Question about linearity from a non-mathematician

[GeoffP]

From this thread:

http://www.sciforums.com/showpost.php?p=2572636&postcount=3

So, forgive my probably dumb question, but...doesn't relativity mean time is not linear? Or is it that time experienced as per individual perception is linear? Or are we talking about time in general? Or is it merely that time must advance in a progressive or directional way? (As a geneticist, I use "linear" a little differently.) But can't you go back into the past if you go fast enough?

Sorry about the questions. Anyone help me here?

 

[GeoffP]

Special occasions as in as per the observation of an outsider?

This is fascinating stuff. Sorry: where time seems not to exist at all? (If the response is too long, I'd gladly take a link.)

 

[GeoffP]

Also, there is a quantized time example from a clock-hypothesis of the electron, which proven experimentally to such a high degree. It was found that the time periods where periodic, so in this sense, it experiences a planck time. Starts and stops.

This is why it seems linearity is the only interpretation physics can use when perception is involved. This has actually been known for quite some time now among many notable physicists.

So...time, at a very basal level, is additive? That is, a multiple of the electron events you describe? (A+A+A+A+A....)

 

[noodler]

So...time, at a very basal level, is additive?

That appears to be the case. If time is strictly linear all you can do is add 'bits' of it together, and say "this is a continuous interval of time".

But we "time" events according to clocks made of atoms, and since these are ultimately wavefunctions, we are required to invoke the notion of infinitesimal linear time, 'acting' via the quantum Hamiltonian. Or, the linear evolution is actually a possibly infinite sequence of infinitely small 'quantum events', or transformations, of/by the Hamiltonian; there is no reason to limit an infinitesimal time interval to greater than Planck time, for instance.

I use the labels "quantum time" and "gravitational time" for comparison, except I know that special relativity is connected (it must be) to quantum time (the details are not yet understood I believe).

The QM 'time paradox' and SR are both free of gravitational influence (or at least, massless particles in SR are). Electrons aren't influenced by gravity anywhere near the strength of EM coupling.

So when we 'measure' time we are really only comparing one wavefunction with another wavefunction, and both appear to be linear. It's tautological, you can't use a quantum timer to define what time is.

The 'timer' is: $$ -i \hbar \frac {\partial} {\partial t} $$. But it has to be 'distributed'; you need another one for reference/synchronization. The phase between two quantum states is the quantum timer.

 

[James R]

So, forgive my probably dumb question, but...doesn't relativity mean time is not linear?

What do you mean by linear?

 

[Pete]

From this thread:

http://www.sciforums.com/showpost.php?p=2572636&postcount=3

So, forgive my probably dumb question, but...doesn't relativity mean time is not linear? Or is it that time experienced as per individual perception is linear? Or are we talking about time in general? Or is it merely that time must advance in a progressive or directional way? (As a geneticist, I use "linear" a little differently.) But can't you go back into the past if you go fast enough?

Sorry about the questions. Anyone help me here?

Hi Geoff,
I'm not an authority, but I can hardly give a worse response than you've had already.

Short answers:
No, you can't go back into the past if you go fast enough.

No, noodler (aka Vkothii, aka Reiku) doesn't know what he's talking about.

I don't know if Serapheous does, but his posts smell suspiciously like someone bullshitting outside their domain. Could be wrong.

There are several domains of understanding involved here. Your question seems to relate to special relativity, but noodler and Seraphous seem to be answering in the context of quantum theories:

• I have a reasonable amateur grasp on special relativity, which models time dilation, length contraction, and other weirdness regarding clocks and rulers in relative motion. Time is linear (in the way I understand the term) in special relativity.
• I have only a vague grasp on the foundations of general relativity, which models gravity as curvature of the space-time geometry established by special relativity. I'm pretty sure that general relativity involves non-linearity, but can't say more than that.
• I have not even the foggiest understanding of quantum mechanics, quantum field theory, quantum electrodynamics. Too hard.

Pay attention to (off the top of my head) James R, AlphaNumeric, BenTheMan, Guest, and QuarkHead. They know what they're talking about, and will say when they're out of their domain of expertise.

 

[noodler]

No, noodler (aka Vkothii, aka Reiku) doesn't know what he's talking about.

No, you don't know what you're talking about.

Time is really just a difference between quantum phases, of some product space. If you think this is bullshit, please show why you think that.

It's illustrating to see how many "in-house" posters here think they can say "that's bullshit", as if this is some kind of proof. Or the other common tactic is something like "I haven't got time, and there are so many mistakes I don't know where to start". But please start, at least, to prove your initial (quoted) statement. Or I will accuse you of talking shit.

Here is something I like to call "a question": why do atomic clocks run slower in a gravitational field?

Any ideas?

 

[AlphaNumeric]

No, noodler (aka Vkothii, aka Reiku) doesn't know what he's talking about.

I don't know if Serapheous does, but his posts smell suspiciously like someone bullshitting outside their domain. Could be wrong.

I heavily suspect noodler is Vkothii but he's not Reiku, Serapheous is.

As for the original post, JamesR has it :

What do you mean by linear?

There's a number of meanings for 'linear', all of them vaguely associated to one another. IMO the question "How is time linear" is a dubious one, it smacks a little too much of people asking questions using terms they don't really know the meaning of (I don't mean that in an insulting way to the OP).

Time is really just a difference between quantum phases, of some product space. If you think this is bullshit, please show why you think that.

I think what you said is BS because its incoherent. What product space? Product of what? What quantum phases? What do you mean by 'phases' since there's more than one meaning to that, depending on context. How do you take their differences? Why does that lead to time?

You're pulling buzzwords out your backside. I really don't get why hacks do that, just because you don't understand technical words why do you think people will blindly accept your spewing of buzzwords, even when you can't make coherent sentences out of them? What do you try to gain?

 

[Pete]

I heavily suspect noodler is Vkothii but he's not Reiku, Serapheous is.

Maybe noodler=Serapheous? I was pretty sure that Vkothii=Reiku.
But yeah, could be wrong.

 

[noodler]

You're pulling buzzwords out your backside. I really don't get why hacks do that, just because you don't understand technical words why do you think people will blindly accept your spewing of buzzwords, even when you can't make coherent sentences out of them? What do you try to gain?

Why do you always parrot stuff like this when you don't understand what someone is trying to say?


You know that a wavefunction has a phase angle, in the complex plane (maybe that should be the hypercomplex plane, but the former will do). What is your problem with a word that has, as you say various meanings? It has a definite meaning that I understand, and I believe there are a lot more who also understand that meaning, when applied to a wavefunction.

Time is the measured phase-difference between two quantum states, namely a cesium atom and its environment. To regain some traction here, prove that the previous statement is wrong. And BTW, are you disagreeing with the statement "quantum evolution is linear because time is linear"?

Really??

 

[noodler]

On second thoughts, I don't want to know.

I expect the question that was asked won't be answered by anyone. None of the sciforums crowd is very good at explaining anything.

That's "anything, at all". You would not be very good teachers, I expect most of the class would want to walk out.

 

[Pete]

That's "anything, at all". You would not be very good teachers, I expect most of the class would want to walk out.

Pretty funny, since Alpha and I both teach at tertiary level (but not I in this field, and not currently). And get feedback.

Personally, I was not the greatest classroom teacher, which was reflected in my feedback. On the other hand I got excellent feedback and results for one-on-one explanations.

Yes, some students do indeed want to walk out (students can be awfully brutal on course evaluations). Some do walk out, as they are free to do. But oddly enough, those who come to classes tend to perform much better than those who don't.

Go figure.

 

[noodler]

Well let's look at the old scoreboard, shall we?

There have been some questions asked, and there is a "path" that leads to where endeth the lesson:
Q1. doesn't relativity mean time is not linear?
Q2. time, at a very bas[e] level, is additive?

Time is really just a difference between quantum phases, of some product space.

What quantum phases? A: the ones that are measured.
Why does that lead to time? A: because of measurement.

Q3. why do atomic clocks run slower in a gravitational field?
Any ideas?

Me, I'm not holding my breath.

 

[GeoffP]

Hi Geoff,
I'm not an authority, but I can hardly give a worse response than you've had already.

Short answers:
No, you can't go back into the past if you go fast enough.

Well, there goes that DeLorean purchase. Bloody eBay.

What do you mean by linear?

That was the DeLorean thing: I was sure that was the "pop phys" theory...somehow.

Not trying to cause a fight, lads. Just sort of soaking up what I can. How about this: recommended physics links ("for dummies", please )?

 

[James R]

GeoffP:

That was the DeLorean thing: I was sure that was the "pop phys" theory...somehow.

It's just that when I hear the word "linear", I have a mathematical definition in mind. Linear relates to straight lines, certain simple algebraic functions etc. So what does it mean for something like time to be linear? It flows in a straight line? What does that mean? What would it be like if it wasn't linear? How could you tell the difference?


noodler:

Time is really just a difference between quantum phases, of some product space.

Please give an example of what you mean. Mathematical, if possible.

Here is something I like to call "a question": why do atomic clocks run slower in a gravitational field?

General relativity explains it in terms of curved spacetime. Why do you think it happens?

You know that a wavefunction has a phase angle, in the complex plane (maybe that should be the hypercomplex plane, but the former will do).

What's the hypercomplex plane?

Time is the measured phase-difference between two quantum states, namely a cesium atom and its environment.

How do you measure that difference? Why is it a phase difference? Can you please post the mathematical expression for the phase difference? Thanks.

I can't prove you wrong unless you can explain what you mean. And who knows? Maybe you're right.

There have been some questions asked, and there is a "path" that leads to where endeth the lesson:
Q1. doesn't relativity mean time is not linear?
Q2. time, at a very bas[e] level, is additive?

What does it mean for time to be additive? Do you think it's additive? This is an idea you've just introduced to the thread, by the way.

 

[Farsight]

Here is something I like to call "a question": why do atomic clocks run slower in a gravitational field?

Because light goes slower. Or if you prefer, electromagnetic phenomena or wavefunction evolution. A location where gravitational potential is lower is a region where processes occur at a slower rate. It's that simple. Time is measured by clocks, and clocks "clock up" motion. They measure motion, not the flow of time. Even the NIST caesium fountain clock is measuring motion in the form of the spin-flip hyperfine transition and the resultant microwaves.

 

[GeoffP]

GeoffP:

It's just that when I hear the word "linear", I have a mathematical definition in mind. Linear relates to straight lines, certain simple algebraic functions etc. So what does it mean for something like time to be linear? It flows in a straight line? What does that mean? What would it be like if it wasn't linear? How could you tell the difference?

Sorry: directional. I do mix them up accidentally sometimes. Although if time was additive, I guess you could plot it out in a linear way against these quantum events, if that's correct. I have no idea, so I'll let you physics types battle this one out.

What does it mean for time to be additive? Do you think it's additive? This is an idea you've just introduced to the thread, by the way.

Actually that was also me, asking about that.

This has been a very interesting thread so far.

 

[QuarkHead]

From this thread:

http://www.sciforums.com/showpost.php?p=2572636&postcount=3

Sorry about the questions. Anyone help me here?

No need whatever to apologize - questions are a lot better than unsupported assertions, which (ahem) one sees enough of here.

First thing to know is that noodler's pronouncements (your link) on any area of physics are equally unreliable as mine own, though I "arrogantly" claim a slight edge on him in mathematics.

As has been said "linearity" is perfectly well defined in the area of mathematics in which it is used, and with a little mental gymnastics it is possible almost to bring these seemingly disparate usages into register.

For time, I really have no clue how to proceed. If it has any meaning at all, I suspect it means something like this: whatever the rate of my clock, whether is "fast" (or "slow") - relative to what I have no idea - due to mechanical defects or some relativistic effect, the interval between, say 1 o'clock and 2 o'clock will be precisely the same as the interval between 2 o'clock and 3 o'clock, today, tomorrow, next year etc.

If you find this slightly circular, I don't blame you; I do too.

In short, I suspect the concept it pretty meaningless, but I am happy to be shown to be wrong

 

[Farsight]

From this thread:

http://www.sciforums.com/showpost.php?p=2572636&postcount=3

So, forgive my probably dumb question, but...doesn't relativity mean time is not linear? Or is it that time experienced as per individual perception is linear? Or are we talking about time in general? Or is it merely that time must advance in a progressive or directional way? (As a geneticist, I use "linear" a little differently.) But can't you go back into the past if you go fast enough?

Time is simpler than you might think. Just open up a mechanical clock and look at the "movement". That's what the mechanism is called. The clock is "clocking up" motion, and displaying a cumulative total as "the time". This motion is regular, proceeding at a constant rate. If you examine a quartz watch or even an atomic clock, the same principle applies. The motion proceeds at a constant rate, and in this sense time is linear.

However when we consider relativity, we can see that in truth, it isn't. If at 2 o'clock, you move to a region where gravitational potential is lower, then then the interval between 2 o'clock and 3 o'clock is not the same as the interval between 1 o'clock and 2 o'clock. However you can't detect this difference locally, because all local processes proceed at a reduced rate. Hence time appears to be linear when it isn't.

There's no issue with saying time advances in a progressive way, but there's no real direction to it. Travelling forward in time is just a figure of speech. And you can't go back into the past if you go fast enough. When you take a fast return trip, your motion through space comes at the cost of local motion. All local processes proceed at a reduced rate, and again the result is time dilation. To go back to the past you need negative motion, which is not real. It isn't possible to reduce a rate of motion to zero and then keep on reducing it so that it's negative.

Note however that time still "exists". It's rather like heat. We have no doubt that heat exists. However when you look at say the kinetic theory of gases, you appreciate that temperature is a measure of average motion, and heat is only an "emergent property". Time is another emergent property, but it's a a cumulative measure rather than an average.

 

[noodler]

GeoffP: "when" someone tells you (like I did) they know what time is (or, they don't), be skeptical. Be very skeptical.

Conjecture: time and measurement are indistinguishable. If today's time is measured with atomic interactions (which is just circumstance, really) then understanding what measurement "really" is, could be useful.

But don't take me at my word, will you?