Time Constant

Hi everyone, I'm new to this - not just discussing physics questions, but chat room protocol too. So feel free to help me out if there is an existing topic I can link into (or I've interupted a coffee break!).In brief, one of the things that occurs to me is that in the Thompson’s lamp paradox it is suggested that as the lamp is turned on and off in ever decreasing time intervals (halved each time), at some point it will be impossible to say whether it is on or off.But this seems to me to simply be a mathematical expedient stating that it would be in a state somewhere between on-ness and off-ness. This is only an averaging device and does not tally with reality (recall Zeno's paradox where you can never finally reach the far side of a room because you continually have to travel half the distance to get there - and again - and again...., but actually you do!).Ok, so why will it be either on or off and not somewhere in between?It seems to me that one explanation is because at a certain point in the series time can no longer bifurcate. Time no longer has the capacity to shorten its length in order to allow another switch to be achieved. So, in the series 128, 64, 32, 16, 8, 4, 2, 1 (being the shortest unit of time imaginable) the next number in the series will be 1. And any further attempts to produce even a shaving off the time will produce the next number 1.My question then is what would be the point of having a time unit smaller than that necessary to carry out the fastest string oscillation possible within the laws set? Oh, they’re not set! Ok then, well faster than those required to maintain a string in any of the observable mathematical patterns known to date?If there isn't one, couldn't we be looking at a standard minimum time constant?

A common statement of the paradox: Another "paradox" that comes from a misunderstanding of countability, same as Zeno's paradox.
Basically think of it this way. The lamp is turned off and on an infinite number of times. Let's assign a number to each time it switches its state.1 = On
2 = Off
3 = On
e.t.c.So for my sequence above, the lamp is On for odd steps and Off for even steps. The paradox then asks is the lamp on or off at the last step. If you think about it, this is the same as asking if the "last" integer is odd or even. There is no "last" integer, the question is nonsensical.The smallest time scale possible in reality is suggested to be 10^-43 seconds. As no action could be performed quicker than this.

and just what "enth" is -43? just for those of us who don't really understand numbers that small or large.

10^-43 is one ten million million million million million million millionth.Does that help ?

In terms of the quickest 'action' I assume we are talking about vibration in superstring theory here. Can you help me understand what such an action would consist of (in broad terms)?

Make it a young man and a young woman moving towards each other. Theoretically they will never meet ...... but they will get close enough for all practical purposes.Likewise the switch will melt long before you reach an unmeasurable interval.Theory is fun, practical is the foundation that good theory rests on.Welcome to the fray!Enjoy.

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Remeber the paradox comes from a time and place where questions about pure mathematics were phrased using crude (impossible) physical situations. The question is attempting to ask "Is there a sensible limit to a countable sequence with two states?". The answer is no, as it eventually turned out.
It isn't a question about reality or lamps to begin with, so in similar paradoxes try to break it down into what it is really asking and avoid refuting it on physical grounds, similar to Zeno's paradox. It doesn't necessarily have anything to do with String Theory, rather it is the time taken to cross the smallest unit of distance, 10^-35 meters, when moving at the speed of light.
Basically, nothing can happen quicker than moving the shortest possible distance at the fastest possible speed.

nope.I get confused with billion billion.I gather its damn large. I want to know just how. like, how much smaller than a pico (which I think is one order smaller than nano, and nano, is, if I'm right, one-billionth).

Is there any way to know for sure that the Plank distance is indeed the shortest possible distance?

Why can't you just take our meta-matha-physical bullshit on the chin, and repeat "thank you sir, may I have another?" like all the others???Anyway, awesome question but minus a mark for missing the c in Planck!Of course there is no way to know for sure becasue to probe such length scales you are talking about staggering particle energies. But from theory, you are essentially at the point where those probe energies at that length scale create energy densities such that you are creating Planck scale black holes and other interesting space-time anomalies.We think of space-time seething and bubbling at that scale, something we call the quantum foam (it is from the foam that we dream of extracting a wormhole and blowing it up to usable size - uh, sorry, forgot I'm not supposed to talk about that - classified, you know) As distance is defined by the metric field, and we are saying that the metric field is in a state of indefined qunatum flux, you can perhaps see that any sense of real distance has broken down.You have to remember that our present understanding suggests that distance is not fundemental but a high level concept similar to electromagnetic field strength.That said, you can't trust everything here. We know that extrapolating GR ideas to that scale is problematic. The electron is a case in point. According to GR, the electron should be what we call a naked singularity black hole, but it doesn't appear to act like one (though we don't really know what a naked singlarity should behave like!)

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According to GR, the electron should be what we call a naked singularity black hole, but it doesn't appear to act like one (though we don't really know what a naked singlarity should behave like!)

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Huh! I've always wondered about that. Thanks.

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Is reality indeed quantized? According to QM it is. So how convienant is it to have the strings be set at the limit of what can be measured. How convientant to have them vibrate at the needed tensions. How "elegant" lol...to quote Brian Greene. Bah Humbug!!If there is no way to observe the unobservable. As the Church Lady would say: "How convienant."

Funny you should mention that. Some years ago I had an idea for a short sci-fi story based on the proposition that someone could induce a frequency resonation in a single string such that it alternated rapidly between some ”normal’ state and one approaching a black hole singularity. In the story they used it to bend light infront of a subject in order to correct their eyesight! Needless to say there were unusual consequences involving the manipulation of the space/time matrix!! (Sort of ”Time Bandits’ meets ”Tales of the Unexpected’).But I digress . This is a perfectly reasonable and, I daresay, well accepted argument. I don’t refute the sense of it.
The problem for me (and I am no more than an enthusiastic amateur - so as soon as I’ve posted this I’ll be donning me flack jacket and taking cover under the stairs) is what happens to the relationship between time and mass if a Planck lengthed something (I’ll use the string analogy because a) it is perfectly likely, and b) because it is easier to understand) is forced to try to vibrate at a rate faster than the time minima will allow?To my mind it has at least 3 options;1. It can blink out of existence within its current universe and enter the foam or whatever.
2. It can conform to a vibrational state that is allowable within the time minima constraint (note that its not necessarily trying to move a shorter distance than the distance minima)
3. It can freeze and stop vibrating altogether.And if a string stops vibrating altogether, can it continue to have a mass value greater than zero? (If I understand correctly, a photon, which has a mass value of zero, is necessarily unaffected by the speed of light - and presumably doesn’t vibrate according to string theory).
Here then is the dilemma - if a string simply freezes or is made to ”conform’, wouldn’t it still carry an energy potential a bit like kinetic energy (ie. it was vibrating away just now, but was made to stop because of universal time constraints), but have no mass? If so, would it necessarily have to become a photon, or could it just sit there being an energy potential with no mass (like dark matter??).

No takers huh?

How do you force something to vibrate at such an energy? The Planckian energy input would be sufficient to ensure you've now got a black hole, so the situation would not arise. All particles we know are essentially massless when it comes to strings, and they gain their mass via some high-level mechanism (e.g. Higgs). Massive string modes are really really massive!Also, dark matter is not massless - it would be bloody useless if it was given that it is supposed to explain localised gravitational inconsistencies (on the galactic to cluster scale)