There cannot be an infinite amount of time between two points in time.

There cannot be an infinite amount of time between two points in time. If someone comes along who can't accept it, and wants to prove it wrong, have a try. You can't prove the statement wrong because it is right. So let me start with that fact in this thread.

I start there because time is a difficult topic to get a consensus on in physics, as demonstrated by the various recent threads. This thread is meant to offer concepts about time that are true, and that we should be able to agree with.

To start, I offer the first premise: time is always passing every where. This premise has some givens with it, i.e. I'm not talking about the measurement of the rate that clocks would display time passing, because we have evidence that clocks in relative motion or under different rates of acceleration or energy density, will measure time differently. No, the first premise is that, no matter what rate clocks in different environments show time passing, time does pass there at some rate. Even if mechanistic clocks were to stop functioning due to acceleration and energy density conditions, time still passes there according to this premise.

Next, clocks are not measuring anything that could be construed as a constant universal time. This premise is conditioned by the fact that there is no absolute rest frame. Yes, there is a CMB rest frame, but clocks at rest relative to the CMB, are all still in relative motion to each other, because the position of rest relative to the CMB is always moving, and therefore each rest position is moving relative to all other such CMB rest positions.

The next related premise is that, given identical clocks stationed in all local environments across the universe, if they could all be started and stopped simultaneously, there wouldn't be much agreement between them; they would generally show a different amount of time had passed. This thought experiment would be impossible to perform due to the relativity of simultaneity, but the premise should be acceptable; the clocks would generally show different amounts of time had been measured to have passed during the interval of the thought experiment.

And lastly, for this OP, if the amount of time on a representative sample of those stopped clocks is added and divided by the number of clocks in the sample, an average amount of time measured during the measuring interval could be determined. That is called the "sampled universal average rate" that time is measured to have passed on clocks across the universe. More simply, that is the concept that there is an average universal rate of time passing on functioning clocks.

 

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It is a simple mathematical truth that there isn't an infinite distance between two defined points on an axis. So what? That doesn't really have anything to do with the rest of the post and is pretty straightforward on its own. So, what is the point of this thread? Is there something coming next? Or was this an offshoot of another thread?

 

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It's probably just a misunderstanding of coordinate time in curved space-time.

 

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You made the first part pretty easy. Even as obvious as it is, I have known people to take exception to that statement.

As to if there is more coming, the answer is no, not if the members can see no logical connection between the title and the first premise. I'm confused why you say that the title statement doesn't really have anything to do with the premise about time always passing, and to the logical steps toward the concept of an "average universal rate of time passing on clocks". It is from that concept that there would be more to come. Why is it unrelated to the concept that a time interval is finite.

I guess I would be seeking an acknowledge that there is at least a chain of logic to get to that concept, whether the logic is sound or not, and to have you explain why you say it is illogical.

Maybe so. My sorry layman grasp of terminology is probably what needs correcting. I'm relating the measurement of time on clocks to each other, when the clocks are in relative motion to each other. That makes it about observational evidence that is generally accepted, I think, i.e. that the amount of time shown to be passing on clocks in relative motion varies.

If that is correct, then the OP leads to the concept of an "average universal rate of time passing on clocks". You mention spacetime, and I mention observational data. Aren't the two compatible in regard to the variable measurement of time? What is my misunderstanding, in layman terms?

 

Nowhere in that post did you say "a time interval is finite" or anything related other than in the title and first paragraph. You never mention the issue again, so how can it be logically connected to the rest of the post?

Anyway, if your goal was really to propose a method for measuring a universal tick rate, you have a misunderstanding of that concept. Typically, such misunderstandings come from not realizing you've declared some arbitrary reference frame to be The Universal Rest Frame. That part of the post though is a bit of a mess and I didn't try to sort it out due to its apparent irrelevancy. So is that what you really wanted to talk about?

 

Well, that is two places, isn't it. What, you can't remember something like the title and first line long enough to craft an intelligent response?

I didn't think making the connection between, "There cannot be an infinite amount of time between two points in time", and an 'interval of time" was so far above your head. But then you also failed to respond to the actual content of my reply to your first post, so I'll wait for that. But I will ask about your intuitive abilities that tell you what I am thinking.

That is filled with your own misconceptions and ignorance of my intentions. It is your intuition that tells you those things. Or does the fact that I mentioned in the OP that the premise is conditioned by the fact that there is no absolute rest frame also go over your head?

 

Now you are just getting upset because you don't like my criticism and it is affecting your ability to process what I'm saying.

Step back.

Breathe.

Relax.

Think.

Saying something in the opening paragraph and title does not automatically make it relevant to the rest of the post -- though it really should. Since you didn't make a logical connection to it anywhere else in the post, you could have opened the post with a Shakespeare sonnet and it would have worked just as well....

...Further, it is not usual to put one of the starting premises (whether it actually is or not) in the title and thesis of a post/article -- that should be reserved for the actual subject and thesis of the thread. That's proper writing technique. Since the rest of the post was irrelevant to the title and thesis, I ignored it. But now that we've established that it was the title and thesis that were irrelevant to the real purpose of the thread, I'll go back and work on the rest. However:

Your fault, not mine, for writing a terribly organized post. Now that I've explained to you that the title and thesis should reflect the actual point of the thread, it would help us all out if you started over and wrote a title and introduction/thesis paragraph that explains the point of the thread.

Could you do that, please, to make it easier to understand what your point is?

 

It was a legitimate question I asked you. Again you don't respond to my response, but offer us a straw man, in this case it is your accusation that I have become upset, and can't think straight in the onslaught of your superior arguments.

New rule noted. Let's see you get the official rules to include that before we all invoke it though.

False, straw man, illogical.

New rule noted. Same response.

Show me you will.

Like I had to tell Farsight in my last thread, get over yourself. I stand by the OP, and my follow on comments, which include my reply to rpenner. I'm relating the measurement of time on clocks to each other, when the clocks are in relative motion to each other. That makes it about observational evidence that is generally accepted, I think, i.e. that the amount of time shown to be passing on clocks in relative motion varies.

If that is correct, then can't logic lead to the concept of an "average universal rate of time passing on clocks" (Note I said "passing on clocks"). Rpenner mentioned spacetime, and I mention observational data. (Note that I am referring to observational data being the difference we observe when identical clocks experience relative motion).

 

Sure you can arbitrarily pick a particular inertial reference frame as the "average universal rate of time passing on clocks", but it is pretty useless. Keep in mind that the "rate of time passing on clocks" is different on earth depending on your elevation. If this is important to you then you can pick the Naval Observatory Master Clock and call that the "average universal rate of time passing on clocks".

 

Thanks, and I'm not picking anything. Read the OP and the method of calculating the "sampled universal average rate that time is measured to have passed on clocks across the universe", in the thought experiment.

That concept doesn't seem to be a violation of the laws of physics. What it does, if deemed correct, is it leads to the next question; what do we know physically about relative motion that causes clocks to measure time to be passing at different rates?

From the OP:

 

OK, so you are saying that if you pick a hypersurface of simultaneity, you're picking a time coordinate.

And?

This has nothing to do with the not obviously true claim that "There cannot be an infinite amount of time between two points in time."

 

It seems obviously true to me. But I'm not trained in physics. Do you know of any contemporary physical theory that posits the existence of an infinite amount of time between two points in time? Bear in mind that the age of the universe is known to be finite; so that you'd have to go back to some prior universes. But even then, if you only go back finitely many universes, each one finite in duration, that's still only a finite amount of time. You'd have to choose two points in time separated by infinitely many finite-duration universes.

We can't rule out the possibility that this is the true condition of the metaverse; but it seems "obviously false" to me until a serious theory comes along.

In fact if you consider a simple mathematical model of an endless continuum, namely the real number line, it has no beginning and no end. Yet between any two points there is a finite distance.

So if one wants to claim that is "not obviously true" that there is only a finite amount of time between any two points of spacetime, the burden of proof or even plausibility is on the one making that claim.

 

Irrelevant content deleted

 

I am afraid I don't follow your example. Can you show me a space with a metric that has the property that there are two points whose distance from one another is infinite?

If I'm understanding your example at all, where the space is two perpendicular axes, the distance between two points is the sum of the distances of each of the points to the origin, which is finite.

I don't follow your points about smoothness or continuity at all.

 

I was wrong, that's why I removed by post - I misread "infinite distance between points" for "infinitely many elements between these points"

Apologies

 

I was hoping to put an acceptable name to this concept, so I don't have to type out, "sampled universal average rate that time is measured to have passed on clocks across the universe in a particular thought experiment". I don't like the imponderable "hypersurface of simultaneity", though I'm sure there is some merit to the name. I'm not interested in Googling your name for it, but feel free to post a link.

I'll suggest "sampled time" unless the concept already as a better name than PhysBang's suggestion. Sampled time can be applied universally via a thought experiment as I have above, with a sampling of many clocks from multiple locations.

See what Someguy1 said.

 

That's ok -- when I first read the OP, my first thought was that he has a vague idea/misunderstanding similar to Xeno's paradox, which your post would have applied to.

 

Actually that's what I thought too, but then realized the OP might be talking about duration rather than the quantity of instants. Perhaps OP can clarify.

 

I did intend it to be duration as opposed to some finite number of points of time between two points in time. I would have thought that the idea of a number of points between two points would generally be considered infinite regardless of the duration.

 

I think the smallest time interval yet defined is the "Plank time" or Tp = 5.39 × 10-44 seconds. If you can prove that time is digital (not analogue) and jumps by Tp steps then your OP may be correct. but if time is continuous (analogue) then the OP is wrong and easy to prove it wrong:

Consider two times, Ta & Tb a later time I.e. Tb - Ta which I'll call D and note > 0. There is a mid-point time Tc = Ta + D/2 and a mid point of that interval (and a mid point of the other half at Tb - D/2 etc. Each of these four intervals D/4 can be split to make 8, all of D/8 duration, etc. and there is no end to this cutting the last steps intervals in half to double the number of intervals, if time is analogue. this doubling can be done an infinite number of times.

SUMMARY: To prove the assertion of the OP, you must defeat the above by proving that time is not analogue - I.e. that it discretely advances in steps of some minimum, non-zero size (Perhaps the Planck interval?)