Some subtle aspects of relativity.

[Erasmus00]

Originally Posted by Doctordick

If that statement is true then Einstein certainly has strong support that his picture is worth the effort; but, the real question is: is it true? I think I have certainly reopened the question and the issue should certainly be reexamined; especially in view of the problems Einstein's GR has with quantum mechanics.

But your picture is the same picture as Einstein's, simply rearranged! You haven't reopened the question, you've rephrased the solution.

And you've never given any convincing reason that reparameterizing GR in your way does anything to help with quantum mechanics! Its not even obvious to me that there is a simple way to recast Einstein's field equations because in your reparameterization the stress energy tensor isn't a tensor but transforms non-trivially observer to observer.

Also, you still haven't responded to my question- if the universe were governed by scale invariant equations, then it should be scale invariant- how come none of the fundamental forces demonstrate this feature? Why isn't the CMB background truly scale invariant instead of merely approximately scale invariant? etc.

If you can appreciate the fact that any information can be mapped/modeled in many different ways, you can probably also understand that a feature that is implied by one of all those possible mapping methods, cannot really be considered "the way reality is".

I agree- which is why Einstein's relativity parameterization is the one I prefer. Einstein/Minkowski SR can be set in a coordinate invariant way- the "maps" as it were can be completely abstracted out. In Dick's formalism, this is simply not so- everything is phrased in terms of things that depend on the coordinates.

. It refers to scale invariance that exists to your model of reality as a whole. In a sense, you could say that if the whole reality - absolutely everything in it - was to scale up ten times suddenly, it would be undetectable. I.e. while your model of reality does assign numerical values to describe the relationships between things, scaling absolutely everything changes absolutely nothing.

I'm aware of what scale invariance means. The thing is it, scale invariance implies testable predictions that we simply don't see around us. None of the physics we've already nailed down is scale invariant.
-Will

[Doctordick]

Originally Posted by Erasmus00

But your picture is the same picture as Einstein's, simply rearranged!

That is simply a false statement. The experimental results verifying the transformation equations of special relativistic results may be identical to Einstein's predictions but the “picture” which yields this as a rational attack is quite violently different from his. Try and find a representation of “tachyons” in my picture. As I say, you just have that brain clamp on too tight and just can not see my picture.

Originally Posted by Erasmus00

None of the physics we've already nailed down is scale invariant.

That is very simple issue, none of the physics which has been “nailed down” takes into account the entire universe. It is all compartmentalized; cast in a form which requires ones understanding of the rest of the universe to be correct.

Have fun -- Dick

[Doctordick]

Sorry Anssi, I never got a notification that you had posted. But you come through as usual and I appreciate it.

Originally Posted by ughaibu

Euclidean hyperspace is incoherent by definition, what advantage is accrued by one incoherent model over another?

I have no idea as to what you have in mind. I believe the term “hyperspace” is a science fiction term. I think you will have to define what you mean by the term. As far as I am concerned, I am using a simple four dimensional Euclidean space and there is nothing incoherent about it at all.

Have fun -- Dick

[Erasmus00]

Originally Posted by Doctordick

That is simply a false statement. The experimental results verifying the transformation equations of special relativistic results may be identical to Einstein's predictions but the “picture” which yields this as a rational attack is quite violently different from his. Try and find a representation of “tachyons” in my picture. As I say, you just have that brain clamp on too tight and just can not see my picture.

Consider your statement of everything moves at c to Einstein/Minkowski's statement that everything has a four velocity with magnitude c. The idea that mass is the conjugate to tau can be of thought as a rearrangement of




Traditionally, energy is conjugate to time and momentum to x, in your picture you rearrange both sides, but it amounts to the same identities!

Further, your relationship leads to a quantum mechanical relationship of



And I'm pretty sure that this doesn't yield much by way of physics, though I've only played around with it for a few minutes, it doesn't seem to yield anything useful. (mostly because mass is a central charge so doesn't traditionally have a nice operator associated with it, unlike energy which has the hamiltonian).

Also, you cannot have tachyons in Einstein's picture either, without violating the rule of particles lines outside the light cone. You can't put tachyons into your picture without violating your everything moves at c rule.

Also, tachyons are, in field theory, now believed to be a sign that you've done a calculation wrong (you've picked the wrong vacuum). Hence, there may be no need to fit them into either theory.

That is very simple issue, none of the physics which has been “nailed down” takes into account the entire universe. It is all compartmentalized; cast in a form which requires ones understanding of the rest of the universe to be correct.

So you can dismiss out of hand any experimental evidence that disagrees with you? Please, name a single piece of evidence that the universe is scale invariant. Its a bold prediction of your theory that seems to fly in the face of everything that has ever been measured, saying "its because the measurement is compartmentalized" seems a cop out. If the universe is scale invariant shouldn't we have some observable evidence? Shouldn't the CMB be scale invariant? What measurement COULD be done to demonstrate this scale invariance?
-Will

[AnssiH]

Originally Posted by Erasmus00

if the universe were governed by scale invariant equations, then it should be scale invariant- how come none of the fundamental forces demonstrate this feature? Why isn't the CMB background truly scale invariant instead of merely approximately scale invariant? etc.

You have misunderstood what exactly is claimed to be scale invariant. Also your comment implies you are looking at this as if it told you what really governs the universe. You should not.

What DD's epistemological analysis (which is the root of this relativity conundrum) tells you is rather what sorts of laws are common to all reasonable predictive models of any datastream whose meaning is fundamentally unknown. The interesting bit being, that those (entirely general) laws appear to be almost exactly what our best physical models take as the laws of the nature.

Let me expand on that before I get to scale invariance. Suppose a newborn baby, or any sort of mechanical learning system, that does not have any information about what reality is like or what to expect from reality. That means, while the learning system is receiving information from its sensory system, it has absolutely no idea about how to interpret any of it in any meaningful way. Nothing can even be "perceived" without being able to interpret that data stream. I.e, it is receiving a datastream whose meaning is fundamentally unknown.

Furthermore, its survival depends on it being able to predict that datastream. You could say, it needs to be able to model reality - or how it believes reality is behind that data stream - so to be able to expect dangers that lie in the future. In simple terms you could say that it tacks identity to certain patterns, and comprehends them as "objects", supposing they are governed by whatever laws explain your perception of how they move.

Now, since the meaning of the datastream is fundamentally unknown, there exists many valid ways to tack identity to those patterns & making up appropriate laws that explain why such "objects" do what they do. At the end of the day, many features of such worldview will be defined through circular logic, which is completely unproblematic as far as the predictive powers go. Each worldview simply handles the same reality with different sorts of terms. (In fact this can be seen as a rather useful feature as it yields semantics, but let's not get into that now)

This much was rather obvious to me before I talked to DD, but I myself had no idea how to even begin to figure out what sorts of mechanisms allow us to start building a worldview from raw data. I just knew it must be possible one way or another since I know nothing about reality for certain, but still I can interpret my sensory data in useful ways.

Now, the important bit with DD's analysis is that there also exists certain features that are common to any possible "identity tacking" scheme. These are the symmetries that DD refers to, and the epistemological analysis merely investigates the logical consequences of those symmetries, with rather surprising results. At least initially surprising; it actually does make a lot of sense once you wrestle it in.

One of those symmetries is scale symmetry, and don't fail to notice it does indeed refer to scale symmetry to the assignment of labels to ontological elements in the x,tau,t -space. I.e. If the raw data is mapped onto the x,tau,t -table, and then your problem is to come up with an explanation as to what that data means, then that problem is completely unchanged if you scale the mapped data one way or another. (If you are wondering, any specific mapping method is a function of your explanation and vice versa, but whatever they are, the scale symmetry exists)

So the scale symmetry does NOT refer to some specific feature of some specific worldview being scale symmetric. It is instead analogous to the entire universe being scaled one way or another. And obviously that would not be observable, as you and all your measuring devices are also part of universe.

I agree- which is why Einstein's relativity parameterization is the one I prefer. Einstein/Minkowski SR can be set in a coordinate invariant way- the "maps" as it were can be completely abstracted out. In Dick's formalism, this is simply not so- everything is phrased in terms of things that depend on the coordinates.

Well different mapping implies different reality, and some ontological interpretations make certain logical consequences more obvious than others. People certainly tend to base their arguments on how they believe reality exists. For example, if you took relativistic spacetime as ontologically true, you may be compelled to investigate whether it can curve into itself in such a sense that one could travel backwards in time. Otherwise you probably would not bother with such ideas.

Well, hopefully that was helpful

-Anssi

[Erasmus00]

Originally Posted by AnssiH

So the scale symmetry does NOT refer to some specific feature of some specific worldview being scale symmetric. It is instead analogous to the entire universe being scaled one way or another. And obviously that would not be observable, as you and all your measuring devices are also part of universe.

It would be observable! All you have to do is make measurements at different scales! As you have said, saying the universe is scale invariant is akin to saying it has no scale- which in turn implies measurements at different scales should be the same. They are not. Imagine using a small telescope to look out at the sky, and then to build another telescope exactly the same but twice as large and using that to look out at the sky. What should the data look like?

Further, one can check if the EXPLANATIONS we have are scale invariant (which is fairly straightforward). Despite the fact that Dick insists his master equation is the backbone of any flaw free explanation, none of the scientific theories we have are scale invariant. This leaves us with two choices:

1. Dick is right, and the other theories wrong.

2. the "standard" theories are right, and Dick has erred somewhere.

To decide between 1 and 2, the simplest way should be to figure out predictions made by the two theories and where they differ, do some experiments. I contend scale invariance is one place.

In regards to Einstein's spacetime, I fear you are once more missing or talking around my point. Assume the following:

Something exists in need of describing

Now, there are two ways we can describe this object- the first is to drop down a bunch of arbitrary labels all around it and come up with relationships between the arbitrary labels.

The second is to (using the miracle of mathematics) figure out properties of your object that are INDEPENDENT of the labels. i.e. no matter how we change the labels (which are arbitrary), these properties are fixed.

Which is better? Dick is doing the first, Einstein the second. I contend the second is better.
-Will

[AnssiH]

Originally Posted by Erasmus00

It would be observable! All you have to do is make measurements at different scales! As you have said, saying the universe is scale invariant is akin to saying it has no scale- which in turn implies measurements at different scales should be the same. They are not. Imagine using a small telescope to look out at the sky, and then to build another telescope exactly the same but twice as large and using that to look out at the sky. What should the data look like?

That has got nothing to do with scale invariance to the reference labels to ontological elements in the x,tau,t-space. If you have a model of reality mapped onto an x,tau,t-space, then scaling the whole thing means your measurement stick gets scaled as well, i.e. it still measures everything at exactly the same length it measured them before.

To scale a telescope but nothing else, is just like scaling only that measurement stick but nothing else. Of course it would measure things differently, but that is only one very specific thing inside your worldview being scaled, not the "whole worldview".

Further, one can check if the EXPLANATIONS we have are scale invariant (which is fairly straightforward). Despite the fact that Dick insists his master equation is the backbone of any flaw free explanation, none of the scientific theories we have are scale invariant. This leaves us with two choices:

1. Dick is right, and the other theories wrong.

2. the "standard" theories are right, and Dick has erred somewhere.

Or 3. the scale invariancy doesn't refer to any single relationship being scale invariant, but rather your whole self-coherent set of explanations being scale invariant if you just managed to scale them all the same way (to put it like that).

It's much like having your self-coherent set of scientific theories in an algebraic equation. They have certain relationships to each others which makes it impossible to just take one term and change it willy nilly. Instead you'd need to carefully change other terms in the equation accordingly too to keep the whole thing valid. Or there can be certain operations that don't change the relationships in any way, such as multiplying each and every term by some X amount.

In regards to Einstein's spacetime, I fear you are once more missing or talking around my point. Assume the following:

Something exists in need of describing

Now, there are two ways we can describe this object- the first is to drop down a bunch of arbitrary labels all around it and come up with relationships between the arbitrary labels.

The second is to (using the miracle of mathematics) figure out properties of your object that are INDEPENDENT of the labels. i.e. no matter how we change the labels (which are arbitrary), these properties are fixed.

Which is better? Dick is doing the first, Einstein the second. I contend the second is better.

I'm afraid I don't really understand what you are saying
Hmmm, or perhaps I am. The thing is that "what constitutes an object" is part and parcel of our worldview. The latter (Einstein) view is essentially assuming that how we perceive reality, is how the ontological reality really is (which is not unproblematic since you can make multitude of assumptions regarding what happens beyond your observations).

The former (DD) view is investigating properties that are found from our model of reality, but not necessarily from reality itself (since we probe reality according to an interpretation that is a function of what we believe reality is like). It could probably be deemed useless if it didn't yield any interesting results. But I do think it is rather interesting that it yields relativistic time evolution to entities, when they are just defined in specific way (which is forced upon us if we are to remain objective). That by itself is an explanation of how relativistic time evolution arises as a feature of a world model, without any knowledge about whether or not it is a feature of reality itself. Without any requirement of it being a feature of ontological reality as is. How's that for surprising?

-Anssi

[Erasmus00]

AnssiH, to avoid talking past each other, please let me know which of the following steps you disagree with

1. The universe is scale invariant
2. This implies the universe has no scale
3. This implies that any scale in a measurement comes from the device
4. Therefore, scale dependence in a measurement should be a function of the scale of the device
-Will

[AnssiH]

Originally Posted by Erasmus00

AnssiH, to avoid talking past each other, please let me know which of the following steps you disagree with

1. The universe is scale invariant
2. This implies the universe has no scale
3. This implies that any scale in a measurement comes from the device
4. Therefore, scale dependence in a measurement should be a function of the scale of the device
-Will

I have a lot of trouble interpreting you unambiguously

I mean, I could agree with #1 it if it meant "the universe - when taken as a whole - is scale invariant", i.e. when not referring to the idea that "everything in universe looks the same from all the distances", which seems to be what you are thinking of (judging from your earlier posts). I believe here's exactly where the miscommunication lies.

I understand that something being scale invariant would in usual physics context mean that it would behave exactly the same way when built in different sizes (against lightspeed or whatever we'd want to use to define size).

That is somewhat different issue than the x,tau,t-mapping being scale invariant. Since the x,tau,t-mapping contains your entire (modelled) universe, scaling the entire thing changes nothing in it, much like scaling an entire "spacetime block" (representing the whole universe) would change nothing in it; nothing inside that spacetime block could determine whether that spacetime was scaled or not.

I.e. scaling your entire universe in its x,tau,t-mapping doesn't mean its size would go from 10 billion lightyears to 100 billion lightyears, since you'd be scaling that light as well, so to speak.

-Anssi

[Erasmus00]

Originally Posted by AnssiH

I.e. scaling your entire universe in its x,tau,t-mapping doesn't mean its size would go from 10 billion lightyears to 100 billion lightyears, since you'd be scaling that light as well, so to speak.

You are scaling the light's speed, you can't scale particles, as they are points. But as you are defining it, "invariance" is tautological (defined in such a way as to always be true).

Any statement that has real content make a prediction. So, lets try this: does the universe have an associated length scale in DD's model?
-Will