## Faster than infinity

Posted by Jeff Id on September 8, 2010

Ok, so this post is not about climate at all, I’m not sure why I’m writing it except that the concepts are fun, it’s controversial amongst those who haven’t spent their lives in science, and it’s well known.

You can’t travel at the speed of light. I’m not saying that other things can’t because the structure of our universe dictates that some things MUST travel at the speed of light. But objects made of clumped energy (matter) and YOU cannot travel at the speed of light.

The concept is disastrously confusing because of the way it is worded. I’ve spent a lot of time at this blog trying to make science simpler so the public can get what is being done. When relativity is discussed in science classes, people ask things like – why not, is there a wall. I know some very smart people who have gone as far as denying the effect exists, simply on the basis that it sounds impossible. Physicists answer by equation in every class I’ve ever taken. They say, naw your mass increases so you can’t accelerate.

While that is completely true, what is missing in that answer is the perspective of the person trying to accelerate. From earth’s perspective if you are zooming away at 1 km/hr slower than the speed of light, you can accelerate faster and faster at a thousand g’s for a billion years and will never reach or cross the speed of light. From your own perspective (visual distortions ignored), Earth starts out receding at 1km/hr. Light inside the ship seems the same as always. If you measure the distance to a star and it’s going to take 5 years to get there, you can just accelerate and cut the time to 2.5. It takes no more effort to double your perceived speed than it would if you were on the surface of the Earth. Odd things happen while you’re doing it, like the distance to the star shortens instead of the expected result, but you get to keep on accelerating all you want.

Now say you want to go to Andromeda galaxy, which is about 200 million light years from here. It takes 200 million years for light to arrive – a long way. What if you wanted to go their in your lifetime, is it possible?

The answer is yes, of course it’s framed in physics that time slows, distance compresses, mass increases, but from the perspective of the spaceship, if you want to go faster, you always can. Always. You can even go so fast as to cross the entire universe in a second.

What you can’t do though, is go as fast as light.

- – wiki Lorentz factor

The Lorentz factor is used in the relativistic forms of classical physics equations. When v (velocity) = c (speed of light) the denominator (bottom) becomes zero and the equation becomes undefined. What is interesting is that as v comes closer to c, γ approaches infinity.

Remember though, math is a representation of physics, not the other way around. Mass increases? Distance shortens? and Time slows? I’ve been around for a while, in my opinion these concepts are fairly strange. It speaks more to the fact that our understanding of what is mass, distance, and time are, is limited than anything else.

I’m too lazy to look up all the details for people not interested enough to do it themselves. (grizzled blogger) but distance, mass, and time approach wild limits as you get closer to light speed. Time goes to zero (frozen in time), distance goes to zero in the direction of travel (you become more 2 dimensional), mass goes to infinity. Below you can see that as gamma approaches infinity, time approaches zero.

T’ = T(1 – (v/c)^{2})^{1/2} = **T/γ,**

Kinda neat, it’s also interesting to note that there is no need to go faster than the speed of light to travel to a star or even a far away galaxy in your lifetime. You can already do it with enough energy. Those who stay behind will age though, equally to the distance you travel in light years. Time travel to the future, is perfectly reasonable and has been demonstrated by experiment. It’s just not very much time travel until you cover a lot of distance and don’t expect to go back.

Oddly, nothing about the equations are undefined for going over the speed of light. They work perfectly, however crossing from below to above is a bit tricky.

So sorry for the strange post, but the point is that light is infinitely fast. It crosses the universe without a single click in time. Faster than light is faster than infinity. Where we monkeyfaces go wrong is in our understanding of time, distance, mass and by combination — velocity.

So why do you want to go faster than infinity anyway?

## Brian H said

No, light doesn’t age while it crosses the universe. Unless it does.

## Murray said

And then there are Tachyons – theoretical particles which always travel faster than the speed of light and with imagionary rest masses.

This gives them some rather odd properties.

Like normal particles they need infinite energy to approach the speed of light, however they speed up as energy decreases – presumably creating stability issues, as they will tend towards infinite speed.

They also have issues with time, eg messages sent by the Tachyonic Antitelephone travel backwards in time and so a message can be exchanged if and only if the exchange does not take place!

There were some (presumably unsuccesful?) efforts to detect them by looking for their Cerenkov radiation – the blue glow you see in water cooled reactors which is emitted by particles travelling at faster than the local speed of light – in a vacuum.

## timetochooseagain said

Hehe, relativity is pretty wild.

Light, from it’s own perspective, does not have velocity, as the passage of time measured within it’s reference frame does not exist-indeed light, from it’s own perspective, does not even have a direction, it exists everywhere on it’s world line in the same instant of it’s own experience.

It is only those of us outside light’s reference frame who see it as otherwise. And no matter our relative motions, light appears to move at the same ratio of distance to our experience of time. Because as we chase light, our experience of time slows, so the proportionally smaller distance we see light travel still comes out to the same speed.

## josh said

Actually, in the reference frame of a relativistic rocket, you don’t exceed the speed of light. The distance to your destination contracts, such that even though it’s taking you much less time to get there, you are also travelling a much shorter distance.

## Brian H said

Tau Zero, Poul Anderson.

Bussard Ramscoop gets damaged, can’t be shut down. Continuous acceleration. With increasing mass, more and more input required to speed up. They take to driving through the hearts of stars, then neutron stars. Get to the Big Crunch, and then …

## Graeme said

Just dont hit any stray grains of interstellar “sand” at such high speeds…

## Nick Stokes said

“Oddly, nothing about the equations are undefined for going over the speed of light.”Defined, maybe, but they do become imaginary if v>c.

## Brian H said

#7;

Just because you aren’t personally OK with the origins and roots of negative squares! We’re purfukly reel, I tell yez.

## Mark Ping said

Note that Andromeda is 2.5 Mly away, not 200Mly.

I hate it when people say, “okay, Einstein says you can’t go as fast as light, but what if you could?” Grrr. Under what physical theory can I answer that q? Everything turns to cabbage–that’s my new answer for what happens when you go at c. It’s an outlandish theory, but as valid as any other if you’re going to throw out special relativity.

Also, it’s the case that as velocity increases, your inertial mass changes, your gravitational mass doesn’t.

## Steve Fitzpatrick said

Jeff,

Nice post. Closed inside your rocket, you can’t perceive anything is changing, no matter how fast you calculate you are going based on your on-board clock and on-board accelerometer. Of course, you might note that the approaching starts are emitting in the hard gamma-ray spectrum, and you will know something really strange has happened when you return to Earth and discover the place is inhabited by super-intelligent cockroaches.

“And while the future’s there for anyone to change,

still you know it seems

it would be easier sometimes to change the past”

## Gnomish said

But the speed of light isn’t infinite; it’s 186,000 miles per second in space, slower in other media.

You can also exceed it in other media – that’s how you get Cerenkov radiation.

http://en.wikipedia.org/wiki/Cherenkov_radiation

## Gnomish said

Here’s a puzzler- when I turn on the flashlight, does it accelerate an infinite mass? (or release one that was kind of hanging out waiting to get jail-broke?)

## Brian H said

Gnomish, you’re simply uninformed about SR theory. It’s the mass and time contraction that approach infinity. Don’t bother your head about it; it involves hard subjects like fractions.

And the flashlight emits photons, which are massless.

## steveta_uk said

Flash-lights don’t “emit” photons, as a photon is “moving” at the speed of light which means it exists for zero time (from it’s point of view) which means a photon is simply an instantaneous transfer of energy from the flash-light to whatever target absorbs the energy, however far away that is (could be in Andromeda, no probs.)

Which also means that entanglement can happen, as both the emission and absorption events happen at the same time from the viewpoint of a photon, so are reversible. Cool stuff.

## Marty said

The correct definition: “In spacetime (!!!), the speed of light is the limit and nothing with mass can reach that limit.”

## Jason Calley said

Hey Mark Ping, you say “Also, it’s the case that as velocity increases, your inertial mass changes, your gravitational mass doesn’t.”

Hmmmm…. I could be wrong here, but are you sure about that? Isn’t the basis of General Relativity the idea that inertial mass and gravitational mass are the same? I thought that was the reason that high speed objects (like photons) are deflected more by gravitational fields than Newton would predict. Am I confused on this?

## Retired Engineer said

Photons are not quite massless. They can exert force. Bell Labs, prior to the breakup, suspended a small glass bead on a light beam from an argon laser in a vacuum. Very much like suspending a ping-pong ball in an air stream. There were many questions as to how it worked, but it was repeatable.

Arthur C. Clarke wrote “when a distinguished and senior scientist says something is possible, he is almost certainly right. When he says something is impossible, he is almost certainly wrong.”

About ten pages later, Dr. Clarke wrote “Faster than light travel is impossible.”

“Impossible” means we don’t know how to do it.

## Andrew said

More accurately, your “mass” going to infinity refers to the mass-equivalent of your kinetic energy added to your “rest mass”. Obviously rest mass is not increased accelerating toward the speed of light. However, you are also increasing your kinetic energy by doing so, so you mass as the total energy divided by c^2 is what increases to infinity. This is your “relativistic mass”. And the problem is NOT that you are approaching infinite mass, so you can’t accelerate. The problem is that the

force necessary to maintain accelerationis approaching infinity as a consequence. If I can exert infinite force on an object, I can indeed accelerate to c. But the difficulty of trying to exert infinite force is that you would need an infinite amount of energy ie mass to do so. The amount of energy and mass in the universe is not infinite, soactuallyaccelerating to c is impossible.## kuhnkat said

Here is an editorial talking about laser trapping touching on the Bell Labs experiments.

http://www.skybooksusa.com/time-travel/timeinfo/laser.htm

It is especially apropos as Steven Chu, Phd. mentions that they developed a NEW theory to explain the observed lower cooling achieved by another group. This should be a reminder that just because an equation, or set of equations, are balanced and APPEAR to explain our reality, they are simply the best we have achieved AT THAT TIME! Time moves on and, hopefully, we learn more.

## David Jay said

Kuhnkat: “Time moves on…”

Not if you’re a photon😉

## M. Simon said

If inertia is electromagnetic it may be possible to manipulate matter so it takes less energy to accelerate than currently. (Heh)

http://inertiaquestion.blogspot.com/2010/07/inertia-question.html

Some weird far out idea? Crazy science? Well no. It is discussed in Book II Chapter 28 of the Feynman lectures. And he has the math to back the idea.

## Gnomish said

Well, photons may be light, but if relativity has any meaning, they’re not exactly massless – or did I miss something about what E is equal to?

It’s true I’ve always had trouble with fractious – but I can handle the integral of acceleration.

However, I’m as sure as anything that everything didn’t happen all at once.

once i took a trip at .9C

just to get a feel of relativity.

upon my return i found my brother to be

Exactly ten years younger than me…

but simultaneously i was 10 years his junior- so it’s true.

he is a special relative, and a conservative too.

Till the next entanglement, then, may your wave functions ne’er collapse. 🙂

## Andrew said

22-IIRC, Photons have a “rest mass” (hah!) of zero, which is to say that the Newtonian “invariant mass” as measured by someone moving along with a photon would be zero. Depending on the energy of light, it has a different relativistic mass, and the energy of light thus would depend on the frame of reference of the observer. Which is how the wavelength of light gets distorted by relative motion, ie redshift.

BTW, the photon is strictly speaking strongly believed to be Massless, but if it were found to have mass, then

cwould NOT refer to the speed of light in a vacuumper se(as having any rest mass makes getting to the speed of light impossible), but would still be the maximum speed attainable in space time, and the speed of gravitational waves and “gravitons”. You would, however, have to modify Coulomb’s law, giving an extra degree of freedom to the EM field. The mass of a photon, if it is non zero, is certainly less than 3*10^-27 eV/c^2## Brian H said

#23;

Why “hah!”?

http://www.seas.harvard.edu/haulab/slow_light_project/ultra_slow_light/ultra_slow_light.htm

BECs can stop light and allow it to carry on later.

## suricat said

Hi Jeff.

As an engineer I usually don’t like to be drawn into relativistic issues, but your post looks to include the main engineers argument against ‘special relativity’ (SR). The ‘self perspective’ reference frame that disproves the trust that quantum mechanics has placed in SR. Which begs the question, if SR is inconclusive then what of GR?

I’ve never forgotten that SR was proposed as a methodology to correlate diverse observations into a ‘merged’ reality. ‘Light speed’ (LS) has its top limit set ‘in vacuum’, but is slowed by the presence of mass. For most purposes this slowing of LS is almost negligible, but as the speed difference between observations proves to provide a greater impact on position it’s seen to give greater differential between the observations (a direct ‘line of sight’ Doppler effect is also introduced).

Wouldn’t this confine the scope of SR to a ‘communications correction’, due to less than instantanaity of communication for the observation of an event?

Thus, SR has a LS limitation within its dynamic. The LS limitation is entirely dependant upon the local mass : vacuum proportion and rationalised by the speed vectors between observation points.

This sounds like a ‘detrained aether hypothesis’ to me. It’s just that SR provides a description of how to integrate multiple observations.

Hope this helps.🙂

Best regards, Ray Dart.

## DeWitt Payne said

Special Relativity can be derived from Maxwell’s equations and vice versa. Saying that light is slowed by the presence of mass is an oversimplification. The speed of light in a medium is related to the index of refraction of the medium. The Wikipedia article on Refractive Index is a good place to start.

If Special and General Relativity were wrong, the Global Positioning system wouldn’t work. GPS uses Special (velocity) and General (gravitational field) Relativity to calculate the correction for the atomic clocks in orbit of about 38 microseconds/day.

## DeWitt Payne said

Re: M. Simon (Sep 9 19:15),

That’s a complete misreading of Feynman. Just because the mass of an electron can be explained by the sum of the energy of its electromagnetic field and the energy required to contain its charge in a small volume does not mean that you could ever conceivably

changethe mass of an electron or anything else for that matter.## jeff id said

Ray,

Nice post. I do still believe that relativity exists because of a form of aether. I see matter and energy as a form of hologram where certain standing waves consist of mass or photons. Noone has determined the number of dimensions to the hologram but that’s what I think matter is.

Relativistic aether is an odd combination of past and future physics. Lorentz aether was tossed to the side because the math made it superfluous, however humans very much equivalent to myself (banana sucking monkey’s) forget that the math is a representation of reality, reality is not a representation of human math. The aether concept at it’s base non-mathematical level had a lot of merit and still does in my guessing opinion, it’s just that the math is/was not complete.

Whatever, I’m a crackpot according to the hyperbright Kloor monkey anyway.

## Brian H said

Re: DeWitt Payne (Sep 13 01:51),

And yet, and yet … one of the surprises offered up by graphene is that electrons appear to move masslessly along it. No explanation is yet in the offing, AFAIK.

Jeff: here’s your informational hologram:

http://www.sciencenews.org/index/feature/activity/view/id/63190/title/A_New_View_of_Gravity

For some perverse reason, the prospect of having all the pompous statements by numberous assophysicists about how dark energy is definitively doing this, that, or the other to the plenum pleases me greatly! 🙂

## Brian H said

Blech. Missing the predicate’s verb!

Corr: “For some perverse reason, the prospect of having all the pompous statements by numberous assophysicists about how dark energy is definitively doing this, that, or the other to the plenum

cut downpleases me greatly!🙂 “## DeWitt Payne said

Re: Brian H (Sep 13 04:58),

Without dark energy, how do you close the Universe? There isn’t sufficient normal and dark matter to do it, AFAIK. If it isn’t at least flat, and other considerations make flatness necessary (see The Grand Design e.g.), then how can there be an event horizon?

## Jeff Id said

#29 Thanks for the link. Very interesting and it doesn’t conflict at all with my view. My early career was spent in holographic interferometry. It was during a lot of long dark hours in the lab that I had time to consider some of these concepts. Since then, I haven’t changed but have never figured out where to start with the math to put some ideas to the test.

In the holographic concept, dark energy would be noise in the multidimensional field of standing waves. The noise has amplitude, pops in and out of existence across the universe and at points where matter exists, it positively reinforces. Dark matter is also noise but it knots up a little further, having temporary mass before it vanishes back into noise. All particles exist as waves at all points in the universe but are physically knotted at only one (standing circulating wave), photons are unknotted matter etc. High velocity matter circulates slower because the wavelength in the direction of travel lengthens (time dialation, distance dialation). Sub electron particles are just partially knotted matter which naturally decay to energy at various rates. Gravity, like the link says is just the grouping of specific wavelengths which creates a lower net energy state, or as your link says, a lower information state. Wavelengths closer to your feet are stretched longer.

It’s just a crazy theory, but I’ve put some time into thinking about it and no real math so it doesn’t qualify as anything more than conceptualizing.

## Jason Miller said

Andrew said at #23

“BTW, the photon is strictly speaking strongly believed to be Massless, but if it were found to have mass, then c would NOT refer to the speed of light in a vacuum per se (as having any rest mass makes getting to the speed of light impossible), but would still be the maximum speed attainable in space time, and the speed of gravitational waves and “gravitons”. “

Gravity has to travel faster than the speed of light or the orbits of the planets would not be stable. Earth is over eight light-minutes and Pluto over five light-hours from the Sun. If gravity traveled at the speed of light the sun would feel the tug of Earth from the location it was at 8 minutes previously and vice versa. Pluto would have traveled 5 hours along its orbit by the time its gravity is felt by the sun. The solar system would not exist if gravity were limited by the speed of light. There would only be a sun lacking a system.

## RickA said

Jason #33:

A gravity does not move faster than the speed of light – at least that is the current status of scientific thought.

Remember we are in orbit around the Sun – so the gravity is pretty constant – because the distance Earth is from the sun is pretty constant (roughly 93,000,000 miles).

The time delay doesn’t make a difference.

## Andrew said

33-You are thinking “Newtonianly” and are in error. I can’t elaborate on this here, or be bothered to try and rehash all of relativity, but you should start here:

http://en.wikipedia.org/wiki/Speed_of_gravity

If you really want to know what the deal with this is.

## Jason Miller said

I think I’m beginning to understand the post-Newtonian speed of gravity. I knew about light cones but had never even thought about a gravity cone.

I found an interesting, but difficult paper on Google Scholar titled, “The Speed of Gravity in General Relativity and Theoretical Interpretation of the Jovian Deflection

Experiment” by Sergei M. Kopeikin, 2004 in

Classical and Quantum Gravity( http://arxiv.org/PS_cache/gr-qc/pdf/0310/0310059v3.pdf ) The paper is also mentioned at the end of the Speed of Gravity article on Wikipedia. In his paper Kopeikin writes:“Einstein had equated the speed of gravity cg to c to preserve the special relativistic character of the Lorentz-invariance of equations of general theory of relativity. In other words, Einstein extrapolated his principle of special relativity to general relativity by assuming that the fundamental constant c characterizing the ultimate speed of propagation of gravitational field is the same as in special theory of relativity where gravitational field does not matter. This Einstein’s postulate is, in fact a hypothesis which can be tested in gravitational experiments conducted in time-dependent gravitational fields ** Making experiment in the gravitational field of a uniformly moving body is sufficient.”The results of the experiment were that the speed of gravity is (1.06 ± 0.21)c.

The basic concept I got from this paper is the effects of general relativity (gravity) and special relativity (velocity) basically cancel each other out. Am I thinking along the correct lines?

Thanks for pointing this out to me.

Jason

## Jason Miller said

In the above comment where I write “the effects of general relativity (gravity) and special relativity (velocity) basically cancel each other out”, I should have added “so that the center of gravity is at about its actual physical position. Although the speed of gravity appears to be approaching infinity, due to relativistic effects the speed of gravity is actually equal to or less than that of light in a vacuum.”

Please let me know if I’m off on this understanding of the speed of gravity.

## Jeff Id said

#37 My understanding is that the speed of gravity is exactly that of light but in the case of your example of the planets, it was confusing as to why the planets would do anything different from what they are doing.

Some interesting facts about gravity might help. —

Gravity is a spacetime gradient. Your feet travel slower through time than your head. The gradient provides the attraction. The rate of gravities propagation has no effect on orbit because it is a field effect and the speed is vast enough to fill our solar system in a short time. Standard theories have gravity at exactly c and I would be entirely shaken to find it was different than c because that wouldn’t make any sense in my world.

Been wrong before though.

## Brian H said

Re: Jeff Id (Sep 13 23:29), “Been wrong before though.”

How often? Once? Twice? 😉

## Jason Miller said

Jeff ID,

When I was told I was wrong about the speed of gravity, I thought about gravity’s effects on what you called the spacetime gradient. That seemed to make sense. Space-time around the sun and planets, or any matter is distorted, so maybe matter, photons, etc. were riding these curves like a skateboarder in a very large pool. But after thinking about it, it didn’t make sense since the curves weren’t there when the skateboarder rode by them. The paper I mentioned puts specific relative effects into equations. I understand some of the equations, but nothing above the basics. Check out the paper, I know I will have to read it again, because I very much want to understand the current scientific understanding of gravity. And that is hard to do when your FF team is losing and the Ravens/Giants game is on.

Jason

## Jeff Id said

Brian,

What day is it?

## Brian H said

Where I am, it’s still Monday. Your time zone may differ.

😀

## Brian H said

Re: DeWitt Payne (Sep 13 11:20),

That rather depends on whether gravity is the only conceivable closer, doesn’t it? The screen is an entropy boundary, not a gravitational field one, as I understand the hypothesis.

## DeWitt Payne said

Re: Brian H (Sep 14 01:28),

Show me an entropy boundary that isn’t an event horizon. The discussion talks about cyclic universes:

A cyclic universe is, by definition, gravitationally closed (Omega total greater than or equal to 1). If there is a mysterious force that causes the universe to be flat or closed that isn’t dark energy, it behaves exactly like dark energy. I don’t see a difference in that distinction.

## Nullius in Verba said

Jeff #28,

“I do still believe that relativity exists because of a form of aether.”

Even physicists tend to think that way most of the time. When physicists say there is no aether, they mean as a physical (if intangible) substance, with a definite position and motion and so on. (Called

‘manifold substantialism’by the pretentious.) Clearly there issomething, but it doesn’t have any of the properties you would expect of a material. Mathematically, it seems most closely related to the curvature of space and time itself (although there are problems even with that – see Einstein’s ‘hole’ argument), but truthfully nobody knows.“I see matter and energy as a form of hologram where certain standing waves consist of mass or photons.”

That’s fairly accurate, if looked at in a certain way. Spacetime has certain symmetries, expressing how things can move and still look the same. Since a periodic wave is about how things all look the same when you move a certain distance further along the wave, the different sorts of matter are basically the different ways you can move through spacetime and still have everything look the same. The different types of particles are therefore deeply connected to the symmetries of spacetime.

Besides the symmetries of the large scale dimensions – 3 of space and 1 of time – there appear to be additional ‘internal’ symmetries, possibly corresponding to additional dimensions (string theory takes this approach) or possibly corresponding to the behaviour of something else, something somehow ‘in’ space, that you might describe as a sort of aether. Whatever. These fancy ‘rotations’ transform one sort of particle into another, or alternatively, show that they are all examples of the same thing seen at different angles, and when the whatever-it-is gets confined, you get periodic waves oscillating in each of these additional ‘directions’.

(That’s probably a highly misleading picture, but it can’t be done properly without some heavy maths, so I fear that’s the best you’re likely to get!)

Jason #33,

“Gravity has to travel faster than the speed of light or the orbits of the planets would not be stable.”

Ah! Laplace’s speed of gravity argument!

If gravity is assumed to be a velocity-independent central force, as Newton conceived it to be, then this is a true statement.

I recall getting involved in a debate many years ago with a nice chap called Van Flandern, who resurrected the same argument. Steve Carlip wrote a quick paper (see ‘Speed of Gravity’ Wikipedia references) explaining that in general relativity, there is a velocity dependence that almost, but not quite, cancels the effect.

There is a similar effect in electromagnetism, where if you have a charged particle placed near a moving charge, the force is not towards where the particle “sees” the moving charge r/c seconds ago (r is the range, c speed of light), but towards where the particle

would be nowif it had carried on in a straight line. This is the case even if it never actually got there, but was diverted in the meantime. This dependence of electrostatic attraction on themotionof charges (i.e. electric currents) is what we call magnetism.Gravity does much the same, except that it extrapolates both the velocity and the instantaneous acceleration, so it acts as if the particle is moving along a parabola, and pulls particles towards where the moving mass would be now if it had continued on that path.

Because planetary orbits are circular, not parabolic, there is still a mismatch, and indeed the forces don’t quite balance. The difference goes into the gravitational field, and is radiated as gravitational waves – ripples in spacetime.

The Earth-sun system emits about 200 Watts in the form of gravitational wave energy, which will clearly take quite a while to de-orbit the planet. But neutron stars and black holes can emit quite a lot more, and the effects on the timing of the rotation of binary pulsars has been detected.

So in fact the effect does exist, but is several orders of magnitude smaller than Laplace calculated.

Jeff #38,

“Gravity is a spacetime gradient.”

Gravity is normally thought of as spacetime

curvature, and in fact it is the curvature in the time direction that is responsible for most of the effect. (One reason I hate those rubber sheet analogies.)The gravity of the Earth is due to the fact that time ‘goes slower’ closer to the planet. That means that if you set up two clocks, one above the other, the one nearer the ground will continually lose time when compared to the upper one. When matter (thought of as a wave) passes through this “time shear”, the wavefront is refracted and its path bent by the top part of the wave travelling at a different speed to the bottom. This turns the trajectory of any particle downwards, and the particle accelerates towards the Earth.

There’s a nice page that gives more of the maths here.

If you think of trying to glue bits of spacetime together, and imagine glueing an elastic strip with ‘more time in it’ to the bottom of one with less time, you will see that the result will be that the strips curl up – you get curvature. The curvature reduces to a gradient when things are static.

## inertia reel said

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## Brian H said

Re: inertia reel (Sep 16 11:24),

Congratulations! The most incoherent and badly formatted comment I’ve ever seen.

## Brian H said

IT’S A DRAG!Something is slowing Pioneer 10 — and other spacecraft. More mysteries in the holographic universe that our physics speaks not of!

## suricat said

Brian H said

September 16, 2010 at 4:01 pm

IT’S A DRAG!

Something is slowing Pioneer 10 — and other spacecraft. More mysteries in the holographic universe that our physics speaks not of!

Is this an indication of an extension to the ‘Casimir’ effect? Do you think the ‘Higgs field’ could be gravitationally responsible for this anomaly?

Best regards, Ray Dart.

## Brian H said

Re: suricat (Sep 19 21:31),

Nah.