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Clarify this? Time and distance; same thing or?

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#1 photonovore

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Posted 28 December 2012 - 10:59 AM

Just curious to understand... during a discussion a friend claimed that since c is a universal constant it can be expressed as 1 without reference to any unitary measure. Therefore time is distance, measurable in the same units as 3 space. e=m; no c squared needed, velocity (and time) are irrelevant.

Another individual simply stated that time is not distance but a different & fundamental scalar quantity.

I was thinking that c is variable from its upper limit downward, dependent upon the media through which it travels and dependent upon the mass of the photon (recognizing that the massless photon is more convenient convention than experimentally verified fact). At any rate, if c is variable then time remains a discreet factor as velocity is not necessarily simply contained within a unitless 1 in any realm but the idealistic.

So what's the story? Is time fundamentally distance or is it a fundamentally discreet factor unto itself? Or what...? :question:

#2 David Knisely

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Posted 28 December 2012 - 12:07 PM

There is a way to sort of "normalize" c to be one by setting up units in Physics so that certain constants are each equal to one (the so-called "natural" set of units). This is often done in equations to help simplify things a bit. The speed of light in a vacuum is the same no matter what the frame of reference is. The units are sometimes not all that relevant, only the number (it could be expressed as furlongs per fortnight if one would want to do that). Below is the link to all the details on natural units:

Natural Units and the Speed of Light

Clear skies to you.

#3 Rick Woods

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Posted 31 December 2012 - 06:27 PM

This thread doesn't seem to be drawing much comment. I find the question very thought provoking; unfortunately, I'm not sufficiently educated nor articulate to form a response of my own.
I wish some of you other brainiacs would chime in.

#4 FirstSight

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Posted 31 December 2012 - 07:34 PM

Just curious to understand... during a discussion a friend claimed that since c is a universal constant it can be expressed as 1 without reference to any unitary measure. Therefore time is distance, measurable in the same units as 3 space. e=m; no c squared needed...


This is pure nonsensical jibberish.

Let's examine how the expression e = mc^2 is meaningless without the inseparably built-in units involved, and irrespective of whether one considers any of the components scalar or vector. Notice that there are no vector quantities or units in e = mc^2 to begin with. Neither mass nor time have any inherent directional (vector) component, even though in the real physical world t never proceeds backwards into the past.

The unit of force is that required to accelerate a given unit of mass a given increase in velocity per unit of time, whereas the unit of energy is the unit of force applied over a given distance, commonly chosen to be the same distance unit as was used in the velocity component of force.

Force (one Newton) = (kg)(meter/second)/second = (kg)(meter)/(second^2)
Energy (one Joule) = (Newton) (meter) = (kg)(meter)(meter)/(second^2) = (kg)(meter^2)/(second^2)

Note that the units of c are (meters/second), and so c^2 becomes (meters^2)/(seconds^2)
...
and so the units of e = mc^2, with mass in kilograms, becomes:

e (joules) = MASS in kilograms * c^2 in (meters^2)/(seconds^2)

I'd ask your friend what he was smoking when he came up with his seemingly brilliant-at-the-time idea that time and distance reduce to equivalents by some intellectual slight-of-hand declaring c to be a nullity somehow because it's a universal constant. That doesn't remove its inherent units of distance^2/time^2.

#5 Jarad

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Posted 31 December 2012 - 08:00 PM

He is thinking that if distance and time are the same unit, then distance^2/time^2 cancels out to 1.

But I agree that he is incorrect - while time and space are related, they are not identical.

Jarad

#6 deSitter

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Posted 01 January 2013 - 04:30 PM

Yes, in the sense that relativity deals with a geometry in which both space and time live under one principle. No, in that the metric has both positive and negative entries, and time and space live in opposite camps. So the answer is literally, yes and no.

-drl

#7 Pess

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Posted 02 January 2013 - 11:02 AM

I think I once heard an analagy that space and time were not the same, but can be converted (in a sense) into one another.

For example, as velocity increases time dilates (gets 'bigger') while space along the line of travel contracts.

So space is swapped for time (to an outside observer) as he notices the accelerating ship get 'shorter' while time inside the ship gets longer.

Like magnetism and electricity are not the same but one can be converted to the other.

Pesse (*shrugs) Mist

#8 llanitedave

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Posted 02 January 2013 - 02:32 PM

So if space is expanding does that mean time is contracting?

#9 Pess

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Posted 02 January 2013 - 03:02 PM

So if space is expanding does that mean time is contracting?


Yup, to an outside the Universe observer.

Since our entire Universe is the relative frame, we can't detect it ourselves.

Pesse (insert your joke here, I can't do all the work!) Mist

#10 Pess

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Posted 02 January 2013 - 03:43 PM

So if space is expanding does that mean time is contracting?


Yup, to an outside the Universe observer.

Since our entire Universe is the relative frame, we can't detect it ourselves.

Pesse (insert your joke here, I can't do all the work!) Mist



An interesting corollary to this is that since the Universe of ours began, an outside observer has seen time contract as space expands. As time contracts (due to space expansion) it would appear as time being sped up to the outside observer.

So, if our Universe is going to continue expanding forever, we will continue to experience faster time elapse (to the observer) until we approach everything happening instantaneously.

Instantaneous is the fastest speed which something can experience time. No mass can every reach it (approach it, yes). So 'i' is the time equivalent of 'c'


Pesse (Sort of like how a weekend off work seems to pass) Mist

#11 llanitedave

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Posted 02 January 2013 - 10:50 PM

I don't think an "outside observer" is even a meaningful concept with respect to any qualities of the cosmos.

#12 Mister T

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Posted 03 January 2013 - 08:13 AM

So if space is expanding does that mean time is contracting?


Yup, to an outside the Universe observer.

Since our entire Universe is the relative frame, we can't detect it ourselves.

Pesse (insert your joke here, I can't do all the work!) Mist


I have observed this first hand

as the space occupied by my waistline expands, the time contracts but shrinking said space always takes much longer than the expansion.

QED :graduate:

ain't science great?

#13 Pess

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Posted 04 January 2013 - 12:20 PM

I don't think an "outside observer" is even a meaningful concept with respect to any qualities of the cosmos.


Pesse (Take your time and expand your mind to embrace
the idea...) Mist

#14 llanitedave

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Posted 04 January 2013 - 03:13 PM

It's not a mind that would have to expand, it's the math.

#15 JKoelman

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Posted 04 January 2013 - 03:41 PM

Distances and durations are different physical quantities. Yet, relativity theory tells us both combine into a single distance in four-dimensional spacetime. In other words, duration and distance are as much different as depth and horizontal separation are different. 

Imagine you are a seafarer and you measure depth using a sonar, and horizontal separation using a ruler. So you are used to statements like: "that ship is 1,000 ft separated from us" and "the sea here is 0.5 seconds deep". There is nothing wrong with such a practice, and all your measurements make perfectly sense. 

However, if you need to work out the distance between your boat and a point at the seabed not directly underneath your boat, you have to use a funny Pythagorean expression like: distance^2 = separation^2 + c^2 depth^2.  Here c is the speed of sound in water expressed in ft/s. 

One day you get the brilliant idea to orient your sonar system horizontally and measure horizontal separation between your boat and other vessels in soundseconds: the time it takes for a sonar signal to reflect back from a distant ship hull. Now something funny happens: the speed of sound in water becomes 1 soundsecond/second, and the formula for the distance to object at the seabed becomes distance^2 = separation^2 + depth^2. 

The point here is that the numerical value for the speed of sound is 1 if you measure separation and depth in compatible units, and it is whatever your system of units defines it to be if you adopt units that are more cumbersome. 

Now you know where I am going. We are seafarers in a four-dimensional spacetime, and only recently (thank you Albert!) have we discovered that spatial distance and duration combines into one single notion of distance in spacetime. Just like the seafarer in the story, we use clumsy units. We measure duration in seconds, and distance in meters or feet or furlongs or whatever. However, it is clear how to define compatible units. Just continue measuring duration in seconds, and measure distance in lightseconds. The speed of light is now  1. If you insist on showing units, that would be 1 ls/s. Distance in spacetime now becomes a simple Pythagorean-like equation without funny factors c^2, and Einstein's famous equation reduces to a much more insightful E = m (saying: rest energy and mass are one and the same thing).

So why don't we use compatible unites for duration and distance? Well, physicists do this all the time. But measuring time in seconds and distance in lightseconds is not very practical in daily life The simple reason is that we and everything around us moves at very slow relative speeds. And it just clumsy to have to say "no officer, I do believe my speed did not exceed 0.0000001 (ls/s)".

#16 deSitter

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Posted 04 January 2013 - 04:38 PM

This isn't true at all. It's wrong to make analogies with simple spatial geometry, because that has a definite metric. The indefinite metric makes a world of difference and brings in the real light cone as a geometric entity. This has no direct analogy in Euclidean geometry. The closet thing is the idea of infinity when conceived as a projective configuration.

-drl

#17 CounterWeight

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Posted 04 January 2013 - 05:50 PM

hard to put special theory of relativity 'in a nutshell'.

I've heard it put that the speed of light and a light year (or other increment)can be looked on WRT to time but as already stated distance is something else. the ideas of relative observed motion, contraction and mass are adressed prior to this as is the concept that as the denominator decreases the fractional value increases so the mass increases, getting near infinate as denominator approaches zero and idea that speed of light a maximum possible velocity. other results being time can appear different for different observers travelling at different related rates, and time dilation effect wrt motion and idea of speed of light as a 'maximum velocity'. But it's more about ideas of time WRT light and observers relative motion observing an event in yet another location. It is never expressed as absolute distance, though it can be applied to distance and time (but at the speed of light).

the equation as stated is more to discuss energy and mass, or more acurately a relationship of energy and mass. The result meaning that a relatively small amount of matter can yeaild a tremendous amount of energy.

in talking about distance, special relativity required that we must include time. Euclid held for two and even three dimensions but not for including time as a 4th, so they came up with tensor calculous to include it, and Reimann 'stuff' for geometry. Time as a 4th dimension or 'spacetime distance'. For most everyday purposes Newton and Euclid hold fine here on relatively very low speed planet earth... but the if non uniform motion then you can use general relativity as was done for Mercury orbit May 1919 experimental perdiction between Newtons math and general rleativity, where results were closer to general relativity.

So no reason to worry about your car odometer ;)

trying to be funny but doesn't always come through.

#18 JKoelman

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Posted 05 January 2013 - 12:44 AM

"Another individual simply stated that time is not distance but a different & fundamental scalar quantity."


Forgot to react to this statement. Reading such a statement hurts the eyes of any physicist. The individual you quote is completely wrong. Duration is not a scalar quantity. It is one of the components of a vector quantity. The other components are the three spatial distance components. So the total fundamental vector thus formed is four-dimensional. It is an 'event-vector' pointing in event-space from one specified event to another. 

Why making a big fuss about a number representing a scalar or not? The important thing to note is that scalars and vectors are absolute concepts independent of your frame of reference. However, components of vectors fail to be absolute. When writing out a vector into it's components, you have to chose a frame of reference, and therefore the individual component values will be different for different observers. Like a vector component, a scalar quantity is represented by a single number. Such a scalar number, however, is independent of the frame of reference chosen.

The fact that duration is a single component in an event-vector makes it a quantity with a value dependent on your frame of reference (that is dependent on your orientation and your movement). The length of the event-vector it is part of, however, is a scalar quantity and therefore its value is absolute. No matter your orientation or your movement, the length of the event-vector is always the same. Physically, this length represents the maximum duration a traveller can experience when making a trip from the starting point to the end point of the event-vector.

The bottom line is that in our physical reality distance and duration have no fundamental meaning. The event-vector they combine into, however, does have a fundamental physical meaning. It therefore makes sense to measure all four components of the event-vector in the same units. If you measure time in seconds, that means you have to measure spatial distance in lightseconds. 

It is funny to see the predictable reaction to my post above indeed immediately showing up. Don't let big words like "indefinite metric" fool you. All this term says is that the trigonometry of event-vectors is slightly different from that of spatial vectors (a minus signs shows up, as exemplified by the fact discussed above that distance in event-space corresponds to a maximum value rather than a minimum value). But the present discussion is not about the details of trigonometry. It is about the basic notion that spatial distance and duration combine into one fundamental concept and that this has consequences when making rational choices for basic units for spatial distance and duration.

#19 CounterWeight

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Posted 05 January 2013 - 08:37 PM

I agree with what you say above, but it is important to be considerate what is being expressed as a scalar quantity or a vector quantity, exactly where and how. I would not completely discard the notion of metrics and metric spaces being embedded in an otherwise scalar appearing field. My comments about time above are only wrt to common notions wrt relativistic speed and directions and notion of local. This gets to in ways notions of very large (space and light year distances) and very small(at the scale of the atom) as well as very fast or slow. Same applies if using euclidian or non-euclidian for your topological space and vectors or vector bundles.

Johannes I'll use your example if that is OK?

Notion of scalar or metric and sound in water, well there can be temp inversion layers in water that might(and do) affect properties of sound -acoustic refraction- if wrongly assuming temperature a constant scalar quantity over the length in such a circumstance could lead to erronious results. There are also same I guess if looking at light and the atm when we look through our scopes. We can say temperature is a scalar quantity as it has no direction, but if something else in the vector (as used) has a property in magnitude or direction that might be affected (by it's not being a scalar quantity in the absolute WRT) magnitude and direction the system is incomplete as we've assigned a constant quantity to something that is an indefinate metric or metric tensor(here with assoc properties). This just an example of difference in on paper and in reality.

Though a bit different we could also discuss the concept of the side travelling sound wave in water, where we are discussing now no longer a flat space but one that is curved... in the very short distance (1000 meters?) maybe trivial but the longer the distance (10,000 meters)the less so. Again depending on how you are talking about locality and distance as the curve gets larger on the sphere the |abs distance (a straight line or chord through the sphere)| between the points will differ from the 'as the crow flies', or specifically in this case 'as the sound wave travells'. Using this example of a closed sphere there is another idea and that is what about when the other boat (assuming there is only one other) is on the opposite side of the sphere(here too i'm using directional side sonar), here the error between absolute distance and relative distance error is a maximum.

So it's more than simply a choice of rational choices for units of measure, it's also about the medium and the characteristics of the medium the units are to be used in, and what in any absolute terms you are trying to deterimine. My reason for introducing temperature and curvature into the examples, in very large scale spacetime you could replace the notion of temperature gradient with that of gravitation and change the soundwave to light.

I hope that makes sense, I'm trying to agree.

#20 JKoelman

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Posted 06 January 2013 - 08:01 AM

Indeed, at large scales bending and distortion occurs. And yes, perhaps one can extend the 'sonar analogy' to include this. However, for the question posed by OP these are just distractions. The whole point I wanted to make is that given we are dealing with vectors (x, y, z, t) in event-space it makes sense to measure all four components in compatible units. Of course you can measure length in inches and width in centimeters, and so on, but that would make things unnecessarily complicated. Making the step from special relativity to general relativity doesn't change this picture.

#21 CounterWeight

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Posted 07 January 2013 - 09:01 AM

back to the original question about time and distance as expressed or implied by general or special relativity.

here should be a good non mathematical treatment, fundamental conclusions wrt time are at the bottom of the page.






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