[varsigma (OP)]

In a universe with four dimensions, you have to move at the speed of light in at least one of them.

In the other three, how you can move is restricted by something called mass-we don't really know what that is--but if you have any, you can't move at the same speed in any of the remaining dimensions. Not according to Einstein. The reason you can, and do, move at the speed of light in one dimension--the time dimension--is because time has to vanish from your local frame of reference, if you want to age at all.

That's a weird but true explanation of a theory.

p.s. a hint as to why it works; photons don't age--the universe of matter does and, the ambient space the photon moves in is stretching the wavelength--an isotopy.

[varsigma (OP)]

Can I connect my weird description of a 4-dimensional universe to the question of aging for two observers, as in the twins paradox?

Photons don't "age". Aging means you can recall a past, so photons don't because they don't have a past, or a future. All moments of time for the life of a photon's ontological existence, are the same moment, or no moment.

Since photons, or electromagnetic radiation in general has this "time equivalence", it should be possible to quotient the total space with it. This is what a Minkowski spacetime diagram represents, a quotient space.

Then, if the universe of matter is what ages, it must be able to remember a past. I mean, we do so, does our solar system? Does the sun "remember"?
 Well, memory is just a store of information I suppose you could posit a weird kind of argument that matter can remember information about its past. Because it has mass, maybe it has angular momentum which can be construed as a kind of store of energy, and there is definitely a connection between energy and information. Perhaps how much can an atom or a particle with mass "remember" could be a way in.

After all, your brain remembers images you've seen, because electrons in your retinal cells "remembered" what they are meant to do, and did it. What memory is, is the capacity to store, not just recall, information. And erasure for a small memory would be a requirement.

Then clocks--what do clocks remember? What information can a clock store? These questions are relevant to the twin paradox. Clock information is actually a critical factor.

[hamdani yusuf]

Photons don't "age". Aging means you can recall a past, so photons don't because they don't have a past, or a future. All moments of time for the life of a photon's ontological existence, are the same moment, or no moment.

How do you reconcile this with Doppler's effect, Sagnac's effect, Fizeau's effect, Interference patterns?

[alancalverd]

Photons have a history, but it's easier to understand and predict with a wave model. 

[Eternal Student]

Hi.

In a universe with four dimensions, you have to move at the speed of light in at least one of them.

    A blunt response would be just to say "No, that's not quite right".   I would have preferred to make a softer response but the reply is going to get too long and too awkward to understand if I do that.

     The more common way of thinking about movement through 4-d spacetime is as follows:
1.    An object always moves with a velocity of magnitude c.   Not "at least" c, always precsely c.
2.    You can share that out between some velocity in the spatial directions and some in the time direction as you wish.

     Examples:    If an object has zero ordinary 3-D spatial velocity, then it advances in the time direction as much as possible.   Proper time for that object advances exactly the same as the co-ordinate time you were using (the thing we used to declare that the object had 0 spatial velocity).  If you use a conversion factor c to convert the proper time elapsed to a space equivalent, then advancing 1 second of proper time per 1 second of co-ordinate time becomes something we can say is a velocity that the object has of   c  metres per second  (instead of  1 proper second per co-ordinate second).
    However, if it has some ordinary 3-D spatial velocity, then the proper time for that object advances more slowly than the co-ordinate time, this is known as "time dialtion".   Conceptually, you have used up some of its light speed velocity in the spatial velocity and so there is less of it left available for advancing into the time direction.    In the most extreme case, a particle of light moves with a 3-D spatial velocity of c, so there is nothing left at all for advancing in the time direction and the proper time for that light particle can never change regardless of how much the co-ordinate time may change.

     I don't especially like this way of looking at how objects move, there's a lot that would need some more precise mathematical formulation.    None the less, it provides some general understanding if we just skip all the details and this is often done in PopSci where this concept of objects always moving at c is used.

    So, I could have taken a softer response approach as follows:   
You said:
   In a universe with four dimensions, you have to move at the speed of light in at least one of them.
As a minimum the words "at least" have to be striked out.    It would be better if we replace the entire sentence with something like this:
   There's nothing special about what we identify as the x,y, z axis of space and the t or time axis.  We can always construct a "direction" of travel for an object that is a combination of the spatial and time directions.   An object will then always move at precisely c in that "direction" and have no velocity at all in the other three directions orthogonal to this.

Best Wishes.

[paul cotter]

I had come across this concept of every object moving at c but never gave it any serious consideration- maybe I should have, maybe not. From an engineering perspective I find it falls short of rigour: "c" has units of m/s and time has units of s, how can one have a speed(m/s) in a dimension of s?

[varsigma (OP)]

How do you reconcile this with Doppler's effect, Sagnac's effect, Fizeau's effect, Interference patterns?

I don't understand your question. All the effects you mention occur in three spatial dimensions. The measuring equipment "ages", right? It changes when it records anything. That is not the case with EM radiation.

Measuring equipment, all classical devices, are constantly "measuring"--thermal changes in the environment, mechanical vibrations (check out the LIGO problems)--everything made of matter ages. We say that light isn't a form of matter, but it is "material"; it has momentum.

Momentum can't be a mathematical (or algebraic) gizmo--it has to be as real as time.
Or maybe that doesn't "really" mean much.

[varsigma (OP)]

There's nothing special about what we identify as the x,y, z axis of space and the t or time axis.  We can always construct a "direction" of travel for an object that is a combination of the spatial and time directions.   An object will then always move at precisely c in that "direction" and have no velocity at all in the other three directions orthogonal to this.

But, why will an object move at c in that direction? Have you seen Penrose's description of two observers walking past each other? That this means they are literally in different 'spaces', at least according to Minkowski. Each observer defines a different direction for the "object moving at c". Each observer has their own "object", maybe it's what they call time.

We do, because we can remember a past.

[varsigma (OP)]

Photons have a history, but it's easier to understand and predict with a wave model. 

If they "have" a history, it's because we give them one.
If a photon, a single photon, can be a clock of some kind, it can have one and only one "tick". Not much room for a history there.

[Eternal Student]

Hi.

"c" has units of m/s and time has units of s, how can one have a speed(m/s) in a dimension of s?

    If you skip all the details, as is often done in PopSci,  it's summarised like this:

If you use a conversion factor c to convert the proper time elapsed to a space equivalent, then.....

   A more rigorous mathematical formulation would require us to be careful about defining 4-vectors and not simply treat them as if they are just ordinary Newtonian 3-velocties with a 4th time-like component strapped on.   For example, we would specify an objects position 4-vector as   (ct, x, y, z)   rather than (t, x, y, z).   That decision alone means that the time co-ordinate for an objects 4-position has units of  metres not seconds.  Next, we would also define the velocity 4-vectors  as a derivative w.r.t. proper time,  d/dτ  of the 4-position vector,   instead of using co-ordinate time t as in newtonian mechanics where the 3-velocity is just d/dt of the Newtonian position 3-vector.  [Reference:   https://en.wikipedia.org/wiki/Four-vector#Fundamental_four-vectors ]
    Note that the last decision makes very little difference at low speeds,   the proper time elapsed for an object is almost exactly the same as the co-ordinate time elpased.   So, it's not too criminal to allow a reader to imagine that a 4-velocity has 3 spatial components which are just the ordinary Newtonian 3-velocity with a 4th component, a velocity in the time direction, strapped on as an extra.   In truth the 3 spatial components of the 4-velocity are not quite the same as the Newtonian 3-velocity and that will become more apparent at higher speeds.
    Anyway, with a proper consideration of 4-vectors we can make all the ideas more rigorous and there is no conflict in the units of measurement for the time component or spatial components of the 4-velocity.
    It is really only the formal 4-velocity of an object that must always have a magnitude of c and it's convenient that the 3 spatial components are a bit like the ordinary Newtonian 3-velocity of the object.

- - - - - - - -

Have you seen Penrose's description of two observers walking past each other?

    I'm not sure that I have, sorry.   Is there any online reference?
I can hazard a guess as to what it was about.

Best Wishes.

[varsigma (OP)]

I'm not sure that I have, sorry.   Is there any online reference?

I'm fairly sure it's something he discusses in The Emperor's New Mind.

Have you seen the Penrose and Hawking book, The Nature of Space and Time?

[alancalverd]

If a photon, a single photon, can be a clock of some kind, it can have one and only one "tick". Not much room for a history there.

It was emitted from x meters away with a different gravitational potential, x/c seconds ago, travelled through refracting and polarising media, and may have been reflected off something, before we detected it. That's quite a lot of known history, and if it had a few companions, like a spectrum, we can probably deduce its original energy before doppler and gravitational red shift altered it.

Suppose you encounter a woman wearing a naval diving suit and speaking French. She may have total amnesia, but you can deduce a lot of history, especially if you can see a warship flying a tricolor flag. Same for the photon! 

[Halc]

In a universe with four dimensions, you have to move at the speed of light in at least one of them.

In a universe with 4 spatial dimensions, the speed at which some object moves through any on dimension is frame dependent, and less than c (assuming similar rules as our universe).
I presume you're talking spacetime, but speed is defined as spatial change over time, and is not a meaningful concept in spacetime. An object traces a worldline through spacetime and is everywhere present on that worldline, hence there is no motion at all.  The speed of an object at some moment is the slope of its worldline in some selected frame, and that speed is less than c for any valid frame.

The reason you can, and do, move at the speed of light in one dimension--the time dimension--is because time has to vanish from your local frame of reference, if you want to age at all.

That's a weird but true explanation of a theory.

Is is not an explanation at all, and neither Einstein nor Minkowski said anything like that.


The only possible meaning of motion through spacetime is something like moving spotlight theory, one version of presentism, a philosophical stance, not a scientific one. In that interpretation, the universe is a block but the present is defined by a moving pointer (the spotlight) that defines which events are current. Given that model, speed through spacetime would be the speed at which the spotlight advances along a particular line.  Problem is, no physical instrument can measure that rate, so it can be anything: Far higher than c, far less, even negative.

Photons don't "age".

In a way they do. There are a number of waves of a photon between two events (in a given frame, its frequency times its duration between the two events). That is an age of sorts.
If you're saying that the photon does not undergo any physical change from one event to the other, that's true, but also true of something like a proton which doesn't move at c. Protons also cannot recall a past.

Since photons, or electromagnetic radiation in general has this "time equivalence", it should be possible to quotient the total space with it. This is what a Minkowski spacetime diagram represents, a quotient space.

Another assertion resulting in these posts getting moved, on top of an unusable suggestion of relevancy to the twin paradox.

Have you seen Penrose's description of two observers walking past each other? That this means they are literally in different 'spaces', at least according to Minkowski.

This is bending what people say beyond the breaking point. Two people walking past each other tend to use the exact same reference frame, and therefore share the same coordinate system, which includes the exact same space.
Penrose, if he worded his statement correctly, would have explicitly identified a pair of different inertial frames, neither of which necessitates an observer to be defined.

All that said, yes, the events which are simultaneous with a given event relative to one inertial frame are mostly different than the events which are simultaneous with the same given event relative to a different inertial frame. That statement actually derives from Minkowski, and is probably what Penrose means. I have no access to any exact quote.

[varsigma (OP)]

In a way they do. There are a number of waves of a photon between two events (in a given frame, its frequency times its duration between the two events). That is an age of sorts.
If you're saying that the photon does not undergo any physical change from one event to the other, that's true, but also true of something like a proton which doesn't move at c. Protons also cannot recall a past.

Protons don't get redshifted by the cosmic expansion, photons do.

[varsigma (OP)]

This is bending what people say beyond the breaking point.

You're saying Roger Penrose published a book, which bends something beyond the breaking point? You don't think he may have been trying to explain how relativity works?

[varsigma (OP)]

It was emitted from x meters away with a different gravitational potential, x/c seconds ago, travelled through refracting and polarising media, and may have been reflected off something, before we detected it. That's quite a lot of known history, and if it had a few companions, like a spectrum, we can probably deduce its original energy before doppler and gravitational red shift altered it.

I think that misses the point I made. Which was that we give them a history. If you didn't know all the above about the paths, what could photons tell  you?

[varsigma (OP)]

Another thing about matter and aging.

I know how to anneal a metal bar, with heating and cooling, and hammering. This process ages the metal.
I know how to age a lot of things made out of matter.

I don't know any way to age light, although it's easy to make light interact with matter, I don't know I can say it ages or anneals the light at all.

Aging appears to be relevant to large collections of particles, such as humans. Particles of light don't age, is kind of a tenet of Einstein's theories, and the man himself said this.

[Eternal Student]

Hi (again),

Sorry, there's been a lot of new posts since I started this one (and some splitting of a forum post, I think).   I'll still start from an old post of @varsigma .

But, why will an object move at c in that direction?

This would be easier if the forum supported LaTeX to write mathematical equations - but I reckon we can get by.

1.   Let's start with special relativity and talking about un-accelerated objects.

2.   An ordinary object, one with mass, has a rest frame which is a perfectly valid co-ordinate system for the world - it's just as good as any other.

3.    In that rest frame, the object is at rest (by definition).   By definition, its 4-position vector is
 (ct, x, y, z)        (reference https://en.wikipedia.org/wiki/Four-vector#Fundamental_four-vectors )
  where x, y, z are fixed (unchanging) with the co-ordinate time t.
   The proper time elapsed for the object is then    c² dτ²  =  c² dt² -  dx²  - dy² - dz²   but there's no changes in the x,y, z components, so we just have dτ = dt.   In words, "the co-ordinate time is identical to the proper time experienced by this object". 
   By definition of the 4-velocity vector we have    d/dτ   of the 4-position vector  is    (c, 0, 0, 0).

4.   So, in the rest frame, the object does indeed have a total magnitude of the 4-vector that is c.    I won't write out the magnitude of that 4-vector but it's the usual Minkowski norm that we would use.   Furthermore, all of this 4-velocity is seen to be in the time component of the 4-velocity.

5.   The 4-velocity is a proper 4-vector.  So it's magnitude, as defined by the Minkowski norm, is invariant under a Lorentz transformation.   [ Reference:   Notes from an MIT course,   https://uspas.fnal.gov/materials/12MSU/Conrad_4vector.pdf  ].    So in any other inertial frame of reference you may choose to use, the object still has a 4-vector of total magnitude c.
     That's the majority of the proof done.

6.    The object we started with was arbitrary.   Which frame of reference we chose to switch to was arbitrary.   So, any object and any reference frame that we chose for some reason (e.g. the observer was stationary in that frame) will still exhibit the property that this object has a 4-velocity with magnitude equal to c.   However, it's also clear that in some frames of reference, the object is not going to be at rest.  Then some of the spatial components of the 4-velocity will not be 0 and the total magnitude of the 4-velocity has been "shared out"  between the time component and the spatial components but the overall magnitude of that 4-velocity remains equal to c.
   
7.   Now we can relax the assumption that the object was un-accelerated if we wish.  It may not have a single inertial rest frame for all time but it will always have an instaneous rest frame we can use at every instance.   That's all we will need.

8.   We can also generalise to GR rather than SR.   In a local enough region, GR is just SR.  We only need a local frame to define something we can call an objects 4-velocity through the spacetime local to it  (rather than some other co-ordinate velocity it may have, which may be quite bizarre and is not required to be of magnitude c).

-------
   That's probably not the explanation you ( @varsigma ) were looking for but it is AN explanation.
I will spend some time digging for the Penrose discussion you suggested, that may take a day.   Penrose is very good at presenting the deeper philosophy and "physics" of a situation.   Meanwhile the above proof is essentially saying stuff the deeper understanding of "the why".  The mathematics says it happens and that's all we need to know and regard as "the why".

- - - - - - - -

From @Halc 's later post:

but speed is defined as spatial change over time, and is not a meaningful concept in spacetime.

   That sort of speed is obtained from a 3-vector and would indeed be much as you describe.   However, the 4-vector velocity is meaningful and could be regarded as an objects movement through 4-dimensional spacetime.
   Minor differences exist, as mentioned.   The 4-velocity is a derivative of the 4-position vector with respect to a differential change in the objects proper time, τ,  not a co-ordinate time, t.   
    Of course,   dt ≡ dτ   when the co-orindates used are obtained from a frame where the object was (spatially) at rest, but in general they are not.   This slight alteration is sufficient to eliminate many of the issues you mentioned  (the speed.... is frame dependent) because we have tied down the frame sufficiently to have a mathematical object, a 4-velocity, that transforms as a tensor.   It turns out that this 4-velocity really will have an invariant magnitude under the Minkowski norm and that magnitude is precisely c.

    I didn't say I like the way that some PopSci articles describe all objects as moving at a speed of c through 4-D spacetime,  I said the opposite a few posts back:   

I don't especially like this way of looking at how objects move, there's a lot that would need some more precise mathematical formulation.

    It can be properly formulated in Mathematics and can be used - but most PopSci articles will just allow a reader to imagine a 4-velocity as if it is just a Newtonian 3-velocity in the 3 spatial components with an extra and naively imagined time-like velocity component bolted on.

Best Wishes.

[varsigma (OP)]

That's probably not the explanation you ( @varsigma ) were looking for but it is AN explanation.

No I think it's a pretty good explanation. Can I suggest showing what setting c to 1 means for the 4-velocity? Some people say it's confusing.

[alancalverd]

I think that misses the point I made. Which was that we give them a history. If you didn't know all the above about the paths, what could photons tell  you?

Dangerous line to take! From my window I can see a large barn. As the photons carry no history, I have to assume it was created spontaneously a few picoseconds ago, but common sense and context tell me it was built about 150 years ago from wood that was already at least 50 years old at the time.

We rely on the precision of photon history to locate tumors by positron emission tomography.

 

This process ages the metal.

I think you should put "ages" in quotation marks - it's engineering jargon for accelerated experience. The metal is no older or younger than the bit you haven't bashed and annealed: you have just made it look and behave older.

Inverting the paradigm, you imply that all photons are the same age. Which means that every electron transition in the universe occurred simultaneously. Thus time, the dimension that separates sequential events, has no meaning. Somewhat counterintuitive.