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The victorious truther

What is time? (Again)

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Posted (edited)
44 minutes ago, Markus Hanke said:

But what if we think of f(x) as an (uncountably) infinite set of real numbers (which it is, mathematically speaking)? Or better still - a 1-parameter family of real numbers? That set would be a static construct, as would be the relationship between the elements in the set. Of course you could externally impose a notion of “going from one element to another”, but I don’t think that is inherent in the set itself.

I fully agree! A function y = f(x) is static. I thought that is what I am saying all the time. But as soon as you say 'y changes as function of the change of x', I think you are implying time. What you are in fact doing is looking at y(t) = f(x(t)). 

This triggered the whole discussion:

On 7/22/2020 at 9:58 AM, Markus Hanke said:

you can always have quantities that change with respect to one another, without reference to any notion of time.

So, no, I would say, as soon as you use 'change' you are implying time. 

Edited by Eise

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53 minutes ago, Markus Hanke said:

Interesting, I haven’t heard this term before! 

What is also interesting is that there is more than one way to viw these relationships, which is why we have several (slightly) different terms.

The condition I meant may be illustrated in the standard equation of an ellipse

This is the locus of a point which moves under the one condition


[math]\frac{{{x^2}}}{{{a^2}}} + \frac{{{y^2}}}{{{b^2}}} = 1[/math]


Alternatively we can introduce what is known as a parameter often denoted t, though sometimes a Greek letter is used.


[math]x = a\cos t[/math]


[math]y = b\sin t[/math]

 

Note the first form has two independent variables and one condition or equation, between them.

The second has one independent variable (the parameter) and two conditions or equations.

Both refer to the same ellipse.

 

The parameter is often (but not always) time and corresponds to what I called the running variable.

You can see how deeply time is embedded in our psyche.

But in fact this parameter t is an angle!

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41 minutes ago, Eise said:

So, no, I would say, as soon as you use 'change' you are implying time. 

While I can easily imagine functions ( or teacups ) changing according to parameters other than time, I suspect the problem is with our common definition of the concept of change; it necessarily involves time. Even though it is not a variable of the system under observation, it is necessary for the observer to detect 'change'.

Sure, the teacup 'changes' with respect to location ( from spout to bowl ), but for us to observe both aspects of the teacup, time must necessarily be involved ( first you observe the spout, then, the bowl ).

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Posted (edited)
20 minutes ago, MigL said:

While I can easily imagine functions ( or teacups ) changing according to parameters other than time, I suspect the problem is with our common definition of the concept of change; it necessarily involves time. Even though it is not a variable of the system under observation, it is necessary for the observer to detect 'change'.

Sure, the teacup 'changes' with respect to location ( from spout to bowl ), but for us to observe both aspects of the teacup, time must necessarily be involved ( first you observe the spout, then, the bowl ).

As a Physicist, would you say it makes no difference if we 'observe'  first the bulb then the tail or first the tail then the bulb or of a p orbital or would Physics be different if we did not experience the entire curve all together in any interaction?

If you don't like a quantum example how about being struck by a large jack (as in the game of jacks) shaped object ?

Do we experience the entire momentum at the moment of impact or do we have to wait for the legs to spin round and hit us?

Edited by studiot

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6 hours ago, michel123456 said:

But after more thinking when you are stating "when all the parts are present together", I suspect that you mean "all the parts are present together at the same time". Or maybe (I don't know to say otherwise) that your cup somehow is existing there in space "out of time". As if the concept of a cup "existing" could be understood without the concept o time. But the concept of "together" has already the idea of time inside it.

I think it might be more a matter of some “idea of time” being inside your thinking.

Which is perhaps why you add, “at the same time” to “all the parts are present together” which to me adds nothing. 

Just for the hell of it, as an experiment, you might try throwing the word “time” out the window (and all its accompanying baggage), and focus on relationships that persist (such as distances between positions on a cup) and the inherent structure as a whole that arises out of those persisting relationships. Instead of thinking “the inherent structure exists at a time” just think: “the inherent structure exists”. Or “it persists”, not “it persists through time”. 

Now if you cry fowl here and say, “The only way the structure can persist is through time”, I submit to you that you’re adding something vague and extraneous in the sense that it doesn’t contradict the notion of change as presented by Marcus. We have to be clear that we are talking about a parameter, not some other notion of time which you or I might espouse.

PS. Although I have to admit, I’m very curious as to how you would define “time” outside the time of physics. Maybe a new thread in the philosophy sub forum. 
 


 

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No,no, Studiot, I have one for you...

If you inhabited a 'space' with just the three orthogonal dimensions and NO time parameter, how exactly would you 'see' the teacup ? Could you interact with one aspect of it, say the spout, and then another ?
Remember the teacup doesn't change with time as it has no time parameter, but you are also intrinsic to that particular space, and there is no time parameter for you either.

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9 hours ago, MigL said:

No,no, Studiot, I have one for you...

If you inhabited a 'space' with just the three orthogonal dimensions and NO time parameter, how exactly would you 'see' the teacup ? Could you interact with one aspect of it, say the spout, and then another ?
Remember the teacup doesn't change with time as it has no time parameter, but you are also intrinsic to that particular space, and there is no time parameter for you either.

Teacup  ?? Spout  ??

You must have been putting the wrong weed in that cigar again.

Just think, without time, you'd never get to smoke it.

 

More seriously perhaps 'you' could only perform this interaction if 'you' and the teacup were exactly like the famous hole in the ground and the puddle. Exactly spatially conformable.

Otherwise if you were not then the relationship would be more like that of a point particle in a 'block universe' where the past and future are inaccessible.
Your 3D space has similarities to this block universe.

But this question about 'seeing' raises another interesting point.

Human sight is serial  in nature in that your focus scans about your field of sight.
Furthermore humans can only see in front of them.
If their sight was constructed differently perhaps see in front of them and behind them together  -  like a fly.

The point is that even in computing we have serial mode and parallel mode and one other interesting one, akin to time travel.
There is a method of computing whereby when the serial flow reaches a decision point, it changes to parallel flow and goes down all the branches of the decision tree together using the then existing step values of the prgram flow variables.
When the appropriate new values become available the results of each side loop are already available and the correct one is selected.

This is a known time saving (pun intended) device which has been used in other decision making situations, for instance

We are about to be invaded. Do we set up defences on the East coast or the West coast ?

 

No how about answering my questions about the p orbital and the jacks?

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Posted (edited)
On 7/28/2020 at 12:16 PM, Eise said:

I fully agree! A function y = f(x) is static. I thought that is what I am saying all the time. But as soon as you say 'y changes as function of the change of x', I think you are implying time.

I think we’ll have to disagree on this :) Which is fine of course, this being just a philosophical exchange. To me, the term ‘static’ (I think it should have been ‘stationary’ actually, I often confuse them) implies precisely the absence of any kind of reference to time, be in implicit or explicit.

On 7/28/2020 at 12:16 PM, Eise said:

What you are in fact doing is looking at y(t) = f(x(t))

This is called a ‘parametrisation’, and it is not what I am doing or suggesting at all.
Note also that there is no necessity whatsoever to interpret a parametrisation parameter as ‘time’ - that’s just an extra ad-hoc assumption. Furthermore, note also that generally there is more than one way to parametrise the same curve.

On 7/28/2020 at 12:16 PM, Eise said:

So, no, I would say, as soon as you use 'change' you are implying time.

So you would say that the hypothetical 3D universe with only a tea cup in it is entirely homogenous (i.e. devoid of changes) in all physical aspects? I definitely (but in a friendly, intellectual way) disagree :)

15 hours ago, MigL said:

If you inhabited a 'space' with just the three orthogonal dimensions and NO time parameter, how exactly would you 'see' the teacup ? Could you interact with one aspect of it, say the spout, and then another ?

There is of course no observer in such a universe, since no act of observation is possible - but does that imply that the tea cup cannot exist? Does existence (in the ontological sense) require a temporal dimension? I think not.

On 7/28/2020 at 1:08 PM, MigL said:

Sure, the teacup 'changes' with respect to location ( from spout to bowl ), but for us to observe both aspects of the teacup, time must necessarily be involved ( first you observe the spout, then, the bowl ).

True, but this issue wasn’t about the observation of change; it was about whether, for two quantities which are not themselves spatiotemporal in nature, one can meaningfully define a notion of ‘change’ of one quantity with respect to the other, and whether this implies a notion of ‘time’ in the physical sense. I think you have answered this correctly in the first part of the above sentence.
I think we can all agree that no act of observation is ever possible without physical time, but that isn’t really the point here. The point is rather that, if there is not some concept of ‘change’ in our hypothetical tea cup universe, then that universe would by definition need to be homogenous in all physical aspects. Clearly that isn’t the case though, because at the very least you have the spatial region occupied by the tea cup, and then vacuum for all the rest of that universe. Whether there is anyone there to observe this is irrelevant, in my opinion. To me, ‘change’ in this particular scenario is equivalent to non-homogeneity, i.e. it is simply the failure of all spatial regions of that universe to be identical. It isn’t a process, it’s a relationship.

Edited by Markus Hanke

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Posted (edited)
23 hours ago, vexspits said:

I think it might be more a matter of some “idea of time” being inside your thinking.

Which is perhaps why you add, “at the same time” to “all the parts are present together” which to me adds nothing. 

Just for the hell of it, as an experiment, you might try throwing the word “time” out the window (and all its accompanying baggage), and focus on relationships that persist (such as distances between positions on a cup) and the inherent structure as a whole that arises out of those persisting relationships. Instead of thinking “the inherent structure exists at a time” just think: “the inherent structure exists”. Or “it persists”, not “it persists through time”. 

Now if you cry fowl here and say, “The only way the structure can persist is through time”, I submit to you that you’re adding something vague and extraneous in the sense that it doesn’t contradict the notion of change as presented by Marcus. We have to be clear that we are talking about a parameter, not some other notion of time which you or I might espouse.

PS. Although I have to admit, I’m very curious as to how you would define “time” outside the time of physics. Maybe a new thread in the philosophy sub forum. 
 


 

Foul.

To me (but that might be only me) in order for something to be, time must be there. Either time arises from the existence, or time is a necessity prior to existence, I don't know. But you cannot "be" out of time. You cannot "persist" in something that you want to cancel. It is a wrong concept. IMHO.

To be more pragmatic and step out of pure philosophy, I have the feeling that in the frame of GR it should be possible to show that Time & Space are inseparable. That one cannot establish the concept of Space without Time. That the concept of 3D space "existing" or "persisting" without the concept of time intertwined  to it does not represent anything close to anything.

 

1 hour ago, Markus Hanke said:

There is of course no observer in such a universe, since no act of observation is possible - but does that imply that the tea cup cannot exist? Does existence (in the ontological sense) require a temporal dimension? I think not.

Interesting how we disagree. Please explain your concept.

Edited by michel123456

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Posted (edited)
57 minutes ago, michel123456 said:

To me (but that might be only me) in order for something to be, time must be there. Either time arises from the existence, or time is a necessity prior to existence, I don't know. But you cannot "be" out of time. You cannot "persist" in something that you want to cancel. It is a wrong concept. IMHO.

To be more pragmatic and step out of pure philosophy, I have the feeling that in the frame of GR it should be possible to show that Time & Space are inseparable. That one cannot establish the concept of Space without Time. That the concept of 3D space "existing" or "persisting" without the concept of time intertwined  to it does not represent anything close to anything.

Let us go back to your desert and savannah example and accept that they can or do exist in and through some amount of time, say from 1900 to 2000 in round numbers.

That is what I mean by persist do you have a different definition.

Now let us take your proposed journey, walking through the desert.

I hope you will agree that the desert persists in space as you move from one place to another ?
(and yes I agree that in this case it also persists in time)

Then you pass from desert to savannah.

Do the places you have just walked through cease to persist?

Was the savannah not persistent just because you were not walking through it?

 

I look forward to your detailed analysis of the situation as you move through the landcape and from one landscape to another.

I am particularly interested in your reason why you consider there is a difference between being in different  parts of the desert and being at different times.

If you say that you can walk through the desert because different places persist in time,

Why can you not say that you can be in different places because the desert persists through space ?

Edited by studiot

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Markus and Studiot
So in this 'dead' 3D universe without time, there can be change, but it is only apparent to an extrinsic observer ( outside that universe ) ?
That universe itself cannot have an intrinsic observer to detect that change.

That seems to me, to be a problem with our common definition of change; it HAS to be observed.
And therefore time is required.

( sorry Studiot, I'll get to your orbital/jacks question when I have more time to review the questions )

 

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45 minutes ago, MigL said:

So in this 'dead' 3D universe without time, there can be change, but it is only apparent to an extrinsic observer ( outside that universe ) ?
That universe itself cannot have an intrinsic observer to detect that change.

 

The whole point of my examples is to show that this is not true.

But in a light hearted way.

:)

Next time I am run over by a bus, I will try (as an intrinsic observer) to determine whether it is just the momentum of the radiator I feel or that of the whole bus.

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6 hours ago, michel123456 said:

To me (but that might be only me) in order for something to be, time must be there. 

Well I was not trying to deny this, I was trying to persuade you to temporarily toss it out the window, because it seemed pointless to point it out: Saying “time is there” in order for the cup to persist is extraneous, as I emphasized, “…in the sense that it doesn’t contradict the notion of change as presented by Markus”. 

In any case, upon re-examining your previous post you appear to have already conceded that point. 

Cheers

 

 

 


 

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Posted (edited)
6 hours ago, studiot said:

The whole point of my examples is to show that this is not true.

And what I'm failing miserably to explain, is that this is not true because you and I are intrinsic to this universe, which has three spatial dimensions and one of time. But it certainly would be true if we were intrinsic to a universe with only three spatial dimensions.
You could NOT get hit by a bus, or a giant jack, and I'm not sure an orbital even makes sense in such a time devoid universe.
Our definition of 'change' applies to a universe which includes a time dimension, OR, we are extrinsic to a universe which has no time.

IOW, I can look at a 2D sheet of graph paper with a teacup drawn on it, and notice 'change' because I'm extrinsic to that 2d graph.
But if I was a flat-lander intrinsic to that 2D graph sans time, I could not possibly note any change.

Edited by MigL

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8 hours ago, MigL said:

So in this 'dead' 3D universe without time, there can be change, but it is only apparent to an extrinsic observer ( outside that universe ) ?
That universe itself cannot have an intrinsic observer to detect that change.

That seems to me, to be a problem with our common definition of change; it HAS to be observed.
And therefore time is required.

 

Like Markus, I agree 100% with you that for an observation to take place, there would be some act of a finite speed involving a range of motion that could be measured with a clock. But also, like Markus, I don’t see how it is relevant to his claim about non-homogeneity in the scenario he describes.

Again, in his words: “it is simply the failure of all spatial regions of that universe to be identical”.

When you say, “that seems to me to be a problem with our common definition of change” in some ways I can very much relate. 

If you look at a sample of definitions of the intransitive verb as described on the Merriam-Webster online dictionary you get:
“to become different”
“to undergo transformation, transition, or substitution”

these all very much point to a process, which suggests a range of motion. But that is not what Markus is describing. As he says, “It isn’t a process, it’s a relationship.” (Studiot also pointed out that there are other notions of change apart from transformation). 

So I get how it conflicts with at least one “common” definition, but I’m not sure about which “common definition” you are speaking of—the one you say “HAS to be observed.”  

Please forgive me if I’ve misrepresented you or misunderstood your remarks.


 

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Posted (edited)
12 hours ago, michel123456 said:

I have the feeling that in the frame of GR it should be possible to show that Time & Space are inseparable

On a manifold that has both spatial and temporal dimensions, these will indeed by inseparable, and in the sense that they both make an appearance in the metric with opposite signs.
A purely spatial 3D universe wouldn't be locally Lorentz invariant since the metric signature must be either {+,+,+} or {-,-,-}, so GR does not apply here.

12 hours ago, michel123456 said:

That one cannot establish the concept of Space without Time.

GR does not in any sense establish concepts of space and time - it is simply a constraint on the form local geometry can take, given local sources of energy-momentum and appropriate boundary conditions. All I can say here is that GR - as being a tensor equation - does not demand any specific number of dimensions nor metric signature (i.e. mix of spatial and temporal parts) to be valid. So there is nothing from stopping you e.g. to write GR with 17 spatial and 6 temporal dimensions, the field equations would look exactly the same. Whether what is described then bears any resemblance to our own universe is a different question.

But again, this is actually irrelevant, because I didn't demand GR (or any other specific law) to hold in my toy universe.

12 hours ago, michel123456 said:

Interesting how we disagree. Please explain your concept.

I find it hard to explain my thought process on this point, as I lack both the formal philosophical background knowledge and the necessary vocabulary to do so. Essentially I am of the opinion that while observation requires existence in the ontological sense (something needs to exist first before anyone can observe it), the reverse is not true in my opinion - I don't see any logical reason why the absence of observers should imply that nothing can exist. Hence, while the tea cup universe is undoubtedly physically unreasonable, it is not philosophically inconsistent.

12 hours ago, michel123456 said:

That the concept of 3D space "existing" or "persisting" without the concept of time intertwined  to it does not represent anything close to anything.

Again, the ontology of existence does not, to me, necessarily imply persistence - but persistence always implies existence. 
Of course my toy universe is not physical - I never claimed that it is. It's simply a philosophical thought experiment.

10 hours ago, MigL said:

So in this 'dead' 3D universe without time, there can be change, but it is only apparent to an extrinsic observer ( outside that universe ) ?

There can be no observer whatsoever in such a universe, neither internal nor external, and I did not postulate one in my original example. This is simply a universe with a single tea cup in it, and otherwise complete empty (vacuum). I also do not require it to be embedded in anything. My point was this:

1. Consider the hypothetical universe as an ordered, uncountably infinite set which consists of all physical locations/points (just like ordinary spacetime manifolds, only in 3D)
2. Each element in the set be of type boolean, i.e. either of value 0 (meaning it is vacuum) or 1 (meaning not vacuum)
3. Not all elements of the set are of value 0, because of the tea cup
4. Because not all elements within the set have identical value, this implies a concept of 'change'
5. Since the elements of the set are abstract entities (it is irrelevant what they physically correspond to), the notion of 'change' introduced here is purely a relationship between elements of an abstract set, and thus neither spatial nor temporal in nature

Whether or not this change is observed by anyone is irrelevant, because it makes no difference to the structure of this mathematical set, or the relationships between its elements. I am simply saying that there is nothing special about 'time', so far as change is concerned - you can have change with respect to time, as well as change with respect to any other quantity. Change simply isn't spatiotemporal, it is an abstract, relational concept - in my opinion. So change does not logically imply the existence of time, and conversely time also does not logically imply any change (you can have a complete empty universe without any processes taking place, that nonetheless has temporal dimensions).

10 hours ago, MigL said:

That seems to me, to be a problem with our common definition of change; it HAS to be observed

Why? When the early universe formed, there was no one to observe that (it was too small and dense to contain any observers, it didn't even contain particles), but the change obviously still happened. Of course that was a change with respect to both time and space, but nonetheless is happened without observers, so the above statement is clearly inconsistent.

3 hours ago, MigL said:

But it certainly would be true if we were intrinsic to a universe with only three spatial dimensions.

Again, the example was specifically about a 3D universe that contains only a tea cup, and nothing else. Postulating an observer would have been pointless, since without a temporal dimension, no act of observation is possible. This does not however negate the existence of the tea cup and the vacuum - which aren't identical.

 

Edited by Markus Hanke

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Posted (edited)

Well,although this seems to be arguing from authority**  if Markus' toy inverse  can be considered on any merit at all we have to concede that not only is it a purely  philosophical structure but also unscientific in that nothing can be predicted about it.

The teacup could persist or it could disappear or reappear.There is absolutely nothing that can be said about it.

In terms of pure non temporal relationships there is nothing to relate the teacup  universe to anything in  the world we observe.

So ,although we can imagine it it is like the belief in deities : one might as well believe in hydrspinacylate gnobbixiis  as  any deity

There is no "output"   one might get from  the scenario(unless the mental process of imagining the teacup somehow lead to a better understanding of related concepts)

Just my two lumps of sugar

** the "authority" being the scientific method.

Edited by geordief

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Posted (edited)
5 hours ago, Markus Hanke said:

There can be no observer whatsoever in such a universe, neither internal nor external, and I did not postulate one in my original example. This is simply a universe with a single tea cup in it, and otherwise complete empty (vacuum). I also do not require it to be embedded in anything.

Yes perhaps my momentum example was flawed, especially since momentum inherently contains time as a 'dimension' in the physics sense.

But before the Science of Electrodynamics there was the Science of Electrostatics.

So let us indtroduce the saucer to your teacup universe, or let us create new static universe exactly the same apart from now including a saucer.

Further let the cup and saucer each have an electrostatic charge.

The the cup will observe the saucer and the saucer will observe the cup via the electrostatic interaction.

Note there is no need for a physics time dimension in this universe.

Electric charge is a fundamental physics dimension in its own right, (although we now use electric current for administrative reasons).

Edited by studiot

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20 hours ago, Markus Hanke said:

I think we’ll have to disagree on this :) Which is fine of course, this being just a philosophical exchange. To me, the term ‘static’ (I think it should have been ‘stationary’ actually, I often confuse them) implies precisely the absence of any kind of reference to time, be in implicit or explicit.

As long as you just look at a teacup, or a graph of a function, I fully agree with you. 

20 hours ago, Markus Hanke said:

This is called a ‘parametrisation’, and it is not what I am doing or suggesting at all.

I would say, yes, you do it, and time is the parametrisation you use.

In my opinion, if somebody says that 'y changes as function of the change of x', she is saying 'if you change x from a to b, then y changes according f(a) to f(b)'. But a change of x is an activity of an observer, and observers exist in time.

And concerning your points with MigL: of course change can occur without observers. But observing a change means either a passive observer sees things changing (you are sitting quietly at a veranda, and you see the streets changing from dry to wet (a very common experience in Ireland...)) or you look at an non-changing object, but you let wander your gaze from one place of the object to another, and e.g. see how the colour 'changes' dependent on the place of the object where you look. But the latter also means a change in time. But the change is in the observer, not in the object. The object is static.

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9 minutes ago, Eise said:

But a change of x is an activity of an observer, and observers exist in time.

Are you suggesting that change is the only activity of an observer ?

My previous post suggests otherwise.

You have also coupled this to a second unproven statement "and observers exist in time."

 

 

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Wish I could give you two up-votes Eise.

I think, Studiot, that our definition of 'change' references the observer, not the universe being 'observed'.
WE need to note a difference in order to call it 'change' )
And that is simply because the concept of 'change' has arisen in a universe with time.

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6 minutes ago, studiot said:

Are you suggesting that change is the only activity of an observer ?

No, of course not. I said:

21 minutes ago, Eise said:

But a change of x is an activity of an observer, and observers exist in time.

Maybe I should have written that activities exist in time, and therefore a 'change of x' exists in time. So your example of the electrostatic objects does not work.

12 minutes ago, studiot said:

You have also coupled this to a second unproven statement "and observers exist in time."

Yes, because only observers that exist in time can say 'if you change x, then y changes according f(x)'. Otherwise, an observer would just see an object, a static form.

I think the subtle point here is that one must take care to distinguish between what we observe, and how we speak about it. I might be wrong, but I have the impression that you and Markus discuss what we observe, and I talk about how we speak about an observation.

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25 minutes ago, MigL said:

Wish I could give you two up-votes Eise.

I think, Studiot, that our definition of 'change' references the observer, not the universe being 'observed'.
WE need to note a difference in order to call it 'change' )
And that is simply because the concept of 'change' has arisen in a universe with time.

No, no and no.

Marcus has already made the point that the change is there whether it is observed or not.

He has also introduced a universe with no observers and no time, but I did think it was now accepted that the teacup universe contains change.

15 minutes ago, Eise said:

Maybe I should have written that activities exist in time, and therefore a 'change of x' exists in time. So your example of the electrostatic objects does not work.

Activities can only exist in time in a universe that includes time.

You have simply declared that my cup and saucer universe does not  work.
You have most definitely not demonstrated that this is the case.

Observations are simply a scientific term for interactions between distince entities.

As Markus points out, an interaction cannot occur in a univese with only one occupant.
That is why is was necessary to introduce another.

In the case of my static universe the interaction will never change, since there is no time.

Yet change exists in that universe since each observer can determine the sign of the interaction.

So a difference of charge sign will inevitably lead to a particular interaction sign and the existence of any difference is a change.

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35 minutes ago, studiot said:

Yet change exists in that universe since each observer can determine the sign of the interaction.

Can you explain this more. I don't get what you are trying to say.

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The concept of 'change' only makes sense in a universe with time.
That is why we can observe a universe without time, such as the teacup universe, or the electrostatic universe, and notice change.
we are 'outside' those peculiar universes.

That is because the concept of 'change', ( in effect, for change to be observed ) has to involve the paradigm of time passing.
So we, in this universe notice change even in the teacup/electrostatic universes, but those universes would never have developed the concept of 'change'. How could they ?

( by the way, that's a lot of nos. Was it for emphasis, or three nos for particular points ? ) :)

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