Why is c the ultimate speed limit? Options

[Tom Rexton]

I've read that it is because the mass of the object increases without limit as its velocity approaches the speed of light. Is this correct? I've had doubts, since I've read from some of your posts that mass is an invariant quantity. And of course, does it not also repudiate the law of conservation of mass?


Disclaimer: I've only taken one general physics course in high school, which taugh me practically nothing because the teacher was incompetent, so much so that we only covered 1/4 of a high school physics textbook in one year--and superficially, I might add.

[Stephen Speicher]

Before we answer the subject line question, "Why is c the ultimate speed limit?", we have to answer the more general question as to why should there exist an ultimate speed limit at all. The answer to that is causality. If actions occurred instantaneously there would be no distinction between cause and effect. The idea of the instantaneous is an invalid concept, at least as far as an actuality is concerned. To say that any effect occurs instantaneously is to assert that the effect occurs without any means. Just as physical objects must be finite in size, so too the separation of causally connected events must be finite in time. To quote Dr. Binswanger: "The idea of an infinitely small amount of length or temporal duration has validity only as a mathematical device useful for making certain calculations, not as a description of components of reality." [*]

Of course, it is not that Nature or some God decreed that since we want to preserve cause and effect we will disallow instantaneous action, but rather that causality is a fundamental axiom of existence, so the existence of an ultimate limit could not be otherwise.

Relativity itself also predicts an ultimate limit. It can be shown in relativity that if the velocity of a signal were to be accelerated past the ultimate limit, a reference frame could be found for which cause and effect is reversed. Clearly contrary to fact, both philosophic and scientific. But relativity alone does not specify what that limit is. It is only by reference to experimental fact that the ultimate limit in special relativity can be set. And, indeed, as experiment after experiment has shown, that ultimate limit is c.

As to the narrower question raised by Tom, about the limit being set because otherwise mass would increase without bound as velocity increases, that is an all too-common misconception that I have addressed several times. As Tom correctly notes, I have previously made the point that the unadorned word "mass" is an invariant quantity in relativity, as almost any particle physicist would acknowledge. The idea of mass increase is actually a hold-over from pre-Einsteinian physics, and though there was a period of time when the concept held its ground after relativity was introduced, and though one finds the notion fairly prevalent in popular writings, it has long been disowned by most physicists, including Einstein.

This notion of mass increase -- often stated as "relativistic mass" -- is really a statement about energy. As has been experimentally confirmed countless times, every day in particle accelerators throughout the world, it takes more and more energy to increase the velocity of a massive object, in exactly the way as quantifiably predicted by relativity. So, conceptually, the relation between the velocity of an object and the ultimate speed can be simply stated as the following: The energy required to increase the speed of an object tends toward infinity, as the speed of the object tends toward c, the object never reaching the speed c.

The closer to c an object gets, the smaller the increase in speed for an ever-growing requirement in energy. As the T-shirt says,

Speed limit, 186,000 miles per second: It's not just a good idea, it's the law.

[*] The Objectivist Forum, H. Binswanger, December 1981, reproduced in The Objectivist Forum, Volume 1 - Volume 8, 1980-1987, TOF Publications, Inc. 1993.

[Stephen Bourque]

It is clear to me that truly instantaneous actions would violate causality, but it does not necessarily follow that there is only ONE cosmic speed limit, c. Of course, there is a vast body of experimental evidence showing that partical/wave motions are limited to 3.0 x 10 ^8 m/s. But could some sort of transport mechanism exist that exceeds (perhaps GREATLY exceeds) c, yet is still not instantaneous?

The motivation for my question is that I'm trying to understand what could account for so-called quantum entanglement, which apparently has been verified experimentally. The phenomenon seems to require some sort of super-luminal propagation of information to explain what appears to be "action at a distance."

[Stephen Speicher]

Stephen Bourque is correct in that philosophically we cannot arbitrarily say that there must be a single ultimate limit for the speed of all phenomena. However, scientifically, we also cannot arbitrarily postulate different limits from that which is experimentally confirmed. Note that the light speed limit has been experimentally verified across all scales, from the quantum in quantum electrodynamics to the cosmic scale of general relativity. It integrates physics from the micro to the macro, which is good reason to have confidence in its value.

But it is wrong to claim that quantum entanglement has been "verified experimentally." For the usual class of experiments associated with the phenomena, what has actually been verified is a correlation between detectors on a local level, not some supposed superluminal action-at-a-distance acting globally. Entanglement is an inference made based on theories that cannot explain local phenomena, a sort of wish-fulfillment self-satisfying prophecy. In my opinion it is just as magical a supposition as that made by religionists who claim that only God can explain miracles.

There are local theories that do not require such faith in superluminal behavior, but these are not as popular as the standard theories. That is not to say that these local theories are necessarily correct, since some posit other ideas just as unsatisfying as that which they seek to cure. But at least there exists one local, causal theory that is consistent with all experimental results, and integrates all of physics together under the same theoretical umbrella; the TEW explains "quantum entanglement" on a local level, and is also a causal theory.

[SteveGrossman]

Speed limit, 186,000 miles per second: It's not just a good idea, it's the law.
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Why light speed? What's the importance of light to speed? What is special to light?

It's very depressing to think that a trip to Alpha Centauri will never take less than 4.1 years regardess of what space ship drives may be invented in a million years. I know that the science-fiction idea of "folding space" with "warp drives" is mere fiction since coordinate systems cant be folded any more than one's idea about baseball can be folded. Yet the fact of compressing things for energy seems promising here. I suppose, however, that you'll say that the energy to compress something for the energy to create translight speed violates some principle. What about two big mechanical hands quickly squeezing a star, much like one might squeeze a balloon to rapidly force out the air? Or goosing a black hole? That should do something dramatic. I'm sorry for these images but I'm very depressed. I really would like to find that Star Wars bar.

[Stephen Speicher]

As a science fiction fan I am sympathetic to SteveGrossman's lament, but fiction is fiction and fact is fact. If special relativity is correct, then light speed is the law because otherwise causality would not be preserved. Based on countless experimental confirmations, we know special relativity is correct, at least within the limited context of non-gravitational influences. Where gravitational effects are small-enough for the purpose at hand, special relativity reigns supreme. Unless someone broadens the context, it's warp 1.

[Arnold]

So, conceptually, the relation between the velocity of an object and the ultimate speed can be simply stated as the following: The energy required to increase the speed of an object tends toward infinity, as the speed of the object tends toward c, the object never reaching the speed c.

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Does this fit my understanding that it is as if the mass has increased?

[Stephen Speicher]

Does this fit my understanding that it is as if the mass has increased?[right][snapback]4561[/snapback][/right]

I am adamantly against the use of "relativistic mass," whether stated directly or in the form of an "as if." The notion is terribly wrong, both mathematically and physically, and any remnant of such a misguided idea should be banished forever. Mathematically it is wrong because mass is the norm of the 4-momentum, not the time component, and therefore it is an invariant. Physically it is wrong because it implies some sort of change to the internal physical structure of the object, which is not the case. There is no value gained by perpetuating this distortion.

[BillSpears]

Physically it is wrong because it implies some sort of change to the internal physical structure of the object, which is not the case.
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Why does there have to be any change to the internal physical structure? Isn't this like time and length distortion? That is the mass appears different to the fixed observer, but to an observer on the mass nothing changes. Perhaps I could word that better, if we have a mass moving along speedily and an observer flying in formation, I wouldn't expect the gravitational force between them to increase. But as the mass flies by a fixed observer, I would expect him to measure or deduce from the flight path a heavier mass.

[Stephen Speicher]

Why does there have to be any change to the internal physical structure?  Isn't this like time and length distortion?  That is the mass appears different to the fixed observer, but to an observer on the mass nothing changes.[right][snapback]4727[/snapback][/right]

Time dilation and length contraction are simply answers to the question of how spatial and temporal coordinates of an event in one frame, relate to the coordinates of that event as measured in a frame in relative motion to the first. When we apply the Lorentz transformation to that question, the result is a simple formula relating the two, having no physical consequences, such as forces on objects.

Physically, mass is defined as a scalar quantity. In a Newtonian world if you measure how much force is needed to accelerate a mass to a given speed, the magnitude of that force is the same regardless of how the force is oriented with respect to the velocity of the mass. But there is a physical difference predicted and noted for relativistic velocities, in that the physical force applied in the transverse direction is not the same magnitude of force applied longitudinally. To think of this in terms of relativistic mass would then physically require mass to be a matrix quantity, not the physical scalar quantity it is.

Even at its best, relativistic mass only obscures rather than illuminates both the mathematical and the physical circumstances. And, it gets even worse to attempt to carry this mistake over from special to general relativity. As I previously noted, what is called relativistic mass is really energy, and in general relativity energy gravitates, which would be utterly senseless for relativistic mass as appearance.

[PhilO]

Even at its best, relativistic mass only obscures rather than illuminates both the mathematical and the physical circumstances. And, it gets even worse to attempt to carry this mistake over from special to general relativity. As I previously noted, what is called relativistic mass is really energy, and in general relativity energy gravitates, which would be utterly senseless for relativistic mass as appearance.
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That's a question I've had for some time, i.e. the relationship between so-called relativistic mass increase and gravity. Logically such a mass increase would result in a corresponding gravitational field from the moving object. In fact this idea was mentioned in a science fiction book Tau Zero, about a starship that had lost its deceleration capability - the travellers decided that the best thing they could do would be to keep gaining speed and increasing time dilation. One of the characters muses that the ship would be very destructive eventually because of the huge relativistic mass' effects on star systems as it passed by. Even when I read this as a teenager I found the idea disturbing and something wrong with it.

So it is the case the energy increase of the moving object would not manifest any additional gravitational effects?

[Stephen Speicher]

So it is the case the energy increase of the moving object would not manifest any additional gravitational effects?

In general relativity the stress-energy-momentum tensor provides a combined effect on all gravitational interactions. So, yes, energy gravitates. In fact, it was only less than a decade ago that experimental results were reviewed and confirmed that kinetic energy gravitates. This is interesting for several different reasons, not the least being that most of the kinetic energy of an atom lies in the nucleus.

But the intricacies of general relativty are both profound and enormous. Take, for instance, the case of two beams of light. The stress-energy-momentum tensor that I mentioned not only folds in the energy but also the relative momentum between the beams. If you do the calculation (not trivial) it turns out that two light beams that are traveling parallel to each other do not exhibit any gravitational attraction, but two beams traveling anti-parallel attract each other gravitationally. A surprising result. But these are the sort of complexities that explain the vast differences between Newtonian and Einsteinian gravitation.

p.s. Regarding the mention of the science fiction book. These books are often as bad in their physics as are the popularizations of the theories. However, I must admit I have noticed a trend in the last five to eight years. There have been an increasing number of requests from science fiction writers asking for clarifications, not just the wild scenarios of wormholes and the like, but for more realistic applications of general relativity. I find that encouraging.

[Rada]

Stephen Speicher,

what about the speed of gravity? For example, Flandern says there is no gravitational aberration, meaning Newton's Third Law gives gravitational force vectors between Sun and Earth pointing to the "true" positions of each other, not the delayed 8 minutes lightspeed positions.

[Stephen Speicher]

Stephen Speicher,

what about the speed of gravity? For example, Flandern says there is no gravitational aberration, meaning Newton's Third Law gives gravitational force vectors between Sun and Earth pointing to the "true" positions of each other, not the delayed 8 minutes lightspeed positions.

As I have pointed out to Van Flandern first privately, and then later publicly, he takes this argument from Eddington and quotes him to this effect, but he ignores the fact that Eddington then states:

The argument is fallacious ... In the theory given in this book, gravitation is propagated with the speed of light, and there is no discordance with observation.

Indeed, as Eddington realized many years ago, the argument is completely falacious. For more modern refutations of the fallacy that Van Flandern continues to propagate, see:

1. "Aberration and the speed of gravity," S. Carlip, Physics Letters A, 267 (2-3): pp. 81-87, March 13, 2000.

2. "Speed limits in general relativity," R.J. Low, Classical and Qunatum gravity, 16 (2): pp. 543-549, February 1999.

[Nate Smith]

Before we answer the subject line question, "Why is c the ultimate speed limit?", we have to answer the more general question as to why should there exist an ultimate speed limit at all. The answer to that is causality. If actions occurred instantaneously there would be no distinction between cause and effect. The idea of the instantaneous is an invalid concept, at least as far as an actuality is concerned. To say that any effect occurs instantaneously is to assert that the effect occurs without any means. Just as physical objects must be finite in size, so too the separation of causally connected events must be finite in time. To quote Dr. Binswanger: "The idea of an infinitely small amount of length or temporal duration has validity only as a mathematical device useful for making certain calculations, not as a description of components of reality."

Does positing no ultimate speed limit imply instantaneous speeds? If an object can go faster and faster, that doesn't mean it will eventually be going "infinitely fast". No matter how fast it goes, it always has some speed, right?

[Stephen Speicher]

Does positing no ultimate speed limit imply instantaneous speeds? If an object can go faster and faster, that doesn't mean it will eventually be going "infinitely fast". No matter how fast it goes, it always has some speed, right?

Nate makes a valid point. Philosophically, as far as causality is concerned, all we can rule out is instantaneous action, and all we can demand, not simply for the speed of an object, but for all causal effects as well, is that they occur in finite time. However, scientifically, we can say a great deal more, as does relativity and experiment.

[Paul's Here]

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However, scientifically, we can say a great deal more, as does relativity and experiment.

Just curious, but is any of the theory of relativity dependent on the specific value of c or just on the fact that there is a ultimate speed of light? Would the theory change in any way had experimental results discovered that the speed of light were 400,000 miles per second?

[Stephen Speicher]

Just curious, but is any of the theory of relativity dependent on the specific value of c or just on the fact that there is a ultimate speed of light? Would the theory change in any way had experimental results discovered that the speed of light were 400,000 miles per second?

Special relativity itself does not depend on any specific value for c. In the theory, the Lorentz transformation does depend on one invariant speed, and in order to preserve causality the speed of particles and signals are limited by c, the value of which can be determined experimentally.

[Lady Brin]

The closer to c an object gets, the smaller the increase in speed for an ever-growing requirement in energy. As the T-shirt says,

Speed limit, 186,000 miles per second: It's not just a good idea, it's the law.

Here is part of an article from the New York Times

http://www.nytimes.com/2006/05/16/science/16ligh.html

An article describing the experiment appears in the current issue of the journal Science.

In the vacuum of space, light travels at a constant 186,282 miles per second. When it passes through a transparent material like glass or water, it slows slightly, in effect bouncing off atoms as it moves.

For Dr. Boyd's trick, the scientists used an optical fiber of glass with small amounts of the metal erbium, which acts as an amplifier. In the experiment, a pulse of laser light was fired into the fiber. Even before the peak of the pulse entered the fiber, another pulse appeared, seemingly out of nowhere, at the far end of the fiber.

This new pulse then split in two. One, a twin of the original pulse, moved forward, while the other moved backward through the fiber.

The backward pulse, which traveled faster than the speed of light, and the original pulse met at the front end of the fiber, where they canceled each other.

Even though one pulse momentarily became three, the experiment did not violate the law mandating conservation of energy because the amplifying effect of the erbium added a temporary surge of energy.

At first glance, the experiment appears to flout the usual speed limit on the transmission of signals as the original pulse jumped to the forward-moving pulse on the other side of the fiber.

However, the pulses were in a shape known as Gaussian, which is, in principle, infinite in width, though in practice not quite that wide.

What do they mean by the last statement: infinite in width, though in practice not quite that wide? If the experiment was performed in a tube wouldn't it have a finite width? This confused me obviously.

Dr. Boyd stated he thought it was a nifty trick, but couldn't energy be captured from this somehow? Or am I totally off base?

[rich]

I am adamantly against the use of "relativistic mass," whether stated directly or in the form of an "as if." The notion is terribly wrong, both mathematically and physically, and any remnant of such a misguided idea should be banished forever.

What about the phrase, "conversion of mass into energy"? This phrase is commonly printed, in places from newspaper articles to textbooks. But A is A, and mass is mass, so how can mass become energy? Mass and energy don't even have the same units!