Suppose I have a right triangle. Two of the legs are equal to planck length. Mathematically, the hypotenuse would be ~1.41421356 planck lengths. But what about physically?
Thanks.
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Suppose I have a right triangle. Two of the legs are equal to planck length. Mathematically, the hypotenuse would be ~1.41421356 planck lengths. But what about physically?
Thanks.
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You mean, if three objects were separated by those pair of measurements? Would the third leg agree with the Pythagorean theorem? Or would the physical forces act, as if the third leg agreed with the Pythagorean theorem?
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Both. They're both what I was trying to get at and something I would certainly like to know. Sorry for being a bit vague D:
I guess at the heart of this is, how long would it take a photon to traverse the hypotenuse? Planck time? Two planck times?
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Are they bigger, or smaller, than a Planck mass?
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I don't understand how that's relevant.
I hadn't imagined the triangles legs to have mass.
What would happen if the legs are bigger than Planck mass?
What would happen if the leg's are equal to Planck mass?
What would happen if they were less than Planck mass? (am I correct in guessing that such isn't possible?)
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I meant the three objects.Originally Posted by Hungry4info
A Planck mass is about 22 micrograms. I think it might be possible to see with the naked eye something with a Planck mass.What would happen if they were less than Planck mass? (am I correct in guessing that such isn't possible?)
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well, the hypotenuse is found by taking the square root of x^2+y^2 (x squared plus y squared) where x and y are the lengths of the other sides of the triangle.
so your answer would be c (the speed of light) over the hypotenuse (the distance)..
is that right??
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Ah. The objects. What about for all three options? (I didn't know planck mass was so large).
It makes sense but it seems naive. Planck length is the smallest meaningful length, so I'm not sure what a distance of a non-integer amount of planck lengths would physically mean.
Edit: Just found a reference saying that contrary to popular belief, space isn't quantized into planck lengths. I'm no longer convinced that my question is really as meaningful as I thought, but I'll stick through and see where this leads.
Last edited by Hungry4info; 2010-Feb-14 at 06:46 AM. Reason: Ugh, found myself misinformed.
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Maybe the hypotenuse would be both one and two?
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Really?Maybe the hypotenuse would be both one and two?
Anything sandwiched between planck units of something is considered to be both of them?
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it seems like you answered your own question.
the square root of (1.61×10−35 meters)^2 + (1.61×10−35 meters)^2
2.5921e-70 + 2.5921e-70 = 5.18e-70
the sqr root of 5.18e-70 is
2.26x10-35 meters
so how long does it take light to travel 2.26e-35 meters?
299792458 m/s is c (the speed of light)
1.32 x 10 -43 seconds
which is almost as fast as a plank time..
(5.3x10-44 seconds)
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Sabianq, I know how to do the math...
I'm asking for the physical interpretation
What does almost a planck time actually mean?
(if planck length is how far light moves in planck time, then the hypotenuse would be traversed by a photon in more than planck time since the hypotenuse is longer than the legs)
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It is the time required for light to travel, in a vacuum, a distance of 1 Planck length..
lol
http://en.wikipedia.org/wiki/Planck_time
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hmmm...
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sabianq, please stop toying with me.
If time is quantized into units of Planck time (as I've heard thrown about), then what physically would non-integer units of Planck time mean?
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No, I said "maybe"
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yes, it takes light a little longer to travel the distance equal to the hypotenuse of a right angle with sides equal to a plank length..
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the answer is the square root of planck length squared plus planck length squared
what 1.414 planck time?
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That's a new one on me. I've heard that the Planck Time and Planck length are the smallest meaningful distances and times. But, I've never heard it claimed that they are quantized at that level.
If, however, they are quantized at that level, then there wouldn't be any meaning to non-integer units, of those types. It would be like having non-integer units of spin or non-integer units of h-bar.
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If we're considering a triangle whose sides are measured in (single) planck lengths, then surely it would be impossible to say that two of the sides are at right angles? One cannot use a planck-sized protractor!
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True. do we know how the curvature of spacetime affects measurements at that scale? Can we even be sure a planck-sized triangle has 180 degrees? Or is area a limiting factor? What would the lenths of the side of a trinagle with an area of 1 planck-length(sqrd) be?
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It would really depend on the curvature of space-time. Actually, since space-time probably wouldn't be Euclidean, it would be possible to have three right angles and have not only two, but all three legs be one Planck length long.
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That's what I was getting at. In this case, you don't have to define (sqrt)2 h.
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What does "meaningful" mean in this context? (if not quantized)
ETA: I have seen it implied, if not explicitly stated, in popular science articles that they are quantized.
ETA: http://www.physlink.com/Education/As...?CFID=25709718 says (or strongly implies) they are quantized.
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Interesting idea about non-Euclidean geometry in the case of a triangle. But it would seem to only work for the case of a triangle. What if we have a pentagon with lengths of planck length, how long would it take for a photon to go from one vertex to any other non-adjacent vertex?
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I assume you mean from one vertex to a non adjactent vertex, not travelling along the edges.
If it can't travel in non-integer amount planck time or planck distance, I would say that it follows a curve (on a plane prepandicular to the plane with the pentagon, for example) such that the total distance travelled and travel time (both in planck units) are integers. This might be the reason that extra degrees of freedom are necessary, and why they are so small: they're not observable in scales that don't vary at that degree. Or, it might just be nonsense.
Order of Kilopi
Meaningful means, that, at present, our equations don't really work at distances smaller than a Planck length, nor is there any reality to anything smaller. Look at size of the Planck length ~1.6 x10[dup]-35[/sup]m. Electrons and quarks are thought to be point particles. But in actual measurements, electrons have been found to have a maximum quantum radius of ~10-22 m. Even if the electron's size is off by a couple of order of magnitude, you'll notice that this is still huge compared to the planck length. If the smallest thing we can measure is orders of magnitudes larger than the Planck length, then how meaningful is it?
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I'd agree with that. It maybe makes sense to think of it like the resolving limit for a telescope. There is a smallest possible size of feature that we can make out, but that does not mean that bigger objects have to look like integer multiples of this limit. We don't assume that the universe is a grid marked out in Planck lengths, with particles destined to sit only at the nodes, but, even if we did, that would still not mean that every separation was a multiple of the grid size.
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I just skipped to the end here, I apologize if this has been addressed.
For this discussion, you have to separate natural and observational. The shortest distance in nature is not a Planck length. There surely exist 'things' smaller than 1 planck length (be they particles, strings, lengths of space, etc.), or the 1 planck length 'grid' would be well known, and scientists would rejoice in having found the lower limit of the universe. This, however is not the case. The reason the planck length is the smallest meaningful measurement is due to our shortcomings as observers. The problem is that once you get down to distances shorter than 1 planck length, the energies required to make measurements are so great that they have a significant effect on the quantities measured. Because of this, the unceartainty of the measurements is greater than the values measured. So, quite literally, measurements at smaller than planck scale are meaningless, and although the planck length may not be the smallest 'natural' distance (if such a thing even exists) it is the smallest observational distance.
In fact, many theorists believe that this is why physics has hit a dead end. We have come to the point where we can continue making discoveries through pure mathematics, thought experiments, and the study of contradictions and paradoxes, but it may not be possible to learn anymore through physical experimentation and direct observation.
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