Do we ever real reach a moment in time?+

[SamBridge]

Time is continuous because it can be indefinitely broken down into indefinitely smaller increments, which implies that the limit of spacing between the smallest unit of time is zero. There is no single unit or discrete interval which you can settle on to say that all larger units of time occur from or are compounded from, so it must be continuous, or smooth. This property of smoothness is also invariant of objects specified to be smooth or continuous, you cannot have a mathematically "less continuous" or "more continuous" line, either it is continuous at every point or it isn't. If time were however discrete, we would find that we can only measure events passing at a rate up to a specific interval of time, which we have not, you can get indefinitely closer to the speed of light and therefore measure an indefinably smaller rate at which time passes for other objects.

[Alan McDougall]

Time is continuous because it can be indefinitely broken down into indefinitely smaller increments, which implies that the limit of spacing between the smallest unit of time is zero. There is no single unit or discrete interval which you can settle on to say that all larger units of time occur from or are compounded from, so it must be continuous, or smooth. This property of smoothness is also invariant of objects specified to be smooth or continuous, you cannot have a mathematically "less continuous" or "more continuous" line, either it is continuous at every point or it isn't. If time were however discrete, we would find that we can only measure events passing at a rate up to a specific interval of time, which we have not, you can get indefinitely closer to the speed of light and therefore measure an indefinably smaller rate at which time passes for other objects.

 

As far as known physics, your statement above underlined in green is incorrect

 

Plank divided both length and time into discrete quanta, thus, according to this very enlightened physicists you cannot go on breaking down time into infinitesimally smaller and smaller discrete units as you suppose

 

The smallest possible unit of discrete time is the Planks Constant of .00000000000000000000000000000000000000000001s

 

This is an unimaginably tiny infinitesimal of time

 

https://en.wikipedia.org/wiki/Planck_length

 

The Planck length is about 10⁻²⁰ times the diameter of a proton, and thus

is exceedingly small; it is considered the smallest length known/possible, also

see quantum

foam.

 

 

 

[SSDS]

Time is continuous because it can be indefinitely broken down into indefinitely smaller increments, which implies that the limit of spacing between the smallest unit of time is zero. There is no single unit or discrete interval which you can settle on to say that all larger units of time occur from or are compounded from, so it must be continuous, or smooth. This property of smoothness is also invariant of objects specified to be smooth or continuous, you cannot have a mathematically "less continuous" or "more continuous" line, either it is continuous at every point or it isn't. If time were however discrete, we would find that we can only measure events passing at a rate up to a specific interval of time, which we have not, you can get indefinitely closer to the speed of light and therefore measure an indefinably smaller rate at which time passes for other objects.

 

 

To state so is necessary to understand – what is the time? For that seems useful to read http://arxiv.org/abs/1110.0003 (for Matter in our Universe).

Besides – if the continuum hypothesis is true, then the cardinalities of the continuum set and of the “discrete” power set of the natural numbers set, 2^N, are equal, so the continuous and the discrete are in certain sense equivalent; so the time can be discrete (by some way) also.

 

Cheers

[swansont]

 

As far as known physics, your statement above underlined in green is incorrect

 

Plank divided both length and time into discrete quanta, thus, according to this very enlightened physicists you cannot go on breaking down time into infinitesimally smaller and smaller discrete units as you suppose

 

The smallest possible unit of discrete time is the Planks Constant of .00000000000000000000000000000000000000000001s

 

This is an unimaginably tiny infinitesimal of time

 

https://en.wikipedia.org/wiki/Planck_length

 

The Planck length is about 10⁻²⁰ times the diameter of a proton, and thus

is exceedingly small; it is considered the smallest length known/possible, also

see quantum

foam.

 

The Planck scale units are not what many people claim they are. AFAIK, they are the scale at which quantum gravity is important and classical explanations necessarily break down. This does not make them the smallest unit, or necessarily mean there is quantization at the Planck scale. The Planck mass, for example is about 22 micrograms and the Planck energy about 2 billion Joules. Anyone claiming these are the quantum units, or that we cannot distinguish below them, is bonkers.

 

Further, Planck length and time scales have not been tested. It's wrong to draw concrete conclusions from the hypothesis.

[Alan McDougall]

The Planck scale units are not what many people claim they are. AFAIK, they are the scale at which quantum gravity is important and classical explanations necessarily break down. This does not make them the smallest unit, or necessarily mean there is quantization at the Planck scale. The Planck mass, for example is about 22 micrograms and the Planck energy about 2 billion Joules. Anyone claiming these are the quantum units, or that we cannot distinguish below them, is bonkers.

 

Further, Planck length and time scales have not been tested. It's wrong to draw concrete conclusions from the hypothesis.

 

Please then give a smaller scale of units in which our reality has meaning?

[swansont]

Please then give a smaller scale of units in which our reality has meaning?

 

I'm not sure what you mean. Masses smaller than 22 micrograms are discernible, as are energies below 2 billion Joules.

[md65536]

Please then give a smaller scale of units in which our reality has meaning?

Not having meaning (as I think Planck time implies according to current theory???) and not being possible (as you wrote earlier) are two different things.

 

Smaller units of time would need a working theory of quantum gravity to make sense, and since we don't have that, we don't know what the meaning of smaller times would be. It neither makes sense to say you can keep breaking time down into smaller units, nor that it's impossible to. No accepted current theory answers that.

 

So whether time is quantized is not answered, but treating Planck time as a quantum of time doesn't mean that time actually divides into discrete pieces, it just means that speaking of smaller pieces has no known physical meaning or measurable effect.

 

 

 

 

This is based on what I think I know and I'm certainly no expert.

[Alan McDougall]

I'm not sure what you mean. Masses smaller than 22 micrograms are discernible, as are energies below 2 billion Joules.

 

I am talking about length, I don't think you can go on subdividing a line forever of to nearer and nearer infinitely smaller and smaller divisions. There must be a limit and at present Planks Constant as it refers to length seems the best answer.

[swansont]

I am talking about length, I don't think you can go on subdividing a line forever of to nearer and nearer infinitely smaller and smaller divisions. There must be a limit and at present Planks Constant as it refers to length seems the best answer.

 

And I'm presenting some evidence that shows that the Planck scale is not evidence of this.

[md65536]

And I'm presenting some evidence that shows that the Planck scale is not evidence of this.

Isn't it something like: A black hole less massive than 22 micrograms makes no sense in current theory? You've shown that despite that, measurements of mass smaller than that have *other* theoretical and measurable meaning.

 

So you could argue that times smaller than a Planck time might have *other* meaning and may be measurable, but that doesn't prove that it is necessarily so, because there is no currently known such other measurable thing.

 

 

As it relates to the topic, I think you could no more certainly say "Yes, there are precise moments of time and everything passes continuously through every moment" than "No, at the smallest scale time is like a quantum foam-like thing, and particles leap back and forth with certain statistical chances of leaping clear over a quantized moment (even backward)" and I think you could build a philosophical case around either argument, maybe even using proposed theories, but you couldn't settle it using only accepted theory.

 

So while as you've shown, we currently don't rule out meaningful measurements of times smaller than Planck times, it's also true that we currently can't be certain of them.

[swansont]

Isn't it something like: A black hole less massive than 22 micrograms makes no sense in current theory? You've shown that despite that, measurements of mass smaller than that have *other* theoretical and measurable meaning.

 

I think it means that a BH with that mass doesn't make sense in GR somehow. The Compton wavelength would be of comparable size to the size of the BH, meaning the deBroglie wavelength would necessarily be larger than the BH. So you would have to account for quantum effects of that BH.

 

However, masses in general can be smaller than this.

 

So you could argue that times smaller than a Planck time might have *other* meaning and may be measurable, but that doesn't prove that it is necessarily so, because there is no currently known such other measurable thing.

 

Right. We can't measure them with our technology, but they may or may not be unmeasurable in general. We don't know.