Basic understanding of time

[mooeypoo]

 

An unstable atom sitting, unchanging, eventually decays. So the answer to this is yes, or at least it appears that way.

 

Wait wait, if the atom decays, it emits radiation, which means it *is* changing. How is it 'unchanging'? Is there even ever anything that is unchanging at all?

 

 

(Note: This has always been the sort of thing that blew my mind in quantum undergrad course(s), so I hope you guys bear with me here)

[Strange]

 

Wait wait, if the atom decays, it emits radiation, which means it *is* changing. How is it 'unchanging'? Is there even ever anything that is unchanging at all?

 

Because, until it decays, it doesn't change. Atomic (or better, muon) decay is not a gradual process that takes place over the average decay time. It is a spontaneous, acausal event that takes place after a (somewhat random) period of time during which nothing happens.

 

What I'm saying is that time only makes sense in terms of change.

 

That may be true of our perception of time but clearly isn't true of time itself.

[Lizzie L]

 

That may be true of our perception of time but clearly isn't true of time itself.

 

I was talking about our conception of time rather than our perception of time, although our perception of time is interesting in a related way (temporal order illusions for example shed interesting light on how we perceive time). And I'm saying that our conception of time only makes sense in tems of change. I can't say anything about "time itself" because I'd say our own access to "things themselves" are via our models.

[Strange]

 

I was talking about our conception of time rather than our perception of time, although our perception of time is interesting in a related way (temporal order illusions for example shed interesting light on how we perceive time). And I'm saying that our conception of time only makes sense in tems of change. I can't say anything about "time itself" because I'd say our own access to "things themselves" are via our models.

 

I agree that we only have access to "reality" (whatever that is) through our models. Our models include time and, in general, don't depend on "change" to define or use time. It is only our perception of the passage of time that could be argued to be dependent on change.

 

I would, perhaps obviously, disagree that "conception" is a better term because my conception of time is clearly different from yours and doesn't depend on change.

[Lizzie L]

 

I agree that we only have access to "reality" (whatever that is) through our models.

Cool.

 

Our models include time and, in general, don't depend on "change" to define or use time.

 

 

Not sure about that. Can you provide a definition of time that doesn't involve reference to something changing?

 

It is only our perception of the passage of time that could be argued to be dependent on change.

 

 

 

Certainly our perception of the passage time is dependent all kinds of things, and is often contradicted by clock time. But I think I'll still stick with my original claim

 

 

I would, perhaps obviously, disagree that "conception" is a better term because my conception of time is clearly different from yours and doesn't depend on change.

 

 

OK, let me try to make my point a little clearer: by "conception" I meant, I guess "model", and while we can all have different models of reality, we can also share them, using the language of mathematics, for example. We can "operationalise" our conceptions so that they don't differ, at least for current purposes.

 

And my claim, I guess, is that change is intrinsic to at least all operationalisations of time that I am familiar with. I guess that claim can be falsified by an operationalisation of time that doesn't include change

[Strange]

Not sure about that. Can you provide a definition of time that doesn't involve reference to something changing?

 

I suppose the obvious example is General Relativity.

[Lizzie L]

 

I suppose the obvious example is General Relativity.

 

OK, so can you give me the definition in General Relativity?

[Strange]

 

OK, so can you give me the definition in General Relativity?

 

It is just another dimension (of, not surprisingly, space-time). There are several solutions of Einstein's Field Equations which model a universe with no mass or energy, and therefore nothing to change.

 

Even in the model of our universe, nothing changes. It is a fixed 4-dimensional manifold.

Edited February 22, 2014 by Strange

[Lizzie L]

Sure, but that's not a definition. How, for instance, would you define the difference between the spatial dimensions and the temporal dimension?

[Strange]

Sure, but that's not a definition. How, for instance, would you define the difference between the spatial dimensions and the temporal dimension?

 

There is a difference between the space and time dimensions, but I don't know enough of the relevant math to define the difference.

[Schneibster]

 

What proof do you have that they are incompatible for you to be able to say this?

 

Relativity.

 

And there is no "proof." That's pretty good evidence though.

Sure, but that's not a definition. How, for instance, would you define the difference between the spatial dimensions and the temporal dimension?

 

The spatial dimensions are right circular and the temporal dimension is hyperbolic.

 

Here is the article on it, from John Baez: http://math.ucr.edu/home/baez/symmetries.html

 

Here is the hyperbolic trig Lorentz transform:

 

t → (cosh s)t + (sinh s)x

x → (sinh s)t + (cosh s)x

y → y

z → z

 

where, s, the "rapidity", is related to the ordinary velocity v by v = tanh s

[studiot]

 

studiot, on 22 Feb 2014 - 08:27 AM, said:

 

What proof do you have that they are incompatible for you to be able to say this?

 

Relativity.

 

And there is no "proof." That's pretty good evidence though.

 

Lizzie L, on 22 Feb 2014 - 3:49 PM, said:

Sure, but that's not a definition. How, for instance, would you define the difference between the spatial dimensions and the temporal dimension?

 

The spatial dimensions are right circular and the temporal dimension is hyperbolic.

 

Here is the article on it, from John Baez: http://math.ucr.edu/...symmetries.html

 

Here is the hyperbolic trig Lorentz transform:

 

t → (cosh s)t + (sinh s)x

x → (sinh s)t + (cosh s)x

y → y

z → z

 

where, s, the "rapidity", is related to the ordinary velocity v by v = tanh s

 

 

 

Well we seem to be getting somewhere in the second part of that post, since I can now see that you are talking about conic sections and their properties, when you use the word hyperbolic, not for instance, hyperbolic differential equations or other possible meanings of the word.

 

So please spell out exactly what you do mean when you say

 

Time is hyperbolic, space is circular.

[Schneibster]

Ummm, you really ought to read that page by Baez.

 

A lot of people know Baez from his crackpot index, but he's also a mathematician and relativist of note, published and teaching in one of the foremost physics programs in the world.

Edited February 22, 2014 by Schneibster

[Lizzie L]

I'd still like to see someone define "time" in a way that doesn't involve something changing (or moving, as the OP suggested).

[Schneibster]

From our viewpoint as mammals, that's a definition of time; however, it's only a measure of how we see it. Remember we are constantly moving in the t direction at the speed of light from our own relativistic viewpoint. The faster we move relative to another observer, the less t they see us traverse and the more x, y, and z. We're rotated that way, relative to them. The situation remains symmetric until either they accelerate and catch up to us and pass us, or we turn around and go back. That's the explanation of the "twin paradox." That equation I printed above, about t and the hyperbolic sinh and cosh of s turning it to both t and x. That's the real math and it's all the math, Lizzie. It's relativity.

 

The rapidity, s, is a hyperbolic angle, Lizzie. You should look up Poincaire and check out some of Escher's drawings of Poincaire hyperbolic universes. You should take a cruise around the values of s with a graphing calculator. Hyperbolic geometry is very important to a clear understanding of relativity. It is the geometry of time. And the equivalent, in a hyperbolic dimension, of the "right angle," is an imaginary number.

 

You can't get to a "right angle" in spacetime to the time axis. It is an imaginary value. You would no longer exist. And that's why you can't accelerate to the speed of light, and why the speed of light is maximal. Because of the definition and curvature of time.

 

This is merely a repeat of the conversation about tachyons. If anything could turn into tachyons, we could no longer see it and it would appear to violate mass-energy conservation. Anything slowing down from tachyon speed would, in turn, appear as if from nothingness, violating mass-energy conservation the other way.

 

We have never seen either of these. Nor evidence of them in the farthest pictures we can take.

 

The implication of this is something going FTL appears to go backward in time. I hope folks understand that anything real must therefore first attain an imaginary angle, and then go past it and disappear into backtime headed back toward the origin of the universe. That's two impossible things before teatime.I'll believe that a universe went forward in time from the origin, and one went back, and we're in the forward one, but other than that I don't see a time when anything could have disappeared into backtime, and not out of the horizon of our universe.

Edited February 22, 2014 by Schneibster

[studiot]

 

Ummm, you really ought to read that page by Baez.

 

As far as I know, Baez is not a member of this forum, and can't speak for himself.

 

I am asking you to tell me what you mean not what Baez may or may not mean, and in particular to provide a definition/explanation/basic understanding of time as per the OP without reference to t or time.

Unfortunately , your entire post#90 is a circular (pun intended) argument because of this.

You just cannot use words (eg faster) that include time to define it.

[Strange]

I'd still like to see someone define "time" in a way that doesn't involve something changing (or moving, as the OP suggested).

 

It is a dimension in GR.

Edited February 22, 2014 by Strange

[studiot]

Strange, your post#92 incorrectly attributes a statement to myself.

[Strange]

Strange, your post#92 incorrectly attributes a statement to myself.

 

Apologies. I have removed it as I misread/misunderstood the context.

[studiot]

Thanks, +1, I would remove both our entire posts if I could, since they are now redundant.

[Schneibster]

 

As far as I know, Baez is not a member of this forum, and can't speak for himself.

 

I am asking you to tell me what you mean not what Baez may or may not mean, and in particular to provide a definition/explanation/basic understanding of time as per the OP without reference to t or time.

Unfortunately , your entire post#90 is a circular (pun intended) argument because of this.

You just cannot use words (eg faster) that include time to define it.

 

I'm sorry, "You just cannot use words (eg faster) that include time to define it" doesn't seem to me to mean anything.

 

I provided equations in post 86. Did you understand them? They're not very hard. Any decent graphing calculator will do them. Have you played with them like I suggested?

 

Time is a dimension. Unlike the other three "big" space dimensions, which are all circularly symmetric and whose angles and distances can be calculated with circular trigonometry, however, time is hyperbolically symmetric with respect to all three space dimensions.

 

In relativity, the space dimensions and the time dimension can be exchanged with one another to describe different frames of reference. To a person whose frame of reference is moving at a significant fraction of the speed of light, significant physics transforms are necessary to define each observer's view of the others' circumstances. In fact, if you examine the equations I posted in post 86, you will find that the t dimension becomes a combination of t and x, and the x dimension becomes a combination of x and t. In other words, to convert these different observers' viewpoints into one another, each must see the other as experiencing a significant amount of time as motion in x, and a significant amount of motion in x as motion in time. This is the result of the rotation that the hyperbolic trig version of the Lorentz transform describes.

 

Once you understand that time and space are insensibly converted into one another by nothing more complicated than going very, very fast, you are on the way to understanding the real meaning of relativity. There are rotations you cannot see and they happen all the time, but you're too big to notice them, and too slow, and too massive. If rotations like this happened all around you all the time you would die of radiation sickness.

Edited February 23, 2014 by Schneibster

[uncool]

 

Relativity.

 

And there is no "proof." That's pretty good evidence though.

 

The spatial dimensions are right circular and the temporal dimension is hyperbolic.

 

Here is the article on it, from John Baez: http://math.ucr.edu/home/baez/symmetries.html

 

Here is the hyperbolic trig Lorentz transform:

 

t → (cosh s)t + (sinh s)x

x → (sinh s)t + (cosh s)x

y → y

z → z

 

where, s, the "rapidity", is related to the ordinary velocity v by v = tanh s

I wouldn't phrase that as saying that time is "hyperbolic" and the spatial dimensions are "circular"; the way the transformations work deals with the relationships between the dimensions. So for example, if instead we had 2 temporal dimensions and 2 spatial dimensions, the transformation between the two temporal dimensions would be "circular", the transformation between the two spatial dimensions would be "circular", and the other transformations would be "hyperbolic". In other words, you'd get the following transformations:

 

t1 -> (cos s) t1 + (sin s) t2

t2 -> (- sin s) t1 + (cos s) t2

x1 -> x1

x2 -> x2

 

OR

t1 -> t1

t2 -> t2

x1 -> (cos s) x1 + (sin s) x2

x2 -> (- sin s) x1 + (cos s) x2

 

OR

t1 -> (cosh s) t1 + (sinh s) x1

t2 -> t2

x1 -> (sinh s) t1 + (cosh s) t1

x2 -> x2

 

(where you can switch x1 and x2, or t1 and t2 for the last transformation).

 

So as you can see, it's not an aspect of the "temporal dimensions"; instead, the "hyperbola" comes (in some sense) from the interaction between the temporal and spatial dimensions. Between two temporal dimensions, you would still get a "circle".

Edited February 22, 2014 by uncool

[studiot]

Forgive me for not understanding how a transformation of something is used to define that something.

 

I always understood a transformation involved changing something into something else.

 

So for instance how would the transformation
[math]x \to {x^2}[/math]
help me define x?

Edited February 23, 2014 by studiot

[Lizzie L]

Units might help. Spatial dimensions are measure in units of length. What are temporal dimensions measured in units of?

[Schneibster]

I wouldn't phrase that as saying that time is "hyperbolic" and the spatial dimensions are "circular"; the way the transformations work deals with the relationships between the dimensions. So for example, if instead we had 2 temporal dimensions and 2 spatial dimensions, the transformation between the two temporal dimensions would be "circular", the transformation between the two spatial dimensions would be "circular", and the other transformations would be "hyperbolic". In other words, you'd get the following transformations:

 

t1 -> (cos s) t1 + (sin s) t2

t2 -> (- sin s) t1 + (cos s) t2

x1 -> x1

x2 -> x2

 

OR

t1 -> t1

t2 -> t2

x1 -> (cos s) x1 + (sin s) x2

x2 -> (- sin s) x1 + (cos s) x2

 

OR

t1 -> (cosh s) t1 + (sinh s) x1

t2 -> t2

x1 -> (sinh s) t1 + (cosh s) t1

x2 -> x2

 

(where you can switch x1 and x2, or t1 and t2 for the last transformation).

 

So as you can see, it's not an aspect of the "temporal dimensions"; instead, the "hyperbola" comes (in some sense) from the interaction between the temporal and spatial dimensions. Between two temporal dimensions, you would still get a "circle".

 

Sure, absolutely. It's time's relation to x y and z that's hyperbolic; considered in itself it's just a dimension, as we see when x and t interconvert to one another. It's the result of that relation that makes us "see" time as "different." Actually, though, it's just a dimension and we expect that there are ten others that have equally important relations.

 

For starters I just say "time is hyperbolic." That's close enough for most people. The ones who want the math, well, now we want to understand it has to be the relation because time can only make a hyperboloid of revolution in association with another dimension, and as we all know from conic sections that means it has two branches. So you are of course correct.

Edited February 23, 2014 by Schneibster