Boeing tries to defy gravity
An anti-gravity device would revolutionise air travel
Posted on 07/29/2002 2:30:12 PM PDT by vannrox
Dr Podkletnov is viewed with suspicion by many conventional scientists. They have not been able to reproduce his results.
The project is being run by the top-secret Phantom Works in Seattle, the part of the company which handles Boeing's most sensitive programmes.
The head of the Phantom Works, George Muellner, told the security analysis journal Jane's Defence Weekly that the science appeared to be valid and plausible.
Dr Podkletnov claims to have countered the effects of gravity in an experiment at the Tampere University of Technology in Finland in 1992.
The scientist says he found that objects above a superconducting ceramic disc rotating over powerful electromagnets lost weight.
The reduction in gravity was small, about 2%, but the implications - for example, in terms of cutting the energy needed for a plane to fly - were immense.
Scientists who investigated Dr Podkletnov's work, however, said the experiment was fundamentally flawed and that negating gravity was impossible.
The hypothesis is being tested in a programme codenamed Project Grasp.
Boeing is the latest in a series of high-profile institutions trying to replicate Dr Podkletnov's experiment.
The military wing of the UK hi-tech group BAE Systems is working on an anti-gravity programme, dubbed Project Greenglow.
The US space agency, Nasa, is also attempting to reproduce Dr Podkletnov's findings, but a preliminary report indicates the effect does not exist.
Strictly speaking, "infinity" isn't a number. You can't divide by something that isn't a number.
First let me ask you: what is length?
In the space in which we live, there are three spatial dimensions. Within that space, we can define vectors, such as position. Each vector has three components, which measure the vector along the three axes we have chosen to define the space.
Our choice of coordinate system is arbitrary. We can choose a different coordinate system merely by rotating the one we chose. If we do this, the components of the vector will change. However, we can construct out of any vector a quantity that is invariant under rotation: the norm of the vector is the square root of the sum of the squares of the vector's components. Length is the invariant quantity associated with a vector between two positions.
Space and time, considered together, form a four-dimensional space. It's slightly different from the three-dimensional space I just described, because time is irreversible, unlike the spatial dimensions. (Technically, the time component has a different metric sign than the space components.) So while you can't rotate space into time, there is a transformation that can transform between space and time: the Lorentz transformation. Under the Lorentz transformation, the vector norms look like the square root of the time component squared MINUS the space components squared.
There are several vectors that can be defined in this space, and one of them can be defined by taking a particle's energy as the "time" component and the components of its momentum as the "space" components. (I have here chosen units so that c=1, unitless.) We call this vector the 4-momentum. In this case, the invariant vector norm is sqrt(E² - p²), where p is the total momentum. This quantity is what we call the mass.
Mass is the Lorentz-invariant norm of the vector known as 4-momentum.
In the case of light, energy equals momentum (times the speed of light, which is important to remember if you work in more familiar units). Thus, for light, m equals zero.
It's not a dimension. You wouldn't say that the x component of a magnetic field is itself a dimension, would you? It's just the vector component that happens to lie along that axis. Similarly, energy is the component of 4-momentum that happens to lie along the time axis.
Alright, now you're confusing me again. This is what you said in #108: "No, time is a component of a vector, which is to say a dimension." So from there, I figured I could equate "dimension" with "vector component". You lead, I'll follow.
If I may be so bold, I think I see the nature of "inquest's" confusion. ("Inquest": correctly me if I'm wrong in my assumption here....)
I think he wants to know why energy is expressed in terms of the temporal coordinate while other physical quantities (like momentum, to use your example) are expressed in terms of the spatial coordinates.
And if I may be even bolder, I suspect the answer has a great deal to do with Noether's Theorem and Conservation of Energy, yes?
I'll leave the details of that to you; you can do it far more justice than I can.
Yes, indeed, that's what I was trying to get at. Thank you.
Yes, indeed, that's what I was trying to get at.
Ah, I see. Every symmetry in nature implies a conserved quantity. (You may not believe this, but my first attempt at my first reply to you started with exactly that sentence, before I chose a more basic approach.) This is known as Noether's Theorem. The isotropy of space, for example, implies the conservation of angular momentum.
The conservation of momentum is implied by the homogeneity of the universe over distance. The conservation of energy is implied by the homogeneity of the universe over time. So in the case of 4-momentum, it's somewhat intuitive to see why energy is the time component and the three components of momentum are the space components. (Again I remind you that I'm setting units so that c=1; if I were to work in seconds and meters, I'd divide the energy by the speed of light to get the units to work out.)
Other 4-vectors aren't so obvious. For example, there's the 4-potential, which is formed by taking the electric scalar potential, phi, as the time component and the three components of the magnetic vector potential, A, as the space components. I don't have a pat answer as to why they are arranged that way, except to say that that's how they just happen to transform according to the Lorentz transformation. If I start in a frame where the 4-potential is (phi, 0, 0, 0) (that is, I see an electric field and no magnetic field), and I shift into a moving frame, voilá, I start seeing a magnetic field in the same space. Experiment (well, OK, also Maxwell's equations) tells me that (phi, Ax, Ay, Az) behaves as a 4-vector under the Lorentz transformation.
Other 4-vectors aren't so obvious. For example, there's the 4-potential, which is formed by taking the electric scalar potential, phi, as the time component and the three components of the magnetic vector potential, A, as the space components. I don't have a pat answer as to why they are arranged that way, except to say that that's how they just happen to transform according to the Lorentz transformation.
My very uneducated guess would be that since electric potential is, as you've indicated, a scalar, it wouldn't make much sense to break it down into a three-dimensional coordinate system, so it would naturally fall along the temporal coordinate. But I'm sure there's a lot more to it than that.
So is there an analogous "4-potential"-type scheme with gravity as well?
The more deeply you look into it, the more perfectly consistent it will appear.
So is there an analogous "4-potential"-type scheme with gravity as well?
Now you're moving the discussion from the actors to the stage upon which they act. Special relativity (i.e. the Lorentz transformation) doesn't take into account the possibility that spacetime is curved. For that you need the general theory of relativity. The lesson from General Relativity is that gravity is the curvature of spacetime itself.
Well, I guess that'll be the lesson for my next class on FR. Thanks for your time.
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