What is your interpretation of quantum mechanics?

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Offline dlorde

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Re: What is your interpretation of quantum mechanics?
« Reply #100 on: 05/06/2013 23:34:46 »
It should take infinite time to reach the end of an infinite series. 
I can do it in a finite time, and I can even prove it.
Cool, let's see the proof.

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Offline lightarrow

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Re: What is your interpretation of quantum mechanics?
« Reply #101 on: 06/06/2013 10:01:17 »
It should take infinite time to reach the end of an infinite series. 
I can do it in a finite time, and I can even prove it.
Cool, let's see the proof.
Ok. I have set to take 1 second to reach the first term of the series, 0.5 seconds to reach the second term, ... (1/2)n-1 seconds to reach the n-th term, ...
Summing all the times, I reach the end of the series in 2 seconds.

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Offline Bill S

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Re: What is your interpretation of quantum mechanics?
« Reply #102 on: 06/06/2013 16:01:09 »
Quote from: ligharrow
Ok. I have set to take 1 second to reach the first term of the series, 0.5 seconds to reach the second term, ... (1/2)n-1 seconds to reach the n-th term, ...Summing all the times, I reach the end of the series in 2 seconds.

No; because when you reach the n-th term, or any other, you are still infinitely far from the (non-existent) end.
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Offline lightarrow

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Re: What is your interpretation of quantum mechanics?
« Reply #103 on: 06/06/2013 20:35:58 »
Quote from: ligharrow
Ok. I have set to take 1 second to reach the first term of the series, 0.5 seconds to reach the second term, ... (1/2)n-1 seconds to reach the n-th term, ...Summing all the times, I reach the end of the series in 2 seconds.

No; because when you reach the n-th term, or any other, you are still infinitely far from the (non-existent) end.
While you worry about it, I have already reached the end in 2 seconds, as I wrote. If you don't believe it, explain how you could still be in some term of the series after 10 seconds...

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Offline Bill S

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Re: What is your interpretation of quantum mechanics?
« Reply #104 on: 06/06/2013 20:50:10 »
Quote from: lightarrow
While you worry about it, I have already reached the end in 2 seconds, as I wrote. If you don't believe it, explain how you could still be in some term of the series after 10 seconds...

Presumably, you can't; especially if your name happens to be Zeno, but then, you have not explained how you actually reach 2 seconds. 

I am in the fortunate position of not having to explain anything, because I don't accept the infinite series outside mathematics, nor do I believe you can reach infinity.  If you can arrive at the end of it, it is not infinite.
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Offline Bill S

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Re: What is your interpretation of quantum mechanics?
« Reply #105 on: 06/06/2013 20:58:43 »
Quote from: dlorde
The definition of an infinite set is that any proper subset has the same size as the whole set. The elements of the subset can be mapped one-to-one with the members of the whole set.

Surely this is the definition of a countably infinite set, so, at best it is part of the definition of a mathematical infinity.

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I don't know whether Cantor used the set of all infinite sets in his calculations (do you have a source for this?),

Incautious wording on my part.  It would have been better to have said something like: "In my limited knowledge of 2the work of Cantor, I am not aware that he actually used the set of all infinite sets in his calculations. If anyone can provide an example of his so doing I would give it my attention".  That would make more sense than my trying to give examples of where he didn't.  :)

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What precisely does the truly in 'truly infinite' mean? It is generally accepted that there are multiple infinite sets; e.g. the real numbers are infinite, the whole numbers are infinite, neither set contains the other. If you introduce your own concept of 'truly infinite' that way, you're not talking about the same thing; and I don't see how it has any coherent meaning - can you explain?

I used the term "truly" infinite so as not to confuse what I was talking about with "absolutely" infinite.  I did this because it is easy to argue, as you did, that absolute infinity is a mathematical infinity.  Indeed, I was not " talking about the same thing".   

There is also something of a question mark over the concept of absolute infinity. "...  when it is realized in the most complete form". What is the most complete form of infinity?  Does it contain all other infinities?  If not, in what sense is it absolute?  If it does, how can Barrow say:

"Cantor’s most dramatic discovery was that infinities are not only uncountable, they are insuperable.  He discovered that a never-ending ascending hierarchy of infinities must exist.  There is no biggest of all that can contain them all.  There is no Universe of universes that we can write down and capture." 
 


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Offline dlorde

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Re: What is your interpretation of quantum mechanics?
« Reply #106 on: 07/06/2013 09:05:47 »
Ok. I have set to take 1 second to reach the first term of the series, 0.5 seconds to reach the second term, ... (1/2)n-1 seconds to reach the n-th term, ...
Summing all the times, I reach the end of the series in 2 seconds.
Ah, Zeno would be proud  ;)
Problem is, you're trying to do an infinite number of actions in a finite time, and each action takes a finite time (also a finite amount of energy).
From a physics viewpoint, the quantisation of energy (and probably time) prevents you going beyond a certain point.

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Offline dlorde

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Re: What is your interpretation of quantum mechanics?
« Reply #107 on: 07/06/2013 09:19:01 »
Surely this is the definition of a countably infinite set, so, at best it is part of the definition of a mathematical infinity.
The strict definition is 'A set is infinite if and only if for every natural number the set has a subset whose cardinality is that natural number'. So it covers all infinite sets.

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I used the term "truly" infinite so as not to confuse what I was talking about with "absolutely" infinite.  I did this because it is easy to argue, as you did, that absolute infinity is a mathematical infinity.  Indeed, I was not " talking about the same thing".
You have yet to define, describe, or distinguish between them.  Were you talking about Cantor's Absolute infinity?


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Offline lightarrow

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Re: What is your interpretation of quantum mechanics?
« Reply #108 on: 07/06/2013 12:09:13 »
Ok. I have set to take 1 second to reach the first term of the series, 0.5 seconds to reach the second term, ... (1/2)n-1 seconds to reach the n-th term, ...
Summing all the times, I reach the end of the series in 2 seconds.
Ah, Zeno would be proud  ;)
Problem is, you're trying to do an infinite number of actions in a finite time, and each action takes a finite time
Infact it was exactly showing that the total time were finite, that Zeno solved the paradox  [:)]
Every action takes a finite time, indeed. Infact (1/2)(n-1) is *always* a finite time. But their sums is finite as well...
You have to go over calculus?
« Last Edit: 07/06/2013 12:17:00 by lightarrow »

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Offline JP

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Re: What is your interpretation of quantum mechanics?
« Reply #109 on: 07/06/2013 13:36:43 »
I admit I haven't been following this thread that closely, so if I'm repeating someone else's thoughts, I apologize. 

Lightarrow is correct that at any particular step you take a finite amount of time, but the total time taken if you complete the infinite number of steps is also finite.  The reason its counterintuitive is that our brains aren't built to naturally handle the concept of infinity, so it takes training and practice to get comfortable with these ideas.  (If we could deal easily with infinities, calculus wouldn't be such a painful subject!)

The other question being discussed here seems to be whether infinity is physically real or not: can we find examples of infinity in nature or is the mathematics of infinity just a useful approximation to very big or very small things?  We don't know the answer to that.  What we do know is that current models do assume infinitely small things exist since space is continuous.  If I give you a length, you can always chop it in half in our current models and that is the definition of something getting infinitesimally small.  From that, Lightarrow's example/Zeno's paradox follows automatically.  Since we can't currently measure things past some very small scale, we don't know if space and time are really continuous or if there are some smallest building blocks.  In the latter case, infinitesimally small might not exist.

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Offline dlorde

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Re: What is your interpretation of quantum mechanics?
« Reply #110 on: 07/06/2013 18:39:36 »
Lightarrow is correct that at any particular step you take a finite amount of time, but the total time taken if you complete the infinite number of steps is also finite.
But, of course, you can't complete an infinite series...

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What we do know is that current models do assume infinitely small things exist since space is continuous.
Not all current models assume that; for example, Loop Quantum Gravity is quite popular, and potentially resolves the problem of singularities (by removing them).

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Offline dlorde

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Re: What is your interpretation of quantum mechanics?
« Reply #111 on: 07/06/2013 18:41:01 »
You have to go over calculus?
??

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Offline JP

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Re: What is your interpretation of quantum mechanics?
« Reply #112 on: 07/06/2013 19:10:45 »
Lightarrow is correct that at any particular step you take a finite amount of time, but the total time taken if you complete the infinite number of steps is also finite.
But, of course, you can't complete an infinite series...
Of course you can!  Lightarrow just did so mathematically.  You can't write down all the terms explicitly, but you can complete it or write the series symbolically as he did.

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What we do know is that current models do assume infinitely small things exist since space is continuous.
Not all current models assume that; for example, Loop Quantum Gravity is quite popular, and potentially resolves the problem of singularities (by removing them).

True, but those are speculative hypotheses currently.  The primary models that have been well tested and accepted (the standard model, general relativity) do assume continuous space and time.  That doesn't mean anything more than that if they are granular, the granularity is small enough that we haven't seen it yet on the scales of those models.  But on the other hand there's no evidence for granularity. 

Taking a firm stance the existence or nonexistence of physical infinities is stating an opinion without evidence to back it up.  Mathematical infinities, on the other hand, clearly exist.

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Offline dlorde

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Re: What is your interpretation of quantum mechanics?
« Reply #113 on: 08/06/2013 22:39:37 »
Of course you can!  Lightarrow just did so mathematically.  You can't write down all the terms explicitly, but you can complete it or write the series symbolically as he did.
Summing it, or writing it symbolically isn't what I had in mind. What exactly do you mean by 'complete'? It seems to me that if you could complete it, you could give me the value of the final term - but there isn't one.

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Offline yor_on

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Re: What is your interpretation of quantum mechanics?
« Reply #114 on: 09/06/2013 12:31:48 »
You can take a stretch of line, 13 cm, then split it in 13 even chunks, then split those into 26, then those into 52. Where should it end? Doesn't this depend on what mathematics you use. Probably also on where those mathematics stop producing meaningful answers. But I think you can define a infinity to a finite stretch.
=

It also goes back to if there is a 'granularity' to SpaceTime I think. If it is a 'flow' then you won't find a stop, and it should be possible to zoom in for ever. Or you can define it from what is meaningful, in which case you get two answers. One where it stops being meaningful at some scale, another that ignores what we find meaningful.
==

There is actually a third too, as I think, and that would be if it was a fractal describing a SpaceTime. On the other tentacle that should be real close to a definition of a flow.
« Last Edit: 09/06/2013 12:48:45 by yor_on »
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Offline JP

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Re: What is your interpretation of quantum mechanics?
« Reply #115 on: 09/06/2013 14:25:26 »
Of course you can!  Lightarrow just did so mathematically.  You can't write down all the terms explicitly, but you can complete it or write the series symbolically as he did.
Summing it, or writing it symbolically isn't what I had in mind. What exactly do you mean by 'complete'? It seems to me that if you could complete it, you could give me the value of the final term - but there isn't one.

He completed it by writing down an expression for all the terms and then summing them.  The set 1/2n, when n is a whole number is the expression for all the terms.  Like I said, explicitly writing out all the terms is impossible physically, since we can't write arbitrarily fast.  But since both of these methods are abstract mathematical notation for the series, why should we afford one more importance than the other in a mathematical sense?  In a physical sense, the existence of infinities is a matter of opinion whether continuous things exist or not or whether the universe is infinitely large or not--at least until we get some evidence to back up theories one way or the other.

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Offline dlorde

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Re: What is your interpretation of quantum mechanics?
« Reply #116 on: 09/06/2013 14:39:21 »
He completed it by writing down an expression for all the terms and then summing them.  The set 1/2n, when n is a whole number is the expression for all the terms.  Like I said, explicitly writing out all the terms is impossible physically, since we can't write arbitrarily fast.  But since both of these methods are abstract mathematical notation for the series, why should we afford one more importance than the other in a mathematical sense?  In a physical sense, the existence of infinities is a matter of opinion whether continuous things exist or not or whether the universe is infinitely large or not--at least until we get some evidence to back up theories one way or the other.

OK, fair enough. Defeated by the semantics of 'complete', I withdraw my statement.

However, I still can't see how an infinite number of actions can be completed in a finite time, since an action requires energy and there is a minimum energy of action (i.e. the quantum of energy transfer). Though my understanding of 'action' in this context (a force doing work on an object) may be astray too.
« Last Edit: 09/06/2013 14:42:33 by dlorde »

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Offline JP

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Re: What is your interpretation of quantum mechanics?
« Reply #117 on: 09/06/2013 15:00:17 »
Certainly there's no problem with the mathematics, since mathematics exists in a world of thought and doesn't necessarily reflect anything physical. 

Physically speaking, if space and time are continuous, then lightarrow's example is physical--if you move 2 meters, you move 1 meter + 1/2 meter +1/4 meter + 1/8 meter, etc.  Moving 1/2n meters takes 1/2n time.  Since the time and distance get arbitrarily short, there's no problem doing this.  Is space and time have some granularity and a smallest unit, then lightarrow's example will run into problems since there exists some 1/2n length that is a minimum and the smaller terms in the series don't represent anything physical.

Whether arbitrarily short time and distance can physically exist in nature is another question, and I agree with you that it may not be physical.  Personally, I tend to think it is not physical and that time and distance are granular on some scale, but I have to admit that there isn't any good evidence to support my opinion, although some hypotheses in physics propose it.  Our best well-supported models right now assume continuous space and time, but we haven't checked that they're valid on arbitrarily short length and time scales.

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Offline Bill S

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Re: What is your interpretation of quantum mechanics?
« Reply #118 on: 11/06/2013 00:51:04 »
Just letting everyone know I have not abandoned this thread.  I've been off line for a few days, and may continue to be for a couple more.  However, I'm looking forward to catching up, and joining in again asap.
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Offline Bill S

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Re: What is your interpretation of quantum mechanics?
« Reply #119 on: 12/06/2013 20:35:24 »
Quote from: dlorde
Were you talking about Cantor's Absolute infinity?

What is Cantor's Absolute infinity?  Is it the ultimate infinity, beyond which it is not possible to go?  If not, as I already asked, in what sense is it absolute?  If it is, then it does not exist, because Cantor established that there was no overarching infinity.

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For him it was a kind of mathematical deity, possessing a reflection principle that every property of the Absolute Infinite is also held by some smaller object.


If " every property of the Absolute Infinite is also held by some smaller object", then there must be a "smaller object" that is absolutely infinite, which, at best, causes problems; and, at worst, makes no sense.   

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Personally, I think this is a step beyond the coherent, but I'm no set theorist.

I am no set theorist, either, but, apart possibly from the creation of a mathematical deity, I see no problem with the concept of an infinity that is transcendent.   It must contain all other infinities, because it must contain everything.  It cannot be manipulated by mathematics, because it must contain mathematics. 

I feel sure you will object to that last assertion, but think about it; it may be perceived by us as capable of being manipulated mathematically, but we are finite, or so it appears to us, so how can we make infinite judgements about something which according to Cantor's insights into mathematical infinities, cannot exist?
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Offline dlorde

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Re: What is your interpretation of quantum mechanics?
« Reply #120 on: 12/06/2013 22:35:40 »
If " every property of the Absolute Infinite is also held by some smaller object", then there must be a "smaller object" that is absolutely infinite, which, at best, causes problems; and, at worst, makes no sense..
Yes. That's why I said I thought it was a step beyond the coherent. It is possible he was poorly paraphrased and meant each property of the Absolute Infinite is also held by some smaller object, but even this seems incoherent unless you explicitly exclude the property of 'absoluteness' (and probably some others).

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... I see no problem with the concept of an infinity that is transcendent.   It must contain all other infinities, because it must contain everything.  It cannot be manipulated by mathematics, because it must contain mathematics... I feel sure you will object to that last assertion
It's not my cup of tea, but - fine as long as you acknowledge that necessarily makes it metaphysics, not mathematics. Cantor thought Absolute Infinity was mathematical.

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... we are finite, ... so how can we make infinite judgements about something which according to Cantor's insights into mathematical infinities, cannot exist?
I don't know what you mean by 'infinite judgements'.
« Last Edit: 12/06/2013 22:39:18 by dlorde »

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Offline Bill S

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Re: What is your interpretation of quantum mechanics?
« Reply #121 on: 14/06/2013 21:12:47 »
Quote from: dlorde
fine as long as you acknowledge that necessarily makes it metaphysics, not mathematics.

Interesting that you say " metaphysics, not mathematics", rather than "metaphysics, not physics".  Have we reached a point where physics is so ruled my mathematics that a mathematical "reality" automatically becomes a physical reality? 

Quote from: JP
mathematics exists in a world of thought and doesn't necessarily reflect anything physical.

It seems very easy to lose sight of that fact.

Mathematics is, undoubtedly, the language of nature, but I suspect that is because mathematics is the best language we have found to describe nature, rather than because it actually governs nature.


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Cantor thought Absolute Infinity was mathematical.

He also established that it could not exist.

This is why I have been trying to stress the difference between mathematical infinities and physical infinity. 
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Offline dlorde

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Re: What is your interpretation of quantum mechanics?
« Reply #122 on: 15/06/2013 16:08:42 »
Interesting that you say " metaphysics, not mathematics", rather than "metaphysics, not physics".
Why interesting? It seems to me that infinity is a mathematical concept that can be used in physics. There may or may not be infinities in the real world - I don't see how we could know.

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Have we reached a point where physics is so ruled my mathematics that a mathematical "reality" automatically becomes a physical reality?
Depends what you mean by a 'mathematical "reality"'; but assuming your question isn't tautologous (if something is 'real', that usually means physically real), I'd say no, not at all - that's why I said 'mathematics' rather than 'physics'.

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Quote from: JP
mathematics exists in a world of thought and doesn't necessarily reflect anything physical.
It seems very easy to lose sight of that fact.
If you say so.

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Mathematics is, undoubtedly, the language of nature, but I suspect that is because mathematics is the best language we have found to describe nature, rather than because it actually governs nature.
I wouldn't argue with that, although it seems slightly loaded - i.e. if the universe does fundamentally operate in a mathematical way (or if maths does describe it's behaviour precisely), is it governed by maths or does it define maths? It seems a question of semantics. After all, where did the fundamentals of mathematics originate, if not observation of, and interaction with, the universe.

Eugene Wigner had quite strong views on this: The Unreasonable Effectiveness of Mathematics in the Natural Sciences.

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Cantor thought Absolute Infinity was mathematical.
He also established that it could not exist.
Do you have a source for that? my understanding as that he initially called the set-theoretic universe (including transfinites) 'the Absolutely Infinite', and thought that it could be acknowledged but not known, or even approximated. Later, he revised this, calling the set-theoretic universe and other proper classes 'inconsistent multiplicities' or 'absolutely infinite':
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A multiplicity can be of such nature, that the assumption of the togetherness/combining of its elements leads to a contradiction, so that it is impossible to conceive the multiplicity as a unity, as a finished/completed thing. I call such multiplicities absolutely infinite or inconsistent multiplicities.
[Letter to Dedekind]
I haven't seen anything to suggest he abandoned it altogether. Not that it really matters...

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Offline Bill S

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Re: What is your interpretation of quantum mechanics?
« Reply #123 on: 16/06/2013 03:23:29 »
Quote from: dlorde
I haven't seen anything to suggest he abandoned it altogether

Look closely at the wording of the quote, it would be possible to say almost anything without abandoning it altogether, :) 

Have you read: " Barrow. John D. The Infinite Book.  Vintage, Random House, London 2005"?
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Offline dlorde

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Re: What is your interpretation of quantum mechanics?
« Reply #124 on: 16/06/2013 12:48:20 »
Have you read: " Barrow. John D. The Infinite Book.  Vintage, Random House, London 2005"?
No.

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Offline Bill S

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Re: What is your interpretation of quantum mechanics?
« Reply #125 on: 18/06/2013 22:02:34 »
It is not unusual to find references to "infinite speed".  How would one define infinite speed?  Can it exist?
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Offline dlorde

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Re: What is your interpretation of quantum mechanics?
« Reply #126 on: 19/06/2013 09:51:56 »
It is not unusual to find references to "infinite speed".  How would one define infinite speed?  Can it exist?
Speed is distance over time, and increases as time decreases. So speed tends to infinity as time tends to zero; although mathematically dividing by zero is undefined, not infinity, one could define infinite speed as traversing a distance in no time, i.e. instantaneously.

If by 'can it exist?', you're asking if something in the real world can traverse a distance instantaneously, there are relativistic considerations. No physical object can accelerate to or past the speed of light, but if you consider a photon to have its own valid frame of reference, its 'journey' in that frame would appear to be instantaneous. The only other apparently instantaneous effect over distance I can think of is the decoherence of quantum entanglement.

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Offline JP

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Re: What is your interpretation of quantum mechanics?
« Reply #127 on: 19/06/2013 15:41:59 »
Average speed is distance traveled over time taken to travel that distance.  Instantaneous speed is distance over time in the limit as time goes to zero.  As always, dealing with limits requires care.  As time decreases to zero, distance traveled also decreases to zero.  Their ratio as they get tiny determines instantaneous speed.  An "infinite" speed would correspond to an object whose distance traveled did not decrease to zero as the time interval over which it was traveling did decrease to zero.  As an example, if an object moved at least 1 meter no matter how tiny a time interval you measured, that object would have infinite speed.  This would violate relativity  and doesn't seem particularly physical, so I doubt it exists in reality. 

I'm not sure where "infinite speed" gets referenced, but I can't recall seeing any references to it. 

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Offline Bill S

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Re: What is your interpretation of quantum mechanics?
« Reply #128 on: 19/06/2013 21:20:59 »
Quote from: JP
I'm not sure where "infinite speed" gets referenced

Here's one:   “So if a tachyon were created in some violent event in space, it would radiate energy away furiously…..and go faster and faster, until it had zero energy ……and was travelling at infinite speed”.

      Gribbin John.  Companion to the Cosmos.  Phoenix (Orion Books Ltd.), London.  1996.



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Offline Bill S

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Re: What is your interpretation of quantum mechanics?
« Reply #129 on: 19/06/2013 21:35:24 »
One of the characteristics of infinite speed must be that it would be immeasurable.  Consider what this implies: Prior to becoming infinite the tachyon’s speed would be measurable.  It seems hardly credible that it would suddenly reach a point where its speed would no longer be measurable.  What could happen to bring about this change?   

We might argue that we already have the answer to that:  " An "infinite" speed would correspond to an object whose distance traveled did not decrease to zero as the time interval over which it was traveling did decrease to zero."  [JP].  Would that not imply that it must be everywhere at once?  Could we not argue that if tachyons exist, either there is only one, that is everywhere; or, every tachyon in existence is "here" all the time?

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Offline Bill S

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Re: What is your interpretation of quantum mechanics?
« Reply #130 on: 19/06/2013 22:56:48 »
   What if we consider infinite acceleration?  In that scenario the tachyon would just continue to accelerate for ever.  Certainly this would make more sense, but then, it would never actually reach infinite speed, it would simply continue striving for it, and a more accurate term might be unlimited/ unbounded acceleration, rather than infinite acceleration, because, although we could imaging the acceleration going on for ever, it could never reach a point where we could say: "now it is infinite", unless we accept JP's definition (above), in which case, there are some scientists who would equate this with the speed of light.  That would lead to the absurd situation in which a tachyon would accelerate from the speed of light to the speed of light. 
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Offline dlorde

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Re: What is your interpretation of quantum mechanics?
« Reply #131 on: 20/06/2013 12:09:51 »
One of the characteristics of infinite speed must be that it would be immeasurable.  Consider what this implies: Prior to becoming infinite the tachyon’s speed would be measurable.
A tachyon, in this context, is an hypothetical faster-than-light particle with imaginary mass. How would its speed be measurable at all?

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Offline dlorde

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Re: What is your interpretation of quantum mechanics?
« Reply #132 on: 20/06/2013 12:16:58 »
... That would lead to the absurd situation in which a tachyon would accelerate from the speed of light to the speed of light. 
As I understand it, a tachyon would never be able to reach the speed of light; its energy-velocity relation would be a mirror of normal particles, its velocity increasing as its energy decreases. It would require infinite energy to decelerate to c (just as a normal particle would require infinite energy to accelerate to c), so it could only exist by moving FTL.

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Offline Bill S

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Re: What is your interpretation of quantum mechanics?
« Reply #133 on: 20/06/2013 19:35:25 »
Quote from: dlorde
A tachyon, in this context, is an hypothetical faster-than-light particle with imaginary mass. How would its speed be measurable at all?

I'll rethink! 

Tachyons are hypothetical particles that, hypothetically, travel faster than light.  Any measurement of their hypothetical speed would, hypothetically, have to be made by some hypothetical measuring device that, hypothetically, inhabited the hypothetical realm of which tachyons are hypothetical denizens.

Does that put us on the same page?  :D

Back to the serious stuff a little later, I hope.
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Offline JP

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Re: What is your interpretation of quantum mechanics?
« Reply #134 on: 20/06/2013 19:57:11 »
Our classical concept of speed probably doesn't work that well for tachyons, even if they somehow did exist.  All Bradyons (particles with real, non-zero mass) travel slower than light.  One explanation for this is that they can achieve zero momentum but still have energy (from E=mc2).  An object with energy moves through time and an object with momentum moves through space.  So a Bradyon always moves through time but can stop moving through space, obtaining a zero velocity.

A tachyon is in some ways the opposite.  It can obtain zero energy, but it always has non-zero momentum.  At zero energy, it satisfies (mc=p where p is momentum).  This means it can somehow stop moving through time and move only through space.  I'm not sure what this means intuitively, but that's what the equations say.


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Offline Bill S

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Re: What is your interpretation of quantum mechanics?
« Reply #135 on: 20/06/2013 22:37:18 »
Quote from: dlorde
As I understand it, a tachyon would never be able to reach the speed of light; its energy-velocity relation would be a mirror of normal particles, its velocity increasing as its energy decreases. It would require infinite energy to decelerate to c (just as a normal particle would require infinite energy to accelerate to c), so it could only exist by moving FTL.

we're definitely on the same page here.  However, you seem to have missed the point, perhaps because I was not clear enough.

The point I was aiming for was that if we accept JP's definition of infinite speed, which seems quite reasonable to me, a tachyon (at full speed?!) would not experience time.  Some people, including some scientists, believe that this is the case with the photon, which travels at c.  Since we cannot prove, either that the photon does not experience time, or that the tachyon, if it exists, has mass, it must be acceptable to theorise that the tachyon accelerates away from c, where the photon, and possibly the tachyon, experience no time, and arrives at a point where its experience of time is identical to that at its starting point.  Does that make sense?
 

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Offline Bill S

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Re: What is your interpretation of quantum mechanics?
« Reply #136 on: 20/06/2013 22:52:34 »
Quote from: JP
I'm not sure what this means intuitively, but that's what the equations say.
Intuitively, it means very little to me, but, sadly, the equations would probably mean even less.

Congratulations on yet another explanation that does mean something!

I've been having some thoughts about tachyons and their relationship to the Universe.  If they still make sense to me when I get them together, and if I can work out how to include diagrams in posts, :) I might have a go at a new theory.
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Offline dlorde

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Re: What is your interpretation of quantum mechanics?
« Reply #137 on: 21/06/2013 13:52:25 »
if it exists, has mass...
Imaginary mass.

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... the tachyon accelerates away from c, where the photon, and possibly the tachyon, experience no time, and arrives at a point where its experience of time is identical to that at its starting point.  Does that make sense?
It's a bit opaque (see bolding - surely either it 'experiences' time or it doesn't). If you're saying the tachyon arrives at some point having accelerated from c, but no time has elapsed in its frame of reference, I would have to query your definition of acceleration. Acceleration apart, it looks like a way of saying for a zero-energy tachyon what I proposed earlier for the photon: "... if you consider a photon to have its own valid frame of reference, its 'journey' in that frame would appear to be instantaneous".
« Last Edit: 21/06/2013 13:56:09 by dlorde »

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Offline Bill S

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Re: What is your interpretation of quantum mechanics?
« Reply #138 on: 21/06/2013 22:28:26 »
Quote from: dlorde
.....and possibly the tachyon, experience no time, and arrives at a point where its experience of time is identical.....

What is identical to experiencing no time?  It must be experiencing no time.

That's why I asked: "Does that make sense?"

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If you're saying the tachyon arrives at some point having accelerated from c, but no time has elapsed in its frame of reference, I would have to query your definition of acceleration.

Rightly so.  I was simply pointing out the two definitions in question.

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"... if you consider a photon to have its own valid frame of reference, its 'journey' in that frame would appear to be instantaneous".

Convenient as it would be, at times, to consider a photon to have its own valid frame of reference, such would seem not to be the majority view in scientific circles. 

"Therefore, just as bradyons are forbidden to break the light-speed barrier, so too are tachyons forbidden from slowing down to below c, because infinite energy is required to reach the barrier from either above or below."   (From your link)

Presumably, they would be able to travel at c if they were massless; but then, would they be able to travel at any other speed? 

Of course, we must not forget that this is all hypothetical, but I think I'm beginning to like the possibility of a link between c and infinite speed.  That could be good for some crackpottery!  :)
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Offline JP

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Re: What is your interpretation of quantum mechanics?
« Reply #139 on: 22/06/2013 00:14:23 »
I've mentioned this before, but you have to be very careful about applying the idea of reference frame to a photon (and presumably tachyons).  The reason we can discuss what something experiences is that we can compare it's reference frame (a frame in which it is at rest) to another reference frame (in which it's in motion).  Length and times change as measured from the ref. frame of the moving observer.  We cannot do this for a photon since there exists no reference frame in which its at rest--we can't find such a frame to compare to other observers.  It doesn't exist in special relativity.  Perhaps a post-SR theory will describe it.

The usual claim that photons are timeless (which I've occasionally seen in pop-sci books) comes from mis-applying the equations of special relativity which assume that the photon is at rest in some reference frame.

I'm not sure how to think about a tachyon's experience, since it can't ever exist in the reference frame of a bradyon (which we are).  However, there should be frames in which it's at rest, so you might be able to compare it to other tachyons and figure out what it experiences.  I'll have to think about it more.

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Offline dlorde

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Re: What is your interpretation of quantum mechanics?
« Reply #140 on: 22/06/2013 12:14:58 »
I've mentioned this before, but you have to be very careful about applying the idea of reference frame to a photon (and presumably tachyons).
I agree - perhaps I should have emphasised the 'if' in ".. if you consider a photon to have its own valid frame of reference...". I suppose it's an intuitive attempt to understand photons in familiar terms.

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Offline JP

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Re: What is your interpretation of quantum mechanics?
« Reply #141 on: 22/06/2013 17:06:08 »
I've mentioned this before, but you have to be very careful about applying the idea of reference frame to a photon (and presumably tachyons).
I agree - perhaps I should have emphasised the 'if' in ".. if you consider a photon to have its own valid frame of reference...". I suppose it's an intuitive attempt to understand photons in familiar terms.

What I'm trying to point out is that there is a scientific problem with doing so.  If we're going to talk about the properties of this hypothetical frame in scientific terms, we need to have a scientific theory that covers it, i.e. the theory needs to describe the properties of that frame and be testable somehow.  Special relativity explicitly does not cover that reference frame and there is no way we know of to test the properties of such a frame (if it were to exist).  The best we can say scientifically is that we don't know if such a frame exists and don't know its properties if it were to exist.

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Offline Bill S

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Re: What is your interpretation of quantum mechanics?
« Reply #142 on: 01/07/2013 00:29:17 »
What did cantor do?

Cantor revolutionised the mathematical concept of infinity.  He lifted infinity from the realms of philosophy and theology and handed it to mathematicians and scientists.  He identified infinities that were "countable" and "uncountable"; that is, infinities that could be put in one-to-one correspondence with the list of natural numbers 1,2,3,4,5,6… , and infinities that could not.  So, for example, the even numbers are countably infinite, so are all the odd numbers.
   
Cantor defined all countable infinities as being the same size.  This seems to introduce something of a paradox, because the list of natural numbers is infinite, and the list of odd numbers is infinite, intuition would suggest that one of these must be half the size of the other.  We know that intuition is not always our best guide, so we should put aside intuition and look at how we can claim that these two infinities are the same size. the obvious answer is that we can go on putting one into one-to-one correspondence with the other for ever and we will not run out of either; but is that what infinity is really about?  We can do this in theory, but never in practice.   These infinities, undoubtedly, have their uses in the more esoteric realms of set theory and other branches of mathematics, but are of very dubious value when applied to the real world.  One of the major problems with trying to integrate general relativity and quantum theory is that the equations of one, when applied to the other tend to lead to infinities, so the equations become nonsense.

Initially, the mathematics community was not over enthusiastic about Cantor's work, but after a time, mathematicians said "cool", or "hoc frigidulum est" or whatever the expression of the time might have been.  Since then, Cantor has been widely quoted as having established that infinity was mathematically manipulatable. 

What did Cantor really do to infinities?  He discovered that there were ways of making infinities manageable by mathematicians.  However, even he accepts that this is only a partial victory.   

Barrow says: “Cantor’s most dramatic discovery was that infinities are not only uncountable, they are insuperable.  He discovered that a never-ending ascending hierarchy of infinities must exist.  There is no biggest of all that can contain them all.  There is no Universe of universes that we can write down and capture."

Cantor called this "Absolute infinity", he likened it to "God", but at the same time established that this absolute infinity did not exist.  Here is another paradox.  If we argue that "There is no Universe of universes that we can write down and capture." There is no greatest infinity.  Then, surely, we must argue that our so-called infinite series are not infinite, because they lead to no infinity "that we can write down and capture".  They are unbounded, because we can neither see nor imagine an end, but we cannot say that they are infinite in any sense other than mathematical.


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Offline JP

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Re: What is your interpretation of quantum mechanics?
« Reply #143 on: 01/07/2013 15:15:49 »
I suppose picking a "largest infinity"is a bit like picking a "largest number."  No matter what number or infinity you tell me, I can give you a bigger one.  You can get around this by defining a process rather than a number, such as "my number is X, which is defined as X=1/Y as Y tends to zero."  I can no longer pick a single number that is bigger than your X.  I wonder if you could find a "biggest infinity" in a loose sense through a limiting process like this.  For example, start with the set of all real numbers, and replace each number with the set of real numbers--then repeat without end.  I don't know if there are bigger infinite sets--my set theory is a bit limited and rusty.  :)

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Offline Bill S

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Re: What is your interpretation of quantum mechanics?
« Reply #144 on: 01/07/2013 23:25:03 »
Quote from: JP
my set theory is a bit limited and rusty.  :)


You're lucky, I don't have enough set theory to go rusty. :(

I suspect you are right about applying the same technique to infinities as to numbers.  Of course, you would not identify a "biggest infinity", any more than you would identify a biggest number. 

If cantor is right, there is no "biggest infinity", there are mathematical infinities, which are actually unbounded mathematical concepts.  Then there is "absolute infinity" which cannot be reached by any finite process, so, as far as mathematics is concerned, does not exist.
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Offline yor_on

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Re: What is your interpretation of quantum mechanics?
« Reply #145 on: 03/07/2013 23:26:44 »
A frame of reference practically, is you measuring locally (clock and ruler) relative some other. If you you use 'c' for the one measuring, then nothing makes sense anymore. The arrow of time must 'disappear', as the Lorentz contraction should be infinite, etc. But we 'see' photons, and they follow causality, macroscopically defined. It's all about coordinate systems, and their limits. 'c' is one.
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Offline Bill S

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Re: What is your interpretation of quantum mechanics?
« Reply #146 on: 09/07/2013 22:14:40 »
Possibly the discussion of infinity is wearing a bit thin.  No anticipated broadside from Pete as yet. :)

I think this (in part) is where I am at present.

1.  Infinity is not just a very big number.

2.  Eternity is not just a very long time.

3.  Something that is finite can never become infinite.

4.  Mathematical infinities are theoretical concepts that are unbounded, but not infinite.

5.  Cantor’s “absolute infinity” may be infinite, but this cannot be proved nor disproved.

6.  Unbounded entities may be subjected to mathematical processes, but attempting to do this to infinity leads to nonsensical answers.

7.  There cannot be more than one true (absolute?) infinity, because it must contain everything.

8.  Multiplying or dividing infinity makes no practical sense because the result would have to be infinite, and there cannot be more than one "everything".

9.  Practically, nothing can be added to infinity, because it is already everything.

10.  Nothing can be taken away from infinity, because the remaining quantity would still be infinite, therefore it makes no sense to talk of something being taken away.   
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Offline Pmb

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Re: What is your interpretation of quantum mechanics?
« Reply #147 on: 10/07/2013 13:09:20 »
Quote from: Bill S
Possibly the discussion of infinity is wearing a bit thin.  No anticipated broadside from Pete as yet. :)
Huh? I don't get it. Fill me in on the joke. :)

I have strong feelings about a lof of this stuff. Some of it's based in the article

Quantum Theory Needs No 'Interpretation, Christopher A. Fuchs and Asher Peres, Physics Today, March 2000

For anyone who'd like to read it PM your e-mail address to me and I'll e-mail it to you.

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Offline JP

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Re: What is your interpretation of quantum mechanics?
« Reply #148 on: 10/07/2013 17:38:17 »
Possibly the discussion of infinity is wearing a bit thin.  No anticipated broadside from Pete as yet. :)

I think this (in part) is where I am at present.


I can give you a broadside on this one.  :)

The problem with many of your points is that you're not being precise.  There are different ways to get at the concept of infinity.  Most common in physics is to mean something very big, which is represented by allowing numbers to increase without bound.  Very small is another option, in which things decrease without bound.  It's unknown if these concepts match nature: is the universe infinite in size, or can space be broken down into infinitesimally small pieces?  Regardless, the theories based upon them are accurate enough that we can get away with these uses of infinity.

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1.  Infinity is not just a very big number.

2.  Eternity is not just a very long time.
Yes, I agree.  They are more along the lines of concepts of things or times increasing without bound.

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3.  Something that is finite can never become infinite.
This is a blanket claim and I'm not sure it's provable.  I suspect that in physics, this is probably the case--at least for most things, but making a blanket statement like this is metaphysics, not physics.

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4.  Mathematical infinities are theoretical concepts that are unbounded, but not infinite.
I'm not sure what you mean by "mathematical" infinities.  There are certainly infinities that are in a sense bounded but infinite: for example the set of real numbers between 0 and 1 is bounded below by 0 and above by 1, but has an infinite number of elements.

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5.  Cantor’s “absolute infinity” may be infinite, but this cannot be proved nor disproved.
I don't know enough math to derive a proof either way, but if absolute infinity contains all other infinite sets, then it has to at least be as big as any single one of them.  Since all those sets are infinite, absolute infinity must be infinite, if it exists.

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6.  Unbounded entities may be subjected to mathematical processes, but attempting to do this to infinity leads to nonsensical answers.
As stated, this claim is false.  It is a mathematical process to add elements to a set.  I can add all real numbers to the set of all rational numbers and end up with a valid set, for example.  What you can't do is to pretend that "infinity" can stand in as a real number, since it's a concept, not a number.  1+infinity doesn't make sense since the "+" operation isn't defined for the concept infinity.

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7.  There cannot be more than one true (absolute?) infinity, because it must contain everything.
Don't know on this one.

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8.  Multiplying or dividing infinity makes no practical sense because the result would have to be infinite, and there cannot be more than one "everything".
Kind of.  It's more general to go back to the idea that infinity is a concept, not a number, so you can't expect to apply operations which are defined for numbers to it. 

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9.  Practically, nothing can be added to infinity, because it is already everything.
This is false.  You can add elements to an infinite set.  This is precisely what Cantor realized when he established different types of infinity.

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10.  Nothing can be taken away from infinity, because the remaining quantity would still be infinite, therefore it makes no sense to talk of something being taken away.   
Again, false.  You can take an element out of an infinite set and are left with an infinite set without that element.

Edit: Realized I had quoted your list twice.  :p
« Last Edit: 11/07/2013 02:09:07 by JP »

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Offline Bill S

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Re: What is your interpretation of quantum mechanics?
« Reply #149 on: 10/07/2013 23:50:55 »
Thanks JP.

Bit pushed tonight, but will have some comments asap.
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