit (i.e. one second) once defined merely describes a ratio of that distance over change of position.

 

[Nugatory]

1. "duration of 9,192,631,770 periods of the radiation"
Even this article is expressing the time (duration) in terms of wave lengths of light, which in this case is: λ = c/ν = 3*108/ 9*109 = 33mm. Obviously (wave length)*(frequency) = c, the distance light travels in 1 second, or 1 light second.

There's no distance or speed in that definition; it is not based on the wave length, and the distance that light travels in one period is irrelevant to the definition of the second. Put a detector at a fixed location, and measure the direction of the electric field. You'll see that it points up for a while, then points down, then points up again. Count those cycles, and when you've counted 9,192,631,770 of them one second has passed.

2...
You already accepted the current definition of a second, which is based on light speed, so it can't be independent of light speed.

Except that as I said above, the definition of the second is not based on light speed. and once we have a definition of the second that is independent of light speed, we can define the meter in terms of the distance that a light signal travel in a given time - again without ever considering what the speed of light might be. We look at where the light is emitted, look at where it is one second later, divide the distance between these two points by 299,792,458 and declare that to be one meter.

Now, it is indisputable that as a result of the way that we've defined the second and the meter, if we measure the speed of light it will come out to 299,792,458 m/sec. However, that does not mean that we need to know the speed of light to define the meter - it's the other way around.

3. From 'The Meaning of Relativity', Albert Einstein, 1956: page 1.
"The experiences of an individual appear to us arranged in a series of events; in this series the single events which we remember appear to be ordered according to the criteria of "earlier" and "later", which cannot be analyzed further. There exists, therefore, for the individual, an I-time, or subjective time."

True enough, but doesn't have anything to do with the metrological definitions of the second and the meter.

 

[phyti]

There's no distance or speed in that definition; ...

We look at where the light is emitted, look at where it is one second later, divide the distance between these two points by 299,792,458 and declare that to be one meter.

You are contradicting yourself (blue). How do you know when one second (red) has elapsed, i.e. you need a definition?

 

[Nugatory]

You are contradicting yourself (blue). How do you know when one second (red) has elapsed, i.e. you need a definition?

I don't see the contradiction... we have a definition of a second. We're counting the up-and-down transitions of the electric field at a single point near the cesium atom and when we've seen 9,192,631,770 of them we say that one second has passed since we started counting. Because we're doing this at a single point we don't consider any distances, the speed of light, or the speed of anything else; we're just counting twitches of a needle.

Here's the thought experiment:
Place a cesium atom, a counter that counts the oscillations of the cesium atom, a light source, and a light detector at a single point in space. Place a mirror at some distance away, arranged so that when the light source flashes, the flash hits the mirror and is reflected back to the light detector.

Now zero the counter and trigger a flash of light. The light flash travel out to the mirror and back to the detector, and we look at the counter value when the light flash hits the detector. We move the mirror back and forth until we find the distance at which the counter counts exactly 18,385,263,540 (that's two times 9,192,631,770) cycles between the flash and the detection the return flash. That's the distance that light travels in one second.

The meter is defined to be that distance, divided by 299,792,458.

 

[nikkkom]

Spatial dimensions have direction (vectors). Time is only a number (magnitude/scalar).

No. In SR, the location, speed, etc vectors have four components, one of them is time; and more to it, different observers will see these vectors' components transform in such a way that "time" component in one coordinate system partially becomes a spatial component.

You can liken this to an “arrow”, but it has no more significance than the imagined lines connecting the stars to form astrological signs.

In SR, velocity vectors of any objects always have time component > 0 (and moreover, ds^2 > 0).
In general, there *are* other vectors in Minkowski space, and the fact that not all of them can be a velocity vector is significant, and makes time special.

 

[Maxila]

I don't see the contradiction... we have a definition of a second. We're counting the up-and-down transitions of the electric field at a single point near the cesium atom and when we've seen 9,192,631,770 of them we say that one second has passed since we started counting. Because we're doing this at a single point we don't consider any distances, the speed of light, or the speed of anything else; we're just counting twitches of a needle.

It’s not scientifically correct to say, or imply that “speed” or distance have nothing to do with the time value that you get from the 9,192,631,770 waves of radiation counted (See BIPM link below). The “duration” of each wave has everything to with the wavelength that runs perpendicular to a photon and its speed. Increase or decrease the each wave length and count the same number of waves you’d get a “longer second” or shorter second. Change the photons “speed” the same holds true. This is no different than if the speed or distance were to change in an Earth rotation or orbit around the sun that the duration value of a day or year would change if that were the mechanism used to define those values.

That is exactly why we switched to the light clock because of the consistency of light “speed” in conjunction with a consistent wavelength that was a more consistent frequency to measure from the hyperfine transition of the ground state cesium 133, than 1/86400 of a mean solar day. The irregularity in the Earth’s rotation (speed) wasn’t as consistent as a photon.

"The unit of time, the second, was at one time considered to be the fraction 1/86400 of the mean solar day. The exact definition of “mean solar day” was left to the astronomers. However measurements showed that irregularities in the rotation of the Earth made this an unsatisfactory definition" http://www.bipm.org/en/si/si_brochure/chapter2/2-1/second.html

You can't get away from the fact that the "cycles" of radiation we count and that you refer to, have the physical properties of length/speed(photon).

 

[Nugatory]

You can't get away from the fact that the "cycles" of radiation we count and that you refer to, have the physical properties of length/speed(photon).

That's true, but I'm not sure how it matters. We've defined the second in a way that requires neither a definition of the meter nor knowledge of the value of the speed of light; then we've defined the meter in a way that uses our definition of the second but still no knowledge of the speed of light; and then the value of the speed of light follows from those two definitions.

It's true that the cycle time of the cesium atom, upon which the whole chain hangs, is suitably invariant because of physics that is based on the invariance of the speed of light. But we've exploit that invariance without knowing the actual value of the speed of light, or equivalently the frequency-wavelength relationship.

 

[phyti]

I don't see the contradiction... we have a definition of a second. We're counting the up-and-down transitions of the electric field at a single point near the cesium atom and when we've seen 9,192,631,770 of them we say that one second has passed since we started counting. Because we're doing this at a single point we don't consider any distances, the speed of light, or the speed of anything else; we're just counting twitches of a needle.

In reality, light has passed, and has moved 1 light second relative to that point.

You could also let the em signal pass an antenna with a counter.

“..since 1967 the second has been defined as the duration of 9,192,631,770 periods of the RADIATION corresponding to the transition between the two hyperfine levels of the ground state of the caesium 133 atom.”

frequency*wavelength = speed of light = constant per experimental evidence
With s for second and m for meter:
the definition of the second states: 1s = 1m/c = 1m/νλm = 1/νλ.
Any νλ combination equal to c will work.
Please note λ is a distance.
No matter how it’s sliced and diced, the definition is still 1 light second.

 

[phyti]

No. In SR, the location, speed, etc vectors have four components, one of them is time; and more to it, different observers will see these vectors' components transform in such a way that "time" component in one coordinate system partially becomes a spatial component.



In SR, velocity vectors of any objects always have time component > 0 (and moreover, ds^2 > 0).
In general, there *are* other vectors in Minkowski space, and the fact that not all of them can be a velocity vector is significant, and makes time special.

My quote, post 31:
"Numbers are dimensionless thus "time" can only be a dimension in a mathematical sense."

I'm not referring to the 4D theoretical interpretation.

 

[Maxila]

That's true, but I'm not sure how it matters. We've defined the second in a way that requires neither a definition of the meter nor knowledge of the value of the speed of light; then we've defined the meter in a way that uses our definition of the second but still no knowledge of the speed of light;

The two observationally fundamental components of motion are distance and change of position energy (what we observe as speed). When early man used the Earth’s rotation as a clock to define one day they did not know the Earth’s circumferences (distance) at any latitude over the speed at those latitudes, nor did they need know or define those values of distance/speed; because once they define one rotation as a day, they unknowingly defined the distance/speed at every latitude. The reason is because all those values are integral. Simple algebra shows that (where t is time, d is distance, s is speed), whether you write t=d/s or s=d/t or d=s*t each value is integral, in defining one, by default you have defined the other two, whether you knew it or not (note that t=d/s is where you can see time as a simple ratio of d/s).

The least intuitive for most people is distance (separation between two points or objects) being integral to time and speed. In addition to the simple algebraic relationship, if one imagined a universe where nothing could change position (no motion), every distance would be infinitely far away in time, it is only by motion (the ability to change position in space) that distance has meaning. That also explains why space-time is an integral relationship, simply put it is at least one Euclidean length in conjunction with time (a standard of motion or distance/speed), distance has no meaning without motion and is fundamental to a meaning of time. Don’t forget that we usually refer to large distances in time, like a light year, instead of a static distance (roughly 5.878625 trillion miles), exactly because they are merely different ways of stating the same integral relationship.

I hope that explains why, implying that defining one second has no bearing or consideration to the definition of length or speed, is incorrect. Once you define one term you have by default defined the other two, and as we discussed, the fundamental properties of distance (wavelength) and speed (the change of position energy of a photon), are integral to the "periods" that define a standard second.

 

[ghwellsjr]

That is exactly why we switched to the light clock because of the consistency of light “speed” in conjunction with a consistent wavelength that was a more consistent frequency to measure from the hyperfine transition of the ground state cesium 133, than 1/86400 of a mean solar day.

Are you saying that a cesium 133 atom is a light clock?

 

[ghwellsjr]

I hope that explains why, implying that defining one second has no bearing or consideration to the definition of length or speed, is incorrect. Once you define one term you have by default defined the other two, and as we discussed, the fundamental properties of distance (wavelength) and speed (the change of position energy of a photon), are integral to the "periods" that define a standard second.

Are you sure you want to make this claim?

If you do, how does defining the speed of light to be 299792458 m/s give you any clue as to how long a second is or how long a meter is?

 

[Maxila]

Are you saying that a cesium 133 atom is a light clock?

Yes I am saying the radiation frequency used to define a second is EM. While we may measure it in the oscillation of the cesium atom, light speed and wavelength are the cause of that oscillation.

"For the ultimate in accuracy, scientists reach for atoms, or more precisely, an exactly known frequency of light emitted by a chosen atom. The 'ticks' are the crests of a light wave,"

Source:http://www.nsf.gov/discoveries/disc_summ.jsp?org=DMR&cntn_id=114850&preview=false

 

[ghwellsjr]

Are you saying that a cesium 133 atom is a light clock?

Yes I am saying the radiation frequency used to define a second is EM. While we may measure it in the oscillation of the cesium atom, light speed and wavelength are the cause of that oscillation.

"For the ultimate in accuracy, scientists reach for atoms, or more precisely, an exactly known frequency of light emitted by a chosen atom. The 'ticks' are the crests of a light wave,"

Source:http://www.nsf.gov/discoveries/disc_summ.jsp?org=DMR&cntn_id=114850&preview=false

I always thought a light clock had a photon or a burst of photons that oscillated at the speed of light between two mirrors and the ticks occurred when the photon(s) bounced off one of the mirrors. As such, a light clock emits no radiation or it would quickly lose its oscillating photon(s). Even if you did provide an energy source for a practical light clock, the wavelength of the oscillating photon(s) or the wavelength of the amplified flashes coming out of the light clock coincident with each tick would not be significant, it's only the time between flashes that provides the timing of the light clock to an external observer.

You apparently have a different idea of what a light clock is than I have and what I think most other people have. So I need to know more details of what you claim goes on inside the cesium atom that permits it to be called a light clock. For instance, what distance are the photons traveling as they oscillate back and forth at the speed of light? And where does the energy come from that provides for the detectable radiation?

 

[Maxila]

If you do, how does defining the speed of light to be 299792458 m/s give you any clue as to how long a second is or how long a meter is?

First, the standard we use to define the meter is based on the standard we used to define a second (light), "The metre is the length of the path traveled by light in vacuum during a time interval of 1/299 792 458 of a second". Source: http://www.bipm.org/en/si/base_units/metre.html

All clocks (I have examined) use a consistent motion and quantize that motion as a frequency unit to drive their time. Once you assign a motion to a value of time, inherent in that value is a distance. The physical distance inherent in a second is the length of 9,192,631,770 waves, which by definition, now must equal any distance value we assign to lights change of position per second, i.e. 299,792,248 meters, 186,000 miles, etc.

To further illustrate it; if you set the motion of one Earth Rotation to a time standard value of one day, than at the Equator any distance unit you decide to use (arbitrary or current standard) to describe that diameter instantly becomes the value for its speed per day. Using miles, 25,000 miles per day, kilometers 40,000 kilometers per day, if I wanted to use the length of a American football field as a distance standard the speed would become 440,000 football field lengths per day, etc. etc. Distance and speed at other latitudes are merely proportional ratios of those values (if you don't believe me calculate a few).

So I need to know more details of what you claim goes on inside the cesium atom that permits it to be called a light clock.

The exact same thing holds true for the atomic clock, the oscillation is just a quantized unit of light motion (the "speed" and distance between wave crests, see link in previous post), the same as the frequency of a day being the Earth’s motion between rotations. Due to the integral relationship of time, distance and speed, once you set a standard time to a motion, the distance of that motion (for whatever value you assign to it) must also become the speed per that time unit.

That is “how does defining the speed of light give you any clue as to how long a second is or how long a meter is?” We define speed as a unit of distance per time, and empirically time is a change of position within a distance. When defining time you have by default defined a value and ratio relationship for a change of position within a distance.

 

[ghwellsjr]

So I need to know more details of what you claim goes on inside the cesium atom that permits it to be called a light clock.

The exact same thing holds true for the atomic clock, the oscillation is just a quantized unit of light motion (the "speed" and distance between wave crests, see link in previous post)...

The distance between wave crests is 33 mm according to phyti:

λ = c/ν = 3*108/ 9*109 = 33mm.

Let me make sure I have this straight: you're saying that the oscillation of the light motion inside the cesium atom covers a distance of 33 mm, correct?

 

[Maxila]

The distance between wave crests is 33 mm according to phyti:


Let me make sure I have this straight: you're saying that the oscillation of the light motion inside the cesium atom covers a distance of 33 mm, correct?

I'm saying that is the physical distance between light crests resulting in the oscillation. Just as there is a physical distance to the oscillation of a pendulum of a grandfather clock, or the quartz crystal used in most electronic clocks, or the Earths rotation, etc. Time keeping devices (and I suspect all empirical time events), have the same fundamental property of a magnitude for change of position within a distance (we often refer to that magnitude as speed).

As for Phyti's calculation λ = c/ν is simple to calculate so let’s check using meters for our units.

Where c =299,792,458 m/s and ν = 9,192,631,770Hz

λ = 299792458 / 9192631770

λ = 0.032612259265146 meters = 32.612259265146mm ≈ 33mm

A reference link to the equation is here: http://physics.uoregon.edu/~soper/light/frequency.html

 

[Nugatory]

λ = 0.032612259265146 meters = 32.612259265146mm ≈ 33mm

[Not arguing here, just commenting]

That's true, but also something of a tautology: "33mm" is is defined in such a way that it has to be that distance between the crests. This follows from the way that we've started with the statement that no matter what the speed of light is, we're going to define the meter to be whatever length makes that speed come out to 299,792,458 meters/sec, and then defined the millimeter to be one one-thousandth of a meter.

That 299,792,458 is every bit as arbitrary as the 1000 that we use to define the millimeter in terms of the meter. The only reason it's not a round number is that the inconvenience of throwing out all of our existing meter sticks would be far greater than the inconvenience of dealing with a non-round number.

 

[Maxila]

[Not arguing here, just commenting]

That's true, but also something of a tautology: "33mm" is is defined in such a way that it has to be that distance between the crests. This follows from the way that we've started with the statement that no matter what the speed of light is, we're going to define the meter to be whatever length makes that speed come out to 299,792,458 meters/sec, and then defined the millimeter to be one one-thousandth of a meter.

You are correct, that is what I tried to say in an earlier post of the time and distance relationship being integral (defining one by default defines the other). I also tried to illustrate that using one Earth rotation defined as the frequency (or period) of a day, any distance value you assign to the Earth’s diameter also becomes bound to that time unit (one day).

In fact it doesn’t matter if you assigned a distance to a different latitude circumference instead of the diameter, as the period (one day/ one rotation) represents a ratio of the magnitude in change of position within a distance. The magnitude I refer to is commonly known as speed; however with the definition of speed being a change in distance per time you get trapped in the same circular argument of duration (period), distance, and speed. That’s why it helps to look at the fundamental dynamics and causality.

Everything we discussed for any empirical change in time boils down to the dynamics and states of energy. It is energy (in some state) that is the cause, and is observed in the change of position in every oscillator. While we refer to a period in between oscillations as duration, fundamentally it is just two points in between a change of position. In other words the duration (period, oscillation) is the measurement between two points of energy’s change in position. That duration has no fundamental role or existence beyond describing a unit measurement for the change of position in energy that relates to a distance.

 

[ghwellsjr]

Let me make sure I have this straight: you're saying that the oscillation of the light motion inside the cesium atom covers a distance of 33 mm, correct?

I'm saying that is the physical distance between light crests resulting in the oscillation.

So you're saying that a photon is physically oscillating a distance of 33 mm inside the cesium atom, correct?

 

[Maxila]

So you're saying that a photon is physically oscillating a distance of 33 mm inside the cesium atom, correct?

No, photons don't oscillate they propagate electromagnetic waves perpendicular to their direction of travel http://www.physast.uga.edu/~jss/1010/ch5/emwave.jpg ≈33mm is the wavelength between crest, and the length traveled by a photon from crest to crest, of the light emitted by the cesium atom.

Also see: "For the ultimate in accuracy, scientists reach for atoms, or more precisely, an exactly known frequency of light emitted by a chosen atom. The 'ticks' are the crests of a light wave," http://www.nsf.gov/discoveries/disc_summ.jsp?org=DMR&cntn_id=114850&preview=false

 

[ghwellsjr]

So you're saying that a photon is physically oscillating a distance of 33 mm inside the cesium atom, correct?

No, photons don't oscillate

I thought they did inside a light clock so you need to either withdraw your claim that a cesium atom is a light clock or explain to me why you call a cesium atom a light clock.

they propagate electromagnetic waves perpendicular to their direction of travel http://www.physast.uga.edu/~jss/1010/ch5/emwave.jpg ≈33mm is the wavelength between crest of the light emitted by the cesium atom.

Are you saying that the photon is 33 mm wide as it is traveling through space? I still can't figure out where this 33 mm is that is just like the "physical distance to the oscillation of a pendulum of a grandfather clock" but with regard to a cesium atom.

 

[Maxila]

I thought they did inside a light clock so you need to either withdraw your claim that a cesium atom is a light clock or explain to me why you call a cesium atom a light clock.

Are you saying that the photon is 33 mm wide as it is traveling through space? I still can't figure out where this 33 mm is that is just like the "physical distance to the oscillation of a pendulum of a grandfather clock" but with regard to a cesium atom.

This is directly from the National Institute of Standards and Technology (NIST) and their document "NIST-F1 Cesium Fountain Atomic Clock" They are the official keepers of US time, "Those atoms whose atomic state were altered by the microwave signal emit light (a state known as fluorescence). The photons, or the tiny packets of light that they emit, are measured by a detector... This frequency is the natural resonance frequency of the cesium atom (9,192,631,770 Hz), or the frequency used to define the second. http://www.nist.gov/pml/div688/grp50/primary-frequency-standards.cfmIt appears the only purpose of your last two posts is merely to be argumentative; however If your base knowledge of physics and physics terms doesn't allow you to understand what is posted and what was already said, there is little more I can say that will help you understand it. I won't reply again to such nonsensical questions, or comments, or unsupported argumentative comments, such as:

Are you saying that the photon is 33 mm wide

So you're saying that a photon is physically oscillating a distance of 33 mm

I thought they did (referring to photons oscillating) inside a light clock so you need to either withdraw your claim that a cesium atom is a light clock or explain to me why you call a cesium atom a light clock.

 

[Dale]

Since the OP is not actively participating any more and since the conversation is getting a little tense this seems like a good place to call it quits.