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New Theories / Re: In four dimensions, must an object move at c in at least one of them?

« Last post by varsigma on Today at 03:58:16 »

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.

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New Theories / there is no time dilation between between bodies in relative motion

« Last post by LDL on Today at 03:37:19 »

My aim here is to demonstrate that if the speeds of light are affected by a gravitational field, then time dilation between two clocks or observers in relative motion will not occur.

Einstein's accelerating elevator thought experiment demonstrates light from a flashlight to bend when it travels laterally to the accelerating direction. This demonstrates that light traveling laterally in a gravitational field will fall. But what is happening to light in the upward and downward direction? It's obvious that within the upward accelerating elevator, light in the upper direction is decreasing in relative speed with the elevator while light in the downward direction increases in relative speed. The changes are balanced in that the absolute value of increase equals the absolute value of decrease.
 
It would seem then that the equivalence principle directly infers that a gravitational field is a field where the speeds of light, in line with the field, are undergoing balanced changes in opposing speeds.

A gravitational model should incorporate this principle. I present one simple model. The speeds of light around a mass should be sloped. In relation to a body of mass, the speeds of light are constant at any fixed distance but change in balance fashion in relation to the distance from the mass, c+v inbound and c-v outbound where v is the gravitational escape velocity. The rate of change of the balanced speeds of light determine the fall rate. It?s simple and intuitive. We can readily ascertain why increasing time dilation occurs the deeper a clock is placed (and prevented from falling) in a gravitational field.

Now let's picture a body where the surface speeds of light are c+v inward and c-v outward. We place a clock on the right side of the body and it runs at a certain rate of time based on those speeds.

Let's choose three different locations within a section of space, from left to right, C, B and A, equal distance apart in a linear arrangement. If we place the body stationary at location A, we observe the speeds of light to the right of the body to be c+v left and c-v right. If we place the body at position B, the same light speeds are observed but in a further left location. And of course the c+v and c-v speeds are even further left when the body is placed at position C.

Now let's put the body in motion left at speed s traveling through A,B and C. A stationary observer would see the speeds of light to be c+v left and c-v right near location A, then disappear and reappear at location B, then disappear again and reappear at location C. Even though the stationary observer never observes the speeds of light to actually travel any difference in speed, the disappearing and reappearing at a further location creates a wave like motion of these speeds. Note the faster the body moves left the more space between the appearing c+v and c-v speeds. This is a red shift of a wave. Let's define these speeds by vectors. The speed vectors, representing c+v left and c-v right, are moving left at speed s keeping in sync with the moving body and maintaining the speed relationships of the two-way speeds of light near the surface of the moving body. No matter what speed the body travels at, the vectors will follow and maintain this relationship. The rate of time of the clock on the right side of the body will be the same for any speed the body travels at. No dilation of time occurs.

We can consider small body's where the changes in the sloped fields are negligible, where surface speeds of c+v in and c-v out are very close to c in and c out, though there must still be a small gradient of slope.

If we place this body at position A, light in and light out both have the speed of c. When the body is placed at position B, its light in and light out is also c. And we obtain the same result when the body is placed at position C.
When the body is given a constant speed traveling though A, B and C, all emitted and incoming light is swept by a wave. The speed vectors on the right side of the body representing c left and c right, are moving left at speed s keeping in sync with the moving body and maintaining the speed relationships with the moving body and maintaining its rate of time. From the point of view of the other body our speeds are also in sync with our relative motion and light is emitted and received at speed c.

Approaching light from a body that is moving away, is pulled forward by our gravitational field to increase its speed relative to the moving source and stretched causing red shifting of its wave. Red shifted light moves faster than c relative to its source. Approaching light from a body moving toward us, is pushed back by our gravitational field to lower its speed relative to the moving source and compressed causing blue shifting. Blue shifted light moves slower than c relative to its source. The rate of time for both receiver and emitter of light remains constant in all cases.

With this model we can eliminate all the confounding oddities that infiltrate relativity theory. No differences in rates of time between bodies in relative motion, no Twin paradox, no absurd notion that two bodies in relative motion each see the other running at a slower rate of time, no length contraction, and of course, no curved space-time.

It's just that the sloped speeds of light are a consequence of a gravitational field and the gravitational field keeps in sync with a uniform moving mass just like field lines around uniform moving charges.

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Physics, Astronomy & Cosmology / Re: What is the exact cause of the time dilation of the twin?

« Last post by varsigma on Today at 03:35:44 »

There might be a problem with using the word motion, or moving, it's usually a reference to space, or different positions.

In Minkowski spacetime you have a relativistic 4-velocity. It cannot be zero or, well, lots of things just don't happen.

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New Theories / Re: In four dimensions, must an object move at c in at least one of them?

« Last post by Eternal Student on Today at 02:59:23 »

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.

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Physics, Astronomy & Cosmology / Re: What is the exact cause of the time dilation of the twin?

« Last post by varsigma on Today at 02:08:32 »

"Einstein based special relativity on the idea that the speed of light is the same for all observers. You cannot do this in a Euclidean space where all the signs are plusses. But you can do it if one of the signs is different relative to the others.

That's because a space-time distance that is zero for one observer is zero for all observers. This is also the case in Euclidean space, but in Euclidean space, this just means zero in each of the directions of space. But what does a zero distance mean in space-time? Well, let's find out. For simplicity, let us look at only one dimension of space. So if the distance in space-time is zero, this means that the distance in space divided by the distance in time equals plus or minus c. And that?s the same for all observers. So this speed, c, is an invariant speed.

But, well, we are not light, so we do not travel with the speed of light through space, and we do actually cover a distance in space-time. So let us look at this equation for the space-time distance again. Now let us divide this by the time difference. Now what you have on the left side is the space-time distance per time. And under the square root you have roughly something like the squares of the velocities in each of the directions of space. Plus c².

And there you have it. Relative to yourself, you do not move through space, so these velocities are zero. You then only move into the time-like direction, and in this direction, you move with the speed of light. So, we indeed all travel through time with the speed of light."--from a Ph.D blog

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Physics, Astronomy & Cosmology / Re: What is the exact cause of the time dilation of the twin?

« Last post by Halc on Today at 01:43:43 »

I had to move the group of posts due to the assertive tone they took, rather than a questioning one.

Einstein, and Feynman have both said that relativity says we move in the time direction. Time isn't really a thing with extent, but it is a direction. We move at the speed of light in that direction.

John Baez, Roger Penrose, say it too.

Actual quotes (and context) would really help. Are these statements in peer reviewed publications or are they casual comments or from pop articles?
What they are trying to say is that time and space are the same thing, meaning time and length can be used interchangably. So for instance, a worldline segment one second long (the worldline of any clock over one second measured by it) is exactly one light-second in length. The statement is one to define this ratio of translating space to time. But to call it 'speed' totally contradicts the definition of speed, as Paul has correctly pointed out. There is no meaningful motion through spacetime except for the one example I posted in the other topic, and that motion is completely undetectable, given that the interpretation posits a completely undetectable thing.
In particular, with motion, when the object gets to the destination, it is no longer at the former location. With a worldline, the object is present at every event along the line. It doesn't move from one event to another, leaving the former event 'vacant' so to speak.

It is also a common shorthand to identify a frame by an observer stationary in it, but it must be made clear at some point that frame selection is an arbitrary abstract choice, not a physical property of an object or observer. If Penrose did not make that clear in his book, then he's not doing a very good job of explaining relativity.
The vast majority of human observers choose a different frame than the inertial one in which they are stationary. It is far more pragmatic to use say the accelerating rotating frame of the surface of Earth when walking past another person.

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New Theories / Re: In four dimensions, must an object move at c in at least one of them?

« Last post by varsigma on Today at 01:20:36 »

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.

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New Theories / Re: In four dimensions, must an object move at c in at least one of them?

« Last post by varsigma on Today at 01:13:16 »

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?

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New Theories / Re: In four dimensions, must an object move at c in at least one of them?

« Last post by varsigma on Today at 01:10:24 »

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?

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New Theories / Re: In four dimensions, must an object move at c in at least one of them?

« Last post by varsigma on Today at 01:08:22 »

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.