4 four momentum energy component direction

[whatif]

As such, we can decide exactly what they mean.

There should be consistency and it should reflect the physics. I do not think that is happening in this instance. I have explained my position and I will not labour the issue further.

 

[Dale]

There should be consistency and it should reflect the physics.

The reason that units are conventions is that there is more than one way which is both self consistent and also consistent with the physics.

 

[PeterDonis]

It is not known as fact that the same units in name for the timelike and spacelike mean the same thing.

"Mean the same thing" is ambiguous unless you can suggest how we could test experimentally whether it is the case or not. Can you suggest such a test? You suggest things as "evidence", but if that evidence is not conclusive enough, what further evidence would you need?

 

[whatif]

The reason that units are conventions is that there is more than one way which is both self consistent and also consistent with the physics.

That applies when, for example, you decide what is positive or negative.

It does not matter whether we drive on the right hand side of the road or the left hand side of the road, so long as we all drive on the same side of the road.

On the topic at hand, units are removed from the speed of light by a mathematically tool without consideration of the physics.

 

[whatif]

You suggest things as "evidence", but if that evidence is not conclusive enough, what further evidence would you need?

We disagree about what constitutes sufficient evidence. I would say that:

• timelike properties are clearly different from spacelike properties, for reasons I have given.
• others claim timelike and spacelike properties are the same despite those differences and having to measure and treat them differently. If you claim they are the same, then you preclude testing experimentally that they are different because of the relationship between them and the mathematics used.
• others have taken the unification of space and time into spacetime too literally for no good reason. That is, the time direction is not a fourth space direction.

So be it.

 

[PeterDonis]

We disagree about what constitutes sufficient evidence.

We do? As far as I can tell, you are saying that you need a better explanation, and I'm saying that we don't currently have one. So I don't see how what you are saying disagrees with what I am saying. I just think we are emphasizing different aspects.

 

[pervect]

It is not that I do not the geometric units. It is about the conclusion of what the mathematics is saying.
Everything comes at a cost. The cost is realising the units mean for different things for timelike timespace and spacelike timespace; but that is easy.

My impression is that you are arguing philosophy and semantics, but if you can suggest an experiment that can resolve exactly how "timelike timespace and spacelike timespace" (which aren't really standard terms and seem a bit awkwards, but I think I can guess what you mean) are "different things", I'm willing to listen.

If you're arguing about something that isn't even in principle experimentally testable, I don't think there's ever going to be a scientific resolution. Issues that are not testable are not in the realm of science, but philosohpy. Philosophical discussions on PF are currently implicitly discouraged, as they are "permitted at the discretion of the mentors." according to the global guidelines. Presumably the mentors currently no objection since the thread is still open, personally though I don't see where the discussion is going anywhere.

I do have some personal bias (for lack of a better term) against philosophy which can probably be traced to the writings of Feynman, see for example "Is Electricity Fire". This bias aside, it is certainly possible to have good philosophical discussions with references to the philosophical literature. PF forums, though, don't seem to be conducive to such high-quality discussions. Frequently we have people stating closely-held personal opinions without much in the way of logical justifications or references to what other people in the field of philosophy have written. This is the primary reason for the limitations on philosophical discussions mentioned in the PF global guidelines.

 

[whatif]

My impression is that you are arguing philosophy and semantics

My impression is that the use of geometric units is turning the notion of units on its head, by giving the same unit to different physical properties. If you call that philosophy and semantics then so be it. My impression is that it is inconsistent.

 

[Dale]

On the topic at hand, units are removed from the speed of light by a mathematically tool without consideration of the physics.

The SI units, for example, are not found in physics. They are the result of a committee that meets to decide what those units mean. People realize that the size of the units is a matter of convention, that the BIPM committee can arbitrarily choose how large a meter is and how large a kilogram is.

What is not as well appreciated is that the dimensionality of a quantity is also a matter of convention that can be decided by the committee. For example, in SI units electrical charge has dimension $Q$ and units $C=A\;s$. However, in cgs units electrical charge has units $statC=g^{1/2}cm^{3/2}s^{-1}$ and dimension $M^{1/2}L^{3/2}T^{-1}$. So not only the size of the units is a matter of convention but also the dimensionality.

There are systems of units that consider mass and charge to have the same dimensionality. There are systems that consider energy and length to have the same units. There are systems that consider horizontal distance and vertical distance to be different.

All of these systems of units can be used to do physics, and there are good well-considered physics reasons for each of them. Each one is consistent with the outcome of all physical experiments. So each one is equally valid physically. It is purely a matter of convention.

 

[Nugatory]

My impression is that the use of geometric units is turning the notion of units on its head, by giving the same unit to different physical properties. If you call that philosophy and semantics then so be it. My impression is that it is inconsistent.

If your impression were correct then either general relativity, which is based on this equivalence, is also inconsistent or it should be possible to construct a consistent theory of gravity that does not require this equivalence.

Both of these possibilities are unlikely enough that you might want to give more weight to another possibility: Your thinking about time and distance is based on a lifetime of experience at non-relativistic speeds, and this experience is misleading you.

 

[whatif]

So each one is equally valid physically. It is purely a matter of convention.

That is OK, so long as it is understood, that implicitly by convention, the unit of a property does not necessarily have anything to say about the property. That is, the expression of a number, together with units, does not necessarily distinguish between the physical properties to which it is applied.
I do not think that is a matter of semantics.

 

[whatif]

Both of these possibilities are unlikely enough that you might want to give more weight to another possibility

It would be harder but not impossible to construct a consistency theory without using geometric dimensions.

Everything is understood, so long it is understood that the expression of a number, together with dimensions, does not necessarily distinguish between the physical properties to which it is applied. (I hope my use of 'units' did not cause confusion in the above message).​

 

[Nugatory]

It would be harder but not impossible to construct a consistency theory without using geometric dimensions.

Can you produce such a theory? Or failing that, do you have a plausible suggestion for how such a theory might be constructed?

 

[Dale]

implicitly by convention, the unit of a property does not necessarily have anything to say about the property. That is, the expression of a number, together with units, does not necessarily distinguish between the physical properties to which it is applied.

I am not sure I understand what this means, but I think maybe I agree.

 

[whatif]

Can you produce such a theory?

I could not have produced the theory of relativity in the first place.

In principle, it is just a question of accounting. For example, to start off, I would copy the theory but rather than using meters for time I would use seconds. That means that whenever time was used used in calculations it would require the use of the constant for the speed of light, c. The principal is simple, the application is tedious, which makes it more prone to mistakes.

From Taylor and Wheeler:

The parable of the surveyors cautions us to use the same to measure both time and space.

If you know of the context and understand the reference, then I would say that to abide by that caution is not a necessity. Also, the caution does not quite fit with the parable (no analogy is perfect). Time is a different property than space. Timelike is different than spacelike. If everyone used seconds for time and meters for space then they would still agree.

Everything is understood, so long it is understood that the expression of a number, together with dimensions, does not necessarily distinguish between the physical properties to which it is applied (using seconds for time and meters for space distinguishes between time and space).

 

[Ibix]

using seconds for time and meters for space distinguishes between time and space

How do you distinguish between time and space? What I call "time" another frame will call "a bit of time and a bit of space". Should that other frame use seconds to describe intervals in my time direction, even though it includes distance in space?

I think a sensible answer to this will conclude that you mean to distinguish between timelike and spacelike, not between time and space. And distinguishing between timelike and spacelike is what the metric does. Why, then, would you need your unit system to do it too?

The whole argument feels to me like arguing that we ought to use fathoms for vertical distances and meters for horizontal ones because you can't measure horizontal distance with a plumb line. You can, of course, measure any distance with a ruler - you just hold it pointing horizontally or vertically. Similarly you can measure intervals with a radar set - just say you know the distance and it's a light clock, or say you know the time and it's a radar set.

 

[whatif]

Why, then, would you need your unit system to do it too?

You don't.

I am used to dealing with measurements that do reflect the properties to which they are applied and I dare say that applies to many people new to relativity. It just needs to be realized that a meter of time is not the same as a meter of space. "a bit of time and a bit of space" is a mix of two different properties. Timelike and spacelike are different properties.

The whole argument feels to me like arguing that we ought to use fathoms for vertical distances and meters for horizontal ones because you can't measure horizontal distance with a plumb line.

That is not a good analogy, because it is using different units of measurement for the same property.

In my view, I am not arguing semantics.

 

[Ibix]

"a bit of time and a bit of space" is a mix of two different properties.

To you. In my frame it's just time. So is it a mix of different properties or not?

That is not a good analogy, because it is using different units of measurement for the same property

But height and width aren't the same property. You can't use a plumb line to measure width. If you use a ruler to measure height, you can't use it to measure width without rotating through 90°.

 

[m4r35n357]

Is it just me or is this thread veering away from relativity altogether?

 

[Ibix]

Is it just me or is this thread veering away from relativity altogether?

Depends on your unit system.

 

[whatif]

To you. In my frame it's just time. So is it a mix of different properties or not?

You can regard it as a mix with zero spacelike part or not a mix as you choose. If you choose the latter then it does not have to be a mix.

But height and width aren't the same property. You can't use a plumb line to measure width. If you use a ruler to measure height, you can't use it to measure width without rotating through 90°.

Timespace has one timelike part and three spacelike parts. Height and width have the same property of distance between the points of measurement, as does depth.

You seem to now be heading towards indicating that the units of measurement of timelike and spacelike parts do, indeed, relate to a specific property.

 

[whatif]

Is it just me or is this thread veering away from relativity altogether?

I will make no more contribution.

 

[PeterDonis]

It just needs to be realized that a meter of time is not the same as a meter of space.

@Ibix's comment about "timelike" and "spacelike" being more appropriate here is valid. "Time" and "space" are relative, so it makes no sense to say that a "meter of time" is always a meter of just time, since in a different frame it will, as @Ibix says, be a mixture of time and space. But whether a given spacetime interval is timelike, spacelike, or null is invariant, independent of your choice of frame. So it makes sense to say "a meter of timelike interval" is distinct from "a meter of spacelike interval". Note that that, in itself, does not mean it must be true that a meter of timelike interval is fundamentally not the same as a meter of spacelike interval; it simply means it makes sense to formulate the question and consider it (whereas it doesn't even make sense to formulate the question of whether "a meter of time" is fundamentally different from "a meter of space", since "time" and "space" have no invariant meaning).

Timespace has one timelike part and three spacelike parts.

More precisely: any orthogonal set of basis vectors in spacetime must have one timelike basis vector and three spacelike basis vectors. But there is nothing that requires you to pick an orthogonal set of basis vectors; the only requirement for basis vectors is that they have to be linearly independent, which is a much weaker condition.

Also, not all vectors in spacetime are timelike or spacelike; some are null. Does that mean spacetime has to have a "null part" as well as one timelike and three spacelike parts? How can that be when spacetime has only four dimensions?

 

[sweet springs]

ake the components (magnitudes) of the 4 momentum, 4 vector (I am assuming it is known where these equations come from):

$$p^\mu=mcu^\mu$$ where 4-velocity u is
$$u^\mu=\frac{dx^\mu}{cd\tau}$$ where tau is proper time.

It seems x^\mu, u^\mu and p^\mu are perpendicular from this relation.