How many meters is a second?

[skepticalbip]

dimensions are distortive tags. Contrary to scifi time is not an independent reality. time and space are damsons we contruct to describe and quantify reality.

There is no 'meters' dimension nor 'seconds' dimension. Both are arbitrary units of measure. In common usage we think of them as a kind of independent reality because it is convenient. You can say time is a dimension of space because x,y,z,t are all needed to define a point in space relative to an inertial frame.

x,y,z,t are dimensions of space.

Now I keep hearing the Dr Who theme.

Not quite. Dimensions are just 'axies' we use for convenience in measurement. Each type of dimension will have its own units of measurement. I think Ryan's problem is that he thinks of dimensions only as properties of space-time. Economists will use the dimensions of supply and demand to chart economic activity. Boyle's law of ideal gasses uses dimensions of temperature, pressure, and volume (measured in units of degrees C, pascals, and and cubic centimeters). etc. Each type of dimension is expressed in its particular units though the value of a dimension may effect the value of another. Example; in Boyle's low if the the temperature is changed and volume held constant then the pressure will change. Now how Ryan came up with the idea that the units of measurement that apply to one kind of dimension can be used in a very different kind of dimension escapes me - In Boyle's law, degrees Centigrade certainly would be a nonsense unit to measure volume.

 

[bilby]

dimensions are distortive tags. Contrary to scifi time is not an independent reality. time and space are damsons we contruct to describe and quantify reality.

There is no 'meters' dimension nor 'seconds' dimension. Both are arbitrary units of measure. In common usage we think of them as a kind of independent reality because it is convenient. You can say time is a dimension of space because x,y,z,t are all needed to define a point in space relative to an inertial frame.

x,y,z,t are dimensions of space.

Now I keep hearing the Dr Who theme.

Not quite. Dimensions are just 'axies' we use for convenience in measurement. Each type of dimension will have its own units of measurement. I think Ryan's problem is that he thinks of dimensions only as properties of space-time. Economists will use the dimensions of supply and demand to chart economic activity. Boyle's law of ideal gasses uses dimensions of temperature, pressure, and volume (measured in units of degrees C, pascals, and and cubic centimeters). etc. Each type of dimension is expressed in its particular units though the value of a dimension may effect the value of another. Example; in Boyle's low if the the temperature is changed and volume held constant then the pressure will change. Now how Ryan came up with the idea that the units of measurement that apply to one kind of dimension can be used in a very different kind of dimension escapes me - In Boyle's law, degrees Centigrade certainly would be a nonsense unit to measure volume.

Indeed. And you can define a point in three dimensional space with three distances, measured in metres; But you could equally use two angles measured in radians, and one distance measured in metres; or in a number of other ways.

But asking 'how many metres is a radian' is nonsensical. They are different kinds of things. Distances, angles, and durations are all different kinds of things, each with its own units.

 

[Bomb#20]

Yes, it is possible. Multiply the time value by c, the speed of light in a vacuum, and one gets a distance value. After being measured for centuries, c was fixed in 1983 as 299,792,458 m/s.

Why that speed and not some other? That is because anything that travels at c will always be observed to travel at c, no matter how much one tries to catch up to it.

That is a result of the geometry of spacetime, where combined distance s in terms of space coordinates x, y, z, and time coordinate t is

s² = x² + y² + z² - (c*t)²

If s² > 0, the combined distance is still a distance, while if s² < 0, then it is a time, and if s² = 0, then it is null or lightlike.

Interesting, but if a point particle travels in just the x direction of 400,000,000 meters in 1 second, then s² > 0, but that would be faster than light. Similarly, if it travels in the x direction for 299,792,458 meters, then s = 0. So 1 second would be 0 meters. Do I have this right?

No, 0 seconds would be 0 meters.

Keep in mind that time and distance are both relative to the frame of reference of an observer. From your point of view a photon is absorbed 1 second after it's emitted and it's absorbed 299,792,458 meters away from where it was emitted. But whenever anything moves we get relativistic time dilation and relativistic distance foreshortening. If it moves at the speed of light both of those effects are infinite, which means 1 second becomes 0 seconds and 299,792,458 meters becomes 0 meters. So from the point of view of the photon itself both the elapsed time and the distance traveled are always zero -- the photon is emitted and absorbed at the same time and at the same place. In effect, when the photon is emitted it "sees" the entire universe relativistically collapse into a two-dimensional plane, so the photon doesn't need to travel at all to get to the absorption point -- the absorption point comes to it.

So if we choose to think of the past as a 4-D object, yes, we can measure time in meters. Sometimes physicists do this. In natural units, "Space and time are put on equal footing and are both measured in the same units." How many meters is a second? 299,792,458.

 

[bilby]

Yes, it is possible. Multiply the time value by c, the speed of light in a vacuum, and one gets a distance value. After being measured for centuries, c was fixed in 1983 as 299,792,458 m/s.

Why that speed and not some other? That is because anything that travels at c will always be observed to travel at c, no matter how much one tries to catch up to it.

That is a result of the geometry of spacetime, where combined distance s in terms of space coordinates x, y, z, and time coordinate t is

s² = x² + y² + z² - (c*t)²

If s² > 0, the combined distance is still a distance, while if s² < 0, then it is a time, and if s² = 0, then it is null or lightlike.

Interesting, but if a point particle travels in just the x direction of 400,000,000 meters in 1 second, then s² > 0, but that would be faster than light. Similarly, if it travels in the x direction for 299,792,458 meters, then s = 0. So 1 second would be 0 meters. Do I have this right?

No, 0 seconds would be 0 meters.

Keep in mind that time and distance are both relative to the frame of reference of an observer. From your point of view a photon is absorbed 1 second after it's emitted and it's absorbed 299,792,458 meters away from where it was emitted. But whenever anything moves we get relativistic time dilation and relativistic distance foreshortening. If it moves at the speed of light both of those effects are infinite, which means 1 second becomes 0 seconds and 299,792,458 meters becomes 0 meters. So from the point of view of the photon itself both the elapsed time and the distance traveled are always zero -- the photon is emitted and absorbed at the same time and at the same place. In effect, when the photon is emitted it "sees" the entire universe relativistically collapse into a two-dimensional plane, so the photon doesn't need to travel at all to get to the absorption point -- the absorption point comes to it.

So if we choose to think of the past as a 4-D object, yes, we can measure time in meters. Sometimes physicists do this. In natural units, "Space and time are put on equal footing and are both measured in the same units." How many meters is a second? 299,792,458.

But only for objects with zero rest mass (and therefore constrained to travel at c in a vacuum).

As a non-photon, I expect to get a different answer.

 

[steve_bank]

The point is time is a dimension treated no different than meters.

I learned dimensional analysis in high school chemistry. Look at the SI units, time us a dimension as is kilograms and meters.. It is no more complicated then that.

It is the woo woo folks who want to imbue time in seconds as some reality.

 

[skepticalbip]

The point is time is a dimension treated no different than meters.

???

While it is true that both seconds and meters are both units of measurement, they are very different units of measurement that measure two very different things and are certainly not interchangeable. Just as pascals and cubic centimeters are both units of measurement but it would be absurd and meaningless to try to express a volume in pascals.

It is the woo woo folks who want to imbue time in seconds as some reality.

???
Time is a reality however the second is just a unit of measurement that was arbitrarily assigned so we can all agree to what period of time we are talking about. The second doesn't exist as a natural physical 'thing' any more than the meter or coulomb.

 

[steve_bank]

The point is time is a dimension treated no different than meters.

???

While it is true that both seconds and meters are both units of measurement, they are very different units of measurement that measure two very different things and are certainly not interchangeable. Just as pascals and cubic centimeters are both units of measurement but it would be absurd and meaningless to try to express a volume in pascals.

It is the woo woo folks who want to imbue time in seconds as some reality.

???
Time is a reality however the second is just a unit of measurement that was arbitrarily assigned so we can all agree to what period of time we are talking about. The second doesn't exist as a natural physical 'thing' any more than the meter or coulomb.

'dimensional analysis' is the use of units of measure in equations. Density = kilograms/meters^3. Velocity = meters/seconds.

Due to scifi in large part and pop science the unmitigated treat time as some kind of mystical concept. Scientifict ime is a definition as is meters and kilograms. Meter is a measure of distance. Time is a measure of change. That is as far as it goes.

And then there is time in philosophy and metaphysics as a concept and experience.

As an ancient king I declare the distance between my outstretched fingertips to be the length standard, the bank. I also declare the standard of time to be an hourglass with the resolution of one grain of and. I layout a distance of 100 banks. I start the sand clock and walk the distance. At the end I have velocity dimensionally as grains/bank. Not as accurate and not the same resolution, but functionaly the exact same as using seconds and meters to measure velocity.

We use the second to define the meter because it is convent and repeatable to do so.

Using the above asking how many seconds in a meter is like asking how many grains in a bank from my illustration. The question has no meaning.

Time does not exist, observed change exists. The scientific second measures change.

Try substituting the word change for time. Time is a contextually loaded word. It evokes many images and feelings.

 

[steve_bank]

If anyone is interested measuring dthe most precise distamce measurement is made using a laser interferomter. HP made one at least as far back as the 80s.

As a reflector moves the system essentially counts the wavelengths. Extreme accuracy can be 1/4 wavelength.

http://hp.myway.com/myfuncards/ttab...ot97489&coid=05352cf5e59a4eca9dbc4253d81fd6ff

 

[Bomb#20]

The point is time is a dimension treated no different than meters.

???

While it is true that both seconds and meters are both units of measurement, they are very different units of measurement that measure two very different things and are certainly not interchangeable. Just as pascals and cubic centimeters are both units of measurement but it would be absurd and meaningless to try to express a volume in pascals.

That's not an argument; it's just an analogy, and making an analogy doesn't make things analogous. Look at it this way: our culture could perfectly well have instead adopted the convention that positions east and west are measured in statute miles but positions north and south are measured in minutes (i.e. 60ths of a degree) of latitude. If we'd done that, then somebody inevitably would have proposed converting between the two simply by multiplying by 1.15. And people no doubt would have responded "Miles and minutes measure distances and angles, which are two very different things and are certainly not interchangeable. So real-estate must be measured in mile-minutes. It's absurd and meaningless to try to express a city's area in square miles, like trying to express a volume in pascals."

So what is it that makes north-south distances freely convertible with east-west distances? It's not the linguistic convention that English speakers use the word "distance" for both. We could have instead always called north-south separations "angles", and even then they'd still be freely convertible. What makes them convertible is the physical phenomenon that you can pick up a solid object and rotate it and it will maintain its shape. And when you do that a .00115 mile by .0001 minute piece of lumber will spontaneously transmogrify into a .000115 mile by .001 minute piece of lumber.

So where does that leave us with meters and seconds and pascals and cubic centimeters? It leaves us with the well-known physical phenomenon that you can't rotate pascals into cubic centimeters, and with the well-known physical phenomenon that you can't rotate meters into seconds. And the reason you can't is because, as Newton told us, time and space are absolute.

The trouble is, Einstein and Minkowski discovered that time and space aren't absolute. Only spacetime is absolute. When you observe a system from a moving reference frame, meters rotate into seconds. When people say stuff like "No more possible than measuring your shoe size in coulombs." or "Distances, angles, and durations are all different kinds of things, each with its own units.", they typically think of what they're doing as logic; but actually what they're doing is Newtonian mechanics.

 

[steve_bank]

Yes, but that is overthinking the problem. A dimension is a unit of measure. The fact of time dilation does not affect that.

There is no fundamental difference between a sand clock and an atomic clock. Boyj count particles.

A sand clock or an electronic clock will both vary IOW time dilation.

In sci fi a dimension is another reality you can travel trough.

 

[Wiploc]

Hey, ya never know. I've heard that in galaxies, far, far away a parsec is a unit of time.

And they've seen that in galaxies long, long ago, a parsec is a unit of distance.

 

[Jimmy Higgins]

Well time can be expressed in meters relative to the speed of light, which IMIO is the upper bound limit in the universe.

Hey, ya never know. I've heard that in galaxies, far, far away a parsec is a unit of time.

And they've seen that in galaxies long, long ago, a parsec is a unit of distance.

Seems like galaxies far away in time and distance are pretty loose with their units.