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Time is the distace between two points in space.

im not a person who reads alot of physic books so I don't know alot about the subject. Do you agree or disagree?

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- Thread starter mikelus
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Time is the distace between two points in space.

im not a person who reads alot of physic books so I don't know alot about the subject. Do you agree or disagree?

- #2

mathman

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Sometimes the obvious happens to be true.

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- #4

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let me rephrase it

time is the space between two points in space.

time is the space between two points in space.

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jcsd

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[tex]ds^2 = {x_1}^2 + {x_2}^2 + {x_3}^2 .... + {x_{n-1}}^2 + {x_n}^2[/tex]

which in our three dimensional world is:

[tex]ds^2 = x^2 + y^2 + z^2[/tex]

notice no need for any time dimension to find the distance between two objects in space.

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Is there an exact measurment for time?

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russ_watters

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You mean an exact scale? Yes. The time needed for a cesium-133 atom to perform 9,192,631,770 complete oscillations.Originally posted by mikelus

Is there an exact measurment for time?

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Originally posted by jcsd

[tex]ds^2 = {x_1}^2 + {x_2}^2 + {x_3}^2 .... + {x_{n-1}}^2 + {x_n}^2[/tex]

which in our three dimensional world is:

[tex]ds^2 = x^2 + y^2 + z^2[/tex]

notice no need for any time dimension to find the distance between two objects in space.

The fourth coordinate is ict. This might be important in a thread called time.

- #9

jcsd

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[tex]ds^2 = (x^1)^2 + (x^2)^2 + (x^3)^2 - (x^4)^2[/tex]

Where [itex]x^4 = ct[/itex].

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jcsd

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does it relate in that time does not exist without space and space with out time.

with out two points in time does space exist?

- #12

jcsd

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mikelus:

Above I gave the equation for finding the distance between two points in (Euclidian, i.e. flat) space (if we take one of the points as the origin):

[tex]ds^2 = x ^2 + y^2 + z^2[/tex]

In relativity there are a group of equations which show us how differnt observers travelling at different speeds view time and space:

[tex]x' = \gamma(x - ut)[/tex]

[tex]y' = y[/tex]

[tex]z' = z[/tex]

[tex]t' = \gamma(t - \frac{ux}{c^2})[/tex]

Where the primed dimensions (e.g. [itex]x'[/itex]) is how an observer travelling along the x axis with speed [itex]u[/itex] views these dimesions compared to how an observer in this rest frame views them. [itex]\gamma[/itex] is equal to [itex](1 - u^2/c^2)^{1/2}[/itex]

If we apply these transformations to the first equation, we find:

[tex]d(s')^2 = \gamma^2(x - ut)^2 + y^2 + z^2[/tex]

this means that [itex]ds^2 = d(s')^2[/itex] if and only if [itex]u = 0[/itex]. So**observers travelling at different speeds will not agree on the distance between two objects in space**.

If we look at the metric for (flat) spacetime given in my first post in a simlair way we see it is of the form:

[tex]ds^2 = x^2 + y^2 + z^2 - c^2t^2[/tex]

And we as in the metric for space we perform the same opertaion for an obnserver travelling at a different speed (i.e. perform a Lorentz tarnformation) we get the equation:

[tex]d(s')^2 = \gamma^2(x - ut)^2 + y^2 + z^2 - c^2\gamma^2(t - \frac{ux}{c^2})^2[/tex]

if we expand this out we get:

[tex]d(s')^2 = \frac{x^2 - 2utx + u^2t^2}{1 - \frac{u^2}{c^2}} + y^2 + z^2 - \frac{c^2t^2 - 2utx + \frac{u^2x^2}{c^2}}{1 - \frac{u^2}{c^2}}[/tex]

if we factorise and divide we find:

[tex]d(s')^2 = x^2 + y^2 + z^2 - c^2t^2 = ds^2[/tex]

So we should say that**two observers will always agree on the distance between two points in (flat) spacetime, even if they are travelling at different speeds**. This is why the concept of spacetime is so useful as we use it to find equations valid for all observers not for just one particular observer.

You may of also noticed that the Lorentz transfomration is very simalir to rotating something in space, in this way we can think of velocity as a rotation in spacetime.

Above I gave the equation for finding the distance between two points in (Euclidian, i.e. flat) space (if we take one of the points as the origin):

[tex]ds^2 = x ^2 + y^2 + z^2[/tex]

In relativity there are a group of equations which show us how differnt observers travelling at different speeds view time and space:

[tex]x' = \gamma(x - ut)[/tex]

[tex]y' = y[/tex]

[tex]z' = z[/tex]

[tex]t' = \gamma(t - \frac{ux}{c^2})[/tex]

Where the primed dimensions (e.g. [itex]x'[/itex]) is how an observer travelling along the x axis with speed [itex]u[/itex] views these dimesions compared to how an observer in this rest frame views them. [itex]\gamma[/itex] is equal to [itex](1 - u^2/c^2)^{1/2}[/itex]

If we apply these transformations to the first equation, we find:

[tex]d(s')^2 = \gamma^2(x - ut)^2 + y^2 + z^2[/tex]

this means that [itex]ds^2 = d(s')^2[/itex] if and only if [itex]u = 0[/itex]. So

If we look at the metric for (flat) spacetime given in my first post in a simlair way we see it is of the form:

[tex]ds^2 = x^2 + y^2 + z^2 - c^2t^2[/tex]

And we as in the metric for space we perform the same opertaion for an obnserver travelling at a different speed (i.e. perform a Lorentz tarnformation) we get the equation:

[tex]d(s')^2 = \gamma^2(x - ut)^2 + y^2 + z^2 - c^2\gamma^2(t - \frac{ux}{c^2})^2[/tex]

if we expand this out we get:

[tex]d(s')^2 = \frac{x^2 - 2utx + u^2t^2}{1 - \frac{u^2}{c^2}} + y^2 + z^2 - \frac{c^2t^2 - 2utx + \frac{u^2x^2}{c^2}}{1 - \frac{u^2}{c^2}}[/tex]

if we factorise and divide we find:

[tex]d(s')^2 = x^2 + y^2 + z^2 - c^2t^2 = ds^2[/tex]

So we should say that

You may of also noticed that the Lorentz transfomration is very simalir to rotating something in space, in this way we can think of velocity as a rotation in spacetime.

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- #13

HeavensWarFire

Time doesnt exist, in the way you think a Chair exists. Time is a an abstract concept that relates to change.

- #14

HeavensWarFire

Above I gave the equation for finding the distance between two points in (Euclidian, i.e. flat) space (if we take one of the points as the origin):

You seem to confuse absolute spead measure, with absolute time measure. The question is not about the actual distance between 2 points, but rather, what is in fact the smallest unit of time measurable.

Heres why i think yur formula doesnt work: you fail to take into consideration the idea of infinite divisability. You take a foot, and you dived that in half. Take this half, and divide that in half. Repeat this process of diving each, and every successive half, and you will never find a terminating point. Hence, your math formula for distance is only contextual, and it does not answer any of the paradoxes of Zenos.

To define an absolute unit of time, you need to first define an absolute unit of distance that you can not mathetimatically subdivided, and you need an absolute unit of speed. Once you answer these issues, then maybe you can come up with an actual unit of time that can not be further subdivided into smaller units.

- #15

HeavensWarFire

Knock, knock:

with out two points in time does space exist?

Space is simply the absence of "matter." without matter, you could never have an atomic notion of a void.

Secondly, time seems to only come into consciousness when you start to think about distance, and speed.

But over, and beyond that, theres no such thing as time. Mathetimatically, you an infinitely add, or subdivide, hence theres not absolute measure of any kind in the truest sense.

- #16

jcsd

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Originally posted by HeavensWarFire

You seem to confuse absolute spead measure, with absolute time measure. The question is not about the actual distance between 2 points, but rather, what is in fact the smallest unit of time measurable.

Heres why i think yur formula doesnt work: you fail to take into consideration the idea of infinite divisability. You take a foot, and you dived that in half. Take this half, and divide that in half. Repeat this process of diving each, and every successive half, and you will never find a terminating point. Hence, your math formula for distance is only contextual, and it does not answer any of the paradoxes of Zenos.

To define an absolute unit of time, you need to first define an absolute unit of distance that you can not mathetimatically subdivided, and you need an absolute unit of speed. Once you answer these issues, then maybe you can come up with an actual unit of time that can not be further subdivided into smaller units.

They're not my formulas they're Pythagoras's, Lorentz's and Minowski's, they lie at the heart of special relativity.

I'd also like to tell you taht ds, x, y, z and ct do not take discrete values (this should be rather obvious as there are only a few cases where they can all take on non-zero but discrete values).

I'm not confused, all I was doing was explaining the well-known concept of space-time, It appears YOU are confused.

- #17

HeavensWarFire

How nice of you to ignore the main crux of my thoughts.

To define an absolute unit of time, you need to first define an absolute unit of distance that you can not mathetimatically subdivided, and you need an absolute unit of speed. Once you answer these issues, then maybe you can come up with an actual unit of time that can not be further subdivided into smaller units.

Ok,wise guy, tell me, how much time has there been since the creation of all life? And how much time will there be there once all is killed off in what is called entropy? Surely you know, for you have many theories in your head.

Perhaps you do not understand the idea of "infinite divisability"? Tell, what is the smallest unit of measure that you can think of? Surely you know? Did you not know that mathematically speaking, many things are endless? A foriegn concept to you is it? And perhaps you are equally confused with what is called a Paradox?

x=length

y=width

z=depth

This is just the standard variables for the dimensions of the space, object, continuum, it doesnt tell me anything about what is the smallest unit imaginable of anything, whether we are speaking of distance, time, or speed.

- #18

jcsd

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[tex]ds^2 = x^2 + y^2 + z^2 - c^2t^2[/tex]

You find there are very few values you can put in that would allow ds, x, y, z and ct to be discrete, off the top of my head I can only think of 1 set of values (and therefore mutiples of these values) that allow them all to be natural numbers: ds = 3, ct = 3 and where x y and z take the values 1, 1 and 4 (that's of course not to say there aren't more), the point is you can't make the formula discrete without excluding a whole set of solutions.

Now stop blathering.

- #19

HeavensWarFire

Ahahahahahahahahah...........

Now stop blathering.

Alright man, i will speak at your level: a formula for how you may go about in solving a certain equation is not the same as the demonstration.

Your formula is cute, but, you still havent furnished me with an actual answer to the question of whether or not, mathematically you can actually arrive at the smallest unit possible. And until you do that, your above means nothing to me. Theory, and practise are not of the same realm. So tell me in what way your formula is of any significance? What can you solve with your theory exactly?

- #20

jcsd

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2) I did not make any comment on whether time is discrete or continuous, infact relativity does tactitly assume that time is continuous, so why do you keep on going on about the infinite divisbilty of time?

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Regarding your questions about minimum time and space, here's a paper I wrote recently. Don't know if it makes sense but it addresses those issues exactly. I'm pasting it from my thread from the Strings forum. It probably belongs in theory development anyway.

The Minimum Time

By Edsel Salvana, MD

String theory has generated a minimum size in terms of

physical distance. Planck length is the smallest

possible distance and is purported to be the size of a

string. However, there has been no postulated minimum

time. Since time itself is a dimension, the question

arises as to whether there is a minimum amount of time

beyond which the string becomes undefined.

To tackle this problem, we return to the definition of

matter in light of the string theory. In essence,

matter (and energy, for that matter) is merely a

manifestation of the vibrations of a string as

modified by a Calabi-Yau space. Yet a vibrating object

has a period during which it makes a complete

vibration. If the characteristics of matter are

inherent in the vibration pattern, then the period in

which one vibration is manifested determines the

character of that matter and no less.

As an example, we look at light. Light is made up of

photons. A photon is a string with a distinct

vibration pattern. The speed of light is 300,000 km/s.

The time in which light traverses the Planck distance

is the Planck time. Yet a photon can only fit in a

space no smaller than a Planck distance since it

itself is a string. By that virtue, the photon is

actually taking up the whole of the Planck space. It

cannot be halfway in, or halfway out or any proportion

thereof precisely because it cannot otherwise be

defined as a string (it cannot be half a photon) and

there is no smaller space. Furthermore, the

characteristics of the photon cannot be manifested

without a complete vibration. By this reasoning, the

time it takes a string to produce a photon cannot be

less than the Planck time because the vibration would

not be complete. Taken in another way, you cannot have

a complete vibration if you do not have a complete

string.

Using this analogy, if at the time of the Big Bang

(zero time), photons were produced, they would have a

period of Planck time at least. That is why all

photons travel at the speed of light (not faster or

slower). There is no “in between” state because the

vibration necessary to generate a photon would not be

complete. Precisely because of this point, all photons

in the universe should be “in synch” with each other

in multiples of minimum (Planck) time.

Whether other particles are subject to this “minimum

time” is self-evident since all particles are made up

of strings. The question is whether certain particles

have a larger “minimum time” because it takes longer

for the string to generate a complete vibration. I do

not think this has to be the case since the minimum

requirement for one vibration would be one complete

string. Nevertheless, if some particles (especially

those slower than light) have a longer minimum time

(the time it spends generating one complete vibration

in a Planck space), these should be greater than (they

are multiples of, since there is no smaller unit by

definition) Planck time since nothing can travel

faster than light and each vibration requires a

complete string.

An interesting consequence of these arguments is that

matter and energy is being “created” in multiples of

“minimum” (Planck) time. With each vibration, a string

generates the same particle over and over again over

time. When a string’s vibration is changed, then the

type of matter (or energy particle) it manifests is

changed. Whether the time to generate the properties

of the matter or energy particle remains the same

(Planck time or multiples thereof) remains to be seen.

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