# Explain Theory of Relativity

July 6, 2004 2:12 PM Subscribe

trying to get my head around special relativity filter: Can someone explain to me, in terms as devoid of mathematical formulae as possible, how something traveling less than the speed of light cannot be accelerated to the speed of light?

I am not a physicist, but based on Wikipedia's page on relativity, I suspect it is intrinsically related to the definition of gamma, which is defined as 1/sqrt(1-(v^2/c^2)), with v the velocity and c the speed of light. Upon reaching the speed of light, v^2/c^2 would evaluate to 1, and gamma's denominator would evaluate to 0, which causes all kinds of problems for the equations involving energy and momentum.

Also, relativistic mass is given as a function of gamma, in such a way that it winds up increasing asymptotically as an object approaches the speed of light. So it looks like the faster you're going, the heavier you are, which means that more energy is required to go faster.

posted by alphanerd at 2:36 PM on July 6, 2004

Also, relativistic mass is given as a function of gamma, in such a way that it winds up increasing asymptotically as an object approaches the speed of light. So it looks like the faster you're going, the heavier you are, which means that more energy is required to go faster.

posted by alphanerd at 2:36 PM on July 6, 2004

The Special Theory explains how the energy of a moving object is dependent on its mass and velocity -- or, in other words, how much energy is required for its mass to attain a particular velocity. The denominator of the equation is the square root of (1 - v^2/c^2), where v is the velocity and c the speed of light. As v approaches c, the denominator approaches 0, meaning the ratio approaches infinity. That is, it would take infinite energy to push any mass to the speed of light. (Light itself has no mass.)

posted by macrone at 2:36 PM on July 6, 2004

posted by macrone at 2:36 PM on July 6, 2004

there is no explanation - that is just how the world works. the formulae say the same thing, but using maths - they are not any better an explanation, just a different way of saying "this is how things are".

posted by andrew cooke at 2:54 PM on July 6, 2004

*alternatively:*in physics, many things are closely connected. once you fix some things, others are fixed too. it so happens that "god chose" a world in which the speed of light is the same for everyone, and not a world where velocity = acceleration times time (although that's a good approximation at low speeds). the two choices are incompatible (modulo some other choices about time, space, and energy, i guess). so once you make that choice, things behave in the way you describposted by andrew cooke at 2:54 PM on July 6, 2004

(1) Things moving faster mass more, because of relativistic effects.

(2) It's harder to accelerate a more massive object.

(3) So as things accelerate, it gets harder to accelerate them further.

(4) Add it up, and it turns out you'd need infinite energy to accelerate something to the speed of light.

posted by ROU_Xenophobe at 3:01 PM on July 6, 2004

(2) It's harder to accelerate a more massive object.

(3) So as things accelerate, it gets harder to accelerate them further.

(4) Add it up, and it turns out you'd need infinite energy to accelerate something to the speed of light.

posted by ROU_Xenophobe at 3:01 PM on July 6, 2004

another "explanation" that doesn't really explain anything, but that provides a mental shorthand to the relevant concepts is to think of things in terms or relativistic mass. Along the same lines as the time dilation and length contraction associated with relativity, there is the concept of relativistic mass - the faster something goes the more massive it effectively has. The relativistic mass is related to the rest mass by the Lorentz factor, [gamma], mentioned above:

M = [gamma]*m, where

m = rest mass, and

M = relativistic mass.

[gamma] is equal to 1 at rest, but goes to infinity as your velocity approaches the speed of light. Thus, relativistic mass goes to infinity as you approach the speed of light, and thus steadily more energy is required to accelerate an object to greater velocities until you get to the "infinity" wall of energy required to push that object up to the speed of light.

(or, on preview, what ROU just said. still the real "explanation" we still need, is why relativistic mass happens at all.)

posted by badstone at 3:16 PM on July 6, 2004

M = [gamma]*m, where

m = rest mass, and

M = relativistic mass.

[gamma] is equal to 1 at rest, but goes to infinity as your velocity approaches the speed of light. Thus, relativistic mass goes to infinity as you approach the speed of light, and thus steadily more energy is required to accelerate an object to greater velocities until you get to the "infinity" wall of energy required to push that object up to the speed of light.

(or, on preview, what ROU just said. still the real "explanation" we still need, is why relativistic mass happens at all.)

posted by badstone at 3:16 PM on July 6, 2004

The space we live in is not as simple as what we think we see. It has a different topological shape such that the 3 space dimensions we see are intricately combined with the the time dimension.

Here, this might help: Imagine that moving North-South was harder than moving East-West. If so, then moving NorthWest would depend on knowing just how much North and how much West are involved in order to predict how hard your path will be.

In the same way, when an object "moves" it is actually traveling along a space path AND a time path. You can think of an increase in 'velocity' as an object changing its angle, just as in the NorthWest example.

As it turns out, the time component of spacetime is curved in a really strange way (the hyperbolic component of Minkowski space) such that an increase in velocity radically alters the character of the associated space.

The velocity of an object is an angle in this strange space-time. The Lorentz transformation equations which allow us to switch reference frames are essentially just rotation equations. To add two velocities we end up adding the tanh (hyperbolic tangent) of two angles.

The tanh, like the tangent cannot exceed or even arrive at 1. Only an infinite angle/velocity could have a tanh=1. (Don't ask me why massless particles/photons can achieve this. All I know is that the equations are nonsense unless they do.)

And in this geometry, 1= the speed of light. The speed of light limit is thus an intrinsic definition of the shape of the universe we live in.

posted by vacapinta at 3:47 PM on July 6, 2004 [1 favorite]

Here, this might help: Imagine that moving North-South was harder than moving East-West. If so, then moving NorthWest would depend on knowing just how much North and how much West are involved in order to predict how hard your path will be.

In the same way, when an object "moves" it is actually traveling along a space path AND a time path. You can think of an increase in 'velocity' as an object changing its angle, just as in the NorthWest example.

As it turns out, the time component of spacetime is curved in a really strange way (the hyperbolic component of Minkowski space) such that an increase in velocity radically alters the character of the associated space.

The velocity of an object is an angle in this strange space-time. The Lorentz transformation equations which allow us to switch reference frames are essentially just rotation equations. To add two velocities we end up adding the tanh (hyperbolic tangent) of two angles.

The tanh, like the tangent cannot exceed or even arrive at 1. Only an infinite angle/velocity could have a tanh=1. (Don't ask me why massless particles/photons can achieve this. All I know is that the equations are nonsense unless they do.)

And in this geometry, 1= the speed of light. The speed of light limit is thus an intrinsic definition of the shape of the universe we live in.

posted by vacapinta at 3:47 PM on July 6, 2004 [1 favorite]

A better conceptual way to think about it comes from the assumptions of special relativity. There are two of them:

1) The laws of physics are the same in every inertial reference frame. An inertial reference frame is just a non-accelerating (i.e. not going faster/slower AND not changing direction) basis from which to measure velocities of things. Saying something moves at 5 m/s has no meaning if you don't have any idea what 0 m/s means, so you need to establish that first.

2) The speed of light is the same in all reference frames. This one is a larger pill to swallow, but there are some conceptual reasons that it should be true. The main one I can think of comes from what is called self-inductance. Light waves (which are composed of electric and magnetic waves) propagate by interacting with themselves in such a way that the electric field creates the necessary magnetic field which creates the electric field, etc. But if you could somehow travel alongside one of these waves (and thus at the speed of light), you would not see the sort of movement that is needed for self-inductance to occur. Thus you get a paradoxical scenario. If you trust that this paradox can't happen, and an intuitive leap (often fruitful in physics) was taken to say that the speed of light is the same in all reference frames.

An immediate mathematical result of enforcing these two postulates is that Lorentz factor (oddly enough, developed earlier to resolve Michelson-Morely's results about light through the ether) which is mentioned above. /gamma = 1/sqrt(1-v^2/c^2) tells you (in most cases) how the scaling works. You'll note that (v/c) is always less than one, and thus squaring it gives you small numbers unless you are going VERY fast. Even at a tenth the speed of light, \gamma is only about 1.005.

As an aside, it's best to not think of relativistic mass at all (it isn't terribly useful, and even kind of misleading), and only consider energy, momentum, and rest mass. Rest mass is the mass of a body in its own reference frame, and is given by mc^2. The c^2 bit is there to convert from mass units to energy units. There is then a momentum term pc (this time, c converts from momentum units to energy units) where p = \gamma * mv (m = mass, v = velocity). There is then a relation with energy, namely that E^2 = (pc)^2 + (mc^2)^2. This is (not accidently) like the Pythagorean theorem for the length of the hypotenuse of a triangle. The (mc^2)^2 is constant, but the \gamma term in pc means that as an object goes to the speed of light, its energy approaches infinity. Since one can't add infinite energy, this physically limits something from being accelerated to the speed of light.

As a second aside, the reason a massless particle can (and has to, actually) go the speed of light is that the definition of momentum changes when something has no mass. For a photon, mc^2 = 0 and momentum is related to wavelength.

posted by Schismatic at 4:21 PM on July 6, 2004 [1 favorite]

1) The laws of physics are the same in every inertial reference frame. An inertial reference frame is just a non-accelerating (i.e. not going faster/slower AND not changing direction) basis from which to measure velocities of things. Saying something moves at 5 m/s has no meaning if you don't have any idea what 0 m/s means, so you need to establish that first.

2) The speed of light is the same in all reference frames. This one is a larger pill to swallow, but there are some conceptual reasons that it should be true. The main one I can think of comes from what is called self-inductance. Light waves (which are composed of electric and magnetic waves) propagate by interacting with themselves in such a way that the electric field creates the necessary magnetic field which creates the electric field, etc. But if you could somehow travel alongside one of these waves (and thus at the speed of light), you would not see the sort of movement that is needed for self-inductance to occur. Thus you get a paradoxical scenario. If you trust that this paradox can't happen, and an intuitive leap (often fruitful in physics) was taken to say that the speed of light is the same in all reference frames.

An immediate mathematical result of enforcing these two postulates is that Lorentz factor (oddly enough, developed earlier to resolve Michelson-Morely's results about light through the ether) which is mentioned above. /gamma = 1/sqrt(1-v^2/c^2) tells you (in most cases) how the scaling works. You'll note that (v/c) is always less than one, and thus squaring it gives you small numbers unless you are going VERY fast. Even at a tenth the speed of light, \gamma is only about 1.005.

As an aside, it's best to not think of relativistic mass at all (it isn't terribly useful, and even kind of misleading), and only consider energy, momentum, and rest mass. Rest mass is the mass of a body in its own reference frame, and is given by mc^2. The c^2 bit is there to convert from mass units to energy units. There is then a momentum term pc (this time, c converts from momentum units to energy units) where p = \gamma * mv (m = mass, v = velocity). There is then a relation with energy, namely that E^2 = (pc)^2 + (mc^2)^2. This is (not accidently) like the Pythagorean theorem for the length of the hypotenuse of a triangle. The (mc^2)^2 is constant, but the \gamma term in pc means that as an object goes to the speed of light, its energy approaches infinity. Since one can't add infinite energy, this physically limits something from being accelerated to the speed of light.

As a second aside, the reason a massless particle can (and has to, actually) go the speed of light is that the definition of momentum changes when something has no mass. For a photon, mc^2 = 0 and momentum is related to wavelength.

posted by Schismatic at 4:21 PM on July 6, 2004 [1 favorite]

Andrew Cooke has it: this is one of those "there is no why" questions.

Your question can be restated as: "Why does the relativity work so well?"

Simply put: nobody knows. No one has ever found an exception and not for lack of trying, but no one can explain it either.

General relativity was developed axiomatically, from a few first principles, and is a system rather like Euclidean geometry. GR is, in some ways, a refutation, an expansion of Euclid. Maximum speed =

GR was, and continues to be developed because it appears to be an exact descritpion of the world we live in. However, the description isn't the world. A theory cannot (formally) tell us anything about its axioms. GR doens't explain the assumption that

So no ones knows "why", but we do know that it is. A utilitarian answer, if not a philosphically satisfying one.

posted by bonehead at 4:26 PM on July 6, 2004

Your question can be restated as: "Why does the relativity work so well?"

Simply put: nobody knows. No one has ever found an exception and not for lack of trying, but no one can explain it either.

General relativity was developed axiomatically, from a few first principles, and is a system rather like Euclidean geometry. GR is, in some ways, a refutation, an expansion of Euclid. Maximum speed =

*c*is one (partial) way to state one of those axioms. Alternately, it's saying space-time is curved (in a particular way). Assuming that the universe is a Minkowsi space is a logically equivalent statement (as vacapinta explains above). The formalisms of general relativity are consequences of that assumption (and the other two axioms). "E=mc^{2}" is one of those consequences.GR was, and continues to be developed because it appears to be an exact descritpion of the world we live in. However, the description isn't the world. A theory cannot (formally) tell us anything about its axioms. GR doens't explain the assumption that

*c*is the universe's speed limit, it just builds on it.So no ones knows "why", but we do know that it is. A utilitarian answer, if not a philosphically satisfying one.

posted by bonehead at 4:26 PM on July 6, 2004

the really simple answer, and the one that everything boils down to eventually: because.

posted by Grod at 5:31 PM on July 6, 2004

posted by Grod at 5:31 PM on July 6, 2004

Our ideas about how the universe works are always changing, and relativity isn't that old in the greater scheme of things. I don't accept as a given that travel at light speed isn't possible.

posted by bingo at 6:07 PM on July 6, 2004

posted by bingo at 6:07 PM on July 6, 2004

Because Bush slashed the funding for the Warp Drive Initiative.

posted by inksyndicate at 7:14 PM on July 6, 2004

posted by inksyndicate at 7:14 PM on July 6, 2004

There is a why. It's a topological limit. Just like there is no ‘edge’ on the interior of a sphere.

posted by snarfodox at 8:11 PM on July 6, 2004

posted by snarfodox at 8:11 PM on July 6, 2004

*it so happens that "god chose" a world in which the speed of light is the same for everyone.*

Well, maybe not.

posted by trharlan at 8:58 PM on July 6, 2004

*There is a why. It's a topological limit.*

Ok, but that just pushes the question back to "why do we live in that particular manifold?" Adding another layer of model doesn't answer the problem.

posted by bonehead at 4:40 AM on July 7, 2004

Shortest answer: Because it takes infinite energy to go the speed of light.

Which means relativity is bunk (but useful bunk right now), our math is broken (infinity? what?) and mostly right now we aren't trying to develop models that define and explain, but simply predict.

posted by ewkpates at 5:09 AM on July 7, 2004

Which means relativity is bunk (but useful bunk right now), our math is broken (infinity? what?) and mostly right now we aren't trying to develop models that define and explain, but simply predict.

posted by ewkpates at 5:09 AM on July 7, 2004

Piggybacking on trharlan's link, this book posits a speed of light that varies over time. I'm not really convinced, but it's a fun read in that it lets you see the human side of theoretical physics.

Cosmologists can get pretty bitchy to each other.

posted by COBRA! at 7:15 AM on July 7, 2004

Cosmologists can get pretty bitchy to each other.

posted by COBRA! at 7:15 AM on July 7, 2004

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