md65536

Real physical events only happen within the sphere of the present moment: that would be in your abstraction, the black horizontal line.

That line in 2D is a hyperplane in 4D, not a sphere.

The 4D light cone, if we view it in 3 spatial dimensions, is a sphere whose radius changes at the speed of light. The past cone looks like a sphere that shrinks to a point at "you are here", and the future cone looks like a sphere that grows with time. The intersection of a hyperplane "instant" with the light cone is a sphere. The intersection of the black "present" hyperplane and your light cone is a degenerate sphere with radius 0... it is a point. This point is the intersection of the two "nows" that michel123456 was asking clarification on: The black unobservable, uninteractable distant simultaneous now, and the blue causal, perceived now. That it's a point might be interpreted as that in the misnomer "sphere of the present moment" we can only observe or affect things at a distance of 0; interactions across any greater distance would require more than just an instant.

The events you speak of are not causally related to you. Since the correct geometry can give a lot of meaning to this, I'll restate your quote as how I think it's supposed to be:

"Real physical events only happen on the hyperplane of the present moment: that would be in your abstraction, the black horizontal line."

However, with lack of simultaneity you could also say that the present moment can be simultaneous with anything outside of your light cone (past and future). The "fuzziness" of the black line can extend right to (the sharp outer edge of) the blue line. I think. So you might also say "Real physical events only happen (now) outside of the cone of what is immediately observable." ??? Or something... -- But for simplicity this can be ignored and we can speak of your "now" as the straight black line without fuzziness (a hyperplane). We can ignore the fuzziness and variability of "now" by saying it applies only to other different frames of reference.

but what is the meaning of time im eluding, then? i thought it was a measurement or change... there is nothing specific about that.

The answer to that is the answer to the thread and I don't think anyone knows.

"Time is (a measurement of) change" is also insufficient, because things can change slowly or quickly (the same amount of change can correspond to different amounts of time), and also it can't be "Time is (a measurement of) rate of change" because the same rate of change can be maintained over different amounts of time.

I don't think "change" is the essence of time. Entropy might be. The constancy of the speed of light certainly is related (but if time is defined based on light, it might be cyclical because distance is already defined based on time). If change is expressed in terms of the passing of information across distances, then a definition of time based on change might work.

Personally, I think (so please disregard this as anything more than just an idea) that "time is distance" is true, but as I mentioned distance is based on time. Also, the assumption of isotropic propagation of light makes it false. But if light was anisotropic and time and distance were equivalent, then a non-cyclical definition of time would be defined using something other than distance. My guess would be: Time and distance are emergent measurements of causality's consistency. Or instead of that, maybe something that even makes sense.

The person asking this question wanted the simplest definition of time, not the most clear in the eyes of a child.

 

If they wanted the simplest definition of the word "naked mole rat" I would give them;

 

"A warm-blooded vertebrate animal of a class" aka mammal

Making something more defined or definite means to specify it more precisely, but you're doing the opposite and specifying it more generally.

I think you're literally undefining "naked mole rat" here, and undefining time with "A to B" (both by removing the meaning of time, and by not being specific about what A and B are).

Meanwhile a definition like "time is what clocks measure" specifies it precisely, but doesn't say much about its meaning, which is essentially what the thread is seeking.

That said, "simplest" and "most precise" might be mutually exclusive, in which case the simplest definition would only have to be precise enough to still be considered a definition at all.

FMPOV, the above is irrifutable facts.

The problem is that you'd have to back up those claims with irrefutable evidence.

The question was 'what is the simplest definition of time'. It seems this is an insufficient definition if it has so many interpretations?....

It would be insufficient even if it wasn't left up to interpretation. As in, "time is the difference between two points in time" or "time is the progression from one point in time to another" or something.

"A to B" would leave time still undefined even if it was clarified that it was referring to times. If we allow such meaningless cyclical definitions, then the simplest (non)definition would be "time is time." Either way you'd need time to be predefined for the statement to have meaning.

On the other hand it could be interpreted in different ways that already have predefined meaning, such as "Time is the distance between two events". I don't think this definition would correspond to other accepted definitions, such as "Time is what clocks measure".

Isn't that distance?

If they're points in space, yes.

If they're points in time, no.

If they're events it could be a spacetime interval which I believe can be decomposed into a spatial and a temporal component.

I've had similar thoughts:

Humans desire to know where they come from. Most cultures have creation myths. We tend to explain unknown things in terms of known things. So for example, we see that humans have the ability to create things, so when we imagine a creator it is easiest to imagine it in terms of something already known to be able to create. So I figured that humans imagined the concept of a creator having a human form.

At the time I thought it was a revolutionary idea but it's been thought of before. I recently read the notes in the liner of Jethro Tull's album Aqualung:

1 In the beginning Man created God;

and in the image of Man

created he him.

Their message with this album is that organized religion creates the image of a god that they envision, and then distorts that image in all sorts of ways for all sorts of reasons.

I would agree that we don't have a good understanding of the nature or even questionable existence of gods, but that we as humans have always made assumptions about the unknown based on the known, and that humans are the most god-like known thing.

Depending on your definition of "god", humans may fit that description. For example, a conscious being who is aware of all my thoughts and actions and judges me for what I do... this describes my conscious mind. Or, if you describe god simply as "a giver of life" you might interpret it such that the sun fits your definition of god. It may be only that we assume that a god must be human-like, that we think it foolish for ancient civilizations to call the sun a god, when really it need not be more than just an admiring name for what it really is.

The God that many major religions describe typically has both human and super-human properties, that define something that must be more than just a human.

But I think it would make more sense if you phrased ideas and vague or conditional thoughts as such, rather than stating them as absolute facts.

There are 3 guards, and you can ask one of them a question that can be answered with the guard pointing to one door.

[...]

One guard is insane...

Since no one's answered here's what I had in mind:

I don't know if both the question and the answer are logically and semantically "bullet proof" but if not, I think it should be possible to fix it so that it is. ???

In case that last variation made sense, then continuing the theme...

5-door insane variation:

Assume a similar set up to the last variation, but now there are 5 guards (you don't know which is which) and 5 doors.

One guard always tells the truth.

One guard always lies.

One guard is insane and consistently alternates (as described above).

One guard is a duplicate of one of the above 3 guards (but you don't know which).

One guard alternates between acting like each of the above 4 guards (alternating for each evaluatable atom in your question), in an unknown but consistent order. Assume that it remembers whether the insane guard was last truthful or dishonest, and acts appropriately.

What would you ask?

Grenade?

Does a grenade correspond with danger, not in meaning but in terminal sound of the two words?

I'm having a discussion with several folks about the results of a head on collision of two similar vehicles that have about the same weight and crush properties. I stated that if both vehicles collide head on, at 60 MPH, the impact force and damage to each vehicle would be roughly the same as hitting a solid unmoveable object at 60 MPH, because each vehicle absorbs roughly 50% of the damage.

 

They claim that because both vehicles are traveling at 60 MPH, their combined speed of 120 MPH would increase the damage to twice what it would be if the vehicle hit a solid object at 60 MPH.

 

How can I explain this to them?

Another way to think about it or explain it is that the head-on with each traveling 60 MPH would be like a car traveling 120 MPH slamming head on into a stationary car (in neutral). This would be softer than hitting say a wall (lower deceleration over a longer period of time compared to say brick wall), and the total mass of 2 mangled car should continue moving at half speed (60 MPH -- lower overall deceleration compared to say a brick wall).

If you explain it using the example of a 120 MPH car hitting a movable stationary car, it's clear to see that this isn't the same as hitting an immovable obstacle. With the former your velocity changes by 60 MPH; with the latter it changes 120 MPH.

To clarify a vague idea that I'd posted earlier in this thread:

Doesn't the OPERA result (if verified) only show that the "group velocity" of the neutrino density exceeds the speed of light? Only the amplitude of the probability of detecting a neutrino has been measured and/or interpreted to be exceeding c. In this case, the actual neutrinos would be traveling at slightly less than c, but the probability of detecting them would travel faster. Essentially this would mean that a signal of sparse neutrinos would become easier to detect just before a dense group of neutrinos arrives.

If this is so, then it doesn't necessarily violate relativity. It is already known that a group velocity can exceed c without violating relativity. http://en.wikipedia..../Group_velocity

Also, it would still be impossible to use this to send information faster than c (because you can't determine the changing probability of detecting a neutrino based on a single detection of a neutrino. For 2 or more positive detections, I don't know how the probability would be calculated, but I'll note again that the determination of v > c is based on a best fit of a graph consisting of a lot of neutrino detections over relatively long times, and certainly as the timescale and number of detections decreases the certainty of a change in probability amplitude also decreases. My contention would require that it is theoretically impossible with the OPERA setup to detect a change in the probability amplitude within 60 ns after a measurement (detection of a neutrino)... so that a "dense group of neutrinos" would still arrive before you could detect any change in the probability that it is coming. I have no idea how this would be determined).

Still, this would be considered revolutionary maybe?, because it would demonstrate something like the wave function of some matter being affected by other remote matter. But I don't think it would invalidate any accepted theories that I know of.

This is all speculation and I only know slightly more about what I'm talking about than I did before, which still isn't a lot, but I'm still betting that this is the cause of the OPERA results (admittedly mostly because "I want to believe").

Great question - head full of thoughts but not enough maths. Will put down thoughts later.

 

I hope this is close to being correct

That's correct to the best of my knowledge.

Suppose two snails are having a race.

They both start out at a speed of 1m per day, but they both will slow down:

After every hour, snail A reduces its speed by half.

After every milliimeter covered, B reduces its speed by half.

If the race is 1m long, who would win?

Heh, k, I give up.--What are you?

Go on, take a guess! What's there to lose?

I've already given out so many clues:

Meanings of words. Stems, and danger

The riddle is strange, the answer yet stranger

"Actually?" So it's settled then and those ISASS conferences and papers on spacetime were in vain... probably just a bunch of crackpots anyway.

Cap 'n R admitted that spacetime is not ontologically real when he likened it to a "tie-died rabbit pelt", a non-entity, yes, just a "model" used conceptually in Minkowski's 4-D "spacetime", with no claim to existence as an entity.

Wrong thread.

However, the volume, and therefore the mass, of objects with the same density is proportional to r³.

Yes, where r is the radius (or side length, etc) of the mass.

With astronomical sizes of nebulae, the mass would be astronomically larger (note the 3 dimensions of emphasis!).

Note that this use of r is different from the previous use, where it was used to denote distance from us. However, the ratio of radius_nebula/distance_nebula was chosen to be the same as radius_moon/distance_moon. -- So in this case I guess it's proportional to r³ whether r is radius or distance.

Even though the mass of the mythical moon-density nebula is cubically proportional to r,

its gravitational pull is only linearly proportional to r, as described earlier.

It would still be astronomically greater though, because the radius of the nebula is astronomically many times the moon's.

If it had the same density as the moon i predict that it would form a black hole.

I guess thats just my logic, the mass will clump together and a massive black hole would form.

Scary thought though

I agree.

The idea of a nebulae-sized moon-like mass is pretty absurd in reality.

I'm sure that it would have many (billions of?) times the mass of the entire universe.

Even the sun is a lot less dense than the moon.

I was thinking of calculating it for comparison, but I feel too lazy to.

Nor can "it" be "woven together with space" to create the "fabric of spacetime" as many of the critics in the ISASS contend.

Actually, it can.

The result is a model with well-tested correspondence with observed reality.

Ugh, yawn. I guess the supply of troll food ran out in the other thread. Plenty of fresh blood here! Start suckin!

Dude, this was started in August--when was the answer on the horizon?

 

~suspense is meant for the short term, what'r you doing?

 

 

Blurgh, sorry, thought everyone's forgotten the thread.

It seems that at least it had slipped from my head.

Who am I then? Certainly you don't know me.

Find out and what I mean I'll no longer be.

I am a word, and I have more than one stem,

It takes some license to remove one of them,

but if I've become stronger (look at me, see that I am)

put back the stem and I'm where I began.

In what sense correspondence? Its mention was terse.

It's of terminal sounds of words or of lines of verse.

As riddles go, this one's about fun as cancer

You might roll your eyes when you find out the answer.

there is no such thing as an arrow of time. The only arrow of time which holds any meaning is the psychological arrow of time.

What about causality? Does it work in reverse identically to forward?

What about non-determinism? Certainly the past is determined; does that mean the future must be? Or is the future undetermined and so is the past (if we reverse time we get a different past)? Are you speaking from opinion/belief, or from the standpoint of accepted science?

What about entropy? It has a meaningful arrow.

More specifically, I meant can it be proven that the decimal expansion of a real number has COUNTABLY many symbols to represent it. A proof of this would make my original post make "no sense".

Still out of my league but for fun:

Yes. By the very nature of a "decimal expansion"... just map the n'th decimal place to the n'th natural number, and you have a 1-1 mapping between the number of digits and the natural numbers.

If you have an infinite number of digits on both sides of the decimal (not sure if that makes sense) then alternate between them when counting. The even naturals will map to the digits on one side of the decimal, and the odds will map to digits on the other side.

Thank you for the replies.

 

I think the problem can be summarized as follows:

A cardinal number greater than that of the real numbers can be shown to exist.

If a set with this cardinality could be constructed, then clearly we could construct this paradoxical number I spoke of earlier.

But there is no reason to assume a set with this cardinality can be constructed just because we can show its existence.

 

Thus, the paradoxical number can be shown to exist if the set with cardinality greater than that of the Real Numbers can be constructed.

 

My understanding is that the axioms which would allow for the construction are somewhat open questions, or are not generally excepted in the mathematics community.

I'm out of my league, but I think there are further problems.

See http://en.wikipedia.org/wiki/Aleph_number

The cardinality of the set of symbols representing digits in your proposed irrational number would be countably infinite and so would be aleph-naught.

The cardinality of the reals is 2^aleph-naught, and the set is uncountable. It sounds like the "continuum hypothesis" implies that this really is a valid form of "infinity plus one".

I suspect that the ability to construct a set is similar to the ability to count it, so you could construct a set of symbols representing the digits of an irrational number -- or at least you could construct every given symbol in that set, which I guess isn't the same as constructing the complete set. Either way you couldn't do the same for the set of reals.

I would say that setting C to infinity and then manipulating it arithmetically and expecting relations to hold (like 2^C > C) is an error.

Anyway, your statements above might still be logically true in that "If we can do something impossible, then we can do something else impossible."

The element of the Real Numbers, doesn't have to be (and can't be) infinity. I was thinking more of an irrational number, for instance e. An irrational number has an infinite decimal expansion. If each of these symbols of it's decimal expansion is put into a set, then this set, one would think should not be able to have a cardinality greater than the real numbers. But we could conceive of a number which, when the symbols of it's decimal expansion are put into a set, that set has a cardinality which is greater than the real numbers.

You mean like "infinity plus one"?

Yes, I misread what you wrote. I think the mistake is in treating infinity as a normal number. But the number you're imagining would be a real number. It just wouldn't require "more than infinity" symbols to describe it.

I expect that if had lived another 20 years there would have been some future "cooler" gismos out there

Is that, "there would have had been", or perhaps "there would soon be"?

I suppose you mean relative to the number or quality of future "cooler" gizmos that we should still expect.

It will just have to be someone else who makes them a reality. I suppose if there's something we can learn from Jobs, it's that... If you think that something is possible, don't rest until someone else makes it a reality. That's not meant as an insult; Jobs was a leader more than an engineer, and if we all did only what we're capable of doing ourselves, then we'd probably mostly give up soon after dreaming up an idea.

If more of us work with persistence to make imagined possibilities real, we should have some pretty cool gizmos in the next 20 years.

The cardinality of the reals is infinite.

You're right in that infinity is not in the reals.

Intuitively thinking of this number (infinity) as a real number is the error.