# Relativity Explained Via Movement, Not Time

Dale
Mentor

Oh, I was just thinking that Newtonian time is the t when the equations are expressed in an inertial frame. Would that definition be detectable (in principle)?
I think that would be detectable in principle. I kind of like that definition. It wouldn't be hard to generalize.

No, the count of a set of spacelike separated events is not measuring anyone's time.

In particular, without a definition of time how do you determine "before" and "after"?
This is where Aristotle got all mucked up with the mystical 'Now'. Now's, according to him, are between the before and after. But before and after are just comparisons of how things are, or how we see them. The car was in the driveway before it was in the street. The clock pointed at 1:00 before it pointed at 1:01. Or backwards. If you stick a Now between the before and after, you have two sets of befores and afters.

Here's what's in my craw though, is that starting with Time and trying to define it doesn't work. The reason Time's a count isn't because that's the great definition of Time. It's because we looked at things changing and then called that Time. It's the changes that are at the center. We're just looking at changes and putting some counter to them so that we can compare other changes to that counter.

It's a paradigm shift. You can even forget little t. You take two things changing and compare them. That's what velocity (or speed, rate, frequency, etc.) is - two counts of two things changing and then comparing the two. Instead of calling the count of the clock little t, you just call it the count of the clock.

And of course, all counters work differently under different conditions. Even the second's defined as a count at a specified temperature.

atyy

I think that would be detectable in principle. I kind of like that definition. It wouldn't be hard to generalize.
I've read various versions of this definition of Newtonian time ("time is what makes the equations of motion true") in Stephani's and Misner, Thorne and Wheeler's GR texts. That makes it like the proper time and coordinate times of Lorentz inertial frames which exist even in special relativistic field theories which happen not to have any periodic solutions (although in real life theories, we luckily seem to have solutions that are periodic for all practical purposes).

Dale
Mentor

The reason Time's a count isn't because that's the great definition of Time. It's because we looked at things changing and then called that Time. It's the changes that are at the center.
Then you should define time in terms of changes, not counts.

I am not going to re-hash the conversation that I just went through with my_wan, go back and see all of the reasons why "time is a count of events" is insufficient. You need to add some constraints, and so far those constraints make the definition circular.

@DaleSpam: @my wan: Is the difference between your points of view that physics is always the study of change dy/dx, but if there is only one "dimension" DaleSpam would call that "space" and my wan would call it "time"?
No that would not work for my opinion and almost certainly would not work for DaleSpam even before reading his response. Neither DaleSpam is making any claims that empirically differ from the standard formulation. I am only arguing that as defined such an event based interpretation works.

No, the count of a set of spacelike separated events is not measuring anyone's time.

You are contradicting yourself saying that "counting events" is completely sufficient and then adding constraints. The "time is counting events" definition is clearly insufficient as you have de facto conceded. You must add such enumerated constraints or clarifications as above.

The causality constraints are particularly problematic for a definition of time. Causality requires a notion of time, so putting a causality constraint into your definition of time makes the definition circular. In particular, without a definition of time how do you determine "before" and "after"?

Btw, I am not opposed to a background independent relational definition of time. I just think that "time is counting events" is way oversimplified. Something this important needs quite a bit more effort and care than that. Many things which qualify as counting events do not qualify as measuring time.
I stated that constraint up fron even before you made the first response to me and in my very first response to you. So no that is not a contradiction.

Consider what it we count in a standard derivation of the Lorentz transform. Take the light mirror where light is bouncing back and forth between two mirrors. We are counting the bounce events at each mirror. If we merely watch the clock we are counting ticks of the clock, etc. In fact we cannot measure "anything" without checking off events that are registered. Whether of not there is a smallest or most fundamental event is immaterial to the argument.

I agree simply saying "time is counting events" is a bit oversimplified. Einstein simply said: "Time is what we measure", and I am saying what we measure are events. The statement really does not go much further than that. It is not fundamentally different. Yet since time effects all else we measure a lot more is involved than just the statement itself. Events can be defined in terms of intervals and that is what SR defines. When we "count" such events we plot them on a graph and curve fit them, taking the limit. But The limiting factors work whether the events involve actual limiting points or not.

Why then do physicists persist in using the notion of "time" in explaining relativity? It would be so much easier, more intuitive and correct to talk of (relative) movement and not time.
Can you show how relativity can be defined using relative motion alone in the absence of using space and time?

GrayGhost

Dale
Mentor
I agree simply saying "time is counting events" is a bit oversimplified.
Excellent.

Events can be defined in terms of intervals and that is what SR defines.
Yes, I think that is a better approach since the interval is equal to the scaling you were refering to earlier, it contains the causal structure, and it can be used to exclude the timelike sets of events I mentioned.

Excellent.

Yes, I think that is a better approach since the interval is equal to the scaling you were refering to earlier, it contains the causal structure, and it can be used to exclude the timelike sets of events I mentioned.
There are so many ways to look at relativistic effects that are not wrong it is ridiculous. It is only when you try and say what the "real" (absolute) metric of the interval is that it goes over the edge. That makes it a generally a bad idea to think in terms of specific metrics, but the event count works because it does not specify any metric for such events except relativistically.

Whether or not there is a fundamental Planck cutoff or such intervals are maintained in the limit as Einstein imagined is an open question. Since you can just as easily take the limit on events as you can an interval it makes no empirical difference either way. If there is a Planck cutoff it just means your fit become choppy and irregular at very small intervals, macroscopically normalized by a Poisson distribution.

The thing is the thesis of this post: Relativity explained via Movement, not "Time". In fact, we could re-write the title:

'Relativity Explained by L/t, not "t".'

Well enough. I don't think that's too far from what Einstein said, the L/t in question being c, which is a constant in all observers' frames of reference. Sorta QED, no?

In my humble opinion that is a step in the right direction. If I recall correctly, even Einstein himself was initially inclined towards "invariantentheorie" instead of 'relativity' theory. I can't quite recall who prevailed upon him to name it relativity instead.

The benefit to my mind is that by concentrating on the measure of an absolute, invariant movement reference which is c, you avoid saying things like 'time will do this' or 'time will do that', avoid treating time in the agentive form. It is a linguistic point but important to the layman like me who is trying to understand relativity. It is much easier to conceive and understand of material objects which move than immaterial notions that dilate or flow...

IH

Excellent.

Yes, I think that is a better approach since the interval is equal to the scaling you were refering to earlier, it contains the causal structure, and it can be used to exclude the timelike sets of events I mentioned.
Agreed, time as a notion covers both counting and sequencing, the premise being that the sequence is ever-increasing.

Can you show how relativity can be defined using relative motion alone in the absence of using space and time?

GrayGhost
In terms of definition, one needs an absolute movement reference which is c, a set of events and the notion of simultaneity. The movements linked to relative events can be physically measured in space as can c. The instrument which we use to link these is simultaneity which is elaborated in our minds based on our physical perceptions and measurements. The collective set of simultaneous events provides the structure of our notion of time. Time remains a notion and not a physically measured phenomenon.

To redefine relativity in terms of motion alone, I would imagine one needs to benchmark all movement to the simultaneous movement of a photon. To my mind, simultaneity does not imply the physical measure of time, just the physical measurement of co-perceived events. The co-perception is a product of our willed sequencing and measurement, not in my opinion of 'physical' time.

IH

Dale
Mentor

There are so many ways to look at relativistic effects that are not wrong it is ridiculous. It is only when you try and say what the "real" (absolute) metric of the interval is that it goes over the edge. That makes it a generally a bad idea to think in terms of specific metrics, but the event count works because it does not specify any metric for such events except relativistically.
I don't understand your point here. All the spacetime metrics that I know of are relativistic. I have no idea what you mean by '"real" (absolute) metric' and why you think that would make it "a generally a bad idea to think in terms of specific metrics" (e.g. Schwarzschild metric).

Islam Hassan,

OK. So basically, model relativity w/o the use of time using only the relation of events based upon our sense of simultaneity and using an invariant speed photon as a common reference. IOWs, do what Einstein did, w/o using time, but rather using something else instead. In your estimation, that "something else" should be physical and not a man made notion. For otherwise, you'd simply be replacing what you believe to be one man made notion for another ... and then the big question is, would anything be gained or lost?

Can you give one simple example of how the extent of relative motion would be quantified w/o using time? Have you ever tried this?

GrayGhost

I don't understand your point here. All the spacetime metrics that I know of are relativistic. I have no idea what you mean by '"real" (absolute) metric' and why you think that would make it "a generally a bad idea to think in terms of specific metrics" (e.g. Schwarzschild metric).
The same stuff when you try to ask questions like which clock is "really" go slower. Gr effects makes invariants verses constants issue even more relevant, since it distorts SR in ways that makes the constants more like a choice. Take the apparent mass of an object as its depth in a gravitational field varies. Einstein chose perfectly sensibly to define it as 'apparent' mass. But if you get exactly the same effect if the 'apparent' gravitational constant was what varied, or even the 'apparent' speed of light. In Einstein' words:

"Relativity: The Special and General Theory" said:
In the second place our result shows that, according to the general theory of relativity, the law of the constancy of the velocity of light in vacuo, which constitutes one of two fundamental assumptions in the special theory of relativity and to which we have frequently referred, cannot claim any unlimited validity.
In context this does not invalidate the constancy of the speed of light. This general feature extends to all invariants, not constants. Hence the QG community has their controversy over how much this applies to Planck's constants. This is also the basic theme behind "doubly special relativity". Note why GR gets in trouble with Planck's 'constant' when in terms of Planck length and time:
$$c = \ell_p/t_p$$
Planck mass:
$$m_P=\sqrt{\frac{\hbar c}{G}}$$
So you can take any first order quantity and express it in terms of pure constants, called the indefinables of physics (space, time, and mass/energy), where all must 'locally' be invariant or more generally some multiple thereof. Yet globally they vary, in the same way light speed does in GR, where the manner in which they vary is both frame dependent and definition dependent, like the apparent mass verses apparent value of G. That is where the so called varying speed of light (VSL) theories get their 'theoretical' legitimacy from. Not from any claim that the speed of light 'actually' changed, as Einstein articulated following the quote I give above.

Dale
Mentor
The same stuff when you try to ask questions like which clock is "really" go slower.
Do you have a good definiton of the word "real"? I certainly don't. Without one you will always run into trouble whenever you ask any questions about the reality of anything. That is hardly any kind of argument against that thing.

Gr effects makes invariants verses constants issue even more relevant, since it distorts SR in ways that makes the constants more like a choice. Take the apparent mass of an object as its depth in a gravitational field varies. Einstein chose perfectly sensibly to define it as 'apparent' mass. But if you get exactly the same effect if the 'apparent' gravitational constant was what varied, or even the 'apparent' speed of light. In Einstein' words:

In context this does not invalidate the constancy of the speed of light. This general feature extends to all invariants, not constants. Hence the QG community has their controversy over how much this applies to Planck's constants. This is also the basic theme behind "doubly special relativity". Note why GR gets in trouble with Planck's 'constant' when in terms of Planck length and time:
$$c = \ell_p/t_p$$
Planck mass:
$$m_P=\sqrt{\frac{\hbar c}{G}}$$
So you can take any first order quantity and express it in terms of pure constants, called the indefinables of physics (space, time, and mass/energy), where all must 'locally' be invariant or more generally some multiple thereof. Yet globally they vary, in the same way light speed does in GR, where the manner in which they vary is both frame dependent and definition dependent, like the apparent mass verses apparent value of G. That is where the so called varying speed of light (VSL) theories get their 'theoretical' legitimacy from. Not from any claim that the speed of light 'actually' changed, as Einstein articulated following the quote I give above.
None of this seems to indicate why using the metric is a bad idea.

As you and I have already agreed, you cannot simply count events to get time, you must add some additinal constraints. In particular you mentioned causality and scaling, both of which are provided by the metric. So I don't see any difference between defining time in terms of counting events with scaling and causality constraints and defining time in terms of the metric.

In your estimation, that "something else" should be physical and not a man made notion. For otherwise, you'd simply be replacing what you believe to be one man made notion for another ... and then the big question is, would anything be gained or lost?
GrayGhost,

Yes I believe something would be gained, at least for laymen like myself. The phenomenon which led me to consider movement instead of time as the focus of an explanation for relativity is that of 'time' stopping at the speed of light (or at anything approaching the speed of light for a massive object). I found this very difficult to understand intuitively. Then I tried to reason from a movement perspective and found that an intuitive explanation suddenly snapped into place. The following is how it happened:

- A fan say, or any mechanical object travelling at 0.99999... the speed of light would gain mass according to special relativity. The closer it gets to c, the more massive it becomes and as it tends more to c its mass tends to infinity;
- It takes infinite energy to move a mass tending to infinity; and
- Therefore with the limited electrical energy feeding its motor, the fan's movement will tend to absolute immobility.

Explained this way, the layman that I am understands the phenomenon easily and intuitively. Explained in terms of the semantically funky 'time dilation', such is not the case at all.

I can quite understand that seasoned physicists are quite used to the present terminology and don't really need any other 'interpretation' to make sense of SR; my focus, as I said is on the layman for whom relativity can be quite a daunting proposition...

This is one example but I am sure there are others. My basic thesis therefore is that explaining relativity at the most basic, phenomenological level makes it more easily comprehensible. Just a lay opinion of course, but there you go...

I'm still working on your challenge re a simple example of how the extent of relative motion would be quantified w/o using time; get back to you soon.

IH

All the spacetime metrics that I know of are relativistic.
Euclidean Metric

Do you have a good definiton of the word "real"? I certainly don't. Without one you will always run into trouble whenever you ask any questions about the reality of anything. That is hardly any kind of argument against that thing.
As far as the word real, if someone is asking which clock is really going slower they are almost certainly assuming a Euclidean metric, such as in Newtonian physics. We know the absolutes this entails to be wrong. Hence specifically what is 'meant' by the the word 'real' is moot when the question itself entails demonstrably invalid assumptions.

None of this seems to indicate why using the metric is a bad idea.
Which metric? A Euclidean metric is demonstrably wrong in the general case. In terms of scale any coordinate choice is a nonphysical choice even if you apply the transforms needed to give a Euclidean metric some level of observer dependent validity. By assuming time is an independent variable from the events it 'smells' of Newtonian time with an added feature of malleability. This is not so.

Suppose you go 86% the speed of light getting a dilation factor of 1/2. To you time did not dilate, the distance to your destination was cut in half. Now suppose you decrease gravitational depth to the field around the ship to erase the relative time dilation factor between you and back home. Only now, without changing your proper motion from Earths perspective, you see as measured by you that you have twice as far to travel to get to your destination, hence will take you twice as long. The same amount of time it appears to take you from Earths perspective.

You cannot separate time from the events you observe under any circumstances, at least not without playing 'what if' games with energy conditions outside observable reach.

As you and I have already agreed, you cannot simply count events to get time, you must add some additinal constraints.
I agreed that saying time is a "bit oversimplified", not invalid. I would have left the debate there except that you quoted that naked sentence while the qualifiers that followed was ignored. In fact you can (and it is in fact what we do) to not only define time but to derive all the relativistic Lorentz transforms when event counts do not match.

When we measure something we record a series of events. Then we curve fit these events as if they occur on a continuum. Whether they actually do exist on a continuum or not is immaterial, as what we empirically record is not the continuum but a discrete series of events. So in fact everything we empirically know about time was derived from a discrete series of events, i.e., "what we measure".

In particular you mentioned causality and scaling, both of which are provided by the metric.
So you are using metric in the very narrow sense of a particular type of metric. Euclidean metrics explicitly require transforms for the very fact that they are not valid in the more general case. You say they are "provided by the metric", implicitly meaning Lorentz metric rather than metric. Even so you have a major reversal of logic here. The event count is not "provided by the (Lorentz) metric", the Lorentz metric is provided by the event count. Such as flashes of light on a train in Einstein's SR derivation. This reversal of logic is confusing to a lot of people. The empirical events justify the theory, the theory does not justify the empirical data.

So I don't see any difference between defining time in terms of counting events with scaling and causality constraints and defining time in terms of the metric.
Again, you implicitly referred to the Lorentz metric 'only' as if it was "the" metric. Yet the Lorentz metric was explicitly derived from discontinuities in counting the same discrete events from alternate perspectives and noting that they did not match the local discrete event counts in each of those perspectives. If no events occur there is nothing to count or do the counting hence the notion of time is moot. It is in fact discrete event from which the Lorentz metric was derived, however much we theoretically idealize it after the fact.

atyy

It is in fact discrete event from which the Lorentz metric was derived, however much we theoretically idealize it after the fact.
But if you want to have "theory-free" definitions, how can you even define an event?

Also, if you didn't need the theory to define time, how do you explain that we have theories with a preferred time, as well as theories with many times?

Last edited:
Dale
Mentor

Which metric? ...
So you are using metric in the very narrow sense of a particular type of metric.
This is a relativity forum, so I am using "the metric" in the usual sense in relativity. I.e. the unique metric for a given spacetime manifold. There is only one for any given spacetime, so it is not just narrow, it is unique. It is never Euclidean so the bulk of your post is rather irrelevant.

I thought that this standard meaning of the phrase "the metric" would be well-understood by anyone posting here; I apologize for my poor communication.

The event count is not "provided by the (Lorentz) metric"
I never said it was. The scaling and causality constraints are provided by the metric. When you take a set of events, add a causality constraint, and scale it appropriately, and call the result "time", then you have done nothing more nor less than evaluate the metric between the events.

But if you want to have "theory-free" definitions, how can you even define an event?

Also, if you didn't need the theory to define time, how do you explain that we have theories with a preferred time, as well as theories with many times?
I am not talking about "theory-free" definitions. I am talking about the fact that theory is empirically driven, not the other way around.

With respect to "preferred time" do you mean direction? I do not want to answer that presumptuously as I can relate it to too many concepts. However, I do not know in what way I said you do not need "theory to define time". I said that the legitimacy of theory is predicated on and justified by the empirical data, not the other way around. Without which it is nothing more that philosophy. And that this empirical data, as it relates to time, was in fact the result of counting discrete events. The fact that we need a theory for operational consistency does not raise theory above the empirical constraints it is predicated on.

My initial statement, which has been taken issue with, is that time can consistently be viewed in terms of event counts. A bit simple, but fully defensible empirically. When Einstein said "time is what we measure" it was simplistic also. My statement merely boils down to defining "what we measure", and that is discrete series of events. Theoretically it works whether it comes in discrete steps or not, but the fact remain: We measure discrete series of events.

Dale
Mentor
My initial statement, which has been taken issue with, is that time can consistently be viewed in terms of event counts. A bit simple, but fully defensible empirically.
The complexities glossed over by the "bit simple" are important, as we have discussed. An arbitrary event count is NOT a measure of time without the causality and scaling constraints.

This is a relativity forum, so I am using "the metric" in the usual sense in relativity. I.e. the unique metric for a given spacetime manifold. There is only one for any given spacetime, so it is not just narrow, it is unique. It is never Euclidean so the bulk of your post is rather irrelevant.

I thought that this standard meaning of the phrase "the metric" would be well-understood by anyone posting here; I apologize for my poor communication.
Are you saying that because I am on a Relativity forum I cannot use "metric" in the general sense, which includes any choice of coordinate system? It is GR that prides itself the most on treating all coordinate systems equally.

Perhaps some of these points are a bit on the pedantic side, but no more or less so than taking issue with defining time in terms of event sequences.

I never said it was. The scaling and causality constraints are provided by the metric. When you take a set of events, add a causality constraint, and scale it appropriately, and call the result "time", then you have done nothing more nor less than evaluate the metric between the events.
Funny, I can turn this around again and say "causality constraints" is not "provided by the metric", the "metric" is provided by the "causality constraints".

I wonder, how much of this inversion of logic is behind many of the established controversies in science?

The complexities glossed over by the "bit simple" are important, as we have discussed. An arbitrary event count is NOT a measure of time without the causality and scaling constraints.
The same constraints I qualified with both before you responded and in my first response to you. The "bit simple" was no more or less "bit simple" than "time is what we measure". That was the point of the post where I said that. Only you chose to chop out the "bit simple" part for your quote of me.