4 ms·

Since c is a velocity, 1/c doesn't have units of time; it has units of time/distance. Special and general relativity (at least, as commonly formulated) also as

by aphyr 13y ago

Since c is a velocity, 1/c doesn't have units of time; it has units of time/distance. Special and general relativity (at least, as commonly formulated) also assume that space and time are isotropic and continuous, which means there is no "granule", no "smallest increment" in the field equations. That may or may not be true; we're still trying to figure out if spacetime is quantized or not.

DougWebb 13y ago
Does anyone know what Wolfram would say about the tickrate? I bought the huge book and know that he believes space is quantized, at least, and I assume he believes time is as well, as the rate the universal state machine changes states. But I never read enough to learn what he thinks that rate might be.
- shmageggy 13y ago
  My impression is that Wolfram came to such conclusions because he is obsessed with cellular automata and with their mathematical universality in discrete domains. Of course, they are useless in continuous domains, so it would be ruinous to his world-view if the universe were continuous. So it's a bit like ancient metaphysics a la Plato and Co., where the properties of the universe are inferred from first principles (which come from... where, exactly?) rather than from any empirical observation. A review of Wolfram's book: http://vserver1.cscs.lsa.umich.edu/~crshalizi/reviews/wolfram/ http://vserver1.cscs.lsa.umich.edu/~crshalizi/reviews/wolfra...
  - rossjudson 13y ago
    Fuzzy automata are perfectly happy in a continuous domain.
  - dclowd9901 13y ago
    If reality propogates into infinite possibility subuniverses, would it not be accurate to assume that each of those subuniverses must come from some "tick" of state (or delta of state, rather)?
    - aphyr 13y ago
      I wouldn't say so. Many-worlds is an interpretation of QM, and to my knowledge, all verified QM formalisms treat time as a continuous parameter; not a discrete one.
- aphyr 13y ago
  Cellular automata violate continuity and isotropy, which means they're inconsistent with the continuous spatial formalism used in special relativity, general relativity, classical electrodynamics, and as far as I know, quantum electrodynamics. We have no experimental evidence inconsistent with continuous models of space. We also have evidence that Lorentz symmetry holds over scales smaller than the Planck length, which suggests spacetime is not quantized. One of the problems with quantized spacetime is that the cells would have a size--and sizes change depending on your velocity. Were spacetime to be comprised of cells, you'd be able to establish a single, most privileged reference frame--and that doesn't sit well with the principles of relativity. That said, we really don't have good models for what happens at small spacetime scales yet. Gravity is poorly understood. Theories change as new evidence and mathematics develop. I just wouldn't trust Wolfram's opinion without either a.) experimental evidence or b.) a model which is consistent with (or radically reformulates) significant parts of relativity and quantum electrodynamics.
  - aphyr 13y ago
    Ah, here we go. Aaronson 2002 shows that Wolfram's model cannot be consistent with experimental evidence: In physics, we examine Wolfram's proposal for a deterministic model underlying quantum mechanics, with 'long-range threads' to connect entangled particles. We show that this proposal cannot be made compatible with both special relativity and Bell inequality violation. http://arxiv.org/abs/quant-ph/0206089 http://arxiv.org/abs/quant-ph/0206089
    - 3rd3 13y ago
      For some interesting reads: Just take a look at the summaries, introductions and conclusions in Aaronson’s publications.
  - tokipin 13y ago
    I want to point out that Wolfram doesn't think the universe is a giant cellular automaton. He gives CA as examples of how easy it is to produce impermeable complexity. His more serious proposal is a graph-based system, though I haven't perused enough to know if that's also for the sake of example or if it's intended to be taken as a serious physical theory. Most likely it's an earnest attempt at a heuristic towards the goal of, in his terminology, "finding the program of the universe."
chinpokomon 13y ago
Which is where quantum mechanics comes into the picture. If we could measure something in Planck units, we might discover that there is a smallest increment. Of course Nyquist implies that we may only be able to measure something at most, twice that unit size... but that is still on a scale far beyond our reach.

by aphyr 13y ago

DougWebb 13y ago

Does anyone know what Wolfram would say about the tickrate? I bought the huge book and know that he believes space is quantized, at least, and I assume he believes time is as well, as the rate the universal state machine changes states. But I never read enough to learn what he thinks that rate might be.

shmageggy 13y ago
My impression is that Wolfram came to such conclusions because he is obsessed with cellular automata and with their mathematical universality in discrete domains. Of course, they are useless in continuous domains, so it would be ruinous to his world-view if the universe were continuous. So it's a bit like ancient metaphysics a la Plato and Co., where the properties of the universe are inferred from first principles (which come from... where, exactly?) rather than from any empirical observation. A review of Wolfram's book: http://vserver1.cscs.lsa.umich.edu/~crshalizi/reviews/wolfram/ http://vserver1.cscs.lsa.umich.edu/~crshalizi/reviews/wolfra...
- rossjudson 13y ago
  Fuzzy automata are perfectly happy in a continuous domain.
- dclowd9901 13y ago
  If reality propogates into infinite possibility subuniverses, would it not be accurate to assume that each of those subuniverses must come from some "tick" of state (or delta of state, rather)?
  - aphyr 13y ago
    I wouldn't say so. Many-worlds is an interpretation of QM, and to my knowledge, all verified QM formalisms treat time as a continuous parameter; not a discrete one.
aphyr 13y ago
Cellular automata violate continuity and isotropy, which means they're inconsistent with the continuous spatial formalism used in special relativity, general relativity, classical electrodynamics, and as far as I know, quantum electrodynamics. We have no experimental evidence inconsistent with continuous models of space. We also have evidence that Lorentz symmetry holds over scales smaller than the Planck length, which suggests spacetime is not quantized. One of the problems with quantized spacetime is that the cells would have a size--and sizes change depending on your velocity. Were spacetime to be comprised of cells, you'd be able to establish a single, most privileged reference frame--and that doesn't sit well with the principles of relativity. That said, we really don't have good models for what happens at small spacetime scales yet. Gravity is poorly understood. Theories change as new evidence and mathematics develop. I just wouldn't trust Wolfram's opinion without either a.) experimental evidence or b.) a model which is consistent with (or radically reformulates) significant parts of relativity and quantum electrodynamics.
- aphyr 13y ago
  Ah, here we go. Aaronson 2002 shows that Wolfram's model cannot be consistent with experimental evidence: In physics, we examine Wolfram's proposal for a deterministic model underlying quantum mechanics, with 'long-range threads' to connect entangled particles. We show that this proposal cannot be made compatible with both special relativity and Bell inequality violation. http://arxiv.org/abs/quant-ph/0206089 http://arxiv.org/abs/quant-ph/0206089
  - 3rd3 13y ago
    For some interesting reads: Just take a look at the summaries, introductions and conclusions in Aaronson’s publications.
- tokipin 13y ago
  I want to point out that Wolfram doesn't think the universe is a giant cellular automaton. He gives CA as examples of how easy it is to produce impermeable complexity. His more serious proposal is a graph-based system, though I haven't perused enough to know if that's also for the sake of example or if it's intended to be taken as a serious physical theory. Most likely it's an earnest attempt at a heuristic towards the goal of, in his terminology, "finding the program of the universe."

chinpokomon 13y ago

Which is where quantum mechanics comes into the picture. If we could measure something in Planck units, we might discover that there is a smallest increment. Of course Nyquist implies that we may only be able to measure something at most, twice that unit size... but that is still on a scale far beyond our reach.