Question about linearity from a non-mathematician

An observation: we have attosecond laser pulses, and atomic time.

If you try to go beyond a systematic description of time, you can't do it physically can you (uh uh, I don' know, anybody) ? Beyond attoseconds are femtoseconds, and we're there too.
When does "the length of a pulse of light" become meaningless?
 
I see, you being a mathematician, haven't done any systems, the ones made out of atoms and stuff?

Here's an idea: time is harder to measure in a gravitational field because the operator is more entangled, or "closer" to M.
 
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noodler said:
Here's an idea: time is harder to measure in a gravitational field because the operator is more entangled, or "closer" to M.
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Hmm, here's another idea: time is something we pull out of our asses.

:bugeye:

Yes, that means when we use electrons, the spot on the screen is electron crap.
 
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noodler said:
I see, you..... haven't done any systems, the ones made out of atoms and stuff?
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No, I confess that I haven't. What course would you recommend for that?

the operator is more entangled, or "closer" to M.
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What is "M"? What does it mean for an operator to be entangled? I have heard of (but don't really understand) entangled states, but an entangled operator is a new one to me. as is the degree of entanglement, which is implied by your adverb "more".

Please explain more, but preferably not in this thread, which was started in good faith by a poster who thought - obviously over-optimistically - that (s)he might get a considered response to their honest question from those who claim to be competent in P&M .

And no, I do not include myself in that select group
 
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Perhaps I should step away from the copy of R2R, slowly and carefully with my hands raised?

But seriously, folks, entanglement and superposition are kind of important ideas, in QIS (guess why?).

To measure a state you conjure together an "operator". This is made out of the possible superpositions that two quantum states can be in.
Note: you can't measure one quantum state, unless you use another one as the (entanglement) operator. Entanglement is part of measurement, up until the collapse. The superposition 'condenses' into a measurement, in the operator formalism. You have two systems: a cesium atom and the environment, you use the environment to measure the state of the first system.

Pure states are indistinguishable, measurement generally assumes mixed states and density matrix algebra.
 
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Farsight said:
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.
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To say that a rate of movement is constant, you need a notion of time to start with. Thus, you have things backwards. You can't deduce the regularity of time from the regularity of a clock.

It is interesting to consider what makes a "good clock" and what makes a "bad clock". Have you ever considered that question?

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.
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This is correct, although not completely clear. You can't go back into your own past. But you can go back into a distant observer's past. But then there are qualifications to do with causality etc. In short, it's more complicated.

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.
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What do you think time is an emergent property of? What underlies time?

Please don't say "motion", because motion requires time as a prerequisite. (Consider the definition of velocity, for example: v = dr/dt. See how time is there in the definition?)
 
From now on, noodler, I'll be keeping a special eye on you, because it seems to me that you are trolling.

have a nice day.
 
So that's a "no"?

It's just, in order to move forward here, I need some indication that you have answers to said questions (remember, the ones I asked about the meaning of length, and explanations for the slowing of time?). At the end of the day, the cleaners will be arriving...
 
noodler:

Please list your questions, and provide an undertaking that you will answer mine once I've answered yours.

Thanks.
 
Q1: Why do atomic clocks run more slowly on the earth's surface, than they do above it?
Q2: When does the length of a pulse of light become meaningless?

Also, do you agree that measurement is assumed, in Einstein's theories, to always be possible?

If you are prepared to list your questions, I'll consider them.
 
noodler:

Here are my answers to your questions. I thought I'd answered at least one of these previously - probably in a different thread.

noodler said:
Q1: Why do atomic clocks run more slowly on the earth's surface, than they do above it?
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According to general relativity, massive objects like planets curve spacetime around them. The particular geometry can be modelled, to a first approximation, by the Schwarzschild metric. Being stationary in a gravitational field means that the observer is in a non-inertial reference frame.

When we say "higher clocks run more slowly", we must be careful. This is a relative thing. We're comparing the rates of two clocks at different heights. There is no absolute measure of the rate at which time runs.

So, what's really happening here is that we're comparing clocks in two different reference frames, both of which are non-inertial. Just as relative motion in special relativity affects the relative rates of clocks, so does the difference in reference frames near the Earth.

Q2: When does the length of a pulse of light become meaningless?
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I can't answer this without you first telling me how you define the length of a pulse of light. Let's add this to my list of questions which you have agreed to answer.

Also, do you agree that measurement is assumed, in Einstein's theories, to always be possible?
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No. Einstein's theories are theories. They do not discuss the practicality of measurement. Like many mathematical and physical theories, they deal with an ideal world. They are conceptual. Of course, there are practical limits on all physical measurements, determined by a number of different factors.

If you are prepared to list your questions, I'll consider them.
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My questions are contained in the following post from the current thread:

[post]2573855[/post]

I look forward to your detailed answers. Thanks.
 
Ok. Since you appear to think "because of the theory of relativity" is a detailed answer , here is my effort:



The hypercomplex plane is two words you can google, although it doesn't seem to be in common use.
...
As to why time appears to be slower in a gravitational field, well it seems to also be tied to measurement. Maybe electrons have more mass, or gravity acts like a viscous coefficient, appearing to stretch time like a spring. In fact for a moving reference frame, time would appear to slow down and speed up, as it approached and departed, the gravitational centre of mass.
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And your questions about measurement:
"How do you measure that difference? Why is it a phase difference? Can you please post the mathematical expression for the phase difference? Thanks."
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The mathematical expression for a phase-difference, for a system with two qubits in it, say, is $$ | \psi \rangle_{ab} $$. Measuring it depends on what you know about the state the qubits are in, but say they are photons, then the phase difference is part of some interferometer setup. That is a completely general expression as a ket with abstract indices, BTW.
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Why do I think time is additive? Because it doesn't seem to be multiplicative..?:shrug:
 
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