Time to end all misconceptions for ever!

[WebFeet]

In what sense does it slow? I mean, in a pointlike thing, what velocity

could it have? I don't see the point and I see no argument of relativity by which time

intervals would be zero.

 

If you are a point-like particle, then under SR, if you are accelerated towards the

speed of light you gain relativistic mass. Any normal mass would also experience

time dilation, so why not your point-like particle. If this is true in SR, then it would

follow that it would also be effected by GR.

 

You accept that Optical model produces the same results as GR.

 

Those GR effects are explained in the Optical model by way of photons. If this is the case, then

there is a direct relationship between your point-like particle and photons. But point-like

particles are seen as fundemental because they have no apparent sub-structure, so how can this

be. An electron and a positron will annihilate each other to produce 2 gamma rays (photons).

 

IMHO, this would tend to suggest that there is a point-like particle sub-structure consisting

of photons. Or to put it another way, the point-like particle consists of nothing other than

energy and it is the way this energy is structured that gives theose particles their additional

attributes - attributes that photons don't have.

 

If this is the case, then it would follow that any change in the speed of light would also cause a change

in the behavoir of the point-like particle.

 

So as to what velocity a point-like particle could have, it could have the speed of light - internally.

 

I hope you understand that, which should answer all the other points you raised.

[Qfwfq]

I hope you understand that, which should answer all the other points you raised.

No, it doesn't answer any of the points I raised, certainly none of the questions I posed:

 

1)In what sense does it slow? I mean, in a pointlike thing, what velocity could it have?

2)Constant? Or Lorentz invariant?

3)Any distance? Or any finite distance?

 

These can only be answered by a better understanding of relativity.

 

1)I wouldn't talk about energy "slowing", it doesn't make sense to me (I hadn't asked what velocity a point-like particle could have, I referred to you saying that energy in the particle slows).

 

2)Relativity is based on c being a Lorentz invariant. This isn't the same as saying 'constant'.

 

3)I answered that right after posing it.

 

While some of your arguments are superfluous, others aren't conclusive.

 

if you are accelerated towards the

speed of light you gain relativistic mass

I say that you gain kinetic energy. What do you mean by "Any normal mass"?

 

You accept that Optical model produces the same results as GR.

I put it that, as far as I know, the optical interpretation and the geometrical interpretation may be equally valid.

 

Those GR effects are explained in the Optical model by way of photons.

Not by photons. To be equivalent to the geometrical interpretation, the reduced c must go for anything massless, it must effectively be the c for local Lorentz invariance. Indeed, the refractive index of glass doesn't imply an altered Lorentz invariance inside the glass. Considering this, PV would be only a partial explanation. Perhaps this is why Einstein switched so fully to the geometrical interpretation.

 

If, otoh, you could locally lower the refractive index of the vacuum without changing local Lorentz invariance then it would be a totally distinct thing, you could have Cherenkov light in that region of vacuum. Remember that c isn't just the speed of light, although it has always been called that way. This is actually what the meaning of Special Relativity is, after all.

 

But point-like particles are seen as fundemental because they have no apparent sub-structure

Why? How about spin, charge, charm, colour etc.? If you want to explain all these in terms of "the way this energy is structured" it might be interesting, only providing you do a good enough job of it. You would have to do a mighty good job of it indeed, for people to take it seriously, else it is pure speculation.

 

An electron and a positron will annihilate each other to produce 2 gamma rays (photons).

This only tells me that the rest energies become kinetic energies. Other quantities couldn't be conserved if there wasn't a pair going in and a pair going out.

 

IMHO, this would tend to suggest that there is a point-like particle sub-structure consisting

of photons. Or to put it another way, the point-like particle consists of nothing other than

energy and it is the way this energy is structured that gives theose particles their additional

attributes - attributes that photons don't have.

I don't see such a categoric distinction between photons and other particles.

[WebFeet]

Qfwfq,

 

I know I should be answering the points you have raised, but I have a simple question.

 

Originally Posted by WebFeet

An electron and a positron will annihilate each other to produce 2 gamma rays (photons).

 

Response Posted by Qfwfq

This only tells me that the rest energies become kinetic energies.

 

Originally Posted by WebFeet

if you are accelerated towards the speed of light you gain relativistic mass

 

Response Posted by Qfwfq

I say that you gain kinetic energy.

 

If the property of the kinetic energy in the first example is that it travels at the speed of light, shouldn't there be consistancy when applying that to the second example.

 

I agree that Relativistic mass is no more than energy, but in the case of this kinetic energy would it not be indistinguishable from the rest energy ?

[Qfwfq]

I wasn't really counting on you answering the points I raised, I meant you to ponder them a bit.

If the property of the kinetic energy in the first example is that it travels at the speed of light, shouldn't there be consistancy when applying that to the second example.

There is no inconsistency.

 

I agree that Relativistic mass is no more than energy, but in the case of this kinetic energy would it not be indistinguishable from the rest energy ?

Distinguishable, or indistinguishable, in what sense? For the definitions, look up the 4-tensor formulation of relativity. In particular:

 

m^2 = E^2 - p^2

 

Familiar equation? E is usually called the total energy, m the rest energy, while the kinetic energy just is the difference between these two quantities. Of course, c = 1.

[WebFeet]

I wasn't really counting on you answering the points I raised, I meant you to ponder them a bit.

I have been pondering. :)

There is no inconsistency.

 

while the kinetic energy just is the difference between these two quantities

Does this mean that the kinetic energy portion is consistant that even while appearing as relativistic mass, it is still travelling at c ?

[Qfwfq]

I'm not sure what you mean by the sentence:

Does this mean that the kinetic energy portion is consistant that even while appearing as relativistic mass, it is still travelling at c ?

but I don't say the kinetic energy is travelling at c, not if m isn't zero.

 

A particle has a certain energy and momentum for a given observer. For observers at different velocities it has different values of these; each observer sees it with a different energy and a different momentum. For an observer travelling with the particle it has zero kinetic energy and zero momentum. As in Newton's dynamics based on Galilean relativity, as in Einstein's Lorentz-covariant dynamics.

 

The geometry and the coordinate transformations aren't the same, save for the subgroup of translations and 3-D rotaions, the kinematics are described by 3-vectors in one and by 4-vectors in the other, but Newton's dynamics and Einstein's are nevertheless the same from a formal point of view: F = ma becomes a 4-vector equation but of the exact same form.

 

I have been pondering.

Keep pondering, I think that you should also read a proper treatment of SR, based on Lorentz covariance.

[WebFeet]

but I don't say the kinetic energy is travelling at c, not if m isn't zero.

Let me get this straight.

Kinetic energy travels at c unless there is mass, in which case it doesn't travel at c.

 

That was the reason I asked if the kinetic energy in the form of relativistic mass was consistant with that when a particle's rest mass was converted to kinetic energy.

 

Just for a moment I thought we might be in agreement. :o

 

I have been saying about mass consisting of a structure of energy. If the mass is at rest, then the energy would be in equalibrium - equal movement in all directions. The addition of the kinetic energy alters the structure so that it no longer has equalibrium resulting not only in motion, but also Lorentz Transformations. The structure now not only has more energy (relativistic mass) but also for the whole structure to cycle through once would take longer (time dilation). By doubling the energy, you would double the time.

[paultrr]

The Theory of Special Relativity has as its basic premise that light moves at a uniform speed, c = 300,000 km/s, in the vacuum making all frames of reference in that specific medium as having the same speed of light. It does not imply that all photons will have the same kenetic energy. Inertial Mass is the quantity that determines how difficult it is to alter the motion of an object. It is the mass in Newton's Second Law:

 

F = ma

 

The mass in that equation deals strickly with particles that possess what we term as rest mass. The additional mass coming from relativistic velocity gain is inertial mass or the F in that equation.

 

Gravitational mass is the mass which determines how strongly two objects attract each other by gravity:

 

 

F=GMm/R^2.

 

The second fundamental principle of General Relativity is that the presence of matter curves space. In this view, gravity is not a force, as described by Newton, but a curvature in the fabric of space, and objects respond to gravity by following the curvature of space in the vicinity of a massive object. The description of the curvature of space is the mathematically complicated part of general relativity involving "metrics", which describe the way that matter curves space, and tensor calculus.

 

Light loses energy escaping from a gravitational field. Because the energy of light is proportional to its frequency(Notice that the formulas for such as different), a shift toward lower energy represents a shift to lower frequency and longer wavelength or a shift toward the red for visible light. This gravitational redshift was first observed for the absorption features from White Dwarf stars, whose light is shifted by about 1Å. It was experimentally verified on earth using gamma-rays travelling from the basement to the top of the Jefferson Tower Physics Laboratories at Harvard.

[paultrr]

Time slows down in a strong gravitational field. Newton's concept of time was an absolute quantity flowing uniformly through the Universe. Einstein showed that the measurement of time is relative, depending on the reference frame of the person who is making the measurement. The Special Theory demonstrated that timekeepers in motion with respect for each other will measure different times for events in each others reference frames: a timekeeper "at rest" will find that an event occurring in a rapidly moving reference frame will take a longer time than a timekeeper moving along with the event. A famous example of Special Relativistic Time Dilation is the Twin Paradox.

 

Basically, time is a relative aspect when it comes to relativity. Time changes from one frames perspective to another even though the speed of light at least in a specific vacuum state is seen to stay constant.

[WebFeet]

The second fundamental principle of General Relativity is that the presence of matter curves space. In this view, gravity is not a force, as described by Newton, but a curvature in the fabric of space, and objects respond to gravity by following the curvature of space in the vicinity of a massive object. The description of the curvature of space is the mathematically complicated part of general relativity involving "metrics", which describe the way that matter curves space, and tensor calculus.

 

The concept of SpaceTime was originally a mathematical convenience.

 

The fact that GR and PV display the same results is more than just coincidence. The reason why the results match is because they are both dealing with the same problem, but from different angles. One of them is approaching the problem using a mathematical concept, while the other is attempting to resolve the problem in physical terms.

 

Results from one can be verified by the other, but there is no reason to dismiss the reasoning behind the different sets of results based on the alternate view.

 

Just because SR is based of the premise that light moves at a uniform speed, c = 300,000 km/s in the vacuum, does not mean that the same premise is required for all other theories. That is how SR works and I can live with that. I don't have a problem with any of the results from SR or GR because they are mathematical models.

 

What I'm trying to do is to get you to step beyond the model and try to determine the physical reality. There's no reason to stop using SR & GR, they still work, but maybe there are other answers out there that will provide the same results but with a greater understanding of how it works.

[lindagarrette]

Time slows down in a strong gravitational field. Newton's concept of time was an absolute quantity flowing uniformly through the Universe. Einstein showed that the measurement of time is relative, depending on the reference frame of the person who is making the measurement.

This is a difficult concept to visualize. I think it is not time that slows down, since time is only a means of measuring sequences of events, but the events themselves that occur with longer intervals as gravitation increases. For example, at the event horizon, so called because events cease to occur at all, even photons are at rest. Right?

[Qfwfq]

That was the reason I asked if the kinetic energy in the form of relativistic mass was consistant with that when a particle's rest mass was converted to kinetic energy.

I see nothing inconsistent in the 4-vector formulation of dynamics of SR, and I really can't see what you mean when asking me these questions. Sorry. I think it is due to the terms in which you speak not being the standard Lorentz-covariant terms. I can't take the time out to write a treatise on the topic here but you can find it in a good textbook on the subject.

 

Special Relativity, as it is called, is based on the geometry of space time with Minkowski's pseudo-metric. The kinematics start with 4-velocity defined as the proper time derivative of position. In the dynamics, energy and momentum are the components of a 4-vector which can be written as m times the 4-velocity and so on.

 

I have been saying about mass consisting of a structure of energy. If the mass is at rest, then the energy would be in equalibrium - equal movement in all directions. The addition of the kinetic energy alters the structure so that it no longer has equalibrium resulting not only in motion, but also Lorentz Transformations. The structure now not only has more energy (relativistic mass) but also for the whole structure to cycle through once would take longer (time dilation). By doubling the energy, you would double the time.

This kind of speculation can be interensting, provided it is carried out appropriately.

[paultrr]

This is a difficult concept to visualize. I think it is not time that slows down, since time is only a means of measuring sequences of events, but the events themselves that occur with longer intervals as gravitation increases. For example, at the event horizon, so called because events cease to occur at all, even photons are at rest. Right?

 

I think one of the better laymens accounting of the time slowing down issue can be found in Hawking's book, "The Universe in a Nutshell." In that He too mentions and explains how time does actually slow down. The event horizon of a blackhole is not a point where time or motion stops at all. It is a point at which the escape velocity exceeds C. For any object traveling into a blackhole that horizon would not mean that time has stopped for them at all. Its simply a visual horizon as far as a remote observer goes. For the ingoing observer one could still see the outer universe along any incoming photon tract. The external observer can not see beyond that horizon because nothing internal, except hawking radition from that horizon can escape. There are a lot of msiconceptions out there when it comes to BH's and the event horizon itself. The only point at which time would cease if indead it does is at the singularity itself. I'd forget the somewhat popular science common explinations on such one finds at times online and in some poorer written books on the subject. Time does not cease at the event horizon itself. In fact, that horizon, if Hawking and others are correct can shift as either the BH grows via ingestion of incoming matter or shrinks via Hawking radiation. There is a simular horizon on visual grounds when it comes to an accelerated observer in the form of Unruh radiation that arises out of theory also.

[Qfwfq]

I think it is not time that slows down, since time is only a means of measuring sequences of events, but the events themselves that occur with longer intervals as gravitation increases.

It is neither time that "slows down" nor the events that happen with longer time intervals, it' a matter of different frames of reference having different time coordinates. Time is time, independently of observers. Measure the average decay time of muons, in their proper time, and you will find 2.2 µs. Take the coordinates of the same two points of space time according to a different frame and the space interval and time interval will be different, unless the change of coordinates is only a translation.

 

The locally inertial coordinate frames at a point in the gravitational field are not the same as those far away, so there is something like the effect of boost tranformations between inertial frames without the gravitational field.

[WebFeet]

I think it is not time that slows down, since time is only a means of measuring sequences of events, but the events themselves that occur with longer intervals as gravitation increases.

 

It is neither time that "slows down" nor the events that happen with longer time intervals, it' a matter of different frames of reference having different time coordinates.

 

IMHO, it can be said that both of these are correct. The first from a physical standpoint, the second from a geometric/mathematical one. That doesn't mean that the second argument invalidates the first.

 

Has SpaceTime moved from being a mathematical concept to being a physical entity ?

[Qfwfq]

Has SpaceTime moved from being a mathematical concept to being a physical entity ?

No, it hasn't, don't worry WebFeet, we can still arbitrarily choose it to be whatever manifold we like, without any need for experimental corroboration.

 

I know most people choose 1 + 3 dimensions with real coordinates and Minkowski's metric but you can choose for there to be 3 time and 7 space coordinates, for example, perhaps with some of these being real, some complex and one or two quaternionic. With an imaginative metric, it might even be a lot more fun. not to mention global topology. How about 3 or 4 of the spatial dimensions being closed Möbius style?

[WebFeet]

No, it hasn't, don't worry WebFeet, we can still arbitrarily choose it to be whatever manifold we like, without any need for experimental corroboration.

 

I know most people choose 1 + 3 dimensions with real coordinates and Minkowski's metric but you can choose for there to be 3 time and 7 space coordinates, for example, perhaps with some of these being real, some complex and one or two quaternionic. With an imaginative metric, it might even be a lot more fun. not to mention global topology. How about 3 or 4 of the spatial dimensions being closed Möbius style?

So you have a multitude of options to allow you to measure the effect, but does it get you any closer to determining the cause ?