Speed of Light?

[Mike11]

Hello, I'm reading Brian Greene's "The Fabric of the Cosmos" and am having a hard time understanding the contancy of the speed of light. If I was in a race with a car going twice my speed it stands to reason I am moving at half its speed. But If I am moving at half the speed of light, the difference between me and the particle of light is still the full speed of light??

Now I know that the combined velocity of movement through space and time must be the speed of light and therefore I am not investing ALL my energy moving thru space alone while light moves entirely through space, with a 0 on moving through time. I know that must have something to do with it but I've been thinking about this for months and can't get it.

Anyone care to help the blind man?

[Dragonfly]

Hello, I'm reading Brian Greene's "The Fabric of the Cosmos" and am having a hard time understanding the contancy of the speed of light. If I was in a race with a car going twice my speed it stands to reason I am moving at half its speed. But If I am moving at half the speed of light, the difference between me and the particle of light is still the full speed of light??

Yup. In every frame you'll measure the same speed of light, no matter what the relative speeds of the frames is. You may think that the addition of velocities, as in the example of the two cars, may "stand to reason", but it is only approximately true for speeds that are small compared to the speed of light. It is a good example of a situation in which your intuition has been formed by your experience in daily life, and your intuition may tell you that it's "obvious" or "self-evident", but your intuition may be wrong, as in this case.

[syrakusos]

Hello, I'm reading Brian Greene's "The Fabric of the Cosmos" and am having a hard time understanding the contancy of the speed of light. If I was in a race with a car going twice my speed it stands to reason I am moving at half its speed. But If I am moving at half the speed of light, the difference between me and the particle of light is still the full speed of light??

Yup. In every frame you'll measure the same speed of light, no matter what the relative speeds of the frames is. You may think that the addition of velocities, as in the example of the two cars, may "stand to reason", but it is only approximately true for speeds that are small compared to the speed of light. It is a good example of a situation in which your intuition has been formed by your experience in daily life, and your intuition may tell you that it's "obvious" or "self-evident", but your intuition may be wrong, as in this case.

You did not answer his question. You only asserted the hypothesis, which is a known (and obvious) logical fallacy.

He asked why the speeds do not add up to something more than the speed of light and you said that they do not.

Why not?

[Dragonfly]

The hypothesis is that there is no preferred inertial frame of reference, that the laws of physics have the same form in every intertial frame of reference and that the speed of light is the same in every frame. From this hypothesis follow with some algebra the well-known formulas for the contraction and the time dilation of moving bodies and the relativistic addition of velocities (that implies that they cannot add to more than the speed of light).

You cannot prove this hypothesis, but you can test its predictions, and a century of testing has only confirmed with high accuracy the predictions of the hypothesis. What else do you want?

[BaalChatzaf]

Hello, I'm reading Brian Greene's "The Fabric of the Cosmos" and am having a hard time understanding the contancy of the speed of light. If I was in a race with a car going twice my speed it stands to reason I am moving at half its speed. But If I am moving at half the speed of light, the difference between me and the particle of light is still the full speed of light??

Now I know that the combined velocity of movement through space and time must be the speed of light and therefore I am not investing ALL my energy moving thru space alone while light moves entirely through space, with a 0 on moving through time. I know that must have something to do with it but I've been thinking about this for months and can't get it.

Anyone care to help the blind man?

Help is on the way.

See http://en.wikipedia.org/wiki/Velocity-addition_formula for a clear statement of how velocities are -composed- (NOT added) given the Lorentz Transform.

Also any introductory text to the Special Theory of Relativity will have an explanation. For example -SPACETIME PHYSICS- by Taylor and Wheeler (the first edition, pp60 ff). Or better still Motion Mountain by Christopher Schiller (I gave the URL to reference this book just the other day).

Velocities are correctly composed thus V1 <+> V2 = (V1 + V2 )/(1 + V1.V2/c^2) where V1, V2 are the velocities to be composed, <+> means velocity composition (not addition!), + is normal addition, . is the vector dot product and c is the speed of light. It is assumed that the velocity vectors V1 and V2 are pointing in the same direction. A slightly more complicated formulate is required when velocities are not aligned.

It turns out that (so-called) common sense leads to the wrong conclusion. One of Einstein's brilliances is that he was able to think outside the (so-called) common-sense box.

The problem of grasping the composition of velocities and thinking past the notion of temporal simultaneity is symptomatic of the difficulty of getting at the guts of Special Relativity. It is NOT the mathematics that is the difficulty (S.R. needs only high school math) but intuition. Since we live in a low velocity regime our intuition is naturally biased. When V1 and V2 have small magnitudes relative to c, the term V1.V2/c^2 is very very small so that velocity composition <+> becomes nearly identical to plain old addition. Do NOT kick yourself too hard for not "getting it". It is very difficult to get when you spend the first fifteen (or so) years of your life developing an intuition, so-called common sense, which is singularly incorrect when dealing with the very fast, the very large and the very small. That is why Relativity Theory and Quantum Physics came along so late in the development of physics. You are in good company. Isaac Newton would have had the same difficulty that you do. Galileo also had the same difficulty. The transformation in which velocities merely add (arithmetically) is called, in the literature, the Galilean Transform. It would be identical to the Lorentz Transform if the speed of light were infinite, it turns out.

It turns out the Minkowski geometry in which the spacetime interval is invariant under uniform motions is a hyperbolic geometry, not euclidean. In euclidean geometries, velocity is represented by a trigonometric tangent (the tan function). In hyperbolic geometry the velocity is represented best by a hyperbolic tangent (the tanh function). The addition formula for hyperbolic tangents is

tanh (A + B) = (tanh(A) + tanh(B))/(1 + tanh(A)*tanh(B))

which is exactly the form for velocity composition under the Lorentz Transform.

Minkowsky hyperbolic geometry is the correct geometry to use for Lorentz Invariant systems.

I hope this is helpful.

Ba'al Chatzaf

Edited January 13, 2008 by BaalChatzaf

[merjet]

I pose a similar question. Suppose two objects, each traveling at the speed of light, are moving towards one another. It seems that the "rate of approach" is twice the speed of light. Such "rate of approach" is an abstraction and there is no object moving at faster than the speed of light. But if we were to calculate the time until they meet, wouldn't we assume that the space between them is shrinking at twice the speed of light?

Here is another hypothetical. Suppose a train is traveling at the speed of light. A man on the train fires a missile at the speed of light in the same direction as the train is traveling. At least in this hypothetical the missile will travel at the speed of light is more intuitively plausible -- the train will keep up with the missile.

[BaalChatzaf]

I pose a similar question. Suppose two objects, each traveling at the speed of light, are moving towards one another. It seems that the "rate of approach" is twice the speed of light. Such "rate of approach" is an abstraction and there is no object moving at faster than the speed of light. But if we were to calculate the time until they meet, wouldn't we assume that the space between them is shrinking at twice the speed of light?

Here is another hypothetical. Suppose a train is traveling at the speed of light. A man on the train fires a missile at the speed of light in the same direction as the train is traveling. At least in this hypothetical the missile will travel at the speed of light is more intuitively plausible -- the train will keep up with the missile.

Massive objects (those with non-zero rest mass) cannot go from rest (in a reference frame) to the speed of light. The relativistic mass increases infinitely as the speed of light is approached.

M_rel = M_rest/sqrt(1 - v*v/c*c) where v is the velocity of the mass in the frame of reference. M_rel goes to infinity as v approaches c. Which means any further acceleration requires more and more energy that tending to infinity also. The only particles that can go at the speed of light are those with zero rest mass and they -must- go at the speed of light.

The train cannot keep up with a light beam flashed from the train. Use the addition formula given in the preceding post. Let V be the velocity of train and c be the velocity of the light beam.

V <+> c = (c + V)/(1 + c*V/c*c) = c*(c + V)/(c + V) = c. The composed velocity of the train and a light beam is still c.

Ba'al Chatzaf

Edited January 13, 2008 by BaalChatzaf

[sjw]

Hello, I'm reading Brian Greene's "The Fabric of the Cosmos" and am having a hard time understanding the contancy of the speed of light. If I was in a race with a car going twice my speed it stands to reason I am moving at half its speed. But If I am moving at half the speed of light, the difference between me and the particle of light is still the full speed of light??

Now I know that the combined velocity of movement through space and time must be the speed of light and therefore I am not investing ALL my energy moving thru space alone while light moves entirely through space, with a 0 on moving through time. I know that must have something to do with it but I've been thinking about this for months and can't get it.

Anyone care to help the blind man?

I think the physicists are blind on this one too. They are still arguing about what it means. And significant number of them have thrown their hands up in the air and claim that meaning is meaningless, that you should just look at the equations. Anyone who tries to tell you they know what it means is probably in this camp.

Shayne

[BaalChatzaf]

I think the physicists are blind on this one too. They are still arguing about what it means. And significant number of them have thrown their hands up in the air and claim that meaning is meaningless, that you should just look at the equations. Anyone who tries to tell you they know what it means is probably in this camp.

Shayne

These blind folk have grounded the technology that makes you and me comfortable and prosperous. Some blindness! Your problem is that you seek to base your understanding of reality solely on "self evident" a priori principles. Forget it! To understand reality you have to go out, look and measure.

Ba'al Chatzaf

[Mike11]

So in other words I need another book.

Thanks Robert.

[sjw]

These blind folk have grounded the technology that makes you and me comfortable and prosperous. Some blindness! Your problem is that you seek to base your understanding of reality solely on "self evident" a priori principles. Forget it! To understand reality you have to go out, look and measure.

They're blind to the meaning. Doesn't mean the math doesn't work. You of course won't understand that, you're in the category of physicist who thinks that the math is the meaning.

Shayne

[tjohnson]

They're blind to the meaning. Doesn't mean the math doesn't work. You of course won't understand that, you're in the category of physicist who thinks that the math is the meaning.

Shayne

It's a fact that every attempt at measuring the speed of light gives approximately the same value. What does this mean? Duh, the speed of light is constant? Yep.

[sjw]

It's a fact that every attempt at measuring the speed of light gives approximately the same value. What does this mean? Duh, the speed of light is constant? Yep.

"Duh" indeed...

[BaalChatzaf]

They're blind to the meaning. Doesn't mean the math doesn't work. You of course won't understand that, you're in the category of physicist who thinks that the math is the meaning.

Shayne

The meaning is the predictions of a theory. Instead of worrying about Meaning, applied physicists produce results. What is the cash-value of meaning compared to that of the technology that emerges from applications of the theory?

Meaning and $1.67 will get you a cup of French Roast at the local Dunkin' Donuts ™.

Ba'al Chatzaf

[Michael Stuart Kelly]

Meaning also makes you want the results. Otherwise, why bother?

Michael

[tjohnson]

That the speed of light is constant is an experimental fact but how this fact is reconciled into classical physics is where the conceptual difficulty lies. There are thousands of books about relativity and in each one the author tries to explain as clearly as he/she can this evidence which goes against our intuition. But at some point in each expose the mathematics must be introduced to fully understand the relationships that we are actually measuring. There is no more meaning than that.

[Michael Stuart Kelly]

There is no more meaning than that.

GS,

Sure there is. Plenty. (Reason works, for a minor one.) But I don't want to argue it right now.

Michael

[sjw]

The meaning is the predictions of a theory.

Meaning is about knowing the cause and effect. It's not merely about being able to predict effect.

Shayne

[Michael Stuart Kelly]

Meaning is about knowing the cause and effect. It's not merely about being able to predict effect.

Shayne,

Dayaamm!

That's a great statement.

You verbalized something I have been groping at for a while now.

Michael

[BaalChatzaf]

The meaning is the predictions of a theory.

Meaning is about knowing the cause and effect. It's not merely about being able to predict effect.

Shayne

One never knows causes (for sure). One hypothesizes causes and predicts effects. The prediction implies the cause is is hypothesized. The hypothesized causes are tested experimentally. If the experiment falsifies the prediction, then the hypothesis is wrong or the ancillary conditions under which the prediction is made do not hold.

See

1. The prediction of the planet Neptune.

2. The falsified prediction of the motions of Mercury.

#1 indicated that the anomalous motions of Uranus were probably caused by a yet unknown planet. This worked out. See Couch Adams and Leverier.

#2 indicated that the laws of gravitation stated by Newton do not hold.

Unseen causes are always hypothesized for starters. When they become good predictors they are accepted (provisionally) as fact.

It is interesting to note that Newton did not hypothesize causes for gravitation. He did postulate of law describing the effects of gravitation which was rather close to true, but not true (as the anomalous precession of Mercury showed). To this day no one knows the cause or causes of gravitation. There are a number of hypotheses ranging from a spin 2 boson (the graviton) to strings and super symmetric particles. We know how gravitation works, we do not know its cause.

Ba'al Chatzaf

[tjohnson]

Meaning is about knowing the cause and effect. It's not merely about being able to predict effect.

Shayne

'cause' and 'effect' are outdated ways of looking at things. Very little in life can be analyzed in such simple terms.

But we are not likely to find science returning to the crude form of causality

believed in by Fijians and philosophers, of which the type is “lightning causes

thunder.” (457) BERTRAND RUSSELL

The notion of causality has been greatly modified by the substitution of space-time

for space and time. . . . Thus geometry and causation becomes inextricably

intertwined. (457) BERTRAND RUSSELL

In classical mechanics, and no less in the special theory of relativity there is an

inherent epistemological defect which was, perhaps for the first time, clearly pointed

out by Ernst Mach.... No answer can be admitted as epistemologically satisfactory,

unless the reason given is an observable fact of experience. The law of causality has

not the significance of a statement as to the world of experience, except when

observable facts ultimately appear as causes and effects. (155)

A. EINSTEIN

The chain of cause and effect could be quantitatively verified only if the whole

universe were considered as a single system—but then physics has vanished and only

a mathematical scheme remains. The partition of the world into observing and

observed system prevents a sharp formulation of the law of cause and effect. (215)W.

HEISENBERG

[Michael Stuart Kelly]

'cause' and 'effect' are outdated ways of looking at things. Very little in life can be analyzed in such simple terms.

GS,

I don't want to be mean, but you sound exactly like you crawled out of the wrong side of Atlas Shrugged, word for word.

Michael

[tjohnson]

We usually follow the ‘philosophers’ and ascribe—or, rather feel, as conscious

ascribing would not stand criticism—some mysterious structural continuity, some

mysterious overlapping of ‘cause’ and ‘effect’. We ‘feel’, and try to ‘think’, about

‘cause and effect’ as contiguous in ‘time’. But ‘contiguous in time’ involves the

impossible ‘infinitesimal’ of some unit of ‘time’. But, since we have seen that there

is no such thing, we must accept that the interval between ‘cause’ and ‘effect’ is

finite. This structural fact changes the whole situation. If the interval between

‘cause’ end ‘effect’ is finite, then always something might happen between, no

matter how small the interval may be. The ‘same cause’ would not produce the

‘same effect’. The expected result would not follow. This means only that in this

world, to be sure of some expected effect, requires that there must be nothing in the

environment which can interfere with the process of passing from the conditions

labelled ‘cause’ to the conditions labelled ‘effect’. In this world, with the structure

which it has, we can never suppose that a ‘cause’, as we know it, is alone sufficient

to produce the supposed ‘effect’. When we consider the ever-changing environment,

the number of possibilities increases enormously. If it were possible to take into

account the whole of the environment, the probability that some event would be

repeated, in all details, thus exhibiting the assumed two-valued relation of ‘cause’

and ‘effect’, which we took for granted in the old days, would practically be nil. The

principle of non-elementalism, as we see, requires an ∞-valued semantics of

probability.

The reader should not take what is said here as a denial that in this external

world some regularities of sequence occur; but the above analysis, which is mainly

due to Russell,1 shows clearly that the verbal principle of ‘same cause, same effect’

is structurally untenable. We can never manage to observe the ‘same cause’ in

detail. As soon as the antecedents have been sufficiently ascertained, so as to

calculate the consequences with some plausible accuracy as to details, the relations

of these antecedents have become so complex that there is very little probability that

they will ever occur again.

The clearing up of the problems of ‘cause’ and ‘effect’ is of serious importance,

because powerful semantic reactions are connected with it. To begin with, we must

differentiate between the terms ‘cause’ and ‘effect’, which, linked together, imply a

two-term relation nowhere to be found in this world, and thus represent a language

and a two-valued ‘logic’ of a structure not similar to the structure of the world, and the general ∞-

valued notion of causality. This last notion is the psycho-logical foundation of all

explanations leading toward ∞-valued determinism, and is an exclusive test for

structure; and so of extreme semantic importance.

[tjohnson]

GS,

I don't want to be mean, but you sound exactly like you crawled out of the wrong side of Atlas Shrugged, word for word.

Michael

I'm glad you don't want to be mean but, alas, I don't understand how your statement can be interpreted as mean anyway.

[sjw]

Meaning is about knowing the cause and effect. It's not merely about being able to predict effect.

Shayne

'cause' and 'effect' are outdated ways of looking at things. Very little in life can be analyzed in such simple terms.

Cause and effect are too simple, therefore we should leave out causes and just look at effects?!?

Michael's right, you look like you just climbed out of the wrong end of Atlas! (That was a good one!)

Shayne