Understand Special Relativity and Time paradox

[zonde]

OK, those quotes all show that Einstein didn't like solipsism, which wasn't in doubt. Not one of them support your claim that Einstein said that rejecting the physical meaningfulness of coordinate time leads to solipsism.

Well, not only solipsism but positivism too. For example this one:
“I am not a positivist. Positivism states that what cannot be observed does not exist. This conception is scientifically indefensible, for it is impossible to make valid affirmations of what people 'can' or 'cannot' observe. One would have to say 'only what we observe exists', which is obviously false."

And what you say sounds like positivism: "what cannot be observed does not exist".

 

[PeterDonis]

I've certainly not been claiming that there is no external world just because the observer is always moving at the apex of his light cone. That was my example of the absurdity you arrive at when denying the external world of the hyperplanes of simultaneity.

But in the block universe view, the "external world" is a single 4-D world. It is not a bunch of 3-D hyperplanes of simultaneity. The hyperplanes of simultaneity are completely unnecessary to the block universe view.

You're the one who has been denying the reality of the real external objective world represented by the hyperplanes of simultaneity.

I have been denying that hyperplanes of simultaneity are "real physical things" because they are frame-dependent, and "real physical things" are represented in the theory by frame-independent quantities. So far you have said absolutely nothing that refutes that view. I have certainly not been denying the reality of the "real external objective world"; I just deny that that real external objective world is represented by hyperplanes of simultaneity. And since that is precisely the point at issue, you can't help yourself to it by implying that "the real external objective world" *is* in fact represented by hyperplanes of simultaneity. You have to first *prove* that, and you haven't.

No. 1: I have said nothing of block universe.

Then what position, exactly, are you defending? I'm very confused.

But, what an absurdity for you to come to the conclusion that objects don't exist in the 3-D world because they are 4-D objects.

I said no such thing. What I have been saying is that "3-D worlds" are frame-dependent, and the actual physics of SR is contained in the things that are frame-independent, so the actual physics of SR is *not* contained in 3-D worlds. That in no way denies the "reality" of objects; the only things whose "reality" it denies are the 3-D worlds, and only in the sense that they are frame-dependent, so you don't need them to describe the physics.

That's like saying a thin slice of a wooden 2 x 4 lumber doesn't exist because its length is 8 ft and the slice is only 0.001 inch thick.

No, it's like saying that the 0.001 inch thick slice of the 8 ft. 2x4 is not the same thing as a complete slice out of the entire universe that contains the 0.001 inch thick slice of lumber.

How does a 3-D piece of an object not exist just because it is a piece of a 4-D object. You have lost all logic here.

I didn't say a 3-D piece of an object doesn't exist. See above for further elaboration of what I did say. Please read more carefully.

Sorry to be blunt, but you have just presented a total distortion of what my posts have been conveying

If you're not talking about the "block universe", then you're right, I have no idea what you think your posts have been conveying.

and you logic is totally flawed.

No, my logic is just not what you have been claiming it is.

And, again, I've said nothing of block universe--I don't think the monitor wants any more of that.

There's nothing wrong with talking about the block universe in itself. The only things that have gotten people in trouble are claims that the block universe is the only possible interpretation of SR.

 

[PAllen]

bobc2:

Still waiting for a reference where Einstein used hyperplanes' of simultaneity, or said that the point of view of a non-inertial observer matches that, moment to moment, of instantaneously comoving inertial frames. You claimed your approach matches Einstein's. I checked 4 papers Einstein treated non-inertial motion in SR, and none remotely resemble your approach. Still waiting for a reference on what you explicitly claimed - that your method matches Einstein's.

 

[PeterDonis]

If you're not talking about the "block universe", then you're right, I have no idea what you think your posts have been conveying.

bobc2, on re-reading the thread, I'm still not sure what you think your posts have been conveying, but perhaps I can help re-focus things a bit with a couple of questions.

First, the reason I assumed you were trying to defend a block universe interpretation is that I couldn't see any other reason for bringing in the 3-D worlds. If that wasn't meant as an argument for a block universe interpretation, what was it meant for?

Second, I see that this sub-thread more or less started with you adding the "red" observer's worldline to the spacetime diagram, and then observing that the coordinate times assigned to events on red's worldline "run backwards" in the succession of "blue" frames through the turnaround. What do you think that means? Why did you think it was important to make that observation?

 

[PAllen]

Please note further that the derivation of simultaneity convention for inertial observers relies on:

- being inertial long enough to apply a clock synchronization method (establishing simultaneity), for clocks a given distance apart. It is also preferred only in the sense that all reasonable methods agree.

- A non-inertial observer has a different past than co-moving inertial observer. This means that physical synchronization methods they might use will come out different from the comoving inertial frame. They also won't agree with each other.

I am not arguing solipsism. I think there is a meaningful sense in which inertial simultaneity convention (which is the one you are using) is preferred for inertial observers - for a volume of spacetime proportional to the time they have been effectively inertial. For a non-inertial observer it is not preferred or meaningful at all beyond a spacetime volume where, say, Einstein simultaneity and 'ruler' simultaneity differ to a detectible degree.

You want to give absolute meaning to a convention completely divorced from the way it was derived.

 

[ghwellsjr]

Bobc2, your Sketch III looks kind of like my first diagram in post #23 except that I have an instantaneous turn-around. The lines (or surfaces or volumes or whatever you want to call them) of simultaneity in my diagram are simply the horizontal grid lines (and the infinite number of horizontal lines in between them). In normal orthogonally drawn diagrams of IRF's, the issue of simultaneity is automatically handled by the grid lines and doesn't need any explanation. You don't show any equivalent grid lines either horizontally or vertically (or diagonally??) so it is very difficult for me to tell what is going on with your diagrams. I wonder if the OP is understanding them.

Secondly, I don't see any equivalent yearly messages traveling at c between the OP and his brother as he requested in post #13. Can you please put them in? And can you address his concern that a bunch of messages from him will arrive in a flood during his brother's about-face?

ghwellsjr, sorry I missed your post for a while there. I'll see if I can get back into this and respond to your questions sometime this weekend. Thanks.

The weekend is over. Can you please make the OP's requests a priority especially since you are concerned that the moderators are going to lock this thread?

 

[Dale]

And what you say sounds like positivism: "what cannot be observed does not exist".

Where did I say that? I don't know where you guys are getting this. Bobc2 with his strange obsession with solipsism and now you with positivism.

I am neither a solipsist nor a positivist. However, this is not a forum for philosophy of any kind, including philosophies that I agree with. This forum is for science, and I make a strong effort to keep it that way. I make a sincere effort not to promote my own philosophy and I try to discourage others from presenting theirs even when it happens to agree with mine.

I feel like there has been a weird revival of McCarthyism where people are randomly accused of being a solipsist or a positivist with no evidence to support the accusation.

 

[PeterDonis]

It is not obvious at all to me that he is referring to hyperplanes of simultaneity

It's fairly obvious to me, taking all of Einstein's writings on relativity into account, that he *wasn't*--that he was trying to focus attention on frame-independent things, not frame-dependent things. The particular quotes bobc2 gave, as I said before, are very general and don't even mention relativity specifically; when you look at what he actually wrote about relativity, it's clear that the "physical reality" he was talking about was represented in the theory by invariants, not by frame-dependent things like hyperplanes of simultaneity. His main emphasis on simultaneity is precisely to show that it is *relative*, i.e., to show that it is *not* the right thing to focus on.

 

[zonde]

However, this is not a forum for philosophy of any kind, including philosophies that I agree with. This forum is for science, and I make a strong effort to keep it that way. I make a sincere effort not to promote my own philosophy and I try to discourage others from presenting theirs even when it happens to agree with mine.

Philosophy is foundation of science. We can coherently talk about science as long as we agree about some philosophical foundations.

But if you are trying to put physics on different foundations then there is no way how we can avoid talking about philosophy.

And this idea about doing physics using invariants is attempt to put physics on different foundations.

 

[PAllen]

Philosophy is foundation of science. We can coherently talk about science as long as we agree about some philosophical foundations.

But if you are trying to put physics on different foundations then there is no way how we can avoid talking about philosophy.

And this idea about doing physics using invariants is attempt to put physics on different foundations.

Yes, invariants are the foundation of special and general relativity. Einstein several times said he wished the word relativity was never used - the theory should be called the theory of invariants. That is fundamentally the way it has been pursued since.

If you don't like this foundation, I guess you are left with physics of the 19th century.

 

[Mentz114]

Yes, invariants are the foundation of special and general relativity. Einstein several times said he wished the word relativity was never used - the theory should be called the theory of invariants. That is fundamentally the way it has been pursued since.

If you don't like this foundation, I guess you are left with physics of the 19th century.

Hear, hear. It is tiresome that so many 'objectors' base everything on the study of these old documents.

 

[PeterDonis]

Yes, invariants are the foundation of special and general relativity. Einstein several times said he wished the word relativity was never used - the theory should be called the theory of invariants. That is fundamentally the way it has been pursued since.

Exactly.

 

[Dale]

Philosophy is foundation of science.

I disagree completely. Experiment (scientific method) is the foundation of science and what distinguishes it from philosophy.

I cannot think of any philosophical proposition that has any scientific value except for those which are essentially restatements of Bayesian inference.

And this idea about doing physics using invariants is attempt to put physics on different foundations.

No, it isn't. The foundation of science is the scientific method. The scientific method requires that a theory make experimental predictions, but doesn't otherwise constrain the method of making those predictions. In relativity the experimental predictions of the theory are all invariants. No modification of the scientific method is necessary to do relativity using invariants.

 

[bobc2]

Exactly.

You have totally ignored the importance of Einstein's postulate about the laws of physics and different observer Lorentz frames.

 

[bobc2]

There seems to be confusion over the sequence of inertial frames associated with the traveling twin turnaround. I was simply pointing out what I thought was an interesting result for red clock readings as presented in the traveling twin’s sequence of inertial frames. So, here we will not be concerned about the period on the traveling twin's worldline during the turnaround. To avoid any further anguish over discretizing the turnaround, let’s just simplify the analysis by changing the focus away from the turnaround.

In the sketch below we show the same interesting feature by simply comparing readings on what I now show as the brown clock (red in the earlier sketch) as they are presented in the traveling twins two inertial frames, i.e., the purple frame (before turnaround) and the red frame (after turnaround). Notice that Event C presents a brown clock reading in the purple frame at the start of the outgoing trip of the traveling twin (the purple X1 axis represents the outgoing twin's simultaneous space at the start of his trip).

We show the beginning of the twin return trip as Event A (the traveling twin has just completed the turnaround and has started back home, i.e., the Red frame in the sketch). In this twin’s inertial frame the brown clock is presented on the worldline of the Brown frame as Event B.

When the traveling twin reaches Event D, the Event C is simultaneous with that same event (C simultaneous with D) in the twin’s inertial frame.

So, I am simply making the observation that as the traveling twin moves along his worldline, Event C is encountered at the start of the twin’s outgoing inertial frame before the Event B is encountered in the twin’s return inertial frame, even though as the Brown observer moves along his own X4 (time) axis, he (Brown) naturally experiences Event B before Event C. And Events D and C are simultaneous in the twin’s inertial frame. That’s all. No implications are drawn here—just an interesting observation for one to interpret however one pleases. Some may find nothing of interest here.

So far as the ability to connect the dots beginning with Einstein’s quotes about solipsism, I realized that many forum members may not be familiar with Bertrand Russell’s development of the concepts of sense impressions and ideas and their distinction. Einstein’s comments should be taken in that context. Russell devoted a lengthy discussion to this subject in his book. He develops this platform to launch the argument in support of an external objective reality. The argument between realists (such as Einstein) and idealists (a significant number of philosophers) has to begin on the turf of the inner experience, so that’s where Einstein has taken it up in the quotes presented earlier where he referenced the “objective” physical reality and asserted the logical conclusion that one who rejects this has “no escape from solipsism.” But it is just the logical beginning point for the analysis leading to refuting the positivist’s denial of the external reality out from the apex of an observer’s light cone. I don’t understand why connecting the dots should be that difficult. Einstein claimed emphatically that he was not a positivist.

Now, about invariants. You folks are corrupting the use of the concept to imply what was never intended. You completely ignore the significance of one of Einstein’s postulates: The laws of physics are the same for all frames (we understand this to mean Lorentz frames). The Lorentz inertial hyperplanes of simultaneity are exactly those for which Einstein’s postulate holds. This is fundamental in understanding the sequence of 3-D volumes (hyperplanes of simultaneity) as presenting the physical reality implied by special relativity.

 

[PeterDonis]

You have totally ignored the importance of Einstein's postulate about the laws of physics and different observer Lorentz frames.

Could you elaborate? I don't understand what point you're trying to make. The only "postulate" I can think of that you could be referring to is the one that says the laws of physics must be invariant under Lorentz transformations; that means the laws have to be written in terms of invariant expressions. That would seem to support what I've been saying.

 

[Mentz114]

Now, about invariants. You folks are corrupting the use of the concept to imply what was never intended. You completely ignore the significance of one of Einstein’s postulates: The laws of physics are the same for all frames. The Lorentz inertial hyperplanes of simultaneity are exactly those for which Einstein’s postulate holds. This is fundamental in understanding the sequence of 3-D volumes (hyperplanes of simultaneity) as presenting the physical reality implied by special relativity.

How would you express "The laws of physics are the same for all frames" without using frame independent concepts ? Nor do I believe "inertial hyperplanes of simultaneity are exactly those for which Einstein’s postulate holds". I think you may be confused.

 

[PeterDonis]

No implications are drawn here—just an interesting observation for one to interpret however one pleases. Some may find nothing of interest here.

In other words, this observation is irrelevant to the rest of the discussion? Fair enough; then I won't bother commenting further on it.

So far as the ability to connect the dots beginning with Einstein’s quotes about solipsism, I realized that many forum members may not be familiar with Bertrand Russell’s development of the concepts of sense impressions and ideas and their distinction. Einstein’s comments should be taken in that context.

I am familiar with Russell's writings on these concepts; the best exposition I know of is in Russell's book Our Knowledge of the External World. I have no problem with the general claims Russell makes in that book, and I would agree that the views Einstein expressed in general terms were similar. The basic idea is that, even if we start by only granting "existence" to our direct sense-impressions, we can't make sense of those sense-impressions without committing ourselves to the existence of an "external world".

However, the disagreement we're having is not about whether an external world exists; it's about *what*, specifically, we are entitled to claim "exists" based on a certain set of sense impressions--i.e., what, exactly, is the "external world" that we need to believe in in order to make sense of a given set of sense impressions. See further comments below.

But it is just the logical beginning point for the analysis leading to refuting the positivist’s denial of the external reality out from the apex of an observer’s light cone.

Nobody here is making a "positivist denial" of external reality. But you have assumed, without proof, that the sense impressions we receive from our past light cone *force* us to believe in an "external reality" consisting of an instantaneous 3-D world. That's simply not a valid claim. To see why, contrast it with the following alternative claim:

Based on the sense impressions we receive, we can only make sense of them by believing in the existence of external objects that send us light signals containing information about them. But the information we receive this way is time-delayed; for example, the Sun that I see is the Sun as it was eight minutes ago, *not* the Sun as it is "now". So the "external world" that I am *forced* to believe in based on my sense impressions does not include the Sun "now"; it only includes the Sun up to eight minutes ago.

I can, of course, make the further claim that, since it is highly unlikely that anything significant will have happened to the Sun in the eight minutes it took for the light I am seeing now from the Sun to get to me, it is highly probable that there is in fact a Sun now--i.e., that the Sun's worldline extends beyond the portion I have direct evidence of in my past light cone. But that is a *different* kind of claim from the claim that I have to believe in an external world based on my sense impressions. The claim that the Sun exists now is an *extrapolation* from the direct data in a way that the claim that the Sun existed eight minutes ago is not.

You completely ignore the significance of one of Einstein’s postulates: The laws of physics are the same for all frames. The Lorentz inertial hyperplanes of simultaneity are exactly those for which Einstein’s postulate holds.

Einstein's postulate says nothing about hyperplanes of simultaneity. Go look at the relativistic formulations of any law of physics--Maxwell's Equations, the Einstein Field Equations, quantum field theory--and tell me where in those laws the hyperplanes of simultaneity are.

 

[Dale]

So far as the ability to connect the dots beginning with Einstein’s quotes about solipsism, ... I don’t understand why connecting the dots should be that difficult.

It isn't about connecting dots. You claimed that Einstein said something that he simply did not say. You may believe that he meant to say what you claimed, or that what you claimed is implied by things that he said, but the unavoidable FACT is that he simply didn't say what you claimed he said.

Why don't you take ownership of your own opinions rather than trying to foist them off to Einstein? Say what you think, defend your ideas on their own merits, and simply leave Einstein out of it. Even where he shares your opinion, that is just a fallacious appeal to authority.

Now, about invariants. You folks are corrupting the use of the concept to imply what was never intended. You completely ignore the significance of one of Einstein’s postulates: The laws of physics are the same for all frames (we understand this to mean Lorentz frames).

The invariants are also the same for all frames, so I don't know what makes you think that we are ignoring the significance of the first postulate by focusing on them instead of frame-variant quantities.

 

[bobc2]

I'm really getting confused about what your fundamental objections are aside from the side bars on interpretations and philosophy.

Are you claiming that Event C is not in the traveling twin's simultaneous space at the start of his journey?

Are you claiming that Events A and B are not in the simultaneous space of the twin just after he has completed his turnaround?

Are you claiming that Events D and C are not in the simultaneous space of the twin when the twin has arrived on his worldline at Event D?

 

[PAllen]

I object to giving any physical meaning to simultaneous space. Simultaneity is a convention. For inertial observers (or in an inertial frame used to analyze some overall scenario), there is a standard convention any reasonable person would use; how far it makes sense to extend it (for an observer) depends on how long they have been inertial. For non-inertial observers there is no preferred convention except 'locally'. A non-inertial observer is analogous to the GR situation - only local frames (with standard simultaneity convention reasonably preferred sufficiently locally in time and space).

I believe this is how Einstein viewed it, but that is neither here nor there.

[There is also the sense of relatively arbitrarily chosen simultaneity surfaces used to construct coordinates useful for some problem. Obviously, I don't consider coordinates a feature of physical reality.]

 

[PeterDonis]

I'm really getting confused about what your fundamental objections are

I'm not objecting to any of the statements you have made about what events are in which simultaneous spaces. If those statements are all you've been trying to say, they strike me as too obvious to be worth taking all this time over.

aside from the side bars on interpretations and philosophy

The sidebars are only there because you have made claims about the interpretation and philosophy of simultaneous spaces. If you would refrain from making such claims we wouldn't need any sidebars.

If you had said things like "I find that looking at hyperplanes of simultaneity helps me to make sense of what is going on" (which is pretty much what LastOneStanding said right before you entered the thread to support what he was saying), I doubt we would have had any sidebars. But you insist on saying things like "hyperplanes of simultaneity are fundamental to relativity", which implies (incorrectly) that they are necessary to *any* understanding of relativity, and then claiming that Einstein said so too, which is a strained (at best) interpretation of what he said.

 

[bobc2]

The weekend is over. Can you please make the OP's requests a priority especially since you are concerned that the moderators are going to lock this thread?

ghwellsjr, I have searched through most of my Einstein writings and must concede that I'm not able to find the reference that I am recalling. Of course there is the possibility that I am mistaken in my recollection, so I'll just have to retract my reference to Einstein discretizing the turnaround into incremental boosts (incremental inertial frames) as I've been describing. Of course the concept is not original with me. You were right to have challenged that. If I ever do come up with it I'll let you know.

By the way, you did a very excellent job of explaining the doppler approach. I've read a number of accounts of this, most recently Paul Davies's discussion, and yours is as good as any and better than most--particularly with your use of the diagrams.

 

[bobc2]

I object to giving any physical meaning to simultaneous space. Simultaneity is a convention. For inertial observers (or in an inertial frame used to analyze some overall scenario), there is a standard convention any reasonable person would use; how far it makes sense to extend it (for an observer) depends on how long they have been inertial. For non-inertial observers there is no preferred convention except 'locally'. A non-inertial observer is analogous to the GR situation - only local frames (with standard simultaneity convention reasonably preferred sufficiently locally in time and space).

I believe this is how Einstein viewed it, but that is neither here nor there.

[There is also the sense of relatively arbitrarily chosen simultaneity surfaces used to construct coordinates useful for some problem. Obviously, I don't consider coordinates a feature of physical reality.]

I guess I just don't catch on to your thinking about how to describe external objective reality with objects moving about in space and time without the use of coordinates. And particularly when we need to select the particular coordinate transformations of the Lorentz group if we are to be assured of physical processes unfolding in the various observer spaces in a manner consistent with the laws of physics.

 

[bobc2]

I'm not objecting to any of the statements you have made about what events are in which simultaneous spaces. If those statements are all you've been trying to say, they strike me as too obvious to be worth taking all this time over.

That's all I'm trying to say. Forum members can muse over any possible implications about the simultaneous spaces with regard to physical reality if they are so inclined. In any case I thought the way the order of the brown clock readings, as they are presented in the traveling twins's frames, was kind of interesting after Vandam had pointed it out in another thread (where is Vandam--he was so pasionate about this stuff?). Others may find nothing of interest there. I never intended to get side tracked into the philosophy of solipsism when I first posted--I tried to keep up with responses to new comments and questions but was inexorably drawn into the sid bars.

 

[Nugatory]

I guess I just don't catch on to your thinking about how to describe external objective reality with objects moving about in space and time without the use of coordinates.

It can be done. Any physical situation can be described in terms of proper time along timelike worldlines and the points at which these worldlines intersect lightlike null worldlines.

However, coordinates are a really really convenient calculating tool in many problems... So we use them a lot.

 

[Dale]

I guess I just don't catch on to your thinking about how to describe external objective reality with objects moving about in space and time without the use of coordinates.

Think about different ways you can describe the location of your house. You can give its latitude and longitude. Alternatively you could give some landmarks e.g. 2.3 miles past the post office on Balderdash Rd.

And particularly when we need to select the particular coordinate transformations of the Lorentz group if we are to be assured of physical processes unfolding in the various observer spaces in a manner consistent with the laws of physics.

The thing is that we already know experimentally that physical processes don't in fact transform according to the Poincare group globally, only locally. So we need to write the laws of physics in a manner that is consistent with completely arbitrary coordinate transforms because we know that the Lorentz transforms don't work globally.

Since we need to do that globally anyway, we can also do it locally. We then clearly see that the laws of physics don't care one bit what coordinate systems we use, and the actual laws of physics are expressed entirely in terms of invariant quantities.

 

[PeterDonis]

I never intended to get side tracked into the philosophy of solipsism when I first posted--I tried to keep up with responses to new comments and questions but was inexorably drawn into the sid bars.

I agree that your first post in this thread (#32, unless I missed something) didn't do anything more than draw the simultaneity planes in different frames and comment on them. But your next post (#34) used the word "fundamental":

I certainly have no fuss about doppler. Any special relativity course would not be complete without understanding that. But the real fundamental stuff of special relativity is intimately related to the time dilation, length contraction and hyperplanes of simultaneity as manifest in the Lorentz transformations and the space-time diagrams.

If you had qualified this with "for me", or "in at least one common method of teaching SR", it would have been different. But you made a blanket statement about what's "fundamental", which comes across as being about something more than just what works best when teaching or explaining.

Then, in post #38, you made the statement that I first responded to:

The attempt to replace the direct Lorentz based relativity of simultaneity with the doppler approach is just an argument based on philosophical ideas.

Again, if you had said "I find it much easier to understand and explain SR using relativity of simultaneity, etc., vs. doppler" that would have been different. But you brought in the "philosophical ideas" (that word had only been used once in this thread before your post, and nobody picked up on that one, by LastOneStanding).

 

[zonde]

I disagree completely. Experiment (scientific method) is the foundation of science and what distinguishes it from philosophy.

Discussions about scientific method are philosophy. Improvements in scientific method like falsifiability are philosophy.

The foundation of science is the scientific method. The scientific method requires that a theory make experimental predictions, but doesn't otherwise constrain the method of making those predictions.

Yes

In relativity the experimental predictions of the theory are all invariants.

Can you elaborate on this? First, is invariant defined or is it undefined basic concept?
Because the way it is usually defined i.e. some quantity that does not change under coordinate transformation, is confusing as it is defining invariants using concept of coordinates and consequently coordinate dependant quantities that we are using to construct coordinates. So coordinate dependant quantities are more basic than invariants.

The invariants are also the same for all frames, so I don't know what makes you think that we are ignoring the significance of the first postulate by focusing on them instead of frame-variant quantities.

Invariants are not the same as physical laws. They are certainly two different things.

 

[PAllen]

I guess I just don't catch on to your thinking about how to describe external objective reality with objects moving about in space and time without the use of coordinates. And particularly when we need to select the particular coordinate transformations of the Lorentz group if we are to be assured of physical processes unfolding in the various observer spaces in a manner consistent with the laws of physics.

I don't say you don't use coordinates. But they are analogous to the lines you draw on a globe to label positions. The globe and relief features on it exist independently of what lines I draw. Coordinates are not an aspect of reality. The Lorentz group is simply the group of transforms that preserve the flat space metric in simplest form. The physical principle of relativity is that absolute (inertial) motion cannot be detected. The difference from Galilean relativity is that light speed is included in what is the same for every inertial observer. There is nothing more special about Minkowski coordinates than there is about Cartesian coordinates on a plane (metric is in simplest form). Its geometry is there with no coordinate labels; if I draw polar coordinates, the geometry hasn't changed, only the process of computing things.

Your claim about some preferred meaning to your chosen 'simultaneity space' is equivalent to insisting that only cartesian coordinates are valid on a plane. Even more, that if we draw some arbitrary curve on a plane, and then want treat it as a coordinate axis, we must use lines perpendicular to its tangent at each point.

 

[Dale]

Discussions about scientific method are philosophy. Improvements in scientific method like falsifiability are philosophy.

I already covered this back in post 83 with my statement: "I cannot think of any philosophical proposition that has any scientific value except for those which are essentially restatements of Bayesian inference."

I was specifically thinking of falsifiability and Occham's razor, both of which can be derived from Bayesian inference, which is the mathematical framework for inductive reasoning. So falsifiability is not a counter-example and I stand by my previous assertion.

Can you elaborate on this? First, is invariant defined or is it undefined basic concept?
Because the way it is usually defined i.e. some quantity that does not change under coordinate transformation, is confusing as it is defining invariants using concept of coordinates and consequently coordinate dependant quantities that we are using to construct coordinates. So coordinate dependant quantities are more basic than invariants.

The term "invariant" itself is indeed defined as a quantity that does not change under coordinate transformations, so that term does presuppose the definition of coordinates etc. However, each invariant physical quantity can be defined without reference to coordinates.

For example, proper time can be defined physically as the time measured by a clock. It can also be defined geometrically as the integral of the spacetime interval along a timelike path. Neither of these definitions require coordinates. Similarly with the other invariant quantities used in physics.

You can define all of your physical theories in terms of these invariant quantities without reference to coordinates. Then, once you add coordinates, you can note that all of the quantities that show up in your physical theories are invariants, and you can refer to them collectively as "invariants" without at all implying that they are less basic than coordinates and coordinate-dependent quantities.

 

[zonde]

However, each invariant physical quantity can be defined without reference to coordinates.

So how do I tell apart invariants from everything else?

 

[Ken G]

So how do I tell apart invariants from everything else?

Perhaps your issue is you have not yet connected the concept of "invariant" with the concept of "objectivity", but that is an important connection to draw because all of science is based on what can be objectively established. The latter means, that which different observers can agree on based on their measurements. Or another way to say it is, physics is about predicting measurements, given that we know some things about the state of the measurer. Relativity adds to that the beautiful idea that the laws we use to establish what those predictions must not depend on those things, only the predictions themselves must. Before relativity, this important distinction was not made-- a measurement established something as true for all observers. With relativity, we found that a measurement only establishes something as true for that measurer, and an observer in a different state might arrive at a different measurement, but can still use the same laws of physics to predict either one of those measurer's results--so long as they account for the measurer's state.

Hence we suddenly had a need for the concept of translating between measurement outcomes, and one way to do that is via invariants. But the invariant is more than just a mathematical trick for doing the translation-- it is the thing that the measurements are referring to, in the sense that it is the thing that is objective. So to me, the main lesson of relativity is that measurements are only "objective" if we keep track of the state of the measurer, whereas the invariants we construct from the measurements are objective in the true sense of being the same for all observers. That's also why a special relativistic invariant is indeed just a kind of mathematical trick, a means to an end, whereas a general relativistic invariant is actually what the laws of physics must refer to (at least, insofar as general relativity is a good theory of physics). That was, after all, Einstein's primary motivation for GR-- he never liked singling out the inertial observers, and I imagine that's because it didn't seem very objective to do so.

I think an analogy can help us see deeper into what objectivity means. Imagine a "chick flick" that is being reviewed. Let's rampantly overgeneralize and say that women like this movie and men find it boring. Now imagine a male reviewer who pans the movie and a female reviewer who says it's oscar-worthy. Are either of those reviews making objective claims about the movie? No, the objective claim, and the best review, are simply the statement that women will like this movie and men will hate it (again ignore the absurdity of such sweeping generalizations about movies). Can we say if the movie is good or not? No, we cannot, there is no objective way to do that-- all that is objective is to account for how each person will experience the movie. And how can we tell how each person will experience the movie? By considering what is invariant about that movie-- what aspects can men and women both agree this movie has? So even though we might thus say that experiencing a movie is something subjective, we can still say that accounting for that experience is objective. It is the latter, not the former, that underpins science, and hence the need for invariants.

That's what relativity is trying to tell us, and it was completely new to science at the time, but then quantum mechanics came along and gave us additional reasons to track what the observer is doing. Personally, I'd say the main lesson of physics of the 20th century is that we can never again imagine that physical reality has an existence completely separate from how we perceive it. But then again, Einstein never liked quantum mechanics!

And on the matter of the "reality" of the concept of relativity of simultaneity, I agree completely with DaleSpam. What's more, I'd say the well-known "Andromeda paradox" that bobc2 is talking about makes pretty clear the unreality of the entire concept of global simultaneity. We should have learned from relativity that simultaneity is a strictly local concept whose usefulness gets diluted with larger and larger (invariant) separation between the events. Maybe this lesson will someday prove false, but it's all we have to go on at the present moment (pun intended).

 

[PeterDonis]

So how do I tell apart invariants from everything else?

Mathematically, they are picked out by being either Lorentz scalars, like the invariant mass of an object, or integrals of Lorentz scalars, like the proper time along a curve. Contrast this with, for example, energy, which is a component of a 4-vector.

 

[Ken G]

(nitpick: 4 vectors are also invariants, as are the tensors of GR. Also, the laws built from those objects are themselves invariants, as are the invariant parameters embedded in those laws like e and c. But measurements are always scalars, so the positivist might further restrict the "real" invariants to just the scalars, whereas a more rationalistic philosopher might allow all the classes of tensorial invariants, and the parameters of the theory, to be considered "objectively real." Personally, I hold that no quantity that has units is something real, but here we are just talking about what can be considered an invariant. So perhaps we must allow zonde that even the concept of an "invariant" contains some troubling elements, a suggestion that we have not penetrated the mystery completely!)